1
The Effect of Temperature and Strain-Rate on the Deformation and Fracture of Mild Steel Charpy Specimens
The,,,;.is Submitted in Suppliction for the Degree of Doctor of Thilosophy
by
SLoicor. Rodney Uilshaw D.Sc. A.12.3.M. (London) 1961.
Deprtmeilt of -.ysicalietallurrsy- Imperial College University of London December 1964 2
ABSTRACT
High nitrogen mild steel Charpy specimens were deformed at room temperature in three-point bending; the distribution of plastic deformation revealed by Fry's etch was measured at different applied loads for both substantially plane stress and plane strain conditions. Specimens were deformed to fracture at striker velocities of 0.05, 50 and 30,000 cm/min within the temperature range - 196°C to + 100°C. These studies have revealed the existence of ; a) a transition from ductile tearing at the notch root, to internal cleavage, b) at a lower temperature a bimodal distribution of fracture loads, indicating a transition in the mode of cleavage fracture and c) a decrease in the fracture load associated with the onset of twinning. 3
The relationship between these transition
temperatures and the strain-rate may be expressed by an Arrhenius eauation with different apparent activation energies, which are not comparable with the activation energies for yielding. From this it is concluded that
the effect of temperature and strain-rate on the cleavage stress is not entirely due to their influence on the yield stress. The implication of this when predicting notch impact transitions from tensile data
is disc-p.ssed and a method of predicting the existence of a Crack arrest temperature is postulated.
ERRATA
page line 12 3 degress should read degrees
17 16 slip 11 II ship
27 8. maitrix II 1/ matrix 2 11 49 6PGY - 565 Kg/m pGY = 565 Kg 8 P = 505 40 Kg/mm2 11 PGY = 505 ±40 K GY 51 10 505 ± 40 Kg/mm2 11 II 505 ± 40 Kg
55 13 depositied fl II deposited
63 7 low 11 11 four
69 11 due to plastic zone 11 11 due to the plastic zone
70 6 alip 11 11 slip 9 connot 11 cannot 80 19 fired 11 fixed 81 11 Taly-Surface It Taly-Surf
107 6 at It Il and airx 1 + 2 eic/ez 110 3 Equation 3 II 0; 2 + . 131 11 derivate 11 derivative 161 5 odes 11 modes
199 10 w-isume that condition 11 II assume that the condition 202 12 Marjoine 11 Manjoine 211 16 Llider 11 'Alders
212 19 above If II below -1 22 t= 10s II 11 105 sec 222 11 mode It model 223 5 region which if region in which
229 19 effect 11 11 effects
Reference Alexander J. M. and Komoly T. J. 1962. J. Mech. Phys. Solids 10 265. 14
CONTENTS
Page
Abstract 2 Contents 4 Chapter 1. Introduction and Previous Work 1.1. Introduction 10 Review of Previous Work 1.2. Classical Theories of Fracture 15 1.2.1. Energy Criterion 16 1.2.2. Critical Displacement Criterion 19 1.2.3. Stress Criterion 20
1.3. Micromechanisms of Cleavage Fracture 21 1.3.1. Slip Initiated Mechanisms 21 1.3.2. Deformation Twinning and Crack Initiation 25 1.3.3. The Ductile-Brittle Transition 27
1.4- Deformation and Fracture of Mild Steel at Low Temperatures 29 1.4.1. The Ef_rect of Strain—Rate 32
1.5. The Effects of a Notch 33 5
Page Part I Chapter 2. The Deformation of Charpy Specimens before General Yield 39 2.1.1. Summary 40 2.1.2. Choice of Material 40 2.1.3. Specimens 44 2.1.4. The Deformation Jig 44 2.1.5. The Load Deflection Curve 47
2.2.1. The Distribution of Plastic Strain below General Yield 50 2.2.2. The Schlieren Technique 51 2.2.3. Fry's Etch Technique 55 2.2.4. Plastic Zone Size 57 Discussion 2.3.1. Plane-Stress Deformation 59 2.3.2. Plane-Strain. Deformation 62 2.3.3. Effect of Specimen Width 64 2.3.4. Elastic Stress-Concentration Factor 68 2.3.5. Distribution of Stress below the Notch 72 - 6
Page Chapter 3. The Deformation of Charpy Specimens beyond General Yield 79 3.1.1. Summary 79 3.1.2. Experimental 79 3.1.3. Measurement of Root Strain 81 3.1.4. Calibration 87 3.1.5. Strain-Measurement 92 Discussion 97 3.2.1. Deformation Sequence 98 3.2.2. Strain at the Notch Root 101 3.2.3. Crack Opening Dislocation (C.O.D.) 1014 3.2.4. Strain-Rate 107 3.2.5. Biaxiality 109 7
Page Part II Chapter 4. The Effect of Temperature on the Fracture of Notched Bars
4.1.1. Summary 112 4.1.2. Experimental 112
4.2.1. Initiation Transition 119 4.2.2. Results 120 4.2.3. Metallographic Examination 133
4.3.1. Cementite Cracks 137
4.4.1. Brittle Fracture above General Yield 148
4.5.1. The Bimodal Transition 151 4.5.2. The Probability of Microcrack Formation 154 4.5.3. The Stability of Microcracks 155 4.5.L. Double Notched Charpy Tests 161
4.6.1. The Twinning Transition 162 - 8
Page Chapter 5. The Effect of Strain-Rate on the Fracture of Notched Bars
5.1.1. Summary 172
5.1.2. Instrumented Charpy Impact Tests 173 5.1.3, Intermediate and Slow Bend Tests 177 Discussion 5.2.1. The Effect of Strain-Rate on the Load-Deflection Curve 182
5.2.2. Instrument Impact Tests 185 5.2.3. Slow Bend Tests 188 5.2.4. The Effect of Strain Rate on the Fracture Load Temperature Diagram 188 5.2.5. Measurement of Dynamic Yield Stresses 199 5.2.6. Prediction of Dynamic Transition Temperatures from Tensile Data 200 9 Page Chapter 6, Tensile Tests 205 6.1. Experimental 206 6.2. Impact Tensile Tests 207 6.3. Discussion 210 6.4. Strain-Hardening 214 6.5. Fracture at - 190C 216 Chapter 7. Discussion of Conclusions 7.1. Stress and Strain Distributions around a Notch 219 7.2. Cementite Cracks 221 7.3. Crack Initiation 223 7.4. Crack PPopagation 225 7.5. Adiabatic Heating 227 7.6. The Char:Dy Impact Test 228 7.7. Summary of Conclusions 232 Acknowled7ements 236 Referenco 237 - 10 -
CHAPTER 1
Introduction and Literature Survey
1.1. Introduction Mild steel structures have been known to fracture in a catastrophic and unpredictable manner. This phenomenon is generally termed brittle fracture and is recognised by the small amount of plastic deformation accompanying such a fracture. The source of failure is usually a stress concentration in the form of a sharp notch, or a crack, which is the result of metallurgical damage occurring during construction or service. A brittle crack can propagate through steel olates under a nominal stress of about 30 per cent of the yield stress, absorbing a relatively small amount of energy and travelling at a velocity of about one third the velocity of sound in the material. It is well known that conditions of low temperature, high strain-rate and a triaxial state of stress, which prevails beneath a notch, all tend to - 11 — favour the initiation of fracture. A number of large and small scale laboratory tests have been devised to simulate the actual service failures and to assess a material's susceptibility to such failures. (see Tipper 1963). Whilst some of these tests appear to emphasise the initiation of cleavage cracks and others the stopping of a propagating brittle crack, almost all of them involve the introduction of a notch and the observation of the onset of brittle behaviour as the test temperature is lowered. Since each of these tests emphasise different features of the brittle-fracture phenomenon to varying degrees it is not surprising that they evaluate the ability to resist brittle fracture in different ways. (A.A.C.S.S. Report P.9. H.M.S.°. 1960). The most common laboratory test for brittle fracture is the V-notch Charpy impact test. The details of this test are given in B.S. 131 : Part 2 1959. British Standards Inst itut ion. A small rectangular prismatic specimen containing a notch is broken in three point bending under impact loading at various temperatures and the energy absorbed — 12 — during fracture is measured. This energy changes considerably over a transition range of a few tens of degrees, and the fracture appearance changes accordingly from the fibrous appearance associated with the high energy ductile fractures to the shiny crystalline appearance resulting from cleavage on the -c1001 planes. The temperature at which 15 ft lbs of energy is absorbed is defined as a ductility transition temperature Td and is associated with the temperature region in which cleavage cracks initiate the final fracture. At higher temperature, a fracture transition Tf for 50 per cent fibrous appearance satisfies a condition for which brittle fracture may be initiated by a ductile crack, and is also used as a design criterion. Although the use of such data has met with some degree of success, particularly in the design of ships, each type of service requires a new correlation. The inability to correlate data, from various tests on a variety of steels, has made it desirable to pursue this problem on a fundamental basis. - 13 -
The most detailed studies of deformation and fracture in notched bars have been performed by Green and Hundy (1956), Cmssard et al (1956) and Knott (1962). The latter author fractured deeply notched specimens under slow four point bend and related the fracture mechanisms to the deformation characteristics of the specimen, at various temperatures. Later both Stone (1963) and Fearnehough (1963) instrumented the Charpy test to obtain dynamic load-time curves. The fracture load measurements as a function of the temperature were apparently more complicated than the equivalent measurements made by Knott under different conditionsy and a satisfactory interpretation of the observations was not suggested. Thus the present work began as a systematic study of the Charpy test and the first stage was to determine the deformation characteristics of the Charpy specimen. Previously7 Green and Hundy (1956) had examined the state of deformation in which plastic zones extended from the notch root across the ligament, (general yield), and proposed a slip line field analysis. There had been no comprehensive study of the plastic deformation -114— above and below the condition of general yield, therefore Part I of this thesis was devoted to this end. Subsequently, specimens were deformed to fracture in slow three point bend at different temperatures. Equivalent experiments were then performed at different strain rates up to impact. In this way an analysis of the Charpy test, and at the same time a fundamental study of the plastic deformation and fracture characteristics in the presence of a notcI were performed. - 15 —
Review of Previous Work
The object of this review is to present a critical appraisal of current theories of brittle fracture and to discuss their applicability to the behaviour of mild steel which is a semi-brittle two phase polycrystalline aggregate. There is apparently no simple universal fracture criterion for such a material because of its complex combination of mechanical properties, hence brittle fracture in mild steel represents a specialised problem. Classical macro- and micro-mechanisms of fracture are discussed and the theoretical aspects of a notch, with particular reference to the Charpy notch, are presented.
1.2. Classical Theories of Fracture A value of the theoretical strength of a material may be obtained by considering the stress acting between adjacent atoms as a function of the interatomic distance. Ideally the work done in pulling the atoms apart will be balanced by the energy required to create - 16 - the new surfaces giving a relationship
= / 2E I/ (--- 1.1 a
/ where a is the interatomic spacing, the effective surface energy, and irlia the theoretical strength of the material is of order of one tenth of the E elastic modulus, /10. Strengths of this order have been approached with "whiskerP. crystals of about 10-4 cm diameter, but most brittle materials have a strength of about E/100 ,— E/1000.
1.2.1. Energy Criterion Griffith (1921) equated the rate of release of energy from the elastic stress field around a crack to • the rate of increase of surface energy to obtain the classical formula • 2E ''() 0'G AC (1 — ‘12) ... 1.2 where Cr is the stress required to cause a sharp crack of len.:2-;th C to propagate in a brittle material. - 17 -
Griffiths (1921) tested his relationship for glass which was thought until recently to be an ideal brittle material (Cottrell (1963)). For a quasi-brittle material such as a metal, the Griffith criterion predicts the presence of large cracks in the undeformed material. This is because plastic deformation occurs around the tips of the crack and causes stress relaxation so that the stress derived from equation 1.2 is too small. To account for the energy absorbed by the plastic deformation accompanying the growth of a semi-brittle crack, Orowan (1946) modified the Griffith equation to
= . 1.3 where yp is the plastic work factor and Ys the surface energy. X-ray examination of the surface of a fractured s44p plate revealed the presence of a thin layer of plastically deformed material some 0.5 mm thick which had apparently been strained about 2 per cent. From equation 1.3 the estimated value of y:i_D is 2 106 ergs/cm2 which is a fey,' orders o f magnitude greater than '16, (103 - 104 ergs/cm2). — 18 —
Irwin (1948) proceeded to develop a force concept for fracture, characterising conditions not only in terms of energy balance, but also compatibility in terms of a description of the tensile stress in advance of the crack tip, normal to the plane of expected separation. The term - in the Griffith—Orowan (1 — \02 equation is designated Gc, and is referred to as the fracture toughness, or critical crack extension force, or critical strain—energy release rate. Alternatively Kc /EGc)1, defined as (--- is called the stress intensity factor, \ 71. and like Gc, can be measured from various mechanical tests. Because of its success in explaining fracture behaviour in large structures this fracture mechanical approach is now used extensively. However if the plastic zone around the crack tip is large enough to change the elastic—stress distribution,the approach becomes uncertain, especially for mild—steel. Anderson (1959), summing up the theories of fracture stated that although the Griffith criterion has been modified and extended, it is the basis of most successful explanations of fracture at both the microscopic and macroscopic levels. -19-
1.2.2. Critical Displacement Criterion Recently an assessment of toughness has bean made by measuring the plastic strain at the tip of the crack McClintock (1958), or the displacement Tc at the crack tip, Dilby, Cottrell, and Swindon (1963). Relationships have been derived by these workers relating the displacement and the size of the plastic zone to the applied stress. The value of ic Till depend upon the notch geometry and the mode of crack initiation but it can be measured easily, Wells (1962). Cottrell (1963) has shown how the value ofIc may be related to the
Griffith-Orowan equation through 2Yp = The value of this approach is its applicability to the more ductile materials as it is essentially an elastic-plastic approach, whereas the Irwin approach assumes a purely elastic case. In addition, it also gives an interpretation of the observed size effect associated with brittle fracture Dugdale (1960) has verified experimentally a relationship between the plastic zone size and applied stress for mild-steel, but the results of Dixon and Stral2ahan (196L1.) indicate that the deformation - 20— behaviour at the tip of a crack is strongly dependent upon the yielding characteristics of the material. Hence it is doubtful whether a General relationship for the yielding below a notch exists.
1.2.3. Critical Stress Criterion The earliest theory of fracture in potentially ductile materials was based on the Tesnager-Ludwik principlef OroTan (1959), in which fracture occurred when the maximum principal stress attained a critical value called the fracture stress. This fracture stress Cif, is a Parameter used to denote the maximum macroscopic stress in the material at the time of fracture. It is not directly related to the true fracture stress on an atomic scale which is impossible to measure. If 611 is greater than the yield stress CTST the matobial will be ductile and vice-versa. The effect of a notch is to raise the yield stress by triaxiality from ICT to about 3 16-y and hence increase the tendency towards brittleness. Such a criterion, based on a continuum mechanical model, cannot explain the effects — 21 — of grain size, specimen size, or why fracture always occurs after yieldingand is thus an over simplified approach which cannot lead to essentially new results.
1.3. iAcromechanisms of Cleavage Fracture Early theoretical ideas on fracture were influenced by the work on glass and predicted the existence of flaws or Griffith cracks in metals. These ideas were not consistant with the experimental fracture strengths of metals and when it became generally accepted that yielding always preceded brittle fracture, metal physicists began to create qualitative dislocation models for cleavage and later they predicted the criteria for the ductile—brittle transition.
1.3.1. Slip Initiated Mechanisms The common features of these models are that the materials undergo an inhomogeneous shearing process such as in the formation slip bands, producing localised discontinuities in the shear strain e.g. when - 22 - a clip band is blocked by a grain boundary. Eerier (1948) suggested that the stress on the dislocations in such a model, later calculated by Eshelby, Frank and Nabarro (1951), might be sufficient to cause them to coalesce and form an incipient crack. Both Fetch (1954) and Stroh (1957) examined this model in detail and derived criteria for a ductile-brittle transition. However, experiments by Low and Guard (1959) inferred that a mechanism of dislocation multiplication involving a double cross-slip mechanism was more likely than the existing Frank-Read model, giving a possible explanation as to why no direct evidence of large dislocation pile-ups in b.c.c. metals has been obtained. Also, Low (1964) does not believe that a strong enough barrier to produce a dislocation pile-up is likely, because a concentrated shear stress of approaching the theoretical strength of the material would be reached in order to produce a pile-up large enough to exceed the theoretical cleavage strength. Cottrell (1958) has proposed a model for crack initiation which does not involve grain boundaries, but rather the coalescence of a/2 <111> dislocations -23- moving on intersecting tl slip planes by the reaction
4. al_ a/2 [11A /2 [111-* a LOCi
Stroh (1959) analysed the Cottrell mechanism and concluded that the at,001i dislocation will dissociate rather than form a crack. Theoretical calculations of the stress concentration at the tip of a double pile up by Chou? Garojalo and Whitmore (1960) indicate the high stresses which can develop e.g. if each pile-up contains ten dislocations the stress concentration will be 77.5. Hence if the a101] dislocation could be prevented from dissociating, then such a model would operate. Whereas the Zener model predicts the microcracks will form at 55° to 60° to the tensile axis, the Cottrell mechanism predicts cleavage on planes normal to the tensile axis, which is consistent with the experimental observation of Hahn et al (1959). — —
Another dislocation model was proposed by Bullough (1955) and treated quantitatively by Gilman (1958) which predicts the initiation and propagation of a crack within the actual plane of slip itself. Allen (1959) has cited a number of examples of brittle fracture which have not been preceded by yielding and has considered the possibility of static dislocation arrays as potential initiation sites. The only direct evidence supporting the various dislocation mechanisms has largely been confined to observation in brittle ionic crystals. In the case of a material like mild steel the cracks are initiated from cracked carbide films in the grain boundary McMahon (1964). The subsequent propagation of these small cracks will perhaps be explained using a double inverted pile up model currently being treated quantitatively by Bilby (1964). -25-
1.3.2. Deformation Twinning and Crack Initiation At low temperatures and high rate of strain iron may deform plastically by a mechanism called mechanical twinning which is observed as fine lamellae occurring on a {1121 plane and producing a shear in the (10 direction. Bell and Cahn (1959) suggested tbat twins were nucleated at regions of high stress concentration by in- hoiogeneous shear and were able to propagate because of the high stresses at the twin tip. Hull and Hamer (1964) strained specimens of silicon iron at - 196°C and allowed the load to relax. Both twinning and fracture were observed under a falling load, preceded by slip. The local stress concentrations due to intersecting slip bands may be responsible for twin nucleation, Priestner (1963). Although there is no evidence of a critical resolved shear stress for twinning, a macroscopic twinning stress has been measured in mild steel by Fishhoff (1963) which is independent of both temperature and strain rate. Hull (1960), Honda (1961) and Knott and Cottrell (1963) have observed microcracks at the intersection of twins, - 2 6 -
(a) (b)
UNMXIAL TENSION
(c) (d)
Fig. 1.1. Mechanisms of crack initiation by 'intersecting twins. — 27—
by a mechanism shown schematically in fig. 1.1.(a) together with other possible mechanisms, after Priestner (1963). Sleeswyk (1962) has observed "emissary" glide dislocations pushed out from twins which could intersect on the projected twin planes ahead of the twins and cause cracking. An arrested twin will release part of its energy to the surrounding ma rix and the strain field at its tip must be relieved by slip, accommodation twinning, or cleavage. According to Priestner (1963), mechanisms involving the obstruction of a single twin are to be preferred to double twin mechanisms which are unlikely because they are restricted to certain orientations of the tensile axis in the unit triangle.
1.3.3. The Ductile—Brittle Transition The complete process of fracture may be divided into the initiation and propagation stages. Both Cottrell (1958) and retch (1953) consider that the latter stage is the critical step in the fracture process which becomes possible when the tensile component on the crack will allow it to propagate in a Griffith manner. - 28-
The derivation of the ductile-brittle criterion by Cottrell (1958) requires that cracks be formed during initial yielding,so that by applying the yield point theory he obtained the condition for which a crack of length d will become unstable when the applied stress equals the yield stress, i6.ky.d2 =pa/ where Gir is the lower yield stress, ky a measure of the unpinning stress, d the grain size, G the shear modulus, 'the surface energy and p a geometrical factor dependent on the state of stress. Petch (1959) using the Griffith criterion considered ductile fracture as the linking-up of non-propagating micro-cracks by ductile tearing between them, and a similar criterion to that of Cottrell (1958) was derived. These criteria are useful in that they provide a basis for predicting the quantitative effects of grain-size, temperature, strain-rate and other metallurgical voriables, from their effect on the yield stress parameters. However the ductile-brittle transition occurs above the yield stress suggesting that the propagation stress has been raised by work hardening. - 29 -
Johnson (1962) modified the criteria of Cottrell and Petch to account for the observed behaviour in molybdenum which has a high work hardening rate and a transition temperature which is independent of grain size. No ductile-brittle transition based on the Griffith criterion is consistent with the size of stable micro-cracks observed in mild-steel. Recent experiments by McFahon (1964) on steels of similar grain size indicate that the number of crack sources is another important variable which is not considered in the theories of Cottrell and Petch. Any subsequent development of their approach, or a new approach, must take into account the statistical nature of the fracture process.
1.4. The Deformation and Fracture of Mild Steel at Low-Temperatures Tensile deformation and fracture studies on mild steel and iron have been performed by Eldin and Collins (1951), Wessel (1956), Erickson and Low (1957),
Hahn, Averbach, Owen and Cohen (1959) and McMahon (1964). -30-
The complex fracture behaviour has been classified into various regions in fig. 1.29 which represents the yield and fracture behaviour for a 0.22. steel, after Hahn, Averbach, Owen and Cohen (1959). In region A, the material is ductile, the reduction in area is high and the final fracture is fibrous. As the temperature decreases, (region B), necking still occurs, but the fracture starts as a fibrous tear at the centre of the specimen and converts to cleavage fracture during the instability. At Td, the ductility transition temperature, the fracture is completely cleavage. In region C, the reduction in area at fracture continues to decrease gradually with tealperature and the number of micro-cracks prior to fracture increases. .Also in this region, McMahon (1964), there is a change in the mechanism of plastic deformation, when ti-inninc:5 follows the onset 'of discontinuous yielding. The number of micro-cracks reaches a maximum at Tm, the boundary between regions C and D, and then decrease with further decreases in temperature. In region la the fracture stress and the lower yield -31-
Tm Td 1 T1
120 Fracture.
00 stress
Upper yield stress
Lower yield Elastic stress limit 40 F E C to A —0.10 2 % grains E cracked o Strained 10% — 0.05 4! A Fractured 0 H 0 0 Reduction in area — 100 • fFracture — 50 appearance (%, fibrous) 0 oc, OD 1 —273 —200 —100 0 RT 100 Temperature (°C)
Fig. 1.2. Summary of tensile properties, fracture appearance, and micro-crack data for a 0.22 C steel. (d = 0.106 mm" after Hahn Averbach Owen'and Cohen 1959. -32- stress are coincidental and in region E, fracture occurs at the upper yield stress when the onset of discontinuous yield and twinning occur simultaneously. In region F, twinning occurs in the pre-yield micro-strain region and the fracture stress is equal to the twinning stress. These regions are not always all identifiable in some materials because they may occur so close together that they become irresolvable.
1.4.1. The Effect of Strain-Rate The effect of increasing the rate of straining is to increase the resistance to deformation and hence the stress level for cleavage fracture may be attained at a higher temperature. Lean and Plateau (1959) observed that the effect of strain-rate on the ductility transition temperature Td, may be expressed by an H • Arrhenius equation E = A exp (- /kTd) where E is the strain-rate, H the activation energy and A and k constants. iFendrickson,Wood and Clark (1958) concluded that the influence of temperature and strain-rate on brittle fracture arose entirely from the effects of these variables on the yield stress. -33-
1.5. The Effects of a Notch The presence of grooves, holes, threads and other geometrical discontinuities which are generally classified as notches, cause the local elastic stress to be raised by shifting the lines of force closer together. The capacity of a notch to raise the elastic stress is determined by the elastic stress-concentration factor. This is defined as the ratio of the maximum stress actually occurring, to the nominal stress 6 Crmax deter.-lined from traditional strength theory.
It is independent of the absolute value of crn provided the material remains elastic, and will have a definite value which is a function of the shape of the structural member and the type of loading. It has been Cr designatedCKk by Neuber (1946) such thatC(k = rx. n Yotches are usually classified into basic shapes which may be shallow or deep, external or internal, rounded or pointed. Green and Fundy (1956) have defined a "shallow" notch for the case of an externally t notched prismatic bar in bending as /a < 1.4, where t is the depth of the notch and a the depth of material below the notch called the ligament. -34-
For a shallow notch the stress variation is distributed only in the immediate vicinity of the notch and, at a greater distance it is merely a case of a uniform stress distribution unaffected by the presence of the notch. :The only parameters'which are considered relevant to the stress concentration factor are those which characterise the boundary of the disturbed zone. These parameters include t and a, and the notch radius Q. As the notch becomes deeper the depth of the ligament will become more important and Xk may be considered as a t some function of the non-dimensional ratios and The limiting values which pit assumes in the cases of- shallow and deep notches are for a Charpy specimen; - and cXck = 2.82 e stress concentration factor oek from the Peuber 3.25 Nomograms, Mubor1-946;.which is N:k = for the Charpy geometry. Yielding will occur when the nominal stress at the root satisfies the relation CY = Tn oCiowhere 6y is the yield stress of the material. The distribution of stress will not be purely elastic and the problem of stress analysis becomes elastic-plastic. - 35 — Hendrickson,Wood and Clark (1958) and Barton and Hall (1963) performed an elastic-plastic analysis on notch tensile specimens, Hendrickson, Wood and Clark (1959) on an Izod bar, and recently Rendall and Allen (1964) on a Charpy seecimen, to determine the state of stress along the minimum sections, as a function of the applied stress and the yield stress. The first stage in these analyses involved the calculation of the elastic state of stress from the Neuber (1946) analysis. Then by either using the relaxation technicue" of Allen and Southwell (1949) in the tm examples by Hendricksonl od and Clark, or by satisfying the Von Mises yield criterion in the examples of Barton and Hall (1963) and Rendall and Allen (1964), the maximum stresses were calculated. The analysis of Hendrickson7 Wood and Clark (1959) for the Izod specimen subjected to a stress of do/CST 0.81 is shown in fig. 1.3. The maximum stress represents the position of the elastic-plastic boundary and the dashed lines represent the stress conditions which would exist under the same loading conditions if the deformation were entirely elastic. The maximum - 36 - .3.0k 2.5- A/ 6X (Plastic). 2.0 6x (Elastic). 1.5 •• Cry (Plastic). 6y (Elastic). % •• • • • • • • • , 0.5 • -- --- 0.2 0.4 0.6 0.8 1.0 1.2 DISTANCE BELOW ROOT ymm. Fig. 1.3. Elastic—plastic stress distribution for an Izod specimen loaded to Cn/037,•= 0.81. Oi = ax orgy. = ) after Hendriclion Wood 2 and Clark (1959). -37- value of 05c/0"yd is called the plastic stress concentration factor and will be subsequently used to calculate fracture stresses. Assuming plane strain conditions at the centre of the bar, the stress normal to the plane of fig. 1, lez, can be calculated from 0^Z = xY(0; + 6.y). Thus below the notch root a triaxial state of stress exists which may be divided into a hydrostatic component which is the mean stress 5- =(Crx + 043T + CQ/3 and "deviatoric" components, C'x' = (Orx - OT), = (o;r - 0") and Crz' = (5z - Cr. It is the deviatoric component of the stress which is responsible for plastic flow. Plasticity theory assumes that the hydrostatic component has no effect on the yielding and hence according to the Tresca yield criterion, yield will oc c - Cr occur when -Z = k or Z = k. If Cr is 2 2 large compared with Orx the yielding will be retarded and the maximum principal stress irx must be raised before yielding will occur. In this way the yield stress may be raised by a factor of 3, Orowan (19445)7 and as has been already stated, this effect of a notch - 38 - will raise the yield stress to the stress necessary for cleavage,and cause brittleness at higher temperatures than for a uniaxial state of stress. At a more advanced stage of loading, yielding will spread from the notch and eventually a state will be reached when it is possible to describe a path of plastically deformed material across the whole ligament. Slip line field analyses have been performed for the Charpy siDecimenl for this state of strain, by Green and Hundy (1956) and Alexander and Komoly (1962). From this, they theoretically predict the shape of the plastic zones and the maximum stress below the notch. An additional effect of a notch is to raise the local elastic strain by a factor of the elastic stress concentration factor, Gensamer (19L1.7). Plastic flow at the root will then be initiated at a higher stress than the yield stress measured for the nominal cross—head speed. The actual strain—rate at the elastic—plastic inteTface will probably be a compromise between the local elastic and plastic components, -39- PART 1 The Deformation of Notched Specimens — 40 — CHAPTER T. The deformation of Charpy specimens before general yield 2.1.1. Summary The choice of the material and specimen geometry are discussed, together with an account of the experimental procedure. Deformation patterns revealed by Fry's etchant are compared for both substantially plane stress and plane strain conditions, at various applied loads. The degree of plane strain across the transverse section and the elastic stress concentration factor are measured experimentally. The plastic stress concentration factors for different applied loads are estimated from recent theories. 2.1.2. Choice of material The experiments described in this chapter were designed to determine the nature of the localised plastic deformation in a specimen containing a notch. Hahn (1964), Tetelman (1964), and Griffiths (1964) have used a dislocation etc1,1—:it technique to rovcal -- L1.l — the distribution of plastic strain around notches and cracks in Si-iron. Individual dislocations are preferentially attacked and strains below about 1 per cent can be sensitively revealed. For strains above this value, the etching response diminishes up to about 5 per cent strain when the dislocation density becomes so large that the specimen becomes uniformly attacked. Later work presented in this thesis involves high strains which could not therefore be revealed by this technique. Si-iron may exhibit discontinuous yielding behaviour and have a stress-strain curve similar to that of mild-steel. However, plastic deformation in Si-iron has only been observed on the <111;>} slip system, whereas mild steel deforms on any of the systems, @3 t1121., 3.23i. Therefore, although it would be desirable to use Si-iron because of its property to reveal individual dislocations, the limited mode of slip prevents its use as a substitute for mild steel in the present problem. It was decided then, to use a mild-steel which would react to the macroscopic etch technique of Fry (1921). — L.2 — The requisite of such a steel is that it should have a high-nitrogen content. This governed the choice of the steel used throughout this work, which corresponds approximately to a standard EN 32 specification and has a nominal chemical composition C Mn 0.10/0.15 0.2 0.018 0.01 0.01 It was prepared in 100 lb casts and hot rolled from the billet form into 1. inch square section bar, which was a convenient size for machining Charpy specimens. The specimens were subsequently annealed at 850°C for 1 hour in an atmosphere of hydrogen and nitrogen, to produce uniform micro-structures. Fig. 2.1 is a photo-micrograph of a typdcal structure, Which shows fairly uniform ferrite grains of 304.01u. diameter. The cementite occurs in a massive coalesced form at the ferrite grain boundaries and also in small islands of coarse pearlite. There is a tendency for the pearlite to occur in bands parallel to the rolling direction. -43- Etched 2r Nital. x 150. Fig. 2.1. Microstructure of high nitrogen steel showing the uniformity of the grain size. -44- 2.1.3. Specimens The Charpy specimen was adopted because it is the most frequently used brittle fracture test—piece and as a result there is a certain amount of fundamental data available for this specific geoletry Also, it was convenient to use the standard Charpy Impact machine for high strain rate measurements. (see Chapter 5). The specimens were made according to British Standard 131 : Part 2 : 1959. A specimen is a rectangular prismatic bar, 10 mm x 10 mm x 55 mm, containing a V—notch at the middle of one side. Every notch, (2 mm deep, with a root radius of 0.25 mm and a 45° flank angle) was checked by projection following the machining. 2.1.4, The deformation jig The three point bending method of deformation was chosen to conform to the geometry of the Charpy test. A jig was therefore designed to enable Charpy specimens to be deformed in 3 point bending at various low temperatures (see Fig. 2.2). This jig could be attached to the beam of the Instron testing machine - 45 - Instron Beam. Crosshead Plate. Striker Cage. Load Cell Arm. Striker Plate. Striker. Anvil Cage. Anvil. Fig. 2.2. Three-point low-temperature bending-jig. -146 - available. Referring to Fig. 2.2, it can be seen that the striker is rigidly connected to the cross-head plate by four 1 inch diameter silver steel rods, each 9 inches long. The cross-head plate is bolted to the lower face of the Instron cross-head so that the striker moves as the Instron beam. The anvils are connected to the load cell arm by two 1 inch diameter rods in the anvil cage. Both the anvils and striker have authentic Charpy dimensions according to BS : 131 : Part 2 : 1959. The rods in the anvil cage pass through holes in the striker plate. When a load is applied to a specimen the striker cage is under compression and the anvil cage in tension. The frictional load was negligible when the jig had been aligned. Specimens were located so that the notch and striker were in line, using a specimen holder which fitted between the anvil cage rods. -47- 2.1.5. The Load—Deflection Curve The striker was lowered on to the specimen at a constant rate and the resultant applied load on the specimen was measured by the load cell and recorded on a moving chart. Allowing for the deformation of the jig, it was then possible to plot the relationship between the applied load and the deflection of the specimen. A schematic representation of this curve is shown in fig. 2.3, which is similar in shape to the stress—rtrain curve of mild steel in tension. By continuous observation of a deforming specimen the slTal1 instability or "yield point" was found to coincide with the sudden spread of arcs of plastic deformation, hereafter called plastic "hinges", across the specimen ligament, from the root of the notch to the tip of the striker. This state of strain corresponds to the general yielding of the specimen, When a continuous path of plastic deformation can be traced across the section of the bar. The load at which this occurs is called the general yield load. This load, PITY, is proportional to the tensile yield stress of the material Cy, to which _48 — B PG --General Yield DEFLECTION. Fig. 2.3. Schematic load—deflection diagram. -149- it is related by the equation derived by Green and Hundy (1956) Pav —== = 0.242 'y ... 2.1 wa where w is the width of the specimen and a the depth below the notch. From experimental measurements 2 6y = 29 Kg/mm and hence GY = 565 Kg/m according to equation 2.1, which compared with the value Prly = 505 ± 40 Kg/i7 obtained from measurements on twelve specimens. Since the general yield load, PGY, is a well defined position on the load—deflection curve, it is convenient to use it as a reference point to define any point on the load deflection curve corresponding to a load P, by the ratioP /P Gy. Loads, P < PGy, will be approximately proportional to the nominal stresses feat the notch root, or the elastic plastic interface. Thus 6 PGY -50— which is the notation used by Knott and Cottrell (1962) and will be adopted throughout this study. The reminder of this chapter is devoted largely to the deformation of specimens for /Ory 4:1. 2.2.1. The distribution of plastic strain below general yield Two experimental methods of observing regions of plastic deformation are presented in detail. The size and shape of plastic zones are measured for different values of 6/uy and the elastic stress concentration factor determined as 2.5. Substantially plane stress deformation is characterised by plastic "hinge" formation and plane strain by plastic "wedge" formation. The material used in these experiments had the following chemical composition C Mn N Si 0.12 0.25 0.014 0.16 0.01 0.007 After annealing at 850°C for 1 hour the specimens had a grain size of 30-40,/h — 51 — Initial tests were carried out to determine the general yield load. Twelve specimens were deformed to beyond general yield at room temperature with a striker velocity of 0.05 cm per min. There was a tendency for the plastic "hinges" to propagate separately, each time causing a slight drop in the applied load and resulting in two "kinks" in the load—deflection curve. In this event the general yield load was taken as that load at which the first hinge formed. The average value of PGy was 505 ± 40 Kg/mm2. Specimens, each with one side surface mechanically polished to a lf4 diamond finish, were deformed to various values of 6/Cy. The distribution of the plastic deformation on the side surface was observed using the schlieren technique. 2.2.2. The schlieren technique The principle of this technique is shown schematically in Fig. 2.4. Light from the source illuminates the specimen normally; the image of the source, reflected by the specimen is projected by P, on to the schlieren stop at X; and the image of the - 5- Source Specimen Fig. 2.4. Ray diagram of the sohlieren system. - 53 - specimen is projected by P on to the screen. Plastically deformed regions have inclined planes which give se7Darate images in the plane of X, and may be stopped out to give dark areas on the screen. Alternatively the image of the undeformed plane part of the specimen may be stopped out so that the defemed regions appear light on the screen. A Riechert projection microscope with an opaque annulus stop was used to observe plastic deformation below general yield. For:low magnification work a schlieren apparatus was constructed using an optical bench and a bellows camera. Some schlieren pictures taken on a Riechert are presented in Fig. 2.5. There will be a scatter of ± on the values of 04/uy1,e presented, because the value of PGY is not measured. The specimens were then aged for 12 hours at 150°C. Following this ageing treatment, they were cut longitudinally along their mid-sections, mounted and polished down to the finest silicon carbide paper before being etched in Fry's reagent to reveal the plastic zones below their notches. -54- 2 - 1. o = 0. 9 a-, ay CT = 0.8 = 0.7 Cry ay a- •6 FIG.2.5. SCHLIEREN PICTURES OF SIDE SURFACE DEFORMATION. x 20 -CY O.4 cry -55- 2.2.3. Fry's etching technique This technique of revealing plastically deformed regions, which was discovered by Fry (1921) and developed by Jevons (1925), is only successful on steels which contain .) 0.005 nitrogen. The etchant contains 45 gm cupric chloride, 180 ml hydrochloric acid and 100 ml water. A mechanism of the etch has been proposed. hen the deformed material is aged, the nitrogen atoms diffuse and precipitate as Fe8N on the fresh dislocations, Fisher (1964). Iron nitride is readily soluble in hydrochloric acid and presumably copper is deposit/led where the nitride has been leached out. On the basis of this mechanism it was assumed that Fry's etch might be used on a microscopic scale to reveal individual dislocations following Lovell, Vogel and -,-:ernick (1959) and Hahn (1962). A tensile specimen was deformed to just beyond the upper yield point and the plastic deformation revealed is the usual manner, Fig. 2.6. This confirms the results of Green and Hundy (1956) that the technique is at least sensitive to strains of the LUders order of magnitude. — 56 — Pig. 2.6. Lilders band revealed by Fry's etch in a tensile specimen. - 57 - The specimen was repolished mechanically and then electrochemically before being etched for 30 secs in a solution containing 1 per cent Fry's etchant in absolute alcohol. Etch pits were produced but the initial dislocation density of the steel was so high that it was impossible to distinguish between the deformed and undeformed regions. There appeared to be a greater number of smaller pits in the deformed region which would give the impression of a darker region on a macroscopic scale. 2.2.4. Plastic zone size The plastic zones in the mid—sections were revealed using Fry's reagent and are presented in fig. 2.7. The smallest zone revealed, for /CC.y. = 0.35, is only 0.15 mm long. This zone persisted after repolishing and etching and therefore Fry's etch is capable of revealing regions of plastic deformation of this magnitude. The size of a "wedge" shaped plastic zone, was measured form the tip of the zol.e to the root of the notch, along the axis of the notch. The variation of the plastic zone size with' the applied load is -58- CTy = 1.0 y = 0 •80 0- 0- = 0.70 = 0.40 6y 0-y C3- = 0 •35 = 0.35 x60 0-y (YY FIG.2. 7. MID - SECTION FRY'S ETCH PATTERNS. x 20. -59- represented in the form of the graph of e vs /uy in fig. 2.8. The experimental error in the values ofr juy arises from the amount of scatter obtained from the measurement of general yield loads on twelve specimens. 2.3.1. Plane stress deformation The deformation patterns observed with the aid of the schlieren technique, fig. 2.5, show the development of the plastic zone below the notch under substantially plane stress conditions. The smallest amount of deformation detected was on the specimen deformed to 446'M = 0.5, when a zone of about 0.1 mm extended from the middle of the notch root. No deformation was observed on the specimen deformed to 16/6y = 0.L and therefore plastic deformation begins on the side surface at a stress between /Uy = 0.4 and /uy = 0.5. Further deformation, /Ory = 0.6, produces more LIIders bands which penetrate deeper into the ligament. At`6/(5Y ,=.0,7. the displacement at the root is accommodated by curved Lilders bands or "hinges" extending from the corners of the notch root. These "hinges" broaden and penetrate -60 - ti: b 0.5 1.0 1.5 PLASTIC ZONE SIZE p mm. Fig. 2.8. Effect of applied load on the growth of the plastic zones compared with the theoretical values of Rendall and Allen (1964). -61.- deeper upon further loading, /uy = 0.8 and a second set of "hinges" nucleated inside the strongly developed primary "hinges", /f6 = 0.9. This type of plastic strain pattern has been observed by Knott (1962) using four point bending and Hahn (1964) using a sharp notch in tension. In contrast, Dugdale (1960) using mild steel sheet 0.050 inches thick, with an edge slit in tension, found that the deformation was confined to the axis of the slit. Bateman, Bradshaw and Rooke (1964) using a central slit and a fatigue crack in tension showed that plastic "hinges" developed for an aluminium alloy, but that for mild steel the "hinges" were narrow and elongated giving the impression of occurring on the axis of the slit. Recently Dixon and Strannigan (1964) and Knott (1964) have shown both plastic "hinge" and slit axial deformation occurring simultaneously. Theoretical elastic plastic analyses of the plane stress patterns have been obtained by Allen and Southwell (1949) using the method of relaxation for a 900 notch in tension, and later by Stimpson and Eaton (1961). Both solutions predict the shape of the plastic zones observed in the present work. -62- The nature of the plastic zone, appears to be strongly dependent upon the geometry of the notch, the loading system and particularly the yielding behaviour of the material, Bateman, Bradshaw and Rooke (1964). Sharp notches, yield point materials and uniform applied stresses all tend to produce extended yield zones. 2.3.2. Plane-strain deformation The Fry's etch patterns of the mid-section plastic zones in substantially plane strain conditions, (hereafter referred to as just plane strain) are shown in fig. 2.7. The smallest plastic zone observable using this technique was for a/CY = 0.35 and is in the form of a small triangular wedge, the base of which is much smaller than the root radius. A small increase in applied load to 6/6y = 0.40 causes the wedge to broaden sufficiently to cause yielding across the root accompanied by deeper penetrations of the tip. As the plastic zone extends, it changes shape from triangular to a pear-drop form. From fig. 2.8 it is evident that once general yield occurs the tip of the zone tends to remain stationary due to a form of stress relief caused -63- by the general yield "hinges". This "wedge" type plastic deformation is predicted by the slip line field analyses of Liarris and Ford (1959) and Komoly and Alexander (1962) for the plane strain deformation of bent notched bars. The corresponding deformation patterns obtained by Knott (1962) using a deeper notched specimen in low' point bending show a marked tendency for deformation to spread out almost normal to the notch axis from the root in a similar manner to that predicted by Jacobs (1950) and Stimpson and Eaton (1961) for the plane strain deformation around an edge crack in tension. Plastic "wedge" type deformation has been shown by Koshelev and Ushik (1959) and Kochend8rfer and Schtirenkamper (1961) on double notched tensile specimens. Tensile specimens must be much thicker than bend specimens to produce the same degree of plane strain because of the difference in constraint factors. Therefore the "wedge" type deformation is not necessarily a definite indication of plane strain deformation. -614- Kochend8rfer and Schilrenk4mper (1961) varied the notch geometry and showed that decreasing the flank angle, which increases the available amount of hydrostatic stress, causes a more marked development of the "wedge" pattern. By varying the notch depth it is possible to change the degree of plane strain and it would be interesting to see how the deformation patterns are affected. An alternative method of changing the degree of plane strain is by varying the specimen thickness. 2.3.3. The effect of specimen width From the observations made of Plastic strain patterns it is evident that plane stress deformation is characterised by plastic "hinge" and plane strain by a plastic wedge; at least in these Charpy specimens. In order to estimate the degree of plane strain (or plane stress) as a function of specimen thickness, a specimen was deformed to just before general yield and a sequence of deforziation patterns revealed on successive longitudinal sections, using Fry's reagent. - 65 - The depth of the plastic zone on the axis of notch, below the root, was measured and related to its position on the trmisverse axis of the notch, fig. 2.9.(a). Drawings of the Fry's etch patterns are presented in fig. 2.9.(b). a distance of z = 0.02 mm below the side surface (z = 0), "hinges" had already begun to approach the notch axis and eventually met on it at z = 0.40 mm. The "hinge" then gave way to the formation of the "wedge". Both "wedge" and "hinge" deformation occurred simultaneously at z = 0.65 and z = 1.00 mm. Beyond z = 2 mm, the depth of the "wedge" did not change significantly, fig. 2.9.(a). From this it might be inferred that further increasing the bar thickness will not affect the stress distribution and that the maximum degree of plane strain will be achieved at the centre of a bar 4 mm wide. Using Charily specimens of varying widths Castro and Gusnssier (1949) determined experimentally the effect of triaxiality on the impact transition tempe ature. These results were replotted by Crussard et al (1956) to show that there is a critical specimen 0 Pig. 2.9.(a) DISTANCE ALONGTHETRANSVERSESECTION FROM THESIDESURFACE.Zmm. 1 -66- 2 Pry's etch patterns. of planestrainfrom Estimation ofthe degree 3 4 5 Mid - Section: - 62 - V (Surface.) 0.2. Z.0.4. Z=0.65. Z=1.0. Z=1.5. Z=2.5. Z=5.O. Z= Transverse distance from side surface(mm.). Fig. 2.9.(b). Plastic strain patterns at various transverse sections of a Charpy specimen deformed to = 0,9, - 68 - width, 5-6 mm, at which there was an abrupt increase in the transition temperature. Referring to fig. 2.9, this critical thickness coincides with development of the plastic "wedge" to a maximum depth. Above this thickness the transition temperature (Crussard et al 1956), and the size of the plastic "wedge" (fig. 2.9), remain unaffected by further increase in the specimen width. From a comparison of the strain patterns of the specimen deformed to /uy = 0.L in figs. 2.5 and 2.7, there is no plastic deformation on the side surface while a plastic zone of 0.25 mm length is evident in the mid-section. Thus, first plastic deformation occurs at the mid-section and spreads both along the y and z directions in the form of a plastic "thumbnail". 2.3.4. The elastic stress-concentration factor A value of the elastic-stress concentration factor (S.C.F.)C( may be obtained by plotting e as a function of /1/6y and hence an accurate value at which first slip occurs may be found by extrapolation to the value (:)= 0. Dugdale (1960) determined a theoretical -69— relationship for the spread of Plastic deformation from a sharp notch, of the form r = socirc— — 1 2.2 c 2657- which he verified experimentally using sharp notches length c under a tensile stress Cr. When the plastic zone sizes from fig. 2.8 were plotted in the form loge vs log [sec(0 - in fig. 2.10, a good linear relationship was found for values of C3‘ 0.4, but a marked deviation from the predicted linearity was observed for lower loads. This is probably due toplastic zone becoming small compared with the root radius and also the deformation becomes restricted to only a fraction of the transverse section. Thus an accurate value of /uy for the onset of plastic deformation cannot be obtained by this method for a blunt notch. The first plastic zone at the notch root to be detected by the Fry's etch technique was after an aplied load of /uy = 0.30 ± 0.025, i.e. a nominal stress d = 14 Kg/mm2. The tensile lower yield stress, ey, -70- was found experimentally to be 29 Kg/mm2. The tensile upper yield stress was taken to be 1.2 ey. 1.2 Ory 1.2 x 29 OC - = 2.5 C 14 compared with the theoretical value of 3.25 of Neuber (1946). Griffiths (1964), using silicon-iron and a different specimen geometry, observed alip bands at the load predicted from Neuber's theoretical value ofOl. The value of (X obtained from Fry's etch data may be low because the etch c/nnot reveal plastic zones of a grain diameter size. Also the value of the yield stress in biaxial plane strain is probably greater than that for uniaxial tension. Thus, the true value of 0: for a Charpy specimen will be greater than 2.5. Returning to fig. 2.10, an extrapolation of the linear region may give an approximate value of OC. for a very sharp notch i.e. a crack, for which equation 2.2 will be valid for all values of stress. Griffiths (1964) found that deformation always extended across the whole grain at the notch root and therefore the value of Cr was calculated by extrapolating the linear region - A- 10 1 I I I I I I 1 I I III I 11111 1.0—_ p = Grain Diameter. Extrapolation. / Experimental. / I I Neuber I / I / 0.01 — / / / 0.001 1 t I I i lilt 1 I 111111 0.01 0.1 1.0 10 Fig, 2.10. The effect of applied load 06/4r, on the plastic zone size El, plotted in the form deriVed by Dugdale (1960). -72- to €.= d the grain diameter, at which /G.y. = 0.01 2 1. whence CT = 0.47 Kg/mm , and orL_ x 27 = 70. 02 . 47 This value of olwould represent the stress-concentration caused by a crack of length c = 2 mm and radius esuch that to an approximation j 2 (Neuber) and -I = 70, from which= 0.4/k. This indicates the high elastic stress concentration factors which may occur at the tip of sharp cracks. 2.3.5. The Distribution of Stress below the Notch Renclall and Allen (1964) have adapted the method of Barton and Hall (1963) to determine the magnitude and Position of the maximum stress & below the root of a Charpy specimen for different values of the applied load, /6y. The calculation is based on the elastic stress distribution at the minimum section of an Izod specimen by Hendrickson, Wood and Clark (1959). The values of the elastic stresses as ratios of the yield stress, - 7 3 - /uyd and /uyd are substituted into the von Mises yield criterion for plane strain, and the positions of 7 for which the criterion is satisfied are obtained for different values of dnb ....-/uyd. A slight refinement to the calculation is made by correcting dlabbydA° from a ratio of the bending moments under the elastic curve and under the elastic-plastic curve. The position of the ma:Ktumnstress corresponds to the elastic-plastic interface. The model predicts that the plastic zone hb will spread until /6yd = 0.825 (6 .e/uy = 0.5) and will then remain stationary. The theoretical and measured sizes of the plastic zone show very good agreement in fig. 2.8.up to /uy,ei = 0.5. The model breaks down at /6y = 0.5 because the increase in applied load cannot compensate for the decrease in Gri predicted from the elastic stress distribution; the yield criterion cannot therefore be satisfied. More realistic analyses must take into account the effect of plastic deformation on tha elastic strain distribution. Strain patterns of Koshelev and Ushik (1959) show plastic regions spreading from the tip of the plastic wedge rather than from the notch root. Thus it appears that the wedge -74- can effectively shappen and deeDon the notch. The implication of this effect has been shown by Cottrell (1964) using the results of Allen (1961). Both Rcndall and Allen (1964) and Alexander and Komoly (1962) predict the same value of the maximum stress for the same plastic zone size. This zone size was predicted by Alexander and Komoly for the state of general yield and is only about one third that of the experimental value. This supports that the value of the maximum stress at general yield is higher than they predict. The results of Rendall and Allen are plotted osc (max) in the form /*d against the applied load /uy.in.., fig, 2.11 and xtrapolated to the value ofd = 2,41 calculated by Hendrickson Wood and Clark (1958) for the condition of "incipient instability", which is approximately general yield, for an Izod specimen. The results presented in fig. 2.3 wore combined with fig. 2.11 to obtain the relationship between the maximum stress and the size of the plastic zone, Q, fig. 2.12. This curve tends to flatten as Q increases so that the greatest increase in the plastic stress Cv ..e concentration factor occurs below /uy:=--t 0.5. r -g Extrapolation from Hendrickson,Wood and Clark...". / • 2.0 a Alexander and Komoly. Theoretical. Rendall and Allen. General Yield. Elastic Limit (Neuber). Elastic. 0 1 ,0 2.0 anb 0-yd. 1 0 0.25 0.5 0.75 1.0 a/ oY•- Fig. 2.11, The maximum stress below the notci- root, as function of the applied stress Orib/o.vd and the applied aoad 0/0y. - 76 0.5 P • Fig. 2.12. Variation of maximam stress"" withthe plastic zone size. - 77 - Green and Hundy (1956) presented theoretical plane strain solutions for the initial plastic yielding in notched bars. From the geometry of the field and the Hencky relations,it can be shown (Hill (1950) p. 248) that near the notch whose root is a circular arc of radius r, the slip lines are logarithmic spirals. The tensile stress 6X, perpendicular totne -minimum section, is distributed in the plastic region according to the formula, X = 2k 13: ln(1 + —) 2.3 where x is the distance below the root of the notch. Thus using the Tresca yield criterion, the maximum stress below the root can be calculated from nax 1 + ln(1 + Q/r) 2.4 dryd where o is the depth of the plastic zone and is related to the applied load experimentally in fig. 2.8. - 78 - Ogr Values of Oyd ax calculated from equation 2.4 are in excellent agreement over the whole range of /uy with the values presented in fig. 2.11. - 75 - CHAPTER 3 The deformation of Charpy specimens beyond general yield 3.1.1. pummary The experiments described in this section were designed to determine the mode of plastic deformation, at and beyond the condition of general yield. A number of specimens were deformed various amounts and the resultant geometrical changes in shape were measured and correlated. The measurement of local plastic strains using micro-hardness values is described in detail. The strain-rate in the notch root is related to the striker velocity. 3 1 '7 Experimental The steel used in these experiments had a chemical composition of C Mn Si 0.14 0.21 0.018 0.05 0.012 0.009 •Subsequent to machining, each specimen was annealed in vacuo for 1 hour at 700°C. The grain size was - 80 - about 50-60t Each specimen was polished on one side surface and the top surface with 1p. diamond paste, before being deformed in the jig described in the previous chapter, at room temperature, with a striker velocity of 0.05 cm per min. The load deflection diagrams obtained, were of the form shown schematically in Fig. 2.3. Specimens were loaded to selected values of C/cl, the ratio of the maximum load to the general yield load, and the resultant geometrical changes in shape experienced by each specimen, were measured. The 'Permanent angular displacement between one half of the specimen and the other, is called the angle of bend Op, and was measured on both a Universal Projector and a vernier protractor. The former measures to an accuracy of ± 2 minutes of arc. The transverse contraction of the notch root was measured with a fine focussing microscope. The undeformed polished side surface was first brought in focus and -ne position above a fixed datum measured on a vernier scale. The lowest part of the notch root surface was similarly measured and from the - 81 - difference between the two readings, the contraction in the transverse direction was calculated. The experimental error of the contraction measurements is± Values of Op, C/dy, and the notch Contractions arc correlated in Figs. 3.1 and 3.2 and are presented in Table 3.1. Schlieren pictures of the side surface and the corresponding Fry's etch mid-section patterns are presented in Fig. 3.3. Top surface topographical features were measured using a Taly-Surfe, an instrument capable of measuring top surface tilt to witb.in an accuracy of 1 minute of arc; and the notch profiles were measured on a Universal projector. 3.1.3. The measurement of root strain There are only a few available techniques for measuring the magnitude of localised plastic deformation within the body of a specimen. The dislocation etch-pit technique referred to in the previous chapter is the most sensitive of all the techniques but cannot be used to measure strains greater than about %. PERCENT TRANSVERSE NOTCH CONTRACTION. o Fig. 3.1. PLASTIC ANGLEOFBENDOp. with angleofbend. Variation ofnotchcontraction - 82 10 20 PERCENT TRANSVERSE NOTCH CONTRACTION. Fig. 3.2, Variation of notch contraction with applied load. - 84 - TABLE 3.1 Spepimn , Cr ' % Conventional Natural No. Op Contraction Longitudinal Strain Gy eT = ez %train. eI. = ex 6( N4 1.00 0°40' 0.45 5 0.048 N2 1.13 1°30' 1.04 12 0.113 .N3 1.30 2°50' 1.63 19 0.174 11 1.33 4°30' 2.80 25 0.223 N5 1.40 5°32' 3.10 35 0.300 N8 1.50 5°35' 3.00 - N7 1.60 7°15' 4.08 - N6 1.68 7°27' 4.52 45 0.371 N12 1.73 10°35' 5.66 67 0.512 N10 1.88 15°50' 7.80 N13 2.08 18°30' 9.60 N9 2.12 31°10' 14.50 , , -85 - 0 - 0°40' 9 . 1°30' 9 .2°50' 9 - 5030/ SCHLIEREN PICTURES SURFACE. x.31 FRY ETCH PATTERNS MID-SECTION.x5. FIG. 3.3 — 86 — Lianis and Ford (1958) used the method of scribing reference grids on the metal surface to measure strain fields around notches. Specimens were split down their mid-sections and grids scribed on each polished half before being firmly stuck together with Araldite. After deformation the specimen was then separated into two halves again and the grid remeasured. The accuracy of this method depends upon the ability to poribe closely spaced fine grid lines. Using a diamond indentor, fine grids can be scribed 0.001 ins apart and measured to an accuracy of 0.00001 ins with a high powered microscope. It is then possible to measure strains to an accuracy of 11, over a gauge length of 25p. However this technique suffers from experimental difficulty and it is questionable whether true plane strain conditions are attained at the centre of the specimen. A microhardness technique has been used to measure local strains by Felix and Geiger (1956) and Knott (1962). This is a good technique provided that the micro-hardness value is sensitive to small changes in plastic strain, which will depend largely upon the -87— work hardening characteristics of the material. The gauge length over which the strain is measured will be of the indent size, i.e. 10-30/A. Some high nitrogen steel was strained to known amounts and the corresponding micro-hardness values measured to give a calibration curve. The magnitude of the plastic deformation at the root of deformed Charpy specimens :zas related to that in the calibration specimens, by the micro-hardness values. 3.1.4. Calibration Controlled amounts of plastic deformation were induced by compression rather than tension because the tensile specimens begin to._neck after only about 155 strain; the local strains then become significantly- greater than the average strains measured over the gauge length. 1 Cylindrical specimens /10 inch diameter and 3/20 inch long, were machined out of the same material used in the experiments described at the beginning of this chapter, and were given an identical heat treatment. The ends of the specimens were mechanically -88— polished with 11.c diamond paste in a special jig designed by Shaw (1962) and finally checked for parallelism. The specimens were then compressed various known amounts at a cross-head speed of 3 -1 0.1 cm/min, 2 x 10- sec ), in a compression jig mounted on an Instron. Barrelling was reduced and largely eliminated by inserting thin sheets of p.t.f.e. between the specimen and the polished compression plates. This acts as a lubricant according to Pugh (1962), and as a result, no barrelling could be detected from the shape of the stress-strain curve for strains below about 50,' axial compression. The deformed specimens were mounted in cold setting plastic, mechanically polished to their longitudinal mid-sections and electropolished in a chrome-acetic electrolyte, Morris (19L49), to remove any cold worked material which might have been introduced during mechanical polishing; before being finally etched for 15 secs in 2% nital. Micro-hardness measurements were made by indenting the surface of the polished section with a diamond pyramid under a known load and measuring the size of — 39 — the indent produced. Thus micro-hardness can be expressed as a pressure and can be calculated for a 136° diamond pyramid indenter from the equation P m2 H = 1855.4 -7 Kg/m d where P is the load in grams and d the length of the diagonal of the indent in microns. The Reichert micro-hardness tester was used. The torsional balance was calibrated against standard weights and the distance between the cross-wires calibrated using a graticule. Each specimen was indented five times under six different loads. The load was selected according to the size of the grain in which the indent was to be made so that the indent did not cross the grain boundary. The indents were measured four times to obtain an average indent size d. Values of P and d were plotted on a log-log graph to obtain a family of "iso-strain" Meyer hardness lines, Fig. 3.4, from which the hardness value was calculated for an indent size of 2.5p., for each strain. - 90 - 100 vi trl 25 O O 25 100 INDENT SIZE d microns. Fig. 3.4. Log P vs log d for different values of plastic strain. (Micro—hardness values were calculated ford ='25)µ.) -91- 260 240 N. E E 220 N t:1) ZN 200 LIJ 180 160 140 120 II I I It 1000 10 20 30 40 50 60 70 80 90 CONVENTIONAL TENSILE STRAIN PERCENT. Fig. 3.5. The variation of micro—hardness with strain for an indent size of 25,u, -92- thc calibration curve of H25 against tensile strain is presented in Fig. 3.5 together with the degree of experimental. scatter. 3.1.5. Strain measurement A selection of the deformed. Charpy specimens was cut along the longitudinal mid-section using a spark-electrode cutting machine, to produce a strain free cut. The sections were nickel plated ,around the notch roots, mounted in plastic and polished mechanical17- and electrolytically in exactly the same manner as were the calibration specimens, before being finally etched in nital. All micro-hardness measurements were confined to a region immediately adjacent to the notch root, of dimensions approximately 0.010 inches wide by 0.003 inches deep. This region was chosen following the work of Knott (1962) who found twins uniformly distributed in such a region with the notch in compression. It was therefore assumed that this region was uniformly stressed. Each specimen was indented six times at different loads and the value of calculated from 1125,a -93- the resultant Meyer line. The value of the root strain was then obtained directly from Fig. 3.5 and is related to the applied load 0/15y, the angle of bend Eip and the transverse notch contraction in Figs. 3.6, 3.7 and 3.8 respectively. - 94 - 0 Extrapolated. 1 I I I I 1 I i I 1 I 0 10 20 30 40 50 60 PERCENT LONGITUDINAL STRAIN. Fig, 3.6. Variation of root strain with applied load. CONVENTIONA LLONG ITUDINALSTR AIN. 20 30 50 40 60 70 10 0 Fig. 3.7. 1 Variation in plastic strainwith angle ofbend. 2 3 PLASTIC ANGLE OFBEND.Op. 4 5 6 a • o Knott. xWilshaw. Wells(C.O.D.Theoretical.) Emery andFlanigan. Lubahn andLequear. 7 8 9 10 11 -96- 6 (1) 5 C) c.) 4 0 w 3 c.) cc (i) 2 ti ti C.3 cc 1 14.1 0 0.10 0.20 030 0.40 0.50 0.60 0.70 CONVENTIONAL LONGITUDINAL STRAIN ex . Fig. 3.8. Relationship between transverse and longitudinal strains. -97— Discussion Fig. 3.1 shows the variation of the transverse notch contraction, (which will now be referred to as the transverse strain) with the applied load. The slope of the curve increases with CA5y and tends to infinity as plastic instability and necking are incipient. The curve has been extrapolated below general yield, assuming that the transverse plastic stain is zero at c5Xy = 0.4 (see Fig. 2.5). At (1,/dy = 0.4 the average transverse strain will be of an elastic order of magnitude because deformation does not spread across the whole of the transverse section. The transverse strain increases with the angle of bend Bp at an initial rate of 0.75 per degree and gradually decreases to a constant slope of 0.45 per degree above about ;gip = 7o when gross deformation has set in across the whole bar, as in an unnotched specimen. - 98 - 3.2.1. The Deformation Sequence Prom the observations of the diStribution of plastic strain Fig. 3.3, the measurements of the top surface profiles and the notch profiles, it is possible to deduce a qualitative picture of the plastic deformation sequence in relation to the load-deflection diagram. The distribution of plastic strain at the state of general yield has been calculated from slip line field analysis by Green and Hundy (1953), Lianis and Ford (1958), and Alexander and Komoly (1962), for notch bars under plane strain conditions. There is good overall agreement between the experimental strain patterns as revealed by Fry's etch and the theoretical patterns, but there are local differences especially in the small important region immediately below the notch. Alexander and Komoly (1962), considering the specific case of a Charpy specimen in' three point loading, predict a "plastic" wedge of length 0.395 mm compared with an observed zone 1.1 mm long. The maximum stress :below the root for general yield has been possibly underestimated by this slip line field analysis which assumes a rigid/plastic non-work hardening material. -99- Beyond general yield the plastic "hinges" broaden as in Fig. 3.3, while the tip of the plastic wedge remains approximately fixed; deformation is occurring by shearing along the plastic "hinges" and in effect "shields" the material at the tip of the wedge from further straining. The radius of the notch increases and causes an elastic tilt of about 5 minutes on the top surface about an imaginary line MI Fig. 3.9(a). At a load of about %y = 1.3 the stress at Z on the top surface becomes sufficient to cause yielding which propagates inwards along Zr, forming a plastic "wing" which joins the top surface with the plastic "hinge". The whole region of elastically deformed material, YXZU, then proceeds to shear along ZU causing two tilts on the top surface, Fig. 3.9(b). The slope of ZW is about 30 minutes. At a load of about 045y = 1.7 the region YXZU had become fully plastic and the tilt of the top surface XW was on. of about 10. - 100 - / / / / / (a) (b) Fig. 3.9. Deformation sequence above general yield. - 101- 3.2.2. Strain in the Notch Root The distribution of strain within the calibration specimens was maintained as uniformly as possible by taking precautions to reduce barrelling and the degree of scatter of the micro-hardness values was very small. The hardness lines on Fig. 3.4 obtained by plotting log P against log d each represent an average value of 30 indents. The hardness value is not const7mt, but varies accordinq, to the load P and d, so that a comparison of micro-hardness values must be made for the similar values of P or d. In this case an indent size of 25)µ was selected as the basis for comparing values of H. When smaller values of d were used, the slope of the curve of H against strain, Fig. 3.5, became shallower and hence less sensitive. Provided that good experimental reproducibility can be achieved then the error in the strain measurement will be very small, because the method is one of comparison rather than direct measurement. The total error in the final value of the strain will arise from the initial measurement of the strain in the calibration specimens which is about 25 and a small - 102 - indeterminable error arising from the comparison of the micro-hardness values. The tensile strains in the calibration specimens were calculated from the axial compression and related to 9p in Fig. 3.7, together with the results of other workers. The root strain at general yield is 5 and this increases almost linearly with Gp, such that to a close approximation, the longitudinal tensile root strain eL = 6 op. Lequear and Lubahn (1954) used an x 8.9 scaled up Charpy specimen to measure the root strain by scribing 10 Mils spaced transverse grids on the notch bottom. The distance between them was measured with a travelling microscope after various amounts of bending and the longitudinal strain obtained. Their results are plotted on Fig. 3.7, and approximate to a relationship eL = 10 e°p. These high values of strain indicate that the "Law of Similitude" does not hold and that it is not possible to predict the behaviour of small specimens by scaling them up and vice-versa. -103 - Knott (1962) used 2 inch square bars with a 1/6 inch deep notch and measured the strains at the notch root by scribing grids on the faces of the longitudinal mid-sections. The halves were then bonded together and deformed in pure bend before being unbonded and the grids remeasured. The values of strain plotted in Fig. 3.7 are slightly greater than those obtained in the present work. Emery and Flanigan (1951) welded a central longitudinal bead on to a mild steel plate 4 x 9 x 4 inches and milled a 3/32 inch deep notch across the weld. A grid was transferred on to the notch root to measure the longitudinal strains produced by three point bending, Fig. 3.7. Although it is not possible to provide a quantitative comparison of all the results presented on Fig. 3.7 because of the widely different specimen geometries and loading systems, the general form of the relationship between the root strain and the angle of bend is similar. The results of Emery and Flanigan (1951) indicate that the relationship may vary significantly for different materials and conseauently - 104 - the relationship eT = 66 p, obtained here for the Charpy geometry, is not considered a general one and will not necessarily be applicable to similar shaped specimens of different materials. 3.2.3. The Crack Openila Dislocation (C.O.D.) Wells (1961) sugp:ested a deformation model for a notch specimen to determine theoretically, the d.iE2111.12-Lacnt of the sides of the notch for a given angle of bend. The deformation is assumed to occur along discrete cylindrical slip faces ABC and ADC which pass through the notch root, (Fig. 3.10(a)), and have a radius r but no common centre Green and Hundy (1956) determined the depth of the axis of rotation below the notch root, a = 3.5 mm, for a Charpy specimen. The tangent to the hinge at A makes an angle ib with the longitudinal direction. When the specimen is bent through an angle Oc radians, the displacement along ABC will be B'B = r 0c/2, Fig. 3.10(b). This displacement, together with that along ADC is resolved in a direction normal to the notch axis. - 105 - C (a). Fig. 3'.10. Deformation model after Wells (1961). — 106 — The total displacement u = 2.r 0/2 cos 56, but as AEC and ADC are both arcs of a circle then a = r coscS and hence u = a 0°. Thus the C.O.D. = 2.5 x 10-3 9° ins for an angle of bend 0 This theoretical relationship was found to agree extre-oely well with the displacements measured from the notch -profiles. The root strain has sometimes been calculated by assuming that the C.O.D. is accommodated within a gauge length equivalent to the root radius. These values are plotted on fig. 3.7 and indicate that this assumption is not valid, the discrepanc7 becoming greater for higher values of Op. This is because the C.O.D. is the integral value of the resolved components of the strains tending to open up the notch and which can be situated away from the notch root. For example, at general yield Op = 40' and el = 5',.;; the Wells C.O.D. relationship predicts a displacement of -3 u = 1.6 x 10 ins. When the displacement is calculated from the e over the root radius 1, r = 0.010 ins, u = 0.5 x 10-3 ins. For a larger degree of deformation Op = 71°, eL = 4.5; u = 18.5 x 10-3 ins (C.O.D.) and u = 4.5 x 10-3 ins from the strain measurement, - 107 - Below t3eneral yield, when the plastic zone is confined to the region of the notch root (see Fig. 2.7), the strain at the root will become more proportional to the displacement. The importance of this interpretation of displacement ,,t/root strain is stressed because present theories relating the degree of deformation to the applied stress consider displacements rather than strains. 3.2.4. Strain-rate The natural longitudinal strain Ex was calculated and related to Bp in Fig. 3.11. The angle of bend is related direatly to the deflection rate, which was 0.05 cm/min, and hence the strain-rate in the notch root was calculated. The initial value of the strain-rate E = 3.8 x 10-3 sec-1 decreases over the first 3° degrees of bend to a constant value of -3 - 1.8 x 10 sec-1. Assuming that Fig. 3.11 will remain unchanged by increasing the striker velocity, then for the impact test, in which the striker velocity is 16.5 ft per sec, 0.6 0-5 'ccc 0.4 ti E--3 03 CO 0 0.2 +.1 QC I 0.1 0 1 2 3 4 5 6 7 8 9 10 11 PLASTIC ANGLE OF BEND. 9p. Fig. 3.11, Natural. longitudinal strain vs. Op. - 109 - the strain rate in the notch root will vary between -1 -1 2300 sec and about 1000 sec , which is similar to the range of values quoted by Gensamer (1947) for similar impact bend tests. 3.2.5. Biaxiality The transverse notch contraction represents an average value of the transverse compressive strain ez and is directly proportional to the tensile longitudinal strain ex measured at the mid-section, Fig. 3.8. From this graph the average degree of biaxiality which exists on the notch can be calculated from the von Mises criterion, - Oy Oy - Oz Ox ex - ey ey - ez ez - ex and assuming constant volume ex + ey + ez =0 •• • 2 - 110 - Then, combining equation 1 and 2 for plane stress = 0) ex 1 + 2 ex/ez . • • 3 ez 2 + ex/ez From Fig. 3.8 ex = - 0.09 ez and substituting this in equation 3 lex 0.43 dz Lecquear and Lubahn (1954) measured the local values of ez at both the mid-section and close to the side surface. A biaxiality of 0.48, representing almost complete transverse restraint, was found at the mid-section, which decreased to about half this value at the side surface. The average value of the degree of biaxiality is close to the maximum; consequently a high degree of transverse restraint must exist across a large fraction of the transverse section. — 111 — Part II The Effect of Temperature and Strain—Rate on the Fracture of Notched Bars - 112 - CHAPTER 4 The Effect of Temperature on the Fracture of Notched Specimens 4.1.1. Summary Charpy specimens were deformed to fracture, in throe point bending, with a striker velocity of 50 cm/min, and within a temperature range, 10°C to - 196°C. The fracture instability loads vary discontinuously with temperature and the nature of the discontinuities are discussed in detail. 4.1.2. Experimental The experimental high nitrogen steel used in this section was similar to that used in Part 1, but had a slightly different chemical composition. C Mn N Si 2 0.14 0.17 0.016 Tr 0.016 0.007 Following machining, each specimen was annealed at 850°C for one hour, in an atmosphere of hydrogen and nitrogen, to produce a uniform grain size of 4014. — 113— The specimens were then loaded to fracture instability in the low temperature bend jig, (see fig. 2.2), at temperatures within the range + 10°C to — 196°C. Cooling baths were prepared within the range + 10°C to — 100°C using Isceon 11, (a commercially produced liquid coolant with a freezing point of — 111°C) cooled to a specific temperature with liquid nitrogen; and in the range — 100°C to — 160°C, with Isceon 12, (freezing point —'166°C) cooled with liquid nitrogen. The cooling baths were contained in a 4 inch diameter Dewar and the temperatures measured with a calibrated chromel—alumel thermocouple, held in close proxii;lity to the notch root. The cooling baths were very stable and temperatures above about — 90°C could +1 0 be maintained to — 7 C; lower temperatures to about ± 1°G. All tests were carried out on a 5000 Kg Instron testing machine at a cross—head speed of 50 cm per min. The loading rate at this speed was too high for the mechanical pen recorder to follow, consequently the load—deflection curves (see fig. 2.3) were obtained on a O.R.O., in the form of load—time curves. — 114— A schematic diagram of the basic load measuring system is shown in fig. 4.1. The four strain—gauges in each load cell are connected in the form of a Wheatstone Bridge and are excited by an oscillator at a stabilised frequency of 375 cycles per sec. An applied load on the cell changes the resistance balance of the bridges and the resulting signal is amplified by a circuit which also includes a means of initially balancing the bridge. The signal is then attenuated in the load—selection circuit before being amplified again. The output voltage signal from the second amplifier has a sinusoidal form, with an amplitude directly proportional to the applied load. This signal was fed into a C.R.O. and the time base reduced to zero. The Instron was calibrated in the conventional manner and a suitable combination of the load—selection and voltage range were selected to give an optimum range of amplitude on the C.R.O. The amplitude of the oscilloscope trace was calibrated against the load measured on the automatic pen recorder of the Instron, and recorded on 35 mm film in a variable speed Cossor First Balancing Amplifier Load Second Network and Selection. Amplifier Calibration. Oscillator. Load Cell. Fig. 4.1. Schematic diagram of the basic load measuring system. -- 116 - camera. A specimen was placed in the jig with a special holder so that the notch and striker were in line. A small load of about 50 Kg was applied and the specimen holder removed. When the required temperature was obtained, the film was set in motion at a known speed, and the specimen loaded to fracture at a cross-head speed of 50 cm per min. Typical load-time traces are shown in fig. 4.2 with the load represented on the vertical axis and the time on the horizontal axis. The loads were measured by projecting the traces on a screen and comparing the amplitudes with those of the calibration specimens. In this manner loads were measured to an accuracy of - 10 Kg. The loads at which fracture instability occurred i.e. the maximum loads, and the general yield loads, are plotted vs temperature, in fig. 4.3. The strain-rate in the notch root for a striker velocity of 50 cm per min will be 3.8 sec-1 (see Section 3.2.4.). From experimental values of the tensile yield stresses at this strain-rate (Chapter 6), the general yield loads were then calculated from the equation derived by Green and Hundy (1956) (Section 2.1.5.), to extrapolate -117- Fig.4.2. Load/Time traces. Striker velocity=50cm/min. + 10°C Fracture above Td. -45°C Fracture below Id. -69°C Fracture at General Yield. -76°C Fracture at Upper General Yield. -196°C Fracture at IC =0-26 say 1 2000 — Cross-Head Speed - 50 cm/min. t 3.8 x 108 soc.-1 a_ Fracture Instability Load. o_General Yield Load. 1500 — • 61 • o • • .0 1000 CI • • • • • 0 • • • • • 1.• • • • Twins at Notch Root. 500 — ------Load for First 5:17: ubo .78) I I I 0 ' I I -200 -150 -100 -50 0 50 100 TEMPERATURE °C. F ig • 14. 3. General yield load and fracture .load. vs temperature for high-nitrogen steel Char-by specimens deformed at a cross-head speed of 50.cm/min. -119- the general yield vs temperature curve into the temperature region in which fracture instability occurs before this state of strain, fig. 4.3. Similarly the loads at which plastic deformation is initiated were calculated from Neuber's value of the elastic stress concentration factor (0(. 3.5) and are represented by a dashed line in fig. 4.3. The various features of the fracture load - temperature curve fig. 4.3 will be discussed in sequence, beginning with the most ductile fractures. The drop in fracture load at - 36°C corresponds to a sudden change in the amount of ductility. A separate series ofmperiments were performed to determine the nature of this transition. 4.2.1. The Initiation Transition High nitrogen steel of the following chemical composition was used:- C Mn N Si 0.12 0.17 0.016 0.03 0.017 0.007 The specimens were annealed in vacuo at 700°C for one hour to produce a uniform grain size of 50-60/4. - 120 - They were then loaded to fracture under a striker velocity of 0.05 cm/min, at small temperature intervals in an equivalent region to - 36°C in fig. 4.3. The angles of bend at instability, GI", were calculated from the load-deflection curve and the notch contractions measured using a travelling microscope. Almost all the specimens were nickel plated, cut along their longitudinal mid-sections, and examined metallographically before being finally etched in Fry's reagent to reveal the extent of the macroscopic plastic deformation. 4.2.2. Results The loads at which instability occurs will be referred to as the fracture loads, C5f are presented along with the general yield loads GY in Table 4.1 and plotted vs temperature in fig. 4.4. There is a sudden drop in Orf at a temperature which will be called Td, the initiation transition temperature. Above Td, CT does not vary significantly with temperature and has a value of 1075 ± 25 Kg. At Td, this load decreases sharply to about 850 Kg and then goes through a minimum - 120A - Table 1 151 (5i Temp C3-1 Gcnt r C5 6:. --6y Kg Kg °C.', 95. e 1.-; e, N28 1.00 970 970 -100 0°40' 0.41-, 40' Y14 1.021 795 825 -86 2°18' 1.5 795 1° N31 1.09 850 930 -86 3°26' 2.7 N15 1.07 740 790 -80 2°50' 2,C 750 1030' N16 1.19 755 930 -73 7°10' 5.0 830 N36 1.20 725 875 -73 7026' 4.0 805 4°30' N23 1.46 755 1100 -73 19°42' 10.0 N37 1.24 715 875 -72.5 6°00' 4.0 845 N40 1.49 705 1050 -70 18°30' 8.0 850 6° N39 1.58 685 1080 -69 15°50' 8.5 840 6° N27 1,60 680 1090 -67.5 24°28' 12.0 N22 1.48 705 1040 -67 18036' 8.9 835 6°4' N18 1.59 660 1050 -60 21°12' 10.0 N19 2.4 710 1000 -55 15°20' 10.0 N17 1.74 625 1090 -47 34°50' 14.0 - 121 -- 1200—, I Td. 1100 x 1000 CI 900 800 x_Fracture Load. 700- a_ Ductile Initiation Load. o—ar Load. 600 10 c_) -qc ti 8 6 2 0 4 2 2 11. 0 -100 -90 -80 -70 -60 -50 -40 TEMPERATURE °C. Fig. 4.4. Deformation and fracture behaviour of Charpy siiecim(- ,rns in the .initiation transition region, - 122-- P9 Td. 1.8 1.7 1.6 1-5 1.4 1.3 1.2 1.1 x 1.0 25 0 20 0 0— 9r 0_9; 5 )r ,.0' ______-0- - 0 -100 -90 -80 -70 -60 -50 -40 TEMPERATURE °C. Fig. 4.5, Effect of temperature on parameters related to the load-deflection curve in the initiation transitio2) region. (see Fig. 4.4-. -123- - 73°C -86°C -80°C -67°C FIG.4.6. FRY'S ETCH PATTERNS.x7 - 124 - value, rising towards the point at which fracture occurs at the state of general yield, (- 100°C). The drop in fracture load is also accompanied by a sharp decrease' in the notch contraction from 9;'- to 47g, Cf see fig. 4. 4. The relative changes in and Gf, as a function of the temperature, are shown in fig. 4.5. The Fry's etch patterns of specimens broken above and below Td, (- 73°C), are presented in fig. 4.6. At this stage it is important to note that while there is a sudden discontinuity in the shape of load-deflection curves at Td, there is no equivalent discontinuity observed in the macroscopic distribution of plastic strain. A specimen was deformed through an angle of bend of 9° 30' at - 74°C and unloaded before instability had occurred. It was then cut along the longitudinal mid-section and examined metallographically. A photo-micrograph of this specimen is presented in fig. 4.7. A large number of cavities were observed at the notch root where the grains have been heavily strained and a few of the cavities have joined up to form a small tear about 80ikulong. Starting at 1 mm r 4 „Fr ihC ,7 .7 1 ..,. • (-4 '7? , --,, ..- - • • '-"%t- r ,..'--) '---r- $ 1.,- ... -;, • . ,r) .E- 4-A-7-1--t '4_4.)-• s. ,•i.b.• ,. '--*,c(- <":".14 ,..0..r -.—...*-.".i. ..,_*,c---",• ,-4' , ,.,"4.,c, .-)-::,c; ii ,.. tc_ 1 8.-i , : , - : Tr k .!_*i ,. • - • `• • •1 - ., .,••-,:- • , , ,. - ' 1471 ;CI: . .,. 1.'.„..„,f.,2• . , •... • . •,- •=y,,..,...,___ \,.? m__.'°,, _ . ,.., • _,, .,;""`--..:- . - •-• - - --,_)z• ,,-,ti(- - . ' x 55. Fig. L..7. The distribution of stable microcraaks in a Charpy specimen defoEmed to an angle of 9 30' at — 75 C. - 126 - PERCENT LONGITUDINAL STRAIN. 0 10 20 30 40 . m 0.5 m TCH. NO E 1.0 W TH LO E B CE TAN 1.5 DIS 2.0 Fig, 4.8. Distribution of plastic strain below the notch for the specimen deformed 9°30' at 7L (see Fig. 4.7.)• — 127 — below the notch root, a string of stable microcracks have formed, and have been severely blunted as a result of the plastic flow in the surrounding material. The distribution of tensile longitudinal strain was measured using the micro—hardness technique reported in Chapter 3, and is presented in fig. 4.8 using the same scale as the photomicrograph fig. 4.7 so that a.. direct comparison may be made. There is a steep strain gradient close to the notch where the strain decreases steeply from over 31W to about 7i within a 2 mm region. The strain around the stable ductile cleavage cracks is of the order of a few percent, while the strain in the root causing ductile tearing, is equivalent to that measured in a fractured tensile specimen at the same temperature. The macroscopic distribution of plastic strain revealed by Fry's reagent corresponded to an angle of bend of 5° when compared with the room—temperature patterns in fig. 3.3. The experimental relationship between the angle of bend and the root strain fig. 3,7 predicts a root strain of 30 for an angle of bend of 5°, which is in agreement with the observations made at the low temperature. - 128 - The plastic strain patterns of the broken test-pieces presented in fig. 4.6 were compared with the room temperature patterns in fig. 3.3. Because the relationship between the root strain, and the strain pattern, is not signifi6antly'altered2by: changea in the temperature, (see previous) then the distribution of plastic strain at the low temperatures will be equivalent to that at room temperature. However, it-is evident from a comparison of the strain patterns that they are significantly less developed in the broken test pieces than would be expected from the calculated angles of bend at instability. For example, the specimen broken above Td at - 67°C was deflected through an angle of 18° before instability occurred, but the strain pattern (see fig. 4.6) corresponds to an angle of bend Gi of 6°. When a small ductile tear starts at the surface of the notch root the geometry of the specimen is suddenly altered and the stress distribution will become localised around the tip of the ductile tear in a manner postulated by McClintock (1964). The overall macroscopic plastic strain pattern will be in effect -129- "frozen" shortly after the initiation of the tear. There is a very steep strain gradient below the notch, (see fig. 4.8) so that the material ahead of the tear will have a capacity for further straining before rupture. The material ahead of the propagating tear will strain harden, causing the applied load to increase until instability finally occurs. This final instability may be caused by the onset of brittle propagation, or by the decrease in cross-sectional area as a result of necking, in the more ductile specimens. The angle of bend at approximately the moment of ductile fracture initiation, gi, may therefore be obtained from a comparison of the plastic strain patterns (fig. 3.3 and fig. 4.6), and hence an approximate value of the load at which the tear starts CI, may be obtained from the load-deflection diagram. The values of i shown in fig. 4.4 and presented in Table 4.1 do not vary significantly in the immediate region around Td. The difference between Oaf and CI is caused by.,the stable propagation of the ductile tear. - 130 - Similar load-drops observed by Kochendorfer and Scholl (1957), Stone (1963) and Fearnehough and Hoy (1963), indicate that the magnitude of the load-drop is a function of both the specimen geometry and the material. Orowan (1955) considered the energy to propagate a fracture TITdA was supplied by a simultaneous release of - dE elastic stored energy of the specimen aT so that the critical length of the crack above which it can propagate spontaneously (i.e. instability) is determined by the condition dG dE = _ ... 4.1 dA dA If M(C) is the elastic compliance of a specimen containing a crack of length C, the elastic strain x will be given by x = P.M(C) 441111 4412 where P is the load on the specimen. - 131 - The elastic energy of a specimen containing a crack of a fixed length C will be 2 P dE = - . dM 4.3 2 or dE P2 = . 4.4 dA 2t )0 where t is the thickness of the specimen. Thus from 4.1 a crack will propagate simultaneous and instability will occur when P2 \ dE O M dG = .>, - -- ... 4.5 dA 2t oC dA The condition of instability will depend upon the ekorw-51-- square of the applied load, and the de-r-i-va.te- of the 3M compliance, AC, which is a function of C. The value of 'AC has been determined theoretically by Winne and 0 Mundt (1958) as a function of /B, the ratio of the crack length to the specimen depth. - 132- Using geometrically similar specimens7 Guiu (1962) determined the relationship between --/)C and 0/B. On this basis it is possible to offer an explanation to 'the results of Knott (1962), which did not show any change in fracture load at Td using specimens with C/B = 0.33 compared with C/B = 0.2 for a Charpy speciJ:nen. The value c,T7- V 1/6C will be greater for the deeper notched specimen, hence instability will occur almost as soon as the ductile crack has started. From eouation 4.5 it is possible to calculate the dE value of a, which is equivalent to the Perm in the Griffith eouation e,T1 -1 B2 . = 2.5 x 10-4 mm2 Kg (Guiu 1962) t = B = 10 mm. P = 1100 Kg at instability,from experiment. 6 2 dE = 1.2 x 10 ergs/cm dA -133— which is comparable with the value of the plastic work accompanying the growth of a brittle crack, 6 Xp = 2 x 10 ergs/cm2 determined by Orowan (1955) from X—ray back reflection measurements. 4.2.3. Metallographic Examinations Specimen N42 was unloaded before instability had occurred. (see fig. 4.7). Stable ductile cleavage cracks were initiated at about 1 mm below the notch root. Crussard et. al (1956) atte,thpted to locate the precise origin of the fracture in a broken Charpy specimen by following the direction of the river markings on the cleaw,ge facets. The attempt was not successful and he concluded that the origin was approximately 1 mm from the notch. The fracture profile of specimen N22 which was fractured at — 67°C, above Td, is shown in fig. 4.9. Pronounced cavitation has occurred in the notch root and a ductile tear about 0.3 mm is evident from the serrated nature of the fracture profile. At about 0.7 mm below the root the fracture profile is typical of that caused by large stable cleavage cracks which Fig. 4.9. Fracture profile of specimen N22 broken at - 67°C i.e. above Td. The root of the notch is at the top of the page and the specimen has been nickel plated. Etched in 2 Nital. x 60. -135— have been blunted by plastic deformation. It is probable that this region would represent a group of micro-cracks before instability occurred, similar to those shown in fig. 4.7. When instability and fast cleavage fracture occurred7 the fracture followed the line of the stable cracks; the plastic bridges between the cracks show flat cleavage cracks. Further away from the notch root the stable micro-cracks become smaller and more widely spaced and the main fracture is observed to have propagated in a manner which -ras independent of the pre-existing stable microcracks. Specimen N15 was fractured below Td at - 80°C, fig. 4.10. Only a small amount of plastic deformation has occurred in the notch root. From the shape of the fracture profile there is evidence that stable ductile cleavage occurred between 0.3 mm and 0.5 mm below the root. It is probable that the fracture originated here and then pro,?agated- both towards and away from the notch root in a brittle manner. Above Td, the onset of instatility is brought about by the propagation of a ductile tear which starts at the root of the notch. Below Td, the stable ductile - 136 - Etched in Nital. x 125. Fig. 4.10. Fracture profile of specimen N 15 broken at - 800C. i.e. below Td (notch root at the top). — 137 — cleavage cracks form an unstable configuration, and instability occurs before the strain in the root is sufficient to cause ductile tearing. Stable ductile cleavage cracks may initiate prior to instability at temperatures above Td, and hence tl.e initiation transition temperature is not simply a transition from ductile tearing to ductile cleavage fracture but rather a transition in the mode of fracture which causes the instability. The value of Td is so strongly dependent upon the specii,:en geometry, Stone (1963), that it cannot be used as a fundamental assessment of a material's susceTyLibility to brittle fracture. 4.3.1. Cementite Cracks Further careful microscopical examination of the arrested and broken specimens indicated that cracks occur in cementite plates, prior to the rupture of the ferrite grains, as observed by Allen, Rees and Hopkins (1953), Bruckner (1956) and McMahon (1964). -138- The nature of the subsequent growth of these cementite cracks depends largely upon the stress system , temperature and strain-rate. They may either grow into large cavities, which are directly responsible for ductile tearing, or propagate in a brittle manner across the ferrite grains. An estimate of the stress required to cause cementite cracking is made from tensile specimens. Cementite, Fe C occurs in this material mainly in 3 the massive grain boundary form, due to the slow rate of cooling from the austenite region. The crystallographic structure of cementite was determined by Lipson and Petch (1940) to be orthorhombic. According to Danko and Stout (1955) the interface between cementite and ferrite is coherent and'xecently Andrews (1963) has suggested possible crystallographic relationships between the two phases. Keh (1963) observed the defect structure of massive grain boundary cementite in a rimming steel, by transmission electron microscopy. In the annealed condition the cementite particles may be considered as single crystals, although 10-20 per cent contained — 139 — defect structures in the form of sub-grain boundaries, and straight lines interpreted as possible stacking faults in the (001) cementite planes. When the steel was given a 50 per cent reduction at room temperature, the density of defects in the cementite was not significantly higher than the annealed condition although there was a high density of dislocations in the ferrite matrix. However when the same material was deformed at 700°C the cementite deformed readily and dislocations were observed after only a 10 per cent reduction. These dislocations, which were not dissociated, nucleated at the ferrite-cementite interface and were confined to one major slip plane, which was established at the (001) plane. The original imperfections in the annealed cementite were thus concluded to be growth faults. In contrast, observations on the deformation of pearlite by Danko and Stout (1955), Pickering (1962), Kaldor (1962) and Wellinger and Pr8ger (1963) indicate that cementite has some ductility even at low temperatures. Pearlite may deform by a kinking process, similar to that observed by Orowan (19L1.2) in hexagonal metals, - 140 - involving a co-operative movement of cementite and ferrite. The role of the ferrite may be to promote a higher ductility in the cementite by supporting high hydrostatic pressures, Bridgeman (1952). From the large elastic strains measured in cementite by Wilson (1955) it seems unlikely that cementite can crack before plastic deformation has occurred in the ferrite matrix. The stress on the aggregate sufficient to fracture the cementite plates was measured from tensile specimens. Beevers (1964) made similar measurements on a material containing a brittle Phase in a ductile matrix using a tapered tensile specimen to produce an axial stress gradient. In the present work, Hounsfield No 13 tensile specimens of high nitrogen steel were deformed at a rate of 0.05 cm/min until slight necking had occurred. In this way an axial stress gradient was obtained;which was determined by measuring the cross-sectional areas at various positions on the tensile axis,and knowing the maximum load that had been applied to the specimen. -141- The deformed specimen was then sectioned longitudinally, and examined metallographically for the occurrence of cementite cracks. A specimen was given a 20 per cent extension at - 75°C. A few isolated examples of cracks in cerilentite plates oriented along tile tensile axis were observed where the stress on the section had been 2 50 Kg/mm , and occurred more frequently as the stress 2 increased to 55 Kg/mm . Cracked plates within pearlite colonies were not observed until much higher stresses of 65-70 Kg/mm2. Similar observations were made on specimens deformed at other temperatures. At - 25°C the cementite cracked under an aggregate stress of 45-50 Kg/mm2, and at - 125°C approximately 60 Kg/mm2, indicating that the cementite fracture stress has a slight temperature dependence of about 0.1-0.2 Kg/Mm2/°C. Webb and Forgeng (1958) extracted cementite plates, 1-2p thick and about 1 mm long, from mild steel and were able to bend them to strains between 2 and 5 per cent before fracture. This is also in agreelent with the elastic strains measured in — 142 — cementite whilst within the aggregate by Wilson (1955). According to Metals Handbook 514, Cleveland (1948), 12 2 the Young's modulus of cementite is 1.7 x 10 dyne.cm , hence the fracture stress of cementite is abOur8 500 Kg/mm2. This is an order of magnitude greater than the . agrogate stress necessary to rupture the cementite, indicating a stress concentration factor of about 10. Wilson and Konnan (1964) have shown that coarse dispersed cementite particles may act as strong barriers to slip and hence cause a stress-concentration at the interface. Fig. 4.11 shows an electron-micrograph of some cracked cementite plates taken from a 1 per cent Formvar replica. The maximum resolution of this technique is 0.04j'. according to Nutting and Cosslett (1950). The cementite plates stand out in relief when etched in 2 per cent nital and hence appear lighter than the ferrite matrix in fig. 4.11. The apparently larger plate on the right contains a number of very small cracks which have originated at the forrite-cementite interface, possibly as a result of slip band stress-concentration. The Plate on the x 30,000. Fig. 4.11, Electron-micrograph of fractured cementite plates. The wavy lines are due to the crinkling of the replica. -144- left has apparently cracked at a point where there is a sudden change in the plate size. There is a possibility that the crack and the others are a result of the growth process. However, such sharp discontinuities are not a common feature of the morphology of the pro-eutectoid cementite, Aarenson (1960). Consequently the discontinuities are probably cracks nucleated as a result of stress-concentrations associated with the irregularities in the ferrite-cementite boundaries. Fig. 4.12 shows a larger number of cracked cementite plates at a smaller magnification. Further biaxial straining of these cracks would result in the formation of cavities. In fig. 4.13 the broken plates have been pulled apart, and dislocations entering the cavities from slip bands in the ferrite matrix may help the growth. After about 30•-4.0 per cent strain at Td, a number of such cavities provide a path of weakness and join together by internal necking to form a small tear. At and above Td, it is this tear which eventually causes the instability. In the same temperature region the yield stress is raised by the - 1145 - Etched in Nital. x 1500. Fig. 4.12. Cracked cementite plates. Etched in e3 Nital. x 1500. Fig. 4.13. Ductile cavities at cementite cracks. - 146 - I • Fig. 4.14(a). Brittle ferrite micro-crack extending from a cementite crack. Fig, 4.14(b). Brittle crack running through a pearlite aggregate. -147— triaxial stress conditions 7hich exist below the notch root, and cause cementite cracks to propagate into the ferrite matrix to form a micro-crack, as in figs. 4.14(a) and 4.14(b). McMahon (1964) has considered the cementite crack as a Griffith crack and has calculatedlthe critical Griffith crack size to be about 3/i. If the stress at the tip of a cementite crack can be relieved by plastic deformation in the ferrite, the Griffith equation will be inapplicable and a micro-crack will not form, nor will one form at any subsequent stage in the deformation process at the same temperature. The capacity for a cementite crack to propagate will depend not only upon its size, but the stress system acting on it, and the crystallography of its surroundings. Of the many cementite cracks that McMahon (196)4) observed in broken tensile specimens, only a relatively small number had propagated. Hence, the formation of a micro-crack in the ferrite from a cementite crack is considered to be a statistical event. -148- 4.4.1. Brittle Fracture above General Yield As V-7e temperature is decreased from Td, to that at which fracture occurs at general yield, TGy, instability occurs following successively smaller amounts of plastic deformation, at approximately the same value of the fracture load, fig. 4.3. In this region, the general yield load increases with decreasing temperatures, intersecting the fracture load curve at TGY. At around Td, the ductile—cleavage stress, 0f' is attained by strain—hardening. As the temperature decreases, the yield stress is raised, so that the contribution of strain—hardening to at, becomes less. At temperatures well above Td, di, can never be attained below the notch root before ductile tearing occurs at the root, C in fig. 4.3), fracture instability At TGY' (— 75° occurs when the plastic "hinges" have just spread across the specimen (fig. 3.3). A slip line field analysis has been performed by Alexander and Komoly (1962) for this state of strain, and a value of the plastic stress concentration factorcKp was determined. -1149— A continuum mechanical theory of fracture assumes that the maximum stress is equal to the cleavage stress q (Chapter 1) and may be calculated from, 6f =rs(p"' Cr y ... 4.6 where ocp = 1.93 Alexander and Komoly (1962) or ',Xp = 2.5 Chapter 2. Fig. 2.12. The value of 6y at the appropriate strain-rate and temperature may be obtained using , the. tensile data presented in Chapter 6. Thus cry = 54 Kg/mm2 for = 4 x 100 sec-1 at T = 75°C. Substituting in equation 4.6 6= 105 or 135 Kg/mm2 = 62.5 or 82.5 tons/in2 depending upon the value of (Xp. Values of 6f calculated using the same method by Hendrickson et al (1963), Knott and Cottrell (1963) and Fearnehough and Hoy (1963) for different steels of similar grain size, vary between 60-80 tons/in2. - 150 - The physical significance and the practical implications of these values will be discussed in the final chapter. fracture instability occurs at the Below TG upper general yield load, point B on fig. 2.3. This represents the point of plastic instability caused by the onset of the plastic "hinges", The temperature dependence of the fracture load in this region is equivalent to that of the extrapolated general yield load. This type of behaviour has been reported by Fearnehough and Hoy .() 963); Who propobe that this.upper general yield load is due to the delay time for the spread of the plastic "hinges" across the ligament,: and will result in "superstressing" below the notch root. However, fractures at general yield, below the upper general yield, were observed. Therefore, if fracture instability is dependent upon a stress criterion, then the applied load gives no indication of the magnitude of the stress below the root. -151 — The temperature dependence of the fracture load in this region is greater than would be expected from a consideration of the temperature dependence of the fracture stress (see Chapter 5), so that a critical stress criterion is apparently inapplicable in this range, which is in contrast to the observations of Knott (1962). The results obtained in the small temperature conform to a critical displacement region below 91GY'- criterion, Which is possibly associated with the attainment of an unstable configuration of stable microcracks. Within this same temperature range there is sudden decrease in the fracture load which will be discussed in the next section. 4.5.1. The Bimodal Transition There is a temperature or small temperature range, at or in which fracture instability occurs at different values of 46/0'y which are outside the range of experimental scatter. For example, at the slow and intermediate rates of loading there is a temperature -152— at which fracture occurred at either the upper:general yield load or significantly below general yield • (i.e. 6/0'y 0.8) , figs. 4.3 and 5.4. At the impact rate of loading fracture occurred at either significantly above general yield or below itIfig. 5.2 and was manifested by a well defined bimodal distribution of the impact energies, fig. 5.3. Similar behaviour was not observed by Knott and Cottrell (1963) or Fearnehough and Hoy (1963) but will be shown in the next chapter to correspond to the bimodal behaviour reported by Crussard et al (1956) from impact energy measurements, and by Lean and Plateau (1959) from notched and plane tensile stress measurements. Wells (1964) has observed what is probably the corresponding behaviour in notched tension and bend specimens from measurements of the crack opening displacement, and suggests that this is due to a transition from plane stress to plane strain fracture. As there is no discontinuity in the growth of the plastic zone within the range /6Y = 0.75 and general yield, the maximum stress must be increasing -153- monotonically and hencel as both fracture modes may occur before actual general yield,it seems most unlikely that this behaviour can be explained from a simple consideration of the state of stress. Similar bimodal behaviour was observed by Lean and Plateau (1959) in notched and unnotched tensile specimens and hence it is considered the behaviour is due to a mechanical property of the material and is not simply due to a transition in the state of stress. In order to explain the experimental observations, this property will have to be a discontinuous function of the temperature. The onset of twinning would fulfil this criterion as it occurs at a unique value of GY = 6y(T). However, from metallographic examinations it was concluded that twinning was not responsible for the fracture instability within the bimodal region. -154- 4-5.2. The Probability of Micro-Crack Formation Hahn et al (1959) and McMahon (1964) have shown that there is a temperature within the region Td to Td - 20°C at which there is a maximum density of micro-cracks in fractured tensile specirms fig. 1.2. An explanation for this behaviour has been given by McMahon (1964). The number of cementite cracks which are potential ferrite micro-crack nucleii increase with increasing strain. The probability of these nucleii forming micro-cracks by propagating into a ferrite grain increases with the applied stress. As the temperature is decreased the strain to fracture decreases but the stress to fracture increases/ which gives at some temperature a maximum probability of micro-crack formation. This phenomenon may cause a discontinuity in the fracture strain-temperature curve for a tensile specimen. However the stress and strain distributions below a notch are such that it is improbable that this phenomenon is directly related to the bimodal transition. -155- 4.5.3. The Stability of Micro-Cracks When a micro-crack is nucleated in the ferrite e.g. by a cementite crack, its subsequent mode of growth will depend largely upon the stress acting on it and the crystallography of its surroundings. At relatively high temperatures, around Td, a micro-crack may be arrested at a grain boundary; partly as a result of the degree of misorientation across the boundary and partly because of the tendency for intergranular fracture. When the crack slows down or stops the tip of the crack may become blunted by plastic deformation and stress relaxation may occur, (Friedel (1959)) depending upon the toriperature. Additional straining at the same temperature will not cause repropagation of the crack, 1;icMahon (1964), and the crack is simply pulled apart to accommodate the strains in the surrounding material. Fig. 4.15 shows an example of a crack which propagated across three grains of similar orientation, arrested and propagated a small distance along the grain boundary. The apparent missi...ma.tch across the upper boundary of the lowest grain is an unusual feature. x 1500. Fig. 4.15. Stable micro-crack three grains long. -157— Cracks of this length are not common, but the fact that they are observed indicates thatinstability cannot arise from cracks of only a few grain diameters in this temperature range. As the temperature decreases, the probability of a micro-crack overcoming a greater degree of misorientation increases and hence there is a stronger tendency for a micro-crack of a few grain diameters causing a chain reaction, and instability. This may be achieved by actual propagation across the grain boundary or the crack may act as a notch and reinitiate in the grain or grains ahead of itself. In the case of a notched specimen fracture will occur in the plane of the notch. Cottrell (1963) has called this unstable mode of cleavage, cumulative fracture. In the temperature region between Td and TGY the instability is apparently caused as a result of stable micro-cracks forming an unstable configuration within the specimen. The material between two micro-cracks will act as a plastic bridge and will be a region of high strain concentration, failing ultimately by shear. The type of plastic zone existing between -158- two micro-cracks is shown in fig. 4.16 by kind permission of Professor Cohen. A schematic model of this non-cumulative fracture is shown in fig. 4.16(b). According to Cottrell (1963) this mode of fracture requires an increasing stress to continue its growth and is similar to the larger scale discontinuous crack growth postulated by Tipper (1957) for propagating cracks in mild steel plates. The theoretical strength of a series of such bridges has boon calculated by Irwin, Kies and Smith (1959) and is given by ... 4.1 whore G is the shear modulus, 20 the crack length, 2h the spacing between the crack centres and the surface energy. Thus as the temperature docrases, C increases because of the increased probability of crack propagation, and h decreases because of the increased probability of micro-crack nucleation. -159 - Fig. 4.16. Plastic deformation between stable microcracks. Reproduced from Trans 50 1958 6j4- by kind permission of Professor Morris Cohen. e • e / • e , ••• • • • `.›. V Fig. 4.16.(b) 7echanism of stable or non—cumulative crack growth. -160 - There is a possibility that these two properties may comhine to form a discontinuity in the function f = C"f(T) (where 16 is defined by equation 4.1) and hence cause bimodal behaviour. 7hen applying these ideas to the notched specimen the situation is complicated by the stress and strain gradients and by the degree of triaxiality. A simple explanation based upon the ideas of cumulative and non-cumulative modes of fracture is not consistent with the experimental observations. A cumulative fracture mode is expected to obey a critical stress criterion which would infer a gradual transition in behaviour) rather than a sudden change. The fundamental nature of the bimodal behaviour cannot be explained by a continuum mechanical approach and at the present the mechanisms require further investigation. -161- 4.5.4. Double Notched Charpy Tests In order to elucidate the nature of the bimodal transition experimentally, specimens containing two notches 5 mm apart, were fractured in the bimodal region to produce the two modes of fracture. The object of this type of test was to produce symmetrical loading conditions on each notch, eo that the material below the unfractured notch would be in a similar deformed condition as was that below the fractured notch just prior to instability. Hetallographic examination of the unfractured notches did not reveal any conclusive evidence. Fry's etch patterns revealed that the deformation zones from each notch had interacted. Hence, the conditions of stress around each notch were not considered representative of those around a single notch, and no conclusions were made from these tests. - 162 - 4.6.1. The Twinning Transition Below the bimodal region, there is a trend for the fracture loads to decrease with decrease in temperature, together with a significant decrease in the values of /uy. There is apparently more scatter in the results obtained at the intermediate rate of strain fig. 4.3 than for the impact tests fig. 5.2. This is probably because in the former tests the bimodal transition and the behaviour caused by twinning, are not resolved as in the impact tests, for which the temperature dependence of the yield stress is very small, Similar behaviour has been reported by Knott and Cottrell (1962) and Fearnehough and Hoy (1963) who refer to this region as the fracture "cliff" or the low stress fracture region. Knott (1962) observed twins at the notch root in this "cliff" region and proposed a deformation seq.uence; slip -÷twinning--*fracture, with varying amounts of slip prior to fracture responsible for the different fracture loads. In contrast / Fearnehough and Hoy (1963) did not observe twins at the notch root in -163- this region, but found concentrations of twins at various distances below the root, A statistical survey of the distribution of twins along the fractures of impacted Charpy specimens was made by Verbraak (1961). He counted the number of twins within 0.8 mm regions and found that as the temperature was decreased, the region of maximum twin density approached the notch root. This analysis was too coarse to resolve the distribution within the small important region close to the notch root, in which fracture is initiated. Hence a more detailed survey was performed (see fig. 4.17) on the impacted specimens whose fracture loads are presented in fig. 5.2. The numbers of twins were counted within regions of 0.1 mm to a depth of 1.0 mm below the root and are presented in the form of histograms in fig. 4.17. The positions of the elastic-plastic interface at the 7iloment of instability werb estimated by relating the :values of 0-1My at instability to the previously determined relationship between My and the plastic zone size, fig. 2.8, and are represented by dotted lines in fig. 4.17. -80 °C. -70°C. -60°C. -52°C. -40 °C. -30 °C. -25 °C. -18 °C. -10°C. 0 °C. 2°C. 10 °C. 22 °C. 30°C. V_J I VJ 1 T 0.1 02 03 mm. 04 OOT. R 0.5 W 04 BELO 0.7 TANCE 04 IS D 04 10 I 1 I Scale I—, -10 Twins F14.4.17 IMPACT. TWIN DENSITY DISTRIBUTION. ----Elastic-Plastic Interface at Instability. -165— Above - 10°C only a few isolated twins were observed within the estimated plastic zone prior to instability, and it is therefore reasonable to conclude that instability is brought about by a slip initiated mechanism above this temperature. At successively decreasing temperatures below -10°C, twins were observed closer to the notch root, but never at the notch root, as observed by Knott:(1962). The dashed fracture load curves in fig. 5.2 were drawn on the basis that different initiation mechanisms operating above and below - 10°C. The location of the twins is very similar to the observations made by Fearnehough and -boy (1963). Twins occur at about 0.8 mm below the root at the top of the "cliff" and gradually approach the root, apparently occurring at the elastic-plastic interface. It is possible that they are responsible for the initiation of fracture and cause the apparent decrease in fracture stress in this region. Mechanisms of fracture initiation involving twins have been discussed in Chapter 1 and will not be re-discussed. — 166 — On the basis of the previous observations it is reasonable to assume that fracture will occur when the maximum stress, (the plastic stress concentration factor times the yield stress) is equal to the twinning stress. From the intermediate strain—rate tests, fig. 4.3, the trend is for the fracture load to decrease from CY' about /6y f%0.75 to /6y . 0.25 between about — 100°C and — 196°C. According to fig. 2.11 this would result in a corresponding decrease in the plastic stress concentration factor from 2.2 to 1.2, approximately a factor of 2. This is compensated by an increase in the yield stress by the same factor, so that the value of the twinning stress (which is temperature independent) is attained. A similar agreement was made for the Charpy impact tests presented in fig. 5.2. Thus, the low stress fracture behaviour may be explained on the basis of a critical stress criterion. The variation of the fracture load will then depend upon the temperature dependence of the yield stress, and also the variation of the plastic stress concentration factor with the applied load (fig. 2.11). -167- At high strain-rates, the yield stress-temperature dependence is linear and consequently it is expected that the fracture load-temperature curve will reflect the form of fig. 2.11. The results in fig. 5.2 show a slight tendency towards this but more results at lower t&dperatures are required. Iowever, some of the results of Fearnehough and Hoy (1963) are of this predicted form. At lower strain-rates the yield stress-temperature dependence has a form which is approximately the inverse of fig. 2.11. The predicted form of the fracture load temperature dependence will ther'efore be approximately linear. There is too much scatter in the fracture loads presented in fig. L.3 to verify this but the results of Knott and Cottrell (1963) conform to this predicted behaviour. Specimens deformed at - 196°C at the intermediate strain-rate fractured at a load of 550 Kg and = 0.26, which is greater than the load predicted for the initiation of yielding calculated from the Neuber elastic stress concentration factor. When the broken specimens were examined metallographically, twins were observed within some grains adjacent to the — 168 — x 700. Fig. 4.18. Fracture at — 196°C9 striker. velocity 50 cm/min uIy = 0.26, showing twins at the surface of the notch root. -169— notch root, fig. 4.18. The deformation sequence is therefore considered to be slip—twinning—lbsfracture as determined by Griffiths (1964) in notched silicon—iron specimens at — 196°C. The nominal fracture stress at — 196°C for the Charpy specimens was 51,5 Kg/mm2 compared with a twinning stress of about 100 Kg/mm2 determined from the tensile tests reported in Chapter 6. This infers that a plastic stress concentration factor of 1.95 will be necessary to cause twinning, which is significantly greater than the value of 1.4 predicted from fig. 2.11. A metallographical examination of broken specimens ' containing twins failed to reveal any evidence which might suggest possible mechanisms of twin initiated fracture. Several examples of cracks apparently arrested by twins were observed and one example is presented in fig. 4.19. Also a few examples of crack propagation along the 4121 twin boundary, fig. 4.20, were obtained, indicating that this is a plane of easy propagation as reported by Berry (1959). - 171 - x 1500. Fig. 4.19. Micro-cracks arrested by twins x 1000. Fig. 4.20. Fracture along a t win boundary (loropa,r,ation from left to right) — 172 — CHAPTER 5 The Effect of Strain—Rate on the Fracture of Notched Bars 5.1.1. Summary- Charpy specimens are loaded to fracture in three point bending over a wide range of temperature with striker velocities of 0.05, 50 and 30,000 cm/min. It is found that the strain—rate dependence of the transition temperatures may be expressed by an Arrhenius equation. A comparison of the apparent activation energies with those for yielding is made. The combined effects of both temperature and strain—rate on the cleavage stress is discussed, together with its implication in predicting transition temperatures from tensile data. -173-- 5.1.2. Instrumented Charpy Impact Tests The conventional Charpy impact test has been instrumented by many workers, Tanaka and Umekawa (1958), Sakui, rakamura and Ohmori (1961), Cotterell (1962), Augland (1962), Stone (1963), Tardif and Ilarqads (1963) and Fearnehough (1q63), to obtain a. recording of the applied load as a function of time. If the velocity of the hammer is assumed to remain constant, a dynamic load-deflection curve can hence be obtained. Stone (1963) measured the change in hammer velocity with time and hence explained the discrepancy which he and other workers have found between the energy absorbed by the specimen as recorded by the machine, and that,obtained from an integration of the load-time curve. It is suspected that the stress-system becomes very complex upon impact, due to the generation of shock waves, and consequently the validity of such dynamic measurements is questionable. However, Fearnehough (1963) has obtained a good energy correlation with load-times of similar shape to the load-deflection curve in fig. 2.3 and therefore it was -1714- decided to use his instrumented Charpy machine for the high strain-rate tests. Experimental Fearnehough (1963) instrumented a 120 ft lb Avery impact machine which has a striker velocity on impact of 16.5 ft/sec (30,000 cm/min), to produce load-time curves. Two 100011. resistance gauges of gauge factor 2.16, were attached separately in.recesses machined into each side face of the striker (hammer4, They were then coated with Araldite cement to protect them from damage during the test. The striker was then loaded statically under simulated test loading conditions to calibrate the applied load against the strain in striker, measu.red by the gauges. These were connected in series to a Wheatstone bridge to cancel out any side effects which might be induced by assymetric loading. The out of balance voltage in the bridge circuit was amplified before being fed into a CR0 and deflected the fluorescent spot in proportion to the applied load. This spot was focused by a lens on to -175— film on the periphery of a rotating drum camera which had a linear speed of 1200 in/sec. A time marker signal from a one millesecond pulse was fed into the CR0 through another channel so that load/time traces could be obtained. A set of traces are shown in fig. 5.1 and represent the different degrees of brittleness experienced over a range of temp6rature. The v.lues of absorbed energy quoted were measured directly on the machine. There are two principal features on these traces which were not observed at the lower strain—rates (see fig. )4.2). On the rising part of the trace there is a "kink" representing a load discontinuity. A characteristic of this "kink" is that its magnitude remains unaffected by temperature and was therefore considered to be due to the mechanics of impact, e.g. reflected stress waves in the striker, rather than a feature of the deformation process (Fearnehough (1963)). The fracture at — 52°C (fig. 5.1) occurred at a lower load than the "kink", hence it would seem improbable that the load at the maximum of the "kink" could have been acting on the specimen. -176- FIG.5.1. LOAD/ TIME RECORDINGS OF IMPACT CHARPY TESTS. 01 millesecs i +59°C. 96 ft.lbs. ...."-'- i. 4 ... *45°C. 47 ft. lbs. +22°C. 21 ft. lbs. 1,- • 26°C. 9ft. lbs. -52°C. -177- Secondly, some high frequency oscillations were present, and a mean line was drawn through them to determine the general yield load, by a method adopted by Erafft, Sullivan and Tipper (1954), who determined dynamic yield stresses in compression. The values of the fracture loads and general yield loads are presented in fig.-.522anddth.e.,energy -valUes measared on the machine are shown in fig. 5.3. 5.1.3. Intermediate and Slow-Bend Tests The intermediate tests at a striker velocity of 50 cm/min were described in the previous chapter and the fracture loads presented in fig. 4.3. The slow-bend tests at a striker velocity of 0.05 cm/min were performed on an Instron and the load-deflection curves recorded mechanically. The results of these tests are presented graphically in fig. 5.4. Fig. 4,3 is also included to facilitate comioarisons of the load-temperature diagrams at the three different rates of straining. 2000 — Striker Velocity = 30,000 cm/min. 2.5 x 10 3 sec-1. e_Fracture Instability Load. 1500 — o_Generat Yield Load. t • • • C moo — ...cz ... .11-- -..• • .:1 - i—B, v., 00 / $ **. 5/ • 'It 500 — Load for First Slip(Neaber1 0 I I I I I I I I -200 -150 -100 -50 0 50 100 TEMPERATURE °C. . Fig. 5.2. General load and fracture load vs temperature for high-nitrogen steel Charpy specimens deformed at a strier velocity of 30,000 cm/min. IMPACT ENERGY F t. lbs. Fig. 5,3. -10 I Charp3' specimens. of thetemperature, for high nitrogensteel Energy absorbed duringimpact, asafunction '0 1 i -17- 10 I TEMPERATURE °C. i 20 30 40 50 60 2000 Cross-Head Speed - 50cm/min. - 3.8 x 10° sect •_ Fracture Instability Load. o__ General Yield Load. 1500 • 'cc3 1000 • • • • • • • • • • • e* Twins at Notch Roof. 500 ------ ------Load for First SHp(Neuber). ------g 0-18. CrY 0 -200 -150 -100 -50 0 50 100 TEMPERATURE °C. F 4.3. General yield load and fracture load vs temperature for high-nitrogen steel °harpy specimens deformed at a cross-head speed of 50 cm/min. 2000 Cross-Head Speed . 0.05cm I min. I - 3.8 x 10-3 secI. 1500 Fracture instability Load. o_Getieral Yield Load. 45, 1000 0 500 -- Load for First Slip (Neuber). ------ 0 I I 1 I I I I 1 -200 -150 -100 -50 0 50 TEMPERATURE °C. Fig. 5.4. General yield load and fracture load vs temperature for high nitrogen steel Charpy specimens deformed at a cross-head speed of 0.05 cm per min. - 182 — Discussion 5.2.1. The Effect of Strain-Rate on the Load-Deflection Curve A comparison of the load-time traces obtained for striker velocities of 50 cm/min and impact in figs. 4.2 and 5.1 respectively, reveals the appearance of high frequency load oscillations at the impact strain-rate. The oscillation on the steep initial part of trace which has been previously referred to, may be due to the imperfect contact between the specimen and the anvils which would result in tensile shock wave being transmitted into the striker. Tardif and Marquis (1963) claim to have eliminated this source of vibration by placing a film of grease on the anvils. They identified the other oscillations which occur after general yield with the frequency of oscillation of the specimen itself and are hence an inherent characteristic of the test. The presence of these vibrations infers that the specimen is continually "bouncing" off the striker which has been observed by Robertson (1961). The amplitude of these vibrations decreases with time, possibly because they become damped by the increasing volume of plastically deformed material. -183- In order to convert the load-time trace into a load-deflection curve it is necessary to know how the velocity of the pendulum varies as a function of time. Stone (1963) and Tardif and Marquis (1963) have shown that the striker velocity decreases suddenly upon the initial impact and then continues to decrease in an almost linear fashion. From an energetic consideration the overall decrease in striker velocity is only about 15;;:l. A comparison of the static and dynamic load-deflection curves was made by relating the increase in the applied load over general yield k/Cr/ / uy)\ to the angle of bend above general yield Op, fig. 5.5. In this diagram no correction has been made for the changes in striker velocity but even so the difference in the slopes is significant. This is apparently due to the low work hardening capacity of mild steel when deformed at high rates of strain, Tardif and Chollet (1959). 5 10 15 20 ANGLE OF BEND ABOVE G.Y. 9°p. Fig. 5.5. The effect of loading conditions on the shape of the load—deflection curve. -185— The rate of increase in applied load with angle of bend is thus much smaller at the high rates of strain. The load—deflection curve is "flattened" out and the resultant effect on the fracture load—temperature diagram will be discussed later. 5.2.2. Instrumented Charily Tests The fracture loads and general yield loads are presented graphically in fig. 5.2 and the impact energies, measured on the testing machine, are related to the testing temperature in fig. 5.3. There are additional results on this latter diagram from specimens for Which no load/time traces were obtained. Because of the apparent amount of scatter in the fracture loads, which seems inevitably associated with this type of measurement, it is not justifiable to represent the experimental results,by,cotinuous curves. However, from a consideration of the energy—diagram, twin observations and low strain—rate observations, idealised curves were drawn to represent the fracture behaviour, and are in the form of dashed lines, in fig. 5.2. -186 - The sudden decrease in fracture load at + 40°C is associated with the initiation transition which is manifested by a discontinuity in the energy diagram, fig. 5.3 and was predicted from a detailed study of this transition in the previous chapter. This discontinuity occurs in the energy range L5 to 35 ft lbs. Below Td, in the range + 40°C to + 20°C the energy absorbed to fracture may be represented by a well defined bimodal distribution, fig. 5.3. On the upper "arm" of this bimodal energy distribution, fracture occurred above general yield, and on the lower "arm" fracture occurred below general yield. The slopes of the arms are thought to be due to the varying amounts of energy absorbed in propagating the crackfollo.wing instability. This may be seen in fig. 5.1 on the load-time trace for the specimen deformed at + 26°C and has been called "post brittle" energy by Fearnehough (1963). The existence of a bimodal energy transition region was first observed by Crussard et al (1956) in an energy relage corresponding to that in the -187— present work. They attributed this behaviour to the mechanisms which are associated with the initiation transition. This transition must occur at higher energies because of the amount of strain required in the root for ductile tearing. The bimodal transition occurs in the completely brittle region and is thought to be due to a transition in the mode of cleavage. Possible mechanisms were discussed in the previous chapter. More recently, the discontinuous nature of the energy-temperature diagram has been shown by Wellinger and Wittwer (1960) but no fundamental explanations of this behaviour were offered. Below the bimodal transition temperature Tb, the fracture loads decrease with decrease in temperature with an apparent large degree of experimental scatter. The dashed form of the curve was drawn from a knowledge of the twin distribution, section 4.6.1. Above - 10°C it was concluded that fractrere is slip initiated and below - 10°C there is a possibility that fracture is initiated by the stress concentrations developed by twinning. -188- 5.2.3. Slow-Bend Tests The fracture load-temperature diagram obtained using a striker velocity of 0.05 cm/min is presented in fig. 5.4. Only a small degree of experimental scatter is evident and the transitions are well defined. The transition temperatures and the details of the diagram will be discussed in relation to figs. 5.2 and 4.3 in the next section. 5.2.4. The Effect of Strain-Rate on the Fracture Load-Temperature Diagram The overall effect of increasing the strain-rate is to cause the fracture load-temperature diagram to shift to higher temperatures (see figs. 5.2, 5.4 and 4.2). However,on closer inspection the actual form of the diagram is changed also. As the strain-rate increases the temperature dependence of the general yield load decreases and the drop in load associated with the initiation transition approaches the bimodal region, so that under impact straining fracture does not occur at general yield. -189— The Initiation Transition The effect of strain-rate on various parameters at Td are presented in table 5.1. The general yield loads at Td increase with If the internal ductile cleavage at Td is a stress dependent mechanism, then the contribution to this stress by strain hardening will decrease as the strain-rate is increased, and hence the contribution from the yield stress must be greater. From the values of OrLys in table 5.1 it is evident that the values of maximum stress at Td which are calculated from Tm ax LYS x the plastic stress concentration factor, *p = 2.5 Knott (1962)), are not constant. If it is assumed that the maximum stress is the cleavage stress, so that cax = 6f = 2.5 TLys then an 6 -1 increase in strain-rate of 10 sec has increased Td 2 by 116°C and of by 50 Kg/mm . Effectively this means a rate of increase in cleavage stress with temperature, dOrf dal = + 0.43 Kg/mm2/°C. (The positive sign indicates increase with temperature). However it is well established that increasing the temperature at constant strain-rate results in a decrease in the cleavage stress. - 190- Table 5.1 The effect of strain-rate on the initiation transition temperature Td end the bimodal transition temperature Tb Strier velocity 1 0.05 50 30;000 cli/min. Strain-rate in root sec-1 3 x 10 predicted from Chapter 3. -3 3 x 10° 2 x 103 The initia- ion transition temp. Td. C. - 76 - 35 4- 40 1000 o(-1 Td 1' 5.07 4.20 3.18 Fracture loads at Td 1070 1200 1300 Pf Kg. 900 1060 1140 Pf /.0 at Td 1.410 1.43 1.37 'GY 1.20 1.26 1.20 qeneral yield load at Td 750 840 950 PGY" K.7s Gi,vs at Td from tensile 2 60+ data at predicted LKg/mm - 3 Bimodal transition - 135 - 86 temp.' Lb. C. 30 1000 o7-1 Pb l' 7.55 5.35 3.27 Decrease in C-,/c:5:1,- 1.0 1.0 .--,0 1.13 at Tb 0.66 ,---, 0.7 p.,, 0. r'0 51- f', Tb YS 53 f'?('-' 60 M/mm - .- 1 - 1 - 3 - 191- def Therefore the measured value of ---dT represents the combined effects of the temperature and the strain-rate. As Cr is proportional to the temperature then from table 5.1, it is proportional to lnt so that Cif (T, In E ) .. 5.1 = f (lief It will be shown later that the value of dT obtained from yield stress measurements at Td is not representative. This is because of the complicated effect of strain-rate and temperature on the strain-hardening behaviour, associated with this transition. - 192 - il.LElrent Activation Energy Wellinger and Wittwer (1963) found the relationship between the deformation rate and the transition temperature for impacted tensile specimens, was of the form of an Arrhenius equation, t..= A exp (- H/kTt), where F is the activation energy and k is Boltzmann's constant. The results from table 5.1 were plotted in the form lnt s 1000 °K in fig. 5.6 where T = Td or Tb. Both transitions were found to obey an Arrhenius equation and the apparent activation energy for the initiation transition was calculated. HTd d(1118 ) 5 x 2.303 „,, k = d( /Td) 1.66 10-3 " HTd = 13,300 ± 300 cal/mole = 0.58 ± 0.0.2 FT. 10 4 1 1 1 103 10 2 i H60 0 .16 at 10 •Ier. ••• 10° 'NX to4 itsolt 0.32e.1%, 10 2 10 3 I I I I 1 3 4 5 6 7 1000/ T °K.-1 Fig. 5.6. Comparison of the apparent activation energies for the ductility transition Td, the bimodal transition Tb with the activation energies for yielding at a constant stress. -194- "lean and Plateau (1959) measured HTd for tensile specimens and correlated the value with those obtained by other workers to show that ITTd is temperature dependent, obeying an eollation,H Td B T cals per mole, where B = 40 or 50 and T is the absolute temperature. Thus for T = 313°K,HTd 12,500 to 15,500 cals per mole which is in agreement with the measured value for the Charpy specimens. However HTd was temperature independent in the present work. The nature of this transition may be better understood by considering the cleavage stress to be attained by contributions from the yield stress ly and the work hardening ,60- so that 6foCo'y 4-1N01 As the strain rate increases Cr increases and po decreases, so that the contribution of 6- must be greater. Hence the value of HTd is significantly higher than that for 7ielding. Because HTd is a function of so many variables there is no theoretidal: reason why Td should be temperature independent and it may be coincidental that it is in the present work. Nevertheless the value of HTd is a good empirical measure of all the variables considered, but the possibility of it being both size and temperature dependent should be taken into account. -195- The Bimodal Transition The bimodal transition temperature Tb is the highest temperature at Which fracture will occur on the lower "arm" of the energy bimodal distribution, Or the lover load on the fracture load-temperature diagram. The measurements relevent to this transition are presented in table 5.1,and lni vs 1000 plotted in fi. 5.6. This transition may also be expressed by an krrhenius equation, the apparent energy . F - Tb = 5,100 ± 200 cals per mole or 0.26 ± 0.01 ee11. The effect of strain-rate on Tb was compared with that on the yield stress,. and is represented in fig. 5.6, for three yield stresses, 40, 50 and 60 Kg/mm2 from the tensile data presented in Chapter 6. The activation energies were calculated from (l = - k ) after Conrad (1961), end are FYSTiT pdn/ r- -LYS presented in fig. 5.6. Because there is no agreement and then the bimodal behaviour is not between HTb 11LYS- simply related to the lower yield stress. -196— As there is only a small degree of plastic strain associated with this transition it is assumed that lid = 0 in the ecuation 6f OC6y Aec so that the effect of temperature and strain-rate on the yield-stress at Tb is directly related to fri, by the plastic stress concentration factor(Xp. (Obtained from fig. 2.11). 7ence 6.f = max =:Xp.5y ac dffy then -0(p = + 0.17 Kg/mm2/°C dT dTb It has already been shown that d6faT is the integral effect of both temperature and strain. According to equation 5.1 ... 5.1 -197- differentiating with respect to T /'\\ d lni ... 5.2 dTu T In dT Eldin. and Collins (1951) and Lean and Plateau (1959) determined the rate of decrease in the fracture stress with temperature at constant strain-rate as if - 0.17 Kg/mm2/°C in E - 0.1 Kg/mm2/oC respectively. Assuming that the temperature dependence of the cementite fracture stress (Chapter 4) controls that of the aggregate, then for this material = - 0,15 ± 0.05 Kg/mm2/°C — 198 — Substituting this value into eruation 5.2, d in E. 0.17 = — 0.15 ± 0.05 dT d lra, 2.303 x 6 , dT 105 so that = 2.4 ± 0.4 Kg/mm 2 measured within the range 3 x 10-3 < E < 2 x 103 sec-1. - (5‘1- The importance of considering /60 f blnL 71' lnt and when predicting notch impact data from tensile data will be discussed in the last section of this chapter. -199- 5.2.5. The Feasurement of Dynamic Yield Stresses Fearnehough (1963) has suggested that the values of the general yield loads obtained from instrumented Charily tests give an indirect way of measuring Olys -1 at high strain-rates of the order 103 sec . This may be done by either applying the formula derived by Green and Hundy (1956) -.Presented in Chapter 2, or alternatively by multiplying the static value of ar_LYS by the ratio of the dynamic to static general yield loads. Both methods assume that / condition of general yield is unaffected by the strain-rate. At + 25°C, PGy (impact) = 1000 Kg, Poy, (static) = 500 Kg and Icys, (static) = 29 Kg/mm2 1000 2 and C3-LYS (dynamic) would be given by 56 x 29 = 58 Kg/mm from the Green and. Fundy formula 51ys = 52 Kg/mm2 The vilue obtained by the ratio method is comparable with the value 60 -± 3 Kg/mm2 obtained by impact tensile tests. This agreement is evidence to support the validity of the instrumented Charpy results. There was a surpi-isingly small amount of scatter in the measurement of the general yield loads and consequently - 200 - this technique seems as good as the impact tensile - technique for measuring 6LYS' and from an experimental point of view it is easier. 5.2.6. Prediction of Notch Impact Transitions from Tensile Data Hendrickson, Wood and Clark (1958) using notch tensile specimens showed t-hat the initiation of fracture in mild steel was governed by a critical tensile stress, or fracture stress 5f, independent of both temne7.ature and strain-rate. Thus, the influence of the latter variables on brittle fracture arises However, from entirely from their influences on 6LYS' a comparison of the activation energies in the present work this is not the case, and 61-• is in fact both temperature and strain-rate del)endent. In a second paper, Hendrickson, Wood and Clark (1959) attempted to predict in an Izod impact test the temperature at which brittle fracture occurreC, "before the limited region of plastic deformation near the root of the notch becomes unstable and rapidly expands". In the light of the present work this means -201 - fracture before general yield i.e. the bimodal transition, and would correspond to the 15 ft lbs energy transition for a mild steel. (see Fearnehough (1963)). They based their prediction on the hypothesis that brittle fracture is initiated in the vicinity of the notch whenever the true tensile stress in the material max .--, (5'f' An elastic plastic analysis for the Izod notch was performed for the condition /uy = 0.8. From which 0-max = 2.14 6y, and the bimodal -ill occur * when 6m ax = 2.41 uy . ():y• was called the critical value of the upper yield stress). The value of was determined experimentally from notched tensile tests and hence OY was calculated. The transition temperature was then estimated from tensile data for the condition, 6Y = Oy f at the appropriate strain-rate. (in their case, stress-rate). The elastic stress-rate was determined theoretically from the rate of elastic deflection assuming an elastic stress concentration factor c4= 3.71, and was found to be 9 x 109 p,s.i. per second. For Young's modulus 6 E = 30 x 10 p.s.i. this gives a theoretical straining - 202 - -1 rate of 3 x 103 sec which is in agreement with the experimental value obtained in Chapter 3, 3 -1 - * of 2.6 x 10 sec . The value of Oy for t= 3 x 103 sec-1 was determined experimentally by extrapolating the values of Ofy measured at < 3 x 10_1 sec-1. The two stage strain-rate dependence of the yield stress for mild steel (see Chapter 6) could be a large source of error, especially in the temperature range under consideration. For the high nitrogen steel at + 25°C the error would be 2570 and from the results of h. HalNoine (1944) this source of error in Dry might be as high as 100,. The scatter arising from high strain-rate measurements is about 10%, which would double the degree of uncertainty in their prediction. .A similar alDproach to the one used by T-Tendrickson, Wood and Clark (1959) will now be used to predict 1,11t1 from the data in this work. Instead of measuring Cri, and calculating 6y from the elastic-plastic analysis, was measured at Tb and obtrlined directly. - 203 - -3 For a t= 3 x 10 sec, Tb = - 135°C and 61YS = 53 ± 1 Kg/mm2 (table 5.1). If the transition occurs when GLyS equals this critical value, then using the basic method of Hendrickson, Wood and Clark (1959) and. the impact tensile data presented in Chapter 6, Tb (impact) would be + 120°C ± 20°C compared with the experimental value of + A repetition of this approach for t= 3 x 100 sec-1 predicts Tb (impact) to be 90°C ± 20°C. Therefore, by neglecting the strain rate and temperature dependence of the fracture stress the method of T7Tendrickson, Wood and Clark (1959) cannot be generally applied successfully. Their prediction was as they report, "surprisingly close" and there is the possibility that the values of rS) and ( 1a/C5-f ) bT 1nc ?) were eoual and opposite in their steel, giving an apparent effect that brittle fracture was controlled by the value of the yield stress. d6f It is considered that provided the value of -TT is measured and taken into account, a reliable value of the transition temperature can be predicted from tensile data, the accuracy of which is largely - 20L1. controlled by the degree of scatter in the high strain rate yield stress measurements, and will be of the order of -+ 20 oC. - 205 - CHAPTER 6 Tensile Tests Summary Tensile tests were carried out at temperatures in the range 1000C to 1960C and with strain-rates of 3 -1 between 10-4 and 10 sec , to determine the effect Of these variables on the tensile lower yield stress. As the strain-rate increases both the temperature dependence of the yield-stress and the work hardening rate decrease. There is no simple relationship between the yield stress and the strain-rate, and at high temperatures a well defined two stage dependence was observed. - 206- 6.1. Experimental Three types of tensile specimens were used in these experiments. (1) For all tests at - 196°C the specimens were Hounsfield No. 11 having a gauge length 0.447 ins 1 and a cross-sectioned area /80 sq. ins. (2) For tests performed on the N.P.L. Impact Tensile machine special specimens designed by Harding (1964) which were about one inch long and had a diameter of 1.5 mm. (3) The remaining tests were performed on standard Hounsfield No. 13 specimens which have a gauge length of 0.632 inches and a cross-sectional 1 area /40 sq. ins. The low strain-rate tests were performed on an Instron testing machine using a conventional low temperature jig. For tests using cross-head speeds of 0.05 and . 0.50 cm per min the applied load and the cross-head movement i7Tere mechanically recorded. For the higher cross-head speeds of 5.0 and 50 cm per min, load time curves were obtained using a C.R.O. as described in Chapter 4. -207- A typical load-time trace is shown in fig. 6.1 which was re-plotted as a stress-strain curve, and from this the value of the lower yield stress was obtained. The..values of Cr.LYS are presented 0.rworlidally in fig. _6.3 as a function of the temperature; , and ,as a fun6tion of the strain=rate. in fig. .6.4. 6.2. Impact tensile tests A technique for measuring yield stresses at very high rates of strain (17.: 103 sec-1) has been developed by Harding (1964) at the National Physical Laboratory. A tensile stress-wave is generated magnetically in a system within which reflected stress waves are avoided. The duration of the stress pulse is about 50 micro-secs. The strain-rate was observed to change from 500 to 1200 sec-1 during the test and a 3 -1 mean value of 10 sec was thus taken. A load-time trace is shown in the lower part of fig. 6.2. The time interval between each dot is 1 micro-second and the horizontal lines are load calibrated lines. The profile of the stress-pulse is represented by the -207A- Air - ams. Fig.6.1. Load/Time trace of tensile test at - 125°C = 5 x10-2 sec') Fig. 6.2. Load/Time traces for impact tensile test at -78°C (E'-103 sec'). The upper trace represents the stress pulse in the bar. The lower trace represents the load on the specimen. L OWERYIE LDSTRE SS OKg /m m? 100 25 50 75 0 -200 Fig. 6.3. I I with temperature atdifferent strain—rates. Variation oftheloweryield stress If ••• *is -100 ••• ••• .4•• 44. TEMPERATURE °C. 1 I I 0 V 0 x -208- I I 5 x107 5x10- 5 x 5 x Strain Rate.sec. 0 107 10'! lo7 III!! 1 2 3 4 1 ~ , 100 -209- 80 - .25°C. 30 - .100 °C. • 20 - 10 164 10-3 10-2 160 10° 101 102 103 104 103 106 I see Fig. 6.14. Effect of strain—rate on the lower yield stress at different temperatures. - 210 - upper curve. Since there is no well defined Lildei;s plateau at tese high strain-rates . the degree, of uncertainty in the measurement of OFLys is greater than for the low strain-rates. Three tests were performed at room temperature, and two at - 7800 and the average value of 0LY5 calculated. 6.3. Discussion The tensile stress-strain curve for mild-steel is characterised by an abrupt drop in stress at the yield-point. The upper yield stress, although apparently well defined, is not a reliable measurement of the elastic strength because the initiation of yield is very sensitive to test conditions, and is therefore difficult to reproduce. Alternatively the stress necessary to drive an initiat-ed band of yielded material through a.specimen, the lower yield stress 461_,YS' is measured. At slow strain rates this is a very reproducible parameter. However at high strain-rates the yield stress is not generally constant and may be subject to misinterpretation. - 211 - The overall strain measured in the Ididers region is comprised of two components, (Krafft 1962). One due to the actual spread of the Lfiders front i.e. the amount of yielded material; and the other due to the attainment of an eauilibrium strain behind the front. When the alders front propagates slowly there is ample time for the eouilibrium or "static" strain to be reached close behind the fronts and there will be an abrupt strain transition. In contrast, at lalgher rates of strain the Lfiders front moves too fast for. the static strain to follow it and the strain will decrease gradually toward the yield front. This has been measured by Hart (1955), Butler (1962) and Krafft (1962). As the Ifiders band lengthens/ an increasing portion of the cross-head movement will be diverted to accommodate "behind the front" flow. Hence the LfideOfront velocity will decrease and lower the value of the lower yield stress even though the cross-head speed remains constant. The number of Lfiders fronts is also a variable in the tensile test. According to Krafft (1962) the components of the Lfiders strain are sensitive to strain rate in different ways and hence the lower yield — 212 — stress provides an irresolvable mixture of both different effects. Consequently the high strain rate results presented in fig. 6.3 and 6.4 are presented without a complete knowledge of thir fundamental physical significance. The temperature dependence of the yield stress decreases as both the temperature and the strain—rate increase, (fig. 6.3). The small value of LYS/dT is in accordance with the observations of Fischhof (1963). The variation of the gys with strain—rate at different temperatures is shown in fig. 6.4 in which all extrapolated values are represented by dashed lines. At temperatures above — 75°C a two stage strain—rate dependence becomes increasingly evident. The transition LYS/d(:n) occurs at about between the values of (dO- T t= 10-1 sec-1 as reported by both Morrison (1934) and Manjoine (1944). Similar behaviour was observed by Fischhof (1963) but the transition occurred at a lower below strain—rate. Above — 75°C, extrapolated values of dfLYS • indicate a decrease in (d5LYS/d2AE.)T above about -1 -1 L= 10 sec . The overall effect is an apparent convergence of the lines at about E.= 10 /.'Ic` At this - 213 - strain-rate 6LYS would be independent of the temperature. In contrast, Fischhof (1963) observed a dra:iatic increase in (dC1- LYS/cif/0i.) -1 T at about 102 sec . This type of behaviour would be predicted from the observations of Johnson and Gilman (1959) on lithium fluoride who found that even at several orders of magnitude below the limiting dislocation velocity, the stress dependence of the dislocation velocity began to show a marked increase. Theoretically,the value of C3-LYS would approach infinity at very high strain rates. According to Weertman (1963) the velocity- of a dislocation has an upper limit which is the velocity of sound in the material at which it will have infinite energy. For steel this would correspond to a 8 -1 strain-rate of 10 sec . — 214 — 6.4. Strain-hardening An estimation of the strain-hardening characteristics of this steel was made by measuring the amount of stress required above 06:Lys to strain a specimen by 'This parameter A6(5) was measured from the stress strain curves and related to the strain-rate in fig. 6.5. The specimen deformed at -1 -1 - 125°C at 5 x 10 sec began 'necking" in the beginning of the 'Alders plateau, hence A would be negative. The value of ,66 (5) is a measure of two effects; a) the length of the Lilders plateau, which is pro-;Dortional to Lys' and b) the rate of increate in stress beyond the Lilders strain. The effect of increasing the strain-rate is to decrease the amount of strain-hardening in accordance with the observations of Manjoine (1944). At 100°C the value of 86 (5) is very large due to the occurrence of strain-ageing during plastic deformation. This was manifested by discontinuous flow producing a serrated stress-strain curve which smoothed out as the strain-rate increased. The amount of strain-hardening due to strain-ageing was so large that - 215- 15 5 0 5x104 5 x10-3 5x10-2 5x10-1 E. sec-1 Fig. 6.5. Effect of temperature and strain—rate on the apparent strain—hardening characteristics, - 216 the stress after 5% strain was equivalent to that in a specimen deformed at - 75°C. The raising of the stress by strain ageing will produce a form of high temperature brittleness called blue-brittleness, or the Portevin-Le Chatelier phenomenon,. and is caused by-the diffusion of interstitial atoms. 6.5. Fracture at- 196°C Of all the specimens broken at - 196°C, only one specimen exhibited a yield drop prior to fracture. The remaining specimens fractured before any plastic deformation was evident from the stress strain curve. However a few specimens were mounted so that the broken halves were matched. They were polished down to the mid-longitudinal section and Fry's etched. A typical specimen is shown in fig. 6.6 showing two symmetrical plastic zones adacent to the fracture, each about 2 mm deep. Metailographical examination revealed th presence of a large number of twins evenly distributed throughout the plastic regions. The size of the plastic zone was surprisingly large and it is concluded that the yield point instability and fracture instability were coincident. - 217 - x 8. Pig. E.E. 2rittle fracture in a tensile specimen deformed at - 1960C ( 5 x 10-2 sec-1). Etched in Fry's reagent to reveal the extent of the plastic deformation around the crack. - 218 — Also because twinning is the predominant mode of plastic deformation at this temperature, the fracture stress will be approximately equal to the twinning stress i.e. 95 Kg/mm2. This value is independent of the strain-rate at this temperature in accordance with measurements on the twinning stress by Fischhof (1963). — 219 — CF ATTER 7 Discussion of Conclusions This chapter is a resume of the conclusions to the discussions of the previous chapters and an attempt to apply them to the problem of brittle fracture. Suggestions for future work are made wherever possible. 7.1. The Stress and Strain Distribution at a Notch Plastic deformation is initiated at the notch under biaxial plane strain. conditions. The yield stress under biaxial stressing is higher than that in uniaxial tension, so that the stress at the centre of a Charpy specimen must be significantly greater than that on the surface. Plastic deformation did not occur on the surface until a load of about twice that required to initiate yielding had been applied. :Fence, in this type of specimen it is not possible to determine the state of stress within its body simply from surface observations and measurements. — 220 — The difference may not be as great for notched tensile specimens and it would be interesting to extend the present 7ork to this type of specimen. The wedge shaped plastic zone which occurs under plane strain conditions,.ay effectively deepen and sharpen a blunt notch and conversely, relax the stresses at a sharp notch. The importance of this effect has hot been fully realised, and only Cottrell (1964) in his analysis of the results obtained by Allen (1961), has adopted a fundamental approach to this problem. One of the possible souroes of inconsistencies arising from the attempt to explain the fracture behaviour below general yield by a continuum mechanical approach, is the theoretical elastic—plastic stress distribution. Although it is encouraging to find that the analyses of Hill (1950) and Randall and Allen (1964) are consistent 77ith one another, it would be valuable to perform a detailed theoretical analysis on this problem; possibly using Fry's etch patterns to detine the elastic—plastic boundary, so that the analysis will be based on a realistic model. — 221 — Recent experimental observations have shown that the distribution of plastic strain around a notch is a complicated function of the geometry of the notch or crack, the properties of the material, and the loading conditions. Thus a more unified approach to this problem is required. 7.2. Cementite Cracks It is well established that cementite cracks may be directly responsible for the initiation of both ductile and brittle fracture in mild steel. McP!ahon (196L has investigated the effect of varying the amount of cementite, in two specimens of similar grain size, which produced a prounced change in the ductility transition temperature. Observations in the present work show that cementite is stronger when associated with pearlite and hence a possible reason why a normalised steel is less brittle than an annealed one. A more fundamental study of the effect of carbide distribution and morphology is needed and the possibility of improving the toughness of the cementite Tight be considered. — 222 — This represents a general problem for the class of material containing a brittle phase in a ductile matrix. A statistical approach based on idealised models has been developed by Gficer. and Gurland (1962). To present a more fundamental analysis, it is necessary to know the material properties of the components of the aggre,gate, and their crystallographic relationships within the aggregate. Unfortunately cementite cannot be obtained in larger sizes than it grows within the aggregate, hence its properties are uncertain. 1evertheless work is being performed on mod aggregates ( e.g. tungsten carbide and cobalt, by Nishimatsu and Gurland (1960), and the results from this type of work migt be extended to mild steel. - 223-- 7.3• Crack Initiation The fracture mechanisms below general yield show a number of characteristics which would not be predicted from a continuum mechanical approach. The bimodal behaviour occurs in a regionwhich it is expected from tensile data that microcracks will become unstable, producing a ductile-brittle transition similar to the later models of ?etch and Cottrell. These models, based on a critical stress criterion and having a statistical nature, would predict a transition in fracture behaviour over a range of temperature, rather than bimodal behaviour. Experimental results indicate a tendency towards an increase in brittleness with both decreasing hydrostatic tension and maximum stress, which is inconsistent with established ideas. As similar bimodal behaviour has been reported for uniaxial tension, this is not thought to be a notch effect and requires further investigation. - 224 - The distribution of stable microcracks below the notch is not known, nor is it known exactly where the cracks arc initiated,or how an unstable configuration of micro-cracks is formed. This could be determined by either unloading before the pre-established instability load,or from series notched tensile tests. A three dimensional metallographic examination would be tedious but informative. The fracture behaviour in the "cliff" region may be explained by a continuum mechanical approach, assuming that a critical stress ecual to the twinning stress is the fracture criterion. The evidence supporting this twinning concept, arises from metallographical observations and a consideration of the discontinuous nature of the fracture load-temperature diagram. It is well established that pre-yield inhibits twinning, Biggs and Pratt (1958). Consequently, pre-yielded specimens ought to shift the fracture "cliff" to a lower temperature, if twinning is the fracture controlling mechanism in this region. A series of experiments could be designed to confirm this. — 225 — The twinning phenomenon may possibly be applied to the problem of stress analysis. Because twinning is independent of the hydrostatic state of stress and.temperature, its appearance would be an indication that a spec7i_fic value of the stress, (the twinning stress), had been acting within a small volume of material. Microscopical examinations of the most brittle specimens showed that although twins occurred in the initiation zone, they were not generally observed along the fracture surface. Both twinning and fracture are slip initiated processes, and at high stresses it would appear that the latter mechanism is preferred. 7.L1.. Crack Propagation An estimation of the plastic strain—rate at the tip of a propagating crack nay be made by assuming that the distribution of plastic strain is unaffected by the rate of strain. Then from static observations, the plastic strain at the crack tip E0:".= the plastic zone size cm and a typical crack velocity is -1 u = 2 x 105 cm sec . The plastic strain—rate is then -1 given by E= O x u ti 104 sec . — 226 — Fig. 5.6 shows that the bimodal transition and the initiation transition temperatures are convergent with increasing strain—rate, meeting at about E.= 5 x 103 sec—l. From this it may be inferred that at strain—rates higher than this value e.g. at the tip of a propagating crack, cleavage fracture will always occur irrespective of the temperature. in fig. 6.4, The extrapolated values of CrLYS the results of Fischhof (1963), and theoretical predictions from dislocation dynamics, indicate that the yield stress is insensitive to changes in temperature and may be strongly strain—rate dependent, at these very high rates of strain. Thus it is predicted for this material, that a Propagating crack cannot be arrested by increasing the temperature and there will be no crack arrest temperature (C.A.T.). The possibility of predicting the (C.A.T.) for other materials, using a method similar to that outlined here, ought to be considered. — 227 — 7.5. Adiabatic Heating A significant fraction of the work done in plastically deforming a metal is converted into heat energy. This phenomenon was applied by Wells (1953)• to calculate the surface energy from measurements of local rises in temperature accompanying the propagation of a semi—brittle crack. Recently Eftis and Krafft (1964) have expressed the local temperature rise as a function of the yield stress, specific heat and the plastic strain. For steel a local temperature rise of about 1000 is predicted after a plastic strain at a flow stress of 60 Kg/mm2. At low rates of strain it is reasonable to assume that any local heat generated by plastic deformation will be dissipated. At high strain rates local heating will occur, but because the flow stress is temperature insensitive at high rates of strain, the fracture properties will not be significantly affected. Although it is considered that adiabatic heating will not have a significant effect on the deformation and fracture properties of mild steel, its effect on high strength steels may be significant. — 228- 7.6. The Charpy Impact Test The discontinuities in the Charily energy curve for mild steel are manifested by transitions in the modes of fracture initiation. In this material the initiation or ductility transition temperature, Td, represents the highest temperature at which fracture instability is brought about by ductile cleavage corresponding to an impact energy of 35 ft lbs and is not as generally thought, the 15 ft lb transition. This latter transition is identified by its bimodal nature and is due to a transition in the mode of cleavage, the mechanism of which is not fully understood. The 15 ft-lb energy criterion was adopted empirically following extensive tests on service failures connected mainly with ships. Although this approach has proved successful in ship construction, the impact test still remains one of comparison rather than fundamental measurement. The pertinent question arises, what material properties are being compared? - 229 - From the results of instrumented Charpy tests performed by Fearnehough and Foy (1963) on a wide variety of steels, together with those for the high nitrogen steel with a similar grain size in the present work, it is observed, with one exception, that the dynamic general yield-temperature curves are coincident. Thus the controlling influence on the transition temperature is apparently the cleavage stress. Because the temperature dependence of the yield stress is small at these high rates of strain, a small difference in the value of the cleavage stress will make a relatively large difference in the transition temperature. In general, steels with the lowest transition temperatures have the highest cleavage stress and the smallest strain-rate sensitivities (table 7.1.) Fence, the l'") ft-lb energy criterion for mild steel gives an indirect estimation of the cleavage stress. A The effect/of metallurgical variables on the cleavage stress have been predicted from their effects on the yield stress through the Cottrell-Petch theory of the ductile-brittle transition. Although the mechanisms of - 230 - Table 7.1 -__.- .....r 15 ft lbs General yield (5,Y (dynamic) Steel transition load at 20oC temp at 7 Kg 6yr (static) T °C ' 15 15 High Nitrogen + 30 980 2.0 P + 10 910 2.0 U - 30 1020 1,6 KY - 50 1130 1.8 S - 70 1180 1.4 T - 90 1210 1.3 - 231 - cleavage and yielding are compliqlentary, no fundamental relationship between them has been established even though many models of cleavage have been proposed. Until the concept of cleavage is more fully understood the factors affecting the cleavage parameter, (this apears as the surface energy term lin the Cottrell-Patch theory) cannot be evaluated. Essentially the Charpy test is used to determine a material's capacity for fracture initiation. If it is considered that the propagation of a brittle crack may be represented as a series of separate initiations, then the crack arrest phenomenon will be the inverse of crack initiation. A reproducible correlatien between Charpv data and the C.A.T. has been shown by Cowan and Vau7han (1962). The possibility of predicting the C.A.T. from measurement of the strain-rate dependence of t1:1_c tr-nsition temperatures has been considered in section 7.4. Thus the applicability of Charpy data to a structural design problem may be in its assessment of crack propagation behaviour. - 232 - 7.7. Summary of Conclusions 1. ilastic Cefortiati= is initiated at the mid-section of a Charpy specimen under a n^minal stress equal to only C.4 ti-,es the tensile yield stress. 2. in substantially plane stress conditions the Plastic ic accommodated by curved Inders bands which extend towards the neutral axis from the corners of the notch root. In contrast, at the mid-section (plane strain) the deformation occurs as a "wedge" shaped zone. The effect of applied load on the size of this "wedge" may be expressed by the relationships derived by Dugdale and Hill, except when the size of the "wedge" becomes small compared with the radius of the notch root. 3. The strain distributions within geometrically similar specimens are not identical. Above general yield the notch displacement is not a simple function of the root strain. -233- 4, Ductile tearing at the notch root gives way to internal ductile cleavage as the mode of instaI)ility, at a temperature Td. The mechanisms of both _lodes of fracture are controlled by the fracture of cementite plates. 5. Below Td, there is a s7all tem-eerature range in which the fracture loads occur at values outside the range of experimental scatter. Under impact loading, this behaviour is manifested by a bimodal distribution of impact energies and corresponds to the 15 ft. lb. energy criterion. It is believed that this bimodality is associated with a transition in the mode of cleavage instability, the fundamental mechanisms of which are not fully understood. - 2514- 6, A decrease in fracture load at temperatures below the bimodal region is coincident with the appearance of twins at the approximate Position of the elastic-plastic interface prior to instability. The experimental observations are explained from a continuum mechanical approach assuming a critical stress criterion of fracture. 7. The effect of strain-rate on the ductility and bimodal transitions may be expressed by an Arrhenius equation with apparent activation ener,gias 0.58 ± 0.02 eV and 0.26 ± 0.01 eV respectively. These values were not comparable with the activation energies for the initiation of yielding;, hence it is concluded that the effect of tellIperature and strain-rate on the cleavr2.ge stress is not entirely due to their influence.: on the yield stress. -235- 8. The temperature dependence of the cementite fracture stress is 0.1-0.2 K,7/mm2/ °C and the strain-rate dependence of the aggreTate cleavage = 2.4 ± 0.4 Kg/mm2. stress is calculated as d 6-lne‘f 4 . ( JJJ T A technique for predicting the existence of a crack arrest temperature is postulate', andit is concluded that this .latcrial, will not have a crack arrest te7peraturc. -236-- ACKNOWLEDGEMENTS This work forms part of a programme of research on brittle fracture financed by the Admiralty. I would like to thank Professor P. L. Pratt for supervising this research and Professor J. G. Ball the Head of the Metallurgy Department for providing research facilities. I am indebted to G. D. Fearnehough of the U.K.A.E.A. for the use of an instrumented Charpy machine and to Dr. J. Harding of the N.P.L. for the use of an impact tensile machine. Throughout this work Mr. P. R. Christopher of the N.C.R.E. Rosyth has been a source of encouragement and arranged the machining of Charpy specimens through Mr. G. Wilson also of the N.C.R.E. Rosyth and provision of the experimental steel through Mr. A. Muscott of the Bragg Laboratory. I have had many stimulating discussions with Dr. J. F. Knott of the C.E.G.B., Mr. F. Guiu and the rest of my colleagues in this Department. Finally, my sincere thanks to Ken Camichel for invaluable assistance with the experimental work. -237- REFERENCES Aaronsen H. I. 1960. "Decomposition of Austenite by Diffusional -processes". Trans. A Allen D. N. de G. and Southwell R. 1949. Phil. Trans, Roy. Soc. A242 379. Allen N. P., Rees ; Hopkins B. E. and Tipler H. R. 1953. J.I.S.1. 17t. 108. Allen Y. -a. 1959. "Fracture" Swampscott, Wiley p. 123. Allen T F. 1961. Iron and Steel Inst. Special Report No. 69 419. Ande-oso_i L. 1959. "Fracture" Simmpscott, Wiley p. 331. Andrews W. 1963. Acta l'et. 11 939. Au7land 1962. 7 elding J. 2 454. Barton. F. ard T7 i11 T J. 1964. V. S. Navy Rep SSC-147. Bateman D. A., Bradshaw F. J. and Rooke D. P. 1964. loyalAircraft Est. Tech. Note No. CP:it 63. Beevers C. J. 1964. Private Communication. Bell and Cahn B. A. 1957. Proc. Roy. Soc. A239 494, Berry J. Tr. 1959. Trans. A.S.M. 51 556. Bir,:c!;s B. and Pratt P. L. 1958. Acta Met. 6 694- Bilby B. A., Cottrell A. H. and Srinden K. W. 1963. Proc. Roy. Soc. A272 304. D. A. 1964. To be -Jubliched. -238- Bridge'lan P. W. 1952. Large plastic flow and fracture. NcGraw-Fill. Bruckner H. 1950. i-elding J. 29 467. Bullough R. 1955. r.uoted in J.I.M. 84 337 1956. Butler J. F. 1962. Jones and Laughlin Steel Co. Private Rep. Castro R. and Gneussier A. 1949. Rev. Met. 517. Chou Y. T., Garafalo F. and WP.itaore R. W. 1960. Acta Met. 8 480. Conrad Y. 1961. J.I.S.I. 198 366. Cottrell B. 1962, Welding J. 2 83. Cottrell A. H. 1958. Trans. A.I. ..E. 212 192. Cottrell A. H. 1963. Bakerian Lecture. Proc. Roy. Soc. A276 1. Cottrell A.. H. 1964. Royal Soc. (London) to be published. Cowan A. and Vaughan H. G. 1962. Nucl. Eng. 2 69 57. Crussard C., Bomone R., Plateau J., Morillon Y. and Haratray F. 1956. J.I.L.I. 183 146. Danko J. C. and Stout R. D. 19-5. Welding J. 113-5. Dixon J. R. and Stranahan J. S. 196L1. J. tech. Eng. Sc. 6 2 132. Dugdale D. S. 1960. J. Mech. Phys. Solids 8 100. Eft is J. and Krafft J. M. 1964. Trans. A.S.F.E. 64-Net-16. Eldin A. S. and Collins S. C. 1951. J.A.P. 22 1296. - 239 - Emery E. M. and Flanigan A. E. 1951. `.gelding J. 607-5. Erickson J. S. and Low J. R. 1957. Acta Met. 5 405. Eshelby J. D., Prank F. C. and Nabarro F. R. N. 1951. Phil. Mag. 42 351. Fearnel.ough G. D. 1962. U.K.A.E.A. T.R.G. Re:). 450(c. Fearnehoth G. D. and Hoy C. J. 1963. Ibid Rep. 635(c) and 196L1.. J.I.S.I. 202 912. Felix Y. and Geiger Th. 1956. Eutzer Tech. Rev. No. 1 14. Fischhof T. J. 1963. D. Phil. Thesis Oxford. Fisher R. M. 1964. Private Communication. Friedel J. 1959. "Fracture" S.7!ascott, 7%iley P. 498. Fry 4. 1921. Stahl u. Eisen 11 1 1093. Gensier 1947. Fracture of Metals. American 7eldin; Soc. N.Y. Gilman J. J. 1958. Trans. 212 783. Green A. P. and Fundy B. B. 1956. J. Mech. Phys. Solids 4 128.. Griffiths J. 1964. Private Communication. Gacer D. and Gurland J. 1962. J. Tech. Phys. Solids 10 365. Guiu 12'. 1962. Rev. Inst. Hierro y del Acero 15 82. Hahn G. T., Averbach B. L., Owen 7. S. and Cohen N. 1959. "Fracture" Sr=pscott 7ilev 191. G. T. 1962. Trans. A.I.V.E. 224 395. -240 -- Har G .T. 1964. Battelle 1107a. Inst. Rep. SR-164. Harding J. 1964. To be published. Hart E. 7. 1955. Acta. Met. 2 102. Hendrickson J. A., Wood D. S. and Clark D. S. 1958 Trans. A.S.M. 50 656. Hendrickson J, A., wood D. S. and Clark D. S. 1959. Ibid 51 629. Hill R. 1950. Mathcmatical Theory of Plasticity (Clarendon Press) Honda R. 1961. J. .;hys. Soc. Japan 16 1309. Hull D. 1960. Acta, Met. 8 11. Hull D. and Hamer F. 1964 Ibid 12 682. G.. R. 1948. Fracturing of Metals (Cleveland). Irwin G. R. Kies J. i. and Sc:Ath F.L. 1958. A.S.T..r1. 58 647:. Jacobs J. A. 195n. Phil. Mag. 41 349. Jevons D. 1925. J.I.S.I. 111 191. Johnson A.A. 1962. Phil. Mac:. 7 177. Johnson W.G. and Gilman J. J. 1959. J.A.P. 30 2 129. Kaldor ii. 1962. Acta. Hot. 10 887. Key A. S. 1963. Ibid. 11 11(U. Knott J. F. 1962. Ph.D. Theri.,is Cnmbrid7e. Knott J. F. and Cottrell A. H. 1963 J.I.S.I. 2m1 249. Knott J. F. 1964. Private Communication. Zochonaorfer von A. and Scholl F. 1957. Stahl u Eisen 22 - 241- Kochendorfer von A. and Schurenkapor A. 1961. Arch. f. Eisen hu7n. 32 689. Kosholov R. F. and Ushik G. V. 1959. Izr. Akad. Nauk. SSSR. Otn. -okhahika I. Mashinostrostroeniyo 1 111. Krafft J . Tr 1062. Acta. Plot. 10 85. Krafft J. M., Sullivan A.H. and Tipper C. F. Proc. Roy. Sec. A221 128. Lean G. and Plateau J. 1959. Rev. do Met. 56 427. ACSIL. Trans. +- No. 1337. 1.(3quear F. A. and Lubahn J. D. 1994. Welding J.585-5 Lianis G. and Ford H. 1958. J. Mech. Phys. Solids. I 1. Lipson H. and Petch Y. J. 194'. J.I.S.I. 142 95. Lovell L. C., Vogell F. L. and 'rnick J. E. 1959. Metal Prog. 75 5. 96. Low J. R. 1964. to be published. Low J. R. and Guard R. W. 1959. Acta. Met. 7 171. Manjoine M. J. 1944. J. Appl. i'cch. 11 A211. McClintock F. A. 1958. Trans. A.S.M.1. 25 582. McClintock F. A. 1964. Royal Society (London) to be published. McMahon C. J. Jr. 1964. U.S. Navy Ref. 9SC - 161. Morris C. F. 1949. Metal Pro7. 56 5 696. Morrison J. L. M. 1934. Enginaor 158 183. Neuber F. 1946. "Theory of Notch Stresses" David Taylor, Model Basin, U.S. Navy Tran:lation. - 242- Nichimatsu C. and Gurland J. 1960 Trans. A.S.M. 52 469. Nutting J. and Cosslett V. E. 1950 Inst. of Metals. Mon. No. 8. 1198. Orowan E. 1942„ Nature 149. 643. Orowan E. 1946, Trans. Inst. Shipbuilders Scotland. 12 165. °rowan E. 1955. Weld in? J. 3L. 357 - 5. Orowan E. 1959. "Fracture" Swampscott, Wiley p.147. Fetch N. J. 1954. Progress in Metal Phys. V. p.3. Petch N. J. 1958. Phil. Eag. 3 1- 89. Fetch N. J. 1959. "Fracture" Swampscott, Wiley, D.54 Pickering F. B. 1962. Proc. 5th Int. conp% on Elect. Micro. cc - 11. (Acade•nic PreP:21. Prie;-stner R. 1963. Gainsvillo Conf. on Twinning. A.I.M.E. Pugh H. Ll. D. 1962. Private communication. Rendall J. H. and Allen Y. P. 1964 Private communication. Robertson T. S. 1961. Navy Dept. Adv. Comm. Struct. Steel RP/183 Sakui B., Nakamura T. and Ohmori M. 1961 Totcu - To - :anc, Overseas 1 38. Shaw B. 1962. Private communication. Sleeswyk A. W. 1962. Acta. 10 927. Stimpr!or. L. D. and Eaton D. 1961. Wright-Patterson U.S, Air Force Base ARL - TR 24. Stone D. E. W. 196. Ph.D. Thesis London. Zti-oK . K. Y. 1957. Adv. in .7h7TL. 6 418. - 2L3 - Tanaka M. and Umeka7a S. 1958. Proc. 1st Jap. Cong. Test. Mat. p.95. Tardif H. P. and Chollet P. 1959. Nature 155 1917. Tardiff H. P. and Marquis H. 1955. Canadian Met. c;uat. 2 373. Totelman A. S. 196L.. Acta. 993. Ti-x2er C. 7_ . 1957. J. I.5.1. 185 L. C. F. 1967,. "Tile Bri-110 Fracture Story". 11 Verbraak C. A. 1961. is aterial-orilfung 383. Webb W. W. and Forgen W. D. `mot. 6 402. Weertman J. 1965. "Rs1--)onr?e of m otals to high strain-rate deformation". conferenc. Wallin3'er K. and rr8= Faturel-issenschaften Heft 21. Wellinger K. and Witti-er J. 1965. Arch. Eisenhlit 2 125. Wells A. 1953. Weldirs. J. F=r -p. 7 34-1. Wells A. A. 1961 - 19r2. Proc. Crack Propagati-11 Symp. (Clanfield) Wells A. A. 1964 Royal Societv- (london) to be published. ,e7.se: E. T. 1956. ..'roc. A.9.T.Tr. 56 541). Winno D. H. and Wundt. B. M. 1958. Acta. 12 626. WiJson D. V. 1955. Trans. A.., LI 7,21. —il:on D. V. and Konnon Y. 1964. Acta. Met. 12 626. Zener C. 1948. A.S.H. FracturL-1- of 1.etals (Cleveland) p.3