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Miniaturized Testing of Engineering Materials

V. Karthik, K.V. Kasiviswanathan, Baldev Raj

Miniature Specimens for and Properties

Publication details https://www.routledgehandbooks.com/doi/10.1201/9781315372051-4 V. Karthik, K.V. Kasiviswanathan, Baldev Raj Published online on: 23 Aug 2016

How to cite :- V. Karthik, K.V. Kasiviswanathan, Baldev Raj. 23 Aug 2016, Miniature Specimens for Fatigue and Fracture Properties from: Miniaturized Testing of Engineering Materials CRC Press Accessed on: 02 Oct 2021 https://www.routledgehandbooks.com/doi/10.1201/9781315372051-4

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The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 and Fracture Properties Miniature Specimens for Fatigue 3 to dimensions as small as 1×20 as mm small as to dimensions 3.1, Figure shown in as long) down sizes specimens other various well as as of Jor K terms data in generated be can for evaluating fracture energy-displacementand curves force-time, side-grooved force-displacement, and precracked specimen, and pendulum hammer instrumented of Using an amaterial. characteristics ness widely to evaluate one methods test of used tough is the the length, 55 mm V-notchCharpy employs which (CVN) testing, of a10 bar square mm 3.1 the half-size (5 ×523.6 half-size the mm 1988; al. et Lucas 1988; al. et Lucon 1998) have investigated, been including of FS specimens were based on normalization factors (NFs). were on normalization based of FS specimens Common NFs that with relate (USE) upper energy shelf DBTT specimens and subsize from volume attempts earliest to corsmaller process. The involved fracture the in reduced is due size reduced to the is when specimen energy absorbed The at DBTTs. the agiven failure motes temperature, ductile decreasing thereby pro and (FS) size specimens for failure) brittle compared to as full essary (nec conditions strain for plain constraints the minimizes size specimen the Decreasing size. specimen state hence the sensitive and to are cesses propagation pro and root. notch These initiation the crack from during prior to and specimen the plastic and in elastic the oftion both temperature (DBTT).temperature transition ductile-brittle and energy absorbed as such of parameters scaling available However, the materials. archive RPV using been has issue main the of extension LWR for life programs vessels pressure surveillance materials reactors (LWRs). greatly benefitedthe specimens of subsize utilization The of water light steels vessel of (RPV) embrittlement reactor the pressure ing for need monitor was the specimens motivation CVN of subsize use for the A variety of scaled-down versions of conventional CVN specimens (Louden of versions scaled-down of conventionalA variety specimens CVN The energy absorbed in fracturing a notched specimen is acomplex is func specimen anotched fracturing in absorbed energy The Subsize Charpy Specimen Impact TestingSubsize Charpy 3 long) and third-size (3.33 long) ×3.33 third-size and ×23.6 mm I . 3 (Kayano 1991). al. et primary The 85 ------3

Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 specimen span and K and span specimen 86 specimen dimensions and notch geometry such as Bb as such geometry notch and dimensions specimen account into of both USE > 150 J. materials factors taking tile Normalization volume (Bb fracture Kumar, 1990; Garner, Hamilton and Lucon 1998) revealed parameter that Most Hougland early (Corwin of and 1986; the studies Lucas 1988; al. et Correlation Energy 3.1.1 factors.or of acombination these volume, concentration fracture area, at root, notch stress the include fracture geometries. specimen CVN subsize and size full the showing Schematic FIGURE 3.1 slightly different fracture volume factor fracture (Bbslightly different Vitek Klueh, and area) correlation. Corwin, (1984) yielded better employed a the factor flatfractures, B.b condition predominantly brittle with (fracture (USE >200 of J), materials ductile in for materials while FS specimens and belowligament root) notch USE worked of subsize well for normalizing of precracked specimens reflects only crack only propagation reflects componentof specimens precracked (USE of previously sum the is mentioned components,of specimens USE notched for USE and propagation. crack the for initiation crack While required those (1993) al. et ditions, Kumar USE partitioned components: two into namely, the USEthe over arange of USE to below 300 from 100 J(Louden 1988). al. et dimensions) were shown to accurately radiusroot specimen and normalize To develop factors applicable con normalization brittle and ductile to both Half siz F ird size ull size e 2 t , where B = specimen thickness and, b = specimen and, b=specimen thickness , where B=specimen is the stress concentration factor as a function of notch concentration factor a function stress as the is 45° 55 23.6 23.6 30° 30° 0.06R 0.06R 0.25R (ma Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized 11.8 11.8 27.5 0.75 x) 0.75 3.33 5 3/2 ), worked which well for duc All dimensionsinmm 2 /LK t (where the Lis 2.0 10 p ). ). - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 where (NF) normalized USE of subsize CVN specimens as small as 1×20 as mm small as USE specimens CVN of subsize normalized factors, and SHEAR the percentage of shear fracture on the fracture surface. fracture on the factors, percentage SHEAR the and of fracture shear The difference in USE values between the two cases (USE =USE USE cases two the in –USE values between difference The Properties Fracture and Fatigue for Specimens Miniature ture volumeture factor. volume Incorporating factor as modes ductile as high-energy low-energy into and process brittle ture frac the a new correlation by methodology for partitioning energy absorbed Sokolov formulated specimens, Nanstad and subsize for different data from DBTT. correlation procedure would known no that single work Observing impact velocity range of (in 2.25 to the 5.5 m/s) USE the and did not affect USE, well identical as as did not span affect and dimensions remaining the reduced USE.cantly 30° to 45° the from keeping Varying angle notch while of depth signifi notch radius the and of notch, were Increasing studied. depth, angle, including dimensions, of specimen effects steels, RPV four the (30°, angles notch different with 45°, 60°) (L =20, on spans and 22, 40 mm) (3.33size ×3.33 ×23.6 mm stress concentration factorstress ( methodology for the USE plastic in included the correlation Q, and straint range of J. 50–200 lower the value, ±7% in USE actual of the particularly was found to within be (1993) al. et by Kumar USE for predicted FS specimens specimens, cracked pre methodology involving and notched partition both Using size. men this 1.5 ×1.5 ×20 mm including the specimen span (L) in the normalization factor (Bb as (L) span normalization the specimen in the including improved 1995) (Schubert al. odology et was further for USE by prediction

(Bb volume. volume fracture USE the fracture in correlated the well with rial mate the deforming in expended energy initiation macrocrack the resents with different subsize CVN specimen geometry (5 ×5, geometry 3×4, specimen CVN 3.3 subsize ×3.33 mm different with and unirradiated condition, based on half-size (5 ×523.6 condition, on half-size based mm unirradiated and USE values predicted of of The FS A533B irradiated specimen both in steel The ratioThe of USE USE and Kayono (1991) al. et plastic con and of angle notch effects considered the In another exhaustive work exhaustive by Sokolov another In (1995), undertaken Nanstad and 2 ); is, that EE brittle =    Fr = (Bb) = su ac bs 3 tu iz correlated well with that of FS specimens. This meth This of correlated that FS well specimens. with ∆∆ eb re US ** FS    vo /(Bb) E NF lu 3 ), 10% were within of data for FS specimens. Q me ri ttl subsize p =− ed was also shown to be invariant with speci with shown to invariant be was also    1 fu 100 ll , NF si θπ 22 ze − − = 100 ductile SH    , where angle) notch frac θis the in Fr EA was geometry-specific empirical empirical was geometry-specific ac R tu + re US NF vo E (Bb llu uct me ile 2 Q SH    FS 100 su EA )/(K bs iz R e (3.1) t    3 Q ) and third- ) and

subsize 2 /K p ) rep 3 ), the t and and QL). QL). (3.2) 87 2 - - - ) ------Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 span. Computing P Computing span. simulations of the impact test and a cleavage fracture model that is based acleavage based model impact and of test is that the simulations fracture element impact test. rate Using finite Charpy generated the at strain the in using data of various steels that normalized DBTT (DBTT normalized data that of steels various using half-size (5 ×523.6half-size mm on FS, to valid for be measured DBTT seen change was also equality This stress and a material constant and σ and constant a material and stress where P of DBTTthe ratioas was defined of and σ′ DBTT value of acritical σ′ exceeds stress when the fracture plane,crack (1993) al. et Kumar propagates, crack the that proposed causing to the of normal ahead tip acrack stress tensile by controlled is maximum fracture that hypothesis on the Based cleavage stress. critical as such fracture size/geometry DBTTrelating to specimen factor of anormalization or use odologies of relationships either developed empirical use on the based are meth the DBTT the specimens, regards correlation of As subsize FSgies. and upper lower the and at midpoint temperature between the the ener as shelf DBTT. as taken is appearance or It fracture expansion, defined commonly is value of energy, absorbed indexed to temperature aparticular The lateral temperature. transition for numerous definitions ductile–brittle are There 3.1.2 88 as at expressed root notch the stress tensile elastic straint was defined as was defined straint factor, loss. Aconstraint to α constraint due on DBTT arise effects size specimen that premise on the based tion of A533B due steel 1995). (Schubert al. to et neutron irradiation general yielding, K general yielding, (DBTT could related be as specimens subsize and specimens subsize FS and 1993) al. et (Kumar heat or precracking treatment for was found to equal be DBTT in due to aging). shift The of or condition thermal (precracking dependent, material and size but was both independentwhere constant the In a different approach, (2004) al. et adifferent Kurishita In formulated DBTT correla Transition Temperature Correlation m is the maximum load observed in a Charpy test at test point of the aCharpy load in observed maximum the is m t is the stress concentration factor, stress the specimen is the Lis and in terms of the cleavage fracture stress ( cleavage stress of the terms fracture in α Δ = 3 (DBTT ) and third-size (3.33 ×3.33 third-size ) and ×23.6 mm n ) σ FS */ = (DBTT = σ σ Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized y n , where ) ′ FS = =Δ y KL is the uniaxial stress at DBTT the yield stress uniaxial the is 2 tm n Bb (DBTT ) subsize 3 that is an index of the plastic of index con the an is that σ P 2 * is the critical cleavage critical the fracture * is

+constant n ) subsize where σ′ (3.5) . A normalized value . Anormalized n = DBTT/ = is the maximum maximum the is σ f ), it was shown 3 ) specimens ) specimens σ′ ) for FS (3.3) (3.4) - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 root volumesroot (V of subsize ratio on the of based notch of to that FS specimens specimens of small-size 3.1 J, corresponded to levels tests CVN of 41 standard 68 J. and in those while KLST of corresponded 1.9 to energies in temperatures transition The and

of DBTT obtained for subsize (5 forof subsize DBTT ×527 mm obtained Korolev (1998) al. specimens. et subsize FS and between values compared the itic steel. on a critical stress–critical area plot, cleavage area σ critical the stress stress–critical on acritical Properties Fracture and Fatigue for Specimens Miniature T 27 ×43mm of version subsize dimensions KLSTthe with designatedas (Kleinst–Proben) and vessel of steels nuclear pressure specimens Charpy FS ISO the between 21°C. where σis 5 ×mm to 6Jin corresponds specimens Charpy standard 47of Jin energy absorbed level criterion the that level Establishing the USE to the ensured. of is energy of ratio solids, of deformation where in constancy the lawon the of similar based was for specimens criterion definition of The subsize tion. using DBTT water–water condi its ofirradiated reactors in reactor energetic (VVER) types the material of Russian for identical configuration notch vessel with pressure of nil transition temperature. transition ductility of nil determination the in 33% used the USE to Jof ~68 corresponds FS specimens to 33% USE. corresponding of respective temperatures It may noted be that (2400–2450 cleavage stress the reaches at MPa on FS CVN) fracture based sizes specimen propagation for crack along different the section direction of mod 9Cr-1Mo geometries subsize at mid the stress total the that steel (20%–80%). USE 0.05 from to percentage to 0.25 ofwhere respect exponentially with mvaries the parameter A*/b parameter the A* area stressed were computed. to correlate with αwas seen parameter The DBTT Recently, Moitra (2015) al. et derived apower law DBTT for the relationship Other studies have resulted in deriving material-specific empirical factors empirical material-specific have deriving studies in resulted Other Similarly, Bohme and Schmitt (1998)Similarly, Schmitt and Bohme relations empirical established Using finite element (FE) simulations, it was further inferred for various inferred elementUsing finite (FE) simulations, further it was 2 specimens, the following correlation was recommended: the specimens, 3 , 1.0 0.1 depth, notch and mm radius as mm 2 for differently sized CVN samples martens of CVN aferritic sized for differently DBTT Nsubsize 10–10 DBTT KLST =50 +DBTT su ) and FS (V ) and bs FS =T iz e = ISO    –55°C V V su NF bs NFS 5–5 iz S e ±2 ) specimens as ) specimens

3    ) and FS Charpy specimens specimens FS Charpy ) and m σ (3.8) , °C * and the the and (3.7) (3.6) 89 - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 the small CVN specimens introduce experimental constraints such as rapid as such constraints experimental introduce specimens CVN small the specimens, subsized from data interpretation in additionIn challenges to the 3.1.4 ±5%. within values of FS specimens experimental with to agree laws given derived by 3.9 Equations scaling theoretically 3.10, and were seen maximum force (F maximum tip opening angle (CTOA), angle opening tip (W energy for equations total scaling the governed phase by growth crack crack controlled)(J-integral atearing and phase initiation crack and of blunting tip acrack consisting tearing ductile 3.1.3 90 Typical load-displacement curve of an instrumented impact test. impact instrumented of an curve Typical load-displacement FIGURE 3.2 where W, B, S, b force (F maximum load-displacement 3.2) of keyfor the parameters (Figure the curve as such Veidt and Schindler specimens, (1998) subsize using laws formulated scaling tests Toward instrumented from properties toughness-related predicting

namely, 3×427 5×27 and mm (a/W) specimens— of subsize loading. For types two for three-point while those of subsize specimens are designated by a prime ( designatedby aprime are specimens of subsize those while energy (W energy Challenges in Subsize Impact Testing in Subsize Impact Challenges Scaling of Instrumented Impact Test Impact Parameters ofScaling Instrumented tot W ). Carrying the analysis for a typical upper behavior shelf of for atypical analysis the ). Carrying W 0 , and a , and to t m s m = F S ) were derived as ), energy at maximum force), (W at maximum energy B B ′ 0 η η are geometrical parameters of full size specimens, specimens, size of full parameters geometrical are b ′ 0 a     0    F b b mm ′ 0 0    = Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized p + B B 1 ′′ W    mp b b ′ 3 0 0 , the W , the    + 2    S S b b ′ ′ 0 0 F F F    m ′ tot 2

( and F and W s mp to ′ ttm − mp m W ), and total fracture ), fracture total and , estimated through through , estimated ′ p W )     mp (3.9) ′ ). ). is factorη is f W t –W tot ) and ) and (3.10) mp s Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 where b is the uncracked ligament and J and ligament uncracked where the bis Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature stable crack growth. The J integral procedure enables testing with samples with procedure enables testing Jintegral stable The growth. crack as condition specified at tip crack the strain ments and dataments interpretation. and ofwith experi reduced volume terms associated in override difficulties the striker. However, of the mass the advantages the specimens CVN of subsize overcome be nation, impact velocity increasing can the and by decreasing yieldthe load influence determi vibrations, can which inertial The tests. impact subsize loads in for of small accurate recording required are sitivity sen of tups high Instrumented oscillations. high-frequency ofistration the (about bounds upper reg higher frequency for correct 250 kHz) required are devices of recording and measuring Electronic FS specimens. than quency control. temperature close 2000),heating/cooling ensuring (Manahan arrangements situ or in overcomeimpact is fast automated by mechanisms using transfer the support until anvil to the furnace the from its transfer during specimens subsize in loss temperature vibrations. The inertial and change temperature specimens for the plane strain K toughness fracture plane for strain the specimens recommended The dimensions. influencedspecimen fields by are strain and stress tip crack the as size dependent is on specimen toughness Fracture 3.2 For a typical ferritic steel with K with steel ferritic For atypical where B is specimen thickness, a is crack length, and σ and length, crack ais thickness, where specimen Bis mination of K mination SE(B)point bend compact or the deter (CT) tension The specimen specimen. more lenient, as such are behavior, material requirements size the account into nonlinear the takes specimens. of preclude subsize use the requirements size the must >150 be thickness men for purposes, avalid test. practical For mm all Because of low stiffness, subsize Charpy specimens vibrate at fre higher specimens Charpy subsize of lowBecause stiffness, For fracture toughness determined using the J-integral procedure, J-integral the which using determined toughness For fracture Fracture ToughnessFracture K IC per ASTM E 399 requires thick specimens to establish plain plain to establish specimens thick E 399 ASTM per requires Ba IC ,. IC Bb /J ~100 MPa√m σ and , ≥ IC 25 ≥ with Subsize Specimens with 25    K σ σ J IC IC ys IC ys is the resistance to initiation of to initiation resistance the is    (3.12) 2 (3.11) IC ys ys testing are the three- the are testing ~ 400 MPa, ~400 speci the is the yield strength. yield strength. the is 91 ------Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 while J while fl resulting in yielding, to suppress gross small too becomes plastic zone size the 1/2 CT as such dimensions 1/4 and specimen minimized CT,­proportionally However, increased. toughness of case latter the fracture the in increased, tion plastic spent deforma on the side energy the Since surfaces. specimen near increases at tip crack plastic zone size the the and predominant becomes state plane stress the thickness, specimen in With proportions. decrease lar minimum thickness required for avalid J required thickness minimum hence the degradation, and tip crack the plastic toughness zone tion near the postirradia and hardening neutron-irradiated of steels, irradiation because by afactor of of E399 ASTM 20. case the specimens the In than thinner 92 pendence of J inde thick The specimens. for small important is growth crack J-controlled for extension on crack ensuring additionthat, restriction criteria, in to size 3.3). (Figure steels ferritic and austenitic irradiated and study The showed 1 mm, Mao (1991)1 mm, formulated J amodified Philadelphia: American Society for Testing and Materials.) Materials.) and Testing for Society American Philadelphia: material irradiated testing for mens speci small-scale of use In The material. of irradiated toughness fracture the evaluating for F. Huang, specimens (From 1986, of subsized Use determination. toughness fracture for sions of dimen combinations possible different with geometry specimen tension compact Round FIGURE 3.3 of thickness from 12 from down to 1.02 forof evaluating thickness J mm The fracture toughness, J toughness, fracture The (1/2 CT, reduced dimensions proportionally CT with 1/4 CT).miniaturized (1 (i.e., astandard as CT) specimen same the being 1/2dimensions T–1 CT) and (2004) by namely, employing variants: other with size two reduced thickness plastic analysis. rigid condition using strain of that plain with fracture mode of J-integral related mixed the and fractographic observations and method etch recrystallization using measurements by fracture shear size 15% J in at alloy tested HT9 28°C 232°C. and However, of uncertainty ameasurement ow instability and a decrease in the J the in adecrease and ow instability Huang (1988) out extensive carried work has of CT specimens round on use Specimen size effects were further studied by Ono, studied Kimura Kasada, and were further effects size Specimen Q d IC decreased when the specimens were miniaturized maintaining simi maintaining were miniaturized specimens when the decreased values was reported. Using specimen thickness ranging from 25 to from ranging thickness values Using was reported. specimen IC was shown for 11.94, 7.62, of CT specimens thick mm 2.54 and D H Q , increased as the specimen thickness decreased, decreased, thickness specimen the as , increased , ASTM STP 888, eds. W.R. Corwin and G.E. Lucas, 290–304. G.E. Lucas, 290–304. and W.R. 888, eds. STP , ASTM Corwin Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized DimensionA B(thk) Q H D values for the smaller specimens. values smaller for the d IC IC further reduce. further procedure for invalid specimen procedure for specimen invalid 5.92 3.2 6.5 16 Sp eci IC 6.67 3.4 7.3 men ty 18 in both unirradiated unirradiated both in BC pe 8.14 7.4 20 4 ------Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 even to miniature specimens that are of 3×4mm are that specimens even to miniature capacity (specimen size) measuring apply criterion the of and scatter initions size) (i.e., Charpy showed the def specimens the that than smaller miniature Master curve methodology. curve Master FIGURE 3.4 described with only one parameter: the reference temperature T temperature reference one only parameter: the with described is regime transition the in toughness approach, fracture curve master the the In region. dependencetemperature of transition cleavage the in toughness and effects, scatter, size to provide statistical of statistical the adescription temperature reference acorresponding with method curve amaster oped theory, Weibull the and statistics (1999) Wallin theory weakest link the devel on Based analysis. for of number tests statistical alarge necessitating large was quite region transition the data in toughness the in scatter steels, the ferritic for all similar virtually is regime transition the in curve perature versus tem shape toughness of the Though the curve. transition Charpy on the based correlations through was established earlier regime transition the in vessel steels of pressure toughness evaluationThe fracture of the 3.2.1 Properties Fracture and Fatigue for Specimens Miniature thick fracture toughness specimen equals 100 equals MPa specimen toughness fracture thick (25.4 for a1in. toughness fracture mm) mean at the temperature which the referencing to an indexing temperature, T indexing to an referencing data generatedfrom and/or temperature at adifferent by thickness, section to estimated be thickness or section temperature to aparticular responding Figure 3.4. Figure adjustment shown in is size presentation of curve master schematic The and toughness. lowerthe fracture mean for curves bound the toeter define al. (2001)al. T between master curve approach. curve master the using estimation toughness fracture for the specimens size miniature the SE(B).section applicability of respects, demonstrated, all comparison The in

KJC cor toughness fracture allows the curve master toughness fracture The Small sp No sizeadjustmen Toughness in Transition Regime eci mens t TT 0 95% and scatter estimates from test results measured with with measured results test from estimates scatter and La rge sp 95% eci mens 5% 5%

KJC 0 . A comparison made et . Acomparison by Wallin Small sp adjustment St at istical size eci 2 and 3.3 and ×3.3 mm mens m . It is the main param . It main the is La rge sp 0 , defined as , defined 95% eci 2 cross cross mens 5% 93 - - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 critical area (A*) area critical body-centered of cleavage in fracture micromechanics and ( stress critical of fieldswith element tip crack (FEM) simulations method size, ligament b, specimen finite wasness) derived fracture by and combining adjustment loss (CLA)dure. constraint The B(specimen thick on both based E1921 ASTM the per statistics was derived weakest link from proce thickness, slope and lower T and slope shape on aT–T on shape MC- of the illustration Schematic FIGURE 3.5 to index a baseline K to abaseline index of specimens arelatively use demonstrated the fewer of number miniature They of geometry,effects margins. rates, loading irradiation, safety and ter curve shift (MC- shift ter curve co-workers and yielding. Odette (1998)small-scale developed mas the from of deviating the possibility with thelack of constraint by influenced 94 an amount Δ amount an 307–311:1600–1608, 2002.) 307–311:1600–1608, Materials Nuclear of al., Lucas, G.E. (From et Journal line. dashed-dotted tical size adjustment (SA) size tical B with scaling specimens. Irradiation shifts the SSY curve by an additional increment increment additional by an curve SSY the shifts Irradiation specimens. of small number a small with indexed temperature been It has line. dotted (SSY) curve ing toughness K toughness NRG, CRPP, Petten and fracture on effective Switzerland effects to address size curve. reference oftion the posi shape and the and models have developed shifts been these to predict Microstructure-based margins. safety and effects, of size types weakest link Δ additionaladjusted shifts, using 3.5, Figure shown position in as curve, of The the is of dimensions. larger The small specimen fracture toughness data in the transition regime are are regime transition the data in toughness fracture specimen small The Systematic studies were undertaken bySystematic Odette, were at studies undertaken UCSB with conjunction in 0 e reference scale. The solid curve represents a small specimen MC with a steeper asteeper MC with specimen asmall represents curve solid The scale. reference T (T) due to weakest link statistics and constraint effects. Astatis effects. constraint and statistics due(T) to weakest link g 0 to conditions of higher constraint associated with specimens specimens with associated constraint to of conditions higher (referenced at 75 MPa√m) (referenced by Δ

KJC/e (T) Δ e 100 200 300 T) method using small specimens accounting for the for the accounting specimens small using method T) , where the curve is adjusted in temperature space temperature adjusted by is in , where curve the ∆T 0 –200 g sp Small Δ T method. The heavy dashed curve shows the basic MC basic shows the curve dashed heavy The T method. ec . –100 Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized SSY T, rate, to account for strain irradiation, ∆T T (C 1/4 T– i T 0 g ) than the corresponding small scale yield scale small corresponding the than , where B is the fracture specimen specimen fracture , where the Bis T 0 SSY ir 100 r. 200 Δ T i , shown by the by the , shown σ *)– ------Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 ( havespace, extensively been DFMB employed specimens the for determining thereactor in advantages savings the Considering of significant specimens. found MC to compared have to the larger shape found with transition steeper previously on 1/3-sized tests bars. bend from Charpy pre-cracked under dynamic loading. shape K of The the dynamic under cleavage the temperature in transition shifts for measuring specimen CVN compared to astandard dimensions all in size in (DFMB), one-sixth nominally minibeam deformation fracture the and called bar bend precracked a small group at (Lucas UCSB 2007). al. et research same developed The techniques reconstruction fracture and microscopy confocal using surface ofsis fracture cubic (Lucas approach (bcc) analy 2007). al. et on the was based This measurements, verificationmaterial,etc.irradiated for (van al. et 2002).Walle input, of qualification weld, temperature lowestdimensions, acceptableinsert heat for testing, reference preparation and recommendations of materials include These technique. reconstitution in parameters critical all in guidelines 1998–2000, during formulated has institutions among European initiated coded RESQUE, aproject specimens, size Charpy irradiated and nonirradiated weld. the plastic zone and the possible between on the interference dependent also is CT specimen of areconstituted use successful The growth. field, crack residualthe influence the stress could and material; which insert the in changes of microstructural possibility the input, minimizes which heat-affected of zone (HAZ); the size low small heat the of is welding process welding, havetion consideration investigated. been choice of main the The fric and arc welding, stud flash welding, beam welding, welding, electron procedure. To end, welding various approaches, machining this laser as such and the not by is influenced welding material loaded the that insert to ensure 3.7. Figure shown in are specimens halves of the Charpy from It essential is (Tomimatsu, CT specimens Iida Kawaguchi, 1998) and reconstituted obtained 1988). Boehmert and (Viehrig of configurations specimen Different Charpy 3.6). another into ter (Figure machined welding is completed The after blank at cen material test the weld the and with them portions Charpy failed the to machine is specimen Charpy for areconstituted general method The rial. volumes for large demand avalid test mens, of requirements where mate size CT speci impact and evaluation Charpy for toughness tool, using especially employing for and conventional them specimen It tests. tested a powerful is of a previously portions undeformed piece test with asmall compounding by geometry involves specimen reconstitution standard Specimen preparing 3.3 Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature Δ T Toward developing of practices of for recommended aset reconstitution d ) of neutron irradiated steels and compared with Δ compared with and ) of steels neutron irradiated Specimen Reconstitution Methods e (T) for the DFMB specimen was was DFMB for(T) specimen the T i shifts determined determined shifts 95 - - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 96 CT specimen geometry reconstituted from broken halves of Charpy samples. of Charpy halves broken from reconstituted geometry specimen CT FIGURE 3.7 halves. broken from specimen impact of Charpy Reconstitution FIGURE 3.6 10 ×mm 24 ×10 10 ×mm 3 3 Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized 10 ×20mm Broken halvesof sp St Re We Stud arcweldin Inse Charpy of endbloc V- andard Char constitute lding slug eci rt notch sp preparatio men V- 3 notch d Char ks eci py V- g men n a py notch Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 the specimen to ensure that net section yielding is minimal and the crack crack the and minimal is yielding net section that to ensure specimen the propagation fatigue crack on Standard requirement size placestest strict 3.4.1 effects. data size due to specimen the test interpreting in cost involved, the loading, tension difficulty the and tension– and loading push–pull imposing plexity of as such conditions test between 20% 30%. and between conventional to the piece, test lives butsimilar were TMF the shorter by were showed evolution stress mechanism that specimens failure and ture minia behavior of from (TMF) fatigue 90. Nimonic results The mechanical a gauge length of 14 mm and a cross section ofa gauge about of 14 section 1mm length across and mm tests. specimen standard with agreement good in curves strain stress– cyclic and of 7.6 results 2and diameter shown S–N and length in mm agauge with geometry specimen cylindrical developedhas miniaturized Using simulations, FE Moslang (2000) byrecommended several researchers. been has gauge section cylindrical with a configuration choice of aspecimen the reason, For this specimens. of hourglass strain diametric of the results the from range strain axial the estimating in some difficulties are there hand, other control. the temperature good and On tests fatigue push–pull in ranges to achieve high-strain length in gauge 7mm and 2 mm diameter (2001) al. et of Hirose specimens hourglass of subsize use demonstrated the tests. for push–pull specimens for issue miniaturizing a very important is 2%, consistently below fell of that FS specimens. life fatigue range of strain to reversed a fatigue loading total cyclic of fully use the ted SS316 irradiated permit and specimens unirradiated steel. subsize Though for both specimens large of from to to cycles that failure) data were similar 3.18 gauge diameter (stress section), amplitude mm versus S–N number the (i.e., specimen ASTM-606 of an size the half demonstrated with They that up for to temperatures test 650°C. specimens subsize using techniques test (1986) Liu Grossbeck and materials. and tests to were first develop the fatigue 5to value 10 from ranges that on acritical the depending than smaller is tion gauge the in sec section cross at minimum the of number when grains the reported been has effect size Specimen dimension. specimen depend on the propagates cycle Therefore, region. high properties fatigue the inward in and surface specimen on the occurs lowthe cracking cycle region, while in defects governed is by internal fracture that tests, fatigue itIn known is 3.4 Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature The limited database on small specimen fatigue testing is due is com to the fatigue testing specimen database on small limited The Pahlavanyali et al. (2008) attempted to use miniature specimens with with specimens (2008)Pahlavanyali al. et miniature attempted to use which have to , resistance good of specimens types Hourglass

Studies Using Subsize Specimens Fatigue and Fatigue Crack Growth Fatigue Crack Studies Growth 2 for thermo 97 - - ­ - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 43:105–110, 2012.) 43:105–110, Fatigue of S. W., Journal Lin, S. C. and International Shin, (From K. of Delta terms in specimen CT standard and specimen miniature the of FCG from rates (b) Comparison specimen. CT men crack growth rates (Figure 3.8) differed with the standard specimen specimen rates standard 3.8) the (Figure growth with crack men differed (2012) Lin and speci by Shin studies Further miniature revealed the that data of conventional growth crack with tests. results long yielded matching mm 42 than larger showed bending, 8–15 specimens that rotating under mm of diameters and to 22 200 mm from ranging lengths with specimens cal obtained. data for a/w could be regime law Paris growth crack of 0.5 full covering the to 1200 300 (YS) MPa. from Reliable ranging yield growth strength crack in (CT) materials for three specimens behavior of to that standard growth crack FCG loading showed produced and tests three-point similar that specimens employed wide, 2.0 mm 7.9 bar notch miniature long, 0.8 thick and mm mm (2002) Stubbins and Li studies. for growth valid crack sizes small extremely to provided platesizes confidence the reduceto the This specimen material. thicker from wide, long) 203 of specimens sions of results mm 50 mm with of 0.254 0.457 and (planar dimen mm thicknesses (CCT) with specimens center tension cracked on miniaturized studies of growth crack fatigue was evidentagreement good the from This growth. crack subcritical ing for measur not is amajor constraint thickness specimen shown that has results. test standard the violatedbe data may at deviate growth crack some and test point of from the Δ parameter mechanics fracture elastic linear the represented by be field correctly can stress tip 98 (a) Single-edge notch (SEN) miniature specimen of 20 × 6 × 0.5 mm specimen (SEN) miniature notch (a) Single-edge FIGURE 3.8 (a) The crack propagation crack (2004)The Cai and cylindri data of Shin small from (FCG) study earliest growth on crack fatigue The James (1986) and by Ermi K. In a small specimen, this size requirement may requirement size this specimen, asmall K. In Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized (b

) da/dN (mm/cycle) 1 ×10 1 ×10 1 ×10 1 ×10 –4 –3 –6 –5 10 ∆K (MPa√m) 3 compared with a standard a standard with compared 100 4340 st sp. trend St Min04 Min03 Min02 Min01 CT CT CT andar ee R =0.5 R =0.3 R =0.1 l d - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 tests are lower than the (FATT) lower the are tests than midposition between the upper lower the and midposition T between The energies. shelf Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature have been established between T have between established been 1998; Fleury (Ha and correlations 1997; Empirical tests. Norris 2012) Matocha CVN state in stress triaxial and loading dynamic compared with as failure state, favorable less is stress which abiaxial in static and for loading brittle of a standard 25 mm thick CT specimen. The growth rates Δ versus growth the The CT specimen. thick 25 mm of astandard results the with alloy could line made Al by of be thick) and steel 0.5 in mm data (single specimen edge notch of long 20 wide by mm 6mm miniature state. plane strain the near is that specimen standard rate the growth in higher acorresponding well as compared as to a lower of closure crack degree of closure, crack degree as ahigher in resulting plastic constraint, asmaller state exerts and plane stress the in is specimen state where effect, avery stress thin to the was attributed discrepancy The results. were specimen consistently below standard the results specimen by miniature afactor mostresults the cases, and, of in 2–4 temperature is estimated by taking the temperature,as T the defined by taking estimated is temperature 3.9). (Figure temperature test the plotted against transition punch A small behavior curve when transition way this showstypical defined SP energy test. The punch load-displacement small of the under the area curves the Buckand 1986; Mao and 1992) Kameda as defined SP on energy the relies Kameda, (Baik, transition ductile–brittle the approachThe for characterizing 3.5.1 previous chapter. the in discussed behavior of materials stress–strain the for defining to those similar are for properties evaluation of fracture V-notch setup Charpy the SP impact in test. experimental The observed that to similar failure ductile-to-brittle from mode transition fracture a distinct temperatures, test load-displacement ofWith SP decreasing show test curves evaluation property for but derivationtensile also parameter. of toughness (SP) punch not small for evolved only The has technique a promising as 3.5 life. fatigue of structural conservative estimate upper to get bound an a as serve data can specimen miniature relation from T is a material-specific constant in the range of in 0.35–0.55. constant where amaterial-specific αis By employing a correction stress intensity range for closure effects, the the effects, range for closure intensity By stress employing acorrection Fracture Toughness from Small Punch Technique Toughness Punch Small Fracture from Ductile–Brittle Transition Punch Small from Ductile–Brittle sp CVN =α(FATT) sp and FATT and kelvins) as in (both as the SP specimen are deformed under are SP specimen the as CVN (3.13) sp from SP from sp , at the K 99 eff

Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 value value σ applied when crack the of load, ahead asharp cleavage initiates the fracture that (RKR) assumes Rice Knot, criterion, on Ritchie, which and based is shelf lower the 1998). in Fleury estimation toughness methodology for The fracture upper lower (Hu the and in and regimes shelf toughness fracture mate the have formulations put to esti stress been forth fracture and Energy-based 3.5.2

100 curve for T for curve temperature versus energy resulting the and temperatures test at different Typical SP curves FIGURE 3.9 age, (2000) al. et Matsushita showed correlation coefficient the (R that composition, percent phase size, and chemical grain variables as such tional over multiple Cr–Mo analyses various addi By steels. regression performing for range of 300–550 the in for values and Bare 2.3–2.8 ofwhere Aare typical tion region and therefore the FATT-T the therefore and region tion transi the in energy dependence temperature of the fracture affected men However, region. transition the in energy orientation SP of the speci test the the temperature fracture dependence of affect not does 2.0 significantly mm of low steels. estimation alloy ferritic temperature of transition reliability the simple for that the relation (as Equation than 3.13),higher in improving thereby f , ahead of the crack tip over a characteristic distance, l distance, over tip crack of, ahead the a characteristic Foulds and Viswanathan (1994)Foulds Viswanathan and form of the relationship derived empirical an Matocha (2015) observed that the change in punch diameter from 2.5 to 2.5 from (2015)Matocha diameter punch in change the that observed

Load1000 (N) 1500 2000 500 0

σ Toughness—Lower and Upper Shelf * f . The fracture toughness is given expression by is the toughness fracture . The SP –196°C determination. 0.5 D efle –160°C 12 ction, mm 1.5 –100°C FATT (°C) =A+BT KI –120°C IC –25°C = β Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized −+ () 2.5 n 12 // sp

correlation. ․

Energy of fracture1000 1500 (N mm)2000 2500 500 12 0 0 50      Emax σ σ       f sp y n n (°C) /2 2 2 + − 1 1 1001       T      SP

(3.15) Te mp 50 erature (K 0 , exceeds a critical a critical , exceeds 2002 ) 50 2 ) was (3.14) 30 0 - - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 J as toughness elastic–plastic location), related could to linearly be strain respectively. fracture biaxial The over some distance x ahead ofover (W x ahead tip crack some distance averaged density energy strain The CT specimen. of tip crack astandard of applied SP is loading analysis FE to the strain large using determined criterion This SP specimen. uncracked an in for initiation crack required sity den energy strain the is for criterion concept fracture the wherein tinuum at loads, peak initiation approachcrack Foulds a con an proposed based on load or assume peak measurements, which strain on equivalent fracture approaches based in shortcomings Citing regime. ductile load the peak in advance load upwell stable undergoes in to peak of and the growth crack initiates crack that observed and of initiation crack onset the for identifying constants. determined empirically where Jare Kand puted from the loadputed the level from at W which where t as state derived expression for and plastic stress an strain biaxial the under strain equivalent by controlled is fracture the SP of specimen the failure the for Cr-Mo tests various CVN standard steels. from obtained values with were agreement good found to in be regime brittle the in ness tough center. loaded fracture of the and periphery the in predictions The supported for at adisk analysis by the Timoshenko determined stress elastic deriving the fracture properties using the area under the load-displacement the under area the using properties fracture the deriving (SP) punch on small forMost employed early research specimens uncracked 3.5.3 of ±25%. accuracy an within of power of awide variety toughness plant could predicted be steels fracture ( extension crack blunting on the based procedures appropriate of an approach estimation x, averaging the one of is the distance where Properties Fracture and Fatigue for Specimens Miniature Foulds (1998) al. et employed time system first for the videoimaging a In the ductile regime (upper regime ductile the (1987) shelf),In Takahashi Mao and suggested that σ coefficient strain-hardening the n is (Hutchinson–Rice– HRR the from obtained constant anumerical β is l For low SP sample, the displacements in σ 0 y is the grain size grain the is is the yield stress the is Small Punch Using Notched Punch Small Specimen Rosengren) small-scale yielding solution yielding Rosengren) small-scale 0 and t are original thickness and deformed thickness (near failure (near failure deformed thickness and thickness original tare and ε IC q = ln (t =ln =K CT ε = W = q 0 –J /t) SP CT (3.16) . However, this in key issue the ) is computed.) is J max is computed as maximum computed is maximum as Δ a). method, Using this IC is then com then is (3.17) 101 - - - - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 lower compared E1921 ASTM shelf well with However, results. curve master of of SA the applied toughness in steel 508 load, afunction b as fracture the and signals acoustic emission point using initiation crack the Determining opening. crack initial of the half the point, ais and initiation crack the P is lower contact radius the the where and care band radius, die respectively, plate force was derived bending under as thin cracked 3.10a Figure factor, shown in as intensity specimen stress K, the of and the center SP of the the in was notch introduced Asharp steels. of different ties order proper in to evaluate fracture SP the precracked specimens using parameters. toughness fracture and temperature of transition estimation forbasis the amore was attempted solid to assure of SP precracked specimens use (SENB) bending notched single-edge theprecracked or CT specimens, and Charpy evaluation notched use toughness that procedures fracture displacement or conventional the to at the Analogous curve failure. 102 (d) notched SP specimen studied by Cardenas et al. (2012). al. et by Cardenas studied (d) SP specimen notched 2015); (Matocha plane and of disc Turba (2011); axis al. et the in Unotch with (c) specimen disc by studied wide) notch 0.5 mm employed Kwon by Ju,and and Jang, (2003); circular (b) sharp (1.0 notch length mm (a) thickness-type geometry. Athrough SP specimen Various notched FIGURE 3.10 One of the earliest studies was performed by was performed Ju, studies earliest of the One Kwon Jang, and (2003) (a) (c) K C = 2 3 P () π 1 Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized h + 2 ν    ln 400 µm    b c (b (d    ) ) + 4 10 mm b c 2 2    a Notch (3.18)

10 mm 1 mm - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 ABAQUS. J The was J-integral evaluated the models in damage and acontour as integral with input, elementductile analysis was finite test modeled the using this With observations. microscope electron aid of scanning the with tests rupted by inter determined was experimentally load of initiation crack at onset the ratio a/t depth-to-thickness a notch =0.4 study. for detailed was chosen The relative (Figure 3.10d) with Lconfiguration ity notch, of the depth the with (2012); al. et were by Cardenas studied triaxial of stress trends on the based (L), notch (L+T), notch +transverse tudinal longitudinal notch, circular and fracture energy was also less steep (Matocha 2015). (Matocha steep less was also energy fracture T 3.10c) (Figure plane disk of the temperature axis the transition in notch shifts notch. However, of presence asharp the aU-shaped with than specimen disk rather effects rate size and to related be strain of to acombination the seems T in shift energies, the SP fracture the and displacement the at both fracture decreased markedly geometry this Though of 1 mm. a thickness with a specimen in to 0.5 wasnotch mm equal 3.10b) (Figure diameter was employed by Turba (2011). al. et of depth the The of Equation 3.18. analysis the in extension results, possiblycurve due of plastic to noninclusion deformation crack and values were toughness temperature room much master the lower the than sented here.sented pre indentation are from estimation developed toughness ods for fracture Various material. of the for toughness evaluation used meth be of fracture also indentation can test load-indentation a ball The in data depth obtained 3.6 leading to a conclusion that the observed shift between T between shift to aconclusion observed leading the that tion using the punch displacement ( punch the using tion simula by numerical event determined initiation crack is to the sponding sample the edge.from displacement value The corre of opening notch 3.10e) (Figure notch of about length crack mm 4.5–5.0 thickness initial with of ablunt use to well the as as notch. SPT of sample the low the from thickness resulting of loss to constraint the J, standard of that the possibly due than was higher method by this obtained into K or J using the classical principles. J The classical the Korinto Jusing Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature gins of ±15%.gins of compared that conventional well confidencesteels with mar with tests SP Different notch configurations in a squared SP specimen, such as a longi such SP specimen, squared in a configurations notch Different A circular notch of 2.5 mm diameter in a disk-shaped specimen of 8.0 adisk-shaped in mm specimen diameter of notch mm 2.5 A circular The notch configuration employed configuration notch The al. et Lacalle by (2012) through lateralis significantly to higher temperatures and the temperature the temperature dependenceand of higher temperatures to significantly Fracture Toughness IndentationFracture Techniques from SPT ( Δ a = 0) for actual crack initiation in a notched SPT anotched sample in a =0) initiation crack for actual δ SP ) from experiments and transformed transformed and experiments ) from toward the (DBTT) the toward c from SP tests for different SP for from tests different SP CVN and (DBTT) and was not seen, 103 CVN ------

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a temperature- (Haggag 1998). al. et as defined IEF is fields are compressive of indentation ahead except acrack that stress the that to are similar contact indenter-specimen aheadtheand fieldsof near stress concentrated that on apremise based curves stress–strain true measured automated from energy indentation (ABI)- ball of fracture tive determination nondestruc (IEF) allows the concept of toThe fracture indentation energy 3.6.1 104 temperature-dependent term (W term temperature-dependent were (1) the identical that to is the contact area unit per indentation energy where terms: atemperature-independent W term, terms: two into area unit per energy fracture the Dividing region. transition the in steels of ferritic toughness fracture the model to estimate a theoretical steels. for temperature carbon transition to depict ductile–brittle was seen the ambient, the temperature dependence of the estimated K ambient, dependence temperature estimated of the the –150°C ABI at from data. steels on RPV temperatures By tests performing to toughness lower the using models fracture and shelf mechanics fracture with ABI from data test was byfracture estimated coupling IEF theory the stress The material. of the stress fracture the reaches contact pressure maximum same as that of the ASTM K ASTM of that the as same employed by Haggag to colleagues compute and h P The slopeThe IEF as (S) to calculate used is load-depth of the curve indentation of the diameter chordal the d is h indentation depth the h is indentation load the P is Byun, Kim, and Hong and (1998) IEF Kim, concept proposed and Byun, this furthered In absence of critical fracture stress for a material, a reference stress was for stress areference amaterial, stress fracture of absence critical In m f is the indentation up depth the to cleavage stress is fracture = Indentation Energy to Fracture Energy Indentation 4 d P 2 is the mean contact pressure mean the is ­dependent (W term, JC IE master curve. master IE F Miniaturized Testing of Engineering Materials Testing of Engineering Miniaturized = F IEF = π SD =W h ln ∫ T 0 f ), the key assumptions in this model this in ), key assumptions the Ph    m Dh T () ), when (2) the and occurs fracture − dh f 0 (= lower energy), shelf and

   (3.20) f . The IEF computed. The JC was found to be (3.19) - Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 Miniature Specimens for Fatigue and Fracture Properties Fracture and Fatigue for Specimens Miniature as expressed face is that nucleation, and increase in void in nucleation, volume E causes increase depth and penetration with due to compressive stresses shear indentation induce localized voidThe where decrease with depth. Expressing E Expressing depth. with decrease variable and its relation to the elastic modulus of the damaged material (E modulusvariable material its damaged elastic relation of and to the the area is related to is area (CDM). mechanics damage contactcontinuum unit per Indentation energy model indentation basic exploiting energy the concepts of acritical posed (2006) al. et Lee of materials, ductile toughness pro fracture For estimating 3.6.2 microstructural analysis is the way the is forward. analysis microstructural models with together fracture and analysis numerical with tests specimen codes for and its ambit acceptance. of Integration ofthe standards small methodologies under specimen imperative small is the totoughness bring on fracture effects constraint of the understanding Abetter specimens. size approach, of smaller example, use enables curve the amaster which through to addressed, be for needs effects of source size underlying the methods, toughness for tests, fracture while specimen size full correlation with on the heavily relies impact tests Charpy of subsize use The ventional counterparts. con compared to as their specimens miniaturized in reduced constraints evaluation the factor the is to considered be of in toughness main The Remarks Concluding 3.7 K and conventional crack tip opening displacement (CTOD)conventional opening tip crack tests. 10% from showed those with within agreement error good tation technique corresponding to the critical critical to the corresponding void acritical volume using and of depth 0.25 fraction the for growth, crack h impression diameter the d is indentation depth the h is applied the P is indentation load This characteristic point was determined using the concept of the damage using point was determined characteristic This * is the critical indentation depth corresponding to the characteristic frac characteristic to the indentation corresponding depth critical the is JC Continuum Damage Mechanics Approach Mechanics Damage Continuum ture initiation point. initiation ture . The estimated fracture toughness values obtained from the inden the from values obtained toughness fracture estimated . The w f , the energy per unit area required to create sur a crack required area unit per energy , the 2 E w * D f was estimated and used for computing w used and was estimated = D hh lim as a function of indentation parameters a function as → * ∫ 0 h π 4 d P 2 dh (3.21) D 105 to to D ). ). - - - - - f

Downloaded By: 10.3.98.104 At: 09:39 02 Oct 2021; For: 9781315372051, chapter3, 10.1201/9781315372051-4 Foulds, J.R.,Wu, M.,Srivastav, S.,andJewett,C.W. 1998.Fracture andtensileproper Foulds, J. R. and Viswanathan, R. 1994. Small punch testing for determining the mate- Ermi, A. M.andJames,L. A. 1986.Miniature center-cracked-tension specimenfor Corwin, W. R., Klueh,R.L.,andVitek, J.M.1984.Effect ofspecimensizeandnickel Hirose, T., Sakasegawa,H.,Kohyama, A., Katoh, Y., andTanigawa, H.2001.Effect of Haggag, F. M.,Byun,T. S.,Hong,J.H.,Miraglia,P. Q.,and Murty, K.L.1998. Ha, J.S.andFleury, E.1998.Smallpunch teststoestimatethemechanicalproperties Corwin, W. R. andHougland, A. M.1986.Effect ofspecimensizeandmaterialcondi- Cardenas, E.C.,Belzunce, F. J.,Rodriguez,C.,Penuelas,I.,andBetegon,C.2012. Byun, T. S.,Kim,J.W., andHong,J.H.1998. 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