Creep-Fatigue Failure Diagnosis

Home , Creep (deformation), Fatigue (material)

Review Creep-Fatigue Failure Diagnosis

Stuart Holdsworth

Received: 22 October 2015 ; Accepted: 6 November 2015 ; Published: 16 November 2015 Academic Editor: Robert Lancaster

EMPA: Swiss Federal Laboratories for Materials Science and Technology Überlandstrasse 129, Dübendorf CH-8600, Switzerland; [email protected]; Tel.: +41-58-765-47-32

Abstract: Failure diagnosis invariably involves consideration of both associated material condition and the results of a mechanical analysis of prior operating history. This Review focuses on these aspects with particular reference to creep-fatigue failure diagnosis. Creep-fatigue cracking can be due to a spectrum of loading conditions ranging from pure cyclic to mainly steady loading with infrequent off-load transients. These require a range of mechanical analysis approaches, a number of which are reviewed. The microstructural information revealing material condition can vary with alloy class. In practice, the detail of the consequent cracking mechanism(s) can be camouﬂaged by oxidation at high temperatures, although the presence of oxide on fracture surfaces can be used to date events leading to failure. Routine laboratory specimen post-test examination is strongly recommended to characterise the detail of deformation and damage accumulation under known and well-controlled loading conditions to improve the effectiveness and efﬁciency of failure diagnosis.

Keywords: failure diagnosis; creep-fatigue; material condition; mechanical analysis

1. Introduction The diagnosis of failures invariably involves consideration of both the associated material condition and the results of a mechanical analysis of prior operating history. Material condition refers not only to a knowledge of the chemical composition and mechanical properties relative to those originally specified for the failed component, but also the appearance and extent of microstructural and physical damage responsible for failure. At the very least, the latter directs the investigator to the mechanism(s) of failure and to the type of mechanical analysis that should be adopted to corroborate the diagnosis. Typically, the required details relating to material condition and prior operating history are incomplete, and it is necessary to exploit the available evidence from both sources of information. Creep-fatigue failures in high temperature power plant components are good examples of this since the failure mechanism can be camouflaged by extensive oxidation and the detail of thermo-mechanical transients can be complex and are not always comprehensively gathered during operation. Oxidation can disguise crack path details in such a way that the actual damage mechanism is no longer apparent, and valuable evidence can be lost by its removal. Furthermore, creep-fatigue damage development can be very material condition-dependent, being influenced not only by creep ductility, but also by creep strength and the way in which it has been attained; that is, by precipitation strengthening or by solid solution strengthening. For these reasons, the accurate microstructural characterisation of creep-fatigue damage often requires a knowledge of operating conditions (and the results of mechanical analysis) and the response of the material to thermo-mechanical fatigue loading (e.g., from laboratory testing experience). In this respect, the routine practice of laboratory specimen post-test examination is strongly advocated. The following review concerns the diagnosis of creep-fatigue failures with due consideration to material condition and mechanical analysis of prior operating history.

Materials 2015, 8, 7757–7769; doi:10.3390/ma8115418 www.mdpi.com/journal/materials Materials 2015, 8, 7757–7769

Materials 2015, 8, page–page 2. Material Condition 2. Material Condition Materials 2015, 8, page–page 2.1. Mechanism of Creep-Fatigue Cracking 2.1.2. Mechanism Material Condition of Creep‐Fatigue Cracking The development of creep-fatigue damage in most power plant steels depends on temperature, The development of creep‐fatigue damage in most power plant steels depends on temperature, strain2.1. range, Mechanism strain of rate, Creep hold‐Fatigue time, Cracking and the creep strength and ductility of the material [1–4]. In the strain range, strain rate, hold time, and the creep strength and ductility of the material [1–4]. In the absence of a significant hold time (and/or at relatively high strain rates), crack initiation and growth absenceThe of adevelopment significant hold of creep time‐fatigue (and/or damage at relatively in most high power strain plant rates), steels crack depends initiation on temperature, and growth is fatigue dominated, even at high application temperatures (Figure1a). With increasing hold time is fatiguestrain range, dominated, strain rate, even hold at high time, application and the creep temperatures strength and (Figure ductility 1a). of Withthe material increasing [1–4]. hold In the time (and/or decreasing strain rate) at high temperatures, the creep damage within the structure becomes (and/orabsence decreasing of a significant strain holdrate) timeat high (and/or temperatures, at relatively the high creep strain damage rates), within crack initiation the structure and growth becomes increasinglyincreasinglyis fatigue influential, dominated,influential, to evento the the limitat limit high beyond beyond application which which temperatures crack development (Figure 1a). becomes becomes With increasingfully fully creep creep hold dominated dominated time (Figure(Figure(and/or1b). 1b). At decreasing At intermediate intermediate strain hold rate) hold timesat times high and temperatures,and strain strain rates, rates, the fatiguefatigue creep damage cracking within interacts interacts the structure with with creep creep becomes damage damage developingdevelopingincreasingly “consequentially” “consequentially” influential, to the or orlimit “simultaneously” “simultaneously” beyond which crack resulting development in in accelerated accelerated becomes fullycrack crack creep propagation propagation dominated and and (Figure 1b). At intermediate hold times and strain rates, fatigue cracking interacts with creep damage reducedreduced crack crack initiation initiation endurance endurance (Figures (Figure 1c,d1c,d and and Figure2). The 2). extent The extent of any of interaction any interaction increases increases with developing “consequentially” or “simultaneously” resulting in accelerated crack propagation and decreasingwith decreasing creep ductility creep ductility [3]. The interaction[3]. The interaction of creep andof creep fatigue and is notfatigue limited is not to thelimited accumulation to the reduced crack initiation endurance (Figure 1c,d and Figure 2). The extent of any interaction increases ofaccumulation damage. Deformation of damage. interactions Deformation are interactions also influential, are also and influential, in a dominant and in a waydominant for a way number for a of with decreasing creep ductility [3]. The interaction of creep and fatigue is not limited to the alloysnumber [2]. of alloys [2]. accumulation of damage. Deformation interactions are also influential, and in a dominant way for a number of alloys [2].

FigureFigure 1. 1. Creep-fatigueCreep‐fatigue crackingcracking mechanisms:mechanisms: (a (a) )fatigue fatigue dominated; dominated; (b ()b )creep creep dominated; dominated; Figure 1. Creep‐fatigue cracking mechanisms: (a) fatigue dominated; (b) creep dominated; c (c) creep‐fatigue interaction (due to “simultaneous” creep damage accumulation); (d)d creep‐fatigue ( ) creep-fatigue(c) creep‐fatigue interaction interaction (due (due to to “consequential” “simultaneous” creep damage damage accumulation); accumulation); (d) (creep) creep-fatigue‐fatigue interaction (due to “consequential” creep damage accumulation). interactioninteraction (due (due to “simultaneous” to “consequential” creep creep damage damage accumulation). accumulation).

Figure 2. Influence of hold time on the cyclic/hold creep‐fatigue endurance of 1CrMoV steel at 550 °C FigureFigure 2. 2.Inﬂuence Influence of of hold hold time time on on the the cyclic/hold cyclic/hold creep creep-fatigue‐fatigue endurance endurance of of 1CrMoV 1CrMoV steel steel at at550 550 °C˝ C where crack development is identified as being pure creep (C), pure fatigue (F) or creep‐fatigue (CF). where crack development is identified as being pure creep (C), pure fatigue (F) or creep‐fatigue (CF). whereLCF crack = Low development Cycle Fatigue. is identiﬁed as being pure creep (C), pure fatigue (F) or creep-fatigue (CF). LCFLCF = Low= Low Cycle Cycle Fatigue. Fatigue. 2 2 7758 Materials 2015, 8, 7757–7769

Materials 2015, 8, page–page 2.2. CreepMaterials Ductility 2015, 8, page–page 2.2. Creep Ductility Creep ductility is inﬂuential in determining the extent of creep-fatigue interaction (Figure3). 2.2. Creep Ductility When creepCreep ductility ductility is is high, influential creep in voids determining typically the tendextent to of form creep‐ predominantlyfatigue interaction at (Figure inclusions 3). as a consequenceWhenCreep creep ofductility ductility particle is is influential matrixhigh, creep decohesion in voidsdetermining typically (Figure the tend extent4a), to creep formof creep predominantly dominated‐fatigue interaction cracking at inclusions (Figure tends as 3). to a be consequence of particle matrix decohesion (Figure 4a), creep dominated cracking tends to be transgranularWhen creep rather ductility than is intergranularhigh, creep voids (Figure typically5a), tend and to creep-fatigue form predominantly failure at is inclusions due to damage as a transgranularconsequence ofrather particle than matrix intergranular decohesion (Figure (Figure 5a), 4a),and creepcreep ‐fatiguedominated failure cracking is due tends to damage to be summation with insigniﬁcant interaction (linear damage summation, see inset with reference to transgranularsummation with rather insignificant than intergranular interaction (Figure (linear 5a),damage and summation,creep‐fatigue see failure inset iswith due reference to damage to FigureFiguresummation6). When 6). When with creep creepinsignificant ductility ductility is interaction low,is low, creep creep (linear cavities cavities damage typicallytypically summation, form form at atsee grain grain inset boundaries, boundaries,with reference and and the to the extentextentFigure of creep-fatigue of6). creep When‐fatigue creep interaction interactionductility can is can low, be be high creephigh (Figure (Figurecavities5 5b).b). typically form at grain boundaries, and the extent of creep‐fatigue interaction can be high (Figure 5b).

Figure 3. Influence of creep ductility on the cyclic/hold creep‐fatigue endurance of 1CrMoV steel Figure 3. Inﬂuence of creep ductility on the cyclic/hold creep-fatigue endurance of 1CrMoV steel atFigure 550 °C. 3. Influence of creep ductility on the cyclic/hold creep‐fatigue endurance of 1CrMoV steel at 550 ˝C. at 550 °C.

Figure 4. Creep damage development: (a) transgranular due to particle‐matrix decohesion in creep ductile 2CrMoNiWV steel at 550 °C; (b) intergranular in a 1CrMoV steel at 565 °C; (c) intergranular FigureFigure 4. Creep 4. Creep damage damage development: development: ( a()a) transgranular transgranular due due to to particle particle-matrix‐matrix decohesion decohesion in creep in creep inductile a 9CrMoVNb 2CrMoNiWV steel steelat 600 at °C; 550 (d °C;) intergranular (b) intergranular in a NiCr23Co12Mo in a 1CrMoV steel alloy at at 565 700 °C; °C. ( c) intergranular ductile 2CrMoNiWV steel at 550 ˝C; (b) intergranular in a 1CrMoV steel at 565 ˝C; (c) intergranular in a 9CrMoVNb steel at 600 °C; (d) intergranular in a NiCr23Co12Mo alloy at 700 °C. in a 9CrMoVNb steel at 600 ˝C; (d) intergranular in a NiCr23Co12Mo alloy at 700 ˝C.

3 3

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FigureFigure 5. Influence 5. Inﬂuence of of creep creep-ductility‐ductility on on creep-fatiguecreep‐fatigue cracking cracking mechanisms. mechanisms. Figure 5. Influence of creep‐ductility on creep‐fatigue cracking mechanisms.

Figure 6. Generic flow diagram representing creep‐fatigue crack initiation assessment procedure. Figure 6. Generic ﬂow diagram representing creep-fatigue crack initiation assessment procedure. 4

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Figure 6. Generic flow diagram representing creep‐fatigue crack initiation assessment procedure.

4 Materials 2015, 8, 7757–7769

In practice, the situation is not always as simple as this. Intergranular creep damage development is not restricted to low creep ductility (creep brittle) materials, that is, with creep-rupture ductility, εR, of less than approximately ﬁve percent. While this is typical for precipitation-strengthened ferritic steels (Figure4b,c), it can also occur in higher ductility solid solution strengthened alloys (e.g., Figure4d). It is therefore important to be familiar with the pedigree and creep response of a material when making judgments concerning its creep-fatigue behaviour.

2.3. Advanced Martensitic Steels The development of creep damage in the more creep resistant of the advanced 9/11%Cr martensitic steels is not limited to the prior austenite grain boundaries and is not always as clear as is shown in Figure4c. Often requiring very careful examination, very ﬁne creep cavities can be observed to form also on lath and packet boundaries in this class of steel. This being the case, creep-fatigue cracking can appear to be transgranular, although crack development is actually along alternative creep-damaged boundaries [5]. Indeed, in this class of steel, the microstructural evidence appears to indicate that creep-fatigue deformation interactions are more important than creep-fatigue damage interactions [2,5–7]. Precipitation-strengthened steels such as the advanced 9/11%Cr martensitic steels typically cyclic soften during fatigue loading as a consequence of dynamic recovery and the development of a sub-grain structure. Sub-grains of a similar size develop during creep deformation, again as the consequence of dynamic recovery. The sizes of sub-grains that develop due to creep-fatigue loading are much greater [6,7], and provide a means of quantifying the extent of deformation interaction in steels that do not always exhibit classical evidence of creep-fatigue damage interaction [7]. This type of familiarity with material condition is invaluable for effective and efﬁcient failure diagnosis.

3. Mechanical Analysis of Creep-Fatigue Cracking

3.1. Crack Initiation While there are a number of published and in-house procedures available to assess the risk of creep-fatigue crack initiation in high-temperature components (e.g., [8–11]), most can be represented by the generic ﬂow diagram shown in Figure6. An important step in any creep-fatigue assessment procedure is a determination of the state of stress and strain at the critical location in the component. This requires a knowledge of the external forces and thermal transients experienced by the structure during service operation, and representations of the cyclic and creep deformation properties of the material(s) of construction in terms of model constitutive equations (e.g., [12]). Irrespective of whether the local stress-strain state is determined by approximate analytical solutions or ﬁnite element analysis (FEA), the constitutive model options are generally the same. With this information, fatigue and creep damage fractions can be determined. Fatigue damage fraction is commonly determined in terms of cycle number fraction, N/Ni(∆ε), where N/Ni(∆ε) can be the low cycle fatigue (LCF) or the cyclic/hold creep-fatigue test crack initiation endurance (depending on procedure). The method of determination of creep damage fraction can depend on whether it is accumulated due to primary (directly applied) or secondary (self-equilibrating) loading. Regardless of the approach adopted, the material properties required are derived from the results of conventional creep-rupture tests. With a knowledge of the fatigue and creep damage fractions accumulated per cycle at the component critical location, it is then possible to determine the creep-fatigue crack initiation endurance; for example, by means of a damage summation construction (Figure6, also [13]). Typically such diagrams are constructed from the results of cyclic/hold (LCF with hold time) creep-fatigue tests or thermo-mechanical fatigue (TMF) tests, which indicate the extent of any creep-fatigue interaction of the material of interest under precisely known thermo-mechanical boundary conditions (e.g., insets in Figures4 and5).

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3.2. Crack Development Materials 2015, 8, 7757–7769 Crack development due to creep-fatigue loading may occur (i) within the confines of a cyclic plastic zoneMaterials (when 2015 the, 8, page–page crack is physically small, i.e., <~5 mm, more typically <~2 mm) or (ii) beyond the limits3.2. Crack of the Development size of the cyclic plastic zone, rp (when the crack is long and loading is nominally 3.2. Crack Development elastic), FigureCrack development7. due to creep-fatigue loading may occur (i) within the conﬁnes of a cyclic plastic zoneCrack (when development the crack isdue physically to creep‐fatigue small, loadingi.e., <~5 may mm, occur more (i) within typically the confines <~2 mm) of a or cyclic (ii) beyond plastic zone (when the crack is physically small, i.e., <~5 mm, more typically <~2 mm) or (ii) beyond the limits of the size of the cyclic plastic zone, rp (when the crack is long and loading is nominally the limits of the size of the cyclic plastic zone, rp (when the crack is long and loading is nominally elastic),elastic), Figure 7Figure. 7.

(a) (b)

Figure 7. Schematic representation of (a) short-crack growth within a cyclic plastic zone; and (b) long (a) (b) crack growth beyond the boundary of a cyclic plastic zone. Figure 7. Schematic representation of (a) short‐crack growth within a cyclic plastic zone; and (b) long Figure 7. Schematic representation of (a) short-crack growth within a cyclic plastic zone; and (b) long crack growth beyond the boundary of a cyclic plastic zone. In thecrack long growth-crack beyond regime the boundary (Figure of 7 ab), cyclic creep plastic-fatigue zone. crack growth is typically represented by fatigue and creepIn thecrack long growth‐crack regime rate (Figure characteristics 7b), creep‐fatigue [11,14 crack], i.e. growth, is typically represented by Infatigue the long-crack and creep crack regime growth (Figure rate characteristics7b), creep-fatigue [11,14], cracki.e., growth is typically represented by (푑푎/푑푁) = (푑푎/푑푁) + (푑푎/푑푁) (1) fatigue and creep crack growth rate/ characteristicsCF / [11,14 F/], i.e., C (1) where where pda{dNq “ pda{dNq ` pda{dNq (1) /CF , , F mC (2) (푑푎/푑푁)F = 퐴(푇, 푣, 푡h) · (훥퐾eq) (2) where and m p { q “ p q ¨ and da dN F A T, v, th ∗ ∆ Keq (2) / / (3) 푡h and ` ∗ 훾 ˘ (푑푎/푑푁)C = ∫t 퐷(휀푅) · (퐶 ) · 푑푡/푣 (3) Creep‐fatigue‐oxidation interaction is accommodatedh through the A(T, v, th) function in 0 * γ Equation (2) which accounts forpda any{dN influenceqC “ of DpriorpεR creepq ¨ pC andq ¨ oxidationdt{v damage at the crack tip, (3) 0 Creep-andfatigue may -beoxidation determined interactionexperimentally is(e.g., accommodatedż Figure 8) [14]. For steady through‐state creep the conditionsA(T, v, aheadth) function in Creep-fatigue-oxidation interaction is accommodated through the A(T, v, t ) function in Equation (2of) whichthe crack accounts tip, the forcreep any rate influence dependent of Cprior* parameter creep andprovides oxidation an acceptable damage sizeh at and the crack tip, Equationgeometry (2) which‐independent accounts function for any for correlating inﬂuence creep of prior crack creepgrowth and rates oxidation for long cracks damage [15]. at the crack and may be determined experimentally (e.g., Figure 8) [14]. For steady-state creep conditions ahead tip, and may be determined experimentally (e.g., Figure8)[14]. For steady-state creep conditions of theahead crack of tip, the the crack creep tip, rate the creepdependent rate dependent C* parameterC* parameter provides provides an acceptable an acceptable size and size geometry and - independgeometry-independentent function for correlating function for correlatingcreep crack creep growth crack rates growth for rateslong for cracks long [ cracks15]. [15].

Figure 8. Long crack cyclic/hold creep‐fatigue crack growth test data for 2¼CrMo cast turbine steel at 538/565 °C. N + T = Normalised and Tempered.

FigureFigure 8. Long 8. Long crack crack cyclic/hold cyclic/hold creep creep-fatigue-fatigue crack crack growth growth test test data data for 2¼CrMo2¼ CrMo cast cast turbine turbine steel steel at 538/565at 538/565 °C. N +˝ C.T = N Normalised + T = Normalised and Tempered. and Tempered.

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6 Materials 2015, 8, 7757–7769

Materials 2015, 8, page–page In the short crack regime (Figure7a), creep-fatigue crack growth rates may be expressed as a function ofIn totalthe short strain crack range, regime as in(Figure Equation 7a), creep (4) [16‐fatigue–19], althoughcrack growth other rates correlating may be expressed parameters as a may be employedfunction of [19 total]. strain range, as in Equation (4) [16–19], although other correlating parameters may be employed [19]. 1 b Q ´2 da{dN “ B ¨ p∆εq ¨ a ¨ p1 ´ DCq (4) (4) / B Δ 1 Typically in Equation (4), Q = 1. For advanced martensitic steels, it has been shown that replacing Typically in Equation (4), Q = 1. For advanced martensitic steels, it has been shown that replacing DC by a microstructural condition parameter (Φ) can be more appropriate [7]. In this case, Φ is a DC by a microstructural condition parameter (Φ) can be more appropriate [7]. In this case, Φ is a function of the sub-grain size, and reﬂects the deformation state due to creep-fatigue loading (see function of the sub‐grain size, and reflects the deformation state due to creep‐fatigue loading Section(see 2.3 Section). An 2.3). example An example of short-crack of short‐crack creep-fatigue creep‐fatigue crack crack growth growth data data for for a cast cast 1¼CrMoV 1¼CrMoV steel steel at ˝ 550 Cat is550 shown °C is shown in Figure in Figure9. Data 9. Data for martensitic for martensitic steels steels are are given given in in [ 7[7,19].,19].

Figure 9. Comparison of short crack growth rates after 0.5 mm crack extension from notch root in Figure 9. Comparison of short crack growth rates after 0.5 mm crack extension from notch root in large SENB feature specimen creep‐fatigue tests on cast 1¼CrMoV steel at 550 °C. large single edge notched bend (SENB) feature specimen creep-fatigue tests on cast 1¼CrMoV steel at ˝ 5504. PostC.‐Test Examination An effective quantitative interpretation of the evidence associated with a component failure 4. Post-Test Examination requires familiarity with the microstructural and damage conditions of the constituent material(s) Anunder effective known quantitativeand well‐controlled interpretation loading conditions. of the evidence For this associated reason alone, with it ais componentimportant that failure requireslaboratory familiarity mechanical with thetest specimens microstructural are routinely and damage subjected conditions to systematic of post the‐test constituent examination. material(s) under knownA classic and example well-controlled is the classification loading of conditions. fatigue fracture For appearance this reason in alone, terms of it K ismean important, ΔK, and that laboratorytemperature. mechanical The collection test specimens of this knowledge are routinely as an subjected integral part to systematic of a fatigue post-test crack growth examination. testing campaign enables rapid indications of loading conditions responsible for service failures (e.g., [20]), A classic example is the classiﬁcation of fatigue fracture appearance in terms of K , ∆K, and in particular those at temperatures where crack surface oxidation is not a complicating issue.mean This temperature.attention to The detail collection can reveal of the this appearance knowledge of beachmarks as an integral associated part of with a fatigue different crack types growth of loading testing campaigntransient enables which rapid can be indications invaluable ofinformation loading conditions when beachmark responsible analysis for is servicebeing used failures to track (e.g., the [ 20]), in particularhistory of those sub‐critical at temperatures crack propagation where during crack surfaceservice to oxidation identify the is not incident a complicating responsible issue.for the This attentioninitiation to detail of cracking. can reveal the appearance of beachmarks associated with different types of loading transientNeedless which can to besay, invaluable the concept information of post‐test when examination beachmark is not analysis always isso beingrevealing used at tohigher track the historytemperatures. of sub-critical The crackcoverage propagation of important during features service with the to identifyproducts theof oxidation incident can responsible disguise the for the initiationexplanation of cracking. for failure, although oxide thickness measurements provide a useful indication of time Needlessof exposure to at say,temperature the concept [21–23], of and post-test thereby examinationthe basis for oxide is not dating. always so revealing at higher temperatures.4.1. Oxide Dating The coverage of important features with the products of oxidation can disguise the explanation for failure, although oxide thickness measurements provide a useful indication of time of exposureMeasurements at temperature from [ 21the–23 post], and‐test thereby examination the basis of specimens for oxide tested dating. under known conditions provide invaluable evidence for subsequent failure diagnosis. One example of this is the collection of 4.1. Oxideoxidation Dating data which can then be used to form the basis of an oxide dating protocol and to determine growth law constants, e.g., Measurements from the post-test examination of specimens tested under known conditions (5) provide invaluable evidence for subsequent failure diagnosis. One example of this is the collection of oxidation data which can then be used to form the basis of an oxide dating protocol and to determine growth law constants, e.g., 7 2 x “ kp¨ t (5)

7763 Materials 2015, 8, 7757–7769 Materials 2015, 8, page–page where kkpp isis a afunction function of ofmaterial, material, temperature temperature and andsurface surface condition. condition. While Whilethe influence the inﬂuence of surface of surfaceconditions conditions such as roughness such as roughness and the states and of the activity states and of stress/strain activity and are stress/strain significant, areuse of signiﬁcant, upper‐bound use ofrelationships upper-bound of the relationships type shown of in the Figure type 10 shown are invaluable in Figure for10 aredating invaluable purposes, for providing dating purposes, there is providingevidence (in there the isform evidence of an outer (in the haematite form of an layer) outer that haematite the oxide, layer) whose that thickness the oxide, is whoseto be measured, thickness is tointact. be measured, is intact.

1E-04 AIR

Fe2O3 1E-05 Fe3O4

(FeCr)3O4 metal

1E-06 Fe2O3

Fe3O4

metal 1E-07 /h 2 , mm

p 5%Cr k 1E-08 Pinder

CMn Pinder 1E-09 11/12%Cr Holdsworth Fe2O3 1E-10 Fe3O4 (FeCr)3O4 metal 650oC 575oC 500oC 1E-11 0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 1/T, K-1

Figure 10. The influence inﬂuence of chromium content on oxidation kinetics for a range of power plant steels in air [[23]23] (Insets indicate oxidation mechanisms forfor thethe low-low‐ andand high-alloyhigh‐alloy steels)steels)..

The results of laboratory specimen post-testpost‐test examination are most effective for failure diagnosis when quantiﬁed,quantified, and the following sections review the way in which this can be achieved for creep, fatigue, and creep-fatiguecreep‐fatigue damage.

4.2. Creep Damage Assessment Creep damage condition can be represented in terms of feature type, development state, or size.

4.2.1. Type Damage may may be simply be simply characterised characterised as either (i) as cavities either on grain/block/lath (i) cavities on boundaries grain/block/lath [24–26] or boundaries(ii) voids arising [24–26 from] or particle/matrix (ii) voids arising decohesion. from particle/matrix When material decohesion. creep ductility When is low material (Figure creep 5b), ductilityboundary is cavities low (Figure occur5 atb), a boundaryrelatively early cavities stage, occur thereby at a relativelyproviding earlya means stage, of assessing thereby providing remaining alife. means Creep of voids assessing forming remaining due to particle/matrix life. Creep voids decohesion forming generally due to do particle/matrix so late in life (Figure decohesion 5a), generallytypically in do creep so late ductile in life materials (Figure5a), when typically the ductility in creep is ductile almost materials exhausted. when The the particles ductility are is typically almost exhausted.inclusions and The carbides particles located are typically at intra inclusions‐granular and sites. carbides located at intra-granular sites.

4.2.2. Development Creep damage is is most most commonly commonly characterized characterized in in terms terms of of a quantity a quantity representing representing its itsextent extent or ordegree degree of ofdevelopment, development, e.g., e.g., by by a aclassification classification based based on on reference reference micrographs micrographs [24], [24], or or a simple density measurement of cavities/mm2 [25–27]. The latter has the advantage that it can be used to density measurement of cavities/mm2 [25–27]. The latter has the advantage that it can be used to quantify the density density of of one one or or both both types types of of damage damage defined defined above, above, in inparticular particular in inthe the vicinity vicinity of ofnon non-uniform‐uniform stress stress fields; fields; for for example, example, adjacent adjacent to to stress stress concentrations concentrations or crackingcracking [[28].28]. For boundary cavitation, cavity number is alternatively quantified by continuous cavity line length [25], or A‐parameter [26]. 7764 8 Materials 2015, 8, 7757–7769 boundary cavitation, cavity number is alternatively quantified by continuous cavity line length [25], or A-parameter [26].

4.2.3. Size Materials 2015, 8, page–page The characterisation of damage size may involve sizing of (i) the damage feature (e.g., cavity diameter);4.2.3. or Size (ii) the damage zone. In reality, the measurement of cavity/void size [27] is not widely practiced, primarilyThe characterisation because of damage the high size sensitivity may involve of sizing damage of (i) feature the damage diameter feature and (e.g., its cavity dependent parametersdiameter); on metallographic or (ii) the damage surface zone. In preparation. reality, the measurement A knowledge of cavity/void of microcrack size [27] length is not widely is required to practiced, primarily because of the high sensitivity of damage feature diameter and its dependent assign advanced damage categories [25]. Damage zones may be sized in terms of parameters of the parameters on metallographic surface preparation. A knowledge of microcrack length is required to type developedassign advanced in [28 ].damage categories [25]. Damage zones may be sized in terms of parameters of the type developed in [28]. 4.3. Fatigue Damage Assessment 4.3. Fatigue Damage Assessment Microstructurally short Stage I fatigue cracks typically extend along persistent slip bands [29] to a depthMicrostructurally of 1–2 grain diameters short Stage before I fatigue becoming cracks typically Stage extend II cracks along propagating persistent slip bands in a transgranular [29] to mannera normaldepth of to 1–2 the grain maximum diameters principal before becoming stress (Figure Stage 11II )[cracks30,31 propagating]. in a transgranular manner normal to the maximum principal stress (Figure 11) [30,31].

Figure 11. Schematic representation of fatigue crack development. Figure 11. Schematic representation of fatigue crack development. In Figure 11, reference is also made to physically short cracks, the maximum length of which Inmay Figure be defined 11, reference by a Kitagawa is also diagram made construction to physically [32], short e.g., ~250 cracks, μm for the 1CrMoV maximum rotor steel. length of which Typically on the surface of a part subjected to cyclic loading, many microstructurally short may be defined by a Kitagawa diagram construction [32], e.g., ~250 µm for 1CrMoV rotor steel. fatigue cracks are formed, a relatively small proportion of which will develop to become physically Typicallyshort cracks, on thedepending surface on of strain a part amplitude. subjected Also to depending cyclic loading, on strain many amplitude, microstructurally one or more short fatiguephysically cracks are short formed, fatigue a crack relatively will become small dominant, proportion extending of which to become will develop a long crack to become responsible physically short cracks,for failure depending [33]. This sort on of strain damage amplitude. distribution Alsocan be dependingquantified (e.g., on as strain crack densities amplitude, [34,35]). one or more physically short fatigue crack will become dominant, extending to become a long crack responsible 4.4. Creep‐Fatigue Damage Assessment for failure [33]. This sort of damage distribution can be quantified (e.g., as crack densities [34,35]). The assessment of creep‐fatigue damage has tended to focus on materials for which creep 4.4. Creep-Fatiguedamage is intergranular, Damage Assessment and for circumstances represented by Figure 1b–d (e.g., [34–37]). In these circumstances, intergranular damage may be quantified as a function of Lf [36] or Lf/Lt [34]. In both Thecases, assessment measurements of creep-fatigue are made away damage from the hasmain tended crack in to order focus to estimate on materials the homogeneous for which creep damagedamage is intergranular, due to creep, and without for circumstances interaction with representedmajor cracks. byCreep Figure‐fatigue1b–d damage (e.g., may [34– then37]). be In these circumstances,quantified intergranular as a function of damagecracked grain may boundary be quantified fraction and as asurface function crack of densityLf [36 [34].] or Lf/Lt [34]. In both cases, measurementsThe traditional view are made of creep away‐fatigue from damage the main development crack in order and tointeraction estimate involves the homogeneous the damagedevelopment due to creep, of transgranular without interaction fatigue cracking with from major the cracks. surface Creep-fatigueand intergranular damage creep damage may then be quantified as a function of cracked grain boundary9 fraction and surface crack density [34].

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The traditional view of creep-fatigue damage development and interaction involves the development of transgranular fatigue cracking from the surface and intergranular creep damage from sub-surfaceMaterials to 2015 the, 8 point, page–page where the intensity of grain boundary damage is sufficient to deflect crack propagation onto the grain boundaries (e.g., Figure1d) [35,38]. It is now appreciated that this type from sub‐surface to the point where the intensity of grain boundary damage is sufficient to deflect of creep-fatigueMaterials 2015 damage, 8, page–page interaction does not always occur for creep ductile alloys (e.g., Figure5), and thatcrack creep-fatigue propagation response onto the grain for theboundaries newer (e.g., advanced Figure 1d) 9/11%Cr [35,38]. It steels is now can appreciated be strongly that this influenced type of creep‐fatigue damage interaction does not always occur for creep ductile alloys (e.g., Figure 5), by both deformationfrom sub‐surface and to the damage point where interactions the intensity [2,6 ,of7]. grain boundary damage is sufficient to deflect andcrack that propagation creep‐fatigue onto response the grain for boundaries the newer advanced(e.g., Figure 9/11%Cr 1d) [35,38]. steels It can is now be strongly appreciated influenced that this by A good example of the development of creep-fatigue damage in a laboratory specimen of typeboth ofdeformation creep‐fatigue and damage damage interaction interactions does [2,6,7]. not always occur for creep ductile alloys (e.g., Figure 5), ˝ 1CrMoVand at 565 thatA good creepC is example‐fatigue shown responseof in the Figure development for 12the. newer Multiple of advanced creep microstructurally‐fatigue 9/11%Cr damage steels canin short a be laboratory strongly fatigue influenced specimen crack development byof occurs at1CrMoVboth the deformation surface, at 565 °C whileandis shown damage creep in Figure interactions damage 12. Multiple [2,6,7]. evolves microstructurally from the center short fatigue of the crack specimen. development When the occurs at the surface, while creep damage evolves from the center of the specimen. When the dominant fatigueA good crack example meets of the the development creep damage of creep zone‐fatigue advancing damage fromin a laboratory the axis, specimen interaction of occurs dominant fatigue crack meets the creep damage zone advancing from the axis, interaction occurs in in the way1CrMoV represented at 565 °C inis shown Figure in1 d.Figure 12. Multiple microstructurally short fatigue crack development theoccurs way at represented the surface, in whileFigure creep1d. damage evolves from the center of the specimen. When the dominant fatigue crack meets the creep damage zone advancing from the axis, interaction occurs in the way represented in Figure 1d.

FigureFigure 12. Creep-fatigue 12. Creep‐fatigue crack crack development development in in a 1CrMoV a 1CrMoV rotor rotor steel steelat 565 at°C. 565 ˝C.

It is important not to underestimate the influence of oxidation on creep‐fatigue crack Figure 12. Creep‐fatigue crack development in a 1CrMoV rotor steel at 565 °C. It isdevelopment. important While not oxidation to underestimate can enhance the the rate inﬂuence of cracking, ofit can oxidation also consume on any creep-fatigue microcrack crack development.developmentIt Whileis important to oxidation the point not whereto can underestimate enhance thermo‐mechanical the the rate influence ofcrack cracking, propagation of oxidation it can is entirely alsoon creep consume creep‐fatigue dominated any crack microcrack developmentdevelopment.(e.g., Figure to the 13). While point In such oxidation where cases, thermo-mechanical can strain enhance‐enhanced the rate oxidation of crackcracking, can propagation consume it can also all consume evidence is entirely any of microcrack creep dominated development and become detached by spalling due to large cyclic thermal transients. (e.g., Figuredevelopment 13). In to such the point cases, where strain-enhanced thermo‐mechanical oxidation crack propagation can consume is entirely all evidence creep dominated of microcrack (e.g., Figure 13). In such cases, strain‐enhanced oxidation can consume all evidence of microcrack development and become detached by spalling due to large cyclic thermal transients. development and become detached by spalling due to large cyclic thermal transients.

Figure 13. Creep dominated crack development in a 1CrMoV rotor steel (the upper and lower profiles are from two specimens following thermo‐mechanical fatigue testing under identical conditions: the upper one breaking open when cold (due to the high density of internal creep cavities); and the lower Figure 13. Creep dominated crack development in a 1CrMoV rotor steel (the upper and lower profiles Figure 13.oneCreep remaining dominated unbroken). crack development in a 1CrMoV rotor steel (the upper and lower proﬁles are from two specimens following thermo‐mechanical fatigue testing under identical conditions: the are fromupper two specimensone breaking followingopen when cold thermo-mechanical (due to the high10 density fatigue of internal testing creep under cavities); identical and the conditions: lower the upper oneone breaking remaining open unbroken). when cold (due to the high density of internal creep cavities); and the lower one remaining unbroken). 10

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It has already been acknowledged that microstructural evidence of a strong creep-fatigue interaction is not always only apparent in the form of physical damage (i.e., as cavities and cracking). For example, the strong deformation interaction exhibited by some advanced martensitic 9/11%Cr steels can be more readily revealed by examination of the sub-grain microstructure [6,7]. Familiarity with the metallurgical characteristics of the material of the failed component is therefore invaluable for effective and efﬁcient failure diagnosis.

5. Concluding Remarks Failure diagnosis invariably involves consideration of both the associated material condition and the results of a mechanical analysis of prior operating history. This review has focused on these aspects with particular reference to creep-fatigue failure diagnosis. Creep-fatigue cracking can be due to a spectrum of loading conditions ranging from pure cyclic to mainly steady loading with infrequent off-load transients. These require a range of mechanical analysis approaches, a number of which are reviewed. The effectiveness and efﬁciency of the diagnosis of failures due to creep-fatigue loading are enhanced by a familiarity with the characteristics of the material of the failed component which can come from the routine post-test examination of laboratory specimens. The concept of routine laboratory specimen post-test examination to quantitatively characterise the detail of deformation and damage accumulation under known and well-controlled loading conditions is strongly advocated, and illustrated with examples.

Conﬂicts of Interest: The author declares no conﬂict of interest.

Nomenclature

a Crack length A(T,ν,th) Constant in mid-∆K fatigue crack growth rate equation b Strain range exponent in short-crack creep-fatigue crack growth equation B' Constant in short-crack creep-fatigue crack growth equation C, F, CF Creep; Fatigue; Creep-fatigue C* Parameter characterising stress and strain rate ﬁelds at tip of crack in material deforming due to creep da/dN Total crack growth rate (per cycle) (da/dN)C, (da/dN)F Crack growth rate (per cycle) due to creep and fatigue respectively DC, DF Total creep damage fraction; Total fatigue damage fraction D(εR) Constant in creep crack growth law, dependent on creep-rupture ductility kp Parabolic oxide growth law constant K, ∆K Stress intensity factor; Range of stress intensity factor Keq Equivalent stress intensity factor (K with a plasticity correction, similar to J) LCF Low cycle fatigue Lf, Lt Cumulative length of cracked grain boundaries per unit length of section; Total length of grain boundaries in the same area (being characteristic of the grain size and shape) J Parameter characterising stress and strain ﬁelds at tip of crack in material deforming plastically m Exponent in mid-∆K fatigue crack growth rate equation N, Ni Number of cycles; Number of cycles to crack initiation N + T Normalised and tempered Q Crack size exponent in short-crack creep-fatigue crack growth rate equation rp Size of cyclic plastic zone

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SENB Single edge notched bend (specimen) t, th, tR Time; Hold time; Time to creep-rupture TMF Thermo-mechanical fatigue x Oxide thickness ε, ∆ε Strain; Strain range εR Creep-rupture ductility Φ Microstructural condition parameter γ C* exponent in creep crack growth law ν Frequency

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