Designation: E2760 − 16Standard Test Method forCreep-Fatigue Crack Growth Testing1This standard is issued under the fixed designation E2760; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the determination of creep-fatigue crack growth properties of nominally homogeneousmaterials by use of pre-cracked compact type, C(T), testspecimens subjected to uniaxial cyclic forces. It concernsfatigue cycling with sufficiently long loading/unloading ratesor hold-times, or both, to cause creep deformation at the cracktip and the creep deformation be responsible for enhancedcrack growth per loading cycle. It is intended as a guide forcreep-fatigue testing performed in support of such activities asmaterials research and development, mechanical design, pro-cess and quality control, product performance, and failureanalysis. Therefore, this method requires testing of at least twospecimens that yield overlapping crack growth rate data. Thecyclic conditions responsible for creep-fatigue deformation andenhanced crack growth vary with material and with tempera-ture for a given material. The effects of environment such astime-dependent oxidation in enhancing the crack growth ratesare assumed to be included in the test results; it is thus essentialto conduct testing in an environment that is representative ofthe intended application.1.2 Two types of crack growth mechanisms are observedduring creep/fatigue tests: (1) time-dependent intergranularcreep and (2) cycle dependent transgranular fatigue. Theinteraction between the two cracking mechanisms is complexand depends on the material, frequency of applied force cyclesand the shape of the force cycle. When tests are planned, theloading frequency and waveform that simulate or replicateservice loading must be selected.1.3 Two types of creep behavior are generally observed inmaterials during creep-fatigue crack growth tests: creep-ductileand creep-brittle (1)2. For highly creep-ductile materials thathave rupture ductility of 10 % or higher, creep strains dominateand creep-fatigue crack growth is accompanied by substantialtime-dependent creep strains near the crack tip. In creep-brittlematerials, creep-fatigue crack growth occurs at low creepductility. Consequently, the time-dependent creep strains arecomparable to or less than the accompanying elastic strainsnear the crack tip.1.3.1 In creep-brittle materials, creep-fatigue crack growthrates per cycle or da/dN, are expressed in terms of themagnitude of the cyclic stress intensity parameter, ∆K. Thesecrack growth rates depend on the loading/unloading rates andhold-time at maximum load, the force ratio, R, and the testtemperature (see Annex A1 for additional details).1.3.2 In creep-ductile materials, the average time rates ofcrack growth during a loading cycle, (da/dt)avg, are expressedas a function of the average magnitude of the Ctparameter,(Ct)avg(2).NOTE 1—The correlations between (da/dt)avgand (Ct)avghave beenshown to be independent of hold-times (2, 3) for highly creep-ductilematerials that have rupture ductility of 10 percent or higher.1.4 The crack growth rates derived in this manner andexpressed as a function of the relevant crack tip parameter(s)are identified as a material property which can be used inintegrity assessment of structural components subjected tosimilar loading conditions during service and life assessmentmethods.1.5 The use of this practice is limited to specimens and doesnot cover testing of full-scale components, structures, orconsumer products.1.6 This practice is primarily aimed at providing the mate-rial properties required for assessment of crack-like defects inengineering structures operated at elevated temperatures wherecreep deformation and damage is a design concern and aresubjected to cyclic loading involving slow loading/unloadingrates or hold-times, or both, at maximum loads.1.7 This practice is applicable to the determination of crackgrowth rate properties as a consequence of constant-amplitudeload-controlled tests with controlled loading/unloading rates orhold-times at the maximum load, or both. It is primarilyconcerned with the testing of C(T) specimens subjected touniaxial loading in load control mode. The focus of theprocedure is on tests in which creep and fatigue deformationand damage is generated simultaneously within a given cycle.It does not cover block cycle testing in which creep and fatigue1This test method is under the jurisdiction of ASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of Subcommittee E08.06 on CrackGrowth Behavior.Current edition approved Nov. 1, 2016. Published January 2017. Originallyapproved in 2010. Last previous edition approved in 2010 as E2760–10ɛ2. DOI:10.1520/E2760-16.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1damage is generated sequentially. Data which may be deter-mined from tests performed under such conditions may char-acterize the creep-fatigue crack growth behavior of the testedmaterials.1.8 This practice is applicable to temperatures and hold-times for which the magnitudes of time-dependent inelasticstrains at the crack tip are significant in comparison to thetime-independent inelastic strains. No restrictions are placedon environmental factors such as temperature, pressure,humidity, medium and others, provided they are controlledthroughout the test and are detailed in the data report.NOTE 2—The term inelastic is used herein to refer to all nonelasticstrains. The term plastic is used herein to refer only to time-independent(that is non-creep) component of inelastic strain.1.9 The values stated in SI units are to be regarded asstandard. The inch-pound units in parentheses are for informa-tion only.1.10 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE83 Practice for Verification and Classification of Exten-someter SystemsE139 Test Methods for Conducting Creep, Creep-Rupture,and Stress-Rupture Tests of Metallic MaterialsE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE220 Test Method for Calibration of Thermocouples ByComparison TechniquesE399 Test Method for Linear-Elastic Plane-Strain FractureToughness KIcof Metallic MaterialsE467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing SystemE647 Test Method for Measurement of Fatigue CrackGrowth RatesE1457 Test Method for Measurement of Creep CrackGrowth Times in MetalsE1823 Terminology Relating to Fatigue and Fracture TestingE2714 Test Method for Creep-Fatigue Testing3. Terminology3.1 Terminology related to fatigue and fracture testingcontained in Terminology E1823 is applicable to this testmethod. Additional terminology specific to this standard isdetailed in section 3.3. For clarity and easier access within thisdocument some of the terminology in Terminology E1823relevant to this standard is repeated below (see TerminologyE1823, for further discussion and details).3.2 Definitions:3.2.1 crack-plane orientation—direction of fracture or crackextension relation to product configuration. This identificationis designated by a hyphenated code with the first letter(s)representing the direction normal to the crack plane and thesecond letter(s) designating the expected direction of crackpropagation.3.2.2 crack size, a [L]—principal lineal dimension used inthe calculation of fracture mechanics parameters for through-thickness cracks.3.2.2.1 Discussion—In the C(T) specimen, a is the averagemeasurement from the line connecting the bearing points offorce application. This is the same as the physical crack size, apwhere the subscript p is always implied.3.2.2.1 original crack size, ao[L]—the physical crack sizeat the start of testing.3.2.3 specimen thickness, B [L]—distance between the par-allel sides of the specimen.3.2.4 net thickness, BN[L]—the distance between the rootsof the side-grooves in side-grooved specimens.3.2.5 specimen width, W [L]—the distance from a referenceposition (for example, the front edge of a bend specimen or theforce line of a compact specimen) to the rear surface of thespecimen.3.2.6 force, P [F]—the force applied to a test specimen or toa component.3.2.7 maximum force, Pmax[F]—in fatigue, the highestalgebraic value of applied force in a cycle. By convention,tensile forces are positive and compressive forces are negative.3.2.8 minimum force, Pmin[F]—in fatigue, the lowest alge-braic value of applied force in a cycle. By convention, tensileforces are positive and compressive forces are negative.3.2.9 force ratio (also stress ratio), R— in fatigue, thealgebraic ratio of the two loading parameters of a cycle. Themost widely used ratio is as follows:R 5minimum loadmaximum load5PminPmax(1)3.2.10 force range, ∆P [F]—in fatigue loading, the alge-braic difference between the successive valley and peak forces(positive range or increasing force range) or between succes-sive peak and valley forces (negative or decreasing forcerange). In constant amplitude loading, the range is given asfollows:∆P 5 Pmax2 Pmin(2)3.2.11 stress intensity factor, K, K1,K2,K3,KI,KII,KIII[FL-3/2]—the magnitude of the mathematically ideal crack tipstress field (a stress-field singularity) for a particular mode in ahomogeneous, linear-elastic body.3.2.11.1 Discussion—For a C(T) specimen subjected toMode I loading, K is calculated by the following equation:K 5P~BBN!1/2W1/2f~a/W! (3)f 5F21a/W~1 2 a/W!3/2G~0.88614.64~a/W! 2 13.32~a/W!2114.72~a/W!32 5.6~a/W!4! (4)3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.E2760 − 1623.2.12 maximum stress intensity factor, Kmax[FL-3/2]—infatigue, the maximum value of the stress intensity factor in acycle. This value corresponds to Pmax.3.2.13 minimum stress intensity factor, Kmin[FL-3/2]—infatigue, the minimum value of the stress intensity factor in acycle. This value corresponds to Pminwhen R 0 and is takento be 0 when R ≤ 0.3.2.14 stress-intensity factor range, ∆K [FL-3/2]—in fatigue,the variation in the stress-intensity factor during a cycle, that is:∆K 5 Kmax2 Kmin(5)3.2.15 yield strength, σYS[FL-2]—the stress at which thematerial exhibits a deviation from the proportionality of stressto strain at the test temperature. This deviation is expressed interms of strain.3.2.15.1 Discussion—For the purposes of this standard, thevalue of strain deviation from proportionality used for definingyield strength is 0.2 %.3.2.16 cycle—in fatigue, one complete sequence of valuesof force that is repeated under constant amplitude loading. Thesymbol N used to indicate the number of cycles.3.2.17 hold-time (th)—in fatigue, the amount of time in thecycle where the controlled test variable (for example, force,strain, displacement) remains constant with time.3.2.18 C*(t)—integral, C*(t) [FL-1T-1], a mathematicalexpression, a line or surface integral that encloses the crackfront from one crack surface to the other, used to characterizethe local stress- strain rate fields at any instant around the crackfront in a body subjected to extensive creep conditions.3.2.18.1 Discussion—The C*(t) expression for a two-dimensional crack, in the x-z plane with the crack front parallelto the z-axis, is the line integral (4, 5).C*~t! 5 *ΓSW*~t!dy 2 T·]u˙]xdsD(6)where:W*(t) = instantaneous stress-power or energy rate per unitvolume,Γ = path of the integral, that encloses (that is, contains)the crack tip contour,ds = increment in the contour path,T = outward traction vector on ds,u˙ = displacement rate vector at ds,x, y, z = rectangular coordinate system, andT·]u˙]xds= the rate of stress-power input into the area enclosedby Γ across the elemental length ds.3.2.18.2 Discussion—The value of C*(t) from this equationis path-independent for materials that deform according to aconstitutive law that may be separated into single-value timeand stress functions or strain and stress functions of the forms(1):ε˙ 5 f1~t!f2~σ! (7)ε˙ 5 f3~ε!f4~σ! (8)where, f1–f4represent functions of elapsed time, t, strain, εand applied stress, σ, respectively and ε˙ is the strain rate.3.2.18.3 Discussion—For materials exhibiting creep defor-mation for which the above equation is path-independent, theC*(t)-integral is equal to the value obtained from two, stressed,identical bodies with infinitesimally differing crack areas. Thisvalue is the difference in the stress-power per unit difference incrack area at a fixed value of time and displacement rate, or ata fixed value of time and applied force.3.2.18.4 Discussion—The value of C*(t) corresponding tothe steady-state conditions is called C*s. Steady-state is said tohave been achieved when a fully developed creep stressdistribution has been produced around the crack tip. Thisoccurs when secondary creep deformation characterized by Eq9 dominates the behavior of the specimen.ε˙ss5 Aσn(9)3.2.18.5 Discussion—This steady state in C* does not nec-essarily mean steady state crack growth rate. The latter occurswhen steady state damage develops at the crack tip.3.2.19 force-line displacement due to creep, elastic, andplastic strain V [L] —the total displacement measured at theloading pins (VLD) due to the initial force placed on thespecimen at any instant and due to subsequent crack extensionthat is associated with the accumulation of creep, elastic, andplastic strains in the specimen.3.2.19.1 Discussion—The force-line displacement associ-ated with just the creep strains is expressed as Vc.3.2.19.2 Discussion—In creeping bodies, the total displace-ment at the force-line, VFLD, can be partitioned into aninstantaneous elastic part Ve, a plastic part, Vp, and a time-dependent creep part, Vc(6).V Ve1Vp1Vc(10)The corresponding symbols for the rates of force-linedisplacement components shown in Eq 10 are given respec-tively as V˙,V˙e,V˙p,V˙c. This information is used to derive theparameters C* and Ct.3.2.20 Ctparameter, Ct[FL-1T-1]—parameter equal to thevalue obtained from two identical bodies with infinitesimallydiffering crack areas, each subjected to stress, as the differencein stress power per unit difference in crack area at a fixed valueof time and displacement rate or at a fixe