Designation: E1823 − 13Standard TerminologyRelating to Fatigue and Fracture Testing1This standard is issued under the fixed designation E1823; 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 terminology contains definitions, definitions ofterms specific to certain standards, symbols, and abbreviationsapproved for use in standards on fatigue and fracture testing.The definitions are preceded by two lists. The first is analphabetical listing of symbols used. (Greek symbols are listedin accordance with their spelling in English.) The second is analphabetical listing of relevant abbreviations.1.2 This terminology includes Annex A1 on Units andAnnex A2 on Designation Codes for Specimen Configuration,Applied Loading, and Crack or Notch Orientation.2. Referenced Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical TestingE23 Test Methods for Notched Bar Impact Testing of Me-tallic MaterialsE28 Test Methods for Softening Point of Resins Derivedfrom Pine Chemicals and Hydrocarbons, by Ring-and-Ball ApparatusE208 Test Method for Conducting Drop-Weight Test toDetermine Nil-Ductility Transition Temperature of Fer-ritic SteelsE338 Test Method of Sharp-Notch Tension Testing of High-Strength Sheet Materials (Withdrawn 2010)3E399 Test Method for Linear-Elastic Plane-Strain FractureToughness KIcof Metallic MaterialsE436 Test Method for Drop-Weight Tear Tests of FerriticSteelsE467 Practice for Verification of Constant Amplitude Dy-namic Forces in an Axial Fatigue Testing SystemE468 Practice for Presentation of Constant Amplitude Fa-tigue Test Results for Metallic MaterialsE561 Test Method forK-R Curve DeterminationE602 Test Method for Sharp-Notch Tension Testing withCylindrical Specimens (Withdrawn 2010)3E604 Test Method for Dynamic Tear Testing of MetallicMaterialsE606 Test Method for Strain-Controlled Fatigue TestingE647 Test Method for Measurement of Fatigue CrackGrowth RatesE739 Practice for StatisticalAnalysis of Linear or LinearizedStress-Life (S-N) and Strain-Life (ε-N) Fatigue DataE740 Practice for Fracture Testing with Surface-Crack Ten-sion SpecimensE813 Test Method for JIc,AMeasure of Fracture ToughnessE992 Practice for Determination of Fracture Toughness ofSteels Using Equivalent Energy MethodologyE1049 Practices for Cycle Counting in Fatigue AnalysisE1152 Test Method for Determining-J-R-CurvesE1221 Test Method for Determining Plane-Strain Crack-Arrest Fracture Toughness, KIa, of Ferritic SteelsE1290 Test Method for Crack-Tip Opening Displacement(CTOD) Fracture Toughness Measurement (Withdrawn2013)3E1304 Test Method for Plane-Strain (Chevron-Notch) Frac-ture Toughness of Metallic MaterialsE1450 Test Method for Tension Testing of Structural Alloysin Liquid HeliumE1457 Test Method for Measurement of Creep CrackGrowth Times and Rates in MetalsE1681 Test Method for Determining Threshold Stress Inten-sity Factor for Environment-Assisted Cracking of MetallicMaterialsE1737 Test Method forJ-Integral Characterization of Frac-ture Toughness (Withdrawn 1998)3E1820 Test Method for Measurement of Fracture ToughnessE1921 Test Method for Determination of ReferenceTemperature, To, for Ferritic Steels in the TransitionRangeE1942 Guide for Evaluating DataAcquisition Systems Usedin Cyclic Fatigue and Fracture Mechanics TestingE2207 Practice for Strain-Controlled Axial-Torsional Fa-tigue Testing with Thin-Walled Tubular SpecimensE2208 Guide for Evaluating Non-Contacting Optical StrainMeasurement Systems1This terminology is under the jurisdiction ofASTM Committee E08 on Fatigueand Fracture and is the direct responsibility of Subcommittee E08.02 on Standardsand Terminology.Current edition approved Feb. 1, 2013. Published May 2013. Originallyapproved in 1996. Last previous edition approved in 2012 as E1823 – 12e. DOI:10.1520/E1823-13.2For 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.3The last approved version of this historical standard is referenced onwww.astm.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E2298 Test Method for Instrumented Impact Testing ofMetallic MaterialsE2443 Guide for Verifying Computer-Generated Test Re-sults Through The Use Of Standard Data SetsE2472 Test Method for Determination of Resistance toStable Crack Extension under Low-Constraint ConditionsE2714 Test Method for Creep-Fatigue TestingE2760 Test Method for Creep-Fatigue Crack Growth TestingG15 Terminology Relating to Corrosion and Corrosion Test-ing (Withdrawn 2010)33. Terminology3.1 Alphabetical Listing of Principal Symbols Used in ThisTerminology:Symbol Terma crack depth, crack length, crack size, estimated cracksizeaeeffective crack sizeannotch lengthaooriginal crack sizeapphysical crack sizea/W normalized crack sizeA force ratio (Pa/Pm)ANnet-section areab remaining ligamentbooriginal uncracked ligamentB specimen thicknessBeeffective thicknessBNnet thickness2c surface-crack lengthC normalized K-gradientD cycle ratio (n/Nf)C*(t) C*(t) − Integralda/dN fatigue-crack-growth rateδ crack-tip opening displacement (CTOD)δd specimen gage length∆a crack extension, estimated crack extension∆K stress-intensity-factor range∆Kthfatigue-crack-growth threshold∆P force rangeεastrain amplitudeεininelastic strainεmmean forceG crack-extension forceGRcrack-extension resistanceH* specimen center of pin hole distanceΓ the path of the J-integralJJ-integralJIcplane-strain fracture toughnessJRcrack-extension resistancekffatigue notch factorkttheoretical stress concentration factor (sometimesabbreviated stress concentration factor)K, K1, K2, K3,KI, KII, KIIIstress-intensity factor (see mode)Kacrack-arrest fracture toughnessKcplane-stress fracture toughnessKEACstress intensity factor threshold for environment-assisted crackingKIaplane-strain crack-arrest fracture toughnessKIEACstress intensity factor threshold for plane strainenvironment-assisted crackingKIcplane-strain fracture toughnessKIvM, KIv, KIvjplane-strain (chevron-notch) fracture toughnessKmaxmaximum stress-intensity factorKminminimum stress-intensity factorKostress-intensity factor at crack initiationKRcrack-extension resistancen cycles enduredNffatigue lifeP forcePaforce amplitudeSymbol TermPmmean forcePMprecrack forcePmaxmaximum forcePminminimum forceq fatigue notch sensitivityr effective unloading slope ratiorccritical slope ratioryplastic-zone adjustmentR force ratio (Pmin/Pmax)s sample standard deviations2sample varianceS specimen spanSaforce amplitudeSffatigue limitSmmean forceSNfatigue strength at N cyclesσccrack strengthσNnominal (net-section) stressσrresidual strengthσssharp-notch strengthσTStensile strengthσx, σy, σznormal stresses (refer to )σYeffective yield strengthσYSyield strengthT specimen temperaturetTtransition timeτttotal cycle periodτxy,τyz, τzxshear stresses (refer to Fig. 1)u displacement in x directionv displacement in y direction2vmcrack-mouth opening displacementVcforce-line displacement due to creepw displacement in z directionW specimen widthY* stress-intensity factor coefficientY*mminimum stress-intensity factor coefficient3.2 Alphabetical Listing of Abbreviations Used:CMOD crack-mouth opening displacementCOD see CTODCTOD crack-tip opening displacementDT dynamic tearDWTT drop-weight tear testEAC environment-assisted crackingK-EE equivalent-energy fracture toughnessNTS notch tensile strengthPS part-through surfaceSCC stress corrosion crackingSZW stretch zone width3.3 Definitions—Each definition is followed by the desig-nation(s) of the standard(s) of origin. The listing of definitionsis alphabetical.alternating force—See loading amplitude.accuracy—The quantitative difference between a test mea-surement and a reference value. E467, E2208applied-K curve—a curve (a fixed-force or fixed-displacement crack-extension-force curve) obtained from afracture mechanics analysis for a specific configuration. Thecurve relates the stress-intensity factor to crack size andeither applied force or displacement.DISCUSSION—The resulting analytical expression is sometimes calleda K calibration and is frequently available in handbooks for stress-intensity factors. E647block—in fatigue loading, a specified number of constantamplitude loading cycles applied consecutively, or a spec-trum loading sequence of finite length that is repeatedidentically. E1823E1823 − 132C*(t) integral, C*(t)[FL−1T−1]—a mathematical expression,a line or surface integral that encloses the crack front fromone crack surface to the other, used to characterize the localstress-strain rate fields at any instant around the crack frontin a body subjected to extensive creep conditions. E1457,E2760DISCUSSION—1 The C*(t) expression for a two-dimensional crack, inthe x-z plane with the crack front parallel to the z-axis, is the lineintegral:C*~t! 5*ΓSW*~t!dy 2 T]u˙]xdsD(1)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 (see Fig. 2),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= rate of stress-power input into the area enclosed byΓ across the elemental length, ds.DISCUSSION—2 The value of C*(t) from this equation is path-independent for materials that deform according to a constitutive lawthat may be separated into single-value time and stress functions orstrain and stress functions of the forms:ε˙ 5 f1~t!f2~σ! or,ε˙ 5 f3~ε!f4~σ!Where f1–f4represent functions of elapsed time, t, strain, ε , andapplied stress, σ, respectively; ε˙ is the strain rate.DISCUSSION—3 For materials exhibiting creep deformation for whichthe above equation is path independent, the C*(t)-integral is equal tothe value obtained from two, stressed, identical bodies with infinitesi-mally differing crack areas. This value is the difference in thestress-power per unit difference in crack area at a fixed value of timeand displacement rate or at a fixed value of time and applied force.DISCUSSION—4 The value of C*(t) corresponding to the steady-stateconditions is called C*s. Steady-state is said to have been achievedwhen a fully developed creep stress distribution has been producedaround the crack tip. This occurs when secondary creep deformationcharacterized by the following equation dominates the behavior of thespecimen.ε˙ss5 AσnDISCUSSION—5 This steady state in C* does not necessarily meansteady state crack growth rate. The latter occurs when steady statedamage develops at the crack tip. For Test Method E1457 this behavioris observed as “tails” at the early stages of crack growth. Test MethodE1457 deals with this region as the initial crack extension perioddefined as time t0.2, measured for an initial crack growth of 0.2 mmafter first loading.NOTE 1—See definition of mode.FIG. 1 Customary Coordinate System and Stress on a Small Volume Element Located on the x Axis Just Ahead of the Crack FrontFIG. 2 Contour and Symbolism for Path-Independent Crack TipIntegralsE1823 − 133Ctparameter, Ct, [FL-1T-1]—parameter equal to the valueobtained from two identical bodies with infinitesimallydiffering crack areas, each subjected to stress, as the differ-ence in the stress-power per unit difference in crack area ata fixed value of time and displacement rate or at a fixed valueof time and applied force for an arbitrary constitutive law.E1457, E2760DISCUSSION—The value of Ctis path-independent and is identical toC*(t) for extensive creep conditions when the constitutive law de-scribed in Discussion 2 of C*(t)-integral definition applies.DISCUSSION—Under small-scale creep conditions, C*(t) is not path-independent and is related to the crack tip stress and strain fields onlyfor paths local to the crack tip and well within the creep zone boundary.Under these circumstances, Ctis related uniquely to the rate ofexpansion of the creep zone size . There is considerable experimentalevidence that the Ctparameter which extends the C*(t)-integralconcept into the small-scale creep and the transition creep regimecorrelates uniquely with creep crack growth rate in the entire regimeranging from small-scale to extensive creep regime.DISCUSSION—for a specimen with a crack subject to constant force, PCt5PV˙CBW~f /f!andf 5dfd ~a/W!circulation rate [L3T−1]—in fatigue testing, the volume rateof change of the environment chamber volume. E1823clipping—in fatigue spectrum loading, the process of decreas-ing or increasing the magnitude of all loads (strains) that are,respectively, above or below a specified level, referred to asclipping level; the loads (strains) are decreased or increasedto the clipping level (see Fig. 3). E1823compliance (LF−1]— the ratio of displacement increment toforce increment. E1820confidence interval—an interval estimate of a populationparameter computed so that the statement “the populationparameter included in this interval” will be true, on theaverage, in a stated proportion of the times such computa-tions are made based on different samples from the popula-tion. E1823confidence level (or coefficient)—the stated proportion of thetimes the confidence interval is expected to include thepopulation parameter. E1823confidence limits—the two statistics that define a confidenceinterval. E1823constant amplitude loading— in fatigue loading, a loading(straining) in which all of the peak forces (strains) are equaland all of the valley forces (strains) are equal. E1049constant life diagram— in fatigue, a plot (usually on rectan-gular coordinates) of a family of curves each of which is fora single fatigue life, N, relating stress amplitude, Sa, to meanFIG. 3 Clipping of Fatigue Spectrum LoadingE1823 − 134stress, Sm, or maximum stress, Smax, or both, to minimum stress, Smin.The constant life fatigue diagram is usually derived from a family ofS-N curves each of which represents a different stress ratio (A or R) fora 50 % probability of survival. E1820control force, Pm [F]—a calculated value of maximum forceto stipulate allowable precracking limits. E1820, E1921corrosion fatigue—the process by which fracture occursprematurely under conditions of simultaneous corrosion andrepeated cyclic loading at lower stress levels or fewer cyclesthan would be required in the absence of the corrosiveenvironment. G15counting method—in fatigue spectrum loading, a method ofcounting the occurrences and defining the magnitude ofvarious loading parameters from a load-time history; (someof the counting methods are: level crossing count, peakcount, mean crossing peak count, range