• • The area in which stresses are to be measured must be accessible to a rather bulky drilling or coring alignment device Preparation of the surface for strain gage adherence may induce residual stresses that introduce substantial error to the subsequent measurement (Ref 71) In conclusion, the drilling and ring coring methods are nearly nondestructive variations of the destructive mechanical stress relief techniques and require only rather simple equipment and instrumentation The state-ofthe-art is relatively well developed compared to many nondestructive methods, some of which require considerable research and development work before they will ever be suitable to general application in terms of alloys and stress field conditions Technological advancements in hole drilling and ring coring have largely been due to advancements in the more general areas of mechanical stress relief methods and research in new metal removal techniques for metal fabrication Indentation Methods For more than six decades, engineers and scientists have proposed the use of indentors, such as those used to perform hardness measurements, as a means to measure or detect surface residual stresses Kokubo in 1932 reported that stresses applied under bending load changed the apparent Vickers hardness values in carbon steel rolled sheets, both as rolled and annealed He showed that tensile stresses tended to decrease the apparent hardness, and compressive stresses tended to increase the hardness The stresses applied in tension and compression were sufficient to cause 0.3% strain Two decades later Sines and Carlson (Ref 72) proposed a method that required various amounts of external loads to be applied to the component in which residual stresses were to be measured while hardness measurements were made The loads were made to cause both tensile and compressive applied stresses The quality—that is, whether the residual stress was compressive or tensile—was then revealed by comparing the effect of the applied stress and whether the applied stress was tensile or compressive on the hardness measurement At about the same time, Pomey et al (Ref 73) proposed that residual stresses could be measured by pressing a ball-shaped penetrator into the component in which residual stresses were to be measured and establishing the relationship between the pressing load while it was progressively increased and the electrical resistance at the interface between the penetration and the component He maintained that a smaller decrease in electrical resistance indicated that portions of material under the ball were plastically yielding and that the corresponding load on the ball could be related to the existing residual stress Later, Chiang et al (Ref 74) provided a critique of several existing indentation analyses and proposed an interpretation of indentations exhibiting hemispherical plasticity Nevertheless, the applications illustrated in this article were focused on brittle materials and not metals There have been numerous papers published proposing various approaches to interpreting the indentation loads and shapes so as to estimate the residual stress field on the surface and near-surface regions of materials However, indentation methods have not earned the degree of confidence of XRD or hole drilling methods for general applications and, thus, are rarely applied Spot Annealing Another semidestructive method that has been proposed to measure residual stresses in metal surfaces is to reduce the residual stresses in a small volume by annealing the metal in the volume It has been proposed that this annealing be performed by intense laser light (Ref 52) This technique was envisioned to be similar to relief of residual stresses by removal of the material as accomplished in the hole drilling techniques However, as Cullity discussed (Ref 53), such localized heating would induce high surface residual tensile stresses in the heat-affected region, and this would be detrimental to the component being tested References cited in this section A.J Bush and F.J Kromer, “Residual Stresses in a Shaft after Weld Repair and Subsequent Stress Relief,” Paper No A-16 presented at Society for Experimental Stress Analysis (SESA) Spring Meeting, 1979 (Westport, CT), 1979 52 C.S Vikram, M.J Pedensky, C Feng, and D Englehaupt, Residual Stress Analysis by Local Laser Heating and Speckle-Correlation Interferometry, Exp Tech., Nov/Dec 1996, p 27–30 53 B.D Cullity, Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley Publishing Co., Inc., 1978, p 469–472 59 J Mathar, Determination of Initial Stresses by Measuring Deformation Around Drilled Holes, Arch Eisenhuttenwes., Vol 6, p 277–281 and Trans ASME, Vol 56 (No 4), 1934, p 249–254 60 “Determining Residual Stresses by the Hole Drilling Strain-Gage Method,” E 837, ASTM, 1983 61 H Wolf and D.C Sauer, “New Experimental Technique to Determine Residual Stresses in Large Turbine-Generator Components,” presented at the American Power Conf., (Chicago, IL), May 1974 62 H Wolf and W Bohn, Origin, Measurement and Assessment of Residual Stresses in Large Forging for Turbines and Generators, Arch Eisenhüttenwes., Vol 42 (No 7) 1971, p 509–511 (in German) 63 H Wolf, E Stucker, and H Nowack, “Investigations of Residual Stresses in the Turbine and Generator Industry,” Arch Eisenhuttenwes., Vol 48 (No 3), March 1977, p 173–178 64 J Lu and J.F Flavenot, “Applications of the Incremental Hole-Drilling Method for Measurement of Residual Stress Distributions—Experimental Techniques, paper presented at the Society for Experimental Mechanics (SEM) Spring Conference,” 5–10 June 1988 (Portland, OR), SEM 65 M.T Flaman and B.H Manning, Determination of Residual Stress Variation with Depth by the HoleDrilling Method, Exp Mech., Vol 25, 1985, p 205–207 66 R.A Kelsey, Measuring Nonuniform Residual Stresses by the Hole Drilling Method, Proc Society for Experimental Stress Analysis, Vol 14 (No 1), 1956, p 181–184 67 A.J Bush and F.J Kromer, Simplification of the Hole-Drilling Method of Residual Stress Measurement, ISA Transactions, Vol 12 (No 3), 1973, p 249–259 68 N.J Rendler and I Vigness, Hole-Drilling Strain-Gage Method of Measuring Residual Stress, Exp Mech., Vol (No 12), Dec 1966, p 577–586 69 J.W Dini, G.A Beneditti, and H.R Johnson, Residual Stresses in Thick Electro-deposits of a NickelCobalt Alloy, Exp.l Mech., February 1976, p 56–60 70 F Witt, F Lee, and W Rider, A Comparison of Residual Stress Measurements Using Blind-Hole, Abrasive-Jet and Treppaning Methods, Exp Tech., Vol 7, Feb 1983, p 41–45 71 P.S Prevey, “Residual Stress Distribution Produced by Strain Gage Surface Preparations,” 1986 SEM Conference on Experimental Mechanics, 1986 72 G Sines and R Carlson, “Hardness Measurements for the Determination of Residual Stresses,” ASTM Bulletin 180, Feb 1952, p 35–37 73 J Pomey, F Goratel, and L Abel, “Determination des Cartraintes Residuelles dans les Pieces Einentees,” Publication Scientifiques et Techniques du Ministere de l'air, 1950, p 263 74 S.S Chiang, D.B Marshall, and A.G Evans, The Response of Solids to Elastic/Plastic Indentations I: Stresses and Residual Stresses, J Appl Phys., Vol 53 (No 1), 1982, p 298–311 Residual Stress Measurements Clayton O Ruud, The Pennsylvania State University Nondestructive Procedures The methods for strain measurement described previously all measure the change in some dimension (strain) of the component produced by the removal of a finite volume of stressed metal from that component Thus, these methods measure the strain induced by removing material so as to perturb the residual stress field On the other hand, the nondestructive procedures measure a dimension in the crystal lattice of the metal or some physical parameter affected by the crystal lattice dimension Whenever a mechanical force resulting in stress that is less than the yield strength is placed on a solid metal component, that component distorts (strains) elastically That elastic strain results in a change in the atomic lattice dimension, and this dimension, or change, is measured by a nondestructive stress measurement procedure For example, the diffraction methods, x-ray and neutron, measure an actual crystal dimension, and this dimension can be related to the magnitude and direction of the stress that the metal is subject to, whether that stress is residual or applied Subsequently in this section, the following methods of nondestructive stress measurement are described: XRD, neutron diffraction, ultrasonic velocity, and magnetic Barkhausen noise X-ray diffraction techniques exploit the fact that when a metal is under stress (applied or residual), the resulting elastic strains cause the atomic planes in the metallic crystal structure to change their spacings X-ray diffraction can directly measure this interplanar atomic spacing; from this quantity, the total stress on the metal can then be obtained Because metals are composed of atoms arranged in a regular three-dimensional array to form a crystal, most metal components of practical concern consist of many tiny crystallites (grains), randomly oriented with respect to their crystalline arrangement and fused together to make a bulk solid When such a polycrystalline metal is placed under stress, elastic strains are produced in the crystal lattice of the individual crystallites In other words, an externally applied stress or one residual within the material, when below the yield strength of the material, is taken up by interatomic strain X-ray diffraction techniques can actually measure the interatomic spacings, which are indicative of the elastic strain in the specimen Stress values are obtained from these elastic strains in the crystals by knowing the elastic constants of the material and assuming that stress is proportional to strain, a reasonable assumption for most metals and alloys of practical concern An article published in Journal of Metals describes the XRD method and instrumentation in some detail References and 75 are excellent sources of practical, more detailed information on XRD stress measurement There are three basic techniques for measuring stresses, based on the XRD method They are the double exposure (or two-angle) technique (DET), the single exposure (or one-angle) technique (SET), and the sinsquare-psi (or multiangle) technique The angle of exposure referred to is that between the incident x-ray beam and the specimen surface normal It should be noted that in any XRD stress measurement technique, x-ray peaks in the far back-reflection range, that is, peaks with Bragg (θ) angles of near 90°, are much preferred because they show the greatest effect with a given amount of applied or residual stress This is illustrated in the following equation: (Eq 34) In Eq 34, θ1 is the Bragg angle of the planes diffracting at ψ1; θ2 is the Bragg angle of the planes diffracting at ψ2 In Fig 13, it can be seen that as θ1 increases, its cotangent decreases; therefore, a larger difference (2θ1 2θψ) would result from a given σφ to maintain an equality Fig 13 One-angle arrangement or the single exposure technique (SET) Ns is the specimen normal, and β is the angle that the incident beam makes with Ns Np1 and Np2 are the normals to the diffracting planes and respectively, and ψ1 and ψ2 are the angles between Ns, Np1, and Np2 respectively η is the angle between the incident beam and the diffracting plane normals Ro is the camera radius, and O is the point of incidence of the x-ray beam of the specimen and represent the diffracting planes at various attitudes to the specimen surface S1 and S2 are the measured parameters representing the distance from a reference point of known distance from the incident beam and the diffracted x-ray beam position S1 and S2 are directly related to the Bragg angles, θ1 and θ2 The stress being measured is parallel to the specimen surface and in the plane containing the x-ray source vector and the specimen surface normal, Ns For a residual stress measurement, the diffracting angle, θ, of interatomic planes of at least two different psi (ψ) angles with respect to the surface normal must be measured (Fig 13) These planes are crystallographically equivalent (same Miller indices, hkl) and in the unstressed state of the metal would have the same interatomic, d, spacing for the planes labeled and in Fig 13 (Ref 53, 76, 77) In a stressed material, however, the two or more orientations of diffracting planes are selected so that they are at different angles to the surface; thus their normals are at different (ψ) angles to the surface normal Then, depending on the angle of these planes to the stress vector, their interplanar atomic spacing is increased or decreased by varying amounts The most common sources of errors and misapplications in stress measurements by x-rays are related to stress constant selection, focusing geometry, diffracted peak location, and cold-working, crystallographic texture, grain size, microstructure, and surface condition The source, significance, and correction techniques for these errors are not elaborated on here; details may be found in an article by Ruud and Farmer (Ref 78) and (Ref 8) A point of interest in the error sources listed above concerns cold working and microstresses Microstresses are usually considered to be those manifested by strain variation across single metallic grain This strain variation is detected in the XRD method as broadening of the x-ray peak—a distinctly different phenomenon from the peak shift caused by residual stresses However, microstrain variation can be measured simultaneously with stress This microstrain phenomenon has been proposed as a means of judging cold work, dislocation density, and fatigue damage (Ref 79) Despite the facts that x-rays provide stress readings only to a depth of less than 0.025 mm (0.001 in.) and that the error sources listed above must be considered, the noncontact XRD method is presently the only timeproven, generally applicable, truly nondestructive method for measuring residual stresses Its reliability has been proved and documented by thousands of engineers and scientists over the past four decades beginning with the classic work of Bolstad et al at Boeing using x-ray film cameras (Ref 80) This documentation includes measurement of stresses in the Brooklyn Bridge (Ref 20) and tempering evaluation of carburized steels The Society of Automotive Engineers (SAE) considers the method of sufficient practical importance to have printed three handbook supplements on the subject (Ref 8), and another supplement is under revision Even so, this nondestructive technology has been largely restricted to the laboratory because of the general lack of knowledge regarding the state-of-the-art instruments and the limitations of the more widely known and available conventional scanning XRD equipment Instrumentation for bringing this technology into the field and manufacturing area has advanced rapidly in the last two decades, especially toward increased portability, compactness, and speed of operation As shown in Fig 14, instrumentation has been developed and is commercially available for stress measurement in situ on the inside diameter of 10 mm (4 in.) diameter pipe (Ref 39) Position sensitive x-ray detectors have been largely responsible for these improvements to both laboratory-based and field deployable residual stress measuring instruments (Ref 10, 21, 22, 39, 81, 82, and 83) Also, with the speed of data collection being less than 0.1 s with conventional x-ray tube sources in some applications, XRD stress measurement can be performed on moving components (Ref 12) Nevertheless, many engineers have been frustrated in applying XRD to residual stress measurement This has been largely due to crystallographers inexperienced in residual stress measurement, attempting to apply conventional scanning x-ray diffractometers and techniques to residual stress measurement For example, in conventional XRD analysis and crystallography, sharp resolution of the diffracted spectra is very beneficial However, in XRD stress measurement, the need to measure (ψ) angles that are not zero defocuses the beam, and attempts to refocus lead to significant error in the stresses read (Ref 84) In XRD stress measurement, what is more important than sharp resolution is the repeatable ability to measure the position of a defocused diffracted x-ray peak (Ref 85) Thus, it is recommended in most cases that XRD residual stress measurement be performed by trained technologists using x-ray instrumentation specifically designed and built for stress measurement, not conventional scanning diffractometers Software packages specifically for residual stress measurement used with conventional scanning diffractometers not in most cases eliminate the mechanical and focusing problems of applying these instruments to residual stress measurement It is necessary to mount the component (or specimen) in which stresses are to be measured on the conventional scanning diffractometer, which usually requires sectioning of the component and which complicates and adds error to the measurement procedure Fig 14 Photograph of a miniature x-ray diffractometer for the one angle technique arrangement of XRD stress measurement This device incorporates a Ruud-Barrett position sensitive scintillation detector and is capable of being inserted in a 101.60 mm (4 in.) inside diameter for measuring residual stress (Ref 39) Neutron diffraction (ND) allows measuring the elastic strains induced by residual stresses throughout the volume of relatively thick steel components with a spatial resolution as small as mm3 Such capability provides for the measurement of residual stress inside of components without the necessity of sectioning or layer removal Principal ND methods, like the XRD methods, measure the spacing between crystallographic planes in a component, and this spacing is affected by residual and applied stress The spacing between a selected set of crystallographic planes (φ) is related to the angle of incidence and diffraction of the neutron radiation, θ, which are equal, and the wavelength of the monochromatic radiation (λ) by Bragg's law: λ = d sin θ (Eq 35) The elastic strain, ε, induced by the residual stress perpendicular to the diffracting crystallographic plane then is related to d by: (Eq 36) where is the distance between the unstressed crystallographic planes If the orientation of principal stresses is known in the component, the stress in any principal direction may be calculated by: (Eq 37) where σA, σB, and σC are the principal stresses and εA, εB, and εC are the strains measured in the corresponding principal stress directions E and ν are the Young's modulus and Poisson's ratio, respectively If the principal stress directions are not known, strains in at least six directions must be measured to determine the residual stresses acting on the volume of material in which strains are being measured For residual stress measurement in most alloys, the unstressed spacing (do) between crystallographic planes at the exact point of strain measurement is not known and not easily measured This means that or θ0 in Eq 36 cannot be precisely established, and this leads to various degrees of error in the accuracy and precision of ND residual stress measurements This condition is aggravated by the fact that the elemental composition, and thus do, vary considerably within a component and markedly within the phase (e.g., martensite, austenite, and ferrite for steel) of the alloy at various locations Additional limitations are that the component must be brought to a nuclear reactor, each strain measurement requires over an hour, a single stress determination in one small volume of the component requires at least three strain measurements, and the measurements are very costly Nevertheless, the ND methods have been applied to residual stress measurements in weldments (Ref 86), cylindrical forgings (Ref 87), plastically deformed plate (Ref 88), rocket case forgings (Ref 86), and many other types of components Ultrasonic Velocity The principle underlying the measurement of stress and thus elastic strain by ultrasonic (acoustic) techniques is the phenomenon of an approximately linear change in ultrasound velocity with applied stress It has been shown that under certain restricted conditions, residual stress can be measured by exploiting this phenomenon Stress is measured by inducing a sound wave in the frequency of several megahertz in the metal specimen and measuring the time of flight or some other velocity-related parameter Because many other characteristics of metals besides stress-induced elastic strain affect velocity, their effect must be sorted out, but neither the technology nor the fundamental knowledge for such sorting is usually available The great interest in ultrasonic techniques for residual stress measurement stems from their promise for three-dimensional nondestructive measurements within the material Principle A number of velocity-related phenomena have been used in various methods to measure stress effects by ultrasound All utilize the deviation of the reaction of the metal from the linearity of Hooke's law of elasticity, σ = Mε, where σ = stress, ε = strain, and M = elastic modulus This has been referred to as the anharmonic property of the solid and may be represented by a power series σ = Mε + Cε2 + Dε3 + …, where C = third order anharmonic constant, D = fourth, and so on Most research done for stress measurement has used expressions in which terms past the third order constant, C, are dropped Of the several anharmonic property effects that may be used to measure stress, the following are probably the most exploited: velocity dependence on the elastic modulus; dispersion of frequency amplitudes in surface waves; birefringence of orthogonally polarized shear waves; and harmonic generation in surface waves A very simplified form of the anharmonic stress strain law has been written as σ = Mε + Cε2 and rewritten as σ = ε(M + Cε) The term in parentheses is approximately related to the velocity of sound as ρV2 M + Cε, where ρ is the density of the medium and V is the velocity of sound This may be approximately rewritten in terms of velocity dependence on strain as: (Eq 38) Then, to solve for strain, ε = 2(V ρ − 2M)/C (Ref 89) A simple view of the dependency of ultrasonic velocity on the elastic modulus and density may be shown by rewriting the equation πV2 = M + Cε in terms of V, differentiating and dividing by V to yield an expression for ΔV/V The result will readily show that a fractional change in elastic modulus or density would affect the velocity The density of metal, for which the Poisson ratio is near 0.3, obviously changes as a compressive or tensile stress is placed on the specimen, and it is reasonable that the speed of sound would then change Limitations and Applications Ultrasonic technology offers a number of types of wave modes in which to probe metals; these include bulk waves, such as longitudinal and shear, and surface waves, usually confined to Rayleigh type Each mode offers many unique parameters for extracting information As has been discussed, the primary effect of stress—induced strain on ultrasonic propagation in metals—is on velocity This may be detected in a number of ways, including measurements of wave velocity, shear wave birefringence, and dispersion However, there are other characteristics of metals that affect the ultrasonic velocity to the same degree as stress These include crystallographic texture, microstresses, multiple phases, coherent precipitates, composition gradients, and dislocation density and distribution Crecraft (Ref 90) discussed velocity effects, manifested as texture, induced birefringence, and the marked change seen with ultrasonic frequency He also reported birefringence due to cold work in nickel-steel specimens but did not attempt to separate the cold-work effects in terms of texture, dislocation density, and so on In the early 1950s, Bradfield and Pursey (Ref 91) and Pursey and Cox (Ref 92) reported showing the influence of small degrees of texture on ultrasonically measured elasticity in polycrystalline bars They showed how the true isotropic elastic constants can be determined by using measurements of both longitudinal and shear wave speeds along several directions They presented stereographic charts that illustrated the relationship between elastic behavior of cubic crystals and results of x-ray texture determinations McGonagle and Yun (Ref 93) noted the cold-work effects in an article comparing x-ray diffraction results with Rayleigh wave velocity measurements Boland et al (Ref 94) also recognized that other material properties can affect ultrasonic velocity and recommended that methods be developed to distinguish stress-induced velocity changes from those from other sources James and Buck (Ref 95) pointed out that since the third order elastic constants for most structural materials are not readily available from the literature, ultrasonic stress measurement must be calibrated relative to the particular material being investigated In the same paper they discounted the possible effect of mobile dislocations on the sound velocity in structural engineering metals with high yield strengths due to the short dislocation loop lengths prevalent However, they did mention that crystallographic preferred orientation (texture) during deformation or fatigue is capable of severely modifying the elastic constants on which the sound velocity depends Papadakis (Ref 96) noted marked velocity changes for ultrasonic waves in various steel microstructures, and Moro et al (Ref 97) measured the effect of microstructural changes caused by tempering on the ultrasonic velocity in low-alloy steel Tittman and Thompson (Ref 98) evaluated the near-surface hardness of case-hardened steel with Rayleigh waves; because hardness in this case is a combination of composition, microstress, and macrostress, the velocity change was due to a combined effect The temperature sensitivity of ultrasonic stress measurements has also been cited as an important source of error Salma et al (Ref 99, 100) proposed that this dependence be used as a means to measure stress but also noted the marked effect of dislocations and did not address a methodology of separating the stress from the dislocation effect Much of the work cited above is concerned with attempts to measure the effects of a variety of material properties on the changes in ultrasonic velocity However, there apparently is no comprehensive study that demonstrates the capability of quantitatively separating stress effects on ultrasonic propagation from other variables found in structural metals, such as dislocation density or crystallographic texture Furthermore, most of the studies cited observed velocity changes in bulk waves Velocity measurements on these waves must be measured through the thickness of a component and, as most metallurgists recognize, obtaining uniform properties through thicknesses greater than a few millimeters, especially in steels, is difficult The subtle property variations to which ultrasound velocity is sensitive, the inherent lack of homogeneity in engineering metals, and the high residual stress gradients often found in manufactured components present additional serious problems for through-thickness stress measurements In spite of the microstructural variations in manufactured steel products, success in the application of ultrasonic methods to residual stress measurement has been achieved in specific cases One is in the measurement of hoop stresses in railroad wheels (Ref 101) Here changes or variations of the residual stress in the hoop direction is of concern, while that in the radial or axial direction can often be assumed to be constant or negligible Some techniques, then, for the measurement of the residual hoop stresses have relied on normalizing the hoop velocity against the axial velocity (Ref 102) Also, European railroads have monitored ultrasonic velocity along the wheel rims during use and attributed changes to residual stress changes (Ref 103) Schramm in his article mentioned a number of approaches for the application of ultrasound to the measurement of residual stresses in railroad wheels, and these examples may find application in the measurement of residual stress in other axially symmetric shapes (Ref 101) Ultrasonic residual stress measurements have also been applied to rails as reported by Egle and Bray (Ref 104) and Bray and Leon-Salamanca (Ref 105) Magnetic Barkhausen Noise The Barkhausen noise analysis technique (BNA) is concerned with measuring the number and magnitude of abrupt magnetic reorientations made by expansion and contraction of the magnetic domains in a ferromagnetic metal These reorientations are observed as pulses somewhat random in amplitude, duration, and temporal separation, and therefore roughly described as noise Applications A few applications of BNA to ferromagnetic metallic components have been made Gardner (Ref 106) mentions a number of applications, which include helicopter rotor blade spans, autofrettaged gun tubes, gas turbine engine components, and rolling element antifriction bearing components In these examples the change in residual stresses caused by known service histories was measured Chait (Ref 107) qualitatively measured the residual stress condition of a high-hardness laminar composite steel weldment and compared some of the BNA data with XRD stress readings Sundstrom and Torronen (Ref 108) applied their BNA method to a number of microstructural measurements, including evaluation of grain size measurement for low-carbon ferritic and ferritic-pearlitic steels, evaluation of anisotropy in deep drawing and textured steels for electrical applications, measurement of the degree of aging in rimmed carbon steels, and pearlite morphology in steel wires These researchers have also measured iron loss in magnetic material used for transformers and have proposed using BNA for residual stress measurements, pointing out that quantitative results can be obtained if the material and its fabrication history are known and calibration is possible Most studies and applications of BNA to stress measurement have focused on the uniaxial stress state However, Sundstrom and Torronen (Ref 108) implied that the instrumentation they used could simultaneously measure stress in two directions to give biaxial stress conditions for magnetic inspection of roller bearing components, including BNA for monitoring residual stress change The BNA method certainly has been demonstrated to be sensitive to the stress condition in ferromagnetic materials (Ref 109) Nevertheless, its possibilities for application are limited by the condition that the material must be ferromagnetic, the narrow total range of stress sensitivity (i.e., ±40 ksi, or 275 MPa), and the shallow depth of measurement The latter condition might be relieved by using magnetomechanical-acoustic emission (MAE) (Ref 110), an ultrasound analog to BNA However, the sensitivity of either of these techniques to other characteristics of metallic components and the consequent need for calibration with a nearly identical specimen severely restricts the general applicability of BNA and MAE Many misapplications have been made that have severely damaged the reputation of the BNA methods (Ref 107, 111) Such restrictions can be removed only if the basic phenomena responsible for the effect of microstructural properties on BNA and MAE are understood and quantified in terms of the signal BNA is not recommended where variations in elemental composition, phase composition, grain size, strain hardening, crystallographic texture, grain shape, grain orientation, carbide size and distribution, and other microstructural characteristics accompany variations in residual stress A recent evaluation of BNA by Allison and Hendricks (Ref 112) confirms the uncertainty of BNA residual stress measurements References cited in this section Residual Stress Measurement by X-Ray Diffraction-SAE J784a, Society of Automotive Engineers Handbook Supplement, Warrendale, PA, 1971 10 M.E Brauss and J.A Pineault, Residual Strain Measurement of Steel Structures, NDE for the Energy Industry, NDE Vol 13 (Book No H00930-1995), D.E Bray, Ed., American Society of Mechanical Engineers, 1995 12 C.O Ruud and M.E Jacobs, Residual Stresses Induced by Slitting Copper Alloy Strip, NDC of Materials VI, Plenum Press, 1994, p 413–424 20 M Brauss, J Pineault, S Teodoropol, M Belassel, R Mayrbaurl, and C Sheridan, Deadload Stress Measurement on Brooklyn Bridge Wrought Iron Eye Bars and Truss Sections Using X-ray Diffraction Techniques, Proc of 14th Annual International Bridge Conf and Exhibition, Engineering Society of Western Pennsylvania, Pittsburgh, ICB-97-51, 1997, p 457–464 21 M.G Carfaguo, F.S Noorai, M.E Brauss, and J.A Pineault, “X-Ray Diffraction Measurement of Stresses in Post-Tensioning Tendons,” International Association for Bridge and Structural Engineering (IABSE) Symposium, 1995 (San Francisco), “Extending the Life Span of Structures,” IABSE, ETH Honggerberg, Zurich, Switzerland, Vol 71/1, 1995, p 201–206 22 J.A Pineault and M.E Brauss, In Situ Measurement of Residual and Applied Stresses in Pressure Vessels and Pipeline Using X-ray Diffraction Techniques, Determining Material Characterization: Residual Stress and Integrity with NDE, PUP-Vol 276, NDE-Vol 12, American Society of Mechanical Engineers, New York, 1994 39 C.O Ruud, P.S DiMascio, and D.J Snoha, A Miniature Instrument for Residual Stress Measurement, Adv X-Ray Anal., Vol 27, Plenum Press, 1984, p 273–283 53 B.D Cullity, Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley Publishing Co., Inc., 1978, p 469–472 75 C.O Ruud, X-Ray Analysis and Advances in Portable Field Instrumentation, J Met., Vol 31 (No 6), 10–15 June 1979 76 H.P Klug and L.E Alexander, X-Ray Diffraction Procedures, 2nd ed., New York, John Wiley & Sons, 1974, p 768–770 77 C.S Barrett and T.B Massalski, Structure of Metals, 3rd ed., McGraw-Hill, 1966, p 474–476 78 C.O Ruud and G.D Farmer, Residual Stress Measurement by X-rays: Errors, Limitations, and Applications, Nondestructive Evaluation of Materials, J.J Burke and V Weiss, Ed., Plenum Press, 1979, p 101–116 79 R.N Pangborn, S Weissman, and I.R Kramer, Dislocation Distribution and Prediction of Fatigue Damage, Metall Trans A, Vol 12 (No 1) 1981, p 109–120 80 D.A Bolstad, R.A Davis, W.E Quist, and E.C Roberts, Measuring Stress in Steel Parts by X-Ray Diffraction, Metals Progress, 1963, p 88–92 81 D.S Kurtz, P.R Moran, K.J Kozaczek, and M Brauss, Apparatus for Rapid Psi Squared Stress Measurement and Its Applications to Titanium Alloy Jet Engine Fan Blades, The Fifth International Conference on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 744–749 82 B.B He and K.L Smith, Strain and Stress Measurements with Two-Dimensional Detector, Adv X-Ray Anal., Vol 41, 1977 83 M.R James and J.B Cohen, The Application of a Position-Sensitive X-Ray Detector to the Measurements of Residual Stresses, Adv X-Ray Anal., Vol 19, Gould, Barnett, Newkirk, and Ruud, Ed., 1976, p 695–708 84 H Zantopulou and C.F Jatczak, Systematic Errors in Residual Stress Measurement Due to Specimen Geometry, Adv in X-Ray Anal., New York, Plenum Press, Vol 14, 1970 85 C.O Ruud, D.J Snoha, and D.P Ivkovich, Experimental Methods for Determination of Precision and Estimation of Accuracy in XRD Residual Stress Measurement, Adv X-Ray Anal., Vol 30, 1987, p 511– 522 86 J.H Root, R.R Hosbaus, and T.M Holden, Neutron Diffraction Measurements of Residual Stresses Near a Pin Hole in a Solid-Fuel Booster Rocket Casing, Practical Applications of Residual Stress Technology, C.O Ruud, Ed., ASM International, 1991, p 83–93 87 R.C Donmarco, K.J Kozaczek, P.C Bastias, G.T Hahn, and C.A Rubin, Residual Stress and Retained Austenite Distribution and Evaluation in SAE 52100 Steel under Rolling Contact Loading, PVP-Vol 322, NDE-Vol 15, NDE Engineering Codes and Standards and Materials Characterization, J.S Cook, Sr., C.D Cowfer, and C.C Monahan, Ed., American Society of Mechanical Engineers, 1996, p 63–70 88 M Hayaski, S Ohkido, N Minakawa, and Y Murii, Residual Stress Distribution Measurement in Plastically Bent Carbon Steel by Neutron Diffraction, The Fifth International Conf on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 762–769 89 G.A Alers, Ultrasonic Methods—Overview, Proc of a Workshop on Nondestructive Evaluation of Residual Stress, NTIAC-76-2, 1975, p 155–161 90 D.I Crecraft, Ultrasonic Measurement of Stresses, Ultrasonics, 1968, p 117–121 91 G Bradfield and H Pursey, Philos Mag., Vol 44 (No 295), 1953 92 H Pursey and H.L Cox, Philos Mag., Vol 45, 1954, p 295 93 W.J McGonagle and S.S Yun, Measurement of Surface-Residual Stress by Nondestructive Methods, Proc of the 5th International Conf on Nondestructive Testing, 1967, p 159–164 94 A.J Boland et al., “Development of Ultrasonic Tonography for Residual Stress Mapping,” Final Report, EPRI RP 504-2, Electric Power Research Institute, 1980 95 M.R James and O Buck, Quantitative Nondestructive Measurement of Residual Stresses, Crit Rev Solid State Mater Sci., August 1980, p 61–105 96 E.P Papadakis, Ultrasonic Attenuation and Velocity in Three Transformation Products of Steel, J Appl Phys., Vol 35 (No 5), 1964, p 1474–1482 97 A Moro, C Farina, and F Rossi, Measurement of Ultrasonic Wave Velocity of Steel for Various Structures and Degrees of Cold-Working, Nondestruct Test Int., Aug 1980, p 169–175 98 B.R Tittman and R.B Thompson, Measurement of Physical Property Gradients with Elastic Surface Wave Dispersion, Proc Ninth Symposium on NDE, 1980, p 20–28 99 K Salama and C.K Ling, The Effect of Stress on The Temperature Dependence of Ultrasound Velocity, J Appl Phys., Vol 51 (No 3) March 1980, 1505–1509 100 K Salama and G.A Alers, Third-Order Elastic Constants of Copper at Low Temperature, Phys Rev., Vol 161 (No 3), Sept 1967, p 673–680 The amount of work per unit volume of a material required to carry that material to failure under static loading See also toughness Mohs hardness test A scratch hardness test for determining comparative hardness using 10 standard minerals—from talc (the softest) to diamond (the hardest) monotron hardness test An obsolete method of determining indentation hardnessby measuring the load required to force a spherical penetrator into a metal to a specified depth multiaxial stress See principal stress (normal) m-value See strain-rate sensitivity N natural strain See true strain necking (1) Reducing the cross-sectional area of metal in a localized area by stretching (2) Reducing the diameter of a portion of the length of a cylindrical shell or tube nominal strain See strain nominal strength See ultimate strength nominal stress The stress at a point calculated on the net cross section by simple elasticity theory without taking into account the effect on the stress produced by stress raisers such as holes, grooves, fillets, etc normal direction Direction perpendicular to the plane of working in a worked metal See also longitudinal direction and transverse direction normal stress The stress component perpendicular to a plane on which forces act Normal stress may be either tensile stress or compressive stress notch brittleness Susceptibility of a material to brittle fractureat points of stress concentration For example, in a notch tensile test, the material is said to be notch brittle if the notch strengthis less than the tensile strength of an unnotched specimen Otherwise, it is said to be notch ductile notch depth The distance from the surface of a notched test specimen to the bottom of the notch In a cylindrical test specimen, the percentage of the original cross-sectional area removed by machining an annular groove notch ductility The percentage reduction in area after complete separation of the metal in a tensile test of a notched specimen notch strength The maximum load on a notched tensile-test specimen divided by the minimum cross-sectional area (the area at the root of the notch) Also known as notch tensile strength n-value See strain hardening exponent O observed value The particular value of a characteristic determined as a result of a test or measurement offset The distance along the strain coordinate between the initial portion of a stress-strain curve and a line parallel to the initial portion that intersects the stress-strain curve at a value of stress (commonly 0.2%) that is used as a measure of the yield strength Used for materials that have no obvious yield point offset modulus The ratio of the offset yield stress to the extension at the offset point (plastics) offset yield strength The stress at which the strain exceeds by a specified amount (the offset) an extension of the initial proportional portion of the stress-strain curve Expressed in force per unit area Olsen cup test A cupping test in which a piece of sheet metal, restrained except at the center, is deformed by a standard steel ball until fracture occurs The height of the cup at time of fracture is a measure of the ductility Compare with Erichsen cup test and Swift cup test orange peel A surface roughening in the form of a pebble-grained pattern where a metal of unusually coarse grain is stressed beyond its elastic limit Also known as pebbles and alligator skin original crack size (ao) The physical crack size at the start of testing oxidative wear A type of wear resulting from the sliding action between two metallic components that generates oxide films on the metal surfaces These oxide films prevent the formation of a metallic bond between the sliding surfaces, resulting in fine wear debris and low wear rates Compare with corrosive wear P parameter In statistics, a constant (usually unknown) defining some property of the frequency distribution of a population, such as a population median or a population standard deviation pebbles See preferred term orange peel percent error For testing machines, the ratio, expressed as a percentage, of the error to the correct value of the applied load permanent set The deformation or strain remaining in a previously stressed body after release of load permissible variation For testing machines, the maximum allowable error in the value of the quantity indicated It is convenient to express permissible variation in terms of the percent error physical crack size (ap) The distance from a reference plane to the observed crack front This distance may represent an average of several measurements along the crack front The reference plane depends on the specimen form, and it is normally taken to be either the boundary or a plane containing either the load line or the centerline of a specimen or plate physical properties Properties of a material the determination of which does not involve the deformation or destruction of the specimen—for example, density, electrical conductivity, coefficient of thermal expansion, magnetic permeability, and lattice parameter Does not include chemical reactivity or the properties more appropriately regarded as mechanical properties physical testing Methods used to determine the entire range of physical properties of a material In addition to density and thermal, electrical, and magnetic properties, physical testing methods can be used to assess simple fundamental physical properties such as color, crystalline form, and melting point pin expansion test A test for determining the ability of a tube to be expanded or for revealing the presence of cracks or other longitudinal weaknesses in it, made by forcing a tapered pin into the open end of the tube, similar to flare test pin or mandrel In bend testing, the plunger or tool used in making semiguided, guided, or wrap-around tests to apply the bending force to the inside surface of the bend In free bends or semiguided bends to an angle of 180°, a shim or block of the proper thickness may be placed between the legs of the specimen as bending is completed This shim or block is also referred to as a pin or mandrel pin shear test See shear test Piobert lines See Lüders lines pitting In tribology, a type of wear characterized by the presence of small, sharp surface cavities formed by processes such as fatigue, local adhesion, wear, corrosion, or cavitation planar anisotropy A variation in physical and/or mechanical properties with respect to direction within the plane of material in sheet form See also plastic strain ratio plane strain The stress condition in linear-elastic fracture mechanics in which there is zero strain in a direction normal to both the axis of applied tensile stress and the direction of crack growth (i.e., parallel to the crack front); most nearly achieved in loading thick plates along a direction parallel to the plate surface Under plane-strain conditions, the plane of fracture instability is normal to the axis of the principal tensile stress plane-strain fracture toughness (KIc) The crack extension resistance under conditions of crack-tip plane strain See also stress-intensity factor plane stress The stress condition in linear-elastic fracture mechanics in which the stress in the thickness direction is zero; most nearly achieved in loading very thin sheet along a direction parallel to the surface of the sheet Under plane-stress conditions, the plane of fracture instability is inclined 45° to the axis of the principal tensile stress plane-stress fracture toughness (Kc) In linear-elastic fracture mechanics, the value of the crack-extension resistance at the instability condition determined from the tangency between the R-curve and the critical crack-extension force curve of the specimen See also stress intensity factor plastic deformation The permanent (inelastic) distortion of a material under applied stress that strains the material beyond its elastic limit plastic flow See yielding plastic instability The stage of deformation in a tensile test where the plastic flow becomes nonuniform and necking begins plasticity The property that enables a material to undergo permanent deformation without rupture plastic strain Dimensional change that does not disappear when the initiating stress is removed Usually accompanied by some elastic deformation plastic strain ratio (r-value) The ratio of the true width strain to the true thickness strain in a tensile test, r = εw/εt Because of the difficulty in making precise measurement of thickness strain in sheet material, it is more convenient to express rin terms of initial and final length and width dimensions It can be shown that r = (ln WoWf) - (ln LfWf/LoWo) where Lo and Wo are initial length and width of gage section, respectively; and Lf and Wf are final length and width, respectively plastic-zone adjustment, rY An addition to the physical crack size to account for plastic crack-tip deformation enclosed by a linearelastic stress field plowing In tribology, the formation of grooves by plastic deformation of the softer of two surfaces in relative motion point estimate The estimate of a parameter given by a single statistic Poisson's ratio (ν) The absolute value of the ratio of transverse (lateral) strain to the corresponding axial strain resulting from uniformly distributed axial stress below the proportional limit of the material population The hypothetical collection of all possible test specimens that could be prepared in the specified way from the material under consideration Also known as universe precision The closeness of agreement between the results of individual replicated measurements or tests The standard deviation of the error of measurement may be used as a measure of “imprecision.” principal stress (normal) The maximum or minimum value of the normal stressat a point in a plane considered with respect to all possible orientations of the considered plane On such principal planes the shear stress is zero There are three principal stresses on three mutually perpendicular planes The state of stress at a point may be: (1) uniaxial, a state of stress in which two of the three principal stresses are zero; (2) biaxial, a state of stress in which only one of the three principal stresses is zero; or (3) triaxial, a state of stress in which none of the principal stresses is zero Multiaxial stress refers to either biaxial or triaxial stress proof stress (1) The stress that will cause a specified small permanent set in a material (2) A specified stress to be applied to a member or structure to indicate its ability to withstand service loads proportional limit The greatest stress a material is capable of developing without a deviation from straight-line proportionality between stress and strain Compare with elastic limit See also Hooke's law punching shear test See blanking shear test R radial marks Lines on a fracture surface that radiate from the fracture origin and are visible to the unaided eye or at low magnification Radial lines result from the intersection and connection of brittle fractures propagating at different levels Also known as shear ledges See also chevron pattern radius of bend The radius of the cylindrical surface of the pin or mandrel that comes in contact with the inside surface of the bend during bending For free or semiguided bends to 180° in which a shim or block is used, the radius of bend is one-half the thickness of the shim or block range of stress (Sr) The algebraic difference between the maximum and minimum stress in one cycle—that is, Sr = Smax - Smin ratchet marks Lines on a fatigue fracture surface that result from the intersection and connection of fatigue fractures propagating from multiple origins Ratchet marks are parallel to the overall direction of crack propagation and are visible to the unaided eye or at low magnification rate of creep See creep rate R-curve In linear-elastic fracture mechanics, a plot of crack-extension resistance as a function of stable crack extension, which is either the difference between the physical crack size,or the effective crack size, and the original crack size R-curves normally depend on specimen thickness and, for some materials, on temperature and strain rate reduction in area (RA) The difference between the original cross-sectional area of a tensile specimen and the smallest area at or after fracture as specified for the material undergoing testing Also known as reduction of area relaxation curve A plot of either the remaining, or relaxed, stress as a function of time See also relaxation rate relaxation rate The absolute value of the slope of a stress-relaxation curve at a given time relaxed stress The initial stress minus the remaining stress at a given time during a stress-relaxation test See also stress relaxation remaining stress The stress remaining at a given time during a stress-relaxation test See also stress relaxation repeatability A term used to refer to the test-result variability associated with a limited set of specifically defined sources of variability within a single laboratory reproducibility A term used to describe test-result variability associated with specifically defined components of variance obtained both from within a single laboratory and between laboratories residual stress Stresses that remain within a body as the result of thermal or mechanical treatment or both resilience The ability of a material to absorb energy when deformed elastically and return to its original shape on release of load See also modulus of resilience response curve for N cycles In fatigue-data analysis, a curve fitted to observed values of percentage survival at N number of cycles for several stress levels, where N is a preassigned number such as 106, 107, etc It is an estimate of the relationship between applied stress and the percentage of the population that would survive N cycles See also S-N curve Rockwell hardness number (HR) A number derived from the net increase in the depth of impression in a Rockwell hardness test as the load on an indenter is increased from a fixed minor load to a major load and then returned to the minor load Rockwell hardness numbers are always quoted with a scale symbol representing the penetrator, load, and dial used Rockwell hardness test An indentation-hardness test using a calibrated machine that utilizes the depth of indentation, under constant load, as a measure of hardness Either a 120° diamond cone with a slightly rounded point, or a or in diameter steel ball is used as the indenter Rockwell superficial hardness number See Rockwell hardness number Rockwell superficial hardness test Same as Rockwell hardness test, except that smaller minor and major loads are used rosette Strain gages arranged to indicate, at a single position, strain in three different directions rupture stress The stress at failure Also known as breaking stress.See also fracture stress r-value See plastic-strain ratio S sample (1) One or more units of product (or a relatively small quantity of a bulk material) that are withdrawn from a lot or process stream and that are tested or inspected to provide information about the properties, dimensions, or other quality characteristics of the lot or process stream Not be confused with specimen (2) A portion of a material intended to be representative of the whole sample average The sum of all the observed values in a sample divided by the sample size It is a point estimate of the population mean Also known as arithmetic mean sample median The middle value when all observed values in a sample are arranged in order of magnitude If an even number of samples are tested, the average of the two middlemost values is used It is a point estimate of the population median, or 50% point sample percentage The percentage of observed values between two stated values of the variable under consideration It is a point estimate of the percentage of the population between the same two stated values (One stated value may be -∞ or +∞.) sample standard deviation (s) The square root of the sample variance It is a point estimate of the population standard deviation, a measure of the “spread”of the frequency distribution of a population This value of sprovides a statistic that is used in computing interval estimates and several test statistics For small sample sizes, s underestimates the population standard deviation sample variance (s2) The sum of the squares of the differences between each observed value and the sample average divided by the sample size minus one It is a point estimate of the population variance S-basis Minimum property value specified by the appropriate federal, military, Society of Automotive Engineers, American Society for Testing and Materials, or other recognized and approved specifications for the material See also A-basis, B-basis, and typical basis Scleroscope hardness number (HSc or HSd) A number related to the height of rebound of a diamond-tipped hammer dropped on the material being tested It is measured on a scale determined by dividing into 100 units the average rebound of the hammer from a quenched(to maximum hardness) and untempered AISI W5 tool steel test block Scleroscope hardness test A dynamic indentation-hardness test using a calibrated instrument that drops a diamond-tipped hammer from a fixed height onto the surface of the material being tested The height of rebound of the hammer is a measure of the hardness of the material Also known as Shore hardness test scoring In tribology, a severe form of wear characterized by the formation of extensive grooves and scratches in the direction of sliding scratch hardness test A form of hardness test in which a sharp-pointed stylus or corner of a mineral specimen is traversed along a surface so as to determine the resistance of that surface to cutting or abrasion See also file hardness and Mohs hardness test scratching In tribology, the mechanical removal or displacement, or both, of material from a surface by the action of abrasive particles or protuberances sliding across the surfaces See also plowing scuffing A form of adhesive wear that produces superficial scratches or a high polish on the rubbing surfaces It is observed most often on inadequately lubricated parts secant modulus The slope of the secant drawn from the origin to any specified point on a stress-strain curve Compare with chord modulus.See also modulus of elasticity semiguided bend The bend obtained by applying a force directly to the specimen in the portion that is to be bent The specimen is either held at one end and forced around a pin or rounded edge, or is supported near the ends and bent by a force applied on the side of the specimen opposite the supports and midway between them In some instances, the bend is started in this manner and finished in the manner of a free bend set See permanent set sharp-notch strength The notch tensile strength measured using specimens with very small notch root radii (approaching the limit for machining capability); values of sharp-notch strength usually depend on notch root radius shear The type of force that causes or tends to cause two contiguous parts of the same body to slide relative to each other in a direction parallel to their plane of contact shear fracture A ductile fracture in which a crystal (or a polycrystalline mass)has separated by sliding or tearing under the action of shear stresses Contrast with cleavage fracture shear lip A narrow, slanting ridge along the edge of a fracture surface The term sometimes also denotes a narrow, often crescent-shaped, fibrous region at the edge of a fracture that is otherwise of the cleavage type, even though this fibrous region is in the same plane as the rest of the fracture surface shear modulus (G) The ratio of shear stress to the corresponding shear strain for shear stresses below the proportional limit of the material Values of shear modulus are usually determined by torsion testing Also known as modulus of rigidity shear strain The tangent of the angular change, as a response to force, between two lines originally perpendicular to each other through a point in a body Also known as shearing strain shear strength The maximum shear stress that a material is capable of sustaining Shear strength is calculated from the maximum load during a shear or torsion test and is based on the original dimensions of the cross section of the specimen shear stress (1) A stress that exists when parallel planes in metal crystals slide across each other (2) The stress component tangential to the plane on which the forces act Also known as tangential stress shear test Any of several tests to obtain shear strength of a metal Common tests used on mill products include the double-shear test, single-shear test, the blanking shear test (also known as the punching shear test) and the torsion test shock load The sudden application of an external force that results in a very rapid build-up of stress Shore hardness test See Scleroscope hardness test short transverse See transverse direction significance level The stated probability (risk) that a given test of significance will reject the hypothesis that a specified effect is absent when the hypothesis is true significant Statistically significant An effect of difference between populations is said to be present if the value of a test statistic is significant, that is, lies outside predetermined limits See also population silky fracture A metal fracture in which the broken metal surface has a fine texture, usually dull in appearance Characteristic of tough and strong metals Contrast with crystalline fracture and granular fracture single-shear test (1) A shear test similar to the double-shear test used for round-bar specimens, but that uses only one stationary shear blade (2) A shear test that uses a sheet or thin-plate specimen size effect Effect of the dimensions of a piece of metal on its mechanical and other properties and on manufacturing variables such as forging reduction and heat treatment In general, the mechanical properties are lower for a larger size slant fracture A type of fracture appearance, typical of plane-stress fractures, in which the plane of metal separation is inclined at an angle (usually about 45°) to the axis of the applied stress slenderness ratio The effective unsupported length of a uniform column divided by the least radius of gyration of the cross-sectional area slip Plastic deformation by the irreversible shear displacement (translation)of one part of a crystal relative to another in a definite crystallographic direction and usually on a specific crystallographic plane Sometimes called glide slip band A group of parallel slip lines so closely spaced as to appear as a single line when observed under an optical microscope See also slip line slip line The trace of the slip plane on a viewing surface; the trace is usually observable only if the surface has been polished before deformation The usual observation on metal crystals (under the light microscope) is of a cluster of slip lines known as a slip band S-N curve A plot of stress, S, against the number of cycles to failure, N The stress can be the maximum stress, Smax, or the alternating stress amplitude, Sa The stress values are usually nominal stresses; i.e., there is no adjustment for stress concentration The curve indicates the S-N relationship for a specified value of the mean stress, Sm or the stress ratio, A, or Rand a specified probability of survival For N, a log scale is almost always used For S, a linear scale is used most often, but a log scale is sometimes used Also known as S-N diagram S-N curve for 50% survival A curve fitted to the median value of fatigue life at each of several stress levels It is an estimate of the relation between applied stress and the number of cycles-to-failure that 50% of the population would survive S-N curve for p% survival A curve fitted to the fatigue life for p% survival values at each of several stress levels It is an estimate of the relationship between applied stress and the number of cycles-to-failure that p% of the population would survive p may be any number, such as 95, 90, and so forth spalling The separation of macroscopic particles from a surface in the form of flakes or chips specimen A test object, often of standard dimensions or configuration, that is used for destructive or nondestructive testing One or more specimens may be cut from each unit of a sample springback The extent to which metal tends to return to its original shape or contour after undergoing a forming operation standard deviation The most usual measure of the dispersion of observed values or results expressed as the positive square root of the variance static fatigue A term referring to a time-dependent reduction in strength with a static (noncyclic) load The term may refer to hydrogen-induced delayed cracking or the effect of creep on the strength of plastics statistic A summary value calculated from the observed values in a sample steady loads Loads that not change in intensity or that change so slowly they may be regarded as steady stiffness (1) The ability of a metal or shape to resist elastic deflection.(2) The rate of stress increase with respect to the rate of increase in strain induced in the metal or shape; the greater the stress required to produce a given strain, the stiffer the material is said to be strain The unit of change in the size or shape of a body due to force Also known as nominal strain See also engineering strain, linear strain, and true strain strain-age embrittlement A loss in ductility accompanied by an increase in hardness and strength that occurs when low-carbon steel (especially rimmed or capped steel) is aged following plastic deformation The degree of embrittlement is a function of aging time and temperature, occurring in a matter of minutes at about 200°C (400 °F), but requiring a few hours to a year at room temperature strain aging The changes in ductility, hardness, yield point, and tensile strength that occur when a metal or alloy that has been cold worked is stored for some time In steel, strain aging is characterized by a loss of ductility and a corresponding increase in hardness, yield point, and tensile strength strain energy A measure of the energy absorption characteristics of a material determined by measuring the area under the stress-strain diagram Also known as deformation energy See also elastic energy, resilience,and toughness strain gage A device for measuring small amounts of strain produced during tensile and similar tests on metal A coil of fine wire is mounted on a piece of paper, plastic, or similar carrier matrix (backing material), which is rectangular in shape and usually about 25 mm (1.0 in.) long This is glued to a portion of metal under test As the coil extends with the specimen, its electrical resistance increases in direct proportion This is known as bonded resistance-strain gage Other types of gages measure the actual deformation Mechanical, optical, or electronic devices are sometimes used to magnify the strain for easier reading See also rosette strain hardening An increase in hardness and strengthcaused by plastic deformation at temperatures below the recrystallization range Also known as work hardening strain-hardening coefficient See strain-hardening exponent strain-hardening exponent (n value) The value n in the relationship σ = Kεn, where σ is the true stress, ε is the true strain, and K, the strength coefficient, is equal to the true stress at a true strain of 1.0 The strain hardening exponent is equal to the slope of the true stress/true strain curve up to maximum load, when plotted on log-log coordinates The n-value relates to the ability of a sheet of material to be stretched in metalworking operations The higher the n-value, the better the formability(stretchability) Also known as the strain-hardening coefficient strain rate The time rate of straining for the usual tensile test Strain as measured directly on the specimen gage length is used for determining strain rate Because strain is dimensionless, the units of strain rate are reciprocal time strain-rate sensitivity (m value) The increase in stress (σ) needed to cause a certain increase in plastic-strain rate ( ) at a given level of plastic strain (ε) and a given temperature(T) strength The maximum nominal stress a material can sustain Always qualified by the type of stress (tensile, compressive, or shear) strength coefficient See strain-hardening exponent (n-value) stress The intensity of the internally distributed forces or components of forces that resist a change in the volume or shape of a material that is or has been subjected to external forces Stress is expressed in force per unit area and is calculated on the basis of the original dimensions of the cross section of the specimen Stress can be either direct (tension or compression)or shear See also engineering stress, mean stress, nominal stress, normal stress, residual stress, and true stress stress amplitude One-half the algebraic difference between the maximum and minimum stress in one cycle of a repetitively varying stress stress-concentration factor (Kt) A multiplying factor for applied stress that allows for the presence of a structural discontinuity such as a notch or hole; Kt equals the ratio of the greatest stress in the region of the discontinuity to the nominal stress for the entire section Also known as theoretical stress-concentration factor stress-corrosion cracking (SCC) A time-dependent process in which a metallurgically susceptible material fractures prematurely under conditions of simultaneous corrosion and sustained loading at lower stress levels than would be required in the absence of a corrosive environment Tensile stress is required at the metal surface and may be a residual stress resulting from heat treatment or fabrication of the metal or the result of external loading Cracking may be intergranular or transgranular, depending on the combination of alloy and environment stress cycle The smallest segment of the stress-time function that is repeated periodically stress cycles endured (N) The number of cycles of a specified character (that produce fluctuating stress and strain) that a specimen has endured at any time in its stress history stress-intensity calibration A mathematical expression, based on empirical or analytical results, that relates the stress-intensity factor to load and crack length for a specific specimen planar geometry Also known as Kcalibration stress-intensity factor A scaling factor, usually denoted by the symbol K,used in linear-elastic fracture mechanics to describe the intensification of applied stress at the tip of a crack of known size and shape At the onset of rapid crack propagation in any structure containing a crack, the factor is called the critical stress-intensity factor, or the fracture toughness Various subscripts are used to denote different loading conditions or fracture toughnesses: stress-intensity factor range (ΔK) The variation in the stress-intensity factor in a fatigue cycle, that is, Kmax - Kmin stress raisers Changes in contour or discontinuities in structure that cause local increases in stress stress ratio (A or R) The algebraic ratio of two specified stress values in a stress cycle Two commonly used stress ratios are the ratio of the alternating stress amplitude to the mean stress, A = Sa/Sm, and the ratio of the minimum stress to the maximum stress, R = Smin/Smax stress relaxation The time-dependent decrease in stress in a solid under constant strain at constant temperature due to creep The stress-relaxation behavior of a metal is usually shown in a stress-relaxation curve stress-relaxation curve A plot of the remaining, or relaxed, stress in a stress-relaxation test as a function of time The relaxed stress equals the initial stress minus the remaining stress Also known as a stress-time curve stress-rupture strength See creep-rupture strength stress-rupture test See creep-rupture test stress-strain curve See stress-strain diagram stress-strain diagram A graph in which corresponding values of stress and strain are plotted against each other Values of stress are usually plotted vertically(ordinates or y-axis) and values of strain horizontally (abscissas or xaxis) Also known as deformation curve and stress-strain curve stress-time curve See stress-relaxation curve stretch-bending test A simulative test for sheet metal formabilityin which a strip of sheet metal is clamped at its ends in lock beads and deformed in the center by a punch Test conditions are chosen so that fracture occurs in the region of punch contact stretcher strains See Lüders lines striation A fatigue fracture feature, often observed in electron micrographs, that indicates the position of the crack front after each succeeding cycle of stress The distance between striations indicates the advance of the crack front across that crystal during one stress cycle, and a line normal to the striation indicates the direction of local crack propagation Swift cup test A simulative cupping test in which circular blanks of various diameters are clamped in a die ring and deep drawn into cups by a flat-bottomed cylindrical punch Compare with Erichsen cup test and Olsen cup test T tangent modulus The slope of the stress-strain curve at any specified stress or strain See also modulus of elasticity temper embrittlement Brittleness that results when certain steels are held within, or are cooled slowly through, a certain range of temperature below the transformation range The brittleness is manifested as an upward shift in ductile-to-brittle transition temperature but only rarely produces a low value of reduction in area in a smooth-bar tension test of the embrittled material tensile strength In tension testing, the ratio of maximum load to original cross-sectional area Also known as ultimate strength Compare with yield strength tensile stress A stress that causes two parts of an elastic body, on either side of a typical stress plane, to pull apart Contrast with compressive stress tensile testing See tension testing tension The force or load that produces elongation tension testing A method of determining the behavior of materials subjected to uniaxial loading, which tends to stretch the metal A longitudinal specimen of known length and diameter is gripped at both ends and stretched at a slow, controlled rate until rupture occurs Also known as tensile testing testing machine (load-measuring type) A mechanical device for applying a load (force) to a specimen theoretical stress concentration factor See stress-concentration factor thermal fatigue Fatigue resulting from the presence of temperature gradients that vary with time in such a manner as to produce cyclic stresses in a structure thermocouple A device for measuring temperature, consisting of lengths of two dissimilar metals or alloys that are electrically joined at one end and connected to a voltage-measuring instrument at the other end When one junction is hotter than the other, a thermal electromotive force is produced that is roughly proportional to the difference in temperature between the hot and cold junctions threshold stress for stress-corrosion cracking (σth) An experimentally determined critical gross-section stress below which stress-corrosion cracking will not occur under specified test conditions tolerance limits The extreme values (upper and lower) that define the range of permissible variation in size or other quality characteristic of a part torsion A twisting deformation of a solid body about an axis in which lines that were initially parallel to the axis become helices torsion test A test designed to provide data for the calculation of the shear modulus, modulus of rupture in torsion, and yield strength in shear torsional stress The shear stress on a transverse cross section resulting from a twisting action total elongation A total amount of permanent extension of a test piece broken in a tensile test See also elongation, percent total-extension-under-load yield strength See yield strength toughness The ability of a metal to absorb energy and deform plastically before fracturing transgranular Through or across crystals or grains Also known as intracrystalline or transcrystalline transition temperature (1) An arbitrarily defined temperature that lies within the temperature range in which metal fracture characteristics (as usually determined by tests of notched specimens) change rapidly, such as from primarily fibrous (shear)to primarily crystalline (cleavage) fracture (2) Sometimes used to denote an arbitrarily defined temperature within a range in which the ductility changes rapidly with temperature transverse direction Literally, the “across” direction, usually signifying a direction or plane perpendicular to the direction of working In rolled plate or sheet, the direction across the width is often called long transverse, and the direction through the thickness, short transverse transverse strain Linear strain in a plane perpendicular to the loading axis of a specimen triaxial stress See principal stress (normal) tribology The science and technology concerned with interacting surfaces in relative motion true strain (1) The ratio of the change in dimension, resulting from a given load increment, to the magnitude of the dimension immediately prior to applying the load increment (2) In a body subjected to axial force, the natural logarithm of the ratio of the gage length at the moment of observation to the original gage length Also known as natural strain Compare with engineering strain true stress The value obtained by dividing the load applied to a member at a given instant by the cross-sectional area over which it acts Compare with engineering stress typical basis The typical property value is an average value No statistical assurance is associated with this basis See also A-basis, B-basis, and S-basis U ultimate strength The maximum stress (tensile, compressive, or shear) a material can sustain without fracture, determined by dividing maximum load by the original cross-sectional area of the specimen Also known as nominal strength or maximum strength uniaxial strain Increase (or decrease) in length resulting from a stress acting parallel to the longitudinal axis of the specimen uniaxial stress See principal stress (normal) uniform elongation The elongation at maximum load and immediately preceding the onset of necking in a tension test uniform strain The strain occurring prior to the beginning of localization of strain (necking); the strain to maximum load in the tension test V variance A measure of the squared dispersion of observed values or measurements expressed as a function of the sum of the squared deviations from the population mean or sample average verification Checking or testing an instrument to ensure conformance with a specification verified loading range For testing machines, the range of indicated loads for which the testing machine gives results within the permissible variation specified vernier A short auxiliary scale that slides along the main instrument scale to permit more accurate fractional reading of the least main division of the main scale See also least count Vicat softening point The temperature at which a flat-ended needle of mm2(0.0015 in.2) circular or square cross section will penetrate a thermoplastic specimen to a depth of mm (0.040 in.) under a specified load, using a uniform rate of temperature rise Vickers hardness number (HV) A number related to the applied load and the surface area of the permanent impression made by a square-based pyramidal diamond indenter having included face angles of 136°, computed from the equation: (Eq 1) where P is applied load, kgf; d is mean diagonal of the impression, mm; and α is face angle of diamond, 136° Vickers hardness test An indentation hardness test employing a 136° diamond pyramid indenter (Vickers) and variable loads, enabling the use of one hardness scale for all ranges of hardness—from very soft lead to tungsten carbide Also know as diamond pyramid hardness test viscoelasticity A property involving a combination of elastic and viscous behavior A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid A phenomenon of time-dependent, in addition to elastic, deformation (or recovery) in response to load volumetric modulus of elasticity See bulk modulus of elasticity W Wallner lines A distinct pattern of intersecting sets of parallel lines, usually producing a set of V-shaped lines, sometimes observed when viewing brittle fracture surfaces at high magnification in an electron microscope Wallner lines are attributed to interaction between a shock wave and a brittle crack front propagating at high velocity Sometimes Wallner lines are misinterpreted as fatigue striations wear Damage to a solid surface, generally involving progressive loss of material, due to relative motion between that surface and a contacting surface or substance wear rate The rate of material removal or dimensional change due to wear per unit of exposure parameter—for example, quantity of material removed(mass, volume, thickness) in unit distance of sliding or unit time welding In tribology, the bonding between metallic surfaces in direct contact, at any temperature Widmanstätten structure A structure characterized by a geometrical pattern resulting from the formation of a new phase along certain crystallographic planes of the parent solid solution The orientation of the lattice in the new phase is related crystallographically to the orientation of the lattice in the parent phase The structure is readily produced in many alloys by appropriate heat treatment workability See formability work hardening See strain hardening wrap-around bend The bend obtained when a specimen is wrapped in a closed helix around a cylindrical mandrel This term is sometimes applied to a semiguided bend of 180° or less wrinkling A wavy condition obtained in deep drawing of sheet metal, in the area of the metal between the edge of the flange and the draw radius Wrinkling may also occur in other forming operations when unbalanced compressive forces are set up Y yielding Evidence of plastic deformation in structural materials Also known as plastic flow or creep See also flow yield point The first stress in a material, usually less than the maximum attainable stress, at which an increase in strain occurs without an increase in stress Only certain metals—those which exhibit a localized, heterogeneous type of transition from elastic to plastic deformation—produce a yield point If there is a decrease in stress after yielding, a distinction may be made between upper and lower yield points The load at which a sudden drop in the flow curve occurs is called the upper yield point The constant load shown on the flow curve is the lower yield point yield-point elongation During discontinuous yielding, the amount of strain measured from the onset of yielding to the beginning of strain hardening yield strength The stress at which a material exhibits a specified deviation from proportionality of stress and strain An offset of 0.2% is used for many metals Compare with tensile strength yield stress The stress level of highly ductile materials, such as structural steels, at which large strains take place without further increase in stress Young's modulus A term used synonymously with modulus of elasticity.The ratio of tensile or compressive stresses to the resulting strain Z zero time The time when the given loading or constraint conditions are initially obtained in creep or stressrelaxation tests, respectively Glossary of Terms Selected References • • • • • • • • • Compilation of ASTM Standard Definitions, 8th ed., ASTM, 1994 H.E Davis, G.E Troxell, and G.F.W Hauck, The Testing of Engineering Materials, 4th ed., McGraw Hill, 1982 J.R Davis, Ed., ASM Materials Engineering Dictionary, ASM International, 1992 G.E Dieter, Mechanical Metallurgy, 2nd ed., McGraw Hill, New York, 1976 Glossary of Metallurgical Terms and Engineering Tables, American Society for Metals, 1979 D.N Lapedes, Ed., Dictionary of Scientific and Technical Terms, 2nd ed., McGraw Hill, 1974 A.D Merriman, A Dictionary of Metallurgy, Pitman Publishing, London, 1958 “Metal Test Methods and Analytical Procedures,” Annual Book of ASTM Standards, Vol 03.01 and 03.02, ASTM, 1984 J.G Tweeddale, Mechanical Properties of Metals, American Elsevier, 1964 ... Hahn, and C.A Rubin, Residual Stress and Retained Austenite Distribution and Evaluation in SAE 52100 Steel under Rolling Contact Loading, PVP-Vol 322, NDE-Vol 15, NDE Engineering Codes and Standards... SWRI Project 1 5-4 600, Contract DOT-FH-1 1-9 133, January 1978 112 H.D Allison and R.W Hendricks, Correlation of Barkhausen Noise Signal and X-Ray Residual Stress Determinations in Grinding-Burned 52100... Hahn, and C.A Rubin, Residual Stress and Retained Austenite Distribution and Evaluation in SAE 52100 Steel under Rolling Contact Loading, PVP-Vol 322, NDE-Vol 15, NDE Engineering Codes and Standards