Volume 08 - Mechanical Testing and Evaluation Part 14 pdf

All peel tests have the common characteristic that failure propagates from an initially debonded area They also generally involve large displacements/deformations For these and other reasons, linear elastic stress analysis is often not well suited to peel tests The stresses and strains in the peel configuration are complex and seldom well understood Test results are generally not given in terms of stress but rather as force per unit length required to peel the specimen It is, therefore, generally difficult to compare the results from a peel test with those from other testing methods Because of the large deformations involved in peel tests, the analysis of such geometries is very difficult except under certain simplifying assumptions (Ref 3, 4, 6, 9, and 10) Some very interesting and informative observations can be made on the basis of simplifying assumptions and approximations Indeed, considerable useful work has been completed using peel tests The informative work of Gardon (Ref 10) and Kaelble (Ref 11) is noteworthy The polymer research group at The University of Akron, under the direction of Professor A Gent, has been particularly adroit in applying peel techniques and the concepts of fracture mechanics (see the section “Adhesive Fracture Mechanics Tests” in this article) to obtain critical information and insight into the behavior of adhesive joints (Ref 12, 13) The peel specimen is, in principle, a very versatile geometry for obtaining adhesive fracture energy because various combinations of mode I and mode II loadings can be applied by varying the peel angle (Ref 3) The stress analyses of Adams and Crocombe (Ref 14) have provided additional insight into the peeling mechanisms They examined the stress distributions in peel specimens using elastic large-displacement, finite-element analysis techniques References cited in this section G.P Anderson, S.J Bennett, and K.L DeVries, Analysis and Testing of Adhesive Bonds, Academic Press, 1977 A.J Kinlock, Adhesion and Adhesives, Chapman and Hall, 1987 K.L Mittal, Adhesive Joints, Plenum Press, 1984 Adhesives, Annual Book of ASTM Standards, Vol 15.06, ASTM (updated annually) G.P Anderson and K.L DeVries, Predicting Strength of Adhesive Joints from Test Results, Int J Fract., Vol 39, 1989, p191–200 10 J.L Gardon, Peel Adhesion, I Some Phenomenological Aspects of the Test, J Appl Polym Sci., Vol 7, 1963, p 654 11 D.H Kaelble, Theory and Analysis of Peel Adhesion: Mechanisms and Mechanics, Trans Soc Rheol., Vol 3, 1959, p 161 12 A.N Gent and G.R Hamed, Peel Mechanics, J Adhes., Vol 7, 1975, p 91 13 A.N Gent and G.R Hamed, J Appl Polym Sci., Vol 21, 1977, p 2817 14 R.D Adams and A Crocombe, J Adhes., Vol 12, 1981, p 127 Testing of Adhesive Joints K.L DeVries and Paul Borgmeier, University of Utah Lap Shear Tests The most popular test geometry for testing adhesive joints is the lap shear specimen Its appeal is probably based on the fact that it closely duplicates the geometry used in many practical joints These lap joints are popular for several reasons: • • • They facilitate use of larger contact areas than, for example, a butt joint They are easier to make and align than butt joints The adhesive is not exposed to “direct” tensile stresses Direct tensile stresses are known to have deleterious effects on adhesives Typical lap shear test specimens for which ASTM standards have been written are presented in Fig (Ref 7) The specimens shown in this figure conform most closely to ASTM Standards D 1002, D 3163, D 3164, D 3165, and D 3528 for testing adhesives used to bond metals, plastics, and laminates These represent only a small sampling of the more than two dozen standards in the Annual Book of ASTM Standards, Volume 15.06, that relate to shear testing These other standards range from descriptions of block-type sample configurations for testing lumber and wood bonding in shear by compression loading, through descriptions of devices to simultaneously expose samples to lap shear stresses and extremes in temperature Still others describe apparatus for exposing lap joints to sustained loads (using springs) to measure long-term creep or time to failure Fig Typical lap shear geometries (a) ASTM D 1002, D 3163, and D 3164 (b) ASTM D 3165 (c) ASTM D 3528 Source: Ref The results from lap shear tests are generally reported as the force at failure divided by the bonded area (overlap area) Such values are listed in a number of reference books and manufacturers' literature for a wide variety of adhesives The reference book on types of adhesives (Ref 1) lists typical lap shear strength values for literally thousands of commercial adhesives Such tables of “shear strength” values are without doubt of considerable utility for comparison and other purposes However, their use also can lead to faulty expectations and conceptions Otherwise knowledgeable designers might logically assume from the tabulations that these average stress values could, in a straightforward manner, be used to design an adhesive joint For example, the tabulated shear stress value for a given adhesive from an ASTM D 1002 test might be given as 3000 psi It might be assumed that this adhesive is to be used to bond two 25 mm (1 in.) wide by mm (0.12 in.) thick 7075-T6 aluminum pieces together to carry a tensile load of 3200 lb with a safety factor of two First, the designer must ascertain whether the aluminum pieces can carry such a load Typically, 7075-T6 aluminum has a yield strength slightly in excess of 65 ksi for an allowable stress of 32.5 ksi The pieces in question would have an allowable load of 4000 lb, which is more than the 3200 lb required in the design The “straightforward” method to design the joint would be to assume that the allowable shear strength for the adhesive used in the joint would be 3000/2 = 1500 psi, suggesting that an overlap of 3200/1500 = 2.13 in would be sufficient to support the load This is, in fact, the approach taught by a variety of otherwise very good texts on material science and mechanical design However, doubling the length of a lap joint almost never doubles its loadcarrying capacity, and the increased joint strength is usually much less than doubled The length of overlap recommended in ASTM D 1002 is 12.7 mm (0.50 in.) Typically, quadrupling the amount of overlap does not increase the load at failure by anywhere near a factor of four For reasons given in the next few paragraphs, it is likely that it is not even the value of the maximum shear stress that determines the failure of the “lap shear joint.” As this article reveals, joint failure is more likely determined by the value of secondary induced cleavage stresses The stresses along the bond line of lap specimens are not constant The bond stress distribution is highly dependent on the thickness of the adherends and the adhesive as well as the length of overlap As a consequence, the load to initiate failure also varies markedly with both the adherend(s) and adhesive-bond thicknesses The failure load increases very nearly linearly with width of the overlap but increases in a very nonlinear manner with length of the overlap As the load is increased in a lap shear test, the debonding generally initiates at or near one of the bond terminations Elastic stress analysis generally indicates that the stresses are singular at these termination points Debond initiation in lap shear specimens can perhaps, therefore, be best characterized in terms of fracture mechanics parameters, which are discussed in the section “Adhesive Fracture Mechanics Tests” in this article In addition, it has been demonstrated that for debonds after initiation, crack propagation is dominated by crack- opening mode displacements (mode I) For this reason and reasons given in the next couple of paragraphs, the word shear in the test titles and generally reported in test results may, therefore, be a misnomer It has been known for many years that the shear stresses in the bond line of lap specimens are accompanied by tensile stresses Many analyses have been completed for lap shear geometries, almost all of which have clearly demonstrated the presence of induced tensile stresses in so-called lap shear specimens under load In 1938, Volkersen (Ref 15) obtained expressions for the stresses in a lap shear joint by considering the differential displacements of the adherends and neglecting bending This study was followed in 1944 by the now classical treatment of Goland and Reissner (Ref 16) who used standard beam theory and strength of materials concepts to obtain expressions for the joint stresses Plantema (Ref 17) combined the results of these two earlier investigations to include shear effects in the system Because the stress state of the lap shear joint is so complex and does not lend itself to closed-form solutions, it is only logical that as numerical methods became available, researchers would apply them to analyze adhesive joints Wooley and Carver (Ref 18), for example, used finite-element methods to calculate the joint stresses They compared their results with the results obtained by Goland and Reissner and reported very good agreement Adams and Peppiatt (Ref 19) used a two- dimensional finite-element code to analyze the stresses in a standard lap shear joint and also reported good agreement with Goland and Reissner These authors also investigated the effect of a spew (triangular adhesive fillet) on the calculated stresses A nonlinear finiteelement analysis of the single lap joint was completed by Cooper and Sawyer (Ref 20) in 1979 Anderson and DeVries conducted a linear elastic stress analysis of a typical single lap joint (Ref 21) making use of plane-strain finite- element computer programs using elements as small as 0.00025 cm (0.0001 in.) They considered steel (modulus of elasticity, 207 GPa; Poisson's ratio, 0.30) adherends of various thicknesses bonded with a 0.25 mm (0.01 in.) thick epoxy (modulus of elasticity, 2.76 GPa; Poisson's ratio, 0.34) The overlap region was taken as 13 mm (0.5 in.) long The results of these analyses are shown in Fig Note that both the shear and tensile stresses are distributed very nonlinearly over the length of the bond region Reference 21 reports stresses resulting from other adherend thicknesses As the bond termini is approached, both shear and normal stresses appear to become singular Careful analysis in this region suggests that the local mode I stresses (tensile or crack opening) are significantly higher than mode II stresses (shear) Perhaps even more importantly, the mode I energy release rate is greater than that for mode II From these results, it might be concluded that lap shear specimens fail by mode I crack growth Therefore, the failure of lap shear specimens is usually governed by tensile stress rather than shear stresses This is true for double lap joints as well as single lap joints (Ref 22, 23) Fig Bond line tensile and shear stresses in lap shear specimen (adherend thickness = 1.6 mm, or 0.06 in.) As noted, the end(s) of the overlap on bond termini on lap shear specimens are points of stress concentration and of large induced tensile stresses While this closely simulates many practical situations, some have suggested that for determination of intrinsic adhesive properties, it would be useful if these termini could be eliminated ASTM E 229 “Standard Test Method for Shear Strength and Shear Modulus of Structural Adhesives” is a test designed specifically for this purpose In this test, the adhesive is applied in the form of a thin annulus ring bonded between two relatively rigid adherends in circular disc form Torsion shear forces are applied to the adhesive through this circular specimen, which produces a peripherally uniform stress distribution The maximum stress in the adhesive at failure is taken to represent the shear strength of the adhesive By measuring the angle of twist experienced by the adhesive and having knowledge of sample geometry, it is possible to calculate the strain A stress- strain curve can then be established from which the adhesive's effective shear modulus can be determined References cited in this section Adhesives, Edition 6, D.A.T.A Digest International Plastics Selector, 1991 Adhesives, Annual Book of ASTM Standards, Vol 15.06, ASTM (updated annually) 15 O Volkersen, Die Nietraftverteilung in Zugbeanspruchten Nietverblendugen mit Knastaten Laschenquerschntlen, Luftfahrt forsch., Vol 15, 1938, p 41 16 M Goland and E Reissner, The Stresses in Cemented Joints, J Appl Mech., Vol 11, 1944, p 17 17 J.J Plantema, “De Schuifspanning in eme Limjnaad,” Rep M1181, Nat Luchtvaart-laboratorium, Amsterdam, 1949 18 G.R Wooley and D.R Carver, J Aircr., Vol (No 19), 1971, p 817 19 R.D Adams and N.A Peppiatt, Stress Analysis of Adhesive-Bonded Lap Joints, J Strain Anal., Vol (No 3), 1974, p 185 20 P.S Cooper and J.W Sawyer, “A Critical Examination of Stresses in an Elastic Single Lap Joint,” NASA Tech Rep 1507, NASA Scientific and Technical Information Branch, 1979 21 G.P Anderson and K.L DeVries, Analysis of Standard Bond-Strength Tests, Treatise on Adhesion and Adhesives, Vol 6, R.L Patrick, K.L DeVries, and G.P Andersen, Ed., Marcel Dekker, 1989 22 J.K Strozier, K.J Ninow, K.L DeVries, and G.P Anderson, Adhes Sci Rev., Vol 1, 1987, p 121 23 G.P Anderson, D.H Brinton, K.J Ninow, and K.L DeVries, A Fracture Mechanics Approach to Predicting Bond Strength, Advances in Adhesively Bonded Joints, Proceedings of a Conference at the Winter Annual Meeting of ASME, 27 Nov-2 Dec 1988 (Chicago), S Mall, K.M Liechti, and J.K Vinson, Eds., ASME, 1988, p 98–101 Testing of Adhesive Joints K.L DeVries and Paul Borgmeier, University of Utah Tensile Tests Generally, the idea of mechanical failure produces a vision of an object being pulled apart by tensile force As noted previously, most practical adhesive joints are designed to avoid (or at least reduce) direct tensile forces across the bond line Examples of such joints are lap joints and scarf joints It was also pointed out that for many joints, where it appears that the primary loading is shear, failure might be initiated by the induced secondary tensile stresses There are, therefore, reasons why an adhesive's or adhesive joint's tensile strength might be of interest Accordingly, the third most common type of adhesive joint strength test is the tensile test ASTM has also formalized this type of test The geometries of several tensile tests for which there are specific ASTM test procedures are shown in Fig (Ref 7) Some of these test geometries seem relatively simple; however, it has been demonstrated that the stresses along the bond line have a rather complex dependence on geometric factors and adhesive and adherent properties (adhesive thickness and its variation across the bonded surface, modulus, Poisson's ratio, and so on) (Ref 21) Fig Typical specimen geometries for testing the tensile strength of adhesive joints Source: Ref It is almost always difficult to load tensile adhesion specimens in an axisymmetric manner, even if the sample itself is axisymmetric Nonaxisymmetric loads have been shown to reduce the bond failure load capability and to cause large scatter in the resulting failure data Superficially, the geometry for standard tensile adhesion tests is deceptively simple The result of the tensile adhesion test, as normally reported by experimentalists, is simply the failure load divided by the cross-sectional area of the adhesive (Ref 22) Such average stress at failure can be very misleading Because of the differences in mechanical properties of the adhesive and adherend, the stresses may become singular at the bond edges when analyzed using linear elastic analysis (Ref 21, 23) Even if the edge singularity is neglected, the stress field in the adhesive is very complex and nonuniform, with maximum values differing markedly from the average value (Ref 21, 23) Some sense of the complex nature of the stresses can be obtained by visualizing a butt joint of a low modulus polymer (e.g., a rubber) between two steel cylinders As these are pulled apart, the rubber elongates much more readily than the steel Poisson's effect will cause a tendency for the rubber to contract laterally However, if it is tightly bound to the metal, it is restrained from contracting, and shear stresses are induced at the bond line Reference provides the results of a finite element analysis that demonstrates how these stresses vary across the sample As noted, for an elastic analysis, both the shear and tensile stresses are singular (tending to infinity) at the outer periphery For the tensile specimen configurations considered to this point, the applied loading is intended to be axisymmetric There is another class of specimen in which the dominant stress is deliberately tensile but in which the loading is obviously “off center.” At least four ASTM standards describe so-called cleavage specimens and tests These tests are a logical preface to the next section in this article, “Adhesive Fracture Mechanics Tests” The reader familiar with cohesive fracture mechanics will see a similarity between the test specimen in ASTM D 1062 (Fig 6) and the compact tensile specimen commonly used in fracture mechanics testing ASTM D 1062 specifies reporting the test results as force required, per unit width, to initiate failure in the specimen, while in fracture mechanics, the results are given as Gc with units of J/m2, which might be interpreted as the energy required to create a unit surface A knowledgeable and enterprising reader may want to adapt the D 1062 specimen for obtaining fracture mechanics parameters ASTM D 3807, “Standard Test Method for Strength Properties of Adhesives in Cleavage Peel by Tension Loading,” uses a different geometry to measure the cleavage strength In this case, two 25.4 mm (1 in.) wide by 6.35 mm (0.25 in.) thick plastic strips 177 mm (7 in.) long are bonded over a length of 76 mm (3 in.) on one end, leaving the other ends free and separated by the thickness of the adhesive Approximately 25 mm (1 in.) from the end of each of these free segments, a “gripping wire” is attached as shown in Fig During testing, these wires are clamped in the jaws of a universal testing machine and the sample pulled to failure The results are reported as load per unit width (kg/m or lb/in.) Again, it would be possible to analyze this sample in terms of fracture mechanics, but it is unnecessary because, as the next section explains, this analysis is done in ASTM D 3433 for a very similar beam geometry Fig Specimen for testing the cleavage strength of metal-to-metal adhesive bonds (ASTM D 1062) Fig Specimen for testing cleavage peel (by tension loading) (ASTM D 3807) ASTM D 5041 also makes use of a sample composed of two thin sheets bonded together over part of their length In this case, forcing a wedge (45° angle) between the unbonded portion of the sheets facilitates the separation The results are typically given as “failure initiation energy” or “failure propagation energy” (i.e., areas under the load deformation curve) This latter test is similar to another test, formalized as ASTM D 3762, that has been found very useful for studying time-environmental effects on adhesive bonds This test is called by various names, but the authors prefer the name “Boeing Wedge Test” (Ref 24, 25) The test has been used by personnel at this and other aerospace companies to screen various adhesives, surface treatment, and so on for long-term loading at high temperatures and humidities For testing, two long, slender strips of candidate structural materials are first treated with the prescribed surface treatment(s) and bonded over part of their length with a candidate adhesive (Fig 8) As in the test described in the previous paragraph, the free ends are forced apart by a wedge The amount of separation by the wedge (determined by wedge thickness and depth of insertion) determines the value of the stresses in the adhesive These stresses can, of course, be adjusted and the values calculated from mechanics of material concepts When the wedge is in place, the sample is placed in an environmental chamber At periodic time intervals, the length of the crack is measured, and a plot of crack length versus time is constructed The more satisfactory adhesives and/or surface treatments are those for which the crack is arrested or grows very slowly While the environmental chamber typically contains hot, humid air, there is no reason why other environmental agents cannot be studied by the same method, including immersion in liquids Fig Boeing wedge test (ASTM D 3762) (a) Test specimen (b) Typical crack propagation behavior at 49 °C (120 °F) and 100% relative humidity a, distance from load point to initial crack tip; Δa, growth during exposure Source: Ref 49 References cited in this section Adhesives, Annual Book of ASTM Standards, Vol 15.06, ASTM (updated annually) G.P Anderson and K.L DeVries, Predicting Strength of Adhesive Joints from Test Results, Int J Fract., Vol 39, 1989, p191–200 21 G.P Anderson and K.L DeVries, Analysis of Standard Bond-Strength Tests, Treatise on Adhesion and Adhesives, Vol 6, R.L Patrick, K.L DeVries, and G.P Andersen, Ed., Marcel Dekker, 1989 22 J.K Strozier, K.J Ninow, K.L DeVries, and G.P Anderson, Adhes Sci Rev., Vol 1, 1987, p 121 23 G.P Anderson, D.H Brinton, K.J Ninow, and K.L DeVries, A Fracture Mechanics Approach to Predicting Bond Strength, Advances in Adhesively Bonded Joints, Proceedings of a Conference at the Winter Annual Meeting of ASME, 27 Nov-2 Dec 1988 (Chicago), S Mall, K.M Liechti, and J.K Vinson, Eds., ASME, 1988, p 98–101 24 V.L Hein and F Erodogan, Stress Singularities in a Two-Material Wedge, Int J Fract.,Vol 7, 1971, p 317 25 J.A Marceau, Y Moji, and J.C McMillan, A Wedge Test for Evaluating Adhesive Bonded Surface Durability, 21st SAMPE Symposium, Vol 21, 6–8 April 1976 49 J.C McMillan, Developments in Adhesives in Engineering, 2nd ed., Applied Science, London, 1981, p 243 Testing of Adhesive Joints K.L DeVries and Paul Borgmeier, University of Utah Adhesive Fracture Mechanics Tests Fracture mechanics originated with the pioneering efforts of A.A Griffith in the early 1920s The field remained relatively dormant until the late 1940s when it was developed into a very effective and valuable design tool to describe and predict “cohesive” crack growth Interested readers are referred to a number of excellent texts on fracture mechanics (e.g., Ref 26 and Fatigue and Fracture, Volume 19 of the ASM Handbook) In the 1960s and 1970s, researchers began exploring the use of the concepts of fracture mechanics in adhesive joint analysis as reviewed in Ref These methods have the potential to use the results from a test joint to predict the strength of other joints with different geometries In a common fracture mechanics approach (including Griffith's papers), the conditions for failure are calculated by equating the energy lost from the strain field as a “crack” grows to the energy consumed in creating the new crack surface This energy per unit area, Gc, determined from standard tests, is called by various names, including the Griffith fracture energy, the specific fracture energy, the fracture toughness, or the energy release rate In 1975, ASTM Committee D-14 adopted a test configuration and testing method with fracture mechanics ramifications based on the pioneering efforts of Mostovy and Ripling (Ref 27, 28) The method is described in ASTM D 3433 “Standard Test Method for Fracture Strength in Cleavage of Adhesives in Bonded Joints.” Figure shows the shape and dimensions for one specimen type recommended for use in this standard The specimen is composed of two “beams” adhesively bonded over much of their length as shown Testing is accomplished by pulling the specimen apart by means of pins passing through the holes shown near the sample's left end This adhesive sample configuration and loading to failure gives rise to the sample's nickname, “split-cantilever beam.” Another recommended geometry in ASTM D 3433 is similar except the adherends are not tapered Fig Specimen for the contoured double-cantilever-beam test (ASTM D 3433) It should now be clear that the stress distribution in adhesive joints is generally complex Furthermore, the details of this distribution are highly dependent on specific details of the joint system The maximum stresses in the bond almost always differ markedly from the average value, and elastic analyses often exhibit mathematical singularities at geometric or material discontinuities From these observations, it should be clear that the use of the conventionally reported results from most tests (i.e., values of the average stress at failure) would be of little use in designing joints that differ in any significant detail from the sample test configuration For the resolution of this problem, the concepts of fracture mechanics have much to offer One of the more popular and graphically appealing approaches to fracture mechanics views the joint as a system in which failure (often considered as the growth of a crack) of a material (or joint) requires the stresses at the crack tip to be sufficient to break bonds and an energy balance It is hypothesized that even if the stresses are very large (often theoretically infinite), a crack can grow only if sufficient energy is released from the stress field to account for the energy required to create the new crack (or adhesive debond) surface as the fractured region enlarges The specific value of this energy (J/m2, or in · lbf/in.2, of crack area) for the adhesive bonding problem uses the same basic titles as given previously but prefaced with the term adhesive Hence, adhesive fracture toughness might be used to distinguish adhesive failure from tests of cohesive fracture The word adhesion is dropped from the comparable term when cohesive failure is being considered The cohesive and adhesive embodiments of fracture mechanics both involve a stress-strain analysis and an energy balance The analytical methods of fracture mechanics (both cohesive and adhesive) are described in Ref and 25 These are not repeated here other than a few comments on the concepts and a brief outline of a numerical approach that can be applied where analytical solutions are tedious or impossible Inherent in fracture mechanics is the concept that natural cracks or other stress risers exist in materials and that final failure of an object often initiates at such points For a crack (or region of debond) situated in an adhesive layer, modern computation techniques are available (most notably, finite element methods) that facilitate the computation of stresses and strains throughout a body, even if analytical solutions may not be possible The stresses and strains are calculated throughout the entire adhesive system (adhesive and all adherends), including the effects of a crack in the bond These can then be used to calculate the strain energy, U1, stored in the body for the particular crack size, A1 Next, the hypothetical crack is allowed to grow to a slightly larger area, A2, and the preceding process is repeated to determine the strain energy, U2 This approach to fracture mechanics assumes that at critical crack growth conditions, the energy loss from the stress-strain field goes into the formation of the new fracture energy The quantity ΔU/ΔA is called the energy release rate, where ΔU = U2 - U1 and ΔA = A2 - A1 The so-called critical energy release rate (ΔU/ΔA)crit is that value of the energy release rate that will cause the crack to grow Loads that result in energy release rates lower than this critical value will not cause failure to proceed from the given crack, while loads that produce energy release rates greater than this value will cause it to accelerate This critical energy release rate value is equivalent to the adhesive fracture energy, or work of adhesion, previously noted While the model just described is conceptually useful, computer engineers have devised other convenient ways of computing the energy required to “create” the new surface, such as the crack closure method (Ref 29, 30) It is hoped that this simple model of fracture mechanics will help the reader who is unfamiliar with fracture mechanics to visualize the concepts of fracture mechanics The molecular mechanisms responsible for the fracture energy or fracture toughness are not completely understood They generally involve more than simply the energy required to rupture a plane of molecular bonds In fact, for most practical adhesives, the energy to rupture these bonds is a small but essential fraction of the total energy The total energy includes energy that is lost because of viscous, plastic, and other dissipation mechanisms at the tip of the crack As a result, linear elastic stress analyses are inexact While fracture mechanics has found extensive use in cohesive failure considerations, its use for analyzing failure of adhesive systems is more recent There has, however, been a significant amount of research and development in the adhesive fracture mechanics area To review it all, even superficially, would take more space than is allocated for this article A small sampling of publications in this extensive and rich area of research is listed as Ref 12, 13, 26, 27, 28, and 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58 Not only is this listing incomplete, but also many of the researchers listed have scores of other publications It is hoped that the one or two listed for each investigator will provide the reader with a starting point from which more details can be found from reference cross listings, searching of citation indexes, abstracting services, and so on These investigators have treated such subjects as theory; mode dependence, effects of shape, thickness, and other geometric dependence; plasticity and other nonlinearities; numerical methods; testing techniques; different adhesive types; rate and temperature effects; fatigue; and failure of composites, as well as a wide variety of other factors and considerations in adhesion Modern finite element or other numerical methods have no difficulty in treating nonlinear behavior Physical understanding of material behavior at such levels is lacking, and effective use of the capabilities of such computer codes depends, to a large extent, on the experimental determination of these properties For many problems, it has become conventional to lump all dissipative effects together into the fracture energy and not be overly concerned with separating this quantity into its individual energy-absorbing components Another fracture mechanics approach, called the J-integral, has some advantages in treating nonlinear as well as elastic behavior (Ref 51, 52, 59, and 60) It was noted previously that most adhesive systems are not linearly elastic up to the failure point Nevertheless, researchers have shown that elastic analyses of many systems can be very informative and useful Several adhesive systems are sufficiently linear so that it is possible to lump the plastic deformation and other energy dissipative mechanisms at the crack tip into the adhesive fracture energy (critical energy release rate) term There has recently been some significant success in explaining many aspects of adhesive performance and (Eq 9) (Eq 10) Differentiation of Eq 8, 9, and 10 with respect to x, y, z, respectively, yields: (Eq 11) (Eq 12) (Eq 13) Subtracting the summation of Eq 11 and 12 from Eq 13, results in: (Eq 14) Variation of Sx along the x-axis is small in the middle portion of the plate; therefore, the first term in Eq 14 can be neglected Equation 14 can be approximated using the following: (Eq 15) where Sy0 = value of Sy at the axis; Sy1 = value of Sy1 at a distance Δy1 on either side of the x axis; and τx2y2 = value of τxy at a distance Δx2 and Δy2 from the y axis and x axis respectively Therefore the stress in the thickness direction Sz can be obtained through double integration with the boundary condition that Sz vanishes at both the top and bottom surfaces In this way the entire triaxial residual stress state was determined Note that this procedure assumes that the residual stresses are uniform along the length of each block A variation on Rosenthal and Norton's (Ref 30) method using electrical resistance strain gages or a nondestructive technique such as XRD is as follows The largest face of the blocks (described by the thickness of the component or plate and the longest dimension of the blocks, Fig 5) is divided into a two-dimensional grid of elements An electrical resistance strain gage is placed on each element, or a nondestructive measurement such as XRD is performed The block is sectioned along the grid lines to produce elements that are assumed to be stress free Note that if a nondestructive technique such as XRD is used, the plastically deformed surface created by removing the block from the original component must be removed This is best done using electropolishing (see the section of this article “Sectioning and Material Removal Methods”) If electropolishing of these cut faces is done to remove the plastic deformation and resultant residual stress induced by a mechanical cutting procedure and XRD is applied, then the blocks need not be sectioned The measured XRD stress will provide the absolute residual stress field condition in the block, and, coupled with the strain relieved by the original removal of the block from the plate, the entire triaxial residual stress condition of the plate may be obtained This variation on Rosenthal and Norton's (Ref 30) method provides the information necessary to derive the biaxial stress condition of each block, which can in turn be used to derive the triaxial condition of the original plate The stresses on each of the measured faces of the blocks must be measured in three directions to provide the information necessary to obtain the principal stresses in the block faces in each element Note that the strain change caused by the sectioning of the blocks must be added to the strains measured in each element This procedure may be applied to a weldment with a single weld through its center as described by Rosenthal and Norton (Ref 30), or to a more elaborate stress field, for example, where two orthogonal welds existed in the component (plate) With a single weld, only the block-intersecting weld needs to be sectioned into elements, because the residual stress field in the block parallel to the weld is likely to be constant along the direction parallel to the weld Moore and Evans (Ref 6) proposed mathematical procedures for the reconstruction of the original threedimensional residual stress fields in cylindrical and flat plate components, and Constantinescu and Ballard (Ref 7) recently proposed a modification of Moore and Evans's work They proposed using XRD as the measurement technique and presented stress reconstruction equations for the following conditions: (a) solid cylinder bar with rotationally symmetric stresses; (b) solid cylinder bar without rotationally symmetric stresses; (c) hollow cylinder bar with rotationally symmetric stresses; and (d) flat plate with biaxial stresses The Moore and Evans procedures are described in the Society of Automotive Engineers Handbook Supplement (Ref 8) and summarized in the following paragraphs Solid Cylinder Bar with Rotationally Symmetric Stresses It was presumed that the residual stress distribution had both rotational and longitudinal symmetry, except near the ends where measurements were avoided Stresses were therefore functions of the radius, r, and did not depend on the angle, θ, measured around the cylinder, nor the distance, z, taken parallel to the axis With repeated removal of thin concentric shells, the stresses on the exposed surface in depth were obtainable The circumferential and longitudinal measures of stress, σθm (r) and σzm (r), respectively, were then used to calculate the original stresses, σθ(r) and σz(r), as well as the radial stress, σr(r) The theory of elasticity provides nine partial differential equations—the three equations of equilibrium and the six equations of compatibility Unique solutions are possible, depending on boundary conditions For the case considered, the nine equations give the following working formulas: (Eq 16) (Eq 17) σθ(r1) = σθm (r1) + σr(r1) (Eq 18) where r is the original radius, and r1 is the radius at the depth of interest Solid Cylinder Bar without Rotationally Symmetric Stresses Stresses were again assumed independent of z but allowed to vary in the circumferential, θ, direction Complex variable methods gave general solutions for stresses in the radial, σr(r1,θ) circumferential, σθ(r1,θ); and axial, σz(r1,θ), directions as well as the shear stress, τrθ(r1,θ) Details of the equations used may be found in the references (Ref or 8) Hollow Cylinder Bar with Rotationally Symmetric Stresses With the inside radius included in the equations used to calculate σr (r1), σz (r1), and σθ(r1), the general solutions for these stresses are developed (Ref 6, 8) Flat Plate with Biaxial Stresses It was assumed that the residual stresses in a flat plate of uniform thickness depended only on the distance from one of the flat surfaces of the plate, except, of course, near the edges It was also assumed that the principal stresses are σx and σy, lying in the plane of the flat surfaces, and that the stress normal to the flat surfaces, σz, was zero at all points sufficiently distant from the edges From the assumptions and conditions of equilibrium, the true stresses σx(z1) at depth z1 could be expressed in terms of the measured stress σxm (z1) by the relation: (Eq 19) where H = original thickness of the plate and z1 = distance from lower surface to uncovered depth of interest A similar expression holds for the y direction Equation 19 holds, even if σx and σy are not principal stresses, but in this case a shear stress also exists, expressed by: (Eq 20) τxym (z) is determined from: σαm (z1) = σxm (z1) cos2 α + σym (z1) sin2 α (Eq 21) + 2τxym (z1) sin α cos α where α is the acute angle that the measured stress σαm (z1) makes with the x axis When measurements are taken 45° apart, τxym (z1) becomes: τxym (z1) = σ45 deg(z1 - (σxm (z1) (Eq 22) + σym (z1)) meaning that three x-ray stress measurements are required after each layer is removed Johanssen (Ref 32) proposed a procedure for the determination of the three-dimensional residual stress field in thick plate (plate weldments) components using XRD techniques to measure the strains on the surfaces of the plate and plate sections and on removal of layers of surfaces The procedure included the measurement of the biaxial stress field existing on the top surface of the component (Fig 6), assuming that the stress perpendicular to the surface is zero Material was removed from this surface by, for example, milling and electropolishing or by electropolishing alone (see the section “Sectioning and Material Removal Methods”), and the biaxial stresses were remeasured at the new depth Each time material was removed, the forces that the removed layer exerted on the remaining component had to be accounted for, and the subsequent measurements required correction for this change in the stress field Johanssen based his method on the following assumptions: • • • • When a layer of material is removed, the resulting changes in the stress condition will be linear elastic; that is, Hooke's law is applicable The residual stress distribution is constant in the z-direction, except at the surface, and σz is a principal stress in the z-direction (Fig 6) On material removal, it is assumed that the strain, εz, remains unchanged Together with the previous assumption, this implies that the change in stresses can be treated as a plane problem It is assumed that the stresses are symmetrical with respect to the y-z plane This assumption is, however, not necessary The procedure can be developed to include asymmetrical stress states Fig A ft by ft by ft weldment showing the layers proposed by Johanssen (Ref 32) where the thickness (T) of the layers are 12.70 mm (0.5 in.) and σI = σy, σII = σx, and σIII = σz Johanssen's (Ref 32) justification for his procedure to measure the three-dimensional stress field in the weldment shown in Fig is as follows Johanssen showed that the change in stresses resulting from the removal of material can be determined by Δσ(x) and ν(x) shown in Fig These were to be measured at a number of positions xi, i = 1, …, N, on the lower side of the plate Δσx(x) and ν(x) are the differences between the stress and deformation measured prior to and following the removal of material Changes in the internal stress conditions are thus calculated directly and need not be calculated as accumulated stress changes resulting from several layers of material being removed The development of equations for the stress reconstruction may be found in Ref 32 Fig Residual stress distributions, forces, and distortion of a plate before and after layer removal (a) Residual stress distribution in the x-direction in the center of the plate in the x-z plane (b) Same as (a) after removal of a layer with the forces Ti(j) caused by the residual stresses tending to distort the plate (c) Same as (b) with the distortion displacement shown (Ref 32) Pickel (Ref 40) described a method for analytical solution of problems with similar boundary conditions to Johanssen's, using infinite, related series, but in this instance, an approximate method was used with trial solutions that were more convenient and numerically more stable than those used by Johanssen Sikarskie (Ref 41) proposed a stress reconstruction procedure (series method) when thin layers were removed from the surface of a component He described procedures applicable to flat plates and solid cylinders The procedure works well for shallow depths (a few percent of specimen diameter or thickness) or in instances where the stress gradient over the total depth removed does not change too rapidly and is of essentially one sign The practicality of this method depends on the fit of the measured stresses in depth by a Taylor's series referred to the surface values of stress and successive derivatives at the surface When the method is applicable, very convenient relations are obtained, which describe the stress correction in terms of the influencing factors; for example, layer depth, stress magnitude, stress gradient, and specimen size Judgment is necessary, however, in using the series approximation, which does not arise when using the exact equations of the previous sections The method is summarized for two of the previous cases as follows Flat Plate (See the previous discussion “Flat Plate, Biaxial Stress” for the Moore and Evans procedures.) A generalized solution is written: (Eq 23) The subscripts x, y, or xy have been dropped, because the form of Eq 19 and 20 are exactly the same σ(z1) represents the true stress in any direction at depth, z1, before a layer was removed, and σm(z1) represents the measured value at that depth The correction in stress, c(z1), at z1 is the difference between the true and measured values, given by: (Eq 24) The integrands are then expanded in a Taylor's series referred to the surface values, after which the integration is performed term by term The final form for the correction is: (Eq 25) where σm(H), σ′m (H) are true surface stress and successive derivatives with respect to z at the surface For shallow depths only, the first terms of the series may be used and: (Eq 26) where Δz1 = H - z1 This correction is seen to be approximately proportional to the magnitude of the surface stress and thickness of the removed layer (Fig 8) It is inversely proportional to the specimen thickness Fig Stresses in flat plate after layer removal By solving for Δz1, the question of proper slice is given by: (Eq 27) Thus, for example, if the measured stress is to be in error by less than 5%, -c(z1)/σm(H) = 0.05, and the appropriate slice depth is: (Eq 28) For a plate 102 mm (4.0 in.) thick, for example, the slice depth is 1.3 mm (0.050 in.) If the stress gradient is high, then the next term in the correction series should be included, and a quadratic in Δz1 should be solved This requires an estimate of σ′m(H) based on experience Solid Cylinder (See the previous discussion “Solid Cylinder Bar with Rotationally Symmetric Stresses” for the Moore and Evans procedures.) A generalized solution from Eq 16 and 17 is written: (Eq 29) where, again, the subscripts r, θ, and z have been dropped because the form is the same When σr(r1) is desired: σ(r1) = σr(r1) σm(r1) = (Eq 30) k=1 σm(r) = σθm(r) When σz(r1) is desired: σ(r1) = σz(r1) σm(r1) = σzm(r1) (Eq 31) k=2 σm(r) = σzm(r) σθ(r1) is calculated from σθm (r1) using Eq 18 The correction term in stress, c(r1), is written as before: c(r1) = σ(r1) - σm(r1) (Eq 32) Again, expanding the integrand of Eq 29 in a Taylor's series and integrating term by term, a final form for the correction is obtained: (Eq 33) where σm(R), σ′m(R) and so on, are the surface stress and successive derivatives with respect to z at the surface Insights into the factors that influence the correction apply exactly as previously discussed, as the limitations of the method Ruud et al (Ref 33, 34) applied a modification of the Johanssen method to measure the triaxial stress condition of thick plate Cr-1 Mo plate weldments They actually measured the strains in all directions and calculated the stresses but did not correct for layer removal due to the complex nature of the stress field Ruud et al also measured the residual stress condition of expanded tubing including 304 stainless steel tubing (Ref 35) but focused on the residual stresses on the inside surface of the heat exchanger tube components Table summarizes the destructive residual stress measurement procedure described in this section of this article Sectioning and Material Removal Methods As discussed in the previous sections on destructive measurement procedures, many procedures require that the component (sample or part) be sectioned and/or some material be removed from it to measure the residual stresses This is especially true for the measurement of internal residual stress fields where the component nearly always must be sectioned to reveal the internal stress field There are two exceptions to the necessity of sectioning and material removal, and these are neutron diffraction and ultrasonic methods, which will be described in the section “Nondestructive Procedures.” Sectioning or material removal may be required by a particular residual stress measurement procedure or method Mechanical chip removal processes are usually applied because of their economy and speed All chip removal processes, including lathe turning, drilling, milling, sawing, grinding, and so forth, introduce surface residual stresses that can be as high as the yield strength of the strain hardened metal and several thousandths of an inch (tens of microns) in depth (Ref 36, 42, 43, 44, and 45) Figures 10 11 show the residual stresses in steels caused by various machining processes Further, some steels are especially prone to strain hardening, for example, austenitic stainless steels, and extra care must be used with these materials when selecting a material removal technique Figure 12 shows plots of the residual stresses in 304 austenitic stainless steel caused by various grinding methods Note that these plots are only samples and may not be typical If the size of the element in which the strain change is measured is smaller, or thinner in the case of surface depth gradients, than about to mm ( in.), then a chemical or electrochemical material removal technique must be used to remove the surface residual stresses caused by mechanical chip removal These techniques may be used solely or in conjunction and after the chip removal method It should be noted that material removal techniques such as electrical discharge machining (EDM) induce residual stresses (Ref 46) as chip removal methods Other methods, such as laser, flame, or plasma cutting, which cause heating of the element, must be applied with caution because they may reduce the stress field to be measured by annealing before measurement Fig Residual stresses at the surface and near the surface due to milling a medium carbon steel workpiece Fig 10 Residual stresses in a 440C stainless steel workpiece induced by facing Fig 11 Residual stresses in an alloy steel workpiece induced by turning Fig 12 Samplings of residual stress distributions induced in 304 stainless steel workpieces by common grinding procedures Thus, the only methods for material removal from a component surface that not induce residual stresses are electrolytic or chemical polishing Electropolishing is described in some detail in Surface Cleaning, Finishing, and Coating, Volume 5, 9th ed., of Metals Handbook (Ref 47), and guidelines are provided for application to various alloys on Table of that publication In electropolishing, the electrolyte and operating conditions depend on the alloy being polished as shown in the Metals Handbook (Ref 47) and the SAE Handbook Supplement (Ref 8) Electropolishing combined with XRD is used extensively to reveal residual stress gradients on machined, ground, and hardened surfaces However, application of these techniques requires that the subsurface stresses be corrected for the removal of prior surface layers (Ref 8) Another concern when reducing components to a more convenient, smaller size when it is necessary in order to place them on or in a measurement device is that the stresses of interest are likely changed by the sectioning Generally plates should be cut to a length and width of at least three times the thickness to avoid end effects Cylinders, both thin-walled and solid, should be a minimum of three diameters in length Where the manufacturing process affects the entire thickness of a component, such as heat treatment or forging, it might not be advisable to section without means of measuring the stress change extensively over the entire component before sectioning In other words, selection of the stress measurement procedure and methods should avoid sectioning unless techniques to measure the effects of sectioning are applied before sectioning is initiated On the other hand, when the processes that have induced the residual stress produce only shallow stress fields, then the three times rule suggested above is applicable Strain Measurement Methods As discussed in the section “Stress Measurement” in this article, all residual stress determination methods measure elastic strain, not stress, and the residual stress is calculated from the strain values Several methods for the measurement of strain have been applied in residual stress studies, and some have been mentioned previously These methods include mechanical gages, electrical resistance gages, brittle coatings, optical gages, laser methods, birefringent methods, diffraction methods (x-ray and neutron), ultrasonic methods, and magnetic methods The last three methods will be discussed in the section “Nondestructive Procedures” in this article Mechanical Gages The application of mechanical gages such as those described by Heyn (Ref 23), Stablein (Ref 24), Gunnert (Ref 27), and others generally preceded the availability of electrical resistance strain gages and are not discussed here due to their general lack of precision, poor spatial resolution, and inefficiency Electrical Resistance Strain Gages Most bonded electrical resistance strain gages are made from either metallic wire or foil materials There are also the recently developed semiconductor gages A variety of sizes, shapes, and configurations are available, including single-element gages and rosettes with two, three, or four elements Electrical resistance strain gages are available in sizes as small as about mm and thus provide a resolution of strain measurement on that order Information on electrical strain gages is available in numerous sources, including the Handbook of Experimental Stress Analysis (Ref 48) and in reviews by Crites (Ref 49) and Masubuchi (Ref 15) as well as by suppliers Changes in temperature tend to cause an apparent strain Some type of temperature compensation, therefore, is needed Frequently, a dummy gage, which is not subjected to the strain, is exposed to the same temperature as the actual gage to provide a basis for comparison A temperature-compensated gage can also be used Gages must be bonded securely to the specimen Various types of cements have been developed Sometimes gages must be protected from metal chips produced during machining as well as from the oil or water A number of systems have been devised for protecting gages under various conditions Brittle Coatings A simple inexpensive strain gage that will only provide qualitative indications of residual stress is used for brittle coatings Here a brittle lacquer is applied to the area where the stresses are to be measured by a material removal method After the lacquer has cured (dried), a change in the stress field is induced, and if the change is sufficient, strain will be produced in the lacquer, causing it to crack If the material removal is in the form of a hole drilled in the lacquer, radial cracks indicate a tensile residual stress in the plane of the component surface, and circular cracks indicate compressive stress Optical Gages In a well-fixtured component that is held securely in place during material removal to change the stress field and, therefore, induce strain change, light reflective methods can be used to magnify the movement of a reflective surface Also, this method can be used if the component can be removed and replaced precisely in a fixture and if the position of the reflected light can be measured before and after removal and replacement, during which a change in the residual stress field is induced Laser Methods Other techniques applying laser light have been proposed as well These have included shearography (Ref 50), interferometry (Ref 51), speckle-correlation interferometry (Ref 52), and others Vikram et al (Ref 52) suggested that a small volume of the material could be stress relieved by heating via a laser to induce a change in the stress field and the strain change measured by an optical technique to reveal the residual stresses existing in the volume before heating However, it must be recognized that heating a volume of metal sufficiently to change the residual stress field will result in tensile residual stresses in the heated volume, as observed by Cullity (Ref 53, p 471–472), and this would likely be detrimental to the component in which stresses were being measured Birefringent Methods Under the action of stresses, transparent materials become doubly refracting (birefringent), and if a beam of a polarized light is passed through a model (under stress) made of such a material, a colored image is obtained from which the stress distribution can be determined This technique is called the photoelastic technique (Ref 48) A practical variation on this technique is to coat a metal component in which the residual stress is to be measured with a photoelastic polymer When residual stress changes are induced in the component, strain changes are caused and transmitted to the polymer coating, which then becomes birefringent This can be observed and measured using a reflection polariscope (Ref 15) Instructions for analyzing fringe patterns in this application (nearly the same as those obtained in ordinary photoelasticity) are provided by the manufacturer of the polariscope The photoelastic coating may be applied by brushing a liquid polymer on the surface of the specimen and polymerizing it by applying heat Alternatively, a prefabricated flat or contoured sheet of polymer may be bonded to the part at room temperature (Ref 54) The maximum strain that can be measured ranges between and 50%, depending on the type of polymer used; the strain sensitivity usually decreases with the increase in the maximum measurable strain Chemical Methods A number of qualitative methods to detect residual stresses that may lead to stress corrosion or hydrogeninduced cracking (HIC) in metals have been applied to specimens representing components to be manufactured Magnesium chloride solutions have been applied extensively to the study of stress corrosion in nickel alloys and austenitic stainless steels, including some recent work by Bouzina et al (Ref 55) Masabuchi and Martin (Ref 56) studied the susceptibility of SAE 4340 steel weldments to hydrogen-induced stress cracking The test procedure was to immerse the weldment specimens in a 4% H2SO4 (sulfuric acid) aqueous solution charged with H2 and to which two drops of a 5% phosphorus (P) solution of CS2 was dissolved A direct current (dc) was applied between a specimen and a lead anode to provide a current density of 0.5 to 1.2 mA/mm2 (0.35 to 0.8 A/in.2) The crack patterns that developed were related to the surface tensile residual stress distribution in each specimen Stress corrosion cracking (SCC) induced by residual stresses in carbon and low-alloy high-strength steels have been investigated by several researchers (Ref 56, 57, and 58) One procedure consisted of immersing the specimens in a boiling aqueous solution of 60% Ca(NO3)2 and 4% NH4NO3 for 31 h The crack patterns that developed were related to the surface tensile residual stress distributions in the specimen A number of standard practices for testing the susceptibility of metals to SCC have been published by ASTM, including the following: Title ASTM No G 38 Standard Recommended Practice for Making and Using C-Ring Stress Corrosion Test Specimens G 58 Standard Practice for the Preparation of Stress Corrosion Test Specimens for Weldments G 39 Standard Practice for the Preparation and Use of the Bent-Beam Stress Corrosion Test Specimens G 30 Standard Recommended Practice for Making and Using U-Bend Stress Corrosion Test Specimens STP 425 Stress Corrosion Testing However, these tests for the most part not reveal the residual stress but the susceptibility of the metal to cracking under known stresses in the specified corrosion medium—not residual stress References cited in this section R Gunnert, “Method for Measuring Triaxial Residual Stresses,” Document No X-184057-OE, Commission X of the International Institute of Welding, 1957, and Weld Res Abroad, Vol (No 10), 1958, p 1725 M.G Moore and W.P Evans, Mathematical Corrections in Removal Layers in X-Ray Diffraction Residual Stress Analysis, SAE Trans., Vol 66, 1958, p 340–345 A Constantinescu and P Ballard, On the Reconstruction Formulae of Subsurface Residual Stresses after Matter Removal, The Fifth International Conf on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 703–708 Residual Stress Measurement by X-Ray Diffraction-SAE J784a, Society of Automotive Engineers Handbook Supplement, Warrendale, PA, 1971 15 K Masubuchi, Analysis of Welded Structures: Residual Stresses, Distortion, and Their Consequences, 1st ed., Pergamon Press, 1980 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 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 23 E Heyn, Internal Strains in Cold Wrought Metals, and Some Troubled Caused Thereby, J Inst Met., Vol 12, 1914, p 1–37 24 E Stablein, Stress Measurements on Billets Quenched from One Side,” Stahl and Eisen, Vol 52, 1932, p 15–17 25 M Mesnager, Methods for the Determination of Stresses Existing in a Circular Cylinder, C.R Hebd Seances Acad Sci., 1926, Vol 169 26 G Sacks, Evidence of Residual Stresses in Rods and Tubes, Feitschriff fur Metallkunde, Vol 19, 1927, p 352–357 27 T.G Trenting and W.T Read, Jr., J Appl Phys., Vol 22 (No 2), Feb 1951, 130–134 28 R Gunnert, Residual Welding Stresses, Method of Measuring Residual Stresses and Its Application to a Study of Residual Welding Stresses, Alquist E Wicksell, Stockholm, 1955 29 R Gunnert, “Method for Measuring Residual Stresses in the Interior of a Material,” Document No X162-57, Commission X of the International Institute of Welding, 1957, and Weld Res Abroad, Vol 6, 1960, p 10–24 30 D Rosenthal and J.T Norton, A Method for Measuring Triaxial Residual Stresses in Plates, Weld J., Vol 24 (No 5), Research Supplement, 194 295s–307s 31 R J-S Chen, “Determination of Residual Stresses in a Thick Weldment,” M.S thesis, The Pennsylvania State University, November 1983 32 P Johanssen, “Determination of Residual Stresses in Thick Welded Plated Utilizing X-Rays and Layer Removal Techniques, Part 1: Theory for Reconstruction of Original Stress State,” Internal Report, Department of Materials and Solid Mechanics, The Royal Institute of Technology, S100, 44, Stockholm, April 1978 33 C.O Ruud, R.N Pangborn, P.S DiMascio, and P.J Snoha, Residual Stress Measurement on Thick Plate Low-Alloy Steel Narrow Gap Weldments by X-Ray Diffraction, ASME, 84-PVP-128, 1984 34 C.O Ruud, J.A Josef, and D.J Snoha, “Residual Stress Characterization of Thick-Plate Weldments Using X-ray Diffraction,” Weld Res J Supplement, AWS, March 1993, p 875–915 35 A.R McIlree, C.O Ruud, and M.E Jacobs, The Residual Stresses in Stress Corrosion Performance of Roller Expanded Inconel 600 Steam Generator Tubing, Proc of the International Conf on Expanded and Rolled Joint Technology, Canadian Nuclear Society, 1993, p 139–148 36 Y.W Park, P.H Cohen, and C.O Ruud, The Development of a Model for Plastic Deformation in Machined Surface, Mater Manuf Process., Vol (No 5), 1994 37 E Schreiber and H Schlicht, Residual Stresses After Turning of Hardened Components, Residual Stresses in Science and Technology, Vol 2, DGM Informationsgesell Schaft, Verlag, Germany, 1987, p 853–860 38 W.J Shack, W.A Ellingson, and L.E Pahis, “Measurements of Residual Stresses in Type-304 Stainless Steel Piping Butt Welds,” EPRI NoP-1413, R.P 449-1, Electric Power Research Institute, Palo Alto, CA, June 1980 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 40 G Pickel, Application of the Fourier Method to the Solution of Certain Boundary Problems in the Theory of Elasticity, J Appl Mech., 1944, p 176–182 41 D.L Sikarskie, On a Series Form of Correction to Stresses Measured Using X-Ray Diffraction, AIME Trans., Vol 39, 1967, p 577–580 42 Y.W Park, P.H Cohen, and C.O Ruud, Sensitivity of Shear Process on Metal Cutting to the Development of Residual Stress, Rev Prog in NDE, Vol 14, 1995, p 1183–1188 43 Y.C Shin, S.J Oh, and C.O Ruud, Investigation of Residual Stresses of Machined Surfaces by an XRay Diffraction Technique, NDC of Materials IV, Plenum Press, 1992, p 408–418 44 J.E Hoffman, D Lohe, and E Macherauch, Influence of Machining Residual Stresses on the Bending Fatigue Behaviors of Notched Specimens of Ck45 in Different Heat Treating States, Residual Stresses in Science and Technology, Vol 2, p 801–814, DGM Informationsgesell Schaft, Verlag, Germany, 1987 45 E Brinksmier, Residual Stressed in Hard Metal Cutting, Residual Stresses in Science and Technology, Vol 2, DGM Informationsgesell Schaft, Verlag, Germany, 1987, p 839–846 46 F Ghanem, H Dishom, C Braham, R Fatallak, and J Leider, An Engineering Approach to the Residual Stresses Due to Electric-Discharge Machining Process, Proc The Fifth International Conf on Residual Stresses (ICRS-5), Vol 1, Ericson, Oden, and Anderson, Ed., Institute of Technology, Linkopings University, Sweden, 1977, p 157–163 47 Electropolishing, Surface Cleaning, Finishing, and Coating, Vol 5, Metals Handbook, 9th ed., American Society for Metals, Vol 5, 1982, p 303–309 48 M Hetenyi, Ed., Handbook of Experimental Stress Analysis, John Wiley & Sons, Inc., 1950 49 N.A Crites, Your Guide to Today's Strain Gages, Prod Eng., Vol 33 (No 4), 17 Feb 1962, p 69–81, and Equipment and Application-Today's Strain Gages, Prod Eng., Vol 33 (No 6), 19 March 1962, p 85–93 50 Y.Y Hung, Shearography: A New Optical Method for Strain Measurement and Nondestructive Testing, Opt Eng., Vol 21 (No 3), 1982, p 391–394 51 K Li, Interferometric Strain/Slope Rosette Technique for Measuring Displacements/Slopes/Strains/Residual Stresses, Proc of the 1997 NSF Design and Manufacturing Grantees Conf., University of Washington, Seattle, National Science Foundation (NSF), 1997, p 571– 572 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 54 C.O Ruud, “Residual and Applied Stress Analysis of an Alloy 600 Row U-Bend,” NP-5282, R.P 5303-3, Elect Power Res Inst., Palo Alto, CA 1987, p 2–11 55 A Bouzina, C Braham, and J Ledion, Evaluation and Prediction of Real Stress State Stress Corrosion Cracking Specimens, The Fifth International Conf on Residual Stresses, Vol 2, Institute of Technology, Linkopings University, Sweden, 1997, p 1060–1065 56 K Masubuchi and D.C Martin, Investigation of Residual Stresses by Use of Hydrogen Cracking, Weld J., Vol 40 (No 12), Research Supplement, 1961, p 553s–556s 57 C.E McKinsey, Effect of Low-Temperature Stress Relieving on Stress Corrosion Cracking, Weld J., Vol 33 (No 4), 1954, Research Supplement p 161s–166s 58 W Radeker, A New Method for Proving the Existence of Internal Stress Caused by Welding, Schneissen Schneider, Vol 10 (No 9), 1958, p 351–358 Residual Stress Measurements Clayton O Ruud, The Pennsylvania State University Semidestructive Procedures Nondestructive methods of residual stress measurement are characterized as methods that in no way affect the serviceability or reduce the mechanical strength or other properties of the component in which stresses are measured Between the nondestructive and destructive methods, which have a severe effect on the serviceability, strength, and properties, are the semidestructive methods These are methods that have a small to negligible effect on the components in which stresses are measured or methods for which the component may be repaired after the measurement The methods that are considered semidestructive are those that require small holes to be drilled, rings to be trepanned in the component, or indentations to be made in the surface The first two methods provide quantitative data, and the third produces only qualitative data Blind Hole Drilling and Ring Coring The hole-drilling method was proposed nearly seven decades ago (Ref 59) and is based on measurement of the change in surface strain caused by stresses relieved by machining a shallow hole in the test piece The principle is that stressed material, on being removed, results in the surrounding material readjusting its stress state to attain equilibrium The method has been standardized in ASTM E 837 (Ref 60) The ring core method (Ref 61) is also based on the strain caused by redisturbing the stress field, but in this case a relatively stress-free island of material is isolated by making a shallow ring around a strain gage This method is also called trepanning These two methods are the least destructive mechanical stress relief techniques and are relatively simple and economical They, as by and large all stress relief techniques do, rely on electrical resistance strain gages to measure the strain change due to metal removal Rosettes of strain gages are available especially for hole drilling The size of the rosettes has been progressively reduced over the last few decades, and rosettes are now available in sizes less than about 10 mm from a number of manufacturers As with most residual stress techniques, hole drilling and ring coring have been applied mostly to steels Most applications have been done on flat plate or cylindrically round parts (Ref 9, 62, 63) Stresses can be determined at various depths into the surface of the material, down to a depth equal to the diameter of the hole or core (Ref 64, 65) Kelsey (Ref 66), however, observed that stresses with depth cannot be measured accurately to greater than half the hole diameter The thickness of the layers in which stresses may be resolved is about 10 to 20% of the hole or core diameter The equipment necessary to perform the measurement is reasonably inexpensive, portable, and can be used in a manufacturing shop environment However, experienced technologists are necessary to perform many tasks in taking the readings—from selecting the area in which stresses are to be measured to preparing the surface, applying the strain gages, and reading and interpreting the data Due to the possibility of residual stresses being induced by the hole drilling or coring technique, prior calibration of the application is recommended in all cases, with the possible exception of certain applications where holes are produced by abrasive jet machining (Ref 67) Rendler and Vigness (Ref 68) developed calibration constants for cold-rolled steel, which they proposed as generally applicable to all metals, provided that the elastic constants were known However, they seem to have overlooked variations in the strain hardening coefficients and the accompanying residual stress, which exist between alloys and even between tempers of the same alloy Dini et al (Ref 69) showed that direct experimental determination of the necessary constants for any isotropic material with known elastic constants can be eliminated by using data available for cold-rolled steel and calculating these constants using a formula presented Despite the success that some researchers have claimed in circumventing the development of calibration constants, experimental calibration is strongly recommended This is best done by applying strain gages and drilling the holes in test pieces prior to stressing them known amounts (Ref 67, 68) The abrasive jet machining (AJM) technique should be applied to any material with high propensity to work hardening during machining, for example, austenitic stainless steel (Ref 70) The following are general limitations and/or concerns of hole drilling and ring coring: • • • • • • Areas of high stress gradients should be avoided because the stress gradient must be assumed to be constant across the hole or ring diameter Areas where stresses are greater than one-third the yield strength of the material are likely to produce erroneous results due to local plastic yielding during metal removal The thickness of the part or specimen must be at least four times the hole or core diameter Strain hardening of the metal in the vicinity of the hole may result during metal removal, which can result in tens of ksi (69 MPa) error Heating may result during the metal removal Holes or cores must be spaced at least eight times their diameter apart ... stress; 12,500 (Fig 7) Ball-rod testing apparatus (Federal Mogul) (Fig 8) Cylinder-to-ball testing apparatus (Fig 9) Cylinder-tocylinder testing apparatus (Fig 10) Ring-on-ring testing apparatus (Fig... B4 Committee on Mechanical Testing of Welds, Mechanical Testing of Welds, Part 1: Summary of Tension Testing of Welds, Weld J., Jan 1981, p 33–37 “Standard Methods for Mechanical Testing of Welds,”... ASTM Standards, Vol 3.01, ASTM, 1999 B4 Committee on Mechanical Testing of Welds, Mechanical Testing of Welds, Part 1: Summary of Tension Testing of Welds, Weld J., Jan 1981, p 33–37 “Standard