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X-ray diffraction (XRD) residual-stress analysis is an essential tool for failure analysis. This article focuses primarily on what the analyst should know about applying XRD residual-stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly and to the subsequent evaluation of corrective actions that alter the residual-stress state of a component for the purposes of preventing, minimizing, or eradicating the contribution of residual stress to premature failures. The article presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection; measurement validation is outlined as well. A number of case studies and examples are cited. The article also briefly summarizes the theory of XRD analysis and describes advances in equipment capability.

X-RAY DIFFRACTION (XRD) residual-stress analysis is an essential tool for failure analysis. X-ray diffraction residual-stress measurement methods are commonly applied to the successful completion of failure analyses and, in many cases, are the only viable ones for the acquisition of the required data. X-ray diffraction residual-stress analysis methods can be used in (but are not necessarily limited to) situations where failures result from overloading, stress corrosion, fatigue, stress concentrations, or inappropriate manufacturing processes. X-ray diffraction residual-stress analysis methods can also be applied to the evaluation of corrective measures and the optimization of production parameters for extending the service life of components.

This article focuses primarily on what the analyst should know about applying XRD residual-stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly, and to the subsequent evaluation of corrective actions that alter the residual-stress state of a component for the purposes of preventing, minimizing, or eradicating the contribution of residual stress to premature failures.

The article presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection; measurement validation is outlined as well. A number of case studies and examples are cited. Failures with root causes other than residual stress are beyond the scope of this article and are not discussed. The article also briefly summarizes the theory of XRD analysis and describes recent advances in equipment capability. Comprehensive, detailed treatments of XRD residual-stress measurement theory can be found in Ref 1 to 9.

X-ray diffraction techniques have been applied as early as 1925 to the measurement of residual stress on a variety of materials (Ref 10). Considerable advances have since been made in detector speed and resolution (Ref 11, 12), data analysis and handling (due primarily to the advent of the personal computer), and equipment portability (Ref 13). The importance of the XRD method resides in its ability to measure residual and applied stress with high spatial resolution, speed, and excellent accuracy, and, in many cases, measurements can be performed nondestructively (Ref 14). The measurement of residual stress via XRD is generally limited to polycrystalline materials (Ref 6), that is, in materials with a grain structure (long-range ordering) as normally found in metals and their alloys as well as in polycrystalline ceramics (i.e., oxides, carbides, nitrides, etc.). Exceptions occur in semiconductor analysis in which strain (Eq 2) can be measured directly (Ref 15). The size of specimens that can be evaluated using XRD can vary widely from as small as the head of a pin to as large as a ship (Ref 13, 1619), a building/structure (Ref 20, 21), or a bridge (Ref 2225). Line of sight for both the incident beam and the detector to the measurement location is required, and the incident x-ray beam must irradiate the volume of interest (Ref 8). The precision and accuracy of results obtained is generally a function of the instrument used, the material condition, the measurement technique used, and subsequent data analysis. Unless otherwise specified, data analysis is based on the assumption that a near-random grain orientation distribution is sampled in a homogeneous and isotropic material (Ref 3). Although a detailed discussion is beyond the scope of this article, XRD techniques can also be used for the measurement of percent retained austenite (Ref 26) as well as other phases, pole figures (Ref 7, 15), and other analyses too numerous to mention.

The residual stresses present in a component can arise in almost every step of processing (Ref 1) and, in many cases, can play a key role in determining the effective service life of a component. When the failure analyst suspects residual stress as a contributing factor to a premature failure, such suspicions may be validated by experiment and by measurement. X-ray diffraction residual-stress measurement analysis should be specified when damaged components:

• Experience static in-service loads that are a significant fraction of the maximum allowable equivalent stress (stress concentrations, overloaded)

• Distort or form cracks without applied loads

• Are placed in corrosive environments (stress corrosion)

• May have been subject to improper processing on manufacture (shot peening, grinding, milling, etc.)

• May have been subject to inappropriate heat treatment (stress relief, induction hardening, service temperature, thermal strains, etc.)

The XRD technique uses the distance between crystallographic planes, that is, d-spacing, as a strain gage. This method can only be applied to crystalline, polycrystalline, and semicrystalline materials (Ref 1, 27), where thousands of grains are sampled in a typical measurement. When the material is in tension, the d-spacing increases in the direction of stress, and when the material is in compression, the d-spacing decreases. The presence of residual stresses in the material produces a shift in the XRD peak angular position that is directly measured by the detector (Ref 6). For a known x-ray wavelength, λ, and n equal to unity, the diffraction angle, 2θ, is measured experimentally, and the d-spacing is then calculated using Bragg’s law:
$nλ= 2d sinθ$
(Eq 1)
Once the d-spacing is measured for unstressed (d0) and stressed (d) conditions, the strain is calculated using the Eq 2 relationship:
$ε=(d−d0)/d0$
(Eq 2)

When applying a plane-stress model, the unstressed lattice spacing, d0, can be substituted with the d-spacing measured for the specimen of interest at ψ (psi) = 0; that is, the unstressed lattice spacing need not be known precisely for the material in question (Ref 3). To evaluate stresses in the direction normal to the specimen surface σ33, the unstressed lattice spacing for the material in question must be known with an accuracy of better than 0.01%. An error in the estimation of the unstressed lattice spacing, d0, as small as 0.1% can lead to large errors in the stress measurement results (Ref 1, 28).

For the sin2ψ method, where a number of d-spacings are measured, stresses are calculated from an equation derived from Hooke’s law for isotropic, homogeneous, fine-grained materials:
(Eq 3)
where ½S2 and S1 are the x-ray elastic constants of the material, variations of σij are the stress-tensor components, φ is the angle of the direction of strain measurement with respect to the frame of reference, ψ is the angle subtended by the bisector of the incident and diffracted beam, with the specimen normal, and εφψ is the strain for a given φψ orientation. Figure 1 is a schematic showing the reference axes and direction of measurement.
Fig. 1

Definition of the reference axes and the direction of measurement in x-ray diffraction residual-stress analysis

Fig. 1

Definition of the reference axes and the direction of measurement in x-ray diffraction residual-stress analysis

Close modal

Evaluation of the stress-tensor components, σij, is generally straightforward and is normally carried out by plotting the measured d-spacing versus sin2ψ, with careful selection of the measurement directions, ψ and φ. A variety of mathematical models and measurement approaches have been proposed to evaluate the stress-tensor components of interest (Ref 19).

Residual-stress measurement d versus sin2ψ data can normally be categorized as follows: linear, elliptical with ψ-splitting, and nonlinear with oscillatory behavior (Fig. 2). Data obtained from near-isotropic and homogeneous samples with no shear stress are linear and resemble that shown in Fig. 2a. Elliptical data, shown in Fig. 2b and commonly defined as ψ-splitting in d-spacing versus sin2ψ plots obtained via XRD, are generally evidence of shear stress and/or instrument misalignment (Ref 1). Data similar to that found in Fig. 2c are most often caused by a nonrandom crystallographic orientation of the coherently diffracting domains in the volume sampled by the incident x-ray beam, that is, material condition.

Fig. 2

Common types of d-spacing versus sin2ψ plots. (a) Linear: exhibiting no shear stress. (b) Elliptical: exhibiting ψ-splitting due to shear stress. (c) Nonlinear: oscillatory behavior due to preferred crystallographic orientation. Source: Ref 1

Fig. 2

Common types of d-spacing versus sin2ψ plots. (a) Linear: exhibiting no shear stress. (b) Elliptical: exhibiting ψ-splitting due to shear stress. (c) Nonlinear: oscillatory behavior due to preferred crystallographic orientation. Source: Ref 1

Close modal

Mechanical surface treatments with forces out of plane with respect to the surface create shear stresses (and thus, ψ-splitting). Shear stresses can typically be found in samples after grinding, turning, rolling, inclined shot peening, and honing processes. Shear stresses can also be created due to material heterogeneity with nonuniform microstrains. This is often seen in multiphase materials (Ref 2). When ψ-splitting is observed, a nonlinear regression should be employed to fit the data points in d-spacing versus sin2ψ plots (Eq 3). A triaxial analysis can also be employed (Ref 1, 2, 5, 9). These analyses generally require the collection of many data points at both positive and negative ψ angles and in many φ directions.

The examples shown in Fig. 3 demonstrate that an elliptical fit gives good results (Fig. 3a), whereas a linear fit using either the ψ > 0 or the ψ < 0 branch leads to incorrect results (Fig. 3b). In this case, the results from the two opening branches of the curve differ by approximately 54 ksi.

Fig. 3

ψ-splitting on steel using (a) elliptical fit and (b) linear fit for ψ > 0 and ψ < 0

Fig. 3

ψ-splitting on steel using (a) elliptical fit and (b) linear fit for ψ > 0 and ψ < 0

Close modal

With recent advances in equipment speed, the full XRD peak profile can be obtained quickly and easily. When using instrumentation having single-channel detectors, the full diffraction profile should always be collected. Equipment that allows the use of only two ψ tilts (typically, ψ = 0° and ψ = 45°) has limited applications. The use of only a few ψ tilts can lead to erroneous results; thus, the double-exposure method with ψ > 0 or ψ < 0 is only viable in special cases and when it is certain that the d-spacing versus sin2ψ plot is linear. This means that, to ensure accurate results on a wide variety of samples and measurement locations, many ψ tilts using both ψ > 0 and ψ < 0 and elliptical fitting methods should be applied. The use of “true ψ” or χ (chi) geometry, sometimes referred to as Ω (omega) and ψ, respectively, is recommended. The use of χ goniometer geometry has advantages, primarily a slightly increased tilt range where the ψ tilt range is limited due to sample geometry constraints. However, when using the modified χ (or side-inclination) geometry, errors may be introduced due to the ψ angle offset and therefore should only be used when the specimen geometry eliminates the preferred methods (i.e., true ψ or χ). True-χ and modified-χ geometry are more sensitive to goniometer alignment, particularly with small goniometer radii; thus, care must be taken in sample and goniometer alignment.

Techniques such as the cos α technique that uses the full Debye ring with only one goniometer orientation have limitations similar to those associated with the two-tilt method (or double-exposure method) in that shear stresses cannot be evaluated; thus, their presence can lead to erroneous results (Ref 29, 30). However, if the goniometer is capable of multiple ψ or ψ, φ orientations with the ability to collect full or partial Debye rings, accurate shear stresses may be obtained. In addition, if a two-dimensional detector is used that collects a large section of the Debye ring, the data-collection time may be reduced if the direction of the major strain is tilted with respect to the physical direction of a sample. Care should be taken when using a limited ψ tilt or ψ, φ range with the cos α method, because the limited ψ tilt range sampled by this approach makes the evaluation of textured or coarse-grained materials questionable, and many geometrically complex parts may be impossible to characterize (Ref 1).

As a general rule, the accuracy of any residual-stress measurement in a given direction is dependent upon the measurement of d-spacings over regions where ψ > 0 and ψ < 0; any deviation from this rule can lead to erroneous and misleading results. This is also valid for triaxial measurements where the d-spacing should be measured in as many directions as possible to cover a hemisphere.

A comprehensive approach to the measurement of residual stress using XRD should address instrument calibration and the validation of results. The five steps required to calibrate instrumentation and to validate stress measurement results are:

1. Alignment of XRD instrumentation

2. X-ray elastic constant determination

3. Surface condition evaluation

4. Collection parameter selection

5. Repeatability and reproducibility determination

Once all of the previous five steps have been completed successfully, residual-stress measurements via XRD techniques can be applied with a high level of confidence.

Alignment is performed according to the ASTM International E 915 standard (Ref 31). This procedure is also performed periodically to verify instrument conformity to specifications. The maximum acceptable normal stress, tensile or compressive, is ±2 ksi (for steel). The verification of instrument alignment is usually performed on a stress-free powder of the material in which residual stress is to be measured. The maximum shear stress should also be on the same order of magnitude as the normal stress, that is, within ±2 ksi, to meet or exceed the ASTM International E 915 specification. Instrumental alignment that meets or exceeds ASTM International E 915 can easily be achieved for a goniometer with a focal radius as small as 30 mm (1.2 in.) (Fig. 4).

Fig. 4

Elliptical analysis on stress-free iron powder with a 30 mm (1.2 in.) focal radius goniometer

Fig. 4

Elliptical analysis on stress-free iron powder with a 30 mm (1.2 in.) focal radius goniometer

Close modal

For stress measurements using XRD techniques, one needs to determine the x-ray elastic constants (XECs). They are a function of the mechanical properties of the material and the crystallographic plane selected to perform the measurements. Once known, they can be used in subsequent measurements on the same alloy but can be affected by preferred orientation. In general, the XECs are determined experimentally or by calculation using theoretical methods. Theoretical models, such as those in Ref 32 and 33, are generally used when a suitable coupon cannot be obtained. The experimental method is usually the preferred method, particularly when the physical parameters of the material structure are not well known. The experimental method uses either a four-point bend or uniaxial tensile specimen, and ASTM International E 1426 (Ref 34) is usually applied. In the case of four-point bend testing, a strain gage is attached to the opposite side of and/or near the measurement location on the specimen. The applied strains are recorded via a strain gage, and the stresses are measured by XRD at different load increments. The maximum applied stress is approximately 70% of the yield stress.

For example, the slope of the stress measured via XRD versus the applied stress for a ground steel coupon (Fig. 5) was used to calculate the ½S2 parameter in Eq 3. S1 is calculated for triaxial methods, and its determination is not described by ASTM International E 1426 (Ref 34).

Fig. 5

Results obtained from a steel four-point bend specimen in round-robin tests. The x-ray elastic constant (½S2) was determined to be 3.687 10−5 ksi−1.

Fig. 5

Results obtained from a steel four-point bend specimen in round-robin tests. The x-ray elastic constant (½S2) was determined to be 3.687 10−5 ksi−1.

Close modal

The effect of factors such as surface condition (surface roughness, oxide layers, etc.) on XRD residual-stress measurement results should be addressed prior to surface-stress measurements on real components.

For example, a steel specimen was machined in three regions, each with different machine tools, to introduce variations in surface roughness on the same specimen (Ref 35). The stress was then measured in the three regions via XRD techniques under independently monitored tensile loads. X-ray diffraction results were plotted versus the applied stress for locations where the average roughness (Ra) was 1, 3, and 6 μm (1 μm = 39.4 μin.). The linear least squares regression for each data set yielded slopes of 1.01, 0.96, and 1.03 for 1, 3, and 6 μm Ra, respectively (Fig. 6a). All of these results are well within the experimental error (less than 5%), thus indicating that an Ra of up to 6 μm for these experimental conditions has no measurable effect on residual-stress results obtained via XRD.

Fig. 6

X-ray diffraction (XRD) stress versus applied stress for varying average roughness (Ra). (a) Samples with Ra of 1, 3, and 6 μm. (b) Samples with Ra of 1, 40, and 56 μm. Source: Ref 35

Fig. 6

X-ray diffraction (XRD) stress versus applied stress for varying average roughness (Ra). (a) Samples with Ra of 1, 3, and 6 μm. (b) Samples with Ra of 1, 40, and 56 μm. Source: Ref 35

Close modal

Another sample was prepared with regions machined to an Ra of 1, 40, and 56 μm. It was loaded in tension, and stresses were measured via XRD. In this case, the slopes were 0.9, 0.15, and 0.18 for 1, 40, and 56 μm Ra, respectively (Fig. 6b). This demonstrates that the surface-stress measurements do not respond as well to the applied stress when the roughness is increased.

The response of stress measurements via XRD to the applied load for an Ra of up to 56 μm is plotted in Fig. 7. In this particular case, it can be seen that the sensitivity to the applied load is reduced when the Ra is greater than 10 μm (0.0004 in.).

Fig. 7

Ratio of measured stress (XRD, x-ray diffraction) and applied stress for varying average roughness, Ra. Source: Ref 35

Fig. 7

Ratio of measured stress (XRD, x-ray diffraction) and applied stress for varying average roughness, Ra. Source: Ref 35

Close modal

When the surface Ra is less than the penetration depth of x-rays in the material, the measured stress results more accurately reflect the applied load (Fig. 8a). However, when the surface Ra is greater than the penetration depth of the x-rays, the measured stress reflects the applied load to a lesser degree (Fig. 8b).

Fig. 8

Effect of surface Ra on x-ray diffraction stress measurements. (a) X-ray penetration depth is greater than Ra. (b) X-ray penetration depth is less than Ra. Source: Ref 35

Fig. 8

Effect of surface Ra on x-ray diffraction stress measurements. (a) X-ray penetration depth is greater than Ra. (b) X-ray penetration depth is less than Ra. Source: Ref 35

Close modal

The depth of penetration of x-rays in a material is dependent on the wavelength, λ, (i.e., the energy) of the incident radiation and the mass absorption coefficient, μ, of the material (Ref 6). The mean depth of penetration can vary but is typically 10 to 20 μm for most metals.

The effect of surface corrosion on measurement response can be demonstrated by an example. A strain gage was attached to the surface of a steel wire on the inner side, adjacent to the XRD stress measurement location of interest. The XRD measurement location was visibly corroded. The wire was then incrementally loaded in tension. The stress was measured using XRD techniques, and the applied stress was monitored via the strain gage. The slope of the XRD stress versus applied stress was 0.889. The same steel wire was electropolished, and the experiment was repeated. The slope of the XRD stress versus applied stress was 0.997.

The results plotted in Fig. 9 indicate that, in this particular case, the electropolished surface (Fig. 9b) responds better than the corroded surface (Fig. 9a). Because the near-surface layers are often of interest to the failure analyst, electropolishing techniques may be used to remove the surface and expose the near-surface material so that residual-stress measurements may be subsequently performed.

Fig. 9

X-ray diffraction stress versus applied stress on (a) as-received and (b) electropolished surfaces

Fig. 9

X-ray diffraction stress versus applied stress on (a) as-received and (b) electropolished surfaces

Close modal

A number of factors can contribute to the introduction of random and/or systematic errors into residual-stress measurements performed via XRD techniques; thus, the data-collection parameters should be carefully selected. Components can exhibit different microstructures that require the use of different collection parameters. In general, these collection parameters can be summarized as:

• Collection time

• Number of ψ tilts used for d-spacing versus sin2ψ plots

• X-ray diffraction peak position determination

• Effects of microstructure

• Effects of surface curvature and beam size

Optimization of the previous collection parameters should be addressed prior to proceeding with residual-stress measurements.

Low collection times can introduce random errors due to insufficient x-ray counting statistics (Ref 1, 7, 36). Random errors become apparent during repeatability tests; therefore, x-ray data-collection times should be increased sufficiently until the desired repeatability is achieved. This technique works well for all detector types, particularly multichannel solid-state detectors that do not resolve individual counts. When using position-sensitive proportional counters, the number of counts can be used as a measure of counting statistics.

Improper selection of the number of ψ angles used can introduce systematic errors (see the section “Analysis of XRD Data” in this article). Systematic errors become apparent during reproducibility tests. In general, a minimum of five ψ tilts are required for a reasonable assessment of the shape of the d-spacing versus sin2ψ curve; however, it is recommended that more than five tilts be used as a general practice.

Improper selection of the peak-location method can also introduce systematic errors in XRD residual-stress measurement results. Depending on the specimen under examination, the XRD Kα1-Kα2 doublet may or may not be resolved. A number of factors can affect how well the doublet is resolved, including material effects such as the dislocation density and the crystallite size in the sample, as well as instrumental effects such as slit size and defocusing if the goniometer is not using a parallel beam (Ref 1). In practice, that is, in most cases, XRD patterns obtained from real-life components exhibit broadening due to cold-working effects such as machining, grinding, shot peening, and so on. If the doublet is not well resolved, the peak position can be determined by fitting the blended doublet as a whole. The position of the blended doublet can thus be determined via analysis of the full profile (e.g., gravity-center methods), and the splitting of Kα1 and Kα2 lines can be quasi-automatically averaged. The application of peak-fitting methods based on the analysis of selected parts of the profile should only be used when peak asymmetry exists (Ref 2).

If the Kα1-Kα2 doublet is reasonably well resolved, it is recommended that the Rachinger correction be applied (Ref 7). This method consists of eliminating Kα2, assuming that it has the same shape as Kα1 and half the intensity. Once the Kα2 portion of the doublet has been eliminated, symmetric functions such as Voigt, Gaussian, Pearson VII, and full-profile methods work well (Ref 2). In contrast to the center-of-gravity method, the Gaussian offers the advantage that it may easily be extended to two or more profiles with their Kα2 peaks removed, using the Rachinger correction. Because the intensity ratio and the difference in wavelength, Δλ, of the Kα1 and Kα2 lines is known for all x-ray tube targets, two functions (such as Pearson VII, Gaussian, modified Lorentzian, etc.) with the appropriate angular separation and relative intensity can be used to fit the doublet. In special material conditions or in the case of high-resolution experiments, it is recommended to use Pearson VII or the more physically based Voigt functions (Ref 2, 9). The cross-correlation method is another method for peak location determination; however, this method is not applicable for textured materials (Ref 1).

All materials at the single-crystal level are anisotropic to some degree. If a nonrandom grain orientation distribution is sampled, the effects become apparent in the shape and/or relative intensity of the diffraction peaks and in the d-spacing versus sin2ψ plots. Typically, large grain size or preferred orientation effects result in nonlinear or oscillatory d-spacing versus sin2ψ plots (Fig. 2c). In the case of large grain size effects, the peak shape generally changes drastically from one ψ tilt to another ψ tilt, and corrective actions may include increasing the aperture size, and/or oscillating the ψ and/or φ axes, and/or using a two-dimensional detector. In the case of preferred orientation, the peak shape generally remains constant with progressive broadening, but the peak intensity varies widely from one ψ tilt to another ψ tilt. As a rule of thumb, an intensity ratio greater than 2.0 indicates there is a potential material condition problem. Corrective actions may include linearization (Ref 2) over the highest ψ tilt range possible and others (Ref 1, 37, 38). In cases of severe texture, multiple diffraction lines may need to be measured and refined simultaneously to obtain reliable residual-stress values (Ref 9).

For specimen curvature effects, the following rule of thumb should be adhered to: for cylindrical specimens of radius R, the maximum incident x-ray spot size to use is R/6 for 5% accuracy and R/4 for 10% accuracy in the hoop direction, and R/2.5 and R/2 for 5 and 10% accuracy, respectively, in the axial direction. In cases where the beam size cannot be made sufficiently small, corrections can be applied (Ref 5).

To assess the effects of random and/or systematic errors in residual-stress measurement results, the repeatability and reproducibility of such measurements may be determined. Repeatability is a measure of the consistency in measurement results collected sequentially without a change in experimental setup. Reproducibility is a measure of the consistency in measurement results when the experiment is set up again at a different time, with a different instrument and/or with a different operator.

The residual-stress measurement data found in Table 1 were collected on a laboratory standard. The repeatability test result average in Table 1 has a standard deviation of 0.7 ksi, and the reproducibility test result average has a standard deviation of 1.1 ksi. The slightly higher standard deviation in the reproducibility test versus the repeatability test is due to:

• A slightly different population of grains sampled

• Small variations in sample positioning and alignment

• The nonuniformity in surface residual stress of the specimen

Table 1
Repeatability and reproducibility of stress results
Measurement No.Stress, ksi
RepeatabilityReproducibility
1−62.8−62.9
2−62.9−61.1
3−63.2−63.0
4−62.6−63.7
5−61.4−63.8
Average−62.6−62.9
Standard deviation0.71.1
Measurement No.Stress, ksi
RepeatabilityReproducibility
1−62.8−62.9
2−62.9−61.1
3−63.2−63.0
4−62.6−63.7
5−61.4−63.8
Average−62.6−62.9
Standard deviation0.71.1

A similar repeatability and reproducibility test should be performed when a new material, material condition, or type of sample is to be analyzed using XRD.

In general, a statistically representative population of specimens should be chosen for analysis to accurately determine if any of the microstructural effects (large grain size, local anisotropy, preferred orientation, etc.) are present or if there is a real sample-to-sample variance in the residual-stress values that is greater than the experimental error. In practice, the number of specimens that are representative of a population may be related to how well the manufacturing processes are controlled. Such scatter (lack of process control or variations inherent to incoming material) in and of itself can be a contributing factor to a wide variability in the effective service-life-to-failure period for components manufactured with poorly controlled processes and/or incoming material certifications. This can result in a drastically reduced predicted life for a given component simply because of the shortcomings of a small percentile of the component population.

If a normal distribution is used to predict the residual-stress distribution at a given location among a population of specimens, then a minimum of five specimens should be chosen to adequately sample the potential distribution within the population. For processes where the standard deviation in the residual stress is less than the experimental error, it makes economic sense to reduce the number of specimens to represent the population. In the authors’ experience, budget constraints often limit the sample population to two or three specimens; however, if variations in results at equivalent locations on equivalent specimens are larger than the experimental error, more specimens should be obtained for measurement.

Separate specimen populations should be selected to represent the manufacturing stage(s) of interest so as to evaluate the effect of a given process on the stress state of the component. This can help identify the manufacturing process or production line that may be introducing an undesirable stress state in the component. Knowledge of the component service history can also help identify how undesirable stress states were introduced in service or how a failure may have occurred. Ideally, samples should be selected from real production populations to more accurately represent the true variance that can be expected within a population. Characterizing a sample population of only one using XRD residual-stress analysis can be risky, because it may inadequately represent the statistical distribution of residual stresses in the component population. Components that have already failed may be of limited use, because residual stresses may have changed or relaxed considerably upon failure. In certain instances, a map of the residual stresses as a function of distance from the failure location using microstress measurement techniques can indicate the extent of the stress and/or stress gradients local to the failure location. Ideally, nonfractured components with a similar history should be considered for analysis as well.

When a failure occurs, the failure analyst must define the damage type and the origin of failure. This may be relatively straightforward or difficult, depending on the type of component and/or structure in question. Generally, the point of origin of a crack can be easily located on a given component with standard nondestructive evaluation techniques (i.e., visual inspection, eddy current, fluorescent dye penetrant, ultrasonic, etc.). In more complicated structures, the failure analyst must identify the components and locations most vulnerable to cracking.

The factors to consider when using the empirical observation method for selecting the locations where cracks are most likely to occur and thus, where residual-stress measurements should be concentrated, are:

• The highest-stressed areas are the areas with the smallest thickness or cross section for a given applied load.

• Regions of stress concentration such as undercuts, necks, radii, weld toes, fillets, etc.

• Locations of dynamic contact (fatigue contact)

• Locations exposed and susceptible to corrosion

Once a crack has already initiated or failure has already occurred, the location of interest for XRD measurement is in that area. It should be noted that in the vicinity of the crack, the residual stress is partially or completely relieved in the direction normal to the crack line, hence the importance of evaluating parts prior to crack initiation. Triaxial XRD stress measurements are preferable to determine the orientation and the magnitude of the stress field when it is possible or practical. In cases where the accessibility around the location of interest is limited to one or two directions (either due to sample geometry, economic constraints, or time constraints), the priority is given to stress measurements in the direction perpendicular to the crack line.

Finite-element methods are very useful to predict the stress distribution in a component under applied loads. This method requires:

• Building a two- or three-dimensional (2D, 3D) map of the component or structure

• Determining the boundary conditions

• Performing calculations in 2D or 3D, depending on the complexity of the loading

• Printing the 2D or 3D stress-distribution results (components in different directions, plastic strains, equivalent strains and stresses, etc.)

The results identify high- and low-stressed areas and stress gradients. The locations with high priority for residual-stress measurements are the areas with the highest tensile stress, that is, the areas most susceptible to localized yielding or cracking. At the boundaries where the stress gradient changes sign, shear stresses may be present; thus, triaxial-stress measurements at these locations are recommended. For components of complex geometry where finite-element methods are not economically practical, the empirical observation method is preferable.

The introduction of stress-mapping techniques has allowed the rapid and precise characterization of entire component surfaces, including areas of interest such as steep stress gradients (as found in welds) and their associated tensile residual-stress maxima. In cases where the component geometry is such that stress measurements can be performed in the areas of interest (near the failure), stress mapping can be performed in both loaded and unloaded conditions. Stress-mapping techniques are routinely applied to welds, ground areas, shot-peened areas, rolled areas, and locally heat-treated areas with temperature gradients. Subsequent measurements should be concentrated in areas identified by stress maps as the most tensile with higher resolution and/or with depth.

The stress-map display makes available to the failure analyst a complete and accurate visual analysis of the magnitude and distribution of residual stresses in components. The plots shown in Fig. 10 and 11 are examples of stress maps collected on components with surface-stress gradients. In Fig. 10, the tensile stresses detected in the center of the map (in the weld metal and adjacent heat-affected zone) may limit the service life of the saw blade (Ref 39). Similarly, in Fig. 11, the unpeened tensile stress region of a 316L stainless steel butt-welded plate may be the location most susceptible to failure (Ref 40).

Fig. 10

Surface residual-stress map of resistance-welded, heat-treated, and ground steel saw blade. Source: Ref 39

Fig. 10

Surface residual-stress map of resistance-welded, heat-treated, and ground steel saw blade. Source: Ref 39

Close modal
Fig. 11

Residual-stress map of welded 316L stainless steel plate. Source: Ref 40

Fig. 11

Residual-stress map of welded 316L stainless steel plate. Source: Ref 40

Close modal

Using XRD, stresses in areas as small as a fraction of a millimeter can be measured. Accessing measurement locations on flat surfaces is straightforward but impossible at locations such as the inside diameter of a 2 mm (0.08 in.) hole. X-ray diffraction residual-stress measurements at locations where access is a problem normally require sectioning of the component to access the location of interest and, in general, require the evaluation of applied stresses caused by relaxation due to sectioning. The most common method to monitor strain relaxation during sectioning is using electrical resistance strain gages. The placement and orientation of strain-gage elements prior to sectioning require careful consideration.

For example, when residual-stress measurements are required on the inner diameter of a small ring and the diameter of the ring is too small for the goniometer to obtain line of sight to the inner-diameter measurement locations, strain gages should be placed on both the outer and inner surfaces so as to measure strains in the direction(s) of interest. Both outer and inner gages should be as close to the stress measurement location as possible. If other directions are to be monitored, dual-element strain gages or rosettes can be used for this purpose. The relaxation is generally assumed to be elastic; however, in highly stressed materials, it can also be elastoplastic. The strain monitoring should therefore be performed in real time, that is, continuous mode. Care must be taken to ensure that the chosen cutting method does not cold work or overheat the XRD stress measurement location of interest.

The steps for sectioning samples prior to XRD analysis can be summarized as:

• Orient strain-gage element(s) so as to measure strains in the direction parallel to XRD stress measurement direction(s).

• Use coolant with the cutting tool (saw blade, cutoff wheel, electrical discharge machining wire, etc.) to keep the sample temperature low, thus minimizing localized thermal effects and preventing stress relaxation due to heat dissipation generated during sectioning.

• Always protect the gages from coolant contact (particularly if the coolant is conductive) with epoxy, lacquer, or equivalent coatings (see strain-gage manufacturer’s recommendations).

• Monitor (in real time) the variation of the strains during sectioning.

• Look for strain peaks during sectioning, and compare the value to the yield stress of the material, because plastic deformation may occur.

• Use the final strains to calculate the stress-relaxation correction due to sectioning. In general, the calculated stress values are subtracted (added with opposite sign).

When complicated sectioning is required, more advanced models may be required and applied (see Ref 8 for more details). Finite-element methods can also be useful in such cases.

X-ray diffraction residual-stress measurement directions can be selected as:

• For characterization of the complete stress tensor (triaxial analysis), the measurement of stresses in six directions is recommended (a minimum of three are required).

• Initial stresses generated during processing can be a good indication; for example, in the case of rolling, grinding, or turning processes, the directions parallel and perpendicular to the rolling, grinding, or turning direction are of interest.

• In specimens where induced stresses are omnidirectional, one direction or two orthogonal directions may be sufficient.

• If a crack has initiated in any direction, the highest-priority measurements are in the direction perpendicular to the crack.

• When measurement directions are constrained by sample geometry, measurements at 0°, 45°, and 90° for any reference frame may be used to calculate principal and shear stresses using Mohr’s circle for the biaxial case. Similar methods can be applied for the triaxial case as well.

A comprehensive residual-stress investigation using XRD is seldom limited to the surface, so subsurface measurements are generally required. If subsurface locations must be measured nondestructively, neutron diffraction is recommended (Ref 5, 8). When surface and subsurface measurements are performed, stress gradients normal to the specimen surface can be characterized, thus exposing potentially beneficial or harmful subsurface residual stresses in the material. When using XRD, the residual stresses should be corrected for stress relaxation using the Moore-Evans method (Ref 41), where the material removed is over the whole surface. The stress correction with this technique requires measurements in one direction for flat surfaces and two directions for cylindrical surfaces (hoop and axial). For more complicated specimen geometry, finite-element techniques can be used to correct for stress relaxation due to material removal (Ref 3, 42). In general, the correction is within the experimental error of the residual-stress measurement (i.e., is negligible) if the deepest layer removed is a small fraction of the total thickness of the component. When steep stress gradients normal to the surface exist in the component, the stress gradient correction should also be applied to collected data (Ref 3).

The number of subsurface residual-stress measurements performed is not limited, and measurement depths are generally selected (as required) to view the full shape of the stress versus depth profile to depths where stress gradients tend to level off. The actual depths required to characterize a subsurface stress gradient are very process- and sample-dependent and should be determined on a case-by-case basis.

Most mechanical and structural components are protected when used in aggressive or harsh environments to prevent or minimize material-degradation mechanisms such as oxidation, wear, erosion, corrosion, and so on. Structures exposed to the elements are often coated with zinc or painted, whereas mechanical components used in a dynamic mode are often lubricated. Protective coatings can partially or completely attenuate the incident x-ray beam and must be removed prior to residual-stress measurement. Removal of coatings must be performed without modifying the surface or subsurface residual-stress state. Mechanical polishing or grinding modifies the residual stress at the surface and the subsurface and is not recommended. If mechanical surface preparation is required for other nondestructive testing techniques (such as eddy current or ultrasonic) to be used in parallel with XRD, the XRD analysis should be performed before the surface is additionally disturbed or cold worked.

It is important that the chemicals used to remove coatings never etch the material. If etching occurs, subsequent electropolishing below the etched layer may be required. To evaluate the appropriateness of the surface-preparation techniques applied and the surface condition of the component to XRD residual-stress measurements, a complete surface-condition evaluation (four-point bend test) must be performed on a coupon taken from the component in the as-prepared condition.

The basis for a quantitative assessment of statically loaded components is dependent on the determination of the maximum allowable equivalent stress, σe, which is determined by the underlying effect chosen (i.e., the resulting normal stresses, shear stresses, deformations, etc.), its location, and the defined failure criterion (i.e., fracture, plastic deformation, etc.). Thus:
(Eq 4)
where R is the resistance to failure (and depends on the failure criterion), s is the safety factor, and the allowable equivalent stress, σe, is a function of the loading stresses and residual stresses. The sign and magnitude of the residual stress may increase or diminish the equivalent stress, and subsequently, surface and subsurface residual-stress gradients can modify their contributions locally. In cases where plastic deformation occurs in ductile materials, their effect may diminish, because residual stresses can change or relax substantially prior to and on failure and thus may or may not play a significant role in the failure (depending on the failure criterion). The effects of residual stresses are generally more dominant in brittle failures or when plastic deformation is the failure criterion (Ref 2).

Tensile residual stresses can significantly reduce fracture loads (Fig. 12), whereas compressive residual stresses generally act to increase the crack-opening thresholds for given loading stresses (Fig. 13).

Fig. 12

Effect of tensile residual stress (RS) on fracture loads as a function of test temperature. Source: Ref 43

Fig. 12

Effect of tensile residual stress (RS) on fracture loads as a function of test temperature. Source: Ref 43

Close modal
Fig. 13

Crack-tip opening of a shot-peened and residual-stress-free Ti-6Al-4V specimen. Source: Ref 44

Fig. 13

Crack-tip opening of a shot-peened and residual-stress-free Ti-6Al-4V specimen. Source: Ref 44

Close modal

When applying linear elastic fracture mechanics, the residual-stress contributions to the stress-intensity factor can be calculated and used to predict whether crack growth and/or arrest will occur. It should be noted that the effect of residual stresses on crack-growth rates tends to diminish with increasing fracture toughness. Residual stresses can also be taken into account when elastic-plastic fracture mechanics are used (Ref 2).

Environmentally assisted cracking, also known as stress-corrosion cracking (SCC), is a major source of potential failures in the process industries, in pulp mills, in storage vessels, and even in aircraft. Quite often, SCC occurs in the heat-affected zone (HAZ) immediately adjacent to a weld simply because the HAZ is left in a state of very high residual tensile stress as a result of the shrinkage and differential cooling occurring in most welds. Tensile stress (resulting from the superposition of residual and applied stresses) (Ref 45) is the main component of the SCC triangle; the other two are a susceptible metal and an environment that often needs to be only slightly corrosive to that metal. For instance, grade 316 stainless steel is essentially inert to the corrosive effect of common salt unless tensile stresses are present, when it becomes very sensitive to chloride-induced SCC.

There are a number of possible solutions to the SCC problem. The obvious one is to change the environment, but that is rarely possible. The next is to change the metal, but that is usually expensive and, if the component in question is already built, impractical. Thermal stress relieving is a partial solution at best, because, to completely relieve all the tensile stresses in a component, it is necessary for the heating to reach the annealing temperature, which may change the material properties. In addition, annealing cannot be used to overcome any subsequently applied tensile service loads. Corrosion engineers have long recognized that an effective solution for the retardation or even prevention of SCC is the introduction of compressive stresses.

For example, it can be seen in Fig. 14 that the shot peening technique used had a significant effect on the stress state of the weld and parent material, as seen by the “step” or drop in residual stress near the center of the stress map. On the left side, a typical weld stress map is observed, with tensile residual stresses present in the weld and in the HAZ, then dropping off in the parent material. The right side of this map was the peened portion. Here, the characteristic profile is much more compressive (or less tensile) and smooth; however, tensile residual stresses still exist. This indicates that the peening process had the effect of reducing the tensile residual-stress field in the weld and HAZ and introducing a much more uniform compressive residual-stress level in the parent material. However, it was not sufficient to make the surface stresses in the HAZ entirely compressive. This would suggest that the postweld treatment could be changed or augmented to increase the compressive residual stress imparted on the weld and HAZ.

Fig. 14

X-ray diffraction residual-stress map showing the introduction of compressive surface residual stresses in the parent material and the reduction, but not elimination, of tensile residual stresses in the weld metal on the unmasked side from shot peening a nickel alloy weldment. Source: Ref 40

Fig. 14

X-ray diffraction residual-stress map showing the introduction of compressive surface residual stresses in the parent material and the reduction, but not elimination, of tensile residual stresses in the weld metal on the unmasked side from shot peening a nickel alloy weldment. Source: Ref 40

Close modal

X-ray diffraction techniques can thus be used to characterize the stress state of components that may be susceptible to SCC either before or after they have been put into service. In the case of corrosion fatigue, compressive surface residual stress has a beneficial effect on lifetime and strength. In the case of the data shown in Fig. 15 (Ref 46), it can be seen that XRD residual-stress measurements can be used to compare the effects of grinding and shot peening on the surface and subsurface residual-stress state.

Fig. 15

Effects of grinding and shot peening on surface and subsurface residual stress in low-carbon (CK45) steel tested in seawater. (a) Residual stress versus depth profiles. (b) Bending fatigue stress/number of cycles curves. Source: Ref 46

Fig. 15

Effects of grinding and shot peening on surface and subsurface residual stress in low-carbon (CK45) steel tested in seawater. (a) Residual stress versus depth profiles. (b) Bending fatigue stress/number of cycles curves. Source: Ref 46

Close modal

The strong impact that surface and near-surface residual stresses have on the fatigue life of components underlies the importance of studying the effect of surface treatments and manufacturing processes (Ref 2, 47, 48). It is now known that if reliable fatigue-life estimates are to be made, it is necessary to characterize the residual-stress fields in test specimens and engineering components (Ref 49).

When a component undergoes cyclic loading, it can be susceptible to fatigue. The fatigue life for a given component is often characterized with a Wöhler diagram or S-N curve, where S is defined as the total stress range the material experiences during cyclic loading, and N is defined as the number of cycles to failure. Consider the simple case of constant-amplitude cyclic loading (Fig. 16) (Ref 50). The peak-to-peak difference in the maximum and minimum stress is defined as the stress range. However, in the case of Fig. 16, the mean stress cannot simply be considered as the mean applied stress but must be considered as the superposition of the mean applied stress and the residual stress. Thus, a nonzero residual stress offsets the mean stress about which the stress amplitude cycles. This principle applies to variable-amplitude cycling as well. Changes in the residual stress for a component in a given application (and thus, the mean total stress) can have the effect of displacing the S-N curve and subsequently changing the fatigue life.

Fig. 16

Fig. 16

Close modal

Figure 17 shows the S-N curves plotted for two identical gears of identical hardness, except one was double shot peened. The stress range of the fatigue limit of gear A is 1256 MPa, whereas an increase of 38% to 1710 MPa is observed for the double-shot-peened gear B (Ref 51).

Fig. 17

Stress versus number of cycles to failure curves for as-hardened (gear A) and as-hardened plus double-shot-peened (gear B) gears. Source: Ref 51

Fig. 17

Stress versus number of cycles to failure curves for as-hardened (gear A) and as-hardened plus double-shot-peened (gear B) gears. Source: Ref 51

Close modal

Plastic strain, which is generally more significant when operating in cyclic fatigue, has a predominant influence in the number of cycles to failure (Ref 52). The relation between the plastic and the elastic strain can be summarized as follows: in high-life ranges, the plastic strain rapidly diminishes to negligible values, and the elastic strain range dominates. In the low-life range, the plastic component of strain dominates the material behavior.

The predominant driving force in fatigue (elastic or plastic) is thus determined by the in-service strain/stress range. In the case of short fatigue lives, plastic strain is more dominant than elastic strain, so low-cycle fatigue (LCF) life is controlled by the ductility of the material. At longer fatigue lives, as in the case of high-cycle fatigue (HCF), the elastic strain is more significant than the plastic strain, and the fatigue life is determined by fracture strength. Another difference between LCF and HCF failures is that LCF is characterized by multiple cracks in highly stressed areas, whereas HCF failures generally initiate at precise stress-concentration sites, with cracks propagating from a single initiation (Ref 53).

In cases of LCF failures, the in-service stress exceeds the elastic limit of the material. Low-cycle fatigue is usually used to define the reverse elastoplastic loading mode (Ref 54, 55). Low-cycle fatigue is characterized by cumulative fatigue damage associated with cycles to failure of up to 104 to 105 cycles. Experience has also demonstrated that LCF life is sensitive to changes in stress (or strain). A 5 to 10% difference in stress can result in a 50% difference in life; thus, errors in the representation of total stress have a profound effect on life if residual stress is not in the equation (Ref 56).

A steel spring used in an automotive application suddenly began to fail in the field. It was understood that nothing had changed in the fabrication process of these springs, yet the incidence of field failures suddenly increased dramatically. Fatigue tests using springs fabricated prior to field failures lasted 500,000 cycles to failure, whereas fatigue tests performed on springs fabricated after field failures lasted only 50,000 cycles to failure. It was discovered that the percent coverage of shot peening prior to and subsequent to the increase in failure incidence was much less than 100%, with a shot peening time of 12 min. Subsequently, a potential corrective action was introduced by the engineers: an increase in the time the spring was shot peened from 12 to 60 min. The residual-stress state of as-fabricated springs in three conditions was evaluated: springs manufactured prior to failure incidence increase, 12 min peen; springs manufactured following failure incidence increase, 12 min peen; and 60 min peen.

The residual-stress measurement results, as seen in Fig. 18, indicate that something had indeed changed, namely, the effective depth and magnitude of compressive residual stresses in the shot-peened springs when comparing springs manufactured before and after the increase in failure incidence. The cause of this change may have been either material or process related. Additionally, increasing the peening time from 12 to 60 min significantly increased the compressive residual-stress levels in the springs. In fact, the springs that were shot peened for 60 min were found to fail at more than 500,000 cycles in fatigue tests. Thus, in this example, the suspicion that inadequate compressive residual stresses were imparted by the peening process was validated, and the validity and effect of the proposed corrective action was substantiated. In this case, an increased peening time resulted in an increased percent coverage and effective compressive stress level. This example demonstrates that once the source of the failure is understood and validated by experiment, corrective measures can be applied, verified, and subsequently monitored with confidence. This example also demonstrates that XRD can be used to explore quality-related issues. The residual-stress benchmarks established in this case study can be referenced by the manufacturer or the customer in future residual-stress measurement audits and/or incorporated into the blueprints for this component.

Fig. 18

Stress versus depth profiles for different steel coil springs

Fig. 18

Stress versus depth profiles for different steel coil springs

Close modal

Experiments were conducted on rotating beam specimens at different loading levels. The specimen conditions are defined as shot peened and not shot peened/polished. Initial surface residual stresses were determined using XRD techniques, and the specimens were divided into three groups: first level, second level, and third level (shot peened), where the third level was the most compressive.

Prior to failure, multiple cracks were observed at 500× magnification adjacent to the macroscopically visible main crack, indicating that damage was not localized in the middle of the gage section, which is evidence of LCF (Fig. 19).

Fig. 19

Observation of failed nickel-base alloy (Waspaloy) specimen after rotating-bend fatigue. (a) Macro view. (b) Micrograph. Source: Ref 53

Fig. 19

Observation of failed nickel-base alloy (Waspaloy) specimen after rotating-bend fatigue. (a) Macro view. (b) Micrograph. Source: Ref 53

Close modal

The S-N curves for all three stress levels can be seen in Fig. 20. Level 1 and level 2 curves are very similar; thus, the difference is negligible, according to the physical mechanism of failure. The number of cycles to failure for shot-peened specimens is greater for low applied bending moments and smaller for high applied bending moments in comparison to non-shot-peened specimens. This can be explained by the effect of two parameters: the level of compressive residual stress and the surface roughness. The roughness of the surface due to peening can act as a stress raiser and may diminish the fatigue life, but the high compressive stresses can counterbalance the effect of the roughness (Ref 57, 58). In addition, the benefit of shot peening at higher applied fatigue loads may be diminished due to the surface roughness and the potentially steeper evolution (i.e., lack of stability) of residual stresses when the yield strength of ductile materials, such as Waspaloy, is exceeded.

Fig. 20

Applied bending load and number of cycles to failure, R = −1, for Waspaloy specimen. Source: Ref 53

Fig. 20

Applied bending load and number of cycles to failure, R = −1, for Waspaloy specimen. Source: Ref 53

Close modal

Residual-stress relaxation is a consequence of micro- and/or macroplastic deformations and is important, whether the superposition of residual, loading, or mean stresses exceeds the monotonic or cyclic yield strength. The fatigue limit of high-strength materials is generally lower than the cyclic yield strength, whereas in low-strength materials, these values may nearly coincide. This explains why residual stresses do not relax in high-strength materials subjected to load amplitudes in the range of the fatigue limit (Ref 2).

In the case of materials such as Waspaloy, the evolution of residual stresses with LCF can be used as a mechanism for tracking the useful fatigue life remaining in the component. It has been shown, in some cases, that a linear relationship holds between the residual-stress relaxation rate and the initial magnitude of residual stress (Ref 53, 55, 56, 59, 60).

The results shown in Fig. 21 indicate that there is a continual degradation of residual compressive stress with an increase in operational engine cycles. Based on the sensitivity of fatigue life with stress, the degradation of compressive residual stress from cold-working processes is an indication of increased “active” stress and therefore could be used as a measure of remaining fatigue life. For this to be realized, a trend must exist whereby the compressive residual stress, introduced by shot peening or other cold-working processes, relaxes to a value below which the disk is at increased risk to crack. In other words, it is assumed that residual-stress degradation is a precursor to fatigue crack initiation in LCF mode where loads exceed the yield strength of the material (Ref 55). (The implications of the comparison in Fig. 21 of the “large spread—process not controlled” versus the “controlled process reduces spread” are discussed in the section “Sample Selection” in this article.)

Fig. 21

Theoretical model versus x-ray-diffraction-generated experimental data plots of residual stress versus number of cycles. Source: Ref 53

Fig. 21

Theoretical model versus x-ray-diffraction-generated experimental data plots of residual stress versus number of cycles. Source: Ref 53

Close modal

High-cycle fatigue may occur when the cyclic load range does not exceed the cyclic yield strength of the material but exceeds the fatigue limit (endurance limit) of the material (although many materials, such as aluminum, do not have well-defined fatigue limits). In components where no initial stresses are present, stresses may develop, and if the stresses that develop are compressive, they may actually add to the life of the component. However, if stresses are induced by processing, they may “fade” at a rate that increases with cycling stress (Fig. 22) (Ref 61).

Fig. 22

Residual stresses in peened 1040 steel samples resulting from tension-tension fatigue (the two symbols represent two samples). Source: Ref 61

Fig. 22

Residual stresses in peened 1040 steel samples resulting from tension-tension fatigue (the two symbols represent two samples). Source: Ref 61

Close modal

There are cases in which the influence of residual stress on fatigue life is negligible. For hardened and ground specimens, a clear positive influence of compressive stresses and a negative influence of tensile stresses are often exhibited. Compressive residual stresses impart the maximum benefit when the volumes with the highest compressive residual stress coincide with the highest loaded component volumes. This explains why the influence of near-surface residual stresses is more pronounced for bending fatigue than in the case of tension-compression loading. For example, in the case of a normalized material with thin-reaching machining residual stresses, they may have very little impact on the resulting tension-compression loading S-N curves. Positive residual-stress effects are also more pronounced in hardened steels if detrimental starting conditions, such as decarburization or oxidation, exist. Thus, the stability of residual stresses is of central importance; that is, their effect is more pronounced when less relaxation occurs during fatigue loading (Ref 2).

Because of the enormous impact of manufacturing processes and loading history on resulting residual-stress states, these factors must be considered in relation to failure analysis (Ref 2, 8). It is assumed, at least in principle, that in-service loads for a given component can be determined either by direct calculation, measurement, or finite-element modeling. X-ray diffraction can be used to measure the residual stress in as-manufactured components so as to enable the detection of stress states that may be potentially harmful to service life and to enable the subsequent identification of unfavorable process parameters.

For example, consider the effects of gentle, conventional, and abusive grinding (Fig. 23) (Ref 3). It is important to note that, in the case of abusive grinding (where grinder burn is present), the surface residual stress may be neutral (as in this example) or even compressive; however, the life-limiting tensile residual stresses may be at very shallow depths below the surface. Thus, failure analysts must consider surface and subsurface residual stresses in their analysis.

Fig. 23

Subsurface residual-stress distribution after grinding hardened steel (stress measured in the direction of grinding). Source: Ref 3

Fig. 23

Subsurface residual-stress distribution after grinding hardened steel (stress measured in the direction of grinding). Source: Ref 3

Close modal

The XRD technique is generally applied to the measurement of residual stress in polycrystalline materials used in mechanical, electronic, and structural components. After machining, casting, shot peening, turning, heat treatment, and so on, the residual stress can vary significantly from the surface through the subsurface (Ref 2). These residual stresses must therefore be characterized at the surface and through the subsurface to evaluate the effects of the process and the stress gradients generated (Ref 62, 63). Changes in the process can then be evaluated via changes in the surface and subsurface stress states. To access subsurface measurement locations, material removal is required and can be performed using electropolishing techniques. Electropolishing is discussed in more detail in the section “Specimen Preparation” in this article. Stress relaxation due to material removal and stress gradient corrections can subsequently be applied to stress versus depth results (Ref 3). Residual-stress characterization in both the surface and subsurface is a powerful and essential tool in failure analysis, process control, and optimization (Ref 6, 62).

The subsurface stress gradients shown in Fig. 24 reflect the effect of varying peening intensity on shot-peened components from the same population. The compressive residual stress is low at the surface for the unpeened sample and high at the surface for the peened ones. Normally, samples such as these are subsequently exposed to fatigue testing in order to select the optimal process. This information can then be used to establish a benchmark for quality control and quality assurance. In cases where the process is adequately controlled, the surface stresses can be used as an indication of the presence and/or effectiveness of the shot peening in line with the subsurface stress profiles confirmed via periodic (hourly/daily/weekly) audits. Indirect information about the effect of the loading history on the residual-stress state of components can also be obtained after they have been placed into service.

Fig. 24

Residual-stress profiles on unpeened and peened samples

Fig. 24

Residual-stress profiles on unpeened and peened samples

Close modal

The residual stress versus depth plots in Fig. 25 indicate that the in-service loads have a profound effect on the near-surface stress state of the material in the gear. The service cycling introduced an increased compressive near-surface residual-stress layer in the region of the pitch diameter. This compressive residual stress as a result of in-service cycling may, in fact, increase the fatigue resistance of the gear at this location. This effect is, of course, localized and does not address the stress state of other locations, such as the root of the gear.

Fig. 25

Comparison of residual stress on the tooth pitch diameter found in two different types of hardened steel gears in new and used conditions using x-ray diffraction. (a) Pinion gears. (b) Sun gears

Fig. 25

Comparison of residual stress on the tooth pitch diameter found in two different types of hardened steel gears in new and used conditions using x-ray diffraction. (a) Pinion gears. (b) Sun gears

Close modal

The residual stress versus depth plot in Fig. 26 indicates that the in-service loads have the effect of reducing the compressive near-surface stress state of the material in the spring. In this case, the service cycling introduced probably decreases the resistance of the spring to fatigue failure.

Fig. 26

Comparison of residual stress on the inner diameter of shot-peened coil springs in new and used conditions using x-ray diffraction

Fig. 26

Comparison of residual stress on the inner diameter of shot-peened coil springs in new and used conditions using x-ray diffraction

Close modal

The examples shown in Fig. 25 and 26 illustrate the potential effects of cold working on manufactured components prior to and subsequent to being placed into service.

Heat treatment processes are also commonly applied to engineering components to obtain the desired microstructure, such as in the case of quenching and/or tempering. Heat treatments may also be applied to relax micro- and/or macroresidual stresses. X-ray diffraction can be used effectively in the characterization of these processes as well.

Shot-peened steel coil springs were heat treated for 45 min through a range of temperatures to observe stress-relaxation effects with various tempering temperatures. The surface residual macrostress was measured prior to and subsequent to heat treatment. The purpose of measuring residual stresses on the same springs before and after heat treatment was to minimize the effect of potential variations in the as-manufactured residual-stress state. The data plotted in Fig. 27 were obtained.

Fig. 27

Plot of the change in compressive residual stress due to heat treatment

Fig. 27

Plot of the change in compressive residual stress due to heat treatment

Close modal

One coil spring was kept as a control, and the reduction in compressive residual stress due to heat treatment was plotted for the remaining springs that were subject to various heat treatment temperatures. A trend of increasingly relaxed residual stress was observed for increased heat treatment temperature.

Similar studies can be conducted on a variety of components to assess the change in residual macrostress due to heat treatment. The effect may be a positive influence, if life-limiting (undesirable) residual stresses are relaxed. Conversely, the impact of life-extending (desirable) residual stresses may be reduced.

As this example demonstrates, XRD can also be applied to the evaluation of both micro- and macrostresses simultaneously. Trends in the relaxation of macrostresses are evaluated using the associated shifts in the atomic lattice spacing and thus the diffraction angle, whereas the distribution of microstresses can be correlated to the XRD peak width.

The residual stress with varying heat treatment temperature for two iron alloys is plotted in Fig. 28. The magnitude (or absolute value) of the residual stress for these specimens tends to decrease for a given increase in heat treatment temperature. The effect is pronounced for the AISI 01 samples because they had significant residual stress prior to heat treatment. The residual stresses in the AISI 1070 samples were lower, on average, prior to heat treatment; thus, there were lower-magnitude macrostresses to relax. The scatter in these data (beyond the quoted error bars) can be attributed to the slightly different residual-stress state prior to heat treatment in the various samples used to represent each heat treatment temperature.

Fig. 28

X-ray diffraction (XRD) residual stress versus heat treatment temperature for various iron alloys. Specimens were held at temperature for 1 h and furnace cooled.

Fig. 28

X-ray diffraction (XRD) residual stress versus heat treatment temperature for various iron alloys. Specimens were held at temperature for 1 h and furnace cooled.

Close modal

Dislocations are typically introduced into materials by cold working. The formation of small crystallites (coherent domains) and the introduction of elastic microstrains both result in broadening of the XRD line profile (Ref 7). Line broadening is also a function of instrumental broadening, that is, the XRD instrument optics.

Despite trends in macrostress (Fig. 28), a trend of decreased hardness with increased heat treatment temperature is often observed in iron alloy sample sets (Fig. 29a). An associated decrease in the XRD peak breadth is also often observed (Fig. 29b). In this example, the range of heat treatment temperatures remained below the annealing temperature for each alloy; thus, the instrumental and particle size contributions to the broadening remained more or less constant. If the heat treatment temperature exceeds the annealing temperature, the observed XRD peak breadth may be reduced either by recovery, recrystallization, or grain growth (Ref 6, 64). Heat treatment with slow cooling has the effect of relieving or reducing microstresses and decreasing the dislocation density, thus decreasing the hardness.

Fig. 29

Effect of heat treatment temperature on (a) hardness (HRC) and (b) x-ray diffraction (XRD) peak integral breadth

Fig. 29

Effect of heat treatment temperature on (a) hardness (HRC) and (b) x-ray diffraction (XRD) peak integral breadth

Close modal

The effects of these mechanisms can be observed in the XRD peak breadth. In general, this is used as a trending tool, and the data are most easily used in empirical form to assess the relative hardness, cold working, or dislocation density in a given material.

More detailed analyses of the source of XRD line broadening can be performed using Fourier space methods, such as the Warren-Averbach method (Ref 65), or real space methods, such as Voigt deconvolution (Ref 66). The XRD peak integral breadth and/or full width at half maximum is generally characterized as a function of depth with the use of electropolishing techniques in parallel with the measurement of residual macrostresses.

In many materials, the presence of more than one phase is not uncommon. Materials that are subject to heat treatment and/or have alloying elements may be composed of two, three, or more phases. For composite materials, the failure analyst should consider all constituent phases. The diffraction conditions and measurement parameters may differ for each phase; however, the additional effort is often worthwhile for a complete analysis.

For example, carbon steel containing more than 0.5% C and other elements added to increase toughness, improve corrosion resistance, and so on can contain ferrite (and/or martensite), austenite, cementite, and/or other phases. The volume fraction of each phase can vary with alloying content, heat treatment, and even cold working; therefore, the stresses must be evaluated for all phases of significant volume fraction. The residual stress in each phase and the weighted-average stress (based on the volume fraction of each phase) should be calculated, because the fracture resistance of the material may vary locally depending on the phase under consideration. For example, untempered martensite is more brittle than austenite; thus, when both phases are present in a component, each may behave quite differently during cyclic loading. The residual stress in all phases present in the material should thus be measured and analyzed.

Stress concentrations and stress raisers can be important contributors to the initiation and/or propagation of cracks and subsequent component or structural failure. Stress concentrations are ubiquitous, found in locations associated with geometric discontinuities such as sharp corners, weld toes, notches, undercuts, machining marks, scratches, microcracks, and so on, and naturally, crack tips themselves. The degree of care taken in the estimation, modeling, and ultimate management of the various stress-concentration contributors in a given structure or component should be dependent on the criticality of the component in the structure.

Typically, stress-concentration factors (SCFs) are either found in publications such as Peterson’s Stress Concentration Factors (Ref 67) or determined via computer-based modeling using various techniques. The application of SCFs obtained using either of these two approaches may involve assumptions regarding component geometry, SCF uniformity, and, in some cases, the residual stresses present. Experimental determination of SCFs using XRD is often possible for specific geometric features by performing stress measurements at concentration locations under an incremental loading regime (Ref 13, 40). Data can also be collected to determine the variation of the SCF due to inhomogeneity of the stress-concentration geometry, that is, where the radius of curvature is nonuniform.

It is important to measure residual stresses local and adjacent to stress concentrations using XRD, because residual stresses are additive to applied stresses and thus influence the ultimate effect of the total stress present in the region of stress concentration (Ref 68). It has been shown that surface residual stresses can significantly affect crack opening behavior (thus, crack growth behavior) even when the crack has grown well beyond the zone of residual stress (Ref 69). This indicates that the residual compressive stress present at the surface can strongly influence the surface crack-tip opening displacement throughout the entire loading cycle (Ref 69).

Cracks initiating from the tip of the cloverleaf pattern in steel cargo tiedown sockets were observed by the builder following installation aboard several cargo vessels in various stages of construction. A root-cause failure analysis was launched, and three possible mechanisms of failure were considered: overload failure, fatigue fracture, and environmentally assisted cracking (stress-corrosion cracking, or SCC). Failure mechanisms of fatigue fracture and environmentally assisted cracking were eliminated because no evidence of SCC or fatigue fracture was observed; thus, the failure analysts focused on the possibility of overload failure. Further tests showed that the overload failure mode and the transition from ductile to brittle fracture were facilitated by the combination of high brittleness of a carbon-rich transformed martensite layer introduced by flame cutting, increased hardness due to the cold-working coining process, and high residual stresses created by the welding process (Ref 70).

Finite-element models (Fig. 30) were used to predict residual stresses in the areas of high stress concentration introduced during the manufacturing (welding) process and additional applied stresses introduced by the “sagging” loads inherent in the ship hull construction and ballast distribution. The high SCF had the effect of locally amplifying the manufacturing-induced welding residual stresses and the in-service dead load stresses.

Fig. 30

Finite-element model showing maximum stress concentration in cloverleaf radius. The highest stress concentration is in the small black area surrounded by white.

Fig. 30

Finite-element model showing maximum stress concentration in cloverleaf radius. The highest stress concentration is in the small black area surrounded by white.

Close modal

To validate the “overload failure” postulate, measurements were performed in the field on cargo ships with the cracking problem. A typical residual-stress profile collected on the tiedown sockets installed on ships can be seen in Fig. 31.

Fig. 31

Typical residual-stress profile as a function of distance from the maximum stress concentration in the radius of a tiedown socket

Fig. 31

Typical residual-stress profile as a function of distance from the maximum stress concentration in the radius of a tiedown socket

Close modal

X-ray diffraction was used to validate the postulated failure mechanism and effectively demonstrated the existence of residual weld-induced stresses in installed tiedown sockets (Ref 71). Subsequently, failure analysts were able to recommend corrective measures: the removal of the brittle, carbon-rich transformed martensite layer introduced by flame cutting, which facilitated the overload failure, and the application of a localized stress-relief heat treatment process. X-ray diffraction residual-stress measurements were then performed on heat treated tiedown sockets to verify the effectiveness of the localized heat treatment process applied.

Additive manufacturing (AM) is increasingly being used as an alternative method of fabricating near-net shape components, and much research and development is currently being carried out in this area. In particular, replacement parts that were manufactured via traditional methods, such as machining or casting, are now being fabricated using AM processes. While AM methods can produce a dimensionally identical part, the process may not produce the same residual-stress distribution in the part. The repeated cycles of heating and cooling that are required to deposit the layers of metal cause localized expansion and contraction, which in turn can create residual stress. Finished components may be similar dimensionally, chemically, and microstructurally; however, their properties, such as fatigue resistance, SCC, and other life-limiting influences, may differ significantly due to differences in residual stress and other effects, including texture and porosity. Figure 32 illustrates the residual stress versus depth profiles for AM-deposited samples of a few select materials. With these examples, it can be seen that the magnitude and sign of the residual stress vary widely with depth in an AM component and that the maximum tensile residual stress may be located below the surface. Moreover, the residual stress may even be compressive near the surface yet tensile below the surface, as shown in the steel sample. As with many metal components, the residual stresses due to fabrication can often be managed and modified to suit the application and improve performance. An example of this can be seen in Fig. 33, where AM parts were characterized in both as-fabricated and as-fabricated plus peened conditions. In this instance, the peening process applied to the as-fabricated plus peened part was able to impart a significant compressive residual-stress field and thus improve the component resistance to SCC and fatigue as compared to the as-fabricated component.

Fig. 32

Residual stress versus depth profiles for a variety of additive-manufactured materials

Fig. 32

Residual stress versus depth profiles for a variety of additive-manufactured materials

Close modal
Fig. 33

Residual stress versus depth profiles for as-fabricated and as-fabricated plus peened additive-manufactured parts

Fig. 33

Residual stress versus depth profiles for as-fabricated and as-fabricated plus peened additive-manufactured parts

Close modal

In some instances, failures may occur despite the application of conventional surface treatments that often have a limited depth of effectiveness. With the advent of enhanced surface treatments such as ultrasonic impact treatment and laser shock peening, compressive residual-stress layers can be realized that are much deeper than those achieved using conventional surface treatments. Deeper compressive stress fields can improve damage tolerance in high-performance applications and may be considered when conventional surface treatments are insufficient to prevent failure.

Ultrasonic impact treatment (UIT) can significantly improve the fatigue strength of welded joints with beneficial compressive residual stress, improve the near-surface grain structure, and act to reduce the stress-concentration geometry in instances where it is applied to a small radius, as may be found in a weld toe, thus further improving the fatigue strength of the treated weld joint. Residual compressive stress increases the fatigue crack propagation threshold, inhibiting the expansion of early fatigue cracks so as to effectively prolong the fatigue life of a component (Ref 72). The grain refinement and work-hardening effects that UIT provides result in improved crack growth resistance and increased local yield strength, respectively. One major advantage of UIT is that it is a portable process, so it can be applied in the field on large structures where conventional peening is too difficult or undesirable. Figure 34 provides an example of UIT applied to the toe of welded joints on a large welded structure. The moderate compressive and tensile residual stresses resulting from the welding process are replaced by deep-reaching and high-magnitude compressive residual stresses after UIT was applied. With the newly installed compressive layer, the structural members that were treated with UIT will benefit from an improved fatigue life; the successful application of the process can be verified via XRD.

Fig. 34

Residual stress versus depth profiles for as-welded and as-welded plus ultrasonic-impact-treated (UIT) structural steel welded joint

Fig. 34

Residual stress versus depth profiles for as-welded and as-welded plus ultrasonic-impact-treated (UIT) structural steel welded joint

Close modal

Laser shock peening (LSP) develops compressive residual-stress profiles that are relatively deep reaching, typically ranging from one to several millimeters deep. The process uses pulses of laser light to generate a shock wave that propagates into the component. The area impacted by each pulse can be a few square millimeters and can be very precisely placed. Laser shock peening can be used to target specific areas of a component to combat recognized peak tensile loads and may be combined with conventional shot peening to provide a uniform topography and overall compressive residual stress and plastic strain. The level of compressive stress imparted by LSP has been associated with acting to increase the fatigue resistance of certain components by up to 10 times. Laser shock peening has been used in many industries, including aerospace, automotive, power generation, and others. X-ray diffraction has been used to characterize the LSP process on a wide variety of alloys, components, and geometries. An example of LSP applied to a titanium-base alloy component is shown in Fig. 35.

Fig. 35

Residual stress versus depth profile for a titanium-base alloy component treated with laser shock peening

Fig. 35

Residual stress versus depth profile for a titanium-base alloy component treated with laser shock peening

Close modal

Cold expansion processes have been applied to holes that are susceptible to fatigue in service in a wide variety of applications and are particularly common in aerospace. Cold expansion processes impart a through-thickness compressive stress local to the hole inside diameter to improve fatigue performance. The process employs a mandrel that is pulled through the hole to generate plastic deformation, as determined by the mandrel/hole interference (Ref 73). The effectiveness of the process can be characterized via XRD; in many instances, this characterization can be performed nondestructively. Figure 36 shows an example of the compressive hoop stresses on the entrance and exit sides of a cold-expanded hole characterized nondestructively. It can be seen that the maximum compressive stress is a small distance from the hole, and the compressive stresses are of greater magnitude on the exit side as compared to the entrance side. The compressive residual-stress field tapers off and crosses over into tension at some distance from the edge of the hole. The compressive stresses are thus balanced by a tensile field farther away from the hole. In some cases, the cold-worked residual-stress field may be mapped around the circumference of the hole and represented in a 2D plot (Fig. 37). These types of data have been used to:

• Verify finite-element modeling predictions and optimize the cold-working process parameters applied

• Verify that the process has been used correctly in production

• Determine if a cracked hole was correctly cold expanded

• Track residual stress with in-service usage

• Determine if the compressive stress field has relaxed with in-service usage, that is, HCF relaxation

Also see the section “Importance of Residual Stress in Fatigue” in this article.

Fig. 36

Entrance- and exit-side residual hoop stress versus distance from edge of hole on an aluminum-base alloy cold-expanded hole

Fig. 36

Entrance- and exit-side residual hoop stress versus distance from edge of hole on an aluminum-base alloy cold-expanded hole

Close modal
Fig. 37

Visualization of surface residual hoop stress measurement data (averaged from 10° to 350°) vs. distance from the edge of a split sleeve cold expanded hole (split centered at 0°).

Fig. 37

Visualization of surface residual hoop stress measurement data (averaged from 10° to 350°) vs. distance from the edge of a split sleeve cold expanded hole (split centered at 0°).

Close modal

This article was revised from J.A. Pineault, M. Belassel, and M.E. Brauss, “X-Ray Diffraction Residual Stress Measurement in Failure Analysis,” Failure Analysis and Prevention, Volume 11, ASM Handbook, ASM International, 2002, p 484–497.

1.
I.C.

Noyan
and
J.B.

Cohen
,
Residual Stress: Measurement by Diffraction and Interpretation
,
Springer-Verlag
,
1987
2.
V.

Hauk
,
Structural and Residual Stress Analysis by Nondestructive Methods
,
Elsevier
,
1997
3.
M.E.

Hilley
et al.
, “
Residual Stress Measurement by X-Ray Diffraction
,” HS784,
Society of Automotive Engineers
,
2003
4.
P.S.

Prevey
, X-Ray Diffraction Residual Stress Techniques,
Materials Characterization
,
Vol 10
,
ASM Handbook
,
American Society for Metals
,
1986
, p
380
392
5.
J.

Lu
et al.
,
Handbook of Measurement of Residual Stress
,
Fairmont Press
,
1996
6.
B.D.

Cullity
,
Elements of X-Ray Diffraction
, 2nd ed.,
,
1978
7.
H.P.

Klug
and
L.E.

Alexander
,
X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials
, 2nd ed.,
Wiley-Interscience
,
1974
8.
C.O.

Ruud
, Residual Stress Measurements,
Mechanical Testing and Evaluation
,
Vol 8
,
ASM Handbook
,
ASM International
,
2000
9.
B.B.

He
,
Two-Dimensional X-Ray Diffraction
, 2nd ed.,
John Wiley & Sons, Inc
.,
2009
10.
H.H.

Lester
and
R.H.

Aborn
,
Army Ordnance
,
Vol 6
,
1925–1926
, p
129
, 200, 283,
364
11.
C.O.

Ruud
,
P.S.

DiMascio
, and
D.J.

Snoha
, A Miniature Instrument for Residual Stress Measurement,
,
Vol 27
,
Plenum
,
1984
12.
H.

Berger
,
Sensing

Stress
,
Research/Penn State
,
Vol 10
(
No. 2
),
1989
13.
M.E.

Brauss
,
G.V.

Gorveatte
, and
J.F.

Porter
,
Development of a Miniature X-Ray Diffraction Based Stress Analysis System Suitable for Use on Marine Structures
,
Nondestructive Evaluation of Materials and Composites—SPIE
,
Vol 2944
,
1996
14.
J.A.

Pineault
and
M.E.

Brauss
,
Stress Mapping—A New Way of Tackling the Characterization of Residual Stress
,
Exp. Tech.
,
March
1995
15.
D.K.

Bowen
and
B.K.

Tanner
,
High Resolution X-Ray Diffraction and Topography
,
Taylor & Francis Inc
.,
1998
16.
J.A.

Pineault
,
M.E.

Brauss
, and
J.F.

Porter
,
Characterization of Plastic Strain in HY-80 Using X-Ray Diffraction Techniques
,
Proceedings of the Conference on Naval Applications of Material Technology
(
Halifax
),
D.R.E.A.
,
1993
17.
K.M.

Lynaugh
,
J.A.

Pineault
,
M.

Belassel
, and
M.E.

Brauss
,
The Application of X-Ray Diffraction Techniques during the Fabrication and Introduction of the Bob Hope Class Support Vessel
,
Proc. 2007 Int. Defence Applications of Materials Meeting
(
Halifax
),
2007
18.
S.P.

Farrell
,
L.W.

MacGregor
,
C.

Bayley
,
J.F.

Porter
, and
J.A.

Pineault
,
Residual Stress on the Pressure Hull of the HMCS Victoria in Proximity to the Dent Repair
,
Proc. 2007 Int. Defence Applications of Materials Meeting
(
Halifax
),
2007
19.
M.E.

Brauss
,
J.F.

Porter
,
J.A.

Pineault
, and
M.

Belassel
,
The State of the Art and the Art of the Possible Using X-Ray Diffraction Technologies on Marine Platforms
,
Proc. 2007 Int. Defence Applications of Materials Meeting
(
Halifax
),
2007
20.
M.G.

Carfagno
et al.
,
X-Ray Diffraction Measurement of Stresses in Post-Tensioning Tendons: Extending the Lifespan of Structures
,
IABSE
,
Zurich, Switzerland
,
1995
21.
M.E.

Brauss
and
J.A.

Pineault
,
Residential Strain Measurements of Steel Structures, NDE for the Energy Industry
,
NDE-Vol 13
,
American Society of Mechanical Engineers
,
1995
22.
M.E.

Brauss
et al.
,
Deadload Stress Measurements on Brooklyn Bridge Wrought Iron Eye Bars and Truss Sections Using X-Ray Diffraction Techniques
,
Proc. 14th Annual Meeting of the International Bridge Conference
,
Engineers’ Society of Western PA
,
1997
23.
M.E.

Brauss
,
J.A.

Pineault
,
M.

Belassel
, and
S.I.

Teodoropol
,
Nondestructive, Quantitative Stress Characterization of Wire Rope and Steel Cables
,
Proc. SPIE, Structural Materials Technology
,
Vol 3400
,
Society of Photo-Optical Instrumentation Engineers
,
1998
24.
J.

Pineault
,
M.

Belassel
,
G.

Grodzicki
,
M.

Brauss
.
C.

Sheridan
, and
D.

Webber
,
Stress Measurements on the George Washington Bridge Using X-Ray Diffraction Techniques
,
Proc. ICSBOC
(
Halifax
),
2016
25.
J.

Pineault
,
M.

Belassel
,
G.

Grodzicki
,
G.

Singletary
,
M.

Brauss
,
C.

Sheridan
, and
M.

Mangione
,
Total Load Measurements on RFK Bridge Eye-Bars: Bridging the Gap between Strain Gages and X-Ray Diffraction
,
Proc. ICSBOC
(
Halifax
),
2016
26.
C.F.

Jatczak
et al.
, “
Retained Austenite and Its Measurement by X-Ray Diffraction
,” SP-453,
Society of Automotive Engineers
,
1980
27.
C.O.

Ruud
, X-Ray Diffraction Methods for Process Monitoring and Quality Control,
Topics on Nondestructive Evaluation Series
,
Vol 1
, Sensing for Materials Characterization Processing and Manufacturing,
ASNT
,
1998
28.
C.O.

Ruud
and
K.J.

Kozaczek
,
Errors Induced in Triaxial Stress Tensor Calculations Using Incorrect Lattice Parameters
,
Proc. 1994 SEM Spring Conference
,
Society for Experimental Mechanics
,
June
1994
29.
T.

Sasaki
and
Y.

Kobayashi
, “
X-Ray Multiaxial Stress Analysis Using Two Debye Rings
,”
JCPDS-International Centre for Diffraction Data
, ISSN 1097-0002,
2009
30.
J.

Ramirez-Ricol
,
S.-Y.

Lee
,
J.J.

Ling
, and
I.C.

Noyan
,
Stress Measurement Using Area Detectors: A Theoretical and Experimental Comparison of Different Methods in Ferritic Steel Using a Portable X-Ray Apparatus, Part I
,
Mater. Sci.
,
Vol 51
,
2016
, p
5343
5355
31.
Standard Test Method for Verifying the Alignment of X-Ray Diffraction Instrumentation for Residual Stress Measurement
,” E
915
-
990
,
ASTM
32.
E.

Kröner
,
Z. Phys.
,
Vol 151
,
1958
, p
504
518
33.
E.

Kröner
,
J. Mech. Phys. Solids
,
Vol 15
,
1967
, p
319
329
34.
Standard Test Method for Determining the Effective Elastic Parameter for X-Ray Diffraction Measurements of Residual Stress
,” E
1426
-
1491
,
ASTM
35.
V.

Li
,
J.L.

Ji
, and
G.E.

Lebrun
,
Surface Roughness on Stress Determination by the X-Ray Diffraction Technique
,
Exp. Tech.
,
Vol 19
(
No. 2
),
March/April
1995
, p
9
11
36.
A.J.C.

Wilson
,
Br. J. Appl. Phys.
,
Vol 16
,
1965
, p
665
37.
J.A.

Pineault
and
M.E.

Brauss
,
Measuring Residual and Applied Stress Using X-Ray Diffraction on Materials with Preferred Orientation and Large Grain Size
,
,
Vol 36
,
1993
38.
C.M.

Mitchell
,
Stress Measurement by X-Ray Diffractometry
, U.S. Patent 4,561,062,
1985
39.
M.

Belassel
,
M.E.

Brauss
, and
J.A.

Pineault
, “
Residual Stress Characterization Using X-Ray Diffraction Techniques, Applications on Welds
,”
American Society of Mechanical Engineers Conference (Atlanta)
,
2001
40.
J.A.

Pineault
,
M.E.

Brauss
, and
J.S.

Eckersley
, Residual Stress Characterization of Welds Using X-Ray Diffraction Techniques,
Welding Mechanics and Design
,
American Welding Society
,
1996
41.
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
42.
A.

Constantinescu
and
P.

Ballard
,
On the Reconstruction Formulae of Subsurface Residual Stresses after Matter Removal
,
Proc. ICRS5
(
),
1997
, p
703
708
43.
C.L.

Formby
and
J.R.

Griffiths
, in
Proc. of Conf. on Residual Stresses in Welded Constructions and Their Effects
,
The Welding Institute
,
1987
, p
359
44.
J.E.

Hack
and
G.R.

Leverant
, “
Residual Stress Effects in Fatigue
,” STP 776,
ASTM
,
1982
, p
204
45.
A.R.

McIlree
,
C.O.

Ruud
, and
M.E.

Jacobs
, The Residual Stress in and the Stress Corrosion Performance of Roller Expanded Inconel 600 Steam Generator Tubing,
Int. Conf. on Expanded and Rolled Joint Tech.
,
,
1993
, p
139
148
46.
R.

Herzog
, Dr. Ing. thesis, University GH Kassel,
1996
47.
V.M.

Faires
,
Design of Machine Elements
, 4th ed.,
MacMillan
,
1965
48.
J.S.

Eckersley
,
Shot Peening Theory and Application
,
IITT-International
,
1989
, p
241
255
49.
J.F.

Throop
et al.
, “
Residual Stress Effects in Fatigue
,” STP 776,
ASTM
,
1982
50.
H.S.

Reedsmeyer
Fatigue and Fracture Analysis of Ship Structures
,
Fleet Technologies Limited
,
1998
51.
K.

Matsui
et al.
,
An Increase in Fatigue Limit of a Gear by Compound Surface Treatment
,
Proc. ICRS6
(
Oxford
),
2000
, p
871
878
52.
D.

François
,
A.

Pineau
, and
A.

Zaoui
,
Comportement Mécanique des Matériaux (Mechanical Behavior of Materials)
,
Vol 2
,
Hermes
,
Paris
,
1993
53.
M.

Belassel
,
M.E.

Brauss
, and
S.G.

Berkley
,
Residual Stress Relaxation in Nickel Based Alloys Subjected to Low Cycle Fatigue
,
Proc. ICRS6
(
Oxford
),
2000
, p
144
151
54.
C.M.

Verpoort
, and
C.

Gerdes
,
Shot Peening Theory and Application
,
IITT-International
,
1989
, p
11
70
55.
S.G.

Berkley
,
U.S.

Patents
5,490,195 and 5,625,664
56.
S.G.

Berkley
et al.
, “Residual Stress Measurement and Its Application to Achieve Predicted Full Life Potential of Low Cycle Fatigue (LCF) Limited Engine Disks,”
Ninth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
,
ISROMAC-9
(
Honolulu, HI
),
2002
57.
C.O.

Nonga
et al.
,
The Influence of Residual Stresses and Surface Finish on the Fatigue of Metal Matrix Composites
,
Proc. ICRS5
(
),
1997
, p
95
100
58.
Fatigue and Fracture
,
Vol 19
,
ASM Handbook
,
ASM International
,
1996
59.
G.

Kuhn
et al.
, Instability of Machining Residual Stresses in Differently Heat Treated Notched Parts of SAE 1045 during Cyclic Deformation,
Proc. ICRS3
,
Elsevier
,
1992
, p
1294
1301
60.
G.

Kuhn
, Dr. Ing. thesis, University Karlsruhe (TH),
1991
61.
M.

McClinton
and
J.B.

Cohen
,
Mater. Sci. Eng.
,
Vol 56
,
1982
, p
259
263
62.
J.A.

Pineault
and
M.E.

Brauss
,
Measuring Residual Stress Using X-Ray Diffraction on Shot Peened Components
,
MAT-TEC
,
IITT-International, France
,
1993
63.
R.

Fathallah
et al.
, Effect of Shot Peening Parameters on Introduced Residual Stresses,
Proc. ICRS4
(
Baltimore, MD
),
1994
, p
340
346
64.
T.H.

Simm
,
Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys
,
Crystals
2018
, p
8
,
212
65.
B.E.

Warren
,
X-Ray Diffraction
,
,
1969
66.
J.I.

Langford
,
A Rapid Method for Analyzing the Breadths of Diffraction and Spectral Lines Using the Voigt Function
,
J. Appl. Crystallogr.
,
Vol 11
,
1978
67.
W.D.

Pilkey
et al.
,
Peterson’s Stress Concentration Factors
, 2nd ed.,
Wiley-Interscience
,
1997
68.
M.E.

Brauss
,
J.A.

Pineault
, and
M.J.

Vinarcik
,
Characterizing Residual Stresses Induced by Rolling in Crankshaft Fillets Using X-Ray Diffraction
,
Proc. of SEM Spring Conference
,
Society for Experimental Mechanics
,
1995
69.
J.E.

Hack
and
G.R.

Leverant
,
Influence of Compressive Residual Stress on the Crack Opening Behavior of Parts through Fatigue Cracks
,
Residual Stress Effects in Fatigue: ASTM Special Technical Publication 776
, ASTM PCN 04-776000-30,
1981
, p
204
210
70.
X.J.

Zhang
and
M.

Gaudett
,
Steel Failure Analysis Results in Stronger Deck Sockets
,
Wavelengths—An Employee Digest of Events and Issues
,
Jan/Feb
1999
71.
M.

Zoccola
,
Division Trio Receive Navy Superior Service Award
,
Wavelengths—An Employee Digest of Events and Issues
,
Aug
1999
72.
B.

He
et al.
,
Effect of Ultrasonic Impact Treatment on the Ultra-High Cycle Fatigue Properties of SMA490BW Steel Welded Joints
,
,
Vol 96
(
No. 5–8
),
May
2018
, p
1571
1577
73.
B.

Kawdi
and
N.

Shanmukh
,
Cold Hole Expansion Process for Stress Analysis and Evaluation of Fatigue Properties
,
OSR J. Mech. Civil Eng. (IOSR-JMCE)
, ISSN: 2278-1684,
2013
, p
21
27

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