Failure Analysis and Prevention (2021 Edition)
- Residual Stress in Failures and X-Ray Diffraction Analysis
- X-Ray Diffraction Theory and Residual-Stress Measurement
- Analysis of X-Ray Diffraction Data
- Instrument Calibration and Validation of Stress Measurements
- Alignment of X-Ray Diffraction Instrumentation
- X-Ray Elastic Constant Determination (ASTM E 1426)
- Surface Condition Evaluation
- Collection Parameter Selection
- Sample Selection
- Measurement Location Selection and Location Access
- Empirical Observation Method for Measurement Location Selection
- Finite-Element Method for Measurement Location Selection
- Stress-Mapping Method for Measurement Location Selection
- Accessing Measurement Locations of Interest
- Selecting Measurement Directions and Depths
- Selecting Measurement Directions
- Selecting Measurement Depths
- Specimen Preparation
- Residual-Stress Effects on Components under Quasi-Static Loading
- Stress-Corrosion Cracking and Corrosion Fatigue
- Importance of Residual Stress in Fatigue
- Examples of Residual Stresses in Fatigue
- Example 3: Using X-Ray Diffraction to Track Residual-Stress Levels at Critical Locations on Turbine Engine Disks as They Accumulate Engine Cycles.
- Residual Stress and High-Cycle Fatigue
- Other Considerations Regarding Residual Stress and Fatigue
- Effect of Manufacturing Processes on Residual Stress
- Characterization of Stress Gradients Using X-Ray Diffraction
- Effects of In-Service Loads on Residual Stress
- Effects of Heat Treatment on Residual Stresses
- Examples of the Effects of Heat Treatment on Residual Stresses
- X-Ray Diffraction Stress Measurements in Multiphase Materials and Composites
- X-Ray Diffraction Stress Measurements in Locations of Stress Concentration
- Example of X-Ray Diffraction Stress Measurement in Evaluating Cracks
- X-Ray Diffraction Stress Measurements on Components Fabricated Using Additive Manufacturing
- X-Ray Diffraction Stress Measurements of Enhanced Surface Treatments
- Examples of X-Ray Diffraction Stress Measurements of Enhanced Surface Treatments
- Use of X-Ray Diffraction to Evaluate the Effects of Cold-Expansion Processes
X-Ray Diffraction Residual-Stress Measurement in Failure Analysis
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, 16–19), a building/structure (Ref 20, 21), or a bridge (Ref 22–25). 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.
Residual Stress in Failures and X-Ray Diffraction Analysis
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)
Experience cyclic loading in service (mechanical or thermal fatigue)
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.)
X-Ray Diffraction Theory and Residual-Stress Measurement
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).
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 1–9).
Analysis of X-Ray Diffraction Data
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.
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.
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.
Instrument Calibration and Validation of Stress Measurements
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:
Alignment of XRD instrumentation
X-ray elastic constant determination
Surface condition evaluation
Collection parameter selection
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 of X-Ray Diffraction Instrumentation
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).
X-Ray Elastic Constant Determination (ASTM E 1426)
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).
Surface Condition Evaluation
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.
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.).
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).
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.
Effect of Corrosion
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.
Collection Parameter Selection
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:
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.
Number of ψ Tilts Used for d-Spacing versus sin2ψ Plots
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.
X-Ray Diffraction Peak Position Determination
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).
Effects of Microstructure
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).
Effects of Surface Curvature and Beam Size
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).
Repeatability and Reproducibility
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
|Measurement No.||Stress, ksi|
|Measurement No.||Stress, ksi|
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.
Measurement Location Selection and Location Access
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.
Empirical Observation Method for Measurement Location Selection
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 Method for Measurement Location Selection
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.
Stress-Mapping Method for Measurement Location Selection
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).
Accessing Measurement Locations of Interest
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.
Selecting Measurement Directions and Depths
Selecting Measurement Directions
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.
Selecting Measurement Depths
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.
Residual-Stress Effects on Components under Quasi-Static Loading (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).
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).
Stress-Corrosion Cracking and Corrosion Fatigue (Ref 40)
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.
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.
Importance of Residual Stress in Fatigue
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.
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).
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).
Examples of Residual Stresses in Fatigue
Example 1: Use of X-Ray Diffraction to Assess Residual Stresses in Steel Springs.
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.
Example 2: Use of X-Ray Diffraction to Assess the Effect of Mechanical Loading on Stress Relaxation of Machined and Shot-Peened Nickel-Base Alloy (Waspaloy).
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).
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.
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).
Example 3: Using X-Ray Diffraction to Track Residual-Stress Levels at Critical Locations on Turbine Engine Disks as They Accumulate Engine Cycles.
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.)
Residual Stress and High-Cycle Fatigue
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).
Other Considerations Regarding Residual Stress and Fatigue
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).
Effect of Manufacturing Processes on Residual Stress
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.
Characterization of Stress Gradients Using X-Ray Diffraction
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.
Effects of In-Service Loads on Residual Stress
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.
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.
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.
Effects of Heat Treatment on Residual Stresses
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.
Examples of the Effects of Heat Treatment on Residual Stresses
Example 4: Use of X-Ray Diffraction to Assess the Effects of Heat Treatment on Residual Stress in Steel Coil Springs.
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.
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.
Example 5: Use of X-Ray Diffraction to Evaluate the Effect of Varying Heat Treatment Temperature on Residual Stress for Iron Alloys.
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.
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.
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.
X-Ray Diffraction Stress Measurements in Multiphase Materials and Composites
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.
X-Ray Diffraction Stress Measurements in Locations of Stress Concentration
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).
Example of X-Ray Diffraction Stress Measurement in Evaluating Cracks
Example 6: Use of X-Ray Diffraction to Evaluate Cracks in Steel Cargo Tiedown Sockets.
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.
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.
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.
X-Ray Diffraction Stress Measurements on Components Fabricated Using Additive Manufacturing
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.
X-Ray Diffraction Stress Measurements of Enhanced Surface Treatments
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.
Examples of X-Ray Diffraction Stress Measurements of Enhanced Surface Treatments
Example 7: Use of X-Ray Diffraction to Evaluate the Effectiveness of Ultrasonic Impact Treatment to Impart Compressive Residual Stresses in Welded Joints on a Large Structure.
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.
Example 8: Use of X-Ray Diffraction to Evaluate the Effect of Laser Shock Peening on a Titanium-Base Alloy Component.
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.
Use of X-Ray Diffraction to Evaluate the Effects of Cold-Expansion Processes
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.
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.
J.A. Pineault, M. Belassel, M.E. Brauss, X-Ray Diffraction Residual-Stress Measurement in Failure Analysis, Failure Analysis and Prevention, Vol 11, 2021 ed., ASM Handbook, Edited By Brett A. Miller, Roch J. Shipley, Ronald J. Parrington, Daniel P. Dennies, ASM International, 2021, p 221–239, https://doi.org/10.31399/asm.hb.v11.a0006768
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