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Several finite element models of the morphology of WC-10 wt.% Co were employed to reproduce the build-up of thermal residual stresses as well as the phase specific strain during loading-unloading in compression. The different models differ only in their geometry of the interpenetrating skeletons of WC and Co. They all respect the given volume proportion of each phase. Thermoelasticity is considered for the brittle WC, while also plasticity is included to model the Co binder phase. We compare the predictions of our FEM models with phase specific strain measurements performed by in-situ neutron diffraction and discuss the model validation. (C) 2014 Elsevier Ltd. All rights reserved.

Thermal residual stresses in cemented carbide composites are large, interact with applied stresses, and affect deformation and toughness. Their magnitudes are high (e.g., + 2 GPa for Co and − 0.4 GPa for WC in WC–10 wt.% Co) and their distributions are complex. Magnitudes depend on expansion coefficients, binder content and particle size; distribution depends on particle angularity — wide ranges of local values occur in both phases. The response of WC-based cemented carbides to applied uniaxial compression and tension is profoundly influenced by thermal residual stresses. They account for long-observed non-linearity at very low strains, plasticity-induced relaxation, unusual Poisson's ratio behavior, and changes in density with loading. Mechanical response is also asymmetric and a function of load direction and history. The response to cyclic loading gives insight into the role of thermal residual stresses in the toughness of these materials, known for their high toughness considering their high hardness. Results for WC–Co and WC–Ni systems are presented. These studies substantially depend on the application of neutron diffraction: neutrons facilitate good bulk sampling of the volumetric thermal residual stresses in the presence of heavy elements and the use of in situ measurements; diffraction enables each phase to be monitored independently. Results show a complex plasticity behavior that comprises a primary source of toughening characteristic in cemented carbides. However, it is now clear that assumptions implicit in the application of fracture mechanics to cemented carbides, including far-field linear elasticity and isotropy are not valid. The emergent view of cemented carbide mechanics seems to require a new, non-linear-elastic model of toughness behavior in these materials, both in terms of bulk “continuum” response and response in the presence of defects. Moreover, such models, if they are to provide accuracy, must also take into account the documented anisotropic relaxation and plasticity effects and their sensitivity to load directionality and history.

The interaction of uniaxial applied stress with the thermal residual stress state in a WC–10 wt.% Ni cemented carbide composite was studied. A previously proposed model, based on results for uniaxial compressive loading, explains the observed asymmetric relaxation of the pre-existing thermal residual stress. This model predicts that the sense of the asymmetry would reverse in the case of tensile loading. The main purpose of the present work was to test this prediction. The reversal of signs was observed. The addition of tensile data has enabled the role of thermal residual stress on stress–strain response to be further elucidated. More complex behavior is observed with respect to the response of the variance in residual stresses, as measured by changes in diffraction peak breadths.

In the present study, the evaluation of the deformation and the determination of the first order residual stresses in shot peened aluminium plate have been performed by neutron diffraction on the strain imaging instrument SALSA at the Institut Laue Langevin, Grenoble, France, in order to validate a model of finite element analysis permitting to predict the final deformation. The sample used in this study is a rolled aluminium sheet (Al 2024 T3 alloy) which was clamped in a steel frame and peened following exactly the industrial production process. The first measurements were performed on the sample while it was still clamped. The second set was made after removing it from the frame. For each case, we measured the lattice strains and determined the stress repartition in the three principal directions.

The interaction of uniaxial compressive load and thermal residual stress was measured in a WC–10 wt.% (16 vol.%) Ni cemented carbide composite using neutron diffraction. Loading was from 0 to −2500 MPa in increments of 250 MPa, and measurements were made in situ during load–unload cycles 1, 2, 3, 10, 25, 50 and 100. Plasticity is observed in the Ni from the lowest levels of applied load, leading to continuous curvature of the WC–Ni stress–strain curves, and is believed to be a significant contribution to the composite’s toughness. It is due to interaction between local extremes of the thermal residual microstress with the applied macrostress and leads to anisotropic relaxation of the thermal residual stress. Strain distribution and plasticity were observed through peak breadths. Although the initially strong hysteresis is reduced as the cycles increase, there are still changes taking place after 100 cycles.

The in-situ strain response of WC-Ni cemented carbides (5, 10, and 20 wt pct Ni) to uniaxial compressive load was measured using neutron diffraction. Strain was measured in both phases parallel and transverse to the loading axis of cylindrical samples. Plasticity is observed in the Ni binder from the lowest levels of applied load. The plasticity occurs locally in the Ni phase, on the scale of the microstructure, and leads to continuous curvature of the WC-Ni stress-strain curves and significant toughness of the material. The plasticity results from the interaction of the thermal residual microstresses created during sample production with the applied macrostress. It also leads to anisotropic relaxation of the initial residual stress and the creation of a residual stress state with cylindrical symmetry in the material. This process was observed over three load-unload cycles. Analysis enables phase-specific stress strain curves to be constructed. Finally, strain distributions were observed through peak breadth responses.

The strain response of WC and Ni in WC–Ni cemented carbide composites (5, 10 and 20 wt.% Ni) was studied under uniaxial compressive load to � 2000 MPa using neutron diffraction. Measurements of elastic strain were made simultaneously in the axial and transverse directions of the samples, for both phases. Thermal residual stresses (TRS) were also measured, before and after loading. Ni plasticity was observed from the earliest load levels. The superposition of tensile Poisson strain (in the transverse direction) on pre-existing tensile Ni strain due to TRS produces anisotropic yielding in binder regions. Yielding is progressive with applied strain, leading to a reversal of transverse binder strain, and anisotropic relaxation of the TRS. The effect is greatest for 20 wt.% Ni, where Ni constraint is much less than for 5 wt.% Ni. These results provide a quantitative basis for the mechanical origins of the toughness of cemented carbide composites. � 2005 Elsevier Ltd. All rights reserved.

In situ neutron diffraction measurements were performed on a tungsten carbide (WC)–10 wt.% cobalt (Co) cemented carbide composite subjected to compressive loading. The sample was subjected to consecutive load/unload cycles to −500, −1000, −2000 and −2100 MPa. Thermal residual stresses measured before loading reflected large hydrostatic tensile stresses in the binder phase and compressive stresses in the carbide phase. The carbide phase behaved elastically at all but the highest load levels, whereas plasticity was present in the binder phase from values of applied stress as low as −500 MPa. A finite element simulation utilizing an interpenetrating microstructure model showed remarkable agreement with the complex mean phase strain response during the loading cycles despite its under-prediction of thermal residual strains.

We studied the effects of WC particle size and volume fraction on the magnitude and distribution of thermal residual stresses (TRS) in WC–Ni cemented carbide composites by neutron powder diffraction. Samples of high (0.3) and low (0.1) Ni volume fraction and coarse (1.7 m) and fine (0.5 m) WC particle size were employed. Thermal residual strain and stress values were obtained at temperatures between 100 and 900 K. Moreover, the magnitude of the mean (compressive) WC stress increased as WC fraction decreased, while the mean (tensile) Ni stress did the opposite. For both phases, stresses were highest for fine WC particles, reaching over 3 GPa in Ni. Elastic strain distributions, due to the sharp edges and corners of WC particles, were characterized by analyzing diffraction peak widths. The range of stress increased with the magnitude of the TRS. Even though the mean TRS is compressive in WC, regions of tension exist, and, for Ni, regions of compression are present.

Thermal residual stresses (TRS) were studied in a series of tungsten carbide (WC)–cobalt (Co) composites using neutron powder diffraction. Samples with 10, 20, and 40 wt.% Co and WC particle sizes of 0.5, 1, 3, and 5 μm were used. As expected, the mean WC TRS increased in magnitude as the Co content increased, i.e. as the WC content decreased. The corresponding stresses in the Co phase were computed from force balance equilibrium requirements. For fixed Co content, the mean (compressive) stresses in the WC increased in magnitude with decreasing WC particle size. The change was most dramatic for the 40 wt.% Co samples, where the mean TRS increased in magnitude from −440 to −1137 MPa as the WC particle size varied from 5 to 0.5 μm, respectively. The stress distribution in the WC phase was studied using the breadths of the WC diffraction peaks. The full-width at half-maximum (FWHM) values indicate a broad range of strain within WC particles that increases with increasing stress in the WC and is attributed primarily to point-to-point variation in the angular WC particles.

Thermal residual macrostresses and their gradients were studied in a series of polycrystalline diamond compacts (PDC) using neutron diffraction. The specimens comprised WC–Co cemented carbides with high temperature/high pressure (HTHP) sintered polycrystalline diamond (PCD) layers. Residual stresses were investigated in two as-sintered variants and after several post-sinter thermal treatments and bonding processes. Measurements were made of (1) the average in-plane stress in the diamond layer for each sample and (2) the average in-plane stress gradient in both the WC–Co substrate and the diamond layer in a subset of the samples. Average in-plane stresses in the diamond layer ranged from −250 to −582 MPa. Sintering process parameters, thermal treatments, and bonding were all found to affect residual stress levels and stress gradient characteristics. Measured average in-plane stress gradients are shown to differ substantially in some cases from linear elastic predictions.

The basic goal of this paper is to convey essential information on neutron macrostress measurements to potential users of the method. After a discussion on residual stresses, the use of neutrons, which makes possible the measurement of triaxial macrostresses through the depth of engineering components due to the lower absorption of neutrons by most engineering materials, is presented. This is followed by a discussion on the physical and analytical basis of the use of diffraction for the measurement of such stresses. Next is a discussion on experimental aspects relevant to potential users, including probe volumes, stress-free reference standards, sample quality, errors, and the determination of full stress tensors. Lastly, an example of the determination of residual macrostress tensors in a welded cylindrical section of a solid rocket motor casing is presented.

The thermal residual macrostresses in a series of polycrystalline diamond compacts were studied using neutron diffraction. Measurements were made of (1) the average in-plane stress in the polycrystalline diamond table as a function of substrate-to-table thickness ratio; (2) the average in-plane residual stress gradient in both the WC–Co substrate and the diamond table; and, (3) the radial and hoop components of the residual stress in the diamond table as a function of radial position. The average in-plane stress in the diamond table increases in magnitude with increasing substrate-to-table thickness ratio, from −462 to −152 MPa as the ratio goes from 4 to 1. An in-plane residual stress gradient was measured that ranges from about −200 MPa at the free surface to +700 MPa at the substrate/diamond interface in the WC–Co substrate, and from about −600 MPa at the interface to −300 MPa at the free surface in the diamond. The hoop and radial stress components were measured at five points along a radius in the diamond table. The hoop stress was essentially constant (≈−470 MPa) and the radial stress ranged between about −150 and −350 MPa.

Large thermal residual microstresses (TRS) can develop in WC-Co composites owing to the difference of the coefficients of thermal expansion (CTE) of the constituents. The variation with temperature of average stresses in a WC-11 wt.% Co sample were studied between room temperature and 1273 K by measuring the cell parameters of cobalt and WC using neutron diffraction. WC powder was also measured to provide stress free reference standards. At room temperature, a hydrostatic compressive stress of about 500 MPa was measured in the WC. The evolution of TRS shows two temperature domains. The low temperature domain (300 1000 K) is characterized by an increase of residual stress in WC, a rapid increase of Co lattice parameter, and a hysteresis between the heating and cooling cycles. A model, based on Eshelby's equivalent inclusion method, predicts the observed behavior in both domains. In the low temperature domain, the CTE mismatch between WC and Co accounts for the decrease of TRS upon heating. In the high temperature domain, the system is modelled by the solution of a layer of WC in the Co, which increases the Co lattice parameter and leads to an increase of compressive stress in WC. The model indicates that there is 2.09 at.% W in solution in the cobalt. The hysteresis is attributed to a difference in the heating and cooling kinetics of solution-precipation of W from WC and WCo3. The results are compared with the mechanical properties of WC-Co.

The thermal residual stress distributions in a series of WC-Ni composites with WC volume fractions of 0.11, 0.21, 0.41, and 0.60 were measured using neutron diffraction and modeled using finite element (FE) analysis. The FE procedure employed enables the local variation of the residual microstress in a composite microstructure to be studied. The mean (compressive) stresses in WC decrease and the mean (tensile) stresses in Ni increase with increasing WC content. The stress distributions are sufficiently extensive to create regions of tension in the WC and compression in the Ni. The maximum tensile stresses in WC increase in magnitude with WC content. They are located in corners and, for higher WC content, normal to WC/Ni interfaces. High compression occurs in narrow portions of the WC skeleton. Regions of compression in Ni occur at WC/Ni interfaces for low WC content and, for composites of higher WC content, in narrow bands between chains of WC particles. It was also determined that models of actual composite microstructures, rather than geometric arrays, are required in order to properly obtain local residual stress distributions using the finite element analysis procedure.

The problem of converting elastic strain distributions determined by diffraction measurements to stress distributions is discussed. The relation of mean strains measured by powder diffraction to the corresponding mean stresses is well known and regularly employed in residual stress measurements. However, the relation between strain variance and stress variance is not so straightforward. The elastic strain distribution depends on both the variation of strain from point to point in a given direction in a volume, and in all directions at each point in the same volume. In this paper, relations between the strain variance and corresponding stress variance are developed in both two and three dimensions for the case of microstress variations in particulate systems. The two components cannot be separated from a diffraction measurement of the strain distribution but the relations developed provide upper and lower limits on the variance in the stress distribution and are useful for relating diffraction results to models of the material. The results are applied to elastic strain distributions obtained in composite systems from measurements of diffraction peak breadths and modeled using two-dimensional finite element methods.

An approach employing the finite element (FE) method to interpret diffraction peak broadening due to elastic strain distributions is presented that provides a model of the local variations of elastic strain and stress in a composite or multiphase microstructure. The method involves averaging elastic strain output from a representative FE model to generate a strain distribution analogous to the averaging taking place in the diffraction process. The procedure assumes that the FE model adequately represents the thermally stressed system, an aspect addressed by comparison of the strain distributions obtained from diffraction data and the FE model. Example applications are presented for thermal residual strain in 11 and 60vol.%WC-Ni composites. The stress in the WC, which is compressive on average, becomes tensile at corners and at locations that are normal to WC-Ni interfaces. The Ni stress, which is tensile on average, is compressive in narrow bands between WC particles. In addition, asymmetry of the Ni distribution on the high strain side, due to localized plastic flow, is successfully modeled for the 60vol.%WC-Ni. Composition effects are also represented. Uniqueness aspects and limitations of the procedure are discussed.

The residual stresses in a cylindrical weldment of HP-9-4-30 steel were measured with neutron diffraction in the as-welded (AW) state and after postweld heat treatment (PWHT). Large residual stresses are present in the interior of the material in the as-welded condition. The maximum principal stresses measured were found around the edges of the cap-pass heat-affected zone and reached up to 1045 MPa (76 pct of the base metal yield strength) in the as-welded condition. The principal stress directions for the residual stress tensors do not in general follow the hoop, axial, and radial axes of the weld and change from position to position within the weld, although the highest values are generally in the hoop direction. The postweld heat treatment relaxed the largest residual stresses, with the maximum value being 30 pct of the base metal yield stress. The need for position-dependent stress-free standards and the implications of stress gradients over the measurement volumes are discussed.

Residual stress measurements using neutron diffraction are inherently triaxial in nature due to the low adsorption, and thus high penetration, of neutrons in samples of interest. This means that stress-free reference standards are required to convert measured changes in peak position to strain and stress tensors. Althogh a number of empirical and analytical approaches have been utilized to obtain accurate stress-free reference cell parameters, they all presume the presence of a single reference value for the material being measured. However, important cases can arise for which the local stress-free cell parameter varies from point to point. One such case, a circumferentially welded cylinder, is presented here. A method of point-to-point correction is employed, involving the sectioning of a companion piece into small cubes corresponding to the positions of stress measurement. The variations in peak position and peak breadth are presented. It is shown that accurate stress tensors can be obtained and that use of a constant value of stress-free reference cell parameter from the unaffected base metal leads to errors of up to 700 MPa in some stress tensor components. Effects on the principal stresses are also presented.

Neutron powder diffraction was employed to investigate the deformation-induced changes of matrix residual stresses in an annealed 20 vol pct SiC whisker-reinforced 6061 Al composite. It was found that the changes are asymmetric in response to a uniaxial external tensile or compressive load applied along the longitudinal whisker axis. In order to investigate this unusual asymmetric behavior and understand the underlying mechanisms, the finite element method (FEM) was employed and a parametric study was conducted. It was found that a gradient of plastic flow in the matrix is responsible for the asymmetric changes.

The anisotropic relaxation of differential thermal residual stress in WC-17wt.%(85Co-15Ni) cermets subjected to compressive plastic strain under monotonic and cyclic loading has been studied. Results were obtained via triaxial stress measurements using neutron diffraction. The residual stress in cylindrical specimens loaded uniaxially along the cylinder axis was observed to decrease with increasing plastic strain. Although relaxation occurred both perpendicular and parallel to the loading direction, i.e. radially and axially, it was observed to be greater in the radial direction and this trend was observed to increase with increasing plastic strain. A qualitative model for the observed behavior is proposed.

The measurement of residual microstresses in composites using neutrons is discussed. The basic theory of the measurements is presented and the advantages of neutrons noted, including a discussion of the limitations of x-rays. A number of experimental issues are considered, including grain size, stress-free standards, sample alignment, and the use of steady state versus pulsed sources. Studies illustrating these issues are presented for which the techniques, problems and potential of the method are emphasized. Measurements of Al-SiC metal matrix composites deal with the anisotropy of the stress state in the presence of aligned fibers, particle shape effects, and changes in residual stress due to uniaxial compressive and tensile plastic deformation. Problems encountered with grain size and composition in the stress-free standards are noted. Studies of WC-Ni cemented carbide composites as a function of temperature deal with effects of microstructure and the interpretation of peak broadening in terms of stress distributions.

Residual microstress was measured, using X-ray and neutron diffraction, in SiCAl composites with SiC in the form of whiskers, platelets and spheres. Average whisker and sphere stresses are similar, with platelet values considerably lower, in disagreement with finite element method analyses. Reasons for the discrepancy, and a comparison of the X-ray and neutron results, are discussed.

The differential thermal stress state in a WC-15.6wt.%Ni cemented carbide composite has been studied using neutron powder diffraction. Absolute stress values have been obtained from the difference in WC cell parameters in a stress-free, loose WC powder and the WC phase in the composite over the temperature range 20–700 K. In addition, the stress distribution in the WC phase was determined by analysis of WC peak breadths in the reference powder and the composite. The peak breadths were corrected for particle size effects using a procedure based on the integral peak breadth method of particle size-strain analysis. The resultant full width at half-maximum values of the elastic strain distribution indicate that a broad range of strain, and thus stress, is present in the carbide phase of the composite. The distribution is centered on an average compressive stress and ranges from very compressive to very tensile values. The stress distribution results are consistent with prior results in other WC-Co and NbC-Co cemented carbides.

The large difference between the coefficients of thermal expansion of the binder and carbide phases leads to substantial differential thermal residual stresses on colling from the sintering temperature. The stress state is of the grain interaction or microstress type common in composite materials. In this study, neutron diffraction has been used to characterize the degree of strain variance and therefore stress distribution in the carbide phase for two types of cermet. Measurements of diffraction peak breadth in materials with rounded (NbCxCo) and angular ((NbCxTiC)Co) carbide phases have provided evidence of greater variance of residual strain for the angular relative to the rounded carbide. This is attributed to a greater stress distribution due to the angular geometry of the carbide particles. Similar measurements on WC-Co cermets with a low and high binder content indicate that increased strain variance is present in the high relative to the low binder material. This indicates that a greater stress distribution may be present owing to the higher average residual stress level present in the high binder material. The magnitudes of the variance have been estimated for the WC phase and are found to be large, the halfwidth being two to three times the average compressive stress in the carbide. This implies that, assuming a normal (gaussian) stress distribution, in excess of 10% of the WC volume experiences tensile stress.

Neutron diffraction has been employed to measure an applied stress gradient through the bulk of a 25.4 mm thick aluminum alloy bar. The experiment was designed to test the feasibility of combining the penetrating power of neutrons with the residual stress measurement methodology developed for near-surface regions using X-rays. The load was applied on a curved beam sample so that the tangential stress (σ θ) ranged from +302.4 MPa (+43851 psi) to −413.7 MPa (−60000 psi). A small radial stress component (σ r) was also present. Three methods of measurement were employed which enabled gradients ofσ θ –σ r/v,σ θ, andσ θ –σ r to be measured(v is Poisson’s ratio) through the sample. Two diffraction peaks, 311 and 333/511, were used. The depth of gradient sampled at each point ranged nominally from 2 to 7 mm; however, the effective depth sampled ranged from 1 to 3 mm. Experiment and theory are in reasonable agreement, suggesting that the method has potential.

Implications of the shallow penetration of X-rays in WC-base cermets are discussed with regard to conventional X-ray residual stress measurements. The principal factors of concern are relaxation of the volumetric differential thermal residual stress state at the surface and residual stress due to surface preparation. Model calculations are made of versus d sin2 Ψ plots, showing the effects of both relaxation and surface preparation for molybdenum, copper, cobalt and chromium X-rays. The occurrence of d versus sin2 Ψ plots with negative slopes, and subsequent biaxial analysis, precludes study of the differential thermal stress state although surface grinding and polishing effects may still be investigated.

The appreciation of cemented carbide composite materials (cermets) has become more sophisticated in recent years. The desire for cermets that yield better performance and/or that contain lower amounts of cobalt has spurred development of a variety of alloy binders, some of which can undergo structural modification through heat treatment. Concurrently, an increasing effort is being made to understand at a more fundamental level the service response of binder and carbide phases in traditional and experimental materials. The success of such investigations depends upon analytical approaches capable of discerning fundamental structure-property relationships. It is the purpose of this paper to discuss one such approach that shows promise as a new analytical tool — neutron diffraction.

The use of neutrons for the measurement of stress is complementary to and extends traditional x-ray diffraction methods to new types of problems. This is due to the lower absorption of neutrons compared to x-rays by most engineering materials, which increases the sampling depth from microns to millimeters. It is particularly suitable for triaxial macrostress gradients through the depth of engineering components and volumetric microstresses in composites. In addition, applied stress studies may also be performed. This paper briefly describes the nature of residual stresses, the use of diffraction for stress measurements, experimental aspects of the use of neutrons, and illustrative applications.