A.D. Krawitz

Use of position-dependent stress-free standards for diffraction stress measurements

Abstract 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.

Residual stress in WC-Co measured by neutron diffraction

Abstract 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 Eshelbys 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.

Residual stress and stress distribution in a WC-Ni composite

Abstract 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.

Effect of particle size on thermal residual stress in WC–Co composites

Abstract 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.

Residual stress and stress gradients in polycrystalline diamond compacts

Abstract 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.

Deformation-induced residual stress changes in SiC whisker-reinforced 6061 Al composites

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.

Thermal residual stress distribution in WC-Ni composites

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 use of X-ray stress analysis for WC-base cermets

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.

Use of finite element modeling to interpret diffraction peak broadening from elastic strain distributions

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.

Residual stresses in discontinuous metal matrix composites

Abstract 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.