Stress-free Lattice Spacing Research Articles

Selfconsistent Evaluation of Non-Uniform Stress Profiles and X-Ray Elastic Constants from X-ray Diffraction Experiments

A method to obtain the triaxial depth profiles of strains and stresses as a function of the depth below the surface is described. Instead of using inverse Laplace transforms to extract the z-profiles from the measured τ-profiles, a numerically stable inverse formalism with trigonometric basis functions is used. The formalism has already been applied with great success to the hole-drilling method for the determination of residual stresses. It requires no prior knowledge of the stress state and is suitable even for strongly non-linear stress fields. This is demonstrated by experimental data sets for the conventional Ω-, ѱ- and modified ѱ goniometers. Furthermore this method enables in situ determination of Poisson's ratio as well as the stress free lattice spacing using a selfconsistency criterion for isotropic materials. It is now possible to find a proper normalization of the residual strains and residual stresses. Because of the formulation as an inverse problem, analytical expressions for the beam path integrals could be derived even for curved surfaces. Inverse problems are often extremely ill-conditioned. Therefore the uniqueness of the solution is discussed in terms of a spectral shift of the corresponding eigenvalues.

New Advantages in Soft X-Ray Stress Measurement and Triaxial Analysis of Nonuniform Stress States

AbstractConventional stress analysis with diffraction techniques is based on the equations of continuum mechanics, but only few materials encountered in X-ray stress analysis satisfy this assumption. In this paper, a new method is formulated yielding quantitative strain tensor fixed to the specimen coordinates. The method enables independent in-situ determination of Poisson's ratio which serves as a self control mechanism for measurement and evaluation. The analysis has been extended from flat to curved surfaces. Thus an exact analysts of spherical or cylindrical shaped specimens is now possible. The method has the capability to evaluate stress tensor and stress free lattice spacing at the surface as well as their variation with depth. This is demonstrated by two experimental data sets.

Influence of measurement and evaluation parameters on stress distributions investigated by X-rays

The complete triaxial X-ray strain or stress analysis including gradients requires a physical description of the beam path through the superficial layer of the material for both the conventional ω and Ψ goniometer. Within this description, a theory has been developed for plane, cylindrical, spherical or any other convex or concave specimen topography which can be described by two different radii. All crystal structures are supported. Measurements and calculations are controlled by the independent in-situ determination of Poisson's ratio and the stress free lattice spacing. The physical boundary conditions are verified or can be postulated depending on the measurement quality. A complete internal strain and stress field analysis is discussed in terms of the ‘X-ray integral method’ on steel specimens of 100 Cr-6 (ASTM: A 295, BS: 97012), Al2O3 ceramics using conventional X-ray diffractometry and on NiO layers on a metal substrate by the use of synchrotron radiation and parallel beam optics.

Simultaneous X‐ray measurements in‐situ of tri‐axial stresses, Poisson's ratio and the stress free lattice spacing

The tri‐axial X‐ray stress analysis allows, together with boundary conditions and fitting curves, a control of measurements and calculations for the determination in‐situ of Poisson's ratio and stress free lattice spacing. A complete internal stress field analysis is discussed in terms of the ‘X‐ray integral method’ on rolled steel discs of 100 Cr‐6 (ASTM: A 295, BS: 970/2).

Slit height smearing correction in small angle X-ray scattering II: Computation of the correction function

In this study, an analysis of elastic residual stress in Inconel® 718 (IN 718) linear friction welds (LFWs) was carried out. In particular, the suitability of LFW for manufacturing and repair of aero engine components was emulated by joining virgin and in-service (extracted from a turbine disk) materials. The evolution in the residual strains and stresses in the heat-affected zone (HAZ), thermomechanically affected zone (TMAZ) and dynamically recrystallized zone (DRX) of the weld was characterized using the neutron diffraction and contour methods.The results provided insight into diverse challenges in quantitative analysis of residual stresses in welded IN 718 using diffraction techniques. Specifically, judicious selection of the beam width, height and stress-free lattice spacing were seen to be crucial to minimize measurement error and increase accuracy. Further, the contour method – a destructive technique relying on capturing the stress relaxation after electrical discharge machining – was used to characterize the residual stress distribution on two-dimensional plane sections of the welds. Both techniques suggested an increasing magnitude of residual stress originating from the base metal that reached a peak at the weld interface. Both methods indicated that the peak magnitude of residual stresses were below the yield stress of IN 718.

The effects of residual stress, thermal stress-relief, and electrolytic polishing on the elastic properties of Australian wire: By John C. Williams, University of Tennessee, College of Dentistry, Memphis, Tenn.

The rapid solidification and subsequent thermal cycles that material is subjected to during additive manufacturing (AM) of a component result in a buildup of residual stresses, which lead to part distortion, and negatively impact the component's mechanical properties. We present a method for using neutron diffraction to validate thermomechanical models developed to predict the residual stresses in Inconel 625 walls fabricated by laser-based directed energy deposition. Residual stress calculations from neutron diffraction measurements depend strongly on the determination of stress-free lattice spacings. After measurement of stressed lattice spacings in Inconel 625 walls, reference samples were obtained by extracting thin slices from the walls and cutting comb-type slits into these slices. Reference lattice spacings were measured in these slices, as well as equivalent slices that were also subjected to stress-relieving heat treatment. These heat treatments changed the reference lattice spacings, and therefore affected residual strain measurements. Further, this study shows the importance of using location-dependent reference lattice spacing, as during AM, the thermal history, and therefore elemental composition and stress-free lattice spacing, vary with position. Residual stresses measured by neutron diffraction along the build direction using comb-type reference samples without heat treatment were in good agreement with thermomechanical modeling predictions.