![]() Deformations caused by the residual stress relaxation can be assessed by considering an equivalent surface traction on the cut plane. Therefore, this condition owing to relaxation of the residual stresses results in deforming of the body on both cut surfaces (step B). The boundary conditions (BCs) of the new traction-free surfaces require that the normal and shear stress components along the line x=0 are zero. When the body is sectioned into two halves along the line x=0, the residual stresses on the cut plane are fully released and new traction-free surfaces are created. ![]() In step A, the two-dimensional body prior to the cutting process has both initial tension and compressive residual stresses. The contour method consists of three main steps and they are outlined in the following paragraphs.Ĭonsider a two-dimensional body possessing the arbitrary residual stress components σ xx( x, y), σ yy( x, y) and σ xy( x, y) as shown in figure 1. As for all destructive methods, this technique is based on elastic stress relaxation after material removal. In 2001, Prime introduced a new residual stress measurement method called the contour method, and it has become one of the most powerful techniques to measure residual stresses as it can determine an arbitrary cross-sectional area map of residual stress. Although there are a number of destructive methods available for measuring residual stresses at the macroscale (hole drilling, slitting, sectioning, curvature and conventional and multi-axial contour methods ), with the rapid advances of nanotechnology in recent decades, a few destructive techniques, such as cantilever, microslotting, hole/core drilling and the inverse problem of eigenstrain have become applicable down to the microscopic scale and allow determination of residual stresses in a variety of amorphous or crystalline materials. Residual stresses are present across multi-scales, and suitable measurement tools have to be used for their evaluation. Therefore, the ability to accurately quantify residual stresses by means of measurements is an important engineering task. Residual stresses play a critical role for structural integrity of materials in terms of service performance, strength, fatigue life and dimensional stability. They arise within a structure when a material undergoes virtually any manufacturing process that causes thermal or compositional gradients or that involve plastic deformations. ![]() Often, the half-circle part of the integral will tend towards zero as the radius of the half-circle grows, leaving only the real-axis part of the integral, the one we were originally interested in.Residual stresses exist in many engineering materials and structures. The integral over this curve can then be computed using the residue theorem. In order to evaluate real integrals, the residue theorem is used in the following manner: the integrand is extended to the complex plane and its residues are computed (which is usually easy), and a part of the real axis is extended to a closed curve by attaching a half-circle in the upper or lower half-plane, forming a semicircle. ∫ V ∖ W d ( f d z ) − ∫ W ∖ V d ( f d z ).
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