Evaluation of residual stresses and strains using the Eigenstrain Reconstruction Method

Abstract

a b s t r a c tThe study of residual stress has long been an important research field in science and engineering, due to the fact that uncontrolled residual stresses are detrimental to the performance of products. Numerous research contributions have been devoted to the quantification of residual stress states for the purpose of designing engineering components and predicting their lifetime and failure in service. For the purposes of the present study these can be broadly classified into two main approaches, namely, the interpretation of experimental measurements and process modelling. In this paper, a novel approach to residual stress analysis is developed, called here the Eigenstrain Reconstruction Method (ERM). This is a semi-empirical approach that combines experimental characterisation, specifically, residual elastic strain measurement by diffraction, with subsequent analysis and interpretation based on the eigenstrain theory. Three essential components of the ERM, i.e. the residual strain measurement, the solution of the inverse problem of eigenstrain theory, and the Simple Triangle (SIMTRI) method, are described. The ERM allows an approximate reconstruction of the complete residual strain and stress state in the entire engineering component. This is a significant improvement compared to the experimentally obtained limited knowledge of stress components at a selected number of measurement points, or to the simple interpolation between these points.

Residual Stress Evaluation by X-Ray Diffraction and Hole-Drilling in an API 5L X70 Steel Pipe Bent by Hot Induction

“…They have elastic behavior and their influence on the material performance depends on their kind, magnitude and distribution in the crystal lattice 2 . A thermal treatment may be performed to relieve stresses harmful to material performance 3 . The UOE tubes are connected in order to produce a pipeline.…”

Evaluation of Residual Stresses in 12%-Cr Steel Friction Stir Welds by the Eigenstrain Reconstruction Method

“…On the other hand, experimental measurements provide a limited level of detail, due to the finite number of discrete data points which restricts the possibility of reconstructing full-field stress distributions. Accurate residual strain measurement also remains challenging due to the limited availability of suitable accurate techniques, each possessing its own limitations [6] . Accurate residual strain measurement remains challenging due to the limited availability of suitable accurate techniques, each possessing its own limitations [6] .…”

“…Accurate residual strain measurement also remains challenging due to the limited availability of suitable accurate techniques, each possessing its own limitations [6] . Accurate residual strain measurement remains challenging due to the limited availability of suitable accurate techniques, each possessing its own limitations [6] . Moreover, even if the strain state induced by a particular processing operation (e.g.…”

“…shot peening) is measured accurately, it will only apply to the specimens of identical shape, since the distribution of residual stresses within a body is strongly dependent on the geometry. Recently, Jun and Korsunsky [6] have developed a novel approach to residual stress analysis, termed the Eigenstrain Reconstruction Method (ERM). This is a semi-empirical approach that combines experimental characterisation with subsequent analysis and interpretation based on the eigenstrain theory.…”

Numerical Reconstruction of Residual Stress Fields from Limited Measurements

“…inferring the complete stress field from a limited number of measurements, can be carried out by finding distributions of residual stress which are consistent both with existing measurements and with elasticity theory. Generally, stress field reconstruction must be formulated as an inverse problem [6]: basis stress distributions are generated which satisfy equilibrium and boundary conditions, and a linear combination of basis distributions is determined which corresponds closely to the existing measurements. Stress basis functions which satisfy equilibrium and boundary conditions can be generated in a number of ways.…”