Measurement of residual stresses using fracture mechanics weight functions

A residual stress measurement method has been developed to quantify through-the-thickness residual stresses. Accurate measurement of residual stresses is crucial for many engineering structures. Fabrication processes such as welding and machining generate residual stresses that are difficult to predict. Residual stresses affect the integrity of structures through promoting failures due to brittle fracture, fatigue, stress corrosion cracking, and wear. In this work, the weight function theory of fracture mechanics is used to measure residual stresses. The weight function theory is an important development in computational fracture mechanics. Stress intensity factors for arbitrary stress distribution on the crack faces can be accurately and efficiently computed for predicting crack growth. This paper demonstrates that the weight functions are equally useful in measuring residual stresses. In this method, an artificial crack is created by a thin cut in a structure containing residual stresses. The cut relieves the residual stresses normal to the crack-face and allows the relieved residual stresses to deform the structure. Strain gages placed adjacent to the cut measure the relieved strains corresponding to incrementally increasing depths of the cut. The weight functions of the cracked body relate the measured strains to the residual stresses normal to the cut within the structure. The procedure details, such as numerical integration of the singular functions in applying the weight function method, will be discussed. (author)