Controlling Deformation Errors in the Contour Method for Residual Stress Measurement

Stewart, Beverly (2019). Controlling Deformation Errors in the Contour Method for Residual Stress Measurement. PhD thesis The Open University.


The contour method is being increasingly utilised for characterising residual stresses in engineering components because it has the ability to measure a two-dimensional map of residual stresses on a plane of interest, it is not limited by the size or geometry of the component and is insensitive to microstructural variations. It involves carefully cutting a component into two halves and measuring the resulting deformation on the cut surfaces due to the relaxation of residual stresses. The measured deformation data is used to back calculate a map of the original residual stresses acting normal to the plane of the cut.

Similar to other mechanical strain relief techniques the contour method is based on elastic relaxation of residual stresses and the cutting technique for material removal should not induce residual stress and plastic deformation. However, there is an assumption unique to the contour method and that is the width of the cut must be constant. Usually wire EDM is employed for cutting as it imposes minimal stress on the material. In practice, the stresses near the cut tip can cause a deviation from the cutting requirement, referred to as the bulge error or elastic bulging. These deformation errors can cause significant bias errors in the contour method stress results. The aim of this research is to understand how to control and correct deformation errors that occur during the cutting step of the technique to help to obtain accurate and reliable residual stress measurements made with the contour method.

In the first part of this thesis the iterative FE based (2D) bulge correction procedure first published by Prime and Kastengren is investigated and applied for a compact tension, C(T), cross-weld specimen that appeared to show bulge error in the residual stresses measured by the contour method. The procedure is also extended to perform a more complex 3D bulge correction. A simpler procedure, which calculates directly the stress error due to bulge, has been developed and applied for the case study.

Following this, numerical mode I stress intensity factor (SIF) correlations were developed for a finite plate with a uniform far field tension loading in the plane stress and plane strain condition to improve the understanding of the factors that influence the bulge error. Then a new analytical solution based on the linear elastic fracture mechanics mode I SIF is developed and validated to replace the cumbersome iterative FE procedure to estimate the bulge error. This solution is used to develop a set of stress error correlations for periodic cosine stress functions to predict the magnitude of stress errors due to bulging in contour method measurements. Finally, a set of guidelines are developed to assist practitioners of the contour method to decide on a suitable approach to correct for the bulge error.

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