RESIDUAL STRESS MEASUREMENTS AND PREDICTIONS Test Specimens The material used in this research was a new aluminium alloy 2650 designed to provide creep resistance. Rectangular specimens with a thickness of 6 mm, a central hole of radius 3 mm, a width of 32 mm and a length of 140 mm were machined from the plate. The hole was cold expanded to a nominal expansion of 4 % using the FTI split sleeve method [5]. Specimens subject to creep relaxation were heated to 150°C inside an electric furnace and a load equivalent to a far field stress of 162 MPa was applied. The temperature and applied load were maintained for 1000 hours. To enable measurement of residual stress, discs of diameter 32 mm were cut from the specimens, centred on the hole. Garcia-Sachs Method Sachs’ boring is a method of measuring the residual stresses around a hole by machining material from the hole edge and measuring the resulting strain change. Sachs boring can only measure an axisymmetric state of residual stress, but in this work non-axisymmetric residual stresses occur. The Garcia-Sachs method [6] has been developed, based on Sachs' boring, to measure such nonaxisymmetric residual stress distributions. In this method the residual stresses are represented by a Fourier expansion. The strain change is measured at a number of angular positions and from these changes the magnitude of each component in the Fourier series or residual stress is inferred. Material Properties To predict the residual stresses arising from cold expansion it is important to measure accurately the reversed yielding behaviour of the material [2]. A series of cyclic tension and compression tests were therefore carried, both at room temperature and at 150°C. To evaluate the creep properties of the aluminium alloy 2650, several tests were carried out for different applied constant loads using static load creep test machines. For the range of temperatures and stresses considered in this work, the principal creep mechanism is power law creep. Finite Element Predictions The ABAQUS 5.7 finite element system was used to provide predictions of residual stress. An axisymmetric model was first used to simulate the cold expansion procedure [7] using a combined hardening model to approximate the cyclic stress-strain behaviour. Following the finite element prediction of the residual stress, a further step was used to model the creep relaxation [4]. A three dimensional model had to be used for this step, obtaining the initial residual stresses from the axisymmetric model. Additional load was applied and creep relaxation allowed to occur using a power law model with time hardening integration. Results Garcia-Sachs measurements of residual stress have been made for specimens after cold expansion and after creep relaxation under applied load. These experimental measurements have been compared with finite element predictions of residual stress using the combination of axisymmetric and three dimensional models described above. For conciseness, only results for the tangential residual stress are provided, in the direction normal to the loading direction. Figure 1 presents a comparison of the residual stresses measured by the Garcia-Sachs method and the averaged through-the-thickness stress from finite element analysis. Error bars on the Garcia-Sachs results are based on the calculation of the standard deviation of stress assuming a standard deviation of strain measurement of ±1 µε [4]. Agreement with the finite element prediction is excellent except very close to the hole edge where likely errors in the Garcia-Sachs method increase and differences between the experimental and finite element material behaviours are more important.
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