We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stressstrain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice, complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.

Manufacturing processes such as machining, surface treatment, welding, plastic forming, and stretching introduce permanent strains into workpieces and engineering components, leading to the creation of residual stresses. Residual stresses exert a significant influence on the deformation behaviour of components, e.g. inducing distortion during further machining, and also affecting their response to thermal and mechanical loading in service. This has important implications for dimensional stability and durability of components and engineering assemblies. In the present study a combined experimental and modelling analysis of a particular case of residual stresses induced in a nickel superalloy plate by heavy surface machining is presented. The residual elastic strain profile in the plate is determined using high-energy synchrotron diffraction. A variational procedure is then used to evaluate the underlying eigenstrain distribution responsible for the observed residual strain state. The relaxation of this residual strain state during subsequent sectioning of the plate is then considered. This example is used in order to assess the difference in the modelled residual strain and stress state obtained using three-dimensional, plane strain, and plane stress models of the coupon. The implications of these results for residual stress interpretation using eigenstrain procedures are discussed.stresses arising in shot peening will depend on the JSA135

Most engineering components made from wrought metallic alloys undergo complex sequences of manufacturing operations. These processing steps frequently include extrusion, forging, or rolling, followed by machining and heat treatment. Since such components will be subjected to service loading as part of engineering assemblies, their durability must be assessed using suitably reliable life prediction models. The present study is aimed at the investigation of a combination of experimental and modelling techniques that involves microstructural investigation, diffraction measurement of residual elastic strains, and finite element simulation of residual stress distributions.Eigenstrain-based modelling approach to the analysis of processing-induced residual stresses has been previously presented in the two-dimensional approximation, i.e. under the assumption that the equivalent permanent plastic strain field induced by processing is equibiaxial. Several different formulations were considered and compared, including plane stress, plane stress, and three-dimensional models. In the present study a further development of the eigenstrain-based analysis approach that incorporates the experimental data obtained from synchrotron X-ray diffraction measurements of residual elastic strains in two complementary cross-sections of a forged and machined nickel superalloy plate is reported. The microstructure was assessed using electron backscattered diffraction, and near-surface residual stresses evaluated using laboratory X-ray diffraction. It is found that the results of fully three-dimensional formulation differ from two-dimensional approximations particularly in the vicinity of machined surfaces, having potentially significant implications for durability assessment and fatigue life models. entire processing history is rarely available. As an JSA260

Autofrettage is a treatment process that uses plastic deformation to create a state of permanent residual stress within thick-walled tubes by pressurizing them beyond the elastic limit. The present paper presents a novel analytical approach to the interpretation of residual elastic strain measurements within slices extracted from autofrettaged tubes. The central postulate of the approach presented here is that the observed residual stress and residual elastic strains are secondary parameters, in the sense that they arise in response to the introduction of permanent inelastic strains (eigenstrains) by plastic deformation. The problem of determining the underlying distribution of eigenstrains is solved here by means of a variational procedure for optimal matching of the eigenstrain finite element model to the observed residual strains reported in the literature by Venter et al., 2000, J. Strain Anal., 35, p. 459. The eigenstrain distributions are found to be particularly simple, given by one-sided parabolas. The relationship between the measured residual strains within a thin slice to those in a complete tube is discussed.

Machining, surface treatment, plastic forming and stretching, welding, and other manufacturing processes introduce residual stresses and distortion into work pieces and engineering components. These phenomena exert a significant influence on the behaviour of components affecting the response to thermal/mechanical in-service loading, e.g. in terms of crack initiation and propagation under the conditions of creep and fatigue, thus ultimately affecting their durability. In the present study, the inertia friction welding process is considered that is used for butt joining of hollow cylindrical components, such as shafts and drums. An inverse eigenstrain framework is used for the interpretation of neutron diffraction measurements in terms of the underlying eigenstrain distributions. Eigenstrain distributions that describe the nature of permanent inelastic deformation are found by minimizing the sum-ofsquares measure of the disagreement between model prediction and experimental measurements of residual elastic strains. Experimental data obtained from neutron diffraction measurements are used in an inverse solution scheme in order to determine the underlying eigenstrain (strains permanently 'locked in') that give rise to the residual stress state. Once these are found, approximate reconstruction of the complete stress tensor within the entire component becomes straightforward. Eigenstrain distributions are first obtained for reduced size test specimens which have been characterized in detail using neutron diffraction. Subsequently, the eigenstrain distributions are scaled and applied to more complex, full-size real engine components, with scaling factors adjusted to match surface hole drilling measurements.

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Residual stresses in titanium alloy samples that were subjected to shot peening followed by fretting fatigue loading were investigated using a combined experimental and numerical analysis procedure based on the concept of eigenstrain. Fretting fatigue loading was carried out in the pad – on-flat geometry using the Oxford in-line fretting rig. Flat-and-rounded pad shape was used to introduce the contact tractions and internal stress fields typical of the target application in aeroengine design. The specimens were in the shape of bars of 10mm square cross-section shotpeened on all sides. Both the pads and specimens were made from the Ti-6Al-4V alloy. Small remote displacement characteristic of fretting fatigue conditions was applied in the experiments. The residual elastic strains in the middle of the pad-to-sample contact and near the rounded pad edge were measured using synchrotron X-ray diffraction on Station 16.3 at SRS Daresbury. A combination of finite element analysis and the distributed eigenstrain method was used in the simulations. Commercial finite element analysis software, ABAQUS ver 6.41, was used to build the finite element model and to introduce the residual stresses into the model using eigenstrain distributions via a user-defined subroutine. In an unfretted shot peened sample an excellent agreement of residual stress profiles was obtained between the experimental data and model prediction by the variational eigenstrain procedure. In a fretted sample the residual stress change due to fretting was observed, and predicted numerically. A good correlation was found between the FE simulation prediction and the experimental data measured at contact edges.