Papers by Keyword: Eigenstrain

Abstract: The aviation industry demands thin-walled structures of high dimensional accuracy. Varying radii and individual use-cases, e.g. for repair purpose, require flexible forming techniques. Laser peen forming (LPF) represents such a forming process providing precise energy input by a pulsed laser over a wide energy range. Among adjustable parameters such as laser intensity and focus size, the spot shape, i.e. square and circular, is usually fixed for a specific laser system. As the spot shape is a crucial parameter, this work focuses on the effect of the spot shape on structural deformation after LPF application. Therefore, models for laser peen forming of thin-walled Ti-6Al-4V strips for LPF systems with circular and square focus shapes are set up. Geometric conditions on both focus shapes ensure equal energy input during the laser processing. The numerical simulation relies on the so called eigenstrain method, leading to a cost-efficient calculation of resulting deformation after the dynamic LPF process. Square-based peening pattern exhibit higher deflection. For increasing spot size, the deflection difference between square and circle-based patterns increase slightly.

Abstract: This paper investigates experimentally and numerically the degree to which the stress relaxation in shot-peened simple geometric features of steel turbine materials can be modelled by using an understanding of simple eigenstrain distributions. The residual stress is determined as the elastic response of whole component when the plastic strains caused by shot peening is incorporated as an eigenstrain in an appropriate finite element (FE) model. The application of a subsequent live load is then modelled as an additional load step in the FE model which will superpose the effect of this loading on the residual stress field. The results show that the eigenstrain approach is particularly useful in predicting residual stress relaxation in shot-peened components.

Abstract: By finding stress states which are consistent both with any existing experimental measurements and with elasticity theory, residual stress fields can often be reconstructed from incomplete measurement data. We discuss such methods of residual stress reconstruction, their implementation using finite element analysis, and the measurement strategies which enable them. In general, reconstruction of residual stress fields must be formulated as an inverse problem, which can usually be solved using stress basis functions. However, prior knowledge of the form of the residual stress field and/or underlying eigenstrain distribution often allows the problem to be reduced such that inverse methods become unnecessary, greatly simplifying the analysis. Two examples of when residual stress field reconstruction can be simplified in this way are given.

Abstract: The interfacial stresses of a segmented Cr coating by the hybrid technique of laser pre-quenching steel substrate plus post-deposition have been investigated. The discrete laser quenched zones (LQZs) were modeled as multiple inclusions, each of which is embedded with a prescribed uniform eigenstrain. Based on the failure criterion of the adhesion strength, the interfacial stresses are considered to be responsible for interfacial debonding. The interfacial stresses were evaluated by using the finite element (FE) method. Dimensional analysis was utilized to identify the scaling variables affecting the stresses. The dependence of a range of dimensionless variables of interest on the interfacial stresses has been assessed through a detailed parametric study.

Abstract: Magnetorheological elastomers (MREs) are a class of smart composites whose mechanical properties can be obviously changed under different magnetic field. Only a few works study its magnetostrictive property, which describes the changes in dimensions of a material in its magnetization. Magnetostriction in the ferromagnetic particle is also called eigenstrain in MREs. It is modeled using the nonlinear function of the magnetization in this article. The eigenstrain due to the magnetostriction is incorporated in the structure of the MREs using a generalized Hookes Law. By means of initial strain, a finite element simulation is presented to describe the magnetostriction of MREs. The results show that the magnetostriction along the magnetic field depends on the magnetization and the volume fraction of particles. As an application, we will present numerical simulations for a magnetostriction and compare these results with measured data.

Abstract: Problems of residual stress analysis can be formulated in terms of so-called eigenstrain or inelastic strain. Although the concept is almost 100 year old, the use of it by the residual stress community is quite limited, due to complexities of the associated mathematics. When mathematical difficulties are resolved and eigenstrain is reconstructed, the use of it can be beneficial in several ways. Firstly, the eigenstrain is essentially a generator function for residual elastic stress and elastic strain and it can be used, for generation of any stress field in FE models. Furthermore, eigenstrain distributions are frequently localized, even though the elastic stress or strain distributions are not. Both these properties can be used for effective data reduction. Another advantage of the use of the eigenstrain concept is that experimental data may be interpreted in a more meaningful way by using a narrower context, in terms of plastic deformation, thermal expansion/misfit and deformation caused by phase transformation, rather than just residual stress/strain field. The sample geometry and symmetry play an important role in resolving eigenstrain distributions from residual stress and elastic strain fields. Generally the equations are difficult to solve, however for a sample geometry of high symmetry, eigenstrain can be resolved and expressed as a solution of a relatively simple integral equation; which is the Fredholm of the second type with the kernel of the integral operator defined by the sample geometry/symmetry. Several such symmetries are investigated, yielding analytical solutions that are applied and contrasted to experimental data. An important issue for residual stress analysis is the uniqueness of the solution is also discussed.

Abstract: Residual strains and stresses associated with the processing steps of the industrial high-velocity oxygen-fuel (HVOF) thermal spray technique, was non-destructively characterised in both the coatings and substrates. A range of substrates, having coefficients of thermal expansion different to that of the as-coated WC-Co material, have been considered to assess the potential role of the thermal misfit associated with the coating procedure. Surface and depth resolved studies of the in-plane and normal components of residual strains have been investigated by exploiting the penetrating capabilities of high energy synchrotron X-rays in conjunction with micron sized gauge volumes to enable strain gradient determination with high positional resolution. Results reveal the presence of large residual strain/stress mismatches at the interface region in all the substrate materials, whereas the strains/stresses in the as-coated material are small, seemingly independent of the substrate material. The different contributions due to the HVOF process are qualitatively assessed in terms of an eigenstrains (plastic deformation) approach.

Abstract: Residual stresses play a fundamental role in mechanical engineering. They can be generated by manufacturing processes or introduced purposely by surface treatment technologies. One of the most recent technologies developed to introduce residual stresses is Laser Shock Peening. Since it is a relatively expensive technology, a fundamental role is played by the Finite Element Analysis approach to predict the final residual stress profile. The FEA approach consists of either direct simulation of the LSP process or the application of the eigenstrain approach. The application of the eigenstrain theory in predicting residual stresses after LSP treatment in curved edges is the subject of this research.

Abstract: The paper is aim to investigate the interaction of a screw dislocation in strained reinforcement with a lip-shaped crack under remote longitudinal shear load using complex variable method of Elasticity. The exact solution of complex function of the matrix and the renforcement layer are obtain in series form; then, the expressions of stress field, image force and stress intensity factor of crack tip can be derived; finally, numerical disccusions are pesented and the results shows that the lip-shaped crack in reinforcement layer has interference effect on the interaction of dislocation and reinforcement layer, and the eigenstrain in x-direction has little effect on image force; however, the eigenstrain in y-direction has great influence on image force.

Abstract: The interaction between a screw dislocation and a reinforced lip-shaped crack embedded in an infinite matrix subjected to a remote longitudinal shear load is investigated in this paper. By combining the sectionally holomorphic function theory, Cauchy singular integral, singularity analysis of complex functions and Riemann boundary problem, the problem is reduced to solve an elementary complex potentials equation. The general expressions of complex function in the matrix and the reinforcement layer are derived explicitly in series form for the case when the screw dislocation is located in the matrix. The image force acting on the screw dislocation and the stress intensity factor are also calculated. Some numerical results are provided to discuss the effects of dislocation position, material parameters, geometric configurations and eigenstrain on the image force.