Influence of the intermediate material on the singular stress field in trimaterial junctions
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INFLUENCE OF THE INTERMEDIATE MATERIAL ON THE SINGULAR STRESS FIELD IN TRIMATERIAL JUNCTIONS A. Carpinteri and M. Paggi
UDC 539.3
By the method of eigenfunctions, we analyze the stresses formed at the vertex of a multicomponent wedge formed by homogeneous elastic wedges under the conditions of plane stress state or plane deformation. The exponent of the singularity of stresses in the case of opening and shift of the wedges is numerically determined. The singular stresses formed near the vertex are investigated both for softer and stiffer wedges.
Introduction According to linear elastic fracture mechanics, stress singularities occur in multimaterial junctions. Problems of this sort were extensively studied for composite plates [1–5]. More recently, the experimental and theoretical studies have emphasized me role of interfaces and grain boundaries in understanding the mechanical properties of polycrystalline materials. In 1996, stress singularities at triple junctions in single-phase polycrystals due to freely sliding grain boundaries were investigated by Picu and Gupta [6]. This study was motivated by the need of modeling the nucleation of cracks and cavities in polycrystalline materials. They found that the exponent of the singular stress field depends only on the grain-boundary positions, i.e., on the amplitudes of the wedge angles formed by the grains at the singular point. Furthermore, supersingularities, i.e., singularities more severe than those due to a crack inside a homogeneous material, were found for some particular junction geometries, indicating critical configurations which can give rise to crack nucleation. In 2001, a theoretical study based on the molecular-dynamics atomistic simulations of the structure and energy conditions for a multiple-twin triple junction in silicon was proposed [7]. By analyzing the calculated excess line and volume energies, as well as the atomic level stress, it was demonstrated that a triple junction can be considered as a true linear defect. It was noticed that these critical points can be a source of residual stresses concentrated at the vertex of the junction. In the present work, the general problem of multimaterial junctions is formulated within the framework of the eigenfunction expansion method [1, 2]. Then the order of the stress singularity arising from trimaterial junctions is carefully analyzed. More specifically, we focus our attention on material junctions between two different polycrystals embedded into a matrix, which represents an intermediate material. Engineering examples may concern material junctions in three-phase polycrystals with an interphase inclusion. On the basis of the proposed method, the order of the stress singularity is determined for different material combinations. According to the criterion of minimum singularity, as also proposed in [8], it is possible to determine the optimum configurations. The influence of initial defects modeled as cracks inside the softer and stiffer materials is also analyzed. Finally, the issue of size-scale eff
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