Research On Stress Concentration Around Planar Holes Or Heterogeneous Inclusions Under Remote Stress And/or Non-Uniform Temperature Loading

The thermoelasticity problem of material with holes and/or heterogeneous inclusions is an important part of the inclusion problem.With in-depth research and wide application of composites,the materials with heat resistance have been paid attention to scholars.Due to the difference of thermal expansion coefficients of materials,the thermal stress caused by the temperature difference results in uneven stress distribution around the hole/heterogeneous inclusion,which may cause stress concentration and induce microcracks.In this paper,based on complex variable function theory and series solution expression,a semi-analytical approach of truncated series is made use to analyze the stress distribution around the hole connecting to the matrix through an interface layer,due to the remote uniform stress and the non-uniform temperature field,as well as the stress distribution around the heterogeneous inclusion due to the remote heat flow and the remote uniform stress(or the non-uniform temperature field inside the inclusion).The main conclusions are listed as follows:(1)The truncated-series solution can satisfy the continuity condition of surface force and displacement on the boundary and/or interface shaped by the hypotrochoids,when the order is large enough.Taking a pentagonal hole as an example,when the shape is the same,the convergence rate of the stress around the boundary of the hard inclusion is faster than that of the soft inclusion.For more complicated shape,more terms are needed to make the stress around the boundary converge.For instance,45 terms are good for the square hole,but 55 terms are needed for the pentagonal hole.(2)In the case of remote uniform stress and/or non-uniform temperature field,the location of the stress maximum/extreme point around the hole/inclusion appears near the corner of the hole/inclusion,which is also the place where the stress concentration most likely occurs.For the stress around the hole boundary,as the ratio of the elastic modulus of the interface layer to the matrix increases and the thickness of the interface layer increases,the maximum stress around the hole boundary gradually decreases.At the same time,the change of Poisson's ratio hasn't much effect on the maximum stress around the boundary of the hole.As for a soft inclusion,as the ratio of the elastic modulus of the inclusion to the matrix increases,the maximum stress around the inclusion interface decreases;and for a hard inclusion,as the elastic modulus of the inclusion and matrix increases as the ratio increases,the maximum stress around the inclusion interface increases.The obtained conclusions provide a certain theoretical reference for researchers who study the stress concentration problem around holes/heterogeneous inclusions,and would be helpful to related studies.