Studyon Approximate Solution Of The Interaction Between Crack And Inclusion Coupling Thermal With Mechanical Loads

The mechanical behavior of composite matrials is strongly affected by the interaction between inclusion and matrix, especially when there is a crack embedded in matrix. The crack tip elastic field will be reduced or enhanced significantly on loading, depending on material parameter, geometry of the inclusion and the relative location for the crack and the inclusion. The high concentrative stress between crack tips and buried components may influence the performance and lifetime of composites. Study on the interaction between cracks and reinforcements with the consideration of coupled mechanical and thermal strains is of particular significance.Based on Eshelby equivalent inclusion method, distributed dislocation technology and transformation toughening theory, the interaction of a crack and an inclusion in composites with the coupled mechanical and mismatched thermal strain is studied, and the interaction of a crack and inclusions embedded in an infinite orthotropic medium is also investigated. The main outcomes are summarized as follow:(1) The expression of transformation strains including the mismatched thermal strains due to the different thermal expansion coefficients for the inclusion and the matrix is established.(2)The interaction between a crack and an inclusion in an infinite medium is studied under plane strain condition,and an approximate formula is developed to predict the SIF variation near a crack due to the mismatched thermal expansion strain between the inclusion and the matrix.(3) The interaction between a crack and an inclusion in an infinite medium is studied under plane stress condition, and an approximate formula is developed to predict the SIF variation near a crack due to the mismatched thermal expansion strain between the inclusion and the matrix. The effect of location, geometry of an inclusion, heating up or cooling down and the ratio for the elastic properties of the inclusion and the matrix on the SIF are also considered.(4) An approximate solution for interaction bewteen a crack and an inclusion in finite elastic medium is developed based on Eshelby equivalent inclusion theory, transformation toughening theory and image theory. And the expression of transformation strains including the mismatched thermal strains is also established.(5) According to Eshelby equivalent inclusion theory, Stroh theory and distributed dislocation technique, an approximate formula for predicting the variation of the SIF induced by an inclusion is developed.