Study On The Crack Tip Field In The Pressure Sensitive Material

The pressure sensitive materials, such as rock, soil, foam metal, polymeric material, rubber and so on, are widely applied in nature. As these materials contain micro-structures (such as micro-voids, defects, inclusions and cracks), the deformation and failure mechanism are complicated under loading. Thus, in-depth study on the deformation and failure mechanism of the pressure sensitive material is an important research subject in solid mechanics at present.Study on crack tip field of the pressure sensitive material is an important subject of fracture mechanics research. Stress, strain and other physical quantities are identified at the crack tip, which provided theoretical evidences for discussing the material parameters on the effect of the crack tip and establishing material damage fracture criterion. Therefore, study on crack tip field in the pressure sensitive material has theoretical significant and broad application prospect.In this paper, we reviewed the research progress of the crack tip field in detail. Since most research is to assume that the material is incompressible, it is a universal significant to study the effect of the volumetric deformation on crack tip field using the constitutive equations of the pressure sensitive material. The main work of this paper is as follows:1. In this paper, the yield criterion for three kinds of two-independent parameters of the pressure sensitive material is discussed in detail. Elliptic equation can be good to maintain continuity of energy from elastic deformation to plastic deformation. Therefore, we established the viscoelastic constitutive equation of the pressure sensitive material and discussed the relationship between Pressure sensitive property coefficient a and Poisson's ratio v using elliptic yield criterion. When Pressure sensitive property coefficient a is equal to 0, materials will be translated into an incompressible viscoelastic material.2. In this paper, the yield criterion is reasonably constructed based on the constitutive equations of the pressure sensitive material using elliptic yield criterion. The basic solution of a crack before growing is deduced under plane stress using self-similar assumption. And mode I, mode II and critical state of a crack before growing problems are studied using these basic solutions. For mode I crack before growing under the condition of plane stress, it is divided into two elastic zones and a fan zone of the "solution with three zones". And for mode II crack, it is divided into two elastic zones, two uniform stress zones and three fan zones "solution with seven zones". Angular variation of stress at the crack tip field is obtained, and the effect of the relevant parameters at the crack tip in a crack before growing is discussed.3. In this paper, the constitutive equations of the pressure sensitive material are deduced under the condition of plane stress. And the analysis of singularity for quasi-static crack tip singularity is obtained, named as?-?-?-1/(n-1). According to the analysis of singularity, the reasonable displacement potential function and stress function are obtained, and the governing equations for quasi-static crack tip of the pressure sensitive material are deduced. The stress field, strain field, displacement field and viscous strain field for quasi-static crack tip of the pressure sensitive material are obtained using the two-parameters shooting method. The effect of pressure sensitive coefficient?and power exponent n at the crack tip is also discussed.4. In this paper, the constitutive equations of the pressure sensitive material are deduced under plane strain. And the analysis of singularity for dynamic growing crack tip singularity is obtained, named as?-?-?-1/(n-1). According to the analysis of singularity, the reasonable displacement potential function and stress function are obtained, and the governing equations for dynamic growing crack tip of the pressure sensitive material are deduced. The stress field, strain field, displacement field and viscous strain field for quasi-static crack tip of the pressure sensitive material are obtained using the two-parameters shooting method. The effect of pressure sensitive coefficient?and power exponent n on the crack tip is also discussed.Study on the crack tip field in the pressure sensitive material is a complex mechanical problem. In this paper, the mechanical model for the crack tip field of the pressure sensitive viscoelastic material is built through theoretical analysis and the corresponding numerical calculation, and the constitution and asymptotic solution of crack tip field are obtained. This study will provide a beneficial exploration for solving the problem that is crack tip asymptotic field, and provide a theoretical reference for solving the corresponding problems encountered in engineering practice and establishing the failure criteria of material.