Study On Asymptotic Crack Tip Field In Pressure Sensitive Material With Holes

Study on asymptotic crack tip field is an important subject of fracture mechanics. In orderto provide theoretical reference for the material failure criterion and the structural reliability, wemust in-depth study the distribution of the crack tip physical quantities (stress, strain, etc.) and itsmechanical essence.Asymptotic analysis of the crack tip field is a complex problem. In order to reduce thecomplexity, we often assume that the material is plastic incompressible in the asymptotic cracktip field. However, a large number of materials called pressure sensitive material (such as rocks,soil, foam metal, polymer, rubber materials, etc.) will produce a large plastic volumetricdegeneration under external loads. These materials contain complex microscopic structures (suchas micro-cracks, inclusions, pores, etc.) which effect the distribution of physical parameters ofthe asymptotic crack tip field under external loads. Therefore, it is a universal significant to studyon asymptotic crack tip field in pressure sensitive material.Based on the study of the history and current situation of the asymptotic crack tip field, thisdissertation researches the asymptotic crack tip field through the damage mechanics, fracturemechanics and elastic-plastic mechanics theory. The main work is summarized as follows:1.From Gurson model, the plastic macroscopic yield surface equation containing themesoscopic parameters and pressure-sensitive parameters are obtained. The effect of themacroscopic yield surface equation with the matrix material parameters and injury parameters(porosity) are discussed. Under the linear hardening conditions, the constitutive equation forpressure-sensitive materials with holes is established.2. Under plane stress condition, with the parabolic yield criterion and orthogonal flow rulethe constitutive equation for pressure sensitive materials is established. The basic structure ofmode I, mode II and the critical state of the asymptotic crack tip field before growing issummarized as follows: For mode I crack, it is divided into two elastic zones and a fan zone ofthe “solution with three zones”. For mode II crack, it is divided into two elastic zones, twouniform stress zones and three fan zones “solution with seven zones”. For the critical state, it isdivided into two uniform stress zones and a fan zone of the “solution with three zones” whenm=0. And it is divided into one uniform stress zones, one elastic zone and a fan zone of the“solution with three zones” when m>0. Angular variation curve of stress for asymptotic cracktip field is obtained. The effect of the pressure sensitive parameters m for asymptotic crack tip field is discussed. The singularity of the strain field is also discussed.3. Under the plane stress conditions, quasi-static propagating crack for thepressure-sensitive materials with holes is studied. According to the analysis of singularity, theplastic zone and elastic zone control equation of the crack tip is deduced for the pressuresensitive material with holes. With the characteristics of the quasi-static propagating crack andboundary conditions, the initial value is calculated. Using the two-parameters shooting method,mode I and mode II asymptotic solutions in crack tip is obtained. Angular variation curve ofstress and velocity for asymptotic crack tip field is obtained. The impact of the crack tip stressfield and velocity field with the different parameters are discussed. The results show that theporosity f take great impact of the asymptotic crack tip field and the pressure sensitivitycoefficient m take greater impact of the mode I than mode on the asymptotic crack tip field.4. Under the plane stress conditions, rigid interface crack propagation for thepressure-sensitive materials with holes is studied. According to the characteristics of theinterface crack and boundary conditions, the initial value is calculated. Using the two-parametersshooting method, mode I and mode II asymptotic solutions in crack tip is obtained. Angularvariation curve of stress and velocity for asymptotic crack tip field is obtained. The impact of thecrack tip stress field and velocity field with the different parameters are discussed. The resultsshow that the porosity f take great impact of the asymptotic crack tip field and the materialconstantsα Gtake greater impact of the mode I than mode on the asymptotic crack tip field.The mechanical analysis of the asymptotic crack tip field is a very complex problem. In thisdissertation, the pressure sensitive materials yield condition and the constitutive model is used.The structure and the control equation of the crack tip deduced and the asymptotic solution isobtained. The angular distribution curve is drawn and the impact of the asymptotic crack tip fieldwith different parameters discussed. This work is useful of the asymptotic crack tip field. It hasimportant significance for the actual project and the failure criterion.