The Effect Of Elastic And Elastic-Plastic Fracture

The common view of elastic-plastic fracture is that the plastic energy is much larger than elastic energy.And elastic deformation which is related to Poisson's ratio was totally omited in HRR model.Another problem is that the full plastic model ofσz / (σr +σθ) = 0.5 are widely employed in yield zones.This assumpation is also employed in high-order term fields. Andσz /(σr +σθ) = 0.5 is employed to caculate out-of-plane stressσzand effective stressσi in elastic-plastic plane strain problems.The energy density distribution in the frame work of HRR model is obtioned.The analysis indicates that the elastic energy is much larger than plastic energy near the ligament.So elastic deformation can not be omitted in the solutions of elastic-plastic problems.The elastic-plastic Poisson's ratio which represents the ratio of elastic to plastic is employed in this paper.Elastic-plastic Poisson's ratio is employed in plane strain problems. A way to determine out-of-plane stresses for plane strain bi-linear elastic-plastic problems is proposed. The relation between out-of-plane stresses and in-plane stresses is examined in detail.And the expression of out-of-plane stresses is derived. These results indicate that out-of-plane stresses could be expressed directly in terms of in-plane stresses,and the distributions of out-of-plane stresses are nearly straight lines.These results could be employedto obtain analytical solutions of the elastic-plastic plane strain problems. The present results might have practical application in the analyses of stress fields near a hole, crack etc.Aand this is a fundamental issue in elastic-plastic mechanics,and the results might be useful in analysing failure modes of engineering structures.