The Ideal Elastic ¢ñ Crack Steady Expansion Of State-of-the-art Field

The asymptotic near-tip solutions of Mode I plane-strain crack growing steadily are studied in three different kinds of materials. When material is uncompressible, a group of four-sectors solutions and a three-sectors solution in which the elastic-unloading region vanishes are given respectively in the condition of supposing some singularity of curvature on the boundary between two regions. The solution obtained by Gao and Rice is just a special case of the four-sectors solutions, and the stresses fields of the three -sectors solutions are the same as Prandtl fields. For the compressible elastic perfectly-plastic medium, following the theory of crack-tip fields which is advanced by Gao and Hwang, it is found that the high order terms of the crack-tip fields are very complex. It remains to seek the appropriate series of asymptotic analyses for obtaining high order terms of asymptotic solution. As a result of research on Rousselier's damage material, all of the basic equations and determinate conditions are given. A scheme properly posed in mathematics for obtaining the solution satisfied all the conditinns is presented.