Star Cracks Orthotropic Composite Plate Stress Analysis

The fracture problem of star cracks is rather typical in fracture mechanics , it is frequent in mutiple cracks , which exists widely in various composite materials or casting , and thus threatens engineer practices production development and production development . As a result , it is of practically importance to study star cracks .Conformal mapping method is a effective one than others, the superiority of conformal mapping method can be said as its mapping curve onto simple circular and soving the former problem in return , this method has its own superiority in problems of multiple cracks . The problem of material fracture was studied in literature[1 ] , in the references[1 ] , by using suitable conformal mapping , dealing with 2-D elastic problem about star cracks . The exact solution of SIFs can be obtained for mode I,II problems at the crack tip , the present model can be used to get the tip SIFs of well-known Griffith cracks, the three straight cracks with common point and uniform distribution , the cross crack and the eight symmetry straight cracks . In literature[9 ],by using this method , the fracture problem of orthotropic composite and the solution formula field of stress can be obtained . However , it is rare to see papers deals with problems about orthotropic material with multiple cracks using complex variable and conformal mapping .A method was proposed dealing with the 2-D elastic problem about the orthotropic composite plate with star cracks by using suitable stress function and the technique of material fracture in this paper . The exact solution of stress intensity factors and stress field at the crack tips were obtained for mode I,II problems at the crack tips .Addtionally , in this paper , dealing with the elastic problem about isotropic benting cracks. The analytic solutions of the stress intensity factors at the crack tips were deduced for mode I problems at the crack The periodic welding problem by two different orthotropic semi-planes the analytic functions of the stress distribution is given in closed form . Theory directions derived in this paper can be obtained for engineer design and related studies for fracture theory or optimization design for resitance of fracture engineer structure .