Analysis Of Crack Propagation Based On The Extended Finite Element Method

The extended finite element method (short for XFEM) is based on the conventional finite element method and then developed to be a new method in solving discontinuous problems. Its’meshing without considering material size and physical state of material surface. There is nothing to comparable its advantage in solving crack tip of high stress area and deformation zone complicated calculation on meshing, in dynamic crack propagation process does not need to update the grid with crack propagation.First of all, this paper using the extended XFEM finite element method for static crack and Ⅰ,Ⅱ mixed mode crack during numerical simulation analysis. With the numerical simulation analysis on static crack stress intensity factors of different algorithm, different initial crack length, different initial crack angle and different grid density. Compared theory and calculated values verify the accuracy of the extended finite element method combined the crack tip stress value Y of σy with the crack tip distance changed. Comparison the results of calculate and theoretical values, the calculation error is in reasonable error range, to verify the reliability of the extended finite element method in calculating the static crack.Secondly, on the basis of static crack, further analysis of dynamic crack propagation calculation:Using the extended finite element method in numerical analysis the dynamic crack propagation process of the finite center cracked plate, the single crack plate with holes, the inclusion of cracked plate, sliding contact and under impact cracked plate.The results shows,1) Finite plate with center crack under simple tension stress, has two directions while crack propagation along the crack line; the center point of crack stress intensity factor and stress intensity factor at crack tip is slightly different, but the error is in allowable range.2) Single straight crack with holes, there is interaction between holes and cracks that lead to greatly reduce the component strength, more easily to failure and the holes with edge crack is more harmful to component than the holes with outboard crack.3) Cracked plate with inclusions under tension stress, hard inclusions shape does not change and the condition is opposite to soft inclusion. Inclusion disorganized the state of symmetrical distribution of stress on crack tip plastic zone. While crack extended to the matrix and inclusions interface, stress mainly concentrated on the interact surface of crack tip and inclusion. If inclusion surface has micropores, the semicropores linked up with crack and fast spread that is greatly harmful to component.4)It is mainly from the aspects of energy on numerical analysis during sliding contact process of crack propagation. As this paper using reduction unit, it’s inevitably to cause pseudo strain energy in calculation process. But the ratio with total internal energy is far less than the manual requirements for 2% error range, meets the calculation requirement.5) This paper simulates the dynamic crack propagation under impact loading, the calculation results show that the rate of crack propagation is proportional to the ball velocity to a certain extent, but has little effect on crack propagation angle.