Analysis Of Integral-M As A Fracture Parameter

Since integral-M was discovered by Knowles and Sternberg who applied Noether's theorem on invariant variational principles in conjunction with the stationary potential energy principle of elastostatics, there have been some studies on computing methods and applications of the integral-M, people pay less attention on it's essential conception and what it stands for physically. In this text, it's path-independence is proved again by selecting a ring-shaped path, and structuring a simply connected domain, which assures that the integral-M could be converted from a curvilinear integral to a surface integral. Furthermore, the relationship between integral-J and integral-M by introducing stress field of the crack tip is derived, which is M=2aJ. We can see the physical implication of M in terms of J.Based on computing software ANSYS, integral-M of several paths of a central crack in a plane are calculated, it's path-independence and connection with J are proved numerically. The results also show that value of M is increasing as the crack length grows; besides, as angle of slope crack increases from 0°to 60°, values of M decrease if the flat is under a simple tension, and increase if the flat is under biaxial tensions.As for crack problems of two-phase isotropy material, the numerical values of M of similarly cases as above are computed. Prospectively, value of M is increasing as the crack length grows; besides, as angle of slope crack increases from 0°to 60°, values of M decrease if the flat is under a simple tension, and increase if the flat is under biaxial tensions. Furthermore, when E₁/E₂, ratio of material elastic modulus of two phases increases, the M decreases, and finally to a steady range.