Explicit formulation of the J_2-integral in anisotropic materials and its application in microcrack shielding problems

The explicit formulation of the J2-integral in anisotropic bodies and its application in microcrack shielding problems are discussed. With analytical treatments and numerical examinations, it is proved that there is a redistribution law for the remote J-integral in a discrete model of microcrack shielding problems, i.e. the projected conservation law of the Jk-vector. In this law, the J2-integral which was disregarded by Herrmann (1981) is proved to be of the same significance as the J1-integral. It is also concluded that the two energy dissipative processes due to the mi crocrack damage, i. e. the reduction in the effective moduli and the release of residual stresses, can be described by using the dissipation of the remote J-integral spreading across the microcrack damage zone.     

Interaction between subinterface cracks and interface in metal/piezoelectric ceramic bimaterials

A class of problems concerning subinterface cracks interacting with the interface in metal/ piezoelectric ceramic bimaterials are studied. The interaction problem is reduced to a system of integral equations with the aid of the pseudo-traction-electric-displacement method. The equations are solved numerically, and the stress intensity factor, the electric displacement intensity factor and the mechanical strain energy release rate are evaluated. Numerical results of a Cu/PZT-4 bimaterial are given and shown in figures, in which three kinds of remote loading conditions are considered to make comparisons . It is found that the electric loading at infinity plays a quite important role in the present interaction problem. In addition, a conservation law of the first component of the Jk-integral vector is found, which does lead to a consistency check to confirm the effectiveness of the PTEDM as well as the numerical results derived in this paper.     

有限中心开裂板的一个混合边值问题

在本文中提出了一个适用于有限中心开裂板的位移和合力模式。这一模式满足:(a)开裂板区域内的平衡和协调条件,(b)裂纹表面自由的条件,(c)环绕裂纹四周的位移单值条件。模式中包含若干待定系数,它们可由开裂板外侧的边界条件定出。已经证明,本模式不仅对于位移或合力边界条件是方便的,并且对于混合边界条件也是方便的。此外,当边值问题求解后,寻求开裂板各点的位移也是很方便的。文中求解了两个混合边值问题,一是方形开裂板的(见图3),二是圆形开裂板的(见图5)。计算得到的数值结果如表1,2和图4,6所示。这些得到的结果可以说明周界上的约束对于裂纹端应力强度因子值的影响。