有限尺寸下双材料界面附近裂纹位置对裂纹尖端的影响

随着复合材料的应用和发展,不同材料组成的界面结构越来越受到人们的重视.界面层两侧材料的性能相异会引起材料界面端奇异性,同时界面和界面附近存在裂纹会引起裂尖处的应力奇异性.因此双材料界面附近的力学分析是比较复杂的.论文建立双材料直角界面模型,在材料界面附近预设初始裂纹,计算了有限材料尺寸对界面应力场及其附近裂纹应力强度因子的影响.运用弹性力学中的Goursat公式求得直角界面端在有限尺寸下的应力场以及其应力强度系数.通过叠加原理和格林函数法进一步得到在直角界面端附近的裂纹尖端应力强度因子.计算结果表明,在适当范围内改变材料内裂纹与界面之间的距离,界面附近裂纹尖端的应力强度因子随着裂纹与界面距离的增加而减少,并且逐渐趋于稳定.分析结果可以为预测双材料结构复合材料界面失效位置提供参考.

The Influence of Crack Location on Stress Intensity Factor at Crack Tip Near the Bi-material Interface of Finite Size

With the application and development of composite materials, the interface structure of different materials has been paid more and more attention. The dissimilarity of material properties on two sides of the interfacial layer can cause singularity of the interface. The interface and the cracks around it can lead to stress singularity at crack tips. The mechanical analysis near the bimaterial interface is thus complicated. In this paper, the rectangular interface model of bimaterial was established, and the initial crack was designed near the interface of the material. The influence of finite material size on stress field and stress intensity factor was calculated. The Goursat formula in elasticity was used to obtain the stress field and the stress intensity factor of the rectangular interface of finite size. The stress intensity factor at the crack tip near the rectangular interface was further obtained by the superposition principle and the Green function method. The results show that the stress intensity factor at the crack tip near the interface decreases with the increase of the distance between the crack and the interface, and gradually becomes stable. The results can provide a reference for predicting the failure position of bimaterial interface.