币形裂纹纤维桥联效应力学分析

本文基于Ｃａｓｔｉｇｌｉａｎｏ＇ｓ定理和界面剪滞模型，得到了含界面相效应的复合材料币形裂纹纤维桥联增韧和裂纹张开位移控制方程。并按照第二类Ｆｒｅｄｈｏｌｍ积分方程的迭代解法给出其数值结果。为便于分析界面相参数对增韧效果等影响，寻求了该控制方程的近似解，对近似解进行了误差估计。在此基础上得到了界面剪切模量、裂纹长度、界面厚度、纤维半径，纤维体积分数以及材料性质等参数对币形裂纹桥联效应的影响。

AN ANALYSIS OF THE BRIDGING EFFECTS ON THE PENNY CRACK IN A FIBER-REINFORCED COMPOSITE

A fracture mechanics analysis of bridge effect on a fiber reinforced composite containing a penny crack is presented. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer are derived from the Castigliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained according to iteration solution of the second Fredholm integral equation. In order to investigate the effect of the various parameters on the toughening of composite. An approximate analytical solution of the equation is provided and its error analysis is performed. A parametric study is therefore conducted of the influence of the crack length, interfacial shear modulus, thickness of interphase,fiber radius,fiber volume fraction and properties of material on composite toughening.