Asymptotic stress field in a cracked orthotropic strip
Asymptotic stress field in a cracked orthotropic strip
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裂纹正交各向异性条带中的渐近应力场
DOI：
10.1016/0263-8223(95)00075-5
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发表时间：
1995
影响因子：
6.3
通讯作者：
D. Benicchio
中科院分区：
文献类型：
--
作者：
J. Chaoufi;D. Gamby;D. Benicchio
克里斯滕森的粘弹性断裂理论允许用耗散来确定裂纹的扩展速度，耗散的计算需要知道裂纹尖端附近的应力场：导致恒定速度的最简单的配置是一条直线半无限裂纹包含在一条无限长条中，其夹紧边缘垂直于裂纹；虽然关于这个问题已经获得了许多材料的实验数据，但没有可用的解析解。当材料是高度各向异性时，可以尝试一个涉及与剪切模量与较大杨氏模量之比相关的小参数的渐近解。由于相应的扰动问题是奇异的，必须使用一个匹配的渐近展开式：它是内外近似的和；这两种方法都是简单边值问题的解，可以用封闭形式求解。所构造的渐近解与有限元结果一致，即使小参数大到0.2时也是如此。
Christensen's theory of viscoelastic fracture allows the crack propagation velocity to be determined in terms of dissipation whose calculation requires the knowledge of the stress field in the vicinity of the crack tip: the simplest configuration leading to a constant velocity is that of a straight semi-infinite crack contained in an infinitely long strip whose clamped edges are displaced normal to the crack; although experimental data pertaining to this problem have been obtained for a number of materials, no analytical solution is available. When the material is highly anisotropic, an asymptotic solution involving a small parameter related to the ratio of shear modulus to the larger Young's modulus can be attempted. As the corresponding perturbation problem is singular, a matched asymptotic expansion has to be used: it is the sum of outer and inner approximations; both of these are solutions to simple boundary-value problems which can be solved in closed form. The so-constructed asymptotic solution is shown to agree with finite element results, even when the small parameter is as large as 0.2.