Modeling cracks and inclusions near surfaces under contact loading
Modeling cracks and inclusions near surfaces under contact loading
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DOI：
10.1016/j.ijmecsci.2014.03.028
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发表时间：
2014-06
影响因子：
7.3
通讯作者：
K. Zhou;Rongbing Wei
中科院分区：
文献类型：
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作者：
K. Zhou;Rongbing Wei
在这项工作中，针对受到接触载荷的半空间表面下方的多个裂纹和任意形状的不均匀夹杂物开发了半解析解决方案。接触表面可以具有粗糙度。该解决方案考虑了所有夹杂物和裂纹之间的相互作用以及它们与表面负载体之间的相互作用。因此，它能够提供表面接触面积和压力以及表面下应力场的准确描述。在开发解决方案时，使用 Eshelby 的等效包含方法将每个非均匀夹杂物建模为具有初始特征应变和未知等效特征应变的均匀夹杂物；混合模式 I 和 II 的每个裂纹都被建模为密度未知的滑移和爬行位错的分布。因此，非齐次半空间接触问题转化为表面接触面积和压力分布未知的齐次半空间接触问题。所有未知数通过数值算法进行积分，然后使用共轭梯度法迭代确定。通过使用快速傅立叶变换算法来实现计算效率。该解决方案通用且稳健，有望广泛应用于异质材料的可靠性分析，特别是磨损和接触疲劳分析。
In this work, a semi-analytic solution is developed for multiple cracks and inhomogeneous inclusions of arbitrary shape beneath a half-space surface subject to contact loading. The contacting surfaces can have roughness. The solution takes into account the interactions among all the inclusions and cracks as well as the interactions between them and the surface loading body. Thus, it is capable of providing an accurate description of the surface contact area and pressure and the subsurface stress field. In developing the solution, each inhomogeneous inclusion is modeled as an homogeneous inclusion with initial eigenstrain plus unknown equivalent eigenstrain using Eshelby’s equivalent inclusion method; each crack of mixed modes I and II is modeled as a distribution of glide and climb dislocations with unknown densities. As a result, the inhomogeneous half-space contact problem is converted into a homogenous half-space contact problem with unknown surface contact area and pressure distribution. All the unknowns are integrated by a numerical algorithm and then determined iteratively by using the conjugate gradient method. Computational efficiency is achieved by using the fast Fourier transform algorithm. The solution is general and robust and will potentially have wide applications for reliability analysis of heterogeneous materials, in particular their wear and contact fatigue analysis.