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Modeling method for periodic cracks in functionally graded strips with arbitrary properties
Mechanics of Materials ( IF 3.9 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.mechmat.2020.103512
Hao Ge , Licheng Guo , Hongjun Yu

Abstract A piecewise exponential model is developed to investigate the problems of periodic cracks in functionally graded strips with arbitrary material properties. The problem of a row of embedded cracks vertical to strip surfaces under a mode I load in a functionally graded strip with arbitrary nonhomogeneous properties is considered in a plane elasticity state. The true properties of functionally graded materials (FGMs) are approached by a series of sub-layers with material properties varying exponentially and without losing continuity. The thicknesses of different sub-layers can be set to improve calculation accuracy and efficiency. The formulation for doing so is derived using Fourier integral transformation and Fourier series, and the problem is finally reduced to an integral equation with Cauchy-type singularity. Crack-surface displacement derivative is selected as an auxiliary function and is numerically solved to calculate the stress intensity factors (SIFs) at crack tips. The results of previous research are compared with those of the current study to verify the present model. Four representative functions of material properties are considered and the SIFs are presented. The effects of crack spacing, nonhomogeneous properties and crack length on SIFs are discussed. The conclusions are beneficial to the knowledge of fracture behaviors of FGMs.

中文翻译:

任意性质功能梯度带材周期性裂纹的建模方法

摘要 建立了分段指数模型来研究具有任意材料特性的功能梯度条带中的周期性裂纹问题。在具有任意非均质特性的功能梯度带钢中,在模式 I 载荷下垂直于带钢表面的一排嵌入裂纹问题在平面弹性状态下被考虑。功能梯度材料 (FGM) 的真实属性是通过一系列子层来实现的,这些子层的材料属性呈指数变化且不会失去连续性。可以设置不同子层的厚度,以提高计算精度和效率。使用傅里叶积分变换和傅里叶级数推导出这样做的公式,最终将问题简化为具有柯西型奇点的积分方程。选择裂纹表面位移导数作为辅助函数,并通过数值求解来计算裂纹尖端的应力强度因子 (SIF)。将以往研究的结果与当前研究的结果进行比较,以验证当前的模型。考虑了材料特性的四个代表性函数,并介绍了 SIF。讨论了裂纹间距、非均匀特性和裂纹长度对 SIF 的影响。该结论有利于了解FGMs的断裂行为。考虑了材料特性的四个代表性函数,并介绍了 SIF。讨论了裂纹间距、非均匀特性和裂纹长度对 SIF 的影响。该结论有利于了解FGMs的断裂行为。考虑了材料特性的四个代表性函数,并介绍了 SIF。讨论了裂纹间距、非均匀特性和裂纹长度对 SIF 的影响。该结论有利于了解FGMs的断裂行为。
更新日期:2020-09-01
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