Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
On delamination of bi‐layers composed by orthotropic materials: Exact analytical solutions for some particular cases
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-10-24 , DOI: 10.1002/zamm.202000239 K. B. Ustinov 1 , D. M. Idrisov 2
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-10-24 , DOI: 10.1002/zamm.202000239 K. B. Ustinov 1 , D. M. Idrisov 2
Affiliation
|
Earlier [1, 2, 3], exact analytical solutions were obtained for three configurations of composed bi‐layers with semi‐infinite interface cracks: (i) the bilayer composed of two isotropic layers of equal thicknesses; (ii) an orthotropic layer with the central semi‐infinite crack; (iii) an isotropic layer on isotropic half‐plane of a different material (may be considered as a bilayer, the thickness of one of its layers tending to infinity). In all cases the second Dundur's parameter were supposed to be equal to zero. Here by using a scaling technique all three solutions have been extended to cover wider range of elastic and geometric parameters (elastic constants and thicknesses). In particular, a 2‐D problem of a bilayer composed by dissimilar anisotropic layers partly separated by semi‐infinite crack arbitrary loaded at infinity is considered. The principle axes of elasticity tensor for both layers are supposed to coincide with the geometrical axes. The problem involves 10 constants: four elastic constants for each layer and two thicknesses of the layers. By choosing the proper scales for length and for elastic moduli, the number of dimensionless constants is reduced to 8. By using a scaling technique exact analytical solutions are obtained for two subclasses of the problem with four conditions imposed on the parameters for each case, so that four out of eight parameters remain arbitrary. Similarly a solution is obtained for 2‐D problem of a layer on a half‐plane partly separated by semi‐infinite crack arbitrary loaded at infinity. For all considered cases two modes of stress intensity factors are found in terms of four integral characteristics of the external loads.
中文翻译：
关于正交各向异性材料组成的双层脱层：某些特定情况下的精确分析解决方案
早先的[1,2,3]，对于具有半无限界面裂纹的双层结构的三种构型，获得了精确的解析解：（i）双层结构由两个相等厚度的各向同性层组成；（ii）具有中央半无限裂纹的正交各向异性层；（iii）不同材料的各向同性半平面上的各向同性层（可以视为双层，其中一层的厚度趋于无穷大）。在所有情况下，第二个Dundur参数均假定为零。在这里，通过使用缩放技术，所有三个解决方案已扩展为涵盖更大范围的弹性和几何参数（弹性常数和厚度）。特别是考虑了由各向异性层组成的双层的二维问题，该各向异性层部分地被无限载荷下的任意无限裂纹所分隔。假定两层的弹性张量的主轴与几何轴线一致。该问题涉及10个常数：每一层有四个弹性常数，层有两个厚度。通过为长度和弹性模量选择合适的标度，无量纲常数的数量减少到8。通过使用标度技术，可以为问题的两个子类获得精确的解析解，并在每种情况下对参数施加四个条件，因此八个参数中的四个仍然是任意的。类似地，对于半平面上一层被任意无限加载的半无限裂纹分开的二维问题，也获得了一个解决方案。对于所有考虑的情况，根据外部载荷的四个整体特性，找到了两种模式的应力强度因子。
更新日期：2020-10-24
中文翻译：
关于正交各向异性材料组成的双层脱层：某些特定情况下的精确分析解决方案
早先的[1,2,3]，对于具有半无限界面裂纹的双层结构的三种构型，获得了精确的解析解：（i）双层结构由两个相等厚度的各向同性层组成；（ii）具有中央半无限裂纹的正交各向异性层；（iii）不同材料的各向同性半平面上的各向同性层（可以视为双层，其中一层的厚度趋于无穷大）。在所有情况下，第二个Dundur参数均假定为零。在这里，通过使用缩放技术，所有三个解决方案已扩展为涵盖更大范围的弹性和几何参数（弹性常数和厚度）。特别是考虑了由各向异性层组成的双层的二维问题，该各向异性层部分地被无限载荷下的任意无限裂纹所分隔。假定两层的弹性张量的主轴与几何轴线一致。该问题涉及10个常数：每一层有四个弹性常数，层有两个厚度。通过为长度和弹性模量选择合适的标度，无量纲常数的数量减少到8。通过使用标度技术，可以为问题的两个子类获得精确的解析解，并在每种情况下对参数施加四个条件，因此八个参数中的四个仍然是任意的。类似地，对于半平面上一层被任意无限加载的半无限裂纹分开的二维问题，也获得了一个解决方案。对于所有考虑的情况，根据外部载荷的四个整体特性，找到了两种模式的应力强度因子。
京公网安备 11010802027423号