The concept of the “effective stiffness” for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson’s ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described.

中文翻译：

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层压板刚度分析中损坏层的有效剪切模量：确定和验证

重新审视了包含层内裂纹的层压板中层的“有效刚度”的概念，为有效刚度与层中裂纹密度的依赖关系提供了相当准确的拟合表达式。在本文中，一定裂纹密度下的有效刚度是根据未损坏和损坏的层压板之间的刚度差异反算出来的。早期对 90 层开裂层压板的有限元方法分析表明，有效纵向模量和层的泊松比在开裂过程中不会改变，而横向模量降低可以通过简单的裂纹密度相关函数来描述。在本文中，重点是剩余的有效常数：面内剪切模量。有限元法参数分析表明，裂纹密度与裂纹密度呈指数关系，拟合函数几乎与周围层的几何和弹性参数无关。上述独立性证明在经典层压板理论的表达式中使用有效层板刚度来预测层内开裂导致具有离轴层板的层压板的刚度降低是合理的。结果与 (a) 有限元方法计算非常吻合；(b) 实验数据，以及 (c) 使用 GLOB-LOC 模型，在准确描述裂纹面张开和滑动位移的情况下，它提供了非常准确的解决方案。上述独立性证明在经典层压板理论的表达式中使用有效层板刚度来预测层内开裂导致具有离轴层板的层压板的刚度降低是合理的。结果与 (a) 有限元方法计算非常吻合；(b) 实验数据，以及 (c) 使用 GLOB-LOC 模型，在准确描述裂纹面张开和滑动位移的情况下，它提供了非常准确的解决方案。上述独立性证明在经典层压板理论的表达式中使用有效层板刚度来预测层内开裂导致具有离轴层板的层压板的刚度降低是合理的。结果与 (a) 有限元方法计算非常吻合；(b) 实验数据，以及 (c) 使用 GLOB-LOC 模型，在准确描述裂纹面张开和滑动位移的情况下，它提供了非常准确的解决方案。