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Analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams

机译：弯矩复合双悬臂梁混合模脱层过程的解析与数值模拟

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摘要

This work aims at studying the mixed-mode delamination process in Moment-Loaded Double Cantilever Beam (MLDCB) specimens. The delamination problem is addressed both analytically and numerically, while considering the interfaces as an assemblage of two sublaminates partly bonded together by an elastic interface. Such interface is modeled as a continuous distribution of elastic-brittle springs acting along the normal and/or tangential direction depending on the interfacial mixed-mode condition. The Timoshenko's beam theory is here applied to determine the governing equations of the differential problem and the associated boundary conditions, whose solution is not straightforward. The Generalized Differential Quadrature (GDQ) method is then applied as numerical tool to solve directly the differential equations of the problem in a strong form. The capability of the proposed numerical approach is first exploited through a comparative evaluation of the results with the analytical predictions resting on a suitable change of variables for delamination test specimens. The local and global response is determined, in terms of interfacial stresses, internal forces and displacements, as well as in terms of compliance, energy release rate, mode mixity angle, and moment-rotation curves. A further check of the proposed numerical method is performed with respect to a Finite Fracture Mechanics (FFM) criterion, which is able to join both stress-and energy-based approaches. A good agreement between results confirms the good feasibility of the GDQ method when studying delamination phenomena occurring within composite materials or laminated joints, usually subjected to mixed-mode conditions.
机译：这项工作旨在研究矩加载双悬臂梁（MLDCB）标本中的混合模式分层过程。脱层问题在分析和数值上都得到了解决，同时将界面视为由弹性界面部分粘合在一起的两个子层压板的组合。这种界面被建模为根据界面混合模式条件沿法线和/或切线方向作用的弹性脆性弹簧的连续分布。季莫申科的梁理论在这里用于确定微分问题和相关边界条件的控制方程，其求解不是简单的。然后将广义微分正交（GDQ）方法用作数值工具，以强形式直接求解问题的微分方程。首先通过对结果进行比较评估来利用所提出的数值方法的能力，分析预测取决于分层试样的变量的适当变化。局部和全局响应是根据界面应力，内力和位移，以及依从性，能量释放率，模式混合角和力矩旋转曲线确定的。针对有限断裂力学（FFM）准则对提出的数值方法进行了进一步检查，该准则能够加入基于应力和能量的方法。结果之间的良好一致性证实了当研究通常在混合模式条件下的复合材料或叠层接头中发生的分层现象时，GDQ方法的良好可行性。

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