复合材料层间I型裂纹内聚力牵引-分离曲线重构

doi:10.3901/JME.2025.24.109

摘要/Abstract

摘要： 内聚力模型被广泛应用于复合材料分层模拟分析，其关键参数包括层间强度、断裂韧性和牵引-分离曲线的形状。其中前两者对分层扩展行为的影响及相关的重演算法已多有报道，在非线性断裂过程中，牵引-分离曲线的形状对分层模拟结果具有重要的影响，但是针对该特性的测试通常需要采用如数字图像相关技术(Digital image correlation, DIC)等特殊设备，且尚未形成标准化的提取方法。提出一种针对I型裂纹内聚力牵引-分离曲线的重构方法，一方面，采用限元法迭代更新内聚力区域内的裂纹张开量(Crack opening displacement, COD)，结合J积分计算分层扩展的能量释放率；另一方面，采用双悬臂梁(Double cantilever beam, DCB)理论公式计算裂纹前沿的能量释放率，基于Dugdale条件建立了基于能量释放率的平衡关系；最终，采用梯度下降算法实现牵引-分离曲线的重构。该方法只需要采用DCB的力-位移数据作为输入，无需物理测量分层尖端的裂纹张开位移，避免了DIC等特殊设备的使用。针对式指数型、梯形和分段线性形式的牵引-分离曲线，开展了验证性虚拟试验，分析了力-位移数据量、有限元网格尺寸和测试噪声对重构结果的影响，验证了所提出重构方法的有效性和适用性。

关键词: 内聚力模型, 牵引-分离曲线, 双悬臂梁, 纤维增强复合材料, 分层模拟

Abstract: Cohesive model is widely used to simulate delamination in composite materials. The most crucial parameters for the cohesive model are the interfacial strength, fracture toughness and the shape of the traction-separation law. Although the effect of the interfacial strength and fracture toughness were extensively reported, the extraction method for the shape of the traction-separation curve is not fully explored, which has significant effect on the simulation results when non-linear damage mechanisms are involved. The measurement of the traction-separation law requires special-purpose equipment such as digital image correlation (DIC), and there is a lack of testing standard. In this work, a reconstruction method for the mode-I traction-separation curve is proposed. Firstly, a finite element model is built to iteratively update the crack opening displacement (COD), which is then used to calculate the strain energy release rate (SERR) of the cohesive zone using J-integral. Secondly, the analytical solution for the double cantilever beam is used, and a SERR equilibrium is established based on Dugdale’s condition. Finally, a reconstruction algorithm based on gradient descent is proposed to calculate the traction-separation curve. The proposed method only requires the load-displacement data of the DCB test configuration as input without the need to physically measure the COD using DIC. Validations are conducted using virtual experiments to test the effectiveness of the proposed method with exponential, trapezoidal and multi-linear shaped traction-separation laws as target. Parametric studies regarding the load-displacement data size, mesh size of the finite element model and measurement noise are also conducted.

Key words: cohesive model, traction-separation law, double cantilever beam, fiber-reinforced compo-sites, delamination simulation

中图分类号:

TB332
TB121

陶翀骢, 张超, 季宏丽, 裘进浩. 复合材料层间I型裂纹内聚力牵引-分离曲线重构[J]. 机械工程学报, 2025, 61(24): 109-117.

TAO Chongcong, ZHANG Chao, JI Hongli, QIU Jinhao. Reconstruction of the Mode-I Traction-Separation Law of Cohesive Model for Composite Materials[J]. Journal of Mechanical Engineering, 2025, 61(24): 109-117.

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