【作者】 黄刘刚；

【导师】 张军；

【作者基本信息】 郑州大学 ， 工程热物理， 2010， 硕士

【摘要】 内聚力模型是弹塑性断裂力学中一个被广泛应用与研究的计算模型。内聚力模型避免了线弹性断裂力学中的裂纹尖端应力奇异性,计算了开裂过程中应力以及断裂能。内聚力模型提出在裂纹尖端存在微小的内聚力区域,该区域内应力为开裂位移值的函数,即为张力位移关系。在对内聚力模型不断研究中,发展出了不同张力位移关系,使其能被广泛应用于各种韧性开裂、复合材料界面脱层以及粘接界面开裂等研究中。指数内聚力模型具有非线性连续的张力位移关系,考虑了开裂过程中各向位移对应力的耦合关系。研究证实,只有在其参数q等于1的条件下,各向应力关系才能完全耦合。本文提出了指数模型单向断裂能计算公式,在各种参数条件下进行计算测试。其结果表明,在复合开裂条件下,当任一向应力首先减小为零时,其对应的单向断裂能亦同时达到其临界的最大值。有限元软件ABAQUS中内聚力单元仅包含双线性内聚力模型,其他类型内聚力模型应用于ABAQUS时需通过子程序编译来实现。本文基于内聚力单元,提出采用自定义材料子程序VUMAT编译内聚力模型。推导了张力位移关系在VUMAT中的应用方法,并分别考虑线性与非线性内聚力模型,设计了内聚力模型VUMAT子程序的程序结构。编译单向开裂条件下指数内聚力模型VUMAT子程序,并与内聚力单元包含的双线性内聚力模型计算结果进行比较,证明其能准确模拟界面单元的承载以及开裂失效过程。在对指数模型耦合关系研究的基础上,采用单向断裂能作为单元失效的判据,编译复合开裂条件下VUMAT子程序。将其应用于复合材料层板脱层模拟,与实验测试值进行比较,结果表明,通过设置合理的模型参数,内聚力模型VUMAT子程序能准确模拟计算裂纹的开裂萌生与扩展过程。本文提出内聚力模型VUMAT子程序方法,能为有限元分析中提供更丰富的内聚力模型,并避免了其他子程序方法中计算收敛问题；通过提出单向断裂能公式,拓展了指数模型在复合开裂模式中应用范围,在此基础上编译其VUMAT子程序,实现了在ABAQUS中应用非线性的指数内聚力模型计算界面开裂过程。感谢国家自然基金对本文研究工作的资助,本文研究课题作为国家自然基金项目各向异性导电胶膜粘接可靠性及界面损伤研究的子课题,编译的指数模型VUMAT子程序以及基于内聚力单元编译内聚力模型的VUMAT子程序方法,将进一步应用到其粘接界面及损伤的界面模型研究中。更多还原

【Abstract】 Cohesive zone model (CZM) is a computational model based on elastic-plastic fracture mechanics. CZM has been extensively researched and used because the stress singularity at crack tip in linear elastic fracture mechanics can be avoided and both the crack interface stress and fracture energy are taken in calculation. A tiny cohesive zone near the crack tip region has been proposed in CZM. The stress in cohesive zone is a function of the crack opening displacement, and this function is usually called traction-separate law (T-S law). As the research and development of CZM, different T-S laws have been proposed, and have been used in ductile cracking and two-phase material interface cracking.The relationship of stress and displacement is a continuous function and coupling of different dimensionality in exponential cohesive zone model. Considering the exponential CZM in two-dimensional plane model, the complete coupling of normal and shear stress can be achieved only when the parameter q equal to 1. The one-dimensional fracture energy formulation has been proposed in this paper. In the mixed cracking mode, the fracture energy calculating by one-dimensional fracture energy formulation reaches its critical maximum value while the stress reduced to zero first in this dimensional.The cohesive element in finite element software ABAQUS has been studied, and the user-define subroutine which can be applied for CZM has also been analyzed. Based on the research, user-defined material subroutine VUMAT combined with cohesive element has been taken to compile the exponential CZM implemented in ABAQUS. The application of T-S law in VUMAT has been derived. By the analysis of damage and fracture of the linear and nonlinear CZM, the program flow of VUMAT for CZM has been designed respectively.The VUMAT of exponential CZM for the pure cracking mode has been complied. The results calculated by VUMAT subroutine of exponential CZM and bilinear CZM contained in cohesive element have been compared. It has confirmed that the crack initiation and evolution can be accurately simulated by VUMAT subroutine. By the analysis of stress coupling and fracture energy, one-dimensional fracture energy has been taken as the failure criterion of cohesive element in the mixed mode. The VUMAT of exponential CZM for mixed mode has been used to simulate the delamination of composite laminates, and has been compared to the experimental test. The result showed that, the VUMAT can accurately simulated crack initiation and propagation process.The VUMAT subroutine of CZM developed in this paper is applicable for various forms of CZM in finite element analysis, and the convergence problem has been solved in the calculation of VUMAT. The application of exponential CZM for mixed mode has been expanded by one-dimensional fracture energy formulation. By the VUMAT subroutine of exponential CZM, Non-linear CZM can be applied to solve the crack opening simulation in ABAQUS. As a part of National Natural Science Foundation projects (the study of the bonding reliability of anisotropic conductive film and the interface damage), the VUMAT subroutine of exponential CZM and compiling method of VUMAT subroutine combined with cohesive element will be applied in further research of interface model for the study of bonding interface and interface damage.更多还原