基于内聚力行为和扩展有限元的砂/树脂复合材料拉伸失效行为的数值计算

基于砂/树脂断裂与砂树脂界面脱粘失效行为的砂/树脂三维微细观单胞模型被构建，用于研究砂/树脂在拉伸载荷作用下的微观应力特征、树脂粘结桥的损伤破坏模式及微观结构（树脂含量、砂粒粒径、砂粒级配及粘结桥有效横截面积比）对其宏观拉伸强度的影响。该三维微细观单胞模型采用内聚力行为方法刻画粘结砂/树脂界面的失效，采用扩展有限元方法（Extented finite element，XFEM）捕捉树脂基体损伤和裂纹扩展。计算结果表明:所构建的三维微细观单胞模型能够显式刻画砂/树脂微细观结构断裂过程，解释微细观结构断裂机制，能够有效地提供树脂含量、砂粒粒径、砂粒级配、粘结桥有效横截面积比等微细观结构对砂/树脂宏观拉伸强度（S_t）影响的信息，可为砂/树脂优化设计提供理论指导。 

Numerical calculation of tensile failure behavior of sand/resin composite model based on extended finite element and cohesive behavior

A 3D microscopic unit-cell model of sand/resin was built based on the failure of sand/resin matrix fracture and sand/resin interface debonding. This model was employed to study the microscopic stress characteristics in resin sands, the damage of resin-bonded bridge, and the effect of microstructure (resin content, sand, sand particle size distribution, and the effective cross-sectional area ratio bonding bridge) on the tensile strength of sand/resin. A fracture mode based on energy mechanism i.e., cohesive behavior method was used to describe the debonding of sand/resin interface, and the extended finite element method (XFEM) was used to capture the matrix damage and crack propagation. The numerical results show that the proposed model can explicitly depict the microscopic fracture behavior of sand/resin and explain their fracture mechanisms. The valuable information involving the influence of the resin content, sand size, sand size grading, and the effective cross-sectional area ratio on the tensile strength (S_t) under the tensile loading is provided. This work can provide theoretical guidance for the resin sand optimization design.