Adhesive Boundary Element Method Using Virtual Crack Closure Technique

In this study, a new adhesive contact model is built upon a boundary element method (BEM) model developed by Pohrt and Popov (2015). The strain energy release rate (SERR) on the edge of the bonding interface is evaluated using Virtual Crack Closure Technique (VCCT) which is shown to have better accuracy and weaker mesh-size dependency than the closed-form SERR formula derived by Pohrt and Popov. A composite delamination criterion is proposed for crack nucleation and propagation. Numerical results predicted by the present model are in good agreement with the analytical solutions of two classic problems, namely, the axisymmetric parabolic contact and the sinusoidal waviness contact in the plane strain condition. The model of Pohrt and Popov can achieve a similar accuracy for the axisymmetric parabolic contact where the mesh grid is non-conforming to the crack front. Once the conforming mesh grid is used, the accuracy of their model is significantly deteriorated, especially at high work of adhesion and high mesh density. In both BEM models, however, the crack nucleation is found to be mesh-dependent which may be solved by introducing an upper limit for the tensile normal traction.

Crack Deflection Near a Ply Interface in a Composite Laminate

The deflection of a matrix crack near 0°/90° interface in a cross-ply laminate was studied numerically. In the finite element (FE) model, an initial matrix crack was introduced in the 90° layers away from the 0°/90° interface. The initial matrix crack could be initiated either at the middle of 90° layer or at one side of 0°/90° interface. The 0° layers and a part of the initial matrix crack were modeled using homogenized layer properties to simplify the model. The nonuniformly distributed fibers were modeled explicitly close to the 0°/90° interface in order to study the influence of this nonuniformity on the crack deflection process. The Energy Release Rate (ERR) of debond crack tip was calculated using Virtual Crack Closure Technique (VCCT) to study the debond growth. Maximum principal stress was then adopted to access the debond crack kinking qualitatively. It’s found that when a macro-size matrix crack forms and propagate towards ply interface, the subsequent debonding and debond cracking process in nearby intact fiber shows some distinct differences compared to the same processes at single isolated fiber without considering the interaction with nearby debonded fiber and existing matrix crack. Meanwhile, present analysis shows clear influence of microstructures on the crack deflection process by affecting the fiber/matrix debonding and debond kinking processes.

MODELLING OF CRACK DEVELOPMENT PROCESSES IN COMPOSITE ELEMENTS BASED ON VIRTUAL CRACK CLOSURE TECHNIQUE AND COHESIVE ZONE MODEL

Fiber composites based on polymer matrices are promising structural materials that meet high requirements for strength, reliability, durability, and hardness. Therefore, composite materials are widely used as structural materials for aerospace products. The problems associated with the destruction of fiber composites were relevant at all stages of technology development. A variety of reinforcing fibers and polymer binders, as well as reinforcement schemes, allow directional control of strength, stiffness, level of working temperatures and other properties of polymer composite materials. This article discusses a methodology for experimental determination of the mechanical properties of carbon-based fiber-reinforced polymer composite materials, including the determination of the interlayer fracture toughness under loading under separation conditions using the doublecantilever beam method (DCB) and the fracture toughness under transverse shear conditions using the ENF (End-Notched Flexure) method and interlayer strength. The test results of samples of polymer composite materials with a carbon reinforcing filler with different surface densities are presented. The experimental data were used to identify the parameters of the VCCT (Virtual Crack Closure Technique) and CZM (Cohesive Zone Model) closure models used to describe the development of cracks in the composites under consideration. It was found that the parameters determining the strength of layered composites are such characteristics as interlayer strength and crack resistance. It was found that the decrease in the strength of individual layers of the composite does not always affect the current stress state of the entire structure, which is often difficult to detect experimentally, but can significantly affect the further behavior of the object under study provided that the crack develops further.

Quarter-Point Elements Are Unnecessary for the VCCT

The virtual crack closure technique (VCCT) is a well-established method for determining energy release rates and stress intensity factors in homogeneous, isotropic materials. It has been implemented with four-noded, eight-noded, quarter-point, and other higher order elements. It is most convenient and accurate when used with eight-noded, isoparametric elements. VCCT produces less accurate results when used with quarter-point elements. Yet, this method continues to be employed with quarter-point elements. It is strongly recommended to use VCCT with regular eight-noded elements. Three examples will be presented to illustrate the inaccuracy when using quarter-point elements with VCCT.