The fracture mode mixity is an important parameter for characterizing the mixed mode fracture behavior of a material. Both the crack propagation direction in brittle materials and the interlaminar fracture toughness of laminated composites strongly depend on the mode mixity. Therefore, partitioning the energy release rate into its mode I and mode II components is crucial in studying many fracture problems.

A delaminated beam under axial forces and bending moments is a widely seen structure in materials science and in industry. Many researches have been conducted to partition the energy release rate of such structures into its mode I (opening) and mode II (shearing) components. However the assumptions adopted in most of the methods resulted in large errors, especially for struct...[ Read more ]

The fracture mode mixity is an important parameter for characterizing the mixed mode fracture behavior of a material. Both the crack propagation direction in brittle materials and the interlaminar fracture toughness of laminated composites strongly depend on the mode mixity. Therefore, partitioning the energy release rate into its mode I and mode II components is crucial in studying many fracture problems.

A delaminated beam under axial forces and bending moments is a widely seen structure in materials science and in industry. Many researches have been conducted to partition the energy release rate of such structures into its mode I (opening) and mode II (shearing) components. However the assumptions adopted in most of the methods resulted in large errors, especially for structures with uneven beam thicknesses configuration. Therefore, this research aims to develop a simple and accurate mode partition method to calculate the mode I and mode II stress intensity factors. Simple analytical expressions of the stress intensity factors, which can be readily used by inputting the model geometry and the external loads, are derived based on classical beam theories and the local non-dimensional stress distribution patterns. The physical meaning of the unknown non-dimensional parameters in the expressions, named the distribution factors, are demonstrated, which helps to better understand the relationships between the loadings and the crack tip stress states. In order to further simplify the problem, the external loading configuration is reduced using global methods, and the relationships between the distribution factors are derived. The independent distribution factor under different thickness ratios r is calculated by simulating the singular field at crack tip with FEM, and the tabulated simulation results are fitted by a simple analytical expression with high accuracy. Furthermore, different mode partition methods are compared, and their performances under different conditions are discussed. Results show that the current method has the highest accuracy while retaining the advantage of simplicity.

This study provides both insightful understandings of the mixed mode fracture and useful tool for calculating the stress intensity factors of delaminated beam structures under mixed mode loading. As an accurate and simple method, it is successfully applied to study the horizontal die cracking in microelectronics industry. This method is proven accurate to calculate the characteristic horizontal crack height and the corresponding critical temperature drop. It is also successfully applied to study the influence of the die and leadframe thicknesses on the die cracking risk. Further discussions of the analytical results revealed that instead of the maximum total energy release rate direction, crack propagates in the maximum mode I energy release rate direction, or more generally the minimum barrier energy direction, in brittle materials, which enriched our understanding of the crack path selection criterion of brittle materials.