THESIS
2015
1 volume (various pagings) : illustrations ; 30 cm
Abstract
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...[
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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.
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