Coupled Hygrothermomechanical Finite Element Reflow Stress Modeling
Coupled hygrothermomechanical finite element reflow modeling resolves moisture diffusion, steam pressure, and thermal expansion to prevent package delamination.
Dundurs Parameters
Elastic Contrast
Dimensionless elastic constants characterize the mismatch in mechanical properties across a bimaterial interface. The dundurs parameters quantify how differences in Young’s modulus and Poisson’s ratio affect the stress distribution near an interface crack. These values are essential for predicting interfacial fracture behavior in layered composites and thin films.
Mathematical Formulation
Two distinct indices, usually denoted as alpha and beta, represent the plane deformation behavior of the joined materials. In terms of the shear moduli and Poisson’s ratios of the two solid phases, the first parameter alpha measures the difference in stiffness, while the second parameter beta describes the mismatch in bulk compressibility. When both materials are identical, both parameters go to zero, which simplifies the interface equations to those of a homogeneous solid.
Physical Influence
Oscillatory stress singularities arise very close to the crack tip due to the beta parameter. This behavior causes contact between the crack surfaces, which complicates the definition of pure fracture modes.
Operational Boundary
Determining these constants requires accurate measurements of the elastic properties of both constituent phases. Standard nanoindentation techniques provide the localized moduli of the film and substrate, which are then used to calculate the parameters. These calculations establish the stress intensity factors for industrial reliability testing.