Elastic Comparison
Nondimensional elastic constants define the mismatch in stiffness and Poisson ratio between two bonded materials in a bimaterial system. These dundurs parameters determine the stress singularity at the edge of an interface, such as where an epoxy encapsulation meets a ceramic substrate or copper lead frame. They reduce the influence of four independent elastic constants down to two values, typically denoted as alpha and beta.
Reliability Prediction
Interface stresses at a corner or crack tip depend heavily on these ratios during thermal cycling. When alpha approaches unity, one material is much stiffer than the other, which often occurs at the junction of silicon die and organic laminate. Engineers use these values to predict delamination risks because a large mismatch concentrates strain at the bond line.
This concentration leads to adhesive failure during reflow or operation. If beta is zero, the stress field remains similar to a homogeneous material, but non-zero beta values introduce an oscillatory singularity that complicates fracture toughness measurements in microelectronics packaging.
Nondimensional Ratio
Calculation involves the shear moduli and Poisson ratios of both constituents. Alpha measures the difference in plane strain bulk moduli. Beta represents the difference in shear moduli modified by the Poisson ratios.
These values stay constant regardless of the geometry of the part.
