Analytical Shear Lag Modeling for Strain Transmission into Bottom Terminated Packages
Analytical shear lag models quantify strain transfer from boards to bottom-terminated packages, showing compliant die attach drops offset drift by 98 percent.
Volkersen Model
Shear Distribution
Analytical calculations of shear stress in bonded joints provide the mathematical foundation for evaluating adhesive strength. A classic formula for this analysis is the volkersen model, which determines the distribution of shear stress along the length of a single-lap joint. This calculation shows that the stress is highest at the ends of the joint and lowest in the middle.
The formula acts as a design tool for optimizing bond lines.
Stress Calculation
Mechanical loads applied to bonded materials cause differential strains that generate shear stress in the adhesive. In the volkersen model, these strains are assumed to be elastic, allowing engineers to calculate the peak stress based on joint geometry and material stiffness. It provides a quick method to assess if the adhesive can withstand the applied loads without failing.
This calculation enables designers to adjust the overlap length or adhesive thickness to reduce the peak shear stresses.
Adhesive Choice
Applying this analysis helps engineers select adhesives with appropriate shear moduli. When the volkersen model indicates that stress concentrations are too high, a more compliant adhesive can be used to distribute the load more evenly across the joint. This selection reduces the peak stress and improves the overall reliability of the assembly.
Bond Boundary
The model assumes that there are no normal stresses acting on the joint, which restricts its use to pure shear scenarios. In practice, peeling stresses also occur, which requires more complex models to analyze.