First Advisor

Sung Yi

Date of Publication

Fall 1-16-2018

Document Type


Degree Name

Master of Science (M.S.) in Mechanical Engineering


Mechanical and Materials Engineering




Viscoplasticity -- Mathematical models, Solder and soldering, Joints (Engineering), Thermal stresses, Strains and stresses



Physical Description

1 online resource (viii, 64 pages)


Embedded active and passive devices has been increasingly used by in order to integrate more functions inside the same or smaller size device and to meet the need for better electrical performance of the component assemblies.

Solder joints have been used in the electronic industry as both structural and electrical interconnections between electronic packages and printed circuit boards (PCB). When solder joints are under thermal cyclic loading, mismatch in coefficients of thermal expansion (CTE) between the printed circuit boards and the solder balls creates thermal strains and stresses on the joints, which may finally result in cracking. Consequently, the mechanical interconnection is lost, leading to electrical failures which in turn causes malfunction of the circuit or whole system.

When a die is embedded into a substrate, Young's modulus of the die is larger than one of the core of the substrate and the CTEs of the die is smaller than those of the substrate. As a result, mismatch in coefficients of thermal expansions (CTE) between the substrate with the embedded device and the solder balls may increase.

In the present study, finite element method (FEM) is employed to find out the stress and strain distribution of ball grid array(BGA) solders under thermal cycling. The ANAND model for viscoplasticity is employed for this purpose.


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