Research Articles

Predicted Size of an Inelastic Zone in a Ball-Grid-Array Assembly

[+] Author and Article Information
E. Suhir

University of California,
Santa Cruz, CA 95060;
University of Maryland,
College Park, MD 20742;
Technical University,
1040 Vienna, Austria;
ERS Co.,
727 Alvina Court,
Los Altos, CA 94024
e-mail: suhire@aol.com

B. Levrier

University of Bordeaux,
33405 Talence, France

Manuscript received January 19, 2012; final manuscript received August 20, 2012; accepted manuscript posted August 27, 2012; published online January 22, 2013. Assoc. Editor: Martin Ostoja-Starzewski.

J. Appl. Mech 80(2), 021007 (Jan 22, 2013) (5 pages) Paper No: JAM-12-1023; doi: 10.1115/1.4007476 History: Received January 19, 2012; Revised August 20, 2012; Accepted August 27, 2012

A simple and easy-to-use analytical (“mathematical”) predictive model has been developed for the assessment of the size of an inelastic zone, if any, in a ball-grid-array (BGA) assembly. The BGA material is considered linearly elastic at the strain level below the yield point and ideally plastic above the yield strain. The analysis is carried out under the major assumptions that, as far as the estimated size of an inelastic zone is concerned, (1) the inhomogeneous (“discrete”) BGA structure can be substituted by a homogeneous (continuous) bonding layer of the same thickness (height) and (2) only the longitudinal cross-section of the package-substrate assembly can be considered. The numerical example carried out for a 30 mm long surface-mount package and a 200μm thick lead-free solder indicated that, in the case of a high expansion PCB substrate, about 7.5% of the interface's size experienced inelastic strains, while no such strains could possibly occur in the case of a low expansion ceramic substrate. The suggested model can be used to check if the zone of inelastic strains exists in the design of interest and, if inelastic strains cannot be avoided, how large this zone is, before applying a Coffin-Manson-type of an equation (such as, say, Anand's model in the ANSYS software) with an objective to evaluate the BGA material lifetime.

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Grahic Jump Location
Fig. 1

Bimaterial assembly with a low-yield-stress bonding layer

Grahic Jump Location
Fig. 2

Yield-stress to maximum-elastic-stress ratios versus product of the parameter of the interfacial shearing stress and half-assembly-length for different ratios of the length of the inelastic zone to half-assembly-length



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