Thermal Stress Measurement of Solder Joints in BGA Packages: Theoretical and Experimental

2008 ◽  
Author(s):  
H. X. Shang ◽  
J. X. Gao ◽  
P. I. Nicholson
Keyword(s):  
Thermal Stresses ◽  
Solder Joints ◽  
Stress Measurement ◽  
Closed Form Solution ◽  
Dissimilar Materials ◽  
Form Solution ◽  
Bga Packages ◽  
Reliability Characteristics ◽  
Bga Package ◽  
Graded Interlayer

In this study, an analytical model to obtain a closed-form solution for thermomechanical behaviours of BGA (Ball Grid Array) package was derived and experimentally validated. In the theoretical analysis, the BGA package was represented by a three-layer axisymmetrical model: two layers of dissimilar materials jointed by a graded interlayer. Based on the classical bending theory, the thermal stresses induced by temperature changes were calculated accurately. 2-D FE (Finite Element) meshes of BGA packages subjected to high temperature were used to verify the theoretical solutions. Furthermore, two types of BGA samples, each with eutectic (63wt%Sn/37wt%Pb) and Pb-free SAC387 (95.5wt%Sn/3.8wt%Ag/0.7wt%Cu) solder joints respectively, were experimentally investigated by high resolution Moire´ Interferometry (MI). Thermal cycling tests were performed on each package with temperature variation from 25°C to 125°C. It was found that the thermal deformation obtained from moire´ tests matched well with those from analytical solutions and FE analyses. Based on the shear strain values, the reliability characteristics of BGA assemblies were also assessed.

Thermal stresses in a rotating, nonhomogeneous, anisotropic disk of varying thickness and density

1975 ◽  
Vol 10 (3) ◽  
pp. 137-142 ◽  
Author(s):  
G V Gurushankar
Keyword(s):  
Thermal Loading ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Annular Disk ◽  
Varying Thickness ◽  
Principal Axes ◽  
Rotationally Symmetric ◽  
Anisotropic Disk

Closed form solution is obtained for stresses in a rotationally symmetric, nonhomogeneous, anisotropic, annular disk of varying thickness and density, subjected to thermal loading. Analysis is presented for a particular type of anisotropy, namely Polar Orthotropy, in which axes of anisotropy coincide with the principal axes of stresses at each point in the disk. The variations of homogenity, density and thickness are assumed to be hyperbolic. Numerical results in the form of graphs presented show the effect of nonhomogenity, density and degree of orthotropy on the stress distribution in a disk subjected to constant and varying temperature gradients. Homogeneous, varying density anisotropic rotating disk of varying thickness forms a special case of the analysis.

A closed-form solution for thermal stresses of structures using generalized variational principles

2018 ◽  
Vol 41 (6) ◽  
pp. 748-757 ◽  
Author(s):  
Zou-Qing Tan ◽  
Xue-Dong Jiang ◽  
Yun-Song He ◽  
Shu-Hao Ban ◽  
Ren-Qiang Xi ◽  
...  
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
Generalized Variational Principles

Thermal Induced Stresses in Bridge-Wire Initiator Glass-to-Metal Seals

2006 ◽  
Vol 129 (3) ◽  
pp. 300-306 ◽  
Author(s):  
Luke M. Thompson ◽  
Michael R. Maughan ◽  
Karl K. Rink ◽  
Donald M. Blackketter ◽  
Robert R. Stephens
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Manufacturing Processes ◽  
Material Degradation ◽  
Element Analysis ◽  
Parametric Plane ◽  
Lumped Models

Cracks have been observed in the insulating glass of bridge-wire initiators that may allow moisture to penetrate the assembly, potentially leading to the corrosion and degradation of the bridge wire and the pyrotechnic material. Degradation of the pyrotechnic or the bridge wire may result in initiator failure or diminished performance. The goal of this research is to determine if the manufacturing processes could produce thermal stresses great enough to crack the glass. A parametric plane stress closed-form solution was used to determine the effects of changing material properties and dimensions of the initiator, and to determine potential stresses within the initiator from two different manufacturing scenarios. To verify and expand the plane stress closed-form solution, a two-dimensional axisymmetric finite element analysis was performed. To reproduce the two manufacturing scenarios, lumped models and models that included the effects of cooling the initiator were used. Both models showed that if the manufacturing process involves pouring molten glass into the initiator, the potential for cracking exists. Furthermore, if the surface of the initiator cools faster than the center, cracking is more likely.

Thermal Stress Analysis of a Multi-Layered Structure

2011 ◽  
Vol 467-469 ◽  
pp. 275-278
Author(s):  
Shiuh Chuan Her ◽  
Chin Hsien Lin
Keyword(s):  
Analytical Model ◽  
Layered Structure ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
Bernoulli Beam ◽  
Compatibility Conditions ◽  
Strain Compatibility ◽  
Good Agreement

Analytical model based on the Bernoulli beam theory and strain compatibility conditions at the interfaces between the two layers have been developed to predict the distribution of thermal stresses within the multi-layered structure due to the mismatch of thermal expansion. The closed-form solution of thermal stresses related to the material properties and geometry were obtained. It is useful to provide a simple and efficient analytical model, so that the stress level in the layers can be accurately estimated. The analytical results are compared with finite element results. Good agreement demonstrates that the proposed approach is able to provide an efficient way for the calculation of the thermal stresses.

A Note on the Determination of the Thermal Stresses in Multi-Metal Beams Subjected to Temperature Variations

1991 ◽  
Vol 113 (4) ◽  
pp. 425-427 ◽  
Author(s):  
A. O. Cifuentes
Keyword(s):  
Linear System ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Technical Note ◽  
Form Solution ◽  
System Of Equations ◽  
Temperature Variations ◽  
Temperature Changes ◽  
Linear System Of Equations

This technical note shows that the determination of the stresses induced in multi-metal beams by temperature changes reduces to solving a linear system of equations. This system of equations has a very particular structure that allows one to obtain a closed form solution easily.

Thermomechanical Stress Analysis of Multi-Layered Electronic Packaging

2003 ◽  
Vol 125 (1) ◽  
pp. 134-138 ◽  
Author(s):  
Yujun Wen ◽  
Cemal Basaran
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Orthotropic Material ◽  
Thermal Stresses ◽  
Order Approximation ◽  
Closed Form Solution ◽  
Accurate Estimate ◽  
Form Solution ◽  
Element Analysis ◽  
Thermomechanical Stress

An accurate estimate of thermal stresses in multilayered microelectronics structures along the bonded interfaces is crucial for design and prediction of delamination-related failures. Compared with a numerical method, analytical closed-form solution can offer a more rapid method to obtain the stresses at the interfaces. An analytical model for ply-level sub-laminate analysis is investigated in this paper. The theory presented treats each layer as a beam-type plate with orthotropic material properties. As an example, the results are shown for a three-layer beam problem with special orthotropic material properties. Analytical model results are compared with the finite element analysis results, as a first order approximation.

A Note on Suhir’s Solution of Thermal Stresses for a Die-Substrate Assembly

2004 ◽  
Vol 126 (1) ◽  
pp. 115-119 ◽  
Author(s):  
M. Y. Tsai ◽  
C. H. Hsu ◽  
C. N. Han
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Good Prediction ◽  
Die Attach ◽  
Warpage Deformation

The well-known, closed-form solution to thermal stresses of a die-substrate assembly is initially provided by Suhir in the mid-1980’s after Timoshenko [1] and Chen and Nelson [2]. It has been revised several times in its die attach (adhesive) peel solution by Suhir [3][4], and Mishkevich and Suhir [5]. However, there still exist some controversies and inconsistencies regarding die stresses, die attach shear and peel stresses, and warpage (deformation) of the assembly. In the study, Suhir’s derivation of the solution is closely examined in details, and the corrections to the solution are suggested and verified by comparing with the finite element results. It is shown that, unlike the original Suhir solution, the corrected one gives very good prediction of thermal stresses and deformations of die-substrate assembly. The limitation of the Suhir solution is also discussed in this study.

Thermal Stresses in a Freezing Sphere and its Application to Cryobiology

1998 ◽  
Vol 65 (2) ◽  
pp. 328-333 ◽  
Author(s):  
Y. Rabin ◽  
P. S. Steif
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Form Solution ◽  
Volume Changes ◽  
Perfectly Plastic ◽  
Parametric Studies ◽  
Elastic Perfectly Plastic ◽  
Biological Solutions

Thermal stresses in an inwardly solidifying sphere are studied analytically. A closed-form solution is given which accounts for thermal expansion associated with temperature gradients and volume changes associated with phase transition. Consistent with the target application of cryopreservation of biological solutions and tissues, the material is modeled as elastic-perfectly plastic. Parametric studies using appropriate material properties and typical cryopreservation protocols suggest that strains associated with phase transition lead to far higher stresses than those associated with thermal expansion, with important implications for cryopreservation procedures.

Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

2020 ◽  
Vol 44 (1) ◽  
pp. 20-50
Author(s):  
Surja Deka ◽  
Ashis Mallick ◽  
Pratyush P. Behera ◽  
Prakash Thamburaja
Keyword(s):  
Closed Form ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Functionally Graded
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