A Nonlinear Multi-Domain Stress Analysis Method for Surface-Mount Solder Joints

1996 ◽  
Vol 118 (2) ◽  
pp. 72-79 ◽  
Author(s):  
S. Ling ◽  
A. Dasgupta
Keyword(s):  
Solder Joint ◽  
Stress Analysis ◽  
Thermal Loading ◽  
Stress And Strain ◽  
Electronic Packages ◽  
Strain Fields ◽  
Surface Mount ◽  
Elastic Plastic ◽  
Solder Joint Fatigue ◽  
Fatigue Endurance

Solder joint fatigue failures are a potential reliability hazard in surface-mount electronic packages under cyclic thermal loading environment. Proper design and reliability assessment are thus crucial to ensure the fatigue endurance of the electronic packages. Accurate modeling of the stress and strain fields within the solder joint under cyclic thermal loading condition is of extreme importance since ultimately, a reasonable fatigue life estimation depends not only on a appropriate fatigue model, but more fundamentally, on accurately predicted stress and strain fields. Modeling stress and strain fields in solder joint in surface-mount electronic packages have never been an easy task since solder undergoes elastic, plastic and time dependent creep during each loading and unloading cycle. Some of the existing closed-form stress analysis models tend to oversimplify this complicated viscoplastic stress state, thus failing to give a reasonable prediction of the solder joint fatigue endurance. Extensive finite element analyses require prohibitive investment in terms of the analysis time and analyst expertise, especially when full scale elastic, plastic and creep analyses are performed. A generalized multi-domain approach proposed earlier by the authors is further developed in this paper to obtain the stress and strain fields in J-leaded surface-mount solder joint undergoing elastic-plastic deformation, under cyclic thermal environment (Ling et al., 1995). The Rayleigh-Ritz energy method based on a multi-field displacement assumption is used. In a previous paper (Ling et al., 1995), the results for analysis within elastic region had been demonstrated and were proved to be in agreement with finite element analysis. In this paper we further develop the methodology into plastic deformation region. Hysteresis loops for both the global and the local CTE mismatch problem can finally be generated. Results for two-dimensional elastic-plastic analysis are presented in the current paper. Creep deformation can be further modeled with this scheme by using time-stepping incremental techniques, and will be presented in a future paper. The final goal of this research is to predict the stress, strain and energy density distributions in the solder joint with reasonable accuracy. The fatigue assessment of the solder joint can then be performed by combining results from this stress analysis model with an appropriate damage model, for example, the energy-partitioning fatigue model (Dasgupta et al., 1992).

A Nonlinear Multi-Domain Thermomechanical Stress Analysis Method for Surface-Mount Solder Joints—Part II: Viscoplastic Analysis

1997 ◽  
Vol 119 (3) ◽  
pp. 177-182 ◽  
Author(s):  
S. Ling ◽  
A. Dasgupta
Keyword(s):  
Solder Joint ◽  
Potential Energy ◽  
Stress Analysis ◽  
Thermal Loading ◽  
Solder Joints ◽  
Stress And Strain ◽  
Thermomechanical Stress ◽  
Cyclic Thermal Loading ◽  
Surface Mount ◽  
Elastic Plastic

This is part II of a two-part paper presented by the authors for thermomechanical stress analysis of surface mount interconnects. A generalized multi-domain Rayleigh Ritz (MDRR) stress analysis technique has been developed to obtain the stress and strain fields in surface-mount solder joints under cyclic thermal loading conditions. The methodology was first proposed in Part I by the authors and results were presented for elastic-plastic loading (Ling et al., 1996). This paper extends the analysis for viscoplastic material properties. The solder joint domain is discretized selectively into colonies of nested sub-domains at locations where high stress concentrations are expected. Potential energy stored in the solder domain and in the attached lead and Printed Wiring Board (PWB) is calculated based on an assumed displacement field. Minimization of this potential energy provides a unique solution for the displacement field, consequently, stress and strain distribution. The MDRR technique was demonstrated to provide reasonable accuracy for elastic deformation (Ling and Dasgupta, 1995) and for time-independent elastic-plastic deformation (Ling and Dasgupta, 1996) for solder joints under cyclic thermal loading conditions. A piecewise linear incremental loading technique is used to solve the nonlinear elastic-plastic problem. The focus in the current paper is primarily on time-dependent viscoplastic deformation of the solder joints. Full field elastic, plastic, and viscoplastic analyses are performed, and the stress, strain hysteresis loops are obtained. Results are presented for a J-lead solder joint as an illustrative example.

Determination of Strain Rate Depended Stress and Strain Fields in PVD Coatings on Cemented Carbide Inserts during the Repetitive Impact Test

2020 ◽  
Vol 404 ◽  
pp. 45-52
Author(s):  
Antonios Bouzakis ◽  
Georgios Skordaris ◽  
Konstantinos Dionysios Bouzakis ◽  
Mehmet Gökhan Gökcen ◽  
Apostolos Boumpakis ◽  
...  
Keyword(s):  
Strain Rate ◽  
Cemented Carbide ◽  
Stress And Strain ◽  
Strain Fields ◽  
Rate Dependent ◽  
Impact Forces ◽  
Repetitive Impact ◽  
Carbide Inserts ◽  
Fatigue Endurance

Recently, stress, strain, strain-rate dependent curves for cemented carbide have become an established tool for evaluating the mechanical properties. In this paper, related strain-rate dependent data of a K05 insert were employed to define the developed stress and strain fields occurring in the compound coating-substrate at impact forces of various durations. In this way, the occurring maximum strains at various impact loads and times were analytically calculated. These maximum values and related fatigue endurance coating strain-rate dependent limits were consequently used to validate published coating fatigue critical impact forces associated with certain impact times.

Stress Analysis of Surface-Mount Interconnections Due to Vibrational Loading

1997 ◽  
Vol 119 (3) ◽  
pp. 183-188 ◽  
Author(s):  
K. Darbha ◽  
S. Ling ◽  
A. Dasgupta
Keyword(s):  
Finite Element ◽  
Solder Joint ◽  
Stress Analysis ◽  
Solder Joints ◽  
Test Time ◽  
Clear Understanding ◽  
Local Curvature ◽  
Surface Mount ◽  
Quantitative Models ◽  
Vibrational Loading

Recently, accelerated testing of surface mount interconnects under combined temperature and vibration environments has been recognized to be a necessary activity to ensure enhanced test-time compression. Successful use of vibration stresses requires a clear understanding of the correlation between vibrational damage and thermomechanical damage in surface mount solder joints. Hence, fatigue due to vibrational loading is important and accurate quantitative models are required to model effects due to vibrational fatigue. The proposed analysis in this paper contributes towards development of such quantitative models. This paper presents an approximate method to analyze stresses in surface mount solder joints subjected to vibration loading, using a generalized multidomain Rayleigh-Ritz approach (Ling and Dasgupta, 1995). The advantage of this approach is in its computational efficiency, compared to general-purpose finite element methods. Ling developed this approach in the context of thermomechanical stress analysis of solder joints. In this paper, the technique is modified and adapted for analyzing stresses caused by out-of-plane flexural dynamic modes of the printed wiring boards (PWBs). The analysis uses a two-step procedure where the local PWB curvatures are first estimated and the resulting deformations in the solder interconnect are then determined. The input boundary conditions for the first step are the bending moments in the PWB due to random vibrations. The stiffness of the interconnect assembly is then predicted using an energy method and curved-beam analysis. The bending moment and the computed stiffness of the interconnect assembly are then used to predict the local curvature of the PWB under any given surface-mount component by using an eigenfunction technique developed by Suhir (Suhir, 1988). In the second step of the analysis, the local curvature of the PWB is used as a boundary condition to predict the state of deformations, stresses, and strains in the solder joint using a modified version of the multidomain Rayleigh-Ritz approach. The overall method is applied to a specific example (J-lead solder joint) for illustrative purposes, and compared to finite element predictions for validation.

Mechanical Modeling and Characterization of the Curing Process of Underfill Materials

2002 ◽  
Vol 124 (2) ◽  
pp. 97-105 ◽  
Author(s):  
L. J. Ernst ◽  
C. van ’t Hof ◽  
D. G. Yang ◽  
M. S. Kiasat ◽  
G. Q. Zhang ◽  
...  
Keyword(s):  
Operating Conditions ◽  
Stress And Strain ◽  
Electronic Packages ◽  
Curing Process ◽  
Strain Fields ◽  
Starting Point ◽  
Polymer Curing ◽  
The Impact ◽  
Insight Into

Thermo-setting polymers are widely used as underfill materials to improve the reliability of electronic packages. In the design phase, the influence of underfill applications on reliability is often judged through thermal and mechanical simulations, under assumed operating conditions. Because of lacking insight into the mechanical processes due to polymer curing, the impact of processing induced residual stress fields is often neglected. To investigate the evolution of stress and strain fields during the curing process it is important to assume a more appropriate starting point for subsequent process modeling. Furthermore, study of possible damage originating from the fabrication process then comes within reach. To facilitate future analysis of stress and strain fields during the curing process a cure dependent constitutive relation is assumed. An approximate investigation method for the process-dependent mechanical properties, based on Dynamic Mechanic Analysis (DMA), is developed. As an illustration the parameter identification is performed for a selected epoxy resin.

Modeling Solder Joint Fatigue Life for Gullwing Leaded Packages: Part I—Elastic Plastic Stress Model

1995 ◽  
Vol 117 (2) ◽  
pp. 123-129 ◽  
Author(s):  
V. K. Gupta ◽  
D. B. Barker
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Solder Joint ◽  
Life Assessment ◽  
Assessment Process ◽  
Stress Model ◽  
Viscoplastic Material ◽  
Elastic Plastic ◽  
Solder Joint Fatigue ◽  
Plastic Stress

It is a challenge to assess solder joint fatigue life in the modern electronics industry because of complex geometries, complex non-linear viscoplastic material properties, and the frequently changing environmental conditions. The first step in the fatigue life assessment process is to find the stress distribution in the solder. Traditionally, this has been done using numerical tools like finite element methods. The finite element approach requires a highly trained and experienced analyst and huge computing resources, while the accuracy is always questioned. This study aims to develop a more accurate analytical-cum-empirical model to predict critical stresses in the solder joint so as to avoid the necessity of finite element simulation. This paper presents a generic elastic-plastic stress model that is obtained based on theoretical stress analysis solutions that is tweaked by using a design of experiments technique with FEA simulations.

Mechanical Deformation Modeling of Diamond/Gaas Structures

1996 ◽  
Vol 445 ◽  
Author(s):  
Nickolaos Strifas ◽  
Aris Christou
Keyword(s):  
Finite Strain ◽  
Volume Fraction ◽  
Mechanical Deformation ◽  
Interfacial Shear ◽  
Stress And Strain ◽  
Uniform Temperature ◽  
Element Analysis ◽  
Strain Fields ◽  
Elastic Plastic ◽  
Plastic Analysis

AbstractIn this study a finite strain elastic-plastic finite element analysis is performed on diamond/GaAs structures. A series of models based upon the principal of superposition are proposed to investigate the mechanical deformation and thermal stress behavior of the diamond/gas structure due to coefficients of thermal expansions (CTE) mismatches. The interfacial shear and peeling stresses in multilayered stacks subjected to uniform temperature variation are studied. Finite strain elastic – plastic analysis is performed on a crack which lies on the interface between the diamond and gas materials. The ductile fracture from the tip of the interface crack, the stress and strain fields and distribution of microvoid volume fraction are analyzed.

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