Yield Function for Solder Elastoviscoplastic Modeling

2004 ◽  
Vol 127 (2) ◽  
pp. 147-156 ◽  
Author(s):  
M. Dube ◽  
T. Kundu
Keyword(s):  
Constitutive Modeling ◽  
Yield Function ◽  
Materials Processing ◽  
Accelerated Tests ◽  
Mechanics Of Materials ◽  
Disturbed State Concept ◽  
Wide Range ◽  
University Of Arizona ◽  
Material Behaviors ◽  
Field Reliability

Field reliability extrapolations from accelerated tests necessitate simulation of a variety of material behaviors under general loading conditions. The Hierarchical Incremental Single Surface (HiSS) yield function (Desai, C. S., 2001, Mechanics of Materials and Interfaces: The Disturbed State Concept, CRC Press, Boca Raton, FL.) has been applied extensively to a wide range of materials, from solders and silicon to ceramics and geotechnical materials, for simulating continuous-yield elastoplastic and elastoviscoplastic behavior. This work presents a continuous-yield function that avoids problems with HiSS for thermal and tensile loading. Validations are presented for eutectic Pb∕Sn data of Wang et al. (Wang, Z., Desai, C.S., and Kundu, T., 2001, “Disturbed State Constitutive Modeling and Testing of Joining Materials in Electronic Packaging,” report to NSF for Materials Processing and Manufacturing Division Grant 9812686, University of Arizona, Tucson, AZ). Limitations on the range of validity of the elastoplastic and the Perzyna elastoviscoplastic formulations are discussed.

Thermomechanical Response of Materials and Interfaces in Electronic Packaging: Part I—Unified Constitutive Model and Calibration

1997 ◽  
Vol 119 (4) ◽  
pp. 294-300 ◽  
Author(s):  
C. S. Desai ◽  
J. Chia ◽  
T. Kundu ◽  
J. L. Prince
Keyword(s):  
Laboratory Test ◽  
Constitutive Modeling ◽  
Electronic Packaging ◽  
Cyclic Fatigue ◽  
Failure Behavior ◽  
Thermomechanical Response ◽  
Disturbed State Concept ◽  
Test Behavior ◽  
New Criterion

The disturbed state concept (DSC) presented here provides a unified and versatile methodology for constitutive modeling of thermomechanical response of materials and interfaces/joints in electronic chip-substrate systems. It allows for inclusion of such important features as elastic, plastic and creep strains, microcracking and degradation, strengthening, and fatigue failure. It provides the flexibility to adopt different hierarchical versions in the range of simple (e.g., elastic) to sophisticated (thermoviscoplastic with microcracking and damage), depending on the user’s specific need. This paper presents the basic theory and procedures for finding parameters in the model based on laboratory test data and their values for typical solder materials. Validation of the models with respect to laboratory test behavior and different criteria for the identification of cyclic fatigue and failure, including a new criterion based on the DSC and design applications, are presented in the compendium paper (Part II, Desai et al., 1997). Based on these results, the DSC shows excellent potential for unified characterization of the stress-strain-strength and failure behavior of engineering materials in electronic packaging problems.

Constitutive Modeling of Multiaxial Deformation and Induced Anisotropy in Superplastic Materials

2000 ◽  
Author(s):  
Marwan K. Khraisheh
Keyword(s):  
Constitutive Modeling ◽  
Continuum Theory ◽  
Yield Function ◽  
Yield Potential ◽  
Induced Anisotropy ◽  
Dynamic Yield ◽  
Fixed End ◽  
Unit Vectors

Abstract The multiaxial deformation of superplastic materials is modeled within a continuum theory of viscoplasticity using a generalized anisotropic dynamic yield function. The anisotropic dynamic yield function is capable of describing the evolution of the initial anisotropic state of the yield potential through the evolution of unit vectors defining the direction of anisotropy. The evolution of the direction of anisotropy is represented by a constitutive spin such that initially it is identical to the Eulerian spin and as deformation continues, it tends towards an orthotropic spin. Experiments on the model Pb-Sn alloy were conducted and used to calibrate and verify the constructed model. It is shown that the model in conjunction with the anisotropic dynamic yield function is capable of predicting the actual trend of the induced axial stresses recorded in fixed-end torsion experiments.

Constitutive modeling of polycarbonate over a wide range of strain rates and temperatures

2016 ◽  
Vol 21 (1) ◽  
pp. 97-117 ◽  
Author(s):  
Haitao Wang ◽  
Huamin Zhou ◽  
Zhigao Huang ◽  
Yun Zhang ◽  
Xiaoxuan Zhao
Keyword(s):  
Constitutive Modeling ◽  
Strain Rates ◽  
Wide Range

Failure and Reliability Analysis Influenced by Various Factors Using Accelerated Disturbed State Concept

2003 ◽  
Author(s):  
Russell D. Whitenack ◽  
Chandra S. Desai
Keyword(s):  
Finite Element ◽  
Reliability Analysis ◽  
Constitutive Modeling ◽  
Electronic Packaging ◽  
Analysis Tool ◽  
Disturbed State Concept ◽  
Powerful Approach ◽  
Finite Element Procedure ◽  
Cycles To Failure

The disturbed state concept (DSC) presented herein represents a unified and powerful approach for constitutive modeling of materials and interfaces in electronic packaging. Together with the computer finite element procedure it provides an analysis tool for calculation of stresses, strains, disturbance and cycles to failure. The accelerated procedure allows economical approximation of cycles to failure and distribution of disturbance at different cycles for design and reliability.

High Strain-Rate Compressive Behavior and Constitutive Modeling of Selected Polymers Using Modified Ramberg-Osgood Equation

2014 ◽  
Vol 566 ◽  
pp. 80-85
Author(s):  
Kenji Nakai ◽  
Takashi Yokoyama
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Compressive Stress ◽  
Constitutive Modeling ◽  
High Strain ◽  
Strain Rates ◽  
Stress Strain ◽  
Strain Behavior ◽  
Least Squares Fit ◽  
Wide Range

The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10-3 to 103/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.

Convective Heat Transfer From a Sphere Due to Acoustic Streaming

1993 ◽  
Vol 115 (2) ◽  
pp. 332-341 ◽  
Author(s):  
A. Gopinath ◽  
A. F. Mills
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Acoustic Streaming ◽  
Reynolds Numbers ◽  
Materials Processing ◽  
Acoustic Levitation ◽  
Simple Experiment ◽  
Wide Range ◽  
Prandtl Numbers

Convective heat transfer from a sphere due to acoustic streaming is examined for large streaming Reynolds numbers. Analytical and numerical solution techniques are used to obtain Nusselt number correlations for a wide range of Prandtl numbers with particular emphasis on the case of Pr~1. A simple experiment performed to confirm some of the predictions is described. The results obtained can be used for the thermal analysis of containerless materials processing in space using acoustic levitation.

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