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RESEARCH PAPERS

# A Practical Viscoplastic Damage Model for Lead-Free Solder

[+] Author and Article Information
A. F. Fossum1

Sandia National Laboratories, Albuquerque, NM 87185affossu@sandia.gov

P. T. Vianco, M. K. Neilsen

Sandia National Laboratories, Albuquerque, NM 87185

D. M. Pierce

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

Indicial notation is used in this section with “33” denoting the axial direction.

In this section, vectors and tensors will be written in symbolic notation in bold face type and such that the number of “tildes” beneath a symbol equals the tensorial order of the variable. Thus, $s$, $v̰$, and $T̰̰$ would denote a scalar, a vector, and a second-order tensor, respectively.

This form differs from that of previous workers (Neilsen et al. (16); Fossum (1)) in that a factor of $2∕3$ multiplying $B$ is omitted in the present work simply for cosmetics.

Indicial notation is used in this section in which $i$ and $j$ range from 1 to 3; and the summation convention is in effect for repeated indices.

For $−25°C$ only the test conducted at $4.2×10−5s−1$ is reported because of experimental complications.

1

Corresponding author.

J. Electron. Packag 128(1), 71-81 (Aug 19, 2005) (11 pages) doi:10.1115/1.2160514 History: Received January 10, 2005; Revised August 19, 2005

## Abstract

This paper summarizes the results of a program to construct an internal variable viscoplastic damage model to characterize 95.5Sn–3.9Ag–0.6Cu (wt.%) lead-free solder under cyclic thermomechanical loading conditions. A unified model is enhanced to account for a deteriorating microstructure through the use of an isotropic damage evolution equation. Model predictions versus experimental data are given for constant strain-rate tests that were conducted at strain rates of $4.2×10−5s−1$ and $8.3×10−4s−1$ over a temperature range from $−25°Cto160°C$; cyclic shear tests; and elevated-temperature creep tests. A description is given of how this work supports larger ongoing efforts to develop a predictive capability in materials aging and reliability, and solder interconnect reliability.

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## Figures

Figure 17

Behavior of damage parameter αω as a function of temperature

Figure 18

Behavior of damage parameter βω as a function of temperature

Figure 19

Model simulation of a tertiary creep (constant force) test at 160°C in which damage development is important

Figure 20

Model simulation of damage during a creep (constant force) test at 160°C

Figure 21

Model simulation compared with test data for cycles 1 and 2 and cycles 124 and 125 of the double lap shear test conducted at 160°C

Figure 22

Model simulation of stress decay compared with test data for all of the 125cycles of the double lap shear test conducted at 160°C

Figure 1

Specimen and test set up used for constant strain-rate and creep experiments

Figure 2

Double lap shear test samples used in the isothermal fatigue experiments: solder joints on the top, center, and bottom plates

Figure 3

Double lap shear test samples used in the isothermal fatigue experiments: assembly piece parts including the spacers

Figure 4

Representative relative stress sensitivities shown for the slow (4.2×10−5s−1) strain rate test conducted at 160°C

Figure 5

Temperature-dependence of model parameter p determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 16

Model prediction of the stress state used in an experimental creep test at 75°C

Figure 23

Model simulation of the damage evolution during 125cycles of a double-lap cyclic shear test conducted at 160°C

Figure 6

Temperature-dependence of model parameter A1 determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 7

Temperature-dependence of model parameter A2 determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 8

Temperature-dependence of model parameter A3 determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 9

Temperature-dependence of model parameter D0 determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 10

Temperature-dependence of model parameter E determined from constant strain rate tests at −25°C, 25°C, 75°C, 125°C, and 160°C

Figure 11

Model prediction compared with measured stress-strain data for a 4.2×10−5s−1 constant strain-rate test conducted at a temperature of −25°C

Figure 12

Model prediction compared with measured stress-strain data for fast (8.3×10−4s−1) and slow (4.2×10−5s−1) constant strain-rate tests conducted at a temperature of 25°C

Figure 13

Model prediction compared with measured stress-strain data for fast (8.3×10−4s−1) and slow (4.2×10−5s−1) constant strain-rate tests conducted at a temperature of 75°C

Figure 14

Model prediction compared with measured stress-strain data for fast (8.3×10−4s−1) and slow (4.2×10−5s−1) constant strain-rate tests conducted at a temperature of 125°C

Figure 15

Model prediction compared with measured stress-strain data for fast (8.3×10−4s−1) and slow (4.2×10−5s−1) constant strain-rate tests conducted at a temperature of 160°C

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