In this paper, a semi-implicit time integration scheme has been developed for a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. The scheme is developed to provide an efficient numerical procedure of integration and iteration for calculating stress and other associated state variables within a strain-driven format. In particular, a novel Newton-Raphson iteration algorithm for the damage coupled constitutive material model involving von Mises viscoplastic potential function with nonlinear mixed hardening is formulated. An algorithmic tangent stiffness tensor is derived and the model is implemented numerically into a commercial finite element (FE) code ABAQUS through its user-defined material subroutine. Several numerical simulations are conducted for validation of the proposed algorithm.

Issue Section:
Technical Papers
Keywords:
tin, lead, solders, elastic constants, fatigue, viscoplasticity, Newton-Raphson method, numerical analysis, finite element analysis, hardening
Topics:
Algorithms, Computer simulation, Constitutive equations, Damage, Hardening, Shear (Mechanics), Solders, Stress, Viscoplasticity, Finite element analysis, Fatigue, Tensors
1.
Chow
,
C. L.
, and
Wei
,
Y.
,
1999
, “
Constitutive Modeling of Material Damage for Fatigue Failure Prediction
,”
Int. J. Damage Mech.
,
8
, pp.
355
–
374
.
2.
Wei
,
Y.
, and
Chow
,
C. L.
,
2001
, “
A Damage-Coupled TMF Constitutive Model for Solder Alloy
,”
Int. J. Damage Mech.
,
10
(
2
), pp.
133
–
152
.
3.
Basaran
,
C.
, and
Yan
,
C. Y.
,
1998
, “
A Thermodynamic Framework for Damage Mechanics of Solder Joints
,”
ASME J. Electron. Packag.
,
129
, pp.
379
–
384
.
4.
Solomon
,
H. D.
,
1986
, “
Creep, Strain Rate Sensitivity and Low Cycle Fatigue of 60/40 Solder
,”
Brazing and Soldering
,
11
, pp.
68
–
75
.
5.
Busso
,
E. P.
,
Kitano
,
M.
, and
Kumazawa
,
T.
,
1994
, “
Modeling Complex Inelastic Deformation Processes in IC Packages’ Solder Joints
,”
ASME J. Electron. Packag.
,
116
, pp.
6
–
15
.
6.
McDowell, D. L., Miller, M. P., and Brooks, D. C., 1994, “A Unified Creep-Plasticity Theory for Solder Alloys,” Fatigue of Electronic Materials, ASTM STP 1153, pp. 42–59.
7.
Frear
,
D. R.
,
Burchett
,
S. N.
,
Neilsen
,
M. K.
, and
Stephens
,
J. J.
,
1997
, “
Microstructurally Based Finite Element Simulation of Solder Joint Behavior
,”
Soldering & Surface Mount Technology
,
2
, pp.
39
–
42
.
8.
Qian
,
Z.
,
Ren
,
W.
, and
Liu
,
S.
,
1999
, “
A Damage Coupling Framework of Unified Viscoplasticity for the Fatigue of Solder Alloys
,”
ASME J. Electron. Packag.
,
121
, pp.
162
–
168
.
9.
Simo
,
J. C.
, and
Taylor
,
R. L.
,
1986
, “
A Return Mapping Algorithm for Plane Stress Elastoplasticity
,”
Int. J. Numer. Methods Eng.
,
22
, pp.
649
–
670
.
10.
Lof
,
J.
, and
van den Boogaard
,
A. H.
,
2001
, “
Adaptive Return Mapping Algorithms for J2 Elasto-Viscoplastic Flow
,”
Int. J. Numer. Methods Eng.
,
51
, pp.
1283
–
1298
.
11.
Johansson
,
M.
,
Mahnken
,
R.
, and
Runesson
,
K.
,
1999
, “
Efficient Integration Technique for Generalized Viscoplasticity Coupled to Damage
,”
Int. J. Numer. Methods Eng.
,
44
, pp.
1727
–
1747
.
12.
Qian, Z., and Liu, S., 1999, “Implementation of Unified Viscoplasticity with Damage Evolution and Its Application to Electronic Packaging,” EEP-Vol.26-2, Advances in Electronic Packaging, Vol. 2, pp. 2099–2106.
13.
Fu
,
C.
,
McDowell
,
D. L.
, and
Ume
,
I. C.
,
1998
, “
A Finite Element Procedure of a Cyclic Thermoviscoplasticity Model for Solder and Copper Interconnects
,”
ASME J. Electron. Packag.
,
120
, pp.
24
–
34
.
14.
ABAQUS, 2001, ABAQUS/Standard User’s Manual, Hibbitt, Karlsson & Sorenson, Inc., Pawtucket, RI, Version 6.2.
15.
Lush
,
A. M.
,
Weber
,
G.
, and
Anand
,
L.
,
1989
, “
An Implicit Time-Integration Procedure for a Set of Internal Variable Constitutive Equations for Isotropic Elasto-Viscoplasticity
,”
Int. J. Plast.
,
5
, pp.
521
–
549
.
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