A damage coupling framework is proposed with a unified viscoplastic constitutive model for the fatigue life prediction of solder alloys, including a consistent and systematic procedure for the determination of material parameters. The model also incorporates the effects of grain size and cyclic hardening/softening. The phenomenological framework of continuum damage mechanics (CDM) is modified to embed intensive researches on the ductile damage fracture by void nucleation, growth, and coalescence, based on a lower bound for the viscoplastic potential of voided materials. The damage coupling with elasticity and viscoplasticity is formulated by irreversible thermodynamic approach. The constitutive model is also extended to large deformation kinematics. The preliminary application of the model to creep damage is presented.

Issue Section:
Technical Papers
Topics:
Alloys, Damage, Fatigue, Solders, Viscoplasticity, Constitutive equations, Creep, Damage mechanics, Deformation, Elasticity, Fatigue life, Fracture (Materials), Grain size, Hardening, Kinematics, Nonequilibrium thermodynamics, Nucleation (Physics)
1.
Becker
R.
, and
Needleman
A.
,
1986
, “
Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
53
, pp.
491
–
499
.
2.
Budiansky, B., Hutchinson, J. W., and Slutsky, S., 1982, “Void Growth and Collapse in Viscous Solids,” Mechanics of Solids, H. G. Hopkins and M. J. Sewell, eds., Pergamon Press, New York, pp. 13–45.
3.
Chaboche
J. L.
,
1989
, “
Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity
,”
Int. J. Plasticity
, Vol.
5
, pp.
247
–
277
.
4.
CINDAS, 1997, SRC Document, Purdue University, West Lafayette, IN.
5.
Cocks
A. C. F.
, and
Ashby
M. F.
,
1980
, “
Intergranular Fracture During Power-Law Creep Under Multiaxial Stresses
,”
Met. Sci.
, Vol.
14
, pp.
395
–
402
.
6.
Cocks
A. C. F.
,
1989
, “
Inelastic Deformation of Porous Materials
,”
J. Mech. Phys. Solids
, Vol.
37
, pp.
693
–
715
.
7.
Frear, D. R., Jones, W. B., and Kinsman, K. R., 1990, Solder Mechanics, A State of the Art Assessment, TMS, New Mexico.
8.
Frear, D. R., Burchett, S. N., and Neilsen, M. K., 1997, “Life Prediction Modeling of Solder Interconnects for Electronic Systems,” Advances in Electronic Packaging, ASME EEP-Vol. 19-2, pp. 1515–1522.
9.
Freed
A. D.
, and
Walker
K. P.
,
1993
, “
Viscoplasticity with Creep and Plasticity Bounds
,”
Int. J. Plasticity
, Vol.
9
, pp.
213
–
242
.
10.
Dasgupta
A.
,
Oyan
C.
,
Barker
D.
, and
Pecht
M.
,
1992
, “
Solder Creep-Fatigue Analysis by an Energy-Partitioning Approach
,”
ASME JOURNAL OF ELECTRONIC PACKAGING
, Vol.
114
, pp.
152
–
160
.
11.
Duva
J. M.
, and
Hutchinson
J. W.
,
1984
, “
Constitutive Potentials for Dilutely Voided Nonlinear Materials
,”
Mech. Mat.
, Vol.
3
, pp.
41
–
54
.
12.
Gurson
A. L.
,
1977
, “
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media
,”
ASME Journal of Engineering Materials and Technology
, Vol.
99
, pp.
2
–
15
.
13.
Hill
R.
,
1965
, “
A Self-Consistent Mechanics of Composite Materials
,”
J. Mech. Phys. Solids
, Vol.
13
, pp.
213
–
222
.
14.
Hong
B. Z.
,
Yuan
T. D.
, and
Burrell
L. G.
,
1996
, “
Anisothermal Fatigue Analysis of Solder Joints in a Convective CBGA Package under Power Cycling
,”
Sensing, Modeling and Simulation in Emerging Electronic Packaging
, ASME EEP-Vol.
17
, pp.
39
–
46
.
15.
Knecht
S.
, and
Fox
L. R.
,
1990
, “
Constitutive Relation and Creep-Fatigue Life Model for Eutectic Tin-Lead Solder
,”
IEEE Trans., Comp., Hybrids, Manuf. Tech.
, Vol.
13
, pp.
424
–
433
.
16.
Lau, J. H., 1995, Ball Grid Array Technology, McGraw-Hill, New York.
17.
Lau, J. H., 1991, Solder Joint Reliability—Theory and Applications, Van Nostrand Reinhold, New York.
18.
Leckie
F. A.
, and
Hayhurst
D. R.
,
1977
, “
Constitutive Equations for Creep Rupture
,”
Acta Metall.
, Vol.
25
, pp.
1059
–
1070
.
19.
Lee
S. M.
,
1995
, “
Cavitational Failure Phenomenon in Pb-Sn Eutectic Solders
,”
Jpn. J. Appl. Phys.
, Vol.
34
, pp.
L1475–L1477
L1475–L1477
.
20.
Lemaitre, J., 1996, A Course on Damage Mechanics, Springer, New York.
21.
Liu, S., and Mei, Y., 1994, “Effects of Voids and Cracks on SMT Solder Joint by a Nonlinear and Time Dependent Finite Element under Thermal Cycling,” J. of Soldering & Surface Mount Technology, Oct., pp. 21–28.
22.
Lowe
T. C.
, and
Miller
A. K.
,
1986
, “
Modeling Internal Stresses in the Nonelastic Deformation of Metals
,”
ASME Journal of Engineering Materials and Technology
, Vol.
108
, pp.
365
–
373
.
23.
McClintock
F. A.
,
1968
, “
A Criterion for Ductile Fracture by the Growth of Holes
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
35
, pp.
363
–
371
.
24.
Pao
Y. H.
,
Jih
E.
,
Siddapureddy
V.
,
Song
X.
,
Liu
R.
,
McMillan
R.
, and
Hu
J. M.
,
1996
, “
A Thermal Fatigue Model for Surface Mount Leadless Chip Resistor (LCR) Solder Joints
,”
Sensing, Modeling and Simulation in Emerging Electronic Packaging
, ASME EEP-Vol.
17
, pp.
1
–
12
.
25.
Ponte Castaneda
P.
, and
Willis
J. R.
,
1988
, “
On the Overall Properties of Nonlinearly Viscous Composites
,”
Proc. R. Soc. Lond
,
A416
, pp.
217
–
244
.
26.
Qian, Z., and Fan, J., 1991, “Constitutive Model for Creep-Plasticity Interaction Based on Continuous Kinetics of Dislocations,” High Temperature Constitutive Modeling—Theory and Application, A. D. Freed and K. P. Walker, eds., ASME MD-26/AMD-121, pp. 49–63.
27.
Qian
Z.
,
Duan
Z.
, and
Fan
J.
,
1993
, “
A Constitutive Model for Creep-Plasticity Interaction Based on Dislocation Dynamics
,”
Acta Mechanica Sinica
, Vol.
9
, pp.
261
–
268
.
28.
Qian, Z., and Liu, S., 1997, “A Unified Viscoplastic Constitutive Model for Tin-Lead Solder Joints,” Advances in Electronic Packaging, ASME EEP-Vol. 19-2, pp. 1599–1604.
29.
Rice
J. R.
, and
Tracey
D. M.
,
1969
, “
On the Ductile Enlargement of Voids in Triaxial Stress Fields
,”
J. Mech. Phys. Solids
, Vol.
17
, pp.
201
–
217
.
30.
Rabotnov, Y. N., 1969, Creep Problems in Structural Members, North-Holland, Amsterdam.
31.
Ren, W., Qian, Z., Lu, M., Liu, S., and Shangguan, D., 1997, “Thermal Mechanical Property of Two Solder Alloys,” Applications of Experimental Mechanics to Electronic Packaging, ASME EEP-Vol. 22/AMD-Vol. 226, pp. 125–130.
32.
Solomon, H. D., 1991, “Predicting Thermal and Mechanical Fatigue Lives from Isothermal Low Cycle Data,” Solder Joint Reliability—Theory and Applications, J. Lau, ed., Van Nostrand Reinhold, New York, pp. 406–454.
33.
Tvergaard
V.
, and
Needleman
A.
,
1984
, “
Analysis of Cup-Cone Fracture in a Round Tensile Bar
,”
Acta Metall.
, Vol.
32
, pp.
157
–
169
.
34.
Vitek
V.
,
1980
, “
Diffusional Growth of Intergranular Cavities in Uniform Stress Field and Ahead of Crack-Like Stress Concentrator
,”
Met. Sci.
, Vol.
14
, pp.
403
–
407
.
This content is only available via PDF.
Copyright © 1999
 by The American Society of Mechanical Engineers
You do not currently have access to this content.