A Theory of Fatigue: A Physical Approach With Application to Lead-Rich Solder

[+] Author and Article Information
S. Wen, L. M. Keer

Department of Civil Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60201

J. Appl. Mech 69(1), 1-10 (Jun 08, 2001) (10 pages) doi:10.1115/1.1412453 History: Received March 07, 2001; Revised June 08, 2001
Copyright © 2002 by ASME
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(a) Striations on the surface of a 96.5Pb-3.5Sn solder specimen after strain-controlled isothermal fatigue test (adopted from S. Vaynman’s Ph.D. dissertation 7, Fig. 45); (b) microcracked grain after strain controlled thermomechanical fatigue test (adopted from L. Lawson’s Ph.D. dissertation 8, Fig. 17)
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Cyclic peak stresses plot for 96.5Pb-3.5Sn solder
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Microcracks appeared on the surface of a 96.5Pb-3.5Sn solder specimen after about 6800 cycles under strain-controlled fatigue test (25°C, Δε=0.006)
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The originally smooth surface of 96.5Pb-3.5Sn solder specimen now shows an agglomeration of extrusions, intrusions, striations of PSB and microcracks, with the pattern orienting at roughly 45 deg to the loading axis (vertical)
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Schmid factor m for a slip system within a crystal that undergoes uniaxial loading
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The Schmid factor and the critical number of cycles to initiate a microcrack: m-N curve
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Contours of a constant Schmid factor for uniaxial tension based on {111}〈110〉 slip (reproduced with modification from Fig. 2 (21))
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Peak shear stresses change with number of cycles for silver modified PbSn solder with a strain rate of 0.003/sec (data taken from J. Liang et al., Fig. 7(a)(38))
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Peak stresses evolution during fatigue testing and definition of fatigue point
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Fatigue process illustration when stresses are assumed uniform throughout the structure
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(a) Fatigue and inelastic strain under strain-controlled isothermal fatigue test (εmin=0,ramp=2.5 s, partial data from S. Vaynman); (b) fatigue and stresses under strain-controlled isothermal fatigue test (εmin=0,ramp=2.5 s, partial data from S. Vaynman); (c) fatigue and inelastic strain under strain-controlled thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989; (d) fatigue and stresses range under strain-controlled thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989; (e) fatigue and inelastic strain under isothermal and thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989 (temperatures are 15–60°C, 25–80°C, 60°C, 80°C, and 100°C; strain ranges from 0.3–3 percent; strain rate from 1.15×10−5∼3.0×10−3 s−1); (f ) fatigue and true stresses under isothermal and thermomechanical fatigue testing—conducted by L. Lawson during 1987–1989 (temperatures are 15–60°C, 25–80°C, 60°C, 80°C, and 100°C; strain ranges from 0.3–3 percent; strain rate from 1.15×10−5∼3.0×10−3 s−1)



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