scholarly journals A Numerical Calculation of Cyclic Stress-Strain Hysteresis Loop and Its Application to Fatigue Problems in Copper.

1991 ◽  
Vol 40 (458) ◽  
pp. 1410-1414
Author(s):  
Kenji HATANAKA ◽  
Yasushi ISHIMOTO
Keyword(s):  
Numerical Calculation ◽  
Hysteresis Loop ◽  
Cyclic Stress ◽  
Stress Strain

Characterization of Hysteresis Loop Evolution in Aged Lead Free Solders

2011 ◽  
Author(s):  
Muhannad Mustafa ◽  
Zijie Cai ◽  
Jeffrey C. Suhling ◽  
Pradeep Lall
Keyword(s):  
Cyclic Loading ◽  
Hysteresis Loop ◽  
Solder Alloy ◽  
Damage Accumulation ◽  
Cyclic Stress ◽  
Lead Free ◽  
Stress Strain ◽  
Effects Of Aging ◽  
Lead Free Solders ◽  
Control Constant

Solder joints in electronic assemblies are typically subjected to thermal cycling, either in actual application or in accelerated life testing used for qualification. Mismatches in the thermal expansion coefficients of the assembly materials leads to the solder joints being subjected to cyclic (positive/negative) mechanical strains and stresses. This cyclic loading leads to thermomechanical fatigue damage that involves damage accumulation, crack initiation, crack propagation, and failure. While the effects of aging on solder constitutive behavior (stress-strain and creep) have been examined in some detail, there have been no prior studies on the effects of aging on solder failure and fatigue behavior. In this investigation, we have examined the effects of aging on the cyclic stress-strain behavior of lead free solders. Uniaxial SAC lead free solder specimens were subjected to cyclic (tension/compression) mechanical loading. Samples were cyclically loaded under both strain control (constant positive and negative strain limits) and stress control (constant positive and negative stress limits). The hysteresis loop size (area) was calculated from the measured cyclic stress-strain curves for a given solder alloy and temperature. This area represents the strain energy density dissipated per cycle, which can be typically correlated to the damage accumulation in the joint. The tests in this investigation were performed with SAC105 solder alloy. Prior to cyclic loading, the specimens in this study were aged (preconditioned) at 125 °C for various aging times (0–6 months). From the recorded cyclic stress-strain curves, we have been able to characterize and empirically model the evolution of the solder hysteresis loops with aging. Similar to solder stress-strain and creep behaviors, there is a strong effect of aging on the hysteresis loop size (and thus the rate of damage accumulation) in the solder specimens. The observed degradations in the fatigue/cyclic behavior of the lead free solders are highly accelerated for lower silver content alloys (e.g., SAC105), and for aging and testing at higher temperatures. In our current work, we are also subjecting aged solder samples to cyclic loading until failure occurs. Our ultimate goal is to understand the effects of aging on the thermomechanical fatigue life.

Description of Closure of Cyclic Stress-Strain Loop and Ratcheting Based on Y-U Model

2016 ◽  
Vol 725 ◽  
pp. 351-356
Author(s):  
Fusahito Yoshida ◽  
Hiroshi Hamasaki ◽  
Takeshi Uemori
Keyword(s):  
Hysteresis Loop ◽  
Kinematic Hardening ◽  
Cyclic Stress ◽  
Cyclic Plasticity ◽  
Plasticity Model ◽  
Stress Strain ◽  
Additional Material ◽  
Material Parameters ◽  
Hardening Law ◽  
Cyclic Plasticity Model

This paper proposes a cyclic plasticity model to describe the closure of a cyclic stress-strain hysteresis loop based on the Y-U model. In this model, the backstress moves in a cyclic memory surface following a newly proposed kinematic hardening law. For this model just the same Y-U parameters can be used, and no additional material parameters are needed. By using a supplementary rule, this model is also able to describe ratcheting.

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