An Instantaneous Power of Strain Approach to the Calculation of Elastoplastic Strain Energy Density in SUS 304 Steel

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Cyprian T. Lachowicz ◽  
Dorian S. Lachowicz
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Cyclic Hardening ◽  
Elastoplastic Strain ◽  
Instantaneous Power ◽  
Hardening Effect ◽  
Life Parameter

Presenting a method of identifying and calculating the elastoplastic strain energy density with the instantaneous power of strain, authors of this paper propose using it as a fatigue life/parameter for materials prone to nonproportional cyclic hardening effect.

Critical Accumulated Strain Energy (Case) Failure Criterion for Thermal Cycling Fatigue of Solder Joints

1994 ◽  
Vol 116 (3) ◽  
pp. 163-170 ◽  
Author(s):  
Tsung-Yu Pan
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Thermal Cycling ◽  
Creep Strain ◽  
Failure Criterion ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Solder Joints ◽  
Field Service ◽  
Accumulated Strain

In the automotive and computer industries, a perennial challenge has been to design an adequate and efficient accelerated thermal cycling test which would correspond to field service conditions. Failures, induced in both thermal cycle testing and field service, are characterized by thermal fatigue behavior. Several fatigue models have been proposed, none of these models take into account all of the many parameters of the test or service environment. In thermal cycling, for example, the temperature range, ramp rate, hold time, and stepped heating and cooling are known to influence the number of cycles to failure. In this study, a critical accumulated strain energy (CASE) failure criterion is proposed to correlate the fatigue life to both the plastic and creep strain energies, which accumulate in solder joints during the thermal cycling. This criterion suggests that solder joints fail as the strain energy accumulates and reaches a critical value. By using finite element analysis with a “ladder” procedure, both time-independent plastic strain energy and time-dependent creep strain energy are quantified. These are related to fatigue life by the equation: C = N*f (Ep + 0.13Ec), where C is the critical strain energy density, Nf is the fatigue life, Ep and Ec are plastic and creep strain energy density accumulation per cycle, respectively, for the eutectic Sn-Pb solders. By analyzing Hall and Sherry’s thermal cycling data (Hall and Sherry, 1986), it is found that creep is the predominant factor in deciding fatigue life. Creep accounts for 51 to 97 percent of the total accumulated strain energy, depending on the cycling profiles. This criterion is used to simulate crack propagation in a solder joint by analyzing the strain energy in small “domains” within the joint.

Creep Analysis and Thermal-Fatigue Life Prediction of the Lead-Free Solder Sealing Ring of a Photonic Switch

2002 ◽  
Vol 124 (4) ◽  
pp. 403-410 ◽  
Author(s):  
J. Lau ◽  
Z. Mei ◽  
S. Pang ◽  
C. Amsden ◽  
J. Rayner ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Energy Density ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Constitutive Law ◽  
Isothermal Fatigue ◽  
Thermal Fatigue Life ◽  
Sealing Ring

Thermal reliability of the solder sealing ring of Agilent Technologies’ bubble-actuated photonic cross-connect switches has been investigated in this paper. Emphasis is placed on the determination of the thermal-fatigue life of the solder sealing ring under shipping/storing/handling conditions. The solder ring is assumed to obey the Garofalo-Arrhenius creep constitutive law. The nonlinear responses such as the deflections, stresses, creep strains, and creep strain energy density of the 3-D photonic package have been determined with a commercial finite element code. In addition, isothermal fatigue tests have been performed to obtain the relationship between the number of cycle-to-failure and the strain energy density. Thus, by combining the finite element results and the isothermal fatigue test results, the average thermal-fatigue life of the solder sealing ring is readily determined and is found to be more than adequate for shipping/storing/handling the photonic switches.

A Model to Predict Fatigue Life of Concrete Based on Total Strain Energy Density

2011 ◽  
Vol 99-100 ◽  
pp. 1018-1022
Author(s):  
Li Zhang ◽  
Si Chu Gong ◽  
Xu Dong Ma
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Damage ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Cumulative Damage ◽  
Total Strain ◽  
Total Strain Energy ◽  
Cumulative Fatigue Damage ◽  
Total Strain Energy Density

A law on the cumulative damage is presented basing on total strain energy induced as damage parameter to calculate the cumulative damage when the specimens of concrete subjected to fatigue loading.Then the maximum of critical cumulative damage and location of production are determined basing on the equation of cumulative fatigue damage combined with experimental result through using the finite element analysis and the critical plane method in fatigue analysis.The relation equation between the standardized critical total strain energy density and stress level is obtained by considering the impact of loading level.The fatigue life of specimens can be predicted by combining the equation of cumulative fatigue damage with the relation equation of damage and stress level and the prediction results coincide with experimental results very well.

Fatigue Life Law Based on Inelastic Strain Energy Density of Solder Alloys and its Simple Prediction Method

2020 ◽  
Author(s):  
Tomoya Fumikura ◽  
Mitsuaki Kato ◽  
Takahiro Omori
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Fatigue Test ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Prediction Method ◽  
Strain Range ◽  
Inelastic Strain ◽  
Stress Strain ◽  
Wide Range

Abstract In recent years, a fatigue life law based on inelastic strain energy density as proposed by Morrow has been applied to solder materials. In this study, the effectiveness of the fatigue life law based on inelastic strain energy density was compared with the conventional law based on inelastic strain range. First, the fatigue properties of Sn-Ag-Cu solder alloy were investigated by a torsional fatigue test with strain control. It was found that the stress–strain hysteresis loop arising from inelastic deformation occurred even under a low strain load with a fatigue life of about 1 million cycles. Therefore, as an extension of the low-cycle fatigue test, evaluation was performed using inelastic strain range and inelastic strain energy density. Experimental results show that when fatigue life was evaluated using inelastic strain energy density, a single power law was found over a wide range from the low-cycle region to the high-cycle region, and the validity of the fatigue life law based on inelastic strain energy density was confirmed. Next, a simple prediction method for the fatigue life law based on inelastic strain energy density was examined, taking the physical background into account. Two material constants of the fatigue life law based on the inelastic strain energy density were estimated from the stress–strain curve for a monotonic load and shown to be close to the actual fatigue test results.

Application of Optimal Design on Twin Die Stacked Package by Reliability Indicator of Average SED Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 135-142 ◽  
Author(s):  
R.-S. Chen ◽  
C.-H. Huang ◽  
Y.-Z. Xie
Keyword(s):  
Fatigue Life ◽  
Optimal Design ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Solder Ball ◽  
Simulation Analysis ◽  
Pattern Search ◽  
Reliability Indicator ◽  
Solder Balls

ABSTRACTThis paper deals with the optimal design for a twin die stacked package. Firstly, the numerical model is built up in terms of a three-dimensional slice model along the diagonal direction of the package. The material behavior of the solder balls is a consequence of the viscoplastic property which can be described by the Anand's model. Secondly, the Darveaux model is applied to predict the solder ball reliability of the stacked die package under a cyclic temperature loading. Since simulation analysis found an obvious relation is found between the fatigue life of the solder ball and the distribution of the accumulated strain energy density (SED) on the critical solder ball of the package through the simulation analysis, the average value of the strain energy density for all solder balls is adopted as the optimization indicator of reliability. With such a viewpoint, the critical solder ball position can be ignored, and accordingly an efficient analysis can be obtained. Finally, the Box-Behnken regression model is adopted to construct all the experiments. Each experiment analyzes the reliability of the package under varying parameters. Subsequently, the pattern search algorithm is applied to search for optimal factors.Through optimal analysis with the fatigue reliability indicator of an average SED, the fatigue life is found to be 59% lower than that of the original design. The fatigue life had clearly improved and the lowest ball fatigue life is found to be 2.859 times longer than the original one.

scholarly journals Low Cycle Fatigue Life Assessment Based on the Accumulated Plastic Strain Energy Density

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2372
Author(s):  
Yifeng Hu ◽  
Junping Shi ◽  
Xiaoshan Cao ◽  
Jinju Zhi
Keyword(s):  
Fatigue Crack ◽  
Fatigue Life ◽  
Energy Density ◽  
Plastic Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Low Cycle Fatigue ◽  
Cycle Fatigue ◽  
Fatigue Initiation ◽  
Plastic Strain Energy

The accumulated plastic strain energy density at a dangerous point is studied to estimate the low cycle fatigue life that is composed of fatigue initiation life and fatigue crack propagation life. The modified Ramberg–Osgood constitutive relation is applied to characterize the stress–strain relationship of the strain-hardening material. The plastic strain energy density under uni-axial tension and cyclic load are derived, which are used as threshold and reference values, respectively. Then, a framework to assess the lives of fatigue initiation and fatigue crack propagation by accumulated plastic strain energy density is proposed. Finally, this method is applied to two types of aluminum alloy, LC9 and LY12 for low-cycle fatigue, and agreed well with the experiments.

scholarly journals A Fatigue Evaluation Method for Radial Tire Based on Strain Energy Density Gradient

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Chen Liang ◽  
Zhi Gao ◽  
Shengkang Hong ◽  
Guolin Wang ◽  
Bentil Mawunya Kwaku Asafo-Duho ◽  
...  
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Density Gradient ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Evaluation Method ◽  
Optimization Method ◽  
Structure Parameters ◽  
Truck Tires ◽  
Fatigue Evaluation

Vehicle tires are major components that are subjected to fatigue loading and their durability is of economic interest as it is directly related to the safety of property and the life of producers and consumers. Tire durability is also a major issue of energy conservation and environmental protection. This research aims to establish a reasonable fatigue evaluation and optimization method that effectively improves tire fatigue life. In the study, 11.00R20 and 12.00R20 all-steel radial truck tires were the research objects, and the guiding hypothesis for the research was that “the maximum area of ​​the strain energy density gradient modulus corresponds to the initial failure area, its direction corresponds to the crack propagation direction, and also the maximum strain energy value is inversely proportional to the tire fatigue life.” Through finite element analysis and durability test, the strain energy density gradient was determined as tire fatigue evaluation index, and the hypothesis of tire fatigue life prediction was validated. At the same time, the sensitivities of strain energy gradient to the tire structure parameters were calculated. Besides, the relationship between the structure parameters and the fatigue life was as well established in this paper. This study has formulated a tire fatigue evaluation method and proposed an effective optimization method for enhancing tire fatigue life. The results obtained are of high application value in offering guidance for tire structural design and useful for refining the fatigue failure theory of truck radial tires and improving durability.

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