Endochronic Fatigue Life Prediction of SN/3.5AG/0.75CU BGA Solder Joints Under Oblique Displacement Cyclic Tests

2011 ◽  
Vol 27 (2) ◽  
pp. 191-200 ◽  
Author(s):  
C. F. Lee ◽  
T. T. Lin ◽  
P. S. Tsai
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Solder Ball ◽  
Inelastic Strain ◽  
Cyclic Tests ◽  
Fatigue Initiation ◽  
Image Position ◽  
Cyclic Damage ◽  
Theory Of Damage ◽  
Relationship Of

ABSTRACTIn this paper, cyclic damage behavior of cyclically load drop curves and their fatigue initiation life of Sn/3.5 Ag/0.75Cu BGA solder joint specimens under oblique displacement cyclic tests were investigated by the theory of damage — coupled endochronic viscoplasticity.By linearly unloading with damage elastic modulus and the linearly damage-free behavior of grip system, the damage loops of force-Φ angle oblique displacement of BGA solder joint specimen were converted successfully into damage loops of the representative solder ball under cyclically proportional straining, which can be predicted by the endochronic constitutive equations. These results established the relationship of the BGA oblique displacement amplitudes da(Φ) and the effective inelastic strain amplitudes of solder ball: da (Φ)= . Based on the phenomena of cyclic damage and its fatigue life, a Φ dependent degree of damage in the evolution equation of damage under proportional strain path was proposed to depend positively on and N cycles. Using this parameter in the damage per cycle computed by the endochronic theory, a Φ modified cycles N(Φ)/β(Φ) can be defined and then derive the Φ modified Lee-Coffin-Manson (Φ-LCM) equation for the fatigue initiation life of solder ball:Finally, a Φ modified Lee's BGA (Φ LBGA) equation for BGA solder joint specimens can be derived:This equation can predict quite well the life data of Sn/3.5Ag/0.75Cu solder joint specimens under Φ ϵ [0π/2]. As a consequence, a vehicle to study the fatigue initiation life of BGA solder joint specimens is constructed completely by the workable methodology and the theory discussed in the paper.

Precision Evaluation for Thermal Fatigue Life of Power Module Using Coupled Electrical-Thermal-Structural Analysis

2011 ◽  
Author(s):  
Tomohiro Takahashi ◽  
Qiang Yu ◽  
Masahiro Kobayashi
Keyword(s):  
Fatigue Life ◽  
Temperature Distribution ◽  
Solder Joint ◽  
Thermal Fatigue ◽  
Thermal Structure ◽  
Inelastic Strain ◽  
Power Module ◽  
Thermal Fatigue Life ◽  
Power Cycling ◽  
Precision Evaluation

For power module, the reliability evaluation of thermal fatigue life by power cycling has been prioritized as an important concern. Since in power cycling produces there exists non-uniform temperature distribution in the power module, coupled thermal-structure analysis is required to evaluate thermal fatigue mechanism. The thermal expansion difference between a Si chip and a substrate causes thermal fatigue. In this study, thermal fatigue life of solder joints on power module was evaluated. The finite element method (FEM) was used to evaluate temperature distribution induced by joule heating. Higher temperature appears below the Al wire because the electric current flows through the bonding Al wire. Coupled thermal-structure analysis is also required to evaluate the inelastic strain distribution. The damage of each part of solder joint can be calculated from equivalent inelastic strain range and crack propagation was simulated by deleting damaged elements step by step. The initial cracks were caused below the bonding Al wire and propagated concentrically under power cycling. There is the difference from environmental thermal cycling where the crack initiated at the edge of solder layer. In addition, in order to accurately evaluate the thermal fatigue life, the factors affecting the thermal fatigue life of solder joint where verified using coupled electrical-thermal-structural analysis. Then, the relation between the thermal fatigue life of solder joint and each factor is clarified. The precision evaluation for the thermal fatigue life of power module is improved.

scholarly journals Research on Reliability of Nano Silver Tin Pulp in Flip Chip Solder Joint

2020 ◽  
Author(s):  
Hui Yang ◽  
Jihui Wu
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Flip Chip ◽  
Equivalent Plastic Strain ◽  
Inelastic Strain ◽  
Second Phase ◽  
Strengthening Effect ◽  
Silver Paste ◽  
Nano Silver ◽  
Life Model

Abstract In order to improve the interconnect properties of nano-silver solders, we have developed a new tin-doped nano-silver paste (referred to as silver tin paste). The hard brittle phase Ag3Sn formed by the soldering of the silver tin paste acts as a second phase strengthening effect, which significantly improves the shear strength of the solder joint and has the potential to be widely used in the power electronics packaging industry. In this paper, the viscoplastic and elastic composite model is used to simulate the inelastic deformation behavior of flip chip nano silver tin solder joint under uniaxial shear load. The simulated stress-strain response curve agrees well with the experimentally measured data. The finite element method is used to simulate the interconnection state of flip chip solder joints under thermal cycling conditions. It can be seen that the inelastic strain of the silver tin solder joint has increased, and it can be inferred that as this strain increases further, the chip connection will be broken. The fatigue life of silver tin paste is predicted by the creep fatigue life model. Compared with the pure nano silver paste, the equivalent plastic strain of the silver tin paste is reduced and the fatigue life is significantly improved. It is indicated that the solder joint reliability of nano silver paste can be improved by tin doping. The analysis results provide reference data for the development of new nano solder.

Predicting Fatigue Initiation Life of Sn/3.8Ag/0.7Cu Solder using Endochronic Cyclic Damage-Coupled Viscoplastic Theory

2008 ◽  
Vol 24 (4) ◽  
pp. 369-377 ◽  
Author(s):  
C. F. Lee ◽  
Z. H. Lee
Keyword(s):  
Strain Amplitude ◽  
Hysteresis Loops ◽  
Inelastic Strain ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Cyclic Behavior ◽  
Dendritic Microstructure ◽  
Fatigue Initiation ◽  
Cyclic Damage ◽  
Good Agreement

AbstractThis paper studied cyclic behavior Sn/3.8Ag/0.7Cu solder with dendritic microstructure. A cyclic damage factor D under constant strain amplitude fatigue tests, was defined by using the reducing rate of maximum cyclic tensile stress σa. The critical cyclic damage DC and it's fatigue initiation life NI were determined very consistently by using separately the experimental σavs. N curves and the percolation theory. The endochronic cyclic damage-coupled viscoplastic theory proposed by the 1st author was used to simulate cyclic stress-strain hysteresis loops with damage under strain amplitude (εa) 0.8% at 298K. The results were in very good agreement with data. Combining the evolution equation of intrinsic damage and the computed cyclic stress-inelastic strain relation, a modified Coffin-Manson relationship was derived. By setting DC = 0.3, it predicted very effectively the NI data under σa from 0.2% to 1.0%.

Deterministic and Statistical Reliability of Surface Mount Components

2002 ◽  
Author(s):  
Zhengfang Qian ◽  
Xiaohua Wu ◽  
Joe Tomase
Keyword(s):  
Fatigue Life ◽  
Crack Initiation ◽  
Solder Joint ◽  
Crack Propagation ◽  
Temperature Profile ◽  
Failure Rate ◽  
Inelastic Strain ◽  
Reliability Prediction ◽  
Joint Geometry ◽  
Statistical Reliability

This paper is to investigate both deterministic and statistical aspects of thermal reliability of solder joints of surface mount leadless components (SMLCs). The emphasis is on bridging deterministic with statistical reliability prediction. A reliable methodology has been established to predict the failure rate at accelerated life tests (ALTs) and field failed rate in terms of key statistical parameters of design, environmental condition, and material selection due to the uncertainty from the component manufacturing/assembly, temperature profile of ALTs and field environmental conditions, and material property. Analytical equations and solutions of inelastic strain range and fatigue life for simplified joint geometry have been developed from deterministic approach. They are furthermore utilized to obtain the failure functions of thermal fatigue caused by both crack initiation and crack propagation from multivariable distributions. First Order Reliability Model (FORM) has been extended by combining Taylor series in technique with central limit theorem (CLT). An important outcome is that the statistical fatigue life is a lognormal distribution in which its parameters can be analytically evaluated by the approximate method with satisfactory accuracy for small COVs (COV=mean/deviation) of random variables (RVs). Specifically, SMLCs have been investigated on inelastic strain distribution, fatigue life distribution, failure and reliability functions, and failure rate prediction based on the statistical distributions of the solder joint height, solder paste size, temperature profile, and the experimental property of the eutectic solder alloy. Moreover, the component failure under two failure modes, i.e., both crack initiation and crack propagation, has been performed to illustrate the significance of failure criteria selection and address the data collection in field. Additionally, the simulation of realistic solder joint geometry and damage-based failure processes will be also presented. The developed methodology can be directly used for the board-level reliability prediction of advanced electronic packages such as BGAs, CSPs, QFPs, and Flip-chips.

Effect of Stress Gradient on Heat Cycle Fatigue Life Prediction of Solder Joints by Repetitive Bending Test

2021 ◽  
Vol 1016 ◽  
pp. 875-881
Author(s):  
Michiya Matsushima ◽  
Kei Endo ◽  
Tetsuya Kawazoe ◽  
Shinji Fukumoto ◽  
Kozo Fujimoto
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Strain Gradient ◽  
Strain Field ◽  
Thermal Cycle ◽  
Solder Joints ◽  
Inelastic Strain ◽  
Bending Test ◽  
Stress And Strain ◽  
Product Model

Strength of solder joints is usually evaluated by a shear test and a pull test. The reliability of the solder joint is evaluated by the repetitive pull tests of solder bulk specimens. However, the stress and strain field that caused by thermal load on the solder joint of the product model for estimating the reliability is different from these tests. Therefore, we proposed a repetitive bending test as a reliability test of solder joints producing the stress and strain field caused at the solder joint of product model. We proposed a repetitive multi-point bending test as a method to predict the fatigue life of the solder joint in the thermal cycle test in a short period of time. The influence of strain gradient on the inelastic strain amplitude used for lifetime evaluation is estimated. The controllability of the strain gradient by the three-point bending test parameters is investigated. The effect of residual stress on inelastic strain amplitude during sample preparation for thermal cycle test is also evaluated.

Damage Mechanics of Surface Mount Technology Solder Joints Under Concurrent Thermal and Dynamic Loading

1999 ◽  
Vol 121 (2) ◽  
pp. 61-68 ◽  
Author(s):  
R. Chandaroy ◽  
C. Basaran
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Thermal Cycling ◽  
Failure Mode ◽  
Dynamic Loading ◽  
Damage Mechanics ◽  
Solder Joints ◽  
Inelastic Strain ◽  
Simultaneous Application ◽  
Reliability Of Solder Joints

In the electronic industry, the dominant failure mode for solder joints is assumed to be thermal cycling. When semiconductor devices are used in vibrating environment, such as automotive and military applications, dynamic stresses contribute to the failure mechanism of the solder joint, and can become the dominant failure mode. In this paper, a damage mechanics based unified constitutive model for Pb40/Sn60 solder joints has been developed to accurately predict the thermomechanical behavior of solder joints under concurrent thermal and dynamic loading. It is shown that simultaneous application of thermal and dynamic loads significantly shorten the fatigue life. Hence, damage induced in the solder joint by the vibrations have to be included, in fatigue life predictions to correctly predict the reliability of solder joints. The common practice of relating only thermal cycling induced inelastic strain to fatigue life can be inadequate to predict solder joint reliability. A series of parametric studies were conducted to show that contrary to popular opinion all dynamic loading induced strains are not elastic. Hence, vibrations can significantly affect the fatigue life and reliability of solder joints in spite of their small mass.

Solder Joint Reliability Analysis of WLCSP Based on Inelastic Analysis

2006 ◽  
Vol 306-308 ◽  
pp. 643-648 ◽  
Author(s):  
Chia Lung Chang ◽  
Tzu-Jen Lin ◽  
Kenny Huang
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Shear Strain ◽  
Prediction Models ◽  
Inelastic Strain ◽  
Temperature Cycling ◽  
Cycling Test ◽  
Inelastic Analysis ◽  
Temperature Cycling Test ◽  
Total Shear

Nonlinear finite element analysis is performed to evaluate the reliability of the solder joint of wafer level chip scale package (WLCSP) under accelerated temperature cycling test. The solder joint is subjected to the inelastic strain that is generated during the temperature cycling test due to the thermal expansion mismatch between the various materials of the package and PCB (printed circuit board). The equivalent stress, equivalent inelastic strain, total shear strain, and hysteresis loop of the solder joint are determined in the simulation. The equivalent inelastic strain and total shear strain range of the joint are obtained as damage criterion to predict the solder fatigue. Both Coffin-Manson and Modified Coffin-Manson fatigue life prediction models are used to estimate the thermal fatigue life of WLCSP solder joints under temperature cycling test. Also, the effects of the material properties of the stress buffer layer (SBL) on the fatigue life of the solder joint are discussed.

Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Oblique Displacement Tests and Endochronic Viscoplastic Predictions

2010 ◽  
Vol 26 (4) ◽  
pp. 453-463 ◽  
Author(s):  
C. F. Lee ◽  
T. K. Lee ◽  
T. T. Lin ◽  
H. Y. Lin
Keyword(s):  
Solder Joint ◽  
Strain Amplitude ◽  
Solder Ball ◽  
Hysteresis Loops ◽  
Independent Study ◽  
Cyclic Behavior ◽  
Strain Rates ◽  
Cyclic Tests ◽  
Material Function ◽  
Joint Specimen

ABSTRACTIn this paper, a methodology with workable procedures was proposed and successfully transferred the hysteresis loops of BGA solder joint specimen held by loading-directionally aligned grip system under oblique displacement controlled cyclic tests, into hysteresis loops of “representative” solder ball itself under proportional straining and constant strain rate cyclic tests. Under the elastic unloading during cyclic test, value of elastic modulus of bulk solder specimens and the linear behavior of grip system were used. Following the study of Endochronic cyclic viscoplasticity, the kernel function ρ(Z) = ρ0 exp (−KZ)/Zα was found to be independent of the oblique angle (Φ) of straining paths. However, the steady cyclic behavior of material function f(ξ) ≡ f0 in the definition of intrinsic time Z contained two functions: (1) is the effective inelastic strain amplitude, and (2) f(Φ) Φ(rad) between Φ = 0 (uniaxial) and Φ = π/2 (shear). With (ρ0, α, K) = (4MPa, 0.84, 46) and f0 = [0.24(π/2−Φ)2 − 0.018(π2−Φ) + 1.2] , the endochronic theory predicted experimental hysteresis loops of BGA Sn/3.5Ag/0.75Cu solder joint specimens and Φ = 0°, 27°, 45°, 63°, 90° quite well.Results of ρ(Z) under f0 = 1 were found under independent study based on cyclic tests of bulk specimens under constant uniaxially strain amplitude and various constant strain rates. The values of (ρ0, α, K) = (7.3MPa, 0.84, 30) with f0 = 1.0 were all independent of strain rates. Comparisons of results of both types of specimens revealed that the values of (α, K) were almost the same but (1) ρ0 was smaller for micro-size solder ball, (2) is a material function of Sn/3.5Ag/0.75Cu itself (3) f(Φ) is not a material function, rather it is a special feature to reflect the effects of detail design of solder joint specimen and its connecting methods to the substrates

scholarly journals Slaves to Rome: The Rhetoric of Mastery in Titus' Speech to the Jews (Bellum Judaicum 6.328-50)

Ramus ◽  
2007 ◽  
Vol 36 (1) ◽  
pp. 25-38 ◽  
Author(s):  
Myles Lavan
Keyword(s):  
Historical Account ◽  
Self Presentation ◽  
Image Position ◽  
Relationship Of ◽  
The Relationship ◽  
Made In

(BJ6.350)Those who discard their weapons and surrender their persons, I will let live. Like a lenient master in a household, I will punish the incorrigible but preserve the rest for myself.So ends Titus' address to the embattled defenders of Jerusalem in the sixth book of Josephus'Jewish War(6.328-50). It is the most substantial instance of communication between Romans and Jews in the work. Titus compares himself to the master of a household and the Jewish rebels to his slaves. Is this how we expect a Roman to describe empire? If not, what does it mean for our understanding of the politics of Josephus' history? The question is particularly acute given that this is not just any Roman but Titus himself: heir apparent and, if we believe Josephus, the man who read and approved this historical account. It is thus surprising that, while the speeches of Jewish advocates of submission to Rome such as Agrippa II (2.345-401) and Josephus himself (5.362-419) have long fascinated readers, Titus' speech has received little or no attention. Remarkably, it is not mentioned in any of three recent collections of essays on Josephus. This paper aims to highlight the rhetorical choices that Josephus has made in constructing this voice for Titus—particularly his self-presentation as master—and the interpretive questions these raise for his readers. It should go without saying that the relationship of this text to anything that Titus may have said during the siege is highly problematic. (Potentially more significant, but unfortunately no less speculative, is the question of how it might relate to any speech recorded in the commentaries of Vespasian and Titus that Josephus appears to have used as a source.) What we have is a Josephan composition that is embedded in the broader narrative of theJewish War.

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