A Damage Integral Approach to Solder Joint Fatigue

1990 ◽  
Vol 203 ◽  
Author(s):  
C.-Y. Li ◽  
R. Subrahmanyan ◽  
J. McGroarty
Keyword(s):  
Solder Joint ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Constitutive Relations ◽  
Failure Criteria ◽  
Integral Approach ◽  
State Variable ◽  
Damage Rate ◽  
Solder Joint Fatigue ◽  
Data Representative

ABSTRACTThe application of a damage integral approach which provides numerical accounting of the accumulated fatigue damage in solder joint is reviewed. The instantaneous fatigue damage rate is determined by the solder stress state, temperature and environment using a phenomenological crack growth law. The stress is calculated using state variable constitutive relations for inelastic deformation. The material parameters for the crack growth law are determined from isothermal fatigue data. Representative damage integral calculations are used to illustrate the application of the approach. Finally, the significance of failure criteria on the apparent fatigue life is discussed in terms of the damage integral approach.

The Reliability Assessment of Flip Chip Type Solder Joints Based on the Damage Integral Approach

1998 ◽  
Vol 516 ◽  
Author(s):  
Peng Su ◽  
Chen Zhou ◽  
Sven Rzepka ◽  
Matt Korhonen ◽  
Che-Yu Li
Keyword(s):  
Fatigue Damage ◽  
Flip Chip ◽  
Solder Joints ◽  
Integral Approach ◽  
Damage Rate ◽  
Power Cycling ◽  
Chip Carrier ◽  
Type Relation ◽  
Accelerated Thermal Cycling ◽  
Total Damage

AbstractThermal fatigue of flip-chip solder joints between a chip and chip carrier is a serious reliability concern. Differences in the temperature and/or in the coefficients of thermal expansion between the chip and substrate lead to stresses which may result in fatigue damage and eventual failure of the interconnect. Conventionally, the solder lives have been estimated by a Coffin-Manson type relation. However, this largely empirical approach becomes inadequate when comparing thermal histories that are widely different, as in the cases of accelerated thermal cycling and power cycling. In this study, we use a damage integral approach where the fatigue damage rate is calculated based on the momentary stress and strain (estimated analytically) experienced by the solder joints. The momentary damage is then integrated over the entire loading history to yield total damage at any moment.

Effects of Strain Rate and Amplitude Variations on Solder Joint Fatigue Life in Isothermal Cycling

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Sa'd Hamasha ◽  
Peter Borgesen
Keyword(s):  
Fatigue Life ◽  
Solder Joint ◽  
Strain Rate ◽  
Solder Joints ◽  
Constitutive Relations ◽  
Snagcu Solder ◽  
Shear Fatigue ◽  
Deformation Properties ◽  
Service Conditions ◽  
Solder Joint Fatigue

The behavior of lead-free solder alloys under realistic service conditions is still not well understood. Life prediction of solder joints relies on conducting accelerated tests and extrapolating results to service conditions. This can be very misleading without proper constitutive relations and without understanding the effects of cycling parameter variations common under realistic service conditions. It has been shown that the fatigue life depends on the inelastic work accumulation, independently of cycling-induced material property variations, which explains the breakdown of damage accumulation rules and allows the development of a modified Miner's rule. This paper discusses the interacting effects of strain rate and amplitude variations on solder joint fatigue life. Individual SnAgCu solder joints with two different Ag contents (SAC305 and SAC105) were tested in low cycling shear fatigue under single and varying amplitudes with different strain rates. Such a shear fatigue experiment allows the measurement of work accumulation and the evolution of solder deformation properties during cycling. The results showed that cycling with a lower strain rate at fixed amplitude causes more damage per cycle. Alternating between mild amplitude at a high strain rate and harsh amplitude at a low strain rate leads to ongoing increases in the rate of damage at the mild amplitude and thus relatively rapid failure. In comparing SAC305 with SAC105, the effect of strain rate on both alloys is almost the same, and SAC305 is still more fatigue resistant than SAC105 in varying amplitude cycling with any strain rate.

scholarly journals Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Aleksander Muc
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Constitutive Relations ◽  
A Priori ◽  
Chemical Properties ◽  
Composite Plates ◽  
Failure Criteria ◽  
Lagrange Equations ◽  
Homogenization Methods ◽  
Mechanics Of Composite Materials

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

Modeling of Fatigue Crack Propagation

2004 ◽  
Vol 126 (1) ◽  
pp. 77-86 ◽  
Author(s):  
Yanyao Jiang ◽  
Miaolin Feng
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Initiation ◽  
Crack Propagation ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Fatigue Crack Propagation ◽  
Fatigue Crack Initiation ◽  
Cyclic Plasticity ◽  
R Ratio

Fatigue crack propagation was modeled by using the cyclic plasticity material properties and fatigue constants for crack initiation. The cyclic elastic-plastic stress-strain field near the crack tip was analyzed using the finite element method with the implementation of a robust cyclic plasticity theory. An incremental multiaxial fatigue criterion was employed to determine the fatigue damage. A straightforward method was developed to determine the fatigue crack growth rate. Crack propagation behavior of a material was obtained without any additional assumptions or fitting. Benchmark Mode I fatigue crack growth experiments were conducted using 1070 steel at room temperature. The approach developed was able to quantitatively capture all the important fatigue crack propagation behaviors including the overload and the R-ratio effects on crack propagation and threshold. The models provide a new perspective for the R-ratio effects. The results support the notion that the fatigue crack initiation and propagation behaviors are governed by the same fatigue damage mechanisms. Crack growth can be treated as a process of continuous crack nucleation.

Modeling the Fatigue Damage Evolution in Welded Joints

2017 ◽  
Author(s):  
Zbigniew Mikulski ◽  
Vidar Hellum ◽  
Tom Lassen
Keyword(s):  
Crack Initiation ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Damage Evolution ◽  
Threshold Value ◽  
Phase Model ◽  
Two Phase ◽  
Initiation Phase ◽  
Weld Toe ◽  
Small Cracks

The present paper presents a two-phase model for the fatigue damage evolution in welded steel joints. The argument for choosing a two-phase model is that crack initiation and subsequent crack propagation involve different damage mechanisms and should be treated separately. The crack initiation phase is defined as the number of cycles to reach a crack depth of 0.1 mm. This phase is modelled based on the Dang Van multiaxial stress approach. Both a multiaxial stress situation introduced by the acting loads and the presence of the multiaxial welding residual stresses are accounted for. The local notch effect at the weld toe becomes very important and the irregular weld toe geometry is characterized by extreme value statistics for the weld toe angle and radius. The subsequent crack growth is based in classical fracture based on the Paris law including the effect of the Stress Intensity Factor Range (SIFR) threshold value. The unique fatigue crack growth rate curve suggested by Huang, Moan and Cui is adopted. This approach keeps the growth rate parameters C and m constant whereas an effective SIFR is calculated for the actual stress range and loading ratio. The model is developed and verified based on fatigue crack growth data from fillet welded joints where cracks are emanating from the weld toe. For this test series measured crack depths below 0.1 mm are available. The two-phase model was in addition calibrated to fit the life prediction in the rule based S-N curve designated category 71 (or class F). A supplementary S-N curve is obtained by the Random Fatigue Limit Method (RFLM). The test results and the fitted model demonstrated that the crack initiation phase in welded joins is significant and cannot be ignored. The results obtained by the Dang Van approach for the initiation phase are promising but the modelling is not yet completed. The fracture mechanics model for the propagation phase gives good agreement with measured crack growth. However, it seems that the prediction of crack retardation based on a threshold value for the SIFR gives a fatigue limit that is overly optimistic for small cracks at the weld toe. The threshold value has been determined based on tests with rather large central cracks in plates. The validity for applying this threshold value for small cracks at the weld toe is questioned. As the present two-phase model is based on applied mechanics for both phases the parameters that have an influence on the fatigue damage evolution are directly entering into the model. Any change in these parameters can then be explicitly taken into account in logical and rational manner for fatigue life predictions. This not the case with the rule based S-N curves that are based on pure statistical treatment of the bulk fatigue life.

Experimental Study on Flexible Bare Pipe Arrays Undergoing Vortex-Induced Vibrations

2018 ◽  
Author(s):  
Y. Liu ◽  
C. Shi ◽  
Z. Liu ◽  
J. Wang ◽  
X. Bao
Keyword(s):  
Fatigue Damage ◽  
Dynamic Responses ◽  
Array Configuration ◽  
Damage Rate ◽  
Flexible Pipes ◽  
Vortex Induced Vibrations ◽  
Helical Strakes ◽  
Preliminary Study ◽  
Single Pipe ◽  
Center Distance

Vortex-induced vibration (VIV) excited by current is a major contributor to the fatigue accumulation of marine risers. For deepwater operations, several risers are often arranged together in an array configuration. In this study, a set of four identical flexible pipes of a rectangular arrangement were tested in a water tunnel. By comparing the dynamic responses of a pipe in an array with that of a single isolated pipe, the effects of the current speed and the center-to-center distance between the up-stream and downstream pipes on their dynamic responses were investigated. Fatigue damages accumulated on each pipe in an array was calculated and a factor, termed “fatigue damage amplification factor”, was defined as a ratio between the fatigue damage rate of pipe in an array and the fatigue damage rate of a single pipe at a same current condition. The results showed that for bare pipes (i.e., without helical strakes), the downstream pipes in an array configuration may have larger dynamic responses and fatigue damage rates than those of a single pipe; and, it is not always conservative to assume that the fatigue damage rate estimated for a single pipe can be used to represent the fatigue damage rates of pipes in an array. This preliminary study provided some meaningful results for the design, analysis and operation of marine riser arrays.

Fatigue Damage From High Mode Number Vortex-Induced Vibration

2006 ◽  
Author(s):  
J. Kim Vandiver ◽  
Susan B. Swithenbank ◽  
Vivek Jaiswal ◽  
Vikas Jhingran
Keyword(s):  
Fatigue Damage ◽  
Field Experiments ◽  
Higher Harmonics ◽  
Vortex Induced Vibration ◽  
Third Harmonic ◽  
The Third ◽  
Damage Rate ◽  
Surface Vessels ◽  
Vortex Shedding Frequency ◽  
First Time

This paper presents results from two field experiments using long flexible cylinders, suspended vertically from surface vessels. The experiments were designed to investigate vortex-induced vibration (VIV) at higher than tenth mode in uniform and sheared flows. The results of both experiments revealed significant vibration energy at the expected Strouhal frequency (referred to in this paper as the fundamental frequency) and also at two and three times the Strouhal frequency. Although higher harmonics have been reported before, this was the first time that the contribution to fatigue damage, resulting from the third harmonic, could be estimated with some certainty. This was enabled by the direct measurement of closely spaced strain gauges in one of the experiments. In some circumstances the largest RMS stress and fatigue damage due to VIV are caused by these higher harmonics. The total fatigue damage rate including the third harmonic is shown to be up to forty times greater than the damage rate due to the vibration at the fundamental vortex-shedding frequency alone. This dramatic increase in damage rate due to the third harmonic appears to be associated with a narrow range of reduced velocities in regions of the pipe associated with significant flow-induced excitation.

Different Fatigue Dynamics Under Statistically and Spectrally Similar Deterministic and Stochastic Excitations

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Son Hai Nguyen ◽  
Mike Falco ◽  
Ming Liu ◽  
David Chelidze
Keyword(s):  
Crack Growth ◽  
Fatigue Damage ◽  
Damage Accumulation ◽  
Growth Dynamics ◽  
Experimental System ◽  
Counting Method ◽  
Random Loading ◽  
Stochastic Excitations ◽  
Fatigue Damage Accumulation ◽  
System Coupling

Estimating and tracking crack growth dynamics is essential for fatigue failure prediction. A new experimental system—coupling structural and crack growth dynamics—was used to show fatigue damage accumulation is different under chaotic (i.e., deterministic) and stochastic (i.e., random) loading, even when both excitations possess the same spectral and statistical signatures. Furthermore, the conventional rain-flow counting method considerably overestimates damage in case of chaotic forcing. Important nonlinear loading characteristics, which can explain the observed discrepancies, are identified and suggested to be included as loading parameters in new macroscopic fatigue models.

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