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%.

Temperature and Frequency Modified Fatigue Initiation Life of Solder Alloys Predicted by Endochronic Cyclic Damage-Coupled Viscoplasticity

2011 ◽  
Vol 27 (2) ◽  
pp. 267-277 ◽  
Author(s):  
C. F. Lee ◽  
S. I. Jeng ◽  
M. T. Liu
Keyword(s):  
Solder Alloy ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Least Square ◽  
Strain Response ◽  
Stress Strain ◽  
Life Data ◽  
Form Equation ◽  
Fatigue Initiation ◽  
Cyclic Damage

ABSTRACTIn this paper, an evolution equation of cyclically internal damage in the intrinsic damage time scale after the threshold cycles N0 was extended by employing its damage parameters proposed to be dependent of frequency (v) and temperature (T) under cyclic fatigue loading. The resulting damage-coupled endochronic viscoplasticity can drive v and T modified power form equations of cyclic damage and its fatigue initiation life = N1 + N0. Under fatigue tests with T effect and N0 = 0, the power form equation of N1(T)/(Th), named as T-LCM (T modified Lee Coffin-Manson) equation for fatigue initiation life can bederived. The T modified factor (Th) depends on the T dependent material elastic modulus, the cyclicstress-strain response and the damage parameters. Theoretical predictions in the life data ofSn/3.8Ag/0.7Cu solder alloy under cyclic strain test with Tϵ [298,393] K were very well.Also under fatigue tests with v effect only, the power form equation of /v-LCM (v modified Lee-Coffin-Manson) equation for fatigue initiation life can be derived. The v modified parameter depends on the v dependent cyclic stress-strain response and the damage parameters. Theoreticalpredictions in the life data of 96.5Sn/3.5Ag solder alloy with surface cracking effect i.e. N0 ≠ 0 during cyclicstrain tests with v ϵ [0.001,1] Hz were quite well.Obviously, the values of power exponents C in the T-LCM and the v-LCM equations can not be determinedsimply by the least square method as in the Coffin-Manson empirical formulae. Also, they must bejustified by constrains imposed in the material parameters defining in the cyclic stress-strain response andthe accumulation behavior of cyclic damage.The resultant equations derived here and the Δ-LCM equation derived under Δ angle proportional cyclicstrain tests can be combined together to form a T-v-ΔLCM equation for fatigue life studies in the solderalloys using bulk specimens or BGA solider joint specimens.

scholarly journals Effect of phase angle on the cyclic behavior of AISI 410 alloy

2019 ◽  
Vol 300 ◽  
pp. 12002
Author(s):  
Muhammed J. Adinoyi ◽  
Nesar Merah ◽  
Jafar Albinmousa
Keyword(s):  
Phase Angle ◽  
Axial Stress ◽  
Axial Strain ◽  
Hysteresis Loops ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Cyclic Behavior ◽  
Additional Stress ◽  
Proportional Loading ◽  
Nonproportional Loading

Multiaxial strain-controlled fatigue tests were conducted on AISI 410 according to ASTM 2207-E08 [1] under proportional (phase angle, θ = 90°) and non-proportional (phase angle, θ = 90º) loadings. Axial strain amplitudes in the range of 0.2%-0.35% are paired with shear strain amplitudes in the range of 0.25%-0.5%. Comparison was made between the hysteresis loops under both loading modes. It was found that peak stresses are higher under nonproportional loading, but with less plastic deformation. Additional stress hardening is exhibited by the alloy, resulting in the tip of the hysteresis loop under nonproportional loading to be rounded. Stress evolution with the number of fatigue cycles, mainly show cyclic stress softening except in axial stress under nonproportional loading where stress stabilization is largely the case after initial hardening. Fatigue life under nonproportional loading is generally lower than that of proportional loading.

Low-Cycled Fatigue Life of S30408 Stainless Steel at Liquid-Nitrogen Temperature

2018 ◽  
Author(s):  
Yingzhe Wu ◽  
Huaijian Xu ◽  
Qunjie Lu ◽  
Jinyang Zheng ◽  
Ping Xu
Keyword(s):  
Stainless Steel ◽  
Fatigue Life ◽  
Liquid Nitrogen ◽  
Strain Amplitude ◽  
Hysteresis Loops ◽  
Cyclic Strain ◽  
Liquid Nitrogen Temperature ◽  
Cyclic Stress ◽  
Cyclic Softening ◽  
Fatigue Tests

This paper is concerned with the low-cycled fatigue life of S30408 austenitic stainless steel at 77 K. Strain-controlled low-cycled fatigue tests were performed in a liquid-nitrogen bath covering a strain-amplitude range of 0.4%–1.0%. The role of the reduced temperature is examined during the low-cycled fatigue tests by comparing the fatigue performance to the one at ambient temperature that was obtained in our previous work. It is found that the cryogenic low-cycled fatigue life is significantly improved by a factor of 5–10 in the low strain-amplitude range of 0.4%–0.5%, resulting from the pronounced hardening effect due to the low temperature. However, the cryogenic improvement gradually reduces with the increasing strain-amplitude. At 77 K, the cyclic stress amplitude increases rapidly at the beginning of the fatigue test, and no cyclic softening is found due to the cryogenically constrained movement of the dislocations. The fatigue hysteresis loops and fatigue stress-strain curves shows that the cyclic plastic strain at cryogenic temperature accounts for a limited proportion in the total cyclic strain, and the damage may occurs explosively at the beginning of the cyclic load at 77 K.

Cyclic and High Strain Behavior of Titanium Alloys Used for Riser Components

2008 ◽  
Author(s):  
C. F. G. Baxter
Keyword(s):  
Stress Relaxation ◽  
Titanium Alloys ◽  
Elevated Temperatures ◽  
Fatigue Testing ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Cyclic Behavior ◽  
Fatigue Data ◽  
Stress Ratios

Grades 23 and 29 titanium alloys are becoming more commonly used offshore for critical components of riser systems. Many of these components, such as compact flanges, operate at high mean strains due to make-up loads, often close to or above yield. Hitherto, weld fatigue data collected at low mean strains have been used for prediction of fatigue lives of such components. However, these analyses have resulted in short but adequate lives. The objective of this work was, therefore, to derive fatigue data that could be applied to components operating at high strains and over a large range of stress ratios. This necessitated strain-controlled fatigue testing. Cyclic material properties evaluated from the tests are presented. In addition, it was found that sustained strain load, a type of stress relaxation that, unlike normal stress relaxation, does not require elevated temperatures, affected the cyclic behavior It also affects the distribution of make up stresses. This phenomenon was also investigated and it was shown that the cyclic stress/strain curve, readily derived from strain-controlled fatigue tests, accounted for sustained strain load effects.

Cyclic Stress in 316L Austenitic Stainless Steel at Low Temperatures

2007 ◽  
Vol 567-568 ◽  
pp. 401-404 ◽  
Author(s):  
Jaroslav Polák ◽  
Martin Petrenec ◽  
Jiří Man
Keyword(s):  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Plastic Strain ◽  
Strain Amplitude ◽  
Stress Component ◽  
Hysteresis Loops ◽  
Cyclic Stress ◽  
Plastic Strain Amplitude ◽  
Test Method ◽  
Step Test

Austenitic stainless steel was cycled at a series of temperatures in the interval from 296 K to 113 K. Constant plastic strain amplitude loading at different levels of plastic strain amplitude and testing similar to multiple step test method were applied at different temperatures. The stress amplitude was continually recorded and selected hysteresis loops were stored and later analyzed using statistical theory of the hysteresis loop. Effective stress component and probability density function as a function of temperature were evaluated. The results were discussed in terms of the temperature dependence of the cyclic yield stress and its sources.

A New Approach to the Evaluation of Fatigue Under Multiaxial Loadings

1981 ◽  
Vol 103 (2) ◽  
pp. 118-125 ◽  
Author(s):  
Y. S. Garud
Keyword(s):  
Fatigue Life ◽  
Constitutive Relations ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Plastic Work ◽  
Strain Response ◽  
New Approach ◽  
Hardening Rule ◽  
Multiaxial Loadings ◽  
Good Agreement

A critical review of the methods for evaluating fatigue of metals under simple (proportional) and complex (nonproportional) loadings indicates that most of the criteria are expressed in terms of either stresses or strains. In this paper a new approach to the evaluation of fatigue under these loadings is proposed. This approach is based upon the idea of relating fatigue life to the plastic work during a cycle of the loading. A procedure is outlined for the calculation of plastic work which involves explicit considerations of the material constitutive relations. It is based on the structure of modern plasticity theories and a new “hardening rule.” Validity of the constitutive relations to predict the cyclic stress-strain response is demonstrated for out-of-phase multiaxial loadings. Available experimental results of fatigue tests under out-of-phase loadings are shown to be in good agreement with the predictions using the new approach.

Axial and Diametral Cyclic Stress—Strain Response in Plain and Circumferentially Notched Cylindrical Bars at 550 °C

2006 ◽  
Vol 41 (4) ◽  
pp. 265-286 ◽  
Author(s):  
R. P Skelton ◽  
G. A Webster
Keyword(s):  
Low Cycle Fatigue ◽  
Notch Root ◽  
Hysteresis Loops ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Gauge Length ◽  
Stress Strain ◽  
Deformation Response ◽  
Notched Specimens ◽  
Observed Behaviour

Cyclic stress-strain tests were undertaken at 550 °C on plain specimens and notched specimens of different notch acuities in several low- and high-alloy ferritic steels (1Cr-Mo-V, NF616, TB12M, and HCM12A). Integrated axial strains were measured between the minimum sections of the notches using a longitudinal extensometer, while surface hoop strains were measured by means of a diametral extensometer with probes located across the notch root. The same extensometry was employed in plain specimens. Over a period of 100 cycles, softening occurred in all plain specimens. These effects were also demonstrated in notched specimens in both axial and diametral directions, although to a lesser degree. From hysteresis loops determined in the notch tests, the cyclic deformation response of the notched regions was expressed in terms of an ‘equivalent gauge length’. Deviations from elastic-plastic behaviour in plain specimens were noted in that the commonly used ‘effective Poisson's ratiO' was greater than calculated. The effect was investigated further by exploring the characteristics of a very shallow notch, induced by straining a plain specimen to the onset of necking and beyond. The implications of observed behaviour in strain-control low-cycle fatigue tests is discussed.

Evaluation on Thermo-Mechanical Fatigue Life of IN738LC Using Finite Element Analysis

2013 ◽  
Vol 467 ◽  
pp. 20-23
Author(s):  
Jeong Min Lee ◽  
Dong Keun Lee ◽  
Jae Mean Koo ◽  
Chang Sung Seok
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Amplitude ◽  
Low Cycle Fatigue ◽  
Hysteresis Loops ◽  
Fatigue Tests ◽  
Plastic Strain Amplitude ◽  
Element Analysis ◽  
Mechanical Fatigue ◽  
Super Alloy

In this paper, thermo-mechanical fatigue tests were performed for the nickel-based super alloy IN738LC, after which the thermo-mechanical fatigue life was evaluated using finite element analysis. Nickel-based super alloy is used as the main material of turbine blades, which are important equipment in thermal power generation plants. In general, such materials receive three types of damage under thermo-mechanical fatigue loading. In the case of low-cycle fatigue behavior in which large plastic deformation mainly occurs, the lifetime can be decided by its relationship with the plastic strain amplitude. In order to obtain the plastic strain amplitude from the measured strain amplitude, a hysteresis loop should be derived. However, low-cycle fatigue tests are difficult. Moreover, precise experimental techniques are required to obtain the hysteresis loops. In this study, after thermo-mechanical fatigue tests were performed, thermal mechanical fatigue tests on IN738LC were simulated using finite element analysis. The results of analysis were verified by comparing with the hysteresis loops of an experiment

scholarly journals Flat-Cladding Fiber Bragg Grating Sensors for Large Strain Amplitude Fatigue Tests

2021 ◽  
Author(s):  
Aihen Feng ◽  
Daolun Chen ◽  
Cheng Li ◽  
Xijia Gu
Keyword(s):  
Fiber Bragg Grating ◽  
Strain Amplitude ◽  
Large Strain ◽  
Hysteresis Loops ◽  
Cyclic Strain ◽  
Fatigue Tests ◽  
Bragg Grating ◽  
Large Strain Amplitude ◽  
Bragg Grating Sensor ◽  
Cyclic Strain Amplitude

We have successfully developed a flat-cladding fiber Bragg grating sensor for large cyclic strain amplitude tests of up to ±8,000 με. The increased contact area between the flat-cladding fiber and substrate, together with the application of a new bonding process, has significantly increased the bonding strength. In the push-pull fatigue tests of an aluminum alloy, the plastic strain amplitudes measured by three optical fiber sensors differ only by 0.43% at a cyclic strain amplitude of ±7,000 με and 1.9% at a cyclic strain amplitude of ±8,000 με. We also applied the sensor on an extruded magnesium alloy for evaluating the peculiar asymmetric hysteresis loops. The results obtained were in good agreement with those measured from the extensometer, a further validation of the sensor.

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.

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