Effect of axial ratcheting deformation on torsional low cycle fatigue life of lead-free solder Sn–3.5Ag

Multiaxial fatigue tests were conducted on Sn–3.5Ag solder specimens under axial/torsional loading at room temperature. It was found that the ratcheting strain increased while the fatigue life decreased with the increase of axial stress and shear strain amplitude. A power relationship of ratcheting strain rate versus fatigue life was observed. Equivalent strain approach and critical plane approaches were evaluated with fatigue life data obtained in the tests. Since those approaches excluded the consideration of the ratcheting strain and mean stress, the methods for fatigue life prediction were improper for multiaxial fatigue with ratcheting strain. Coffin model, considered the effect of ratcheting on fatigue life depending on the ratio of ratcheting strain to material ductility, brought the fatigue life predictions on non-conservative side if the ratcheting deformation was large. For this reason, a model with the maximum shear strain range and axial ratcheting strain rate was proposed as a new damage parameter. The new model could not only describe the fatigue life in torsion test, but also predicted torsional fatigue life of the lead-free solder with axial ratcheting.     

TA17合金薄片材料毫小试样疲劳性能研究

关键工程结构、小尺寸零部件和焊接区的疲劳寿命评估中往往无法采用传统大试样进行疲劳试验,因此本文提出了一种采用毫米级别薄片试样获取材料循环本构关系和低周疲劳寿命的新方法。在Care原位试验机上完成毫米级别薄片漏斗试样的加载工装和低周疲劳试验的基础上,通过变幅对称循环试验和等辐循环试验分别实现了材料循环本构关系和低周疲劳性能的获取。该文提出了一种对不同幂律材料和不同几何尺寸构型均具有良好普适性的材料循环本构关系预测模型,并通过有限元实现了模型准确性的正反向预测验证。将循环本构关系用于有限元计算中,给出了薄片漏斗试样漏斗两侧名义应力、名义应变和漏斗根部真实应力、真实应变的转换方程,进而预测材料的低周疲劳寿命。该文完成了TA17合金等直圆棒试样和1.2 mm厚度薄片漏斗试样的对称变幅循环试验和多级等辐循环试验。由模型预测获得的TA17合金循环本构关系与等直圆棒试样的试验结果比较表明:两种曲线的弹性段和0.009 mm/mm~0.011 mm/mm应变段吻合良好,在弹塑性过渡段（0.004 mm/mm~0.009 mm/mm）模型预测结果最大相对误差小于9%。根据两组应力和应变转换方程获得的漏斗试样材料代表性体积单元疲劳寿命和Manson-Coffin寿命预测模型与等直圆棒试样试验结果均吻合良好。     

复杂面内应力状态下平面编织高铝纤维增强氧化铝基复合材料强度及疲劳寿命预测方法

针对平面编织氧化铝基复合材料提出了一种复杂面内应力状态下的强度准则和疲劳寿命预测方法。通过拉伸、压缩及纯剪切试验,分别获得了材料的静强度指标。考虑材料拉、压性能的差异和面内拉-剪联合作用对材料强度的影响机制,提出了修正的Hoffman强度理论。采用该强度理论预测得到的偏轴拉伸强度与试验结果基本一致,偏差不超过10%。开展了偏轴角θ=0°、15°、30°、45°,应力比R=0.1,频率f=10 Hz的拉伸疲劳试验,试验结果表明随着偏轴角的增加,相同轴向拉伸载荷下的疲劳寿命逐渐降低。由于面内剪切应力分量的作用,疲劳失效由纤维主导逐渐过渡到纤维和基体共同主导的模式。基于单轴疲劳寿命曲线,采用Broutman-Sahu剩余强度模型表征剩余强度随疲劳循环次数的变化规律,结合剩余强度演化模型和修正的Hoffman强度理论,提出了一种面内复杂载荷条件下的疲劳寿命预测模型,并引入疲劳剪切损伤影响因子表征拉-剪应力联合作用对材料疲劳行为的影响。采用本文提出的疲劳寿命预测模型,预测不同偏轴角拉伸疲劳寿命,预测结果与试验结果基本一致,偏差在1倍寿命范围内。比较结果表明在给定应力比、温度和疲劳载荷频率条件下,该疲劳寿命预测模型可以用来预测平面编织氧化铝基复合材料拉-剪复杂面内载荷条件下疲劳寿命。      

Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction

This study deals with simulation for cyclic stress/strain evolutions and redistributions, and evaluation of fatigue parameters suitable for estimating fatigue lives under multiaxial loadings. The local cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures of ABAQUS finite element code for both smooth and notched specimens made of three materials: a medium carbon steel in the normalized condition, an alloy steel quenched and tempered and a stainless steel, respectively. Emphasis is on the studying of ‘intelligent’ material behaviors to resist fracture, such as stress redistribution and relaxation through plastic deformations, etc. For experimental verifications, a series of tests of biaxial low cycle fatigue composed of tension/compression with static and cyclic torsion were carried out on a biaxial servo-hydraulic testing machine (Instron 8800). Different multiaxial loading paths were used to verify their effects on the additional cyclic hardening. The comparisons between numerical simulations and experimental observations show that the FEM simulations allow better understanding on the evolutions of the local cyclic stress–strain and it is shown that strong interactions exist between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the local cyclic elastic–plastic stress–strain responses, the energy-based multiaxial fatigue damage parameters are applied to correlating the experimentally obtained lives. Improved correlations between the predicted and the experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses.     

Torsional fatigue with axial constant stress for Sn–3Ag–0.5Cu lead-free solder

A series of multiaxial ratcheting–fatigue interaction tests have been carried out on Sn–3Ag–0.5Cu lead-free solder specimens. All tests were conducted under cyclic shear strain with the constant axial stress at the room temperature with the shear strain rate of 5 × 10⁻³ s⁻¹. It was found that the ratcheting strain increased with increasing axial stress and shear strain amplitude while the fatigue life decreased at the same time. The ratcheting strain rate was linear with axial stress in double logarithmic coordinate. The Ohno–Wang II constitutive model was employed to simulate the stress–strain responses. Several fatigue life prediction models were applied to predict the multiaxial ratcheting–fatigue life of the Sn–3Ag–0.5Cu lead-free solder. The Gao–Chen model which adopted the maximum shear strain and the ratcheting strain rate as the damage parameter predicted the multiaxial ratcheting fatigue life well.     

Fatigue-life prediction of SiC particulate reinforced aluminum alloy 6061 matrix composite using AE stress delay concept

A study of the residual fatigue life prediction of 6061-T6 aluminum matrix composite reinforced with 15 vol % SiC particulates (SiC_p) by using the acoustic emission technique and the stress delay concept has been carried out. Fatigue damages corresponding to 40, 60 and 80% of total fatigue life were stimulated at a cyclic stress amplitude. The specimens with and without fatigue damage were subjected to tensile tests. The acoustic emission activities were monitored during tensile tests. It was found that a lower stress level was required to reach a specified number of cumulative AE events for specimens fatigued to higher percentage of the fatigue life. This stress level is called stress delay. Approximately a linear relation was found between stress delay and fatigue damage. Using the procedure defined in this study, the residual fatigue life can be predicted by testing the specimen in tension and monitoring the AE events. The number of the cumulative AE events increased exponentially with the increase of strain during tensile tests. This exponential increase occurred when the material was in the plastic regime and was attributed mainly to SiC particulate/matrix interface decohesion and linkage of voids. In high cycle fatigue, it was observed that the residual tensile strengths of the material did not change with prior cyclic loading damages since the high cycle fatigue life was dominated by the crack initiation phase.     

Endurance verification of custom-made hip prostheses

Custom-made stems are a particular class of hip prostheses manufactured in a single sample for a specific patient. Experimental fatigue testing according to ISO standards cannot be performed for pre-clinical validation of these devices. However, the implant manufacturers need to assess the endurance properties of custom-made stems. This study investigates a theoretical protocol to predict the maximum stress induced in the stem by the ISO experimental test set-up. Stress was predicted using beam theory and finite element analysis (FEA). Strain measurements were used to assess the accuracy of the theoretical calculation. Fatigue testing was performed to verify the theoretical prediction about the fatigue stem performance. The results showed that FEA is more accurate than beam theory. Beam theory calculation is able to predict the static stresses induced by the ISO 7206/4 loading set-up with a difference always lower than 20% with respect to a prediction of a simplified FEA. Hence beam theory can be used to estimate the maximum stress. FEA becomes useful for a stem stressed at a limit condition. In both cases precise data about the endurance properties of the material are required for corrected predictions. However, endurance verification should be performed by introducing a safety factor to account for the material and manufacturing variations.     

Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a rubber mount was predicted by combining test of material properties and finite element analysis (FEA). The natural rubber material material’s fatigue life equation was acquired based on uniaxial tensile test and fatigue life tests of the natural rubber. The strain distribution contours and the maximum total principal strains of the rubber mount at different loads in the x and y directions were obtained using finite element analysis method. The critical region cracks prone to arise were obtained and analyzed. Then the maximum total principal strain was used as the fatigue parameter, which was substituted into the natural rubber’s fatigue life equation, to predict the fatigue life of the rubber mount. Finally, fatigue lives of the rubber mount at different loads were measured on a fatigue test rig to validate the accuracy of the fatigue life prediction method. The test results imply that the fatigue lives predicted agree well with the test results.     

The research on failure analysis of fluid cylinder and fatigue life prediction

To analyze the reasons of fluid cylinders’ rupture, macro-analysis, SEM, composition inspection, metallographic analysis, hardness test and mechanics performance test of fluid cylinders materials were implemented. Two different kinds of fatigue life prediction methods have been proposed which are based on total life analysis and strain–life methodology. The results indicate that: the failure cylinders’ material quality is satisfactory. Fatigue damage caused by high working, stress and corrosion is the main reason of cracking. The fatigue life prediction illustrates that strain–life methodology is well adapted to fluid cylinders.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

Comparative analysis of fatigue life predictions in central notched specimens of Al–Mg–Si alloys

The fatigue behaviour of an Al–Mg–Si alloy was studied using notched specimens. Fatigue tests were conducted at two stress ratios R= 0 and R= 0.4 on thin plates with a central hole. Constant and block variable loading amplitudes were applied to the specimens using a servo‐hydraulic machine. The applicability of the local strain approach method to the prediction of the fatigue life was investigated for this type of discontinuity. Two methods, the equivalent strain energy density approach and a modified stress–strain intensity field approach, were used to predict the fatigue strength. For the second one an elastic–plastic finite element analysis was carried out in order to obtain the local strain and stress distributions near the notch root. Based on Miner's rule an equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. The experimental results were compared with the predicted results obtained by the two methods investigated and better agreement was found with the stress–strain field intensity approach, while the strain energy approach gave more conservative results. Miner's rule gives a good correlation between the variable amplitude and constant amplitude results.     

Crack propagation of CCT foam specimen under low strain rate fatigue

The objective of this study is to investigate the effect of holes on the low strain rate fatigue properties of the nickel foam material and to understand the lifetime of this material which is subjected to the repeated loads. Failures of foam materials under single and repeated loads analogous to fatigue are essential to designers and users in military and aerospace structures. The material failure induced by repeated low strain rate loading becomes a critical issue because of significant loss of stiffness and compressive strength in the foam material. Testing methods to study low strain rate (that is, strain rate) fatigue are quite numerous; no single standard testing procedure is defined for studying the low strain rate fatigue property of a material. The increasing application of foam material in aerospace structures, owing to high specific stiffness and strength has attracted a great concern about the high sensitivity to low strain rate damage introduced during manufacture or in service, and the effects of such damage on structural degradation. To investigate this issue, this study sets up an experimental procedure to determine the low strain rate fatigue properties of nickel foam material. This study performs both experimental and numerical investigations to catch the low strain rate fatigue behavior of nickel foam with open-cell type. The experiments are conducted by rod up and down at the strain rate fatigue of loading. The crack length at the specific cycles are measured experimentally by taking pictures with a paper ruler attached on the surface of specimen and these values are apply to the computer simulations as crack seam model. The simulation result of stress intensity factors are compared with a well known theoretical calculation. Design life and probability of failure or survival at specified life can be calculated so that the fatigue life of nickel core material subjected to repeated low strain rate loading is predicted.     

Comparative evaluation of strain controlled low cycle fatigue behaviour of solution annealed and prior cold worked 316L(N) stainless steel

The effect of 20% prior cold work on low cycle fatigue (LCF) behaviour of type 316L(N) stainless steel (SS) was studied at 873 K by conducting total axial strain controlled tests in air with strain amplitudes in the range ±0.25% to ±1.0%. The cyclic deformation behaviour of 20% prior cold worked (PCW) material was compared with the LCF response of solution annealed (SA) alloy tested under similar conditions. The cyclic stress response (CSR) of 316L(N) SS in the PCW condition was characterized by a short period of hardening followed by prolonged softening prior to failure, whereas SA material exhibited a significant hardening regime followed by stress saturation. Interrupted tests on PCW material were carried out at different stages of CSR in order to determine the underlying mechanisms as reflected in substructural changes. The fatigue life in the solution annealed condition was similar to that of the PCW material at higher strain amplitudes of testing (≥±0.5%) while at lower strain amplitudes, the PCW material exhibited longer life.     

Fatigue life prediction: A Continuum Damage Mechanics and Fracture Mechanics approach

Continuum Damage Mechanics (CDM) approach is used to predict crack initiation life and Fracture Mechanics approach predicts crack growth life. Strain controlled fatigue life of a ferrous alloy, EN 19 steel, has been determined using CDM and Fracture Mechanics approach. By combining these two approaches, life could be predicted with damage value in the material. All inputs required for the models have been determined by conducting monotonic, cyclic and fracture tests. Predicted life is also compared by conducting strain controlled fatigue tests. Predicted life in the strain amplitude range of 0.3–0.7% (fatigue life range of 10²–10⁵), compares well with the experimental results. All tests have been conducted at specimen level, stress ratio of −1 and at room temperature. The variation of crack initiation and crack propagation life with strain amplitude shows that maximum life is consumed by crack growth process at higher strain amplitude and at lower strain amplitudes, maximum life is spent for crack initiation process.     

THERMAL-MECHANICAL LOW-CYCLE FATIGUE UNDER CREEP-FATIGUE INTERACTION ON TYPE 304 STAINLESS STEELS

Abstract— In this study, in-phase and out-of-phase thermal fatigue tests at the temperature ranges of 473–823 and 573–873 K were carried out on three kinds of 304 stainless steel as well as isothermal low-cycle fatigue tests at 823 and 873 K, in order to investigate the properties of thermal fatigue strength under creep-fatigue interaction. Based on the relation between the fatigue life and the failure mode, the time-dependent effect on the fatigue life was discussed. Also, an attempt was made to apply the strain range partitioning method to the thermal fatigue life prediction. It is difficult to evaluate the thermal fatigue life at high temperatures simply from the isothermal fatigue life under the same strain condition. It was also found that an unbalanced creep strain during tensile loading, which increased the number of intergranular cracks, gave the largest damage to the material. By the strain range partitioning method, it was possible to predict the isothermal fatigue life and the thermal fatigue life at the low temperature range within a factor of 1·5. On the other hand, the thermal fatigue life at the high temperature range could only be predicted within a factor of 3. However, further detailed investigations are required on the technique of partitioning the inelastic strain range and predicting the effects of dynamic strain ageing and recovery during strain holds.     

Experimental observations and modelling of cyclic and relaxation behaviour of the Ni-based superalloy Haynes 282

In this paper, the high temperature cyclic and relaxation behaviour of Ni-based superalloy Haynes 282 is investigated. Low-cycle fatigue (LCF) tests with and without hold time have been performed at two elevated temperatures, 650 and 730 °C. The test results are presented and analysed with respect to the cyclic behaviour and the stress relaxation behaviour. Based on this analysis, a Chaboche type of elasto-viscoplastic material model is formulated and calibrated with respect to the cyclic experimental data. Furthermore, the effect of the scatter, observed in the initial yield stresses of the LCF tests, is considered in the calibration of the material model. Finally, a Golos–Ellyin strain energy density fatigue criterion is used to predict the fatigue life and how the scatter in the LCF tests influences the predicted fatigue lives is studied. Moreover, to account for the reduction in fatigue life due to stress relaxation, a frequency modification of the Golos–Ellyin fatigue criterion is proposed and evaluated.     

An assessment of three creep–fatigue life prediction methods for nickel‐based superalloy GH4049

High‐temperature low‐cycle fatigue tests with and without a 10‐s strain hold period in a cycle were performed on a nickel base superalloy GH4049 under a fully reversed axial total strain control mode. Three creep–fatigue life prediction methods are chosen to analyse the experimental data. These methods are the linear damage summation method (LDS), the strain range partitioning method (SRP) and the strain energy partitioning method (SEP). Their ability to predict creep‐fatigue lives of GH4049 at 700, 800 and 850 °C has been evaluated. It is found that the SEP method shows an advantage over the SRP method for all the tests under consideration. At 850 °C, the LDS and SEP methods give a more satisfactory prediction for creep–fatigue lives. At the temperatures of 700 and 800 °C, the SRP and SEP methods can correlate the life data better than the LDS method. In addition, the differences in predictive ability of these methods have also been analysed. The scanning electron microscopy (SEM) examination of fracture surfaces reveals that under creep–fatigue test conditions crack initiation mode is transgranular, while crack propagation mode is either intergranular plus transgranular or entirely intergranular, dependent on test temperature.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

Monotonic and low cycle fatigue behaviour of 2024‐T3 aluminium alloy between room temperature and 300 °C for designing VAWT components

In the present study, the results of the monotonic tension tests and low cycle fatigue tests performed on aluminium alloy EN AW‐2024‐T3 under various operating temperatures are presented in order to assess the fatigue behaviour of the aluminium alloy under evaluated temperatures. Monotonic tests were performed to determine the influence of temperature on mechanical properties of the material. The aim of cyclic tests was to acquire the parameters required for Manson–Coffin equation in order to plot strain–fatigue life curves. Moreover, stress–strain behaviour of the alloy and the cyclic hardening behaviour were evaluated using Ramberg–Osgood equation. Finally, P_SWT‐damage parameters for each temperature have been calculated for further investigation of the effects of the temperature on fatigue life using acquired data while taking the account of mean stress effect into calculations. Variations in the experimental data due to various test temperatures are presented for both monotonic and cyclic tests.     

Low cycle fatigue performance of DP900 steel under cyclic shear paths

In this study, a sheet fatigue shear test device is designed and applied to the low-cycle fatigue testing of DP900 with varying strain amplitudes within the range of 0.5%–6.0%. The microstructure is analyzed by using electron backscatter diffraction, and fracture surfaces are examined via scanning electron microscopy. Results indicate that the material exhibits cyclic softening behavior after the first two cycles of hardening, with a stable softening rate and a high damage evolution rate related to loading amplitude. The variation of the hysteresis curve in the cyclic process is shown. Total plastic strain energy absorbed increases as loading amplitude decreases and it reaches the peak at approximately 1%. The life prediction model based on plastic strain energy density and strain amplitude is verified to be suitable for the cyclic shear path. The influence of microinhomogeneity on the distribution of stress and strain, especially the deformation of martensite, is closely related to the bi-linear region of fatigue life curve.