Probabilistic sensitivity analysis in life-prediction of an α+β titanium alloy

Probabilistic sensitivities using the score function method are developed for a lifing analysis of an α+β titanium alloy in a round bar under axial fatigue load. Sensitivities with respect to the statistical inputs of the crack initiation size ( a ), and Paris crack growth intercept ( C ) and exponent ( m ) are developed with consideration of the correlation between C and m . The sensitivities are obtained using a single Monte Carlo sampling analysis and do not involve finite difference approximations. The sensitivities indicate the importance of the random variable input parameters on the mean life and standard deviation of life and can be used as a basis for determining constructive data collection efforts. For this example, the crack growth intercept ( C ) is the dominant variable that affects mean-life and standard deviation of life, indicating that improved confidence in the results can be obtained most efficiently by improving the statistical characterization of C .     

Probabilistic sensitivity analysis of dwell‐fatigue crack initiation life for a two‐grain microstructural model

Crack initiation in Ti‐6242 has been observed to occur in a grain with a hard orientation for basal slip neighbouring a grain with a soft orientation. Because there is significant variability in microstructural features and crack initiation life, it is useful to explore the effects of the variability of the microstructural components through a probabilistic sensitivity analysis. In this paper, a probabilistic crystal plasticity finite element model of a hard−soft grain combination (2 grains) was exercised considering the Schmid factor of the soft grain, the misorientation angle between the two grains, and the soft grain size as random variables. A probabilistic sensitivity analysis of the time‐to‐crack initiation was then employed in order to ascertain the relative importance of the random variables. The results indicate that the variance in the Schmid factor accounts for the majority of the variance in the time‐to‐crack initiation. A local sensitivity analysis found that larger Schmid factors result in smaller mean life and larger variance. The neighbouring soft grain size was found to be less important than the Schmid factor and misorientation angle.     

Variation mode and effect analysis: an application to fatigue life prediction

We present an application of the probabilistic branch of variation mode and effect analysis (VMEA) implemented as a first‐order, second‐moment reliability method. First order means that the failure function is approximated to be linear around the nominal values with respect to the main influencing variables, while second moment means that only means and variances are taken into account in the statistical procedure. We study the fatigue life of a jet engine component and aim at a safety margin that takes all sources of prediction uncertainties into account. Scatter is defined as random variation due to natural causes, such as non‐homogeneous material, geometry variation within tolerances, load variation in usage, and other uncontrolled variations. Other uncertainties are unknown systematic errors, such as model errors in the numerical calculation of fatigue life, statistical errors in estimates of parameters, and unknown usage profile. By treating also systematic errors as random variables, the whole safety margin problem is put into a common framework of second‐order statistics. The final estimated prediction variance of the logarithmic life is obtained by summing the variance contributions of all sources of scatter and other uncertainties, and it represents the total uncertainty in the life prediction. Motivated by the central limit theorem, this logarithmic life random variable may be regarded as normally distributed, which gives possibilities to calculate relevant safety margins. Copyright © 2008 John Wiley & Sons, Ltd.     

On the mechanisms of fatigue facet nucleation in titanium alloys

A crystal plasticity model for near‐alpha hcp titanium alloys embodying a quasi‐cleavage failure mechanism is presented and employed to investigate the conditions necessary in order for facet nucleation to occur in cold‐dwell fatigue. A model polycrystal is used to investigate the effects of combinations of crystallographic orientations (and in particular, a rogue grain combination), the essential role of (cold) creep during hold periods in the loading cycle and the more damaging effect of a load hold rather than a strain hold in facet nucleation. Direct comparisons of model predictions are made with dwell fatigue test results. More generally, the crystal model for faceting is found to be consistent with a range of experimental observations.     

On the giga cycle fatigue behaviour of two-phase (α2+γ) TiAl alloy

Fatigue crack initiation behaviour is investigated at room temperature in the (α₂-Ti₃Al and γ-TiAl) alloy. High cycle fatigue tests ranging up to 10¹⁰ cycles are carried out on the powder metallurgy (P/M) bar specimens under different loading conditions with a stress ratio of R=0.1 and R=0.5. Microstructural characterization and fracture surface analysis are also investigated by optical (OM) and scanning electron microscopy (SEM). Ti–Al alloy studied here shows two phases in microstructure (nearly refined lamellar thickness) composed of α₂-Ti₃Al and γ-TiAl (hereafter called γ+α₂ alloys) and fracture mechanism is explained with different plastic incompatibilities between the two phases.     

Damage mechanics based probabilistic high‐cycle fatigue life prediction for Al 2024‐T3 using non‐intrusive polynomial chaos

This paper proposes a low‐cost method for predicting probabilistic high‐cycle fatigue life for Al 2024‐T3 based on continuum damage mechanics and non‐intrusive polynomial chaos (NIPC). To randomize Lemaitre's two scale fatigue damage model, parameters S and s are regarded as random variables. Based on small sample of test life, inverse analysis is performed to obtain samples of the two parameters. Statistic characteristics of the two parameters are calculated analytically through coefficients of NIPC. Fatigue test of aluminum alloy 2024‐T3 standard coupon and plate with hole under different spectrum loading shows that the proposed method is effective.     

金属材料和结构的疲劳寿命预测概率模型及应用研究进展

疲劳过程的不确定性以及影响疲劳寿命的不确定性因素较多,导致疲劳寿命的分散性难以预测,在疲劳寿命预测模型中采用统计学和概率论的概念和方法是描述疲劳过程不确定性和疲劳寿命分散性的一种重要手段。本文针对疲劳寿命预测概率模型进行综述,总结和介绍了疲劳寿命经验公式和参数的随机化模型、表征疲劳寿命离散性的统计模型、基于材料微结构和疲劳物理机制的疲劳寿命预测概率模型以及研究广布疲劳损伤的概率模型,并对金属材料与结构的疲劳寿命预测方法进行了展望。     

Biodegradable behaviour and fatigue life of ZEK100 magnesium alloy in simulated physiological environment

The fatigue life of ZEK100 magnesium alloy in the phosphate buffered solution for various immersion intervals was investigated by experiments and theoretical predictions. The biodegradable behaviours of ZEK100 magnesium alloy were also studied. Microstructure observation showed that the corrosion behaviours were characterized by pitting corrosion. The corrosion rate decreased a lot in the initial 7 d and then almost stayed unchanged. After 28 d immersion, the elastic modulus almost kept stable, while the yield strength and the ultimate strength decreased a lot, which indicated that corrosion had important effects on the tensile mechanical properties. It showed that the fatigue life of the samples under the same stress conditions decreased with increasing immersion time under the asymmetric stress‐controlled cyclic loading. Considering the effect of corrosion on the material failure, a modified fatigue life model was proposed for magnesium alloy under corrosion.     

Uniaxial ratcheting behavior and fatigue life models of commercial pure titanium

The uniaxial fatigue and ratcheting behavior of commercial pure titanium (CP‐Ti) was investigated by asymmetric cyclic stress‐controlled experiments at room temperature. The effects of mean stress, stress amplitude, stress ratio, and peak stress on ratcheting behavior and fatigue life were discussed. It was found that increasing mean stress, stress amplitude, and peak stress or decreasing stress ratio reduced fatigue life and promoted ratcheting behavior. The applicability of different fatigue life models was analyzed, and a new stress ratio‐related failure model was proposed based on the exponential increase of fatigue life with stress ratio. Among all the models investigated in this study, the exponential stress ratio‐related model has more advantage in fatigue life predictions for CP‐Ti under ratcheting‐fatigue interaction.     

High temperature creep of modified α + β brasses

Good machinability and formability of technical brasses α + β have to be preserved when alternative modifications are developed instead of alloying with toxic lead. Several model brasses of this type, which exhibit satisfactory machinability, are creep tested at 780 °C to compare their high temperature formability. The observed stationary creep rate and local ductility may highly differ for various alloy types. To characterize the impact of individual additions, superposition laws for the respective quantities are proposed and applied to the measured values. The strong effect of even small amounts of some additions on the creep rate and the boundary component of ductility is suggested to be due to segregation phenomenon. Rigid particles, such as phosphides, enhance significantly the creep resistance of the material, though restrict the macroscopic stability of plastic flow. On the other hand, the contribution of liquid particles to the creep damage may be effectively obstructed by phosphides.     

Investigation of α platelet boundaries in a near-α titanium alloy

Transmission electron microscopy (TEM) of a bimodal near-α titanium alloy revealed the existence of retained β phase layers and silicide precipitates at the α platelet boundaries inside transformed β grains. The β to α phase transformation accompanied by the precipitation of silicide resulted in the formation of a large number of dislocations at α platelet boundaries. Orientation relationships between silicide, β phase and α phase were also identified. However high-resolution TEM (HRTEM) revealed crystal mismatches between these phases generating high strains at α platelet boundaries. The strengthening effects of the platelet boundaries are discussed in terms of dislocations slip across the boundaries. The mechanism that governs the β to α phase transformation is also discussed.     

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.     

Prediction of short fatigue crack growth of Ti‐6Al‐4V

It is observed that the short fatigue cracks grow faster than long fatigue cracks at the same nominal driving force and even grow at stress intensity factor range below the threshold value for long cracks in titanium alloy materials. The anomalous behaviours of short cracks have a great influence on the accurate fatigue life prediction of submersible pressure hulls. Based on the unified fatigue life prediction method developed in the authors' group, a modified model for short crack propagation is proposed in this paper. The elastic–plastic behaviour of short cracks in the vicinity of crack tips is considered in the modified model. The model shows that the rate of crack propagation for very short cracks is determined by the range of cyclic stress rather than the range of the stress intensity factor controlling the long crack propagation and the threshold stress intensity factor range of short fatigue cracks is a function of crack length. The proposed model is used to calculate short crack propagation rate of different titanium alloys. The short crack propagation rates of Ti‐6Al‐4V and its corresponding fatigue lives are predicted under different stress ratios and different stress levels. The model is validated by comparing model prediction results with the experimental data.     

Multiaxial low cycle fatigue behavior and life prediction of CP-Ti under non-proportional stress-controlled mode

Multiaxial low cycle fatigue tests under non-proportional stress (NPSS) controlled mode were performed on commercial pure titanium (CP-Ti). Strain responses of axial and torsional channels under highly applied stress amplitudes show an initial hardening phenomenon. Non-proportional hardening coefficient of CP-Ti is independent of the controlled mode. The critical plane of CP-Ti under NPSS controlled mode is aligned with the maximum principal stress plane proved by optical microscopy observation. Optimized FSM model and KBM-PM model with mean axial and torsional strain are established. These models are further integrated into equations related to multiaxial stress ratio with high accuracy of life prediction for CP-Ti under NPSS controlled mode.     

Stress‐life prediction of 25°C polypropylene materials based on calibration of Zhurkov fatigue life model

In this study, to evaluate the chemical and mechanical properties of polypropylene (PP), activation‐energy and tensile tests were performed at room temperature (25°C) on pure PP and PP reinforced with glass fibre (GF). To improve the prediction accuracy of the fatigue life, three models based on the calibration of the Zhurkov model were proposed: a regression model, modified strain‐rate model and lethargy coefficient‐based model. Based on the experimental data analysis and statistical assessment results, we proposed a modified strain‐rate model that satisfies the dependency of the physical parameters and is congruent with the predicted fatigue life data. The experimental data and modified strain‐rate model were compared with the direct cyclic analysis results. The tendency of the frequency factor as a correction parameter in the modified strain‐rate model corresponded to the experimental activation energy and the increasing GF content.     

The effect of porosity on the fatigue life of cast aluminium‐silicon alloys*

Fatigue strength optimization of cast aluminium alloys requires an understanding of the role of micropores resulting from the casting process. High cycle fatigue tests conducted on cast A356‐T6 show that the pore size and proximity to the specimen surface significantly influence fatigue crack initiation. This is supported by finite element analyses (both elastic and elastic–plastic) which demonstrate that high stress/strain concentration is induced by pores which are both large and near to the specimen surface. A new pore‐sensitive model based on a modified stress‐life approach has been developed which correlates fatigue life with the size of the failure‐dominant pore. The model prediction is in good agreement with experimental data.     

Short fatigue cracks in intermetallic γ‐TiAl‐alloys

Fatigue crack growth at room temperature and its relation to the local microstructure is studied for four different γ‐TiAl‐alloys with microstructures ranging from coarse and fully lamellar to fine and partly lamellar. It is shown that the number of cycles to failure depends strongly on the efficiency of the first barrier to crack extension, as crack growth rates may increase rapidly once this barrier has been breached by a specific crack. The crack extension behaviour for two typical barriers (colony boundary and twin boundary) is studied using high‐resolution optical and scanning electron microscopy.     

Cumulative fatigue damage and life prediction of elastomeric components

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.     

Multiaxial fatigue life prediction method in the ground vehicle industry

The extensive progress which has been made in the multiaxial fatigue area over the past 5 to 10 years has allowed wider application of the multiaxial fatigue method in component durability design in the ground vehicle industry. The method adopts the long established local strain–life approach and includes several new features. (1) A three-dimensional cyclic stress–strain model, used to simulate the elastic–plastic material behavior under complicated loadings. (2) The critical plane approach, which requires the fatigue analysis to be performed on various potential failure planes before determining the lowest fatigue life. (3) A biaxial damage criterion, to better quantify fatigue damage under various loading conditions. (4) A multiaxial Neuber equivalencing technique, used to estimate, from the elastic finite element stress results, the multiaxial stress and strain history of plastically deformed notch areas. This paper examines the application of the above features to the fatigue analyses of three generic service/test histories: a constant amplitude (baseline) test history, a history directly recorded by strain gages mounted on the critical location of a structural component, and a loading history recorded in multichannels for a complex structure.     

Mean stress and ratcheting corrections in fatigue life prediction of metals

Ratcheting occurs easily because of the presence of mean stress during the stress‐control fatigue of engineering components. For ductility exhaustion dominated fatigue failure, a new fatigue life prediction model is developed by introducing the mean ratcheting strain rate to incorporate the effects of ratcheting and mean stress on fatigue life. The prediction accuracy of the proposed model was compared with that of the generalised damage parameter, Xia–Kujawski–Ellyin, Walker and Goswami models. Specifically, the model predictions and tested lives were compared using nine sets of experimental data from the literature. In the statistical analysis of these five models, the proposed model provides the highest accuracy and robust life predictions with the lowest model prediction errors.