Microstructural-based physics of failure models to predict fatigue reliability

In spite of the tough pitch copper material is used for the many kinds of conductors of electrical machining devices, the fatigue phenomenon of the tough pitch copper material does not still clarify under variable stresses considering to a service loading. Then, constant stress amplitude fatigue tests were carried out for the tough pitch copper sheet material and then the fatigue life under variable stresses were predicted by Miner's law using constant stress tests results as shown S-Ndiagram. The program fatigue tests consist of two steps and multifold stress levels were carried out for tough pitch copper sheet specimens compared with the fatigue lives predicted by using Miner's law. As it was clear that the fatigue lives predicted by using Miner's law were shorter than the experimental program fatigue lives under variable stresses in service loading, so new practical diagram modified from original S-N diagram was proposed. The fatigue lives predicted by using new S-N diagram coincide with experimental fatigue lives under variable stress consist of two or three step and multifold stress levels.

Structural engineering makes a giant stride forward with this symposium. This book represents an international sym­ posium held in Stockholm honoring Prof. W. Weibull. It drew participants from 21 countries with a total of 55 invited papers. There were 7 scientific sessions. Most of our studies in school revolved about deterministic happenings. Random loading becomes more and more important when we equate events in our world with physical and mathematical reasoning. Probabilistic failure model and stochastic fatigue crack growth play important roles in the safety of nuclear structures, random loading due to wind turbulence, earthquake spectra, offshore structural design, and aircraft design. The initial paper summarizes Prof. Weibull's life and ac­ complishments including a mention of Weibull distribution used in fatigue studies. The initial session deals with extreme value theory (EVT). The first paper reviewed applications of extreme value theory to material behavior and indicates the importance of the accompanying statistical theory. The next paper generalizes Weibull distribution in matrix form. The following papers proclaim (a) extreme value theory as com­ patible to random field theory, (b) incomplete samples can be transformed to a mixed-exponential survival for a more com­ prehensive Weibull distribution, (c) EVT in endurance testing of ball and roller bearings, (d) use of the Slepian model identi­ fying the behavior of Gaussian noise near or between its zero crossing, (e) plastic movement of SDOF elastic plastic oscillator subjected to stationary Gaussian process excitation, and (/) generalized Hermitian polynomial used in the pertur­ bation method for nonlinear random vibrations. The final paper reports on Weibull distribution in large earthquake modelling. Session 2 reports on fatigue crack growth. Beginning with an analysis of stochastic equation models of crack growth, it continues with stochastic models of fatigue crack growth and propagation, prediction of crack growth under spectrum loading employing a cycle-by-cycle technique and fatigue life distribution in a random loading sense with interacting failures. The final paper considers a new approach to fatigue crack propagation under random loading and the use of Monte Carlo simulation in correlating micro fracture process and fatigue crack propagation. This session indicates that more experimental work is required in crack propagation to reach the same level as crack initiation. Session 3 comprises a total of 13 papers and dwells upon probabilistic failure models. The initial paper proposes a generalized probabilistic model for the fatigue life and reliability prediction of a structure containing noninteracting cracks and employs Poisson random sets. The next group of papers focuses upon (a) structural reliability treated as a single stochastic model, (Jb) fatigue life and reliability estimates of mineral pipe lines using probability theory, (c) Weibull-based equation employed in predicting the failure of a stressed brittle material, (d) a preliminary suggestion that specimens failed in proof tests may be used to estimate the parameters of the reliability function for the survivors, and (e) brittle material design using three parametric Weibull distributions. The next set of papers considers ring-in-ring tests on strength of cladded glass using the three-parameter Weibull distribution, prob­ abilistic analysis of plastic plates utilizing yield-line theory plus lower bound reliability analysis of plastic plates evaluated by inclusion-exc lusion theory. The final set of papers ques­ tions the possibility of flaws in the present probabilistic models for unidirectional fibrous composites, strength rela­ tions for cracks in unidirectiona l long fiber composites employing Weibull distribution and a stochastic approach in studying the fracture and fatigue of concrete. Session 4 delves into probabilistic fracture mechanics. The initial paper estimates the probable failure of PWR pressure vessels employing Weibull distribution and updates the wellknown Marshall A(a) and B(a) functions. The final set of papers covers probabilistic assessment of structures with weld defects, probability of fracture in main coolant pipes of PWR, and statistical modelling of shaft predictions (as measured by Charpy impact curve) in the reference temperature of pressure vessel welds. The authors suggested that U.S. Nuclear Regulatory Guide 1.99 be updated to remove excessive conservatism.

A probabilistic fatigue life prediction method under random combined high and low cycle fatigue load history

Multi factor correction is optimized for fatigue life prediction and reliability evaluation of structural components. Based on the optimization of Bayesian theory, reliability evaluation is carried out to improve the efficiency of fatigue life prediction and reliability evaluation of structural components. The research results indicate that the crack propagation length increases with the increase in loading time. The average probability density of the modified method is 3.628, while the probability density of the traditional fracture mechanics model is 1.242. Based on the multi factor modified crack propagation prediction model, the predicted data accuracy exceeds the traditional fracture mechanics model. It is consistent with the experimental results. The crack propagation prediction model based on multi factor correction can ensure the accuracy of the prediction. The reliability of the model is evaluated. The average prediction accuracy of multiple sets of data is over 90%. This research method helps predict the fatigue life of structural components and evaluate reliability to ensure the safe operation of construction machinery.

Metal castings are often questioned for their service life and reliability due to a lot of uncertainties associated with the process. It is important to virtually analyze these aspects of a cast product before it actually put into service. This paper presents a new approach to predict the fatigue life and reliability of ductile iron castings through coupled simulations and experiments. In this work, fatigue specimens are considered as sample cast products which are produced using an optimized mold design for minimum porosity. Radiographic examination is done to observe the quality of cast specimens. Experimental load-controlled fatigue testing of selected specimens is done and compared with simulated fatigue lives in fe-safe (Dassault Systems UK Limited 2015). Reliability of cast specimens under fatigue is computed using stress-strength model by considering the variability in both stress and strength. A safe load-induced stress is estimated to obtain infinite life of ductile iron parts under consideration. Furthermore, the reliability models are developed by fitting probability distributions to reliability estimates and determining the distribution parameters. It is concluded that the mold design optimization using casting simulations can lead to nearly defect free castings which can serve for the similar fatigue lives as their sound counterparts. Moreover, the probability of survival of the cast components for an infinite life can be computed using the classical stress-strength reliability model based on which safe loading conditions can be determined for almost any engineering application.

A comparative analysis of accelerated methods for fatigue life and reliability prediction of machine parts under variable loading: Staevski, K. and Chankov, D. J. Mater. Sci. Technol. (Bulgaria) (1995) 3 (1), 30–39

An autofrettaged thick-walled pressure vessel with an external groove subjected to a pulsating internal pressure can have fatigue failures at the external groove root due to the combination of tensile autofrettage residual stress, operating stress, and stress concentration. To predict the fatigue life of the autofrettaged thick-walled pressure vessel with an external groove, the local strain approach was applied. The residual stress distribution due to autofrettage and the operating stress distribution due to internal pressure were determined using finite element analysis which resulted in theoretical stress concentration factors. To account for the mean stress effects on the fatigue life prediction of the pressure vessel, low-cycle fatigue behavior with several strain ratios was obtained using smooth axial specimens taken from the ASTM A723 thick-walled steel pressure vessel. Fatigue life predictions were made by incorporating the local strains determined from the linear rule and Neuber’s rule and the Morrow and SWT mean stress parameters determined from low-cycle fatigue tests. The predicted fatigue lives were within factors of 2 to 4, compared to simulated experimental fatigue lives based upon fatigue cracks of 2.5 mm in length. These procedures appear to be realistic for evaluating fatigue lives for this complex pressure vessel.

Additively manufactured 316L stainless steel structural components are increasingly utilized across industries, necessitating accurate fatigue reliability assessments. This study develops a comprehensive approach to evaluate the fatigue reliability of such components. First, the stress–life relationship under cyclic loading is analyzed, providing stress calculation formulas for various fatigue lifespans. The residual strength degradation across three fatigue life stages is quantified, yielding values of 512.96 MPa at 800 cycles (1000 fatigue life), 463.27 MPa at 2500 cycles (3000 fatigue life), and 412.26 MPa at 5000 cycles (6000 fatigue life). Next, the fatigue reliability at each stage is determined using the first-order second-moment method, with reliability values of 0.9999, 0.9997, and 0.9291, respectively. The overall fatigue life reliability is computed using a series system approach, resulting in a final reliability of 0.9291. The proposed methodology is practical and user-friendly, making it suitable for real-world engineering applications.

Durability prediction of coil spring through multibody-dynamics-based strain generation

Experimental and numerical investigation on fatigue performance of non-load-carrying fillet welded joints

Fatigue life prediction and failure mechanisms of composite materials are studied based on the fatigue modulus concept and experimental results. Single-stress level fatigue life is predicted using generalized fatigue modulus degradation model and resultant strain failure criterion. Cumulative damage models defined by fatigue modulus and resultant strains are derived as functions of fatigue cycle and applied stress. This approach can predict accurately the multi-stress level fatigue life in addition to single-stress level fatigue life of composite materials. Fatigue modulus is measured by a cyclic stress-displacement behavior and resultant displacements data. The prediction is also made by the fatigue modulus degradation model and fatigue life prediction results. The comparison shows that the predicted values lie within the experimental scatter band. The relationship between physical damage accumulation and material property (such as fatigue modulus) degradation is induced qualitatively through fractograph...

In this study, a model for probabilistic fatigue life that is based on the Zhurkov model is suggested using stochastically and statistically estimated lethargy coefficients. The fatigue life model was derived using the Zhurkov life model, and it was deterministically validated using real fatigue life data as a reference. For this process, firstly, a lethargy coefficient that is related to the failure of materials must be obtained with rupture time and stress from a quasi-static tensile test. These experiments are performed using HS40R steel. However, the lethargy coefficient has discrepancies due to the inherent uncertainty and the variation of material properties in the experiments. The Bayesian approach was employed for estimating the lethargy coefficient of the fatigue life model using the Markov Chain Monte Carlo (MCMC) sampling method and considering its uncertainties. Once the samples are obtained, one can proceed to the posterior predictive inference of the fatigue life. This life model was shown to be reasonable when compared with experimental fatigue life data. As a result, predicted fatigue life was observed to significantly decrease in accordance with increasing relative stress conditions.Highlights Zhurkov fatigue life model is deterministically validated with experiments. Prediction of the S-N curve using Zhurkov fatigue model and lethargy coefficients. Lethargy coefficients of Zhurkov fatigue model are estimated by Bayesian updating. Bayesian updating is useful for quantifying the uncertainty of unknown parameters.

In this study, we propose a novel cumulative-damage model based on continuum damage mechanics under situations where the mechanical components are subjected to variable loading. The equivalent completely reversed stress amplitude accounting for the effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths on high-cycle fatigue under variable loading is elaborated. The effect of mean stress, stress gradients, loading history, and additional hardening behavior related to nonproportional loading paths is considered by averaging the superior limit of the intrinsic damage dissipation work in the critical domain. We developed a novel cumulative-damage model by introducing the equivalent completely reversed stress amplitude into the damage-evolution model. For better comparison, existing cumulative-damage models, including the Palmgren–Miner law, corrected Palmgren–Miner law, Morrow’s plastic work interaction rule, and Wang’s rule, were employed to predict the fatigue life under variable loading. The proposed model performed better, considering the error scatter band obtained by plotting the predicted and experimental fatigue life on the same coordinate system. The model precisely predicts fatigue life under variable loading and easily identifies its material constants.

In this work, a fuzzy design optimization-based fatigue reliability analysis technique is addressed to obtain the optimal fatigue reliability of the structures with random parameters under the minimum fluctuation of fatigue life. The challenge of the problem lies in uncertainties involved from both structural parameters and loads, which renders the fatigue reliability becoming the primary problem to be considered in evaluating structural performance. In order to obtain the optimal fatigue reliability, the optimal mathematical models aiming at the mass and fatigue life of welding robots are constructed respectively, and the genetic particle swarm optimization algorithm and radial basis function neural network (GAPSO-RBFNN) based surrogate model is then presented. Moreover, fuzzy constraints are introduced into the optimization model, and the improved non-dominated sorting genetic algorithm (INSGA-III) optimization strategy is proposed to solve it, which can effectively reduce the workload by increasing the diversity of Pareto solutions during the iterative process. Finally, the optimized structure combined with numerical simulation method is adopted to analyze the fatigue reliability. After analysis steps are given in detail, a practical welding robot structure is presented to demonstrate the validity and reasonability of the developed methodology.

A Walker-based mean strain correction model of low-cycle fatigue (LFC) life prediction is proposed for high loaded parts. The model is based on a function depending on the strain range and strain ratio controlled in the strain-controlled LCF test of fatigue specimens and a constant reflecting the material sensitivity to strain ratio. The independence from the stress cycle parameters which can change during the strain-controlled LCF test is an obvious advantage of the model. The model was verified using the results of strain-controlled LCF tests of smooth titanium alloy Ti-6A1-4V ELI and iron-based alloy specimens conducted at room temperature. The proposed model was compared to the Smith - Watson - Topper and Walker models that take into account the mean stress effect. The proposed model provided the best prediction accuracy for titanium alloy. For Iron-based alloys the results obtained by the Walker model and the model proposed are close to each other. A simplified model based on the analysis of model parameters tailing into account the mean strain effect for predicting fatigue life of aeroengine critical parts is developed using a limited amount of experimental data when only the results of Rε = 0 tests are known. A comparison of the predicted life with the number of cycles to failure showed satisfactory results of fatigue life prediction for Ti-6A1-4V ELI and Iron-based alloys specimens.