Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

Stress–strain curves for steel-fiber reinforced concrete under compression

Steel-fiber reinforced concrete is increasingly being used day by day as a structural material. The complete stress–strain curve of the material in compression is needed for the analysis and design of structures. In this experimental investigation, an attempt has been made to generate the complete stress–strain curve experimentally for steel-fiber reinforced concrete for compressive strength ranging from 30 to 50 MPa. Round crimped fibers with three volume fractions of 0.5%, 0.75% and 1.0% (39, 59, and 78 kg/m³) and for two aspect ratios of 55 and 82 are considered. The effect of fiber addition to concrete on some of the major parameters namely peak stress, strain at peak stress, the toughness of concrete and the nature of the stress–strain curve is studied. A simple analytical model is proposed to generate both the ascending and descending portions of the stress–strain curve. There exists a good correlation between the experimental results and those calculated based on the analytical model. Equations are also proposed to quantify the effect of fiber on compressive strength, strain at peak stress and the toughness of concrete in terms of fiber reinforcing parameter.     

Fatigue behavior of an epoxy polymer subjected to cyclic shear loading

Strain-range-controlled fully reversed cyclic shearing fatigue tests have been performed on thin-walled tubular specimens made of an epoxy polymer. The engineering shear strain was measured by a non-contact real-time strain measurement and control system recently developed in our lab. The synchronized stress–strain data were recorded by the system for full lives of the specimens. Therefore evolutions of mechanical properties of the epoxy polymer during fatigue process could be analyzed based on the retrieved stress–strain data. It was found that life data of the shearing fatigue tests were well correlated with the uniaxial fatigue test data of the material by using the suggested stress-, strain- or strain-energy-density-based multiaxial fatigue criteria.     

A fatigue model for sensitive materials to non-proportional loadings

The present study proposes a novel fatigue model based on virtual strain energy. This model separates loading paths based on their non-proportionality where directly takes into account the loading in fatigue life prediction. The proposed fatigue model is expressed in two tension-based and shear-based equations for two tensile and shear cracking failure modes. The model was validated against several experimental datasets available in the literature. In addition, obtained results were compared to predicted lives through some well-known fatigue models comprising maximum shear strain, Smith–Watson–Topper, and Fatemi–Socie. The results were strongly correlated with the experimental data indicating accuracy of the model.     

Multiaxial creep–fatigue life prediction for cruciform specimen

This paper describes the high temperature multiaxial creep–fatigue life prediction for type 304 stainless steel. Finite element analyses were performed for determining the stress–strain state in the gage part of a cruciform specimen subjected to creep–fatigue loading under four strain waves at three principal strain ratios. Creep–fatigue lives of cruciform specimens were discussed in relation to the principal stress amplitude calculated by finite element analysis. Creep–fatigue damage was evaluated by linear damage rule and the suitability of three low cycle fatigue and three creep damage parameters was discussed.     

Fatigue life prediction under conditions where cyclic creep–fatigue interaction occurs

A stress-based model is proposed for correlating data and predicting fatigue life under conditions where cyclic creep–fatigue interaction occurs. This model is an extension of the Basquin’s stress–life relation and considers that both the fatigue strength coefficient and fatigue strength exponent b are sensitive to mean stress, both decreasing as an exponential function of the ratio of mean stress-to-stress amplitude. By combining the respective mean-stress functions with the Basquin relation, an equivalent stress–equivalent life relation is derived which is very similar to the original Basquin equation. Thus, the Basquin equation is a particular case of the present model for the case where mean stress is zero. The model depends on a single parameter λ, known as the mean stress sensitivity factor to cyclic loading, and depends on material and probably on test conditions as well. The mean stress sensitivity factor may be determined from experimental data at fixed ratio of mean stress-to-stress amplitude, other than zero, or by trial-and-error method to fit experimental mean-stress data onto the S–N curve due to zero mean stress. The model is tested on published creep–fatigue data of copper, steels and β-Ti-alloy and agreement is found to be very good.     

A method for modelling of fatigue life for rubbers and rubber isolators

A method for modelling fatigue life of rubbers and rubber isolators is presented in this paper. Firstly, a fatigue experiment is carried out for a rubber dumbbell cylindrical specimen and a rubber isolator. Based on the finite element analysis, the damage parameters including the strain energy density, the maximum principal Green–Lagrange strain and the effective stress are calculated and discussed. Secondly, three fatigue life prediction models are established by using the three damage parameters and using the relation between the measured fatigue life of a dumbbell cylindrical specimen and the computed value of the damage parameters. Thirdly, three proposed prediction models are used to investigate which one can be best used to predicting fatigue life of rubber isolators, taking a typical powertrain rubber isolator as studying example. The fatigue lives of the rubber isolator predicted by the three models are compared with the experimental life. The results demonstrate that the predicted fatigue lives of the rubber isolator using the three fatigue models agree well with the experimental fatigue life within a factor of four, and the model using the effective stress as the damage parameter can predict the fatigue life within a factor of two, which has the best accuracy among the three models.     

A method to develop a unified fatigue life prediction model for filled natural rubbers under uniaxial loads

Rubber components are widely used in many fields because of their superior elastic properties. Fatigue failures, commonly encountered in rubber components, however, remain a critical issue. In this study, the effect of strain ratio R on the fatigue life of filled natural rubbers used in automotive mounts is investigated experimentally and numerically. A uniaxial tension/compression fatigue experiment was conducted on dumb‐bell cylindrical rubber specimens subject to loads representing different R ratios. The experimental fatigue data are used to formulate two preliminary fatigue models based on peak strain and strain amplitude as the damage parameters. The deficiencies of these two models in predicting fatigue life over a wide range of R ratios are discussed, and an alternative life prediction model is proposed. The proposed model incorporates the effect of R ratio using an equivalent strain amplitude. It is shown that the proposed model could effectively predict fatigue life over a wide range of R ratios with an improved accuracy.     

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.     

Fatigue life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

Fatigue life prediction of composite laminates by FEA simulation method

This paper is to simulate the fatigue damage evolution in composite laminates and predict fatigue life of the laminates with different lay-up sequences on the basis of the fatigue characteristics of longitudinal, transverse and in-plane shear directions by finite element analysis (FEA) method. In FEA model, considering the scatter of the material’s properties, each element was assigned with different material’s properties. The stress analysis was carried out in MSC Patran/Nastran, and a modified Hashin’s failure criterion was applied to predict the failure of the elements. A new stiffness degradation model was proposed and applied in the simulation and then a strength degradation model was deduced, which is coupled with the presented stiffness degradation model. The reduced or discounted elastic constants were determined based on the failure mechanism of the laminates and the restrictive conditions of orthotropic property. The fatigue behavior and fatigue life of six kinds of E-glass/epoxy composite laminates with different lay-up sequences were experimentally studied, and the S–N curves and stiffness degradation models in longitudinal, transverse and in-plane shear direction were obtained. These fatigue data were adopted in the simulation to simulate fatigue behavior and estimate life of the laminates. The simulation results, including the fatigue life predicted and the residual stiffness, were coincident with the experimental results well except for the quasi-isotropic laminate for the lack of consideration of the out-of-plane fatigue character in the simulation.     

Mean stress/strain effect on fatigue behavior of an epoxy resin

Mean stress/strain effect on the fatigue life of an Epon 826/Epi-Cure Curing Agent 9551 epoxy system has been investigated by carrying out series uniaxial fatigue tests with four different mean strain ratios under strain-range-controlled mode. Quantitative analysis of the mechanical properties, such as mean stress relaxation, evolution of stress range and strain energy density, have been performed based on the stress–strain data recorded by a non-contact real-time strain measurement and control system. Mean stress/strain functions have been introduced into the equivalent damage parameters to include the mean stress/strain effect on the fatigue life of the epoxy polymer material. The procedure to characterize the mean stress/strain functions has been demonstrated and material constants were calibrated in the case of either stress, strain or energy approach, respectively. Good agreement can be seen between the predictions and the test data.     

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.     

A model for life prediction in low-cycle fatigue with hold time

In high-temperature and low-cycle fatigue, creep damage reduces fatigue life. In this investigation, a model for life prediction in low-cycle fatigue with hold time at tensile peak strain is suggested in the temperature region of 0.57T _m. This model is based on previously reported theories for creep cavitatation and we predict the creep-fatigue life. It is proposed that the fatigue life may be predicted in terms of plastic strain range, test temperature, hold time and other parameters. An equation for life prediction is given and checked using other investigators' experimental results with various hold times. The predicted creep-fatigue lives are in good agreement with those observed experimentally for 304 stainless steel, 316 stainless steel, CrMoV steel and 13CrMo44 steel.     

Fatigue life prediction of rubber-like materials under multiaxial loading using a continuum damage mechanics approach: Effects of two-blocks loading and R ratio

This contribution presents a continuum damage mechanics model for the high-cycle fatigue life prediction of rubber-like materials. The proposed model is an extension of that proposed by Wang et al. (2002) for multiaxial loadings. The damage strain energy release rate is first derived from a generalized Ogden strain energy density and then from the cracking energy density. A new multiaxial fatigue predictor is proposed and presented in its most general form with the aim of being applicable to all hyperelastic materials. The effects of variable amplitude and mean stretch are explicitly accounted for in the damage evolution law. The fatigue damage behavior of a carbon-filled styrene–butadiene rubber is experimentally investigated under tension, torsion and combined tension–torsion loadings both in constant and variable amplitudes, including the effects of different R ratios (i.e. different minimum and maximum stretches). The proposed model, which requires few damage parameters to be identified, is used to predict the number of cycles to failure and, a satisfactory agreement between predicted values and experimental data is clearly highlighted for the different loading paths.     

An analytical model for estimating deformation in laser forming

Laser forming of metal sheets offers the advantages of requiring no external forces and thus reduces cost and increases flexibility. This paper presents an analytical model to estimate the angle bent during the laser forming of a sheet. Plastic deformation is considered during both heating and cooling and is calculated based on a history-dependent incremental stress–strain relationship. On the basis of the proposed model with known temperature distributions, the bending angle induced by laser can be calculated. Comparison of the present model with experiment data is provided to demonstrate the accuracy of the present model under both TGM and BM.     

Research on low cycle fatigue properties of TA15 titanium alloy based on reliability theory

This paper introduces a method to determine the symmetric cycle fatigue limit of TA15 alloy at given confidence γ and survival probability P. It gives a general method to calculate the true survival probability of this material fatigue limit. The median and data of the LCF at γ = 95% and P = 99.9% are acquired after studying the LCF properties of aircraft construction material TA15 at the temperature of 25 and 250 °C. The strain–life curve, cyclic stress–strain curve and parameters of LCF are also achieved. These provide reference to analyze the reliability of aircraft construction and estimate the life.     

Axial stress–strain relationship for FRP confined circular and rectangular concrete columns

A general mathematical model is developed to describe the stress–strain (f_c–ε_c) relationship of FRP confined concrete. The relationship is applicable to both circular and rectangular columns, and accounts for the main parameters that influence the stress–strain response. These include the area and material properties of the external FRP wraps, the aspect ratio of rectangular column sections, the corner radius used for FRP application, and the volumetric ratio and configuration of internal transverse steel. The proposed model reproduced accurately experimental results of stress–strain or load–deformation response of circular and rectangular columns. In addition to its importance in evaluating the effect of FRP confinement on the ultimate axial strength of concrete columns, the developed f_c–ε_c relationship can be employed very efficiently and effectively for analyzing the response of FRP confined concrete under different types of load application.     

Influence of elevated temperatures on the cyclic deformation behaviour of the magnesium die-cast alloys AZ91D and MRI 230D

The magnesium alloys AZ91D and MRI 230D were investigated in form of die-cast specimens with a cast skin. The fine-grained microstructure consists of a dendritic magnesium solid solution and interdentritic precipitates. The cyclic deformation behaviour was characterised in stress-controlled load increase tests and constant amplitude tests by means of mechanical stress–strain hysteresis measurements at room temperature and at T = 150 °C. The MRI alloy leads to higher plastic strain amplitudes and nevertheless higher lifetimes for both temperatures. Load increase tests allow a reliable short-time estimation of the endurance limit under both, room and elevated temperatures. With the physically based fatigue life calculation method “PHYBAL” the lifetime of the magnesium alloys can be calculated on the basis of cyclic deformation data determined in one load increase test and two constant amplitude tests in excellent agreement with the conventionally determined S–N curve.     

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.