Application of a material fatigue damage model in 4PB tests

The fatigue property of an asphalt mix is an important issue in pavement design. This property is often determined with the aid of a four-point bending (4PB) test in controlled deflection mode. The fatigue property is related to the decrease in the calculated complex stiffness modulus, however, due to the non- homogenous stress and strain field in the beam, the measured response does not represent the stiffness modulus of the material but a weighted stiffness value. For a correct interpretation, a fatigue damage material model like the Asphalt Concrete Pavement-Fatigue model is needed. After integration, the calculated and measured responses are compared. By varying the model parameters, an excellent comparison between the two responses is obtained up to a certain number of cycles. This number of cycles is denoted as the fatigue life N _PH . The accumulated dissipated energy at the surface of the beam in the midsection can be expressed as a constant times the fatigue life N _PH to the power z and also as a constant times the product of the fatigue life N _PH and the initial dissipated energy in the first cycle. Using these two findings, a Wöhler curve was established similar to the one directly based on the strain amplitudes and fatigue life data.     

Corrosion fatigue behaviour and microstructural characterisation of G20Mn5QT cast steel in 3.5‐wt% NaCl solution

Corrosion fatigue behaviour and microstructural characterisation of G20Mn5QT cast steel are investigated in simulated seawater. Fractography is performed by using scanning electron microscopy (SEM). The macroscale fracture surface and microstructure of the failed specimen are acquired including the crack initiation, crack propagation, and pitting evolution. The maximum cyclic stress (S) versus number of cycles to failure (N) curves is derived by three‐parameter fatigue curve method. Fatigue life is predominantly controlled by the corrosion pitting‐induced crack initiation when tested in simulated seawater at lower stress levels. As the maximum cyclic stress is less than 185 MPa, the chloride ion erosion is the main influence factor, which affects the fatigue failure of the G20Mn5QT cast steel in simulated seawater.     

Cumulative nonlinearity as a parameter to quantify mechanical fatigue

The cumulative nonlinearity (Q_f) is proposed as a new parameter to quantify mechanical fatigue. The parameter Q_f represents the (cycle number) integral of the ratio of the third harmonic to the fundamental one (I_3/1), obtained via Fourier transform of the stress (torque), normalized by the square of the strain amplitude (γ₀). The validation is performed on different polymers: polystyrene (PS) with different molecular weights, styrene‐acrylonitrile (SAN), polymethylmethacrylate (PMMA), and polytertbuthylmethacrylate (PtBMA) under strain controlled fatigue tests in a torsion rectangular set‐up. A power‐law correlation between the number of cycles to failure (N_f) and the cumulative nonlinearity was found for N_f > 1000 cycles, and the results were compared with well‐established failure criteria such as the cumulative stress and the dissipated energy density. It was found that the cumulative nonlinearity has superior prediction ability since it can quantify material changes during a test.     

Comparison of fatigue failure criterion in flexural fatigue test

This study compares traditional stiffness and energy based fatigue failure criteria with the fatigue failure criterion based on the viscoelastic continuum damage (VECD) approach. In traditional approach, fatigue failure is defined as the number of cycles at which the stiffness of a material reduces by 50% (N_f50). In energy based approach, fatigue failure is defined by the number of cycles at the maximum energy ratio or Rowe’s maximum stiffness defined by stiffness multiplied by the corresponding number of the cycle (E * N). In VECD approach, fatigue failure is defined by the number of loading cycles at the inflection point of the normalized pseudostiffness (C) versus damage variable (S) curve. It is shown that a correlation exits between traditional criteria and VECD criteria. It is shown that maximum energy ratio or Rowe’s maximum stiffness based fatigue life is higher than the traditional fatigue life (N_f50). This indicates the traditional approach is conservative. A strong correlation of fatigue was observed between the VECD fatigue criterion and energy ratio based fatigue criteria. However, the fatigue life by VECD approach is always less than the fatigue life by energy ratio or Rowe’s maximum stiffness.     

THE ENGINEERING FATIGUE PROPERTIES OF WROUGHT COPPER*†

The paper presents a comprehensive review, supplemented by original data, of the engineering fatigue behaviour of copper. Variations in manufacturing route and softening treatments are shown to have little effect on the fatigue of annealed copper but the high cycle fatigue strength is increased by cold work. The high strain fatigue behaviour is defined in terms of the plastic strain range and the cyclic stress-strain characteristics are documented. Fatigue behaviour in bending and torsion is defined by data and related to that in tension by simple design rules. Notches are found to reduce the laboratory measured fatigue strength of copper by ～ 30% and the effect of surface finish, surface distortion and surface residual stress is defined in the literature. Fatigue crack growth is defined in terms of stress intensity factor range ΔK by an upperbound law and, together with the conditions for non-growth (ΔK₀), shown to relate to the equivalent conditions for steels via the ratio of the respective elastic moduli. The effect of environment on the fatigue of copper has received scant attention in the literature, such results as exist suggesting little if any reduction in strength to be brought about by gaseous or aqueous environments. The most dramatic change is the improvement of about an order of magnitude which results when tests in vacuum are compared with equivalent tests in air. Results of fatigue tests on copper in ammoniacal environments are conspicuously absent from the literature. As the test temperature is reduced below room temperature there is a predictable increase in high cycle fatigue strength, a reduction in fatigue strength occurring above room temperature. High strain fatigue test results presented in terms of plastic strain range appear insensitive to temperature although at very low strain rates and high temperatures a reduction in fatigue strength occurs. A linear life fraction cumulative damage creep-fatigue law appears sometimes to be non-conservative but much more testing is needed to evaluate fatigue damage summation laws generally for copper. Numerical data are given in support of all the aspects of the engineering fatigue behaviour reviewed in the paper.     

Driving forces for localized corrosion‐to‐fatigue crack transition in Al–Zn–Mg–Cu

Research on fatigue crack formation from a corroded 7075‐T651 surface provides insight into the governing mechanical driving forces at microstructure‐scale lengths that are intermediate between safe life and damage tolerant feature sizes. Crack surface marker‐bands accurately quantify cycles (N_i) to form a 10–20 μm fatigue crack emanating from both an isolated pit perimeter and EXCO corroded surface. The N_i decreases with increasing‐applied stress. Fatigue crack formation involves a complex interaction of elastic stress concentration due to three‐dimensional pit macro‐topography coupled with local micro‐topographic plastic strain concentration, further enhanced by microstructure (particularly sub‐surface constituents). These driving force interactions lead to high variability in cycles to form a fatigue crack, but from an engineering perspective, a broadly corroded surface should contain an extreme group of features that are likely to drive the portion of life to form a crack to near 0. At low‐applied stresses, crack formation can constitute a significant portion of life, which is predicted by coupling macro‐pit and micro‐feature elastic–plastic stress/strain concentrations from finite element analysis with empirical low‐cycle fatigue life models. The presented experimental results provide a foundation to validate next‐generation crack formation models and prognosis methods.     

Damage evolution in a [±45]2S CFRP laminate under block loading conditions

Cyclic tests were conducted on [±45]_2S angle ply carbon–epoxy specimens using stress ratios, R (minimum/maximum stress) of 0.1 and −1.0. Damage was monitored by measuring progressive strain changes in the loading direction. The fatigue damage parameter was found to satisfactorily describe the evolution of damage throughout life, facilitating fatigue life prediction. Two distinct stages of damage evolution were identified. In Stage I, the fatigue damage parameter and the density of matrix micro-cracking rapidly increased to a level dependent upon the stress (Characteristic Damage State). This was followed by Stage II which was a long period (90% life) of gradual increase in damage, involving crack coalescence, debonding and delamination.On subjecting the specimens to two step block loading tests, synergistic interaction occurred whereby the total fatigue life was greater than that predicted by the summation of the individual blocks of cycles. The effect of crack density and crack closure appeared to play important roles in extending the fatigue life. For the low to high stress level block transition, more cycles were required to reach the Characteristic Damage State, whereas for the high to low sequence, the presence of a large number of cracks and matrix debris within them resulted in closure at the lower stress. Again, the number of cycles to failure increased.     

Characterization and modeling of stiffness reduction in SCS-6-Ti composites under low cycle fatigue loading

The stiffness reduction and evolution of microstructural damage of a unidirectional silicon carbide fiber reinforced titanium matrix composite under tension-tension fatigue were investigated. Tests were conducted under load control with maximum applied stresses ranging from 750 to 945 MPa. The crack density of the interfacial reaction layer and matrix, matrix crack length, and interfacial debonding length as a function of fatigue cycles and applied stress levels were measured. The results showed that the composites exhibited an initial regime with slow stiffness reduction, followed by a rapid stiffness drop regime and a plateau regime with minimal change in stiffness for the applied stress levels used in this study. The residual stiffness at N = 10⁶ cycles is independent of the applied stress levels, while the microstructural damage accumulation varied with the applied stresses. A partial crack shear-lag model was also developed to predict the residual stiffness as a function of fatigue damage accumulation. Analytical simulation indicated that the profile of the stiffness reduction curves was dominated by the matrix crack density, while the extent of stiffness reduction was dominated by the matrix crack length.     

Fatigue behaviour of borosilicate glass-ceramic matrix,nicalon (silicon carbide) fibre composites

Uniaxial fatigue damage analyses were performed on borosilicate glass-ceramic matrix, Nicalon (silicon carbide) fibre reinforced unidirectional composites. The fibre volume fraction varied from about 0.25 to 0.60. Load-controlled tension-tension fatigue tests (R ratio = 0.1) were conducted at room temperature and 540°C (1000°F). The fatigue life was found to decrease with increasing cyclic stress level and a power-law relationship of the form _app = _uts(2N _f)^b was established where _app is the applied maximum stress, _uts the monotonic tensile strength, N _f is the number of cycles to failure and b is the fatigue strength exponent. The fatigue damage evolution manifested itself as a decrease in stiffness of the composite with fatigue cycles. This stiffness drop was associated with matrix cracking followed by fibre-matrix debonding and fibre sliding breakage/pull-out, and final failure, respectively at 540°C. The damage evolution at room temperature was associated with degradation of the matrix followed by steady breakage of fibres with no debonding/pull-out, leading to eventual failure of the net section of the composite. In general, quantitative microscopic observations of debonded and pulled-out fibres showed a good correlation with the observed reduction in stiffness. A predictive model to interpret the drop in stiffness is presented and validated using experimental results from the current study.     

CUMULATIVE DAMAGE UNDER TWO LEVEL CYCLING: SOME THEORETICAL PREDICTIONS AND TEST DATA

Abstract— Predictions of a new cumulative damage theory established by Hashin and Rotem (HR) are compared with an extensive series of test data for two-level shear strain cycling and a double linear exponential damage rule, all given by Miller and Zachariah (MZ), demonstrating good agreement. While MZ requires determination of two parameters to assess crack development by fit to the two level test data the only testing parameter needed for HR is the fatigue lifetime N_e beyond which the fatigue limit occurs. This parameter has here been estimated on the basis of recent advances in understanding cyclic deformation.     

Compression fatigue performance of a fire resistant syntactic foam

Compression–compression fatigue test study of a fire resistant Eco-Core was conducted at two values of stress ratios (R = 10 and 5). Tests were conducted at S_min/S_o values of 0.9–0.6 for R = 10 and 0.95–0.8 for R = 5. Here S_min is the maximum compression stress and S_o is the compression strength. The study showed that Eco-Core has well defined failure modes and associated fatigue lives. The failure modes are: damage on-set; damage progression, and final failure. The damage on-set, propagation and final failure were characterized by 2%, 5% and 7% changes in compliance. The three failure modes were found to be same for both static and fatigue loadings. The endurance limit was found to be 0.72S_o, 0.75S_o and 0.76S_o, respectively for three failure modes for R = 10 and 0.81S_o, 0.82S_o and 0.82S_o, respectively for R = 5. The fatigue life is defined by a power law equation, S_min/S_o = A_oN^α. Constants of the equation were established for all three modes of failures and the two stress ratios. Finally, fatigue life was found to be less sensitive to R ratio when expressed in terms of stress range versus number of load cycles, which is similar to that of metallic materials.     

Damage evolution with growing cyclic creep and life prediction of MDYB‐3 PMMA

The influence of cyclic creep accumulation rate on the damage evolution of MDYB‐3 polymethyl methacrylate (PMMA) was experimentally investigated. Fatigue tests were carried out at four stress levels by stress control mode. The steady cyclic creep accumulation stage was observed occupying a substantial proportion of all specimens fatigue processes. Cyclic creep strain growth speed and relaxed modulus degradation rate were deduced as two important indicators for describing the damage evolution characteristics. Linear evolution relations of cyclic creep strain and modulus degradation with cycle times were retrieved from different terms of hysteresis loops. A preliminary model was proposed to be able to estimate the damage extent at different cyclic stress levels. The life predictions by the proposed model were compared with the experiment results and the classical power S–N model, which were demonstrated as a good estimation for the fatigue life. It is feasible to make durability evaluations by the characteristics of steady cyclic creep for multiaxis directed PMMA material.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

Fatigue damage of high performance concrete through a 2D mesoscopic lattice model

Based on high-resolution digital images of High Performance Concrete (HPC) microstructures, a two-dimensional mesoscopic lattice model which accounts for fatigue damage is proposed. Fatigue damage is introduced by considering the coupled effects of loading cycles and tensile strain on stiffness degradation of microstructural lattice elements under fatigue loading. The ultimate tensile strain is defined as the failure threshold value for microstructural lattice elements. Further, the effects of the lattice element properties (i.e. size and finite element type) and fatigue loading parameters (i.e. stress levels) on the damage mechanisms of the HPC microstructure are investigated and discussed. It is found that lattice truss elements 1 mm long are satisfactory, giving also their smaller computational requirements in comparison to beam counterparts, to investigate fatigue damage in the HPC microstructure. The numerical results of the present model are consistent with experimental observations.     

Effect of fatigue loading on stiffness degradation,energy dissipation,and matrix cracking damage of CFRP [±45]3S composite laminate

In this study, a concept of using experimental matrix crack density, residual stiffness, and energy dissipation as a comparative life monitoring tool for any arbitrary stacking sequence is proposed. First, IMA/M21 [±45]_3S carbon fibre‐reinforced polymer (CFRP) multidirectional (MD) laminates were fabricated by autoclaving technique. The static tension and compression tests were conducted to determine the fatigue stress levels. Then, constant amplitude tension–tension fatigue tests were carried out at two stress ratios (R = σ_min/σ_max) of 0.1 and 0.5. Three stress levels on the basis of cycles to failure (N_f) were chosen, ie, lower stress run‐out (LSR), lower stress fractured (LSF), and higher stress fractured (HSF). The LSF and LSR specimens primarily degraded due to matrix cracking that caused higher stiffness degradation and lower energy parameter, whereas HSF specimens having the least possibility of matrix crack growth showed lower stiffness degradation and higher energy parameter in a fibre‐dominated failure.     

Schadensakkumulationshypothesen zur Lebensdauervorhersage bei schwingender Beanspruchung. Teil 1. – Ein kritischer Überblick—

Cumulative Damage Theories for the Prediction of Fatigue Life . Most fatigue data are determined in constant stress amplitude tests. Therefore they are not applicable directly for the prediction of fatigue life under service loads: A ?cumulative damage theory”? is necessary. For about 350 program test series (blocked 8 stress level tests) the cumulative damage sum Σ n_i/N_i at failure is calculated. The mean value of this ratio is near 1,0 and thus agrees with Miner's rule; however the scatter is extremely high. Tests in bending give significantly lower damage sums than tests under axial loads. Furthermore about 130 random and flight by flight tests are analysed. Next, modified linear damage theories are discussed and it shows that only theories which take residual stresses into account will improve the accuracy. A relative fatigue life estimation is proposed, where one test under service conditions is the basis and Miner's rule is used as a transfer function.     

Schadensakkumulationshypothesen zur Lebensdauervorhersage bei schwingender Beanspruchung. Teil 2. – Ein kritischer Überblick—

Cumulative Damage Theories for the Prediction of Fatigue Life . Most fatigue data are determined in constant stress amplitude tests. Therefore they are not applicable directly for the prediction of fatigue life under service loads: A “cumulative damage theory” is necessary. For about 350 program test series (blocked 8 stress level tests) the cumulative damage sum Σ n_i/N_i at failure is calculated. The mean value of this ratio is near 1,0 and thus agrees with Miner's rule; however the scatter is extremely high. Tests in bending give significantly lower damage sums than tests under axial loads. Furthermore about 130 random and flight by flight tests are analysed. Next, modified linear damage theories are discussed and it shows that only theories which take residual stresses into account will improve the accuracy. A relative fatigue life estimation is proposed, where one test under service conditions is the basis and Miner's rule is used as a transfer function.     

Monitoring quasi-static and cyclic fatigue damage in fibre-reinforced plastics by Poisson’s ratio evolution

Even if the extent of fatigue damage in fibre-reinforced plastics is limited, it can already affect the elastic properties. Therefore, the damage initiation and propagation in composite structures is monitored very carefully. Beside the use of nondestructive testing methods (ultrasonic inspection, optical fibre sensing), the follow-up of the degradation of engineering properties such as the stiffness is a common approach.In this paper, it is proved that the Poisson’s ratio can be used as a sensitive indicator of fatigue damage in fibre-reinforced plastics. Static tests, quasi-static cyclic tests and fatigue tests were performed on [0°/90°]_2s glass/epoxy laminates, and longitudinal and transverse strain were measured continuously. The evolution of the Poisson’s ratio ν_xy versus time and longitudinal strain ε_xx is studied. As the transverse strain measurement is crucial to monitor the degradation of the Poisson’s ratio, three techniques were applied to measure the transverse strain (strain gauges, mechanical extensometer and external optical fibre sensor).Finally, the technique has been applied to a totally different material: a carbon fabric thermoplastic composite. The results show a very similar degradation of the Poisson’s ratio, although no stiffness degradation can be observed during fatigue loading of this material.It is concluded that the degradation of the Poisson’s ratio can be a valuable indicator of fatigue damage, in combination with the stiffness degradation.     

复合材料疲劳寿命预测

在疲劳载荷作用下,复合材料的弹性模量会随着载荷循环数的增加而不断下降,而材料中的内部损伤则不断增大。为此,本文提出复合材料的疲劳模量和累积应变的概念,并由此定义出三种预测复合材料疲劳寿命的疲劳损伤模型。文中应用这三种模型对单应力水平和多应力水平下的玻璃纤维增强环氧树脂复合材料的疲劳寿命进行了估算,并同实验结果进行了比较。     

A synthesis of the push‐pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss

The energy dissipated to the surroundings as heat in a unit volume of material per cycle, Q, was recently proposed as fatigue damage index, and it was successfully applied to rationalise fatigue data obtained by carrying out stress‐controlled and strain‐controlled fatigue tests on AISI 304 L stainless steel plain and hole specimens. In this paper, it is shown that the Q parameter is independent on thermal and mechanical boundary conditions occurring during experiments. After that, additional stress‐controlled fatigue tests on plain and notched specimens characterised by smaller notch tip radii than those tested previously have been performed. Present data have been compared with previous ones, and it was found that all available results can be synthesised in terms of the energy parameter Q into a unique scatter band, independently on the testing conditions (stress‐controlled or strain‐controlled) and on the specimens' geometry (plain or notched). About 100 data were included in the statistical analysis to characterise the energy‐based scatter band of the material. Finally, some limitations of applicability of the experimental technique adopted in the present paper are discussed.