Constant Fatigue Life Diagram Research Articles

High-throughput experiments for rare-event rupture of materials

High-throughput experiments for rare-event rupture of materials

Accelerated fatigue life diagram characterization of CFRP

There are several ways to obtain the fatigue life behavior of composite materials, such as the application of classical theories or complex progressive damage models. Recently, constant life diagrams have demonstrated good effectiveness in predicting the fatigue life of CFRPs. Nevertheless, the large number of tests required, and the time necessary for the characterization, makes this method very expensive in terms of time and resources. The aim of this work is the evaluation of accelerated characterization techniques in addiction with statistical methods, to obtain constant fatigue life diagrams of CFRPs, with a reduced number of tests and a shorter characterization time. The results show that, combining universal and accelerated testing techniques with statistical methods, it is possible to obtain constant life diagram for the whole range of tension-tension, tension-compression, and compression-compression loading modes, with a reduced number of tests. Moreover, it is observed that, the accelerated characterization techniques show a fatigue life limit similar to the conventional ones.

Effect of fiber orientation distribution on constant fatigue life diagram of chopped carbon fiber chip-reinforced Sheet Molding Compound (SMC) composite

The material behavior of chopped carbon fiber chip-reinforced Sheet Molding Compound (SMC) composite is investigated under both quasi-static and cyclic fatigue loading conditions in the present study. Quasi-static tensile and compressive strength data is collected, followed by a series of fatigue tests under three different cyclic loading conditions, i.e., Tension-Tension (T-T), Compression-Compression (C-C), and Tension-Compression (T-C). The experimental results show a considerable amount of variation for each loading condition, which is found to be induced by the spatial distribution of fiber orientation within the tested specimens. An analytical approach is developed to correlate the fatigue performance of the SMC material with the local modulus, which is determined by the fiber orientation distribution. Additionally, the similar failure modes are observed under different loading conditions. Based on these findings, a new form of Constant Fatigue Life (CFL) diagram is established in which the impact of fiber orientation tensor to the fatigue behavior of SMC is considered. This developed CFL diagram is examined by comparing the measured fatigue performance with prediction where local fiber orientation distribution is quantified from microscopic images.

Numerical modelling and simulation of fatigue damage in carbon fibre reinforced plastics at different stress ratios

A numerical study of damage behaviour in unidirectional Carbon Fibre Reinforced Plastics (CFRP) laminates at different stress ratios is self implemented. The study is conducted using the commercial finite element software ABAQUS employing a layer-based fatigue damage model (FDM) that is capable to regard typical fatigue phenomena like stress redistributions and load sequence effects. A description of the FDM model is provided. At first, the model is calibrated according to experimental findings. Next, a constant fatigue life (CFL) diagram is constructed using actual test data to generate S-N curves for different stress ratios. Finally, different damage behaviour in CFRP laminates is predicted under quasi-static and cyclic loading conditions. The numerical results are discussed and compared to experimental data. The results obtained show the applicability and accuracy of the calibrated FDM.

Theory and Practical Procedure for Predicting S-N Curves at Various Stress Ratios

Predictive models in the past for stress ratio effect on S-N fatigue life have been subject to modifications since the 19th century. Many of them have been developed with limited experimental verifications or beyond the theoretical limit. Also, they have employed weak S-N curve models for the development, resulting in inefficiency in applications. There has been, also, a missing link in the development of predictive models between S-N curve behaviour and stress ratio effect. In this paper, theoretical analysis is presented and subsequently a practical procedure for predicting S-N curves at various stress ratio is proposed. The theoretical and experimental characteristics of the constant fatigue life (CFL) diagram were clarified for capability and limitations, and dependence of experimental fatigue behaviour. Mathematical relationships between linear CFL lines and fatigue damage parameters were successfully derived. As a result, the Kim and Zhang S-N curve model was successfully dovetailed with the linear CFL lines to predict S-N curves for the whole range of stress ratios. Theoretical predictions of fatigue life based on the mathematical relationships were verified with experimental data.

Prediction of S-N curves at various stress ratios for structural materials

Predictive models in the past for stress ratio effect on S-N fatigue life have been subject to modifications since the 19th century. Many of them have been developed with limited experimental verifications or beyond the theoretical limit. Also, they have employed weak S-N curve models for the development, resulting in inefficiency for applications. There has been, as such, a gap in the development of predictive models between S-N curve behaviour and stress ratio effect. In this paper, an efficient procedure is proposed for predicting S-N curves at different stress ratios. The characteristics of the constant fatigue life (CFL) diagram were clarified for theoretical capability and limitations, and dependence of experimental fatigue behaviour. The Kim and Zhang S-N curve model was dovetailed with the linear CFL lines of the four segments for predicting S-N curves for the whole range of stress ratios. With the benefits of damage parameters in the Kim and Zhang S-N curve model, analytical expressions for CFL as functions of two independent variables (i.e. applied stress and stress ratio) were derived for theoretical predictions. The theoretical predictions were found to be in agreement with the experimental results.

Fatigue modeling for carbon/epoxy unidirectional composites under various stress ratios considering size effects

Fatigue tests for unidirectional (UD) CFRP composite specimens of various sizes are conducted under different stress ratios. The results show that the specimen size has considerable influence on the transverse tension-tension fatigue performance of UD laminates. The underlying fatigue mechanisms are also investigated through SEM observations. Moreover, a fatigue life prediction method considering size effects is presented, and a good correlation is observed between the prediction and the test data. Finally, to allow for an evaluation of the effects of mean stress, constant fatigue life diagrams for 0°, 10°, and 90° UD composites are established based on four-segment anisomorphic model.

An integrated methodology for fatigue life prediction of carbon fiber-reinforced polymer matrix composites under constant and variable R-ratio loadings

The progress in the anisomorphic constant fatigue life (CFL) diagram approach for efficiently identifying the fatigue of carbon fiber-reinforced composites under constant waveform loading over the whole range of mean stress is reviewed. The asset of this approach is the concept of critical stress ratio. The anisomorphic formulation of CFL diagram is flexible enough not only to increase the number of segments to accommodate the transient change in sensitivity to mean stress, but also to take a generalized form that considers the effect of temperature as well as the effect of variability in fatigue life. The anisomorphic approach is shown to succeed in describing the asymmetric and nonlinear CFL diagrams for carbon fiber composites of different kinds. It is suggested that the classic procedure for prediction of spectrum loading fatigue life of composites using the Miner rule with the rain flow cycle counting method is powered by integrating with the anisomorphic CFL diagram approach.

Fatigue life of woven fabric carbon/epoxy laminates under alternating R-ratio loading along non-proportional path in the σm-σa plane

Influence of cyclic change in R-ratio on fatigue life of a carbon/epoxy composite is examined. For this purpose, two kinds of cyclic R-ratio loading tests are performed; one is under alternation of equal-life waveforms of different R-ratios, and the other is under alternation of unequal-life waveforms of different R-ratios. Experimental results show that fatigue failure under these alternating R-ratio loadings occurs in a life that is much shorter than the life predicted using the Miner rule with the cycle ratios for the two waveforms alternated, regardless of the pair of R-ratios. The alternation of equal-life waveforms of different R-ratios results in a larger accumulation of fatigue damage than any other kind of alternation of unequal-life waveforms of different R-ratios. These observations suggest that the alternation of equal-life waveforms of different R-ratios accompanies a significant interaction between the two waveforms alternated. An engineering methodology that consists of the Miner rule, the rain flow method and the anisomorphic constant fatigue life diagram approach is tested for the accuracy of prediction of fatigue life of the composite under the variable R-ratio loadings. It is demonstrated that the values of fatigue life for the alternating R-ratio loadings that are predicted using the proposed methodology are close to or even moderately shorter than the results of fatigue tests, regardless of the pair of R-ratios.

Temperature-dependent constant fatigue life diagram for press-formed short carbon fiber reinforced polyamide composite

Fatigue strength of a short carbon fiber reinforced polyamide (SCF/PA) composite fabricated using a press forming technique is examined. Unlike an injection-molded SCF/PA composite, this one exhibits in-plane isotropy as well as through-thickness uniformity. Fatigue tests on the SCF/PA composite are carried out at different stress ratios and temperatures, respectively. The fatigue test results show that the S–N relationship for the SCF/PA composite significantly depends on stress ratio, and fatigue degradation occurs most rapidly at the critical stress ratio, regardless of test temperature. The fatigue stress for a given life decreases with temperature. The reduction in fatigue strength with temperature correlates well with the reduction in static strength with temperature. Accordingly, the effect of temperature on fatigue life for each of different constant values of stress ratio can approximately be removed by normalizing fatigue stress with respect to static strength. The full shape of constant fatigue life diagram for the press-formed SCF/PA composite is identified for each of different test temperatures. It is shown to incline toward the direction of positive mean stress, regardless of test temperature. A difference in shape of CFL diagram between the press-formed and injection-molded composites is addressed. This study demonstrates that the anisomorphic constant life diagram approach with temperature as the parameter allows adequately predicting the constant fatigue life diagram and thus the S–N curve for the SCF/PA composite over the whole range of mean stress at any temperature in the tested range.

Effects of temperature and stress ratio on fatigue life of injection molded short carbon fiber-reinforced polyamide composite

The effects of temperature and stress ratio on fatigue life of short carbon fiber-reinforced polyamide-6 composite have been examined. Static tension and compression tests are carried out at room temperature (RT), 50°C and 70°C, respectively. For each of these temperatures, constant amplitude fatigue tests are performed at different stress ratios. Experimental results show that the temperature dependence of static strength can be described by a single equation of the Arrhenius type in the range higher than room temperature for each of tension and compression. The tensile strength turns to be smaller than the compressive strength at high temperature. The effect of temperature on fatigue life can approximately be removed by normalization of fatigue stress with respect to static strength, regardless of stress ratio. The asymmetry and nonlinearity in constant fatigue life diagram turns to be more significant with increasing temperature, and they can adequately be modeled by means of the anisomorphic constant fatigue life diagram. The temperature-dependent anisomorphic constant fatigue life diagram approach is also tested. It is demonstrated that this method allows adequately predicting the S-N curves for any stress ratios as well as the constant fatigue life curves for the whole range of mean stress at any temperature in a range that includes the test temperatures.

Effects of applied stress ratio on the fatigue behavior of additively manufactured porous biomaterials under compressive loading

Additively manufactured (AM) porous metallic biomaterials are considered promising candidates for bone substitution. In particular, AM porous titanium can be designed to exhibit mechanical properties similar to bone. There is some experimental data available in the literature regarding the fatigue behavior of AM porous titanium, but the effect of stress ratio on the fatigue behavior of those materials has not been studied before. In this paper, we study the effect of applied stress ratio on the compression-compression fatigue behavior of selective laser melted porous titanium (Ti-6Al-4V) based on the diamond unit cell. The porous titanium biomaterial is treated as a meta-material in the context of this work, meaning that R-ratios are calculated based on the applied stresses acting on a homogenized volume. After morphological characterization using micro computed tomography and quasi-static mechanical testing, the porous structures were tested under cyclic loading using five different stress ratios, i.e. R = 0.1, 0.3, 0.5, 0.7 and 0.8, to determine their S-N curves. Feature tracking algorithms were used for full-field deformation measurements during the fatigue tests. It was observed that the S-N curves of the porous structures shift upwards as the stress ratio increases. The stress amplitude was the most important factor determining the fatigue life. Constant fatigue life diagrams were constructed and compared with similar diagrams for bulk Ti-6Al-4V. Contrary to the bulk material, there was limited dependency of the constant life diagrams to mean stress. The notches present in the AM biomaterials were the sites of crack initiation. This observation and other evidence suggest that the notches created by the AM process cause the insensitivity of the fatigue life diagrams to mean stress. Feature tracking algorithms visualized the deformation during fatigue tests and demonstrated the root cause of inclined (45°) planes of specimen failure. In conclusion, the R-ratio behavior of AM porous biomaterials is both quantitatively and qualitatively different from that of bulk materials.

短繊維強化ナイロン複合材料の疲労寿命とその応力比依存性

The static and fatigue behaviors of discontinuous carbon fiber-reinforced polyamide (DCF/PA) composite have been examined. Static tension and compression tests are first performed at different temperatures (RT, 70°C and 130°C) to quantify the temperature dependence of basic mechanical properties of the composite. Then, constant amplitude fatigue tests are carried out for different stress ratios (0.1, χ, -1, and 10) at different temperatures (RT, 70°C and 130°C), respectively. The fatigue test results demonstrate that the S-N relationship of the discontinuous fiber composite significantly depends on stress ratio, and the fatigue degradation occurs most rapidly at the critical stress ratio in line with the observations made thus far for continuous fiber composites. Finally, the anisomorphic constant fatigue life diagram approach developed for continuous carbon fiber composites is applied to the DCF/PA composite, and it is proved that this method can successfully be used to predict the fatigue life of the discontinuous carbon fiber composite at different stress ratios.

Anisomorphic constant fatigue life diagrams of constant probability of failure and prediction of P–S–N curves for unidirectional carbon/epoxy laminates

The effect of stress ratio on statistical distribution of fatigue life of a unidirectional carbon/epoxy composite has been examined. Furthermore, a method for efficiently predicting a family of S–N curves with probability of failure as the parameter for any stress ratio of constant amplitude loading has been developed. For this purpose, fatigue life data are first collected at each of different stress levels for tension–tension (TT), tension–compression (TC) and compression–compression (CC) fatigue loadings, respectively. The experimental results show that the scatter in fatigue life tends to become larger in order of TT, TC and CC loading. Lognormal distribution is used to quantify the statistics of the static tensile and compressive strength data and the fatigue life data for each of different stress levels and stress ratios. It is found that lognormal distribution is applicable approximately not only to the static strength data in tension and compression, but also to the fatigue life data for each of different stress levels and stress ratios. The parameters of the distribution of fatigue life are shown to be dependent on the stress ratio of fatigue loading. The experimental P–S–N curves are established for each of different stress ratios using the distributions fitted to the static strength and fatigue life data. Then, a method for constructing the anisomorphic constant fatigue life (CFL) diagrams of constant probability of failure is developed. The proposed probabilistic anisomorphic CFL diagram approach allows not only accurately predicting the P–S–N curves for different stress ratios, but also adequately describing the stress-ratio dependent scatter in fatigue life of the unidirectional composite.

Probabilistic anisomorphic constant fatigue life diagram approach for prediction of P–S–N curves for woven carbon/epoxy laminates at any stress ratio

A general engineering methodology to construct a family of anisomorphic constant fatigue life (CFL) diagrams with probability of failure as the parameter that allows efficiently predicting P–S–N curves at any stress ratios is developed and validated for a plain weave fabric carbon/epoxy laminate. Constant amplitude fatigue tests are first performed to obtain statistical samples of fatigue life at different stress levels and stress ratios, respectively. Static tensile and compressive strength data are also collected. The Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests suggest that both two-parameter lognormal and Weibull distributions are acceptable as the distributions for the static strength and fatigue life data, respectively, at the significance level of 5%. Then, we attempt to develop a methodology for efficient construction of the anisomorphic CFL diagrams for different constant values of probability of failure. It requires the P–S–N curves for any percentile points of the distribution for the critical stress ratio. To come up with this requirement, a probabilistic scaling law is formulated. It takes account of the probability-of-failure dependence of the critical stress ratio and the stress-ratio dependence of the P–S–N curve for the critical stress ratio. Finally, the anisomorphic CFL diagrams for different constant values of probability of failure are predicted using the proposed methodology, and they are shown to be in good agreement with the experimental results. It is also demonstrated that the P–S–N curves can efficiently and accurately be predicted for the woven CFRP laminate at any stress ratios using the proposed probabilistic anisomorphic CFL diagram approach.

A study on the fatigue performance of a glass fiber-epoxy polymer nanocomposite under random loads

A glass-fiber reinforced plastic (GFRP) nanocomposite containing 10 wt-% silica nano particles in the epoxy matrix was fatigue tested under a standard helicopter random load sequence, Helix-32. Fatigue life was determined at various reference stresses. The stiffness variation and the matrix crack density in the test specimen were monitored at regular intervals during the fatigue test. The random load fatigue life of the GFRP nanocomposite was about four times higher than that of its neat counterpart over the entire range of reference stress levels investigated. The suppressed matrix cracking and reduced crack/delamination growth rate in nanocomposite were responsible for fatigue life enhancement. Further, the random load fatigue life was predicted by empirical method using constant fatigue life diagrams. Three different damage accumulation models, namely, Palmgren–Miner (PM), Broutman–Sahu (BS) and Hashin–Rotem (HR), were used. All the three models predicted similar results, and a good correlation was observed between experimental and predicted fatigue life.

Fatigue Performance of Concrete with Pre-Cracks in Tension-Compression Cycles

A tension-compression cycle fatigue test was performed in order to study the fatigue property of C50 concrete with pre-cracks in cyclic loading. The stress ratio was-1 and the amplitude was 0.2 MPa ~1.30 MPa. The results show that the modified coefficient of fatigue strength is 0.198~0.265 and the infinite life fatigue strength is below 0.45MPa. While the log value of fatigue life is approximately linear with the amplitude of fatigue load stress, the discreteness of fatigue life, the particularity of concrete, has little to do with the amplitude. The S-N, P-N fatigue life curves and the constant fatigue life diagram of pre-crack concrete are obtained.

807 一方向CFRP積層板の非主軸等寿命線図とその温度依存性(OS8-(2),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

807 一方向CFRP積層板の非主軸等寿命線図とその温度依存性(OS8-(2),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

806 クロスプライCFRP積層板のプライベース疲労寿命予測法の開発(OS8-(2),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

A ply-by-ply basis fatigue life prediction method for multi-directional composite laminates that can be applied to fatigue loading at any stress ratio has been developed, taking into account the inelastic deformation and in-situ strength of plies embedded in the laminates. Fatigue failure in embedded plies is evaluated using a quasi-static failure criterion based on the residual principal strengths. The residual principal strengths of unidirectional plies are predicted using the anisomorphic constant fatigue life diagrams that are identified for loading in the principal directions, respectively. The fatigue failure criterion for plies takes into account not only the in-situ principal strengths of plies embedded in a general laminate, but also the progressive reduction in in-situ constraint effect due to the growth of fatigue damage. The actual stress components in the plies embedded in a laminate are evaluated using a laminate constitutive model based on the classical lamination theory, in which the nonlinear plastic deformation of inclined plies under in-plane off-axis loading is taken into account. It is demonstrated that the proposed ply-by-ply basis fatigue model can successfully be used for prediction of on-axis and off-axis fatigue lives of cross-ply CFRP laminates that are subjected to fatigue loading at different stress ratios, respectively.

Anisomorphic constant fatigue life diagrams for quasi-isotropic woven fabric carbon/epoxy laminates under different hygro-thermal environments

The effect of absorbed moisture on the fatigue strength of a plain-weave roving fabric carbon/epoxy quasi-isotropic laminate under constant amplitude loading at different stress ratios has been examined. First, constant amplitude fatigue tests are performed at room and high temperatures (HT), respectively, on the specimens immersed in hot water until saturation as well as on the specimens kept in a dry place. The results indicate that the fatigue lives of wet specimens are shorter than those of dry specimens, regardless of stress ratio as well as test temperature. The fatigue strength is reduced by about 11% due to water absorption at room temperature (RT), regardless of stress ratio. A similar reduction in fatigue strength can be seen in wet specimens at HT as well. Then, the full shapes of constant fatigue life (CFL) diagrams for the woven carbon fiber-reinforced plastic (CFRP) laminate in dry and wet environments are identified using fatigue test data obtained at different stress ratios and at different test temperatures. The results show that the experimental CFL diagrams are asymmetric and nonlinear, and the shape of CFL envelope gradually changes. Finally, the CFL diagrams for the woven CFRP laminate under uniaxial fatigue loading in different hygro-thermal environments are predicted using the anisomorphic CFL diagram approach for composites that was developed in an earlier study. Comparison with experimental results demonstrates that the anisomorphic CFL diagram approach is a promising step in predicting the CFL diagram for the woven CFRP laminate not only in a dry environment but also in a wet environment, regardless of test temperature.