Stress Ratio Dependence Research Articles

Meso-FE modelling for homogenization of the nonlinear orthotropic behavior of PTFE-coated fabric based on virtual fiber method

Compared to traditional textile composites, the coated fabric used in fabric membrane structures is much more flexible. Its macroscopic mechanical behavior is highly nonlinear, anisotropic, and shows stress ratio dependence during the loading process. The main reason is that the yarns within the coated fabric are not completely solidified, and there is a significant crimp interchange process in the yarns under load. This paper proposes a novel mesoscopic finite element (FE) model to predict the nonlinear orthotropic mechanical behavior of PTFE-coated fabric using the virtual fiber method (VFM). By comparing with experimental data, it is shown that the virtual fiber defined by the truss element can visually and effectively simulate the mechanical behavior of the internal fibers and reflect the crimp interchange process between two-way yarns. Combined with PBCs, it can effectively predict the uniaxial and biaxial tensile behaviors of the PTFE-coated fabric. Moreover, a new multi-scale model suitable for structural scale analysis of fabric membrane structures has been attempted by combining the direct FE2 (D-FE2) method with the proposed mesoscopic FE model. Local deformation mechanisms and macro response of fabric membrane structures can be observed simultaneously from these analyses, which provide a better understanding of the mechanical behavior of the fabric membrane structures.

Energy-Based Fatigue Assessment of Defect-Afflicted Cast Steel Components by Means of a Linear-Elastic Approach

Cast steel components are affected by manufacturing process-based imperfections, which severely limit their fatigue strength. In this work, the linear-elastic strain energy density concept is applied to assess the fatigue behaviour of bulk defect-afflicted components made of high-strength cast steel alloy G12MnMo7-4+QT. Based on analytical calculations, an energy-based design limit curve is derived which merges experimental results of notched and unnotched small–scale specimens into a statistically proven scatter band. The stress ratio dependency is also investigated. Moreover, a numerical methodology is introduced, which facilitates the energy-based fatigue assessment of complex spatial imperfections on the basis of radiographs. Validation of the established framework utilizing experimental results of defect-afflicted large–scale specimens leads to sound accordance of numerically and experimentally derived fatigue strength values, showing an average deviation of about only eight percent.

Distortion-induced fatigue behavior of vertical stiffener web gaps in steel girder bridges

This paper reports full-scale fatigue tests, conducted to explore the distortion-induced fatigue behavior of vertical stiffener web gaps in steel girder bridges, considering parameters such as web gap size, nominal stress ratio and distortion ratio (a newly proposed physical parameter). The results show that the fatigue strength of weathering steel web gaps improves with the increase of the web gap size, but worsens with the increase of the stress ratio and the distortion ratio. It was found that the fatigue strength for 20 mm, 40 mm and 60 mm weathering steel web gaps corresponds to categories 36, 71 and 100 in Eurocode 3, when the nominal stress ratio and the distortion ratio are less than 0.3. However, when the nominal stress ratio and distortion ratio are between 0.3 and 0.5, the fatigue strength for 20 mm is below category 36, while for 40 mm and 60 mm, it corresponds to categories 45 and 80, proving the stress and distortion ratio dependency.

Very-high-cycle fatigue induced growth and amorphization of Si particles in additively manufactured AlSi10Mg alloy: Dependence of applied stress ratio

The microstructural evolution at the fracture surface in response to very-high-cycle fatigue (VHCF) under stress ratios (R) of −1 and 0.5 in an AlSi10Mg alloy produced by Laser Powder Bed Fusion was investigated. The results show that appreciable growth of the Si precipitates at the cellular network boundaries in the as-built microstructure was observed under R = −1. Moreover, significant amorphization of the initial crystalline Si precipitates occurred in the vicinity of the fracture surface under this condition. A layer of fine Al grains was developed in the “fish-eye” region of the fracture surface. These microstructural responses are rationalized by the generation of lattice defects including dislocations and sub-grain boundaries during cyclic pressing of crack surfaces under R = −1, which mediates the Si solute diffusion and re-precipitation in the alloy as well as the amorphization of initial Si crystalline precipitation. In contrast, far fewer dislocations were observed near the crack surfaces under R = 0.5, which is attributed to the absence of cyclic pressing of crack surfaces and severe plastic deformation in this scenario. This work provides insights into the stress ratio dependence of the microstructural evolution in the fatigued Al alloys. The obtained knowledge is useful for future understanding of the fatigue failure in Al alloys produced by additive manufacturing.

Set-up of a Generalized Dataset for Crack-Closure-Mechanisms of Cast Steel

In components, crack propagation is subjected to crack-closure-mechanisms which affect the build-up of the relevant threshold stress intensity factor range during cyclic loading. As structural parts are exposed to service loads incorporating a variety of load ratios, a significant change of the long-crack threshold value occurs, leading to a severe stress ratio dependency of crack-closure-mechanisms. Thus, an extensive number of crack propagation experiments is required to gain statistically proven fracture mechanical parameters describing the build-up of closure effects as crack growth resistance curves.The article presents a generalized dataset to assess the formation of crack-closure-mechanisms of cast steel G21Mn5+N. Numerous crack propagation experiments utilizing single edge notched bending (SENB) sample geometries are conducted, incorporating alternate to tumescent stress ratios. The statistically derived, generalized crack growth resistance curve features the impact of closure effects on the crack propagation rate in a uniform manner. To extend the dataset to arbitrary load ratios, the long-crack threshold approach according to Newman is invoked. The generalized dataset for the cast steel G21Mn5+N is validated by analytical fracture mechanical calculations for the utilized SENB-sample geometries. Incorporating a modified NASGRO equation, a sound correlation of analytical and experimental crack propagation rates is observed. Moreover, the derived master crack propagation resistance curve is implemented as a user-defined script into a numerical crack growth calculation tool and supports a local, node--based numerical crack propagation study as demonstrated for a representative SENB-sample. Concluding, the derived dataset facilitates the calculation of fatigue life of crack-affected cast steel components subjected to arbitrary stress ratios.

A new constitutive model on biaxial tensile behavior of architectural fabrics

Accurate and concise constitutive model of biaxial tensile behavior is urgently needed for the analysis of complex membrane structure engineering. A new constitutive model is developed to describe the tensile behaviors of coated fabrics from pre-tension to breaking. The shrinkage curve is employed for the first time and stress-ratio dependence coefficient (SDC) is proposed to represent the proportion of elongation and shrinkage in biaxial monotonic tensile test. The deformation of cruciform specimen is considered as the result of the coupling effect of biaxial tension and Poisson effect. Excellent fitting results were obtained between the data points of biaxial tensile test and stress-stress-strain response surface, which R-squares of both warp and weft response surface were 0.995.

Predicting long-term crack growth dominated static fatigue based on short-term cyclic testing

In the present work, the time to failure of a glass fibre reinforced glassy polymer is studied in cyclic fatigue at various frequencies and stress ratios with the goal to predict long-term crack-growth dominated static fatigue. It is demonstrated that the crack propagation rate can be regarded to consist of two components: a time-dependent creep component, and a frequency dependent cyclic component. In static loading, the time-dependent component prevails, while for cyclic loads with large load amplitudes the frequency dependent, cyclic component dominates. For intermediate load amplitudes, the total propagation rate is shown to be a combination of both. Consequently, the contribution of the cyclic component diminishes with decreasing frequency or load amplitude, revealing the contribution of the static component. As such, extrapolation of the stress ratio dependence of the fatigue life to R=1 allows estimation of the long-term static performance. A phenomenological model is provided that captures all relevant aspects and provides an accurate description of the stress ratio and frequency dependence of the lifetime in fatigue loading and allows prediction of the long-term failure, based on short-term cyclic fatigue experiments only.

Computational Fatigue Analysis of the Pin-Loaded Lug with Quarter-Elliptical Corner Crack

In the present paper, mathematical models based on a new fracture mechanics methodology are developed for the failure analysis of an attachment lug with one/two quarter-elliptical crack(s) emanating from a hole. The strength of lug subjected to cyclic loading is theoretically examined through the following issues: the stress analysis, the estimation of life up to failure and the crack path evolution. The nonlinear stress field along the crack front is simulated by using the [Formula: see text]-integral method together with the finite element method. Furthermore, analytical and numerical methods are employed for the stress intensity factor calculation. The stress-ratio dependence crack growth model is applied in order to evaluate both the life up to failure and the crack growth path. The proposed models are validated through available crack growth data, and the comparison between different results is satisfactory.

Statistical distribution and stress ratio dependence of fatigue life for injection molded short carbon fiber reinforced nylon composite

Statistical distribution and stress ratio dependence of fatigue life for injection molded short carbon fiber reinforced nylon composite

Fatigue damage analysis of wing-fuselage attachment lug

In the present paper, the fatigue behavior of failure critical pin-loaded lug with the through-the-thickness crack at a hole is analyzed. Such an investigation examines the stress analysis and the residual life estimation through a computational model here proposed in which suitable fracture mechanics concepts are employed. Hence, the stress ratio dependence crack growth model is taken into account to assess the fatigue strength of damaged lug. Further, in order to calculate the stress intensity factor, fracture mechanics based analytical and numerical approaches are applied. Finally, to demonstrate the compatibility of developed model, relevant experimental data are used. Such crack growth observations show a fairly good correlation with obtained failure assessments.

Stress ratio dependence of fibre bridging significance in mode I fatigue delamination growth of composite laminates

This paper aims to investigate stress ratio effect on fibre bridging significance in mode I fatigue delamination growth of composite materials. Fatigue resistance curves (R-curves) of different stress ratios are determined and compared with the quasi-static R-curve. The fatigue R-curve of a high stress ratio is similar to the quasi-static results. However, fatigue resistance of a low stress ratio is smaller than quasi-static resistance. These indicate that fibre bridging significance is stress ratio dependent. More bridging fibres can be generated in delamination of a high stress ratio, as compared to that of a low stress ratio. This can lead to fatigue bridging laws are stress ratio dependent and fatigue delamination is block load sequence dependent.

VHCF properties and fatigue limit prediction of precipitation hardened 17-4PH stainless steel

In this work, the very high cycle fatigue properties of precipitation-hardened chromium–nickel–copper stainless steel 17-4PH are investigated, and the factors determining the fatigue strength are discussed. In addition, fatigue test results on comparable materials reported in the literature are evaluated, and the influence of material hardness on the fatigue life and the endurance strength is quantified. Fractographic investigations show that fatigue fracture initiates predominantly from non-metallic inclusions at the surface and in the interior of specimens. It is found that the endurance limit at more than 1010 loading cycles can be predicted by the area parameter model. The stress ratio dependency on the fatigue strength is determined with good accuracy using a simple method. Furthermore, the lower bound of the fatigue limit is predicted by the inclusion rating and use of the extreme value theory. In addition, the role of the optically dark areas observed around internal inclusions is discussed.

高温における平織 CFRP の非主軸切り欠き疲労強度の応力比依存性とそのモデル化

Effect of temperature on notched off-axis fatigue behavior of CFRP laminate has been studied. Static and fatigue tests are performed at different temperatures on unnotched (UN) and center-hole (CH) coupon specimens of a plain woven CFRP laminate for different fiber orientations as well as for different stress ratios. The off-axis static strengths of notched specimens at high temperature are lower than those at room temperature, but the degree of reduction in static strength is different depending on fiber orientation. The off-axis notched fatigue life of the plain woven CFRP laminates at difference temperatures is predicted using the notched fatigue life prediction method that was started to develop in an earlier study on the off-axis notched fatigue life for the plain woven CFRP laminates at room temperature. The values of fatigue life predicted using the method are compared with the fatigue lives observed in this study. The predicted off-axis notched fatigue life of the plain woven CFRP laminates at high temperature agrees well with the experimental fatigue life observed, demonstrating the potential usefulness of the notched fatigue life prediction method for off-axis notched fatigue at high temperature as well.

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 phenomenological fatigue life prediction model of glass fiber reinforced polymer composites

• A comprehensive fatigue life prediction model for GFRP composites is developed. • Strain failure criterion is applied without measuring failure stiffness. • Effects of fiber orientation, stress ratio and frequency on fatigue life are studied. • Prediction model is able to assist fatigue experiment work. In this paper, a macro phenomenological fatigue model is developed for the off-axis fatigue behavior of glass fiber reinforced polymer (GFRP) composite laminates. The residual stiffness method and strain failure criterion are used to characterize the brittle nature of fatigue damage evolution. This allows one to obtain a practical form of multiaxial fatigue model that takes into account of the non-linear effects of fiber orientation dependence, stress ratio dependence as well as the effect of loading frequency on the fatigue behavior of composite laminates. Parameters of the model are fitted out according to relative fatigue experiment data with specific lay-up under certain stress ratio and loading frequency. Fatigue life predictions are verified by different stress ratios and loading frequencies, and the results of the model show a good agreement with experimental data.

G031024 デジタル画像相関法を用いた表面き裂開口変位の計測([G031-02]材料力学部門,一般セッション : 非鉄金属の強度と変形(2))

rack opening displacement of the mode I surface crack was measured using digital image correlation. Pulsating tension tests were carried out with the stress ratio R=0.2 and 0.5 using A7075 aluminum alloy. The crack tip opening stress was determined to various crack length based on the crack opening displacement. Crack tip opening stress was the almost same value as the minimum stress when 7M).5. On the other hand, crack tip opening stress was close to the half of the maximum stress when R=0.2. The stress ratio dependence did not disappear, even if the crack propagation rate was arranged with the effective stress intensity factor range. The relationship between the crack propagation rate and crack opening displacement near the crack tip was hardly dependent on the stress ratio.

Fatigue Crack Growth and Closure of Stainless Casting SCS6 and Carbon Steel Casting SC49 for Hydraulic Turbine Runner

In hydraulic turbine runner, unexpected accidents due to fatigue often occur. In this study, in order to clarify fatigue crack growth and closure properties on SCS6 and SC49 used as hydraulic turbine runner over 27 years, fatigue crack growth test under the stress ratio R-constant were carried out using compact tension specimens of both materials. Fatigue crack growth rate and crack closure were measured by means of an unloading elastic compliance method. The results are summarized as follows:(1) Although the stress ratio dependency on the fatigue crack growth rate is found in both materials, the influence is recognized remarkably in SCS6 except for threshold value. (2) Although the threshold stress intensity factor ΔKth of SCS6 is almost same as that of SC49 when R<0.5, the value of stress ratio of SCS6, when the R-dependency of growth rate disappears, was found to be higher than that of SC49. (3) Fatigue crack growth rates of SCS6 and SC49 could be correlated with the effective stress intensity factor range ΔKeff, and da/dN-ΔKeff relationships of both materials agree well in the low and mid growth rate region except for threshold value. In high ΔKeff, however, the rapid acceleration of crack growth rate due to the change of growth mechanism to cleavage fracture was found only in SC49.

Fatigue crack growth in heat-treated aluminium alloys

Fatigue crack propagation tests have been performed in several heat-treated aluminium alloys under constant amplitude loading. All experiments were performed, in load control, in a servo-hydraulic closed-loop mechanical test machine. The tests were carried out using middle tension, M(T), specimens. The influence of stress ratio and thickness were analysed. Crack closure was monitored in all tests by the compliance technique using a pin microgauge. A strong stress ratio and material dependence effects on the fatigue crack growth were observed. These effects are discussed in terms of the different dominant closure mechanism. The crack growth behaviour of heat-treated aluminium alloys depends mainly on whether the dominant closure mechanism is plasticity-induced or roughness-induced. The enhancement of roughness-induced closure promotes higher crack growth resistance in these alloys. Roughness-induced closure dominates crack closure in aluminium alloys age hardened by naturally ageing and also artificially aged alloys with higher contents of Mn and Cr elements. In alloys aged hardened by artificially ageing and simultaneously with a lower content of these alloying elements plasticity-induced closure is dominant.

Effect of stress ratio on fatigue behaviour in SiC particulate‐reinforced aluminium alloy composite

ABSTRACTAxial fatigue tests have been performed at three different stress ratios, R, of −1, 0 and 0.4 using smooth specimens of an aluminium alloy composite reinforced with SiC particulates of 20 μm particle size. The effect of stress ratio on fatigue strength was studied on the basis of crack initiation, small crack growth and fracture surface analysis. The stress ratio dependence of fatigue strength that has been commonly observed in other materials was obtained, in which fatigue strength decreased with increasing stress ratio when characterized in terms of stress amplitude. At R=−1, the fatigue strength of the SiCp/Al composite was the same as that of the unreinforced alloy, but at R= 0 and 0.4 decreased significantly, indicating a detrimental effect of tensile mean stress in the SiCp/Al composite. The modified Goodman relation gave a fairly good estimation of the fatigue strength at 107 cycles in the unreinforced alloy, but significantly unconservative estimation in the SiCp/Al composite. At R= 0 and 0.4, cracks initiated at the interfaces between SiC particles and the matrix or due to particle cracking and then grew predominantly along the interfaces, because debonding between SiC particles and the matrix occurred easily under tensile mean stress. Such behaviour was different from that at R=−1. Therefore, it was concluded that the decrease in fatigue strength at high stress ratios and the observed stress ratio dependence in the SiCp/Al composite were attributed to the different fracture mechanisms operated at high stress ratios.

2134 CFRP積層版の疲労強度に与える応力比の影響とそのモデル化(S27-2 複合材の長期寿命(1),S27 複合材料の加工と評価)

Effects of stress ratio on the fatigue behavior of CFRP laminates at room temperature have been studied. First, constant-amplitude fatigue tests are performed on quasi-isotropic and cross-ply CFRP laminate for six kinds of stress ratios. The experimental results demonstrate a marked stress-ratio dependence of fatigue behavior. The constant fatigue life diagram is linear in the range of a short life and it turns quadratic in the range of a longer life. To construct such a non-similar constant fatigue life diagram, a phenomenological procedure is developed on the basis of the static strengths in tension and compression and the reference fatigue strengths at the compression-tension strength ratio. The fatigue lives predicted using the proposed method agree well with the experimental results over the range of fatigue life up to 10^6 cycles for all the stress ratios tested. It is also demonstrated that the proposed fatigue life prediction method promisingly works for the off-axis fatigue behavior of cross-ply CFRP laminates.