Equivalent Stress Amplitude Research Articles

Biaxial fatigue behavior of gradient structural purity titanium under in-phase and out-of-phase loading

Biaxial fatigue behavior of gradient structural pure titanium fabricated by surface nanocrystallization technique (SNC) was investigated under in-phase (IP) and out-of-phase (OP) loading. The fatigue life of SNC Ti under 90° OP loading is shorter than that under IP loading, which is attributed to the fact that both the maximum shear stress and maximum normal stress under 90° OP loading are larger than that under IP loading at the same cyclic equivalent stress amplitude. Under IP loading, the fatigue life increases as the stress ratio increases; Under OP loading, the fatigue life decreases as the phase angle increases. The fatigue microcracks nucleate and propagate preferentially along shear bands (SBs) under both IP and OP loading. The growing direction of the microcracks and macrocrack were determined experimentally and predicted using the critical plane approaches. The results indicate that the measured directions of macrocrack under IP and OP loading are closely consistent with the theoretical prediction. After biaxial fatigue tests, the stress-induced nanograins growth was observed on the top surface. As a result of rotation of maixmum shear stress plane uner 90° OP loading. The degree of nanograins growth under 90° OP loading is larger than that under IP loading. The corresponding dislocation substructure in coarse grained region changes from the parallel dislocation lines under IP loading to the dislocation tangles under 90° OP loading.

Probabilistic Fatigue Crack Initiation and Propagation Fields Using the Strain Energy Density

The fatigue crack growth (FCG) has been widely studied by the scientific community. There are several proposed FCG models, the best known being the Paris relation. The fatigue crack initiation and propagation have been studied separately, however, researchers have made an effort to study the relationship between these two fatigue phenomena. In this sense, several fatigue crack growth models based on local approaches have been proposed, the UniGrow model being well-known. The fatigue crack growth process is assumed a succession of crack re-initiations considering a certain elementary material size. Recently, Huffman developed a strain energy density based on Walker-like stress life and fatigue crack growth behavior. In this paper, the Huffman model based on local strain energy density is used to predict the fatigue crack initiation and propagation for the P355NL1 pressure vessel steel. This model is combined with the generalized probabilistic fatigue model proposed by Correia aiming the generation of probabilistic fatigue crack initiation and propagation fields. In this study, the local stress and strains at the crack tip were obtained combining linear-elastic and elastoplastic analyses. The probabilistic fatigue crack growth rates fields for several stress R-ratios are estimated considering strain, SWT, and equivalent stress amplitude damage parameters. A comparison between the experimental FCG data and the generated probabilistic FCG fields is made with very satisfactory correlations being found.

Predicting the multiaxial fatigue limit and the multiaxial high-cycle fatigue life based on the unified equivalent shear stress from axial strength characteristics with various waveforms

A new method for predicting high-cycle fatigue life under constant multiaxial amplitude loading is proposed using a unified equivalent shear stress amplitude proposed by the author. This criterion is an extension of the multiaxial fatigue limit criterion proposed previously by the author. This criterion uses the axial loading S-N curve and the true fracture strength as commonly available material characteristic values. The fatigue test data from the literature such as the bending and torsion combined loadings, the biaxial loadings and the biaxial loadings with sinusoidal, triangular and trapezoidal waveforms, were used to verify the criterion. The fatigue lives estimation error and fatigue limit estimation error of the proposed criterion were better than that of the other criteria used for comparison.

Study on fatigue reliability evaluation method of mechanical system with damage structure under variable amplitude load

The parts of large-scale machinery equipment are mostly welded with each other. Welded structures with internal defects can be regarded as damage structures, which is much easier to suffer from fatigue damage under the action of variable amplitude loads. In this paper, the scale welding structure system - hydraulic support is taken as the object of study. Firstly, combining with the characteristics of its workload, it adopts a new angle: The probabilistic characteristics of the load history of hydraulic support are described and the reliability evaluation of the structure is carried out from 'macro' and 'micro'. Secondly, the equivalent cyclic loading with equivalent stress amplitude is equivalent to the equivalent cyclic loading by applying the damage equivalent mechanism. Based on this, the calculation of the total probability and the statistical average algorithm, the fatigue reliability model was built. It can objectively reflect the real failure, the correlation between the sites of injury.

Mean stress effect in stress-life fatigue prediction re-evaluated

The paper compares various methods for computing the equivalent stress amplitude for stress cycles of non-zero mean value in stress-life fatigue prediction. A set of 11 calculation methods is evaluated. In addition to formulations based on common static or fatigue properties, the Walker formula and the generalized Linear formula are included in the investigation. These two methods use an optimization routine to find the material parameters. The final response of the methods is compared and discussed. The Walker method provides a better solution. The generalized Linear method produces inferior results, i.e. the linear fit of the segment of the Haigh diagram is not an optimal solution.

Influence of inclusion type and size on the fatigue strength of high strength steels

In this investigation the influence of the inclusion type and size on the fatigue strength of different steels is analysed. As database case hardened, quenched and tempered as well as bearing steels in different heat treatment conditions, which have been investigated in several research projects over the last two decades, are used. Based on the approach of Murakami the local stress intensity at inclusions was determined to evaluate the influence of fracture causing inclusions on the fatigue strength. Different fatigue criteria have been used to calculate the local equivalent stress amplitudes considering residual stresses in the specimens, mean stresses during loading and multiaxial stresses in notched specimens. Since many run out specimens were subsequently fatigued at a higher stress amplitude, the critical inclusion type and size which have survived the initial stress amplitude could be determined. As a result the local stress intensity at inclusions which leads to no fatigue failure could be calculated as well. With the knowledge of the stress intensity factor range of the fractured and run out specimens a threshold stress intensity factor range could be derived for the different steels and inclusion sizes.

A New Approach to the Fatigue Life Prediction for Notched Components Under Multiaxial Cyclic Loading

A new fatigue life prediction approach for notched components is proposed under multiaxial cycle loading. Firstly, the pseudo equivalent strain-real equivalent stress relationship is determined by utilizing the Neuber’s rule and the material stress-strain relation under proportional loading. Secondly, the pseudo elastic strain histories at the notch need to be solved for the investigated notched components under multiaxial cyclic loading. Thirdly, for the pseudo elastic strain histories, it is proposed that the Shang–Wang multiaxial fatigue damage parameter can be used to substitute the equivalent strain under proportional loading to take account of the additional hardening due to the non-proportionality of external loadings. Meanwhile, the real equivalent stress amplitude at the notch can be solved. Fourthly, based on the real equivalent stress amplitude at the notch integrated with the Neuber’s rule, the real equivalent strain amplitude can be determined. Finally, the real equivalent strain amplitude is utilized to predict the fatigue crack initiation lifetime of notched components. The proposed method is verified by the experimental data of SAE 1045 notched shaft specimens under proportional and non-proportional cyclic loading. The results showed the prediction errors are mostly within a factor of 2.

Fatigue life estimation algorithm of structures with high frequency random vibration based on hybrid energy finite element method

A hybrid energy finite element method (Hybrid-EFEM) considering direct field is introduced and promoted to general coupling conditions. The equivalent stress amplitude based on energy density is derived. Then combined with zero order moment stress spectrum method, a high-frequency fatigue life prediction method based on Hybrid-EFEM is proposed. A fatigue life prediction example is carried out to verify the feasibility of the method.

Biaxial tension-torsion fatigue behavior of gradient nano-grained pure titanium fabricated by surface nanocrystallization

A gradient nanostructured surface layer was fabricated in the commercial-purity titanium (Ti) thin-wall tubular sample using the modified surface nanocrystallization (SNC) technique. Biaxial tension-torsion fatigue behavior of the SNC Ti was investigated. The SNC Ti shows significant longer biaxial fatigue lives than the coarse grained Ti (CG Ti) at the same cyclic equivalent stress amplitude. Both CG and SNC Ti display hardening during cyclic deformation, and the hardening level in the SNC Ti is larger than that of the CG one. Microstructural analysis reveals that the SNC Ti shows hierarchical deformation mechanisms in different areas across the wall-thickness of tubular samples during biaxial fatigue. In the nano/ultrafine grain region, the stress-driven nanograin growth is the primary deformation mechanism. In the deformed grain region, the interaction between lamella structure and dislocations is observed. In the coarse grain region, prismatic slip is main deformation mode. The initiation of fatigue cracks is restricted in the SNC Ti since the stress concentration is relieved through stress-driven nanograin growth during cyclic deformation. The initiation mechanism of fatigue cracks transforms from slip band and grain boundary cracking in the CG Ti to the shear band cracking in the SNC Ti. Furthermore, since the superposition of residual compressive stress with the exterior applied stress in the SNC Ti, both maximum shear stress and maximum normal stress are decreased. Consequently, the equivalent driving forces for crack initiation and propagation in the SNC Ti are smaller than those in the CG Ti. The higher resistance to fatigue crack initiation and the lower equivalent driving force for fatigue crack initiation and propagation contribute to the enhancement of fatigue properties in the SNC Ti.

Fatigue criterion improvement of Gough and Nishihara & Kawamoto to predict the fatigue damage of a wide range of metallic materials

An improved multiaxial high-cycle model based on the Gough and Nishihara & Kawamoto approaches is presented. The proposal is a compromise between the measure of the equivalent shear stress amplitude, obtained from a prismatic convex hull method, and the amplitude of the first stress invariant. This makes the criterion an effective approach to predict quickly the failure initiation for wide range of materials (from ductile metals to extremely brittle metals). The results obtained from our proposal are compared to experimental data reported in the literature.

Dynamic characteristic analysis and fatigue life estimation of steel-structure bridges under vehicle loading

Influenced by repeated effects of vehicle loads during an operation period, a bridge structure will suffer from cyclic stress, while the corresponding fatigue damage will be generated. Therefore, it is very important to conduct on fatigue performance analysis and life assessment of a bridge during the operation period. Firstly, vehicle load spectrums and dynamic stress are determined through using field vehicle recorder and strain gauge to measure stress responses of steel-structure bridge diaphragm plates. Results show that: No.1 strain gauge was closer to the hole edge than No. 2 strain gauge, and its stress concentration was more obvious; sequence of stress values is as follows: No. 1 strain gauge > No. 2 strain gauge > No. 3 strain gauge. Then, the vehicle load spectrums are loaded into the finite element model of the steel-structure bridge (with and without struts), so stresses at holes, weld and plates are computed. Stresses at holes and plates have the similar variation tendency, but stresses at the hole are larger. Variation of stresses at welds is more complicated than other two positions when vehicles pass by. Equivalent stress amplitudes at holes, plates and other positions in the steel-structure bridge (with struts) model are less than computational results of the steel-structure bridge (without struts) model, but stress amplitudes at the weld don’t vary obviously, indicating that force at holes and plates can be effectively improved by strengthening rigidity of the diaphragm plate using struts. Finally, fatigue lives of detailed parts for the steel-structure bridge are computed. Results show that applying struts can effectively increase fatigue lives of some detailed positions, which can further improve fatigue life of the whole steel-structure bridge.

多軸一定応力振幅下の高サイクル疲労寿命予測

Multiaxial high cycle fatigue life prediction under constant stress amplitude is proposed. This new criterion, which extends the proposed fatigue limit criterion by the authors in the previous papers, uses the unified equivalent shear stress amplitude. The material properties for the proposed criterion are the axial fatigue limit and the true fracture strength. The multiaxial high cycle fatigue tests for life prediction accuracy verification was carried out with S45C and SCM440. The fatigue tests were conducted under combined axial and torsion stresses with mean stress and phase difference. The criterion error is better than that of the Susmel criterion. The proposed criterion predicted the experimental fatigue life to be within a factor of 3.

Multiaxial fatigue strength of type 316 stainless steel under push–pull, reversed torsion, cyclic inner and outer pressure loading

Multiaxial fatigue tests under non-proportional loading in which principal directions of stress and strain are changed in a cycle were carried out using a developed multiaxial fatigue testing machine which can load a push–pull and reversed torsion loading with cyclic inner and outer pressure. This paper presents the developed testing machine and experimental results under several multiaxial loading conditions including non-proportional loading. In strain control tests, the failure life is reduced in accordance with increasing inner pressure at each strain path. The failure life can be correlated by von Mises' equivalent stress amplitude relatively well independent of not only inner pressure but also loading path. In load control tests, the failure life is reduced largely by non-proportional loading but the influence of inner and outer pressure on the failure life is relative small.

Generalization of the moment of inertia method to estimate equivalent amplitudes for simplifying the analysis of arbitrary non-proportional multiaxial stress or strain histories

Several models have been proposed in the literature to account for fatigue damage under multiaxial load histories. Most of them require some measure of an equivalent stress or strain amplitude, in the sense of causing the same damage as the original history, which may be difficult to obtain for generic non-proportional multiaxial variable amplitude load histories. To identify individual load cycles, a multiaxial rainflow-like algorithm must be employed. For each rainflow-counted cycle, the equivalent stress or strain amplitude along its path is often computed using the so-called convex enclosure methods, which find minimum spheres, ellipsoids, or rectangular prisms that contain the load path in a deviatoric stress or strain space. However, such procedure involves information loss, in special if the path shape is very different from the shape of the enclosing convex surface, resulting in poor estimates of equivalent stress or strain amplitudes. To overcome this problem, the moment of inertia (MOI) method has been proposed in Meggiolaro and Castro (Int J Fatigue 42:217–226, 2012) to calculate equivalent amplitudes and mean components of two-dimensional stress or strain paths, generated, e.g., by tension–torsion or biaxial histories. In this work, the MOI method is extended to deal with generic 6D stress or strain paths, which include all normal and shear components. To accomplish that, the load history path is first represented in a 5D deviatoric stress or strain space and then assumed to be a homogeneous wire with unit mass, whose perimeter centroid is used to estimate the location of the path mean component. Then, the polar moment of inertia (PMOI) of such a hypothetical wire with respect to its mean component is calculated. The PMOI represents the distribution of the path about a single point, the perimeter centroid, giving a measure of how much the path stretches away from its mean component, which is used in the calculation of the equivalent amplitudes. Experimental results for 13 different multiaxial load histories prove the effectiveness of the proposed method to predict equivalent amplitudes and multiaxial fatigue lives.

Critical Plane Orientation Influence on Multiaxial High-Cycle Fatigue Assessment

In the present paper, the multiaxial fatigue lifetime of structural components failing in the high-cycle fatigue regime is evaluated by employing the modified Carpinteri-Spagnoli (C-S) multiaxial fatigue criterion based on the critical plane approach. In the above criterion, the critical plane position is linked to averaged principal stress directions through an off-angle 8. Then, the fatigue damage parameter used is determined by a nonlinear combination of an equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane. In the present paper, some modifications of the original expression for the off-angle 8 are implemented in the modified Carpinteri-Spagnoli criterion. In particular, modified expressions recently proposed by Lagoda et al. are in accordance with the assumption originally developed by Carpinteri and co-workers, that is, the off-angle is a function of the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress. Such expressions can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical estimations and, only for materials with hard and very hard fatigue behaviour, the modified 8 relationships are shown to yield fatigue lifetime results slightly better than those determined through the original 8 expression.

Life estimation by varying the critical plane orientation in the modified Carpinteri-Spagnoli criterion

The modified Carpinteri-Spagnoli (C-S) criterion is a multiaxial high-cycle fatigue criterion based on the critical plane approach. According to such a criterion, the orientation of the critical plane is linked to both the averaged directions of the principal stress axes and the fatigue properties of the material. The latter dependence is taken into account through a rotational angle, ?. Then, the multiaxial fatigue strength estimation is performed by computing an equivalent stress amplitude on the critical plane. In the present paper, some modifications of the original ? expression are implemented in the modified C-S criterion. More precisely, such modified expressions of ? depend on the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress (in accordance with the original expression), and can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical results in order to verify if the modified ?expressions are able to improve the fatigue strength estimation capability of the modified C-S criterion.

Load Spectrum and Fatigue Life Computer Analysis of Prestressed Concrete Bridges

With respect to fatigue damage of heavy traffic on the bridge structure, this paper studied on load spectrum and fatigue simulation. The author used manual recording, live cameras, vehicle dynamic weighing system (WIM) to conduct traffic investigation in a continuous 24-hour period. Basing on these data in Hebei province, we established typical vehicle load spectrum using probabilistic and statistical methods, and deduced a standard fatigue vehicle model on this basis. Then we prepared random load spectrum by MATLAB and realized loading it on a finite element model (FEM). Next, the paper assessed the fatigue life of in-service highway bridges that in Hebei by comparing typical vehicle load and random vehicle load. Results showed that vehicle speed has significant influence on fatigue damage under typical vehicle load. Equivalent stress amplitude is small in two operational states under random vehicle load, the general operation state and intensive operation state. Fatigue damage to bridge under general operation is obvious. After verified the applicability of the standard fatigue vehicle model, we can believe that this model developed in this article can be further used as a reference to check highway fatigue damage in the entire Hebei province. Moreover, all the results showed that the bridges wouldn’t get fatigue failure under a normal operation state when there is no impact of environmental factors.

Effect of mean stress on multiaxial ratcheting life: A simplified life prediction model based on average equivalent stress amplitude

This article proposes a model to predict uniaxial and multiaxial ratcheting life by addressing the three primary parameters that influence failure life: fatigue damage, ratcheting damage and the multiaxial loading path. These three factors are addressed in the present model by (a) the stress amplitude for fatigue damage, (b) mean stress-dependent Goodman equation for ratcheting damage and (c) an inherent weight factor based on average equivalent stress to account for the multiaxial loading. The proposed model requires only two material constants which can be easily determined from uniaxial symmetric stress-controlled fatigue tests. Experimental ratcheting life data collected from the literature for 1025 and 42CrMo steel under multiaxial proportional and nonproportional constant amplitude loading ratcheting with triangular sinusoidal and trapezoidal waveform (i.e. linear, rhombic, circular, elliptical and square stress paths) have shown good agreement with the proposed model.

Probability density function of the equivalent stress amplitude using statistical transformation

The shape of a rainflow matrix is complex and cannot be approximated by a simple distribution function. In this paper, the Weibull–normal mixture distribution is used, for which the number of components and unknown parameters are required to be estimated. The scope of the paper is to estimate the number of components and unknown parameters using the FlexMix and REBMIX algorithms, and compare their results. The results are then used in Goodman and Walker mean stress correction methods. This correction is not made as a point-to-point transformation, where the information about the distribution function of the rainflow matrix is lost. Instead, the used distribution function of the rainflow matrix with estimated parameters is transformed in accordance with Goodman and Walker mean stress correction methods. With this procedure, the probability density of the equivalent stress amplitude is immediately obtained, and the information about the distribution function of the rainflow matrix is not lost.

SPR 접합법을 이용한 Al-5052 인장-전단 시험편의 피로강도

Self-piercing riveting(SPR) is a mechanical fastening technique which is put pressure on the rivet for joining the sheets. Unlike a spot welding, SPR joining does not make the harmful gas and <TEX>$CO_2$</TEX> and needs less energy consumption. In this study, static and fatigue tests were conducted using tensile-shear specimens with Al-5052 plates for evaluation of fatigue strength of the SPR joints. During SPR joining process for the specimen, using the current sheet thickness and a rivet, the optimal applied punching force was found to be 21 kN. And, the maximum static strength of the specimen produced at the optimal punching force was 3430 N. During the fatigue tests for the specimens, interface failure mode occurred on the top substrate close to the rivet head in the most high-loading range region, but on the bottom substrate close to the rivet tail in the low -loading range region. There was a relationship between applied load amplitude <TEX>$P_{amp}$</TEX> and lifetime of cycle N for the tensile-shear, <TEX>$P_{amp}=3395.5{\times}N^{-0.078}$</TEX>. Using the stress-strain curve of the Al-5052 from tensile test, the simulations for fatigue specimens have been carried out using the implicit finite element code ABAQUS. The relation between von-Mises equivalent stress amplitude and number of cycles was found to be <TEX>${\sigma}_{eq}=514.7{\times}N^{-0.033}$</TEX>.