Multiaxial Fatigue Damage Model Research Articles

Life prediction based on fatigue-environment damage under multiaxial thermo-mechanical loading

In this paper, the competition mechanism between protectiveness and harmfulness of oxidation, as well as the effects of cycle period, mean stress and temperature on the damage behavior of TA15 titanium alloy are revealed under multiaxial thermo-mechanical fatigue loading. Based on the damage mechanism, a high-temperature environmental damage model is proposed under multiaxial thermo-mechanical fatigue loading first, then a life prediction method is developed by combining a multiaxial fatigue damage model. The experimental verification results under uniaxial and multiaxial thermo-mechanical fatigue loadings showed that almost all of the prediction errors are within a factor of 2.

Static axial tension or compression stress effects on shear cracks initiating under cyclic torsion loads in multiaxial fatigue tests

This work proposes models that can better fit and explain apparently contradictory mean stress effects observed when superimposing axial tension or compression loads on cyclic torsion fatigue tests. It introduces new shear-based multiaxial fatigue damage models, modifying the classic Fatemi-Socie equation to consider the peak deviatoric stress normal to the initiating shear crack as the actual driving force for the peak or mean effects of the normal stresses. This deviatoric hypothesis can quantify the odd detrimental effects of static axial compression observed on axial shear cracks tested under cyclic torsion. Additionally, applying the peak deviatoric correction term only to the elastic component of the shear strain range allows an even better description of the increasing mean normal stress effects in high-cycle fatigue, eliminating the need for a variable normal stress sensitivity coefficient in the multiaxial fatigue damage parameter. To evaluate the proposed shear-based models, their life and crack initiation direction predictions are compared for cyclic torsion experiments both with and without superimposed static axial stresses for steels and aluminum alloys, including both literature and original data. The experiments show that axial compression can be detrimental to fatigue crack initiation lives, depending on the cracking mode and on the presence of bifurcations, which effects could be explained from the proposed deviatoric damage parameters.

Multiaxial fatigue life prediction by equivalent energy‐based critical plane damage parameter under variable amplitude loading

AbstractA new path‐independent multiaxial fatigue damage parameter , which is defined as the largest normal stress range between adjacent turning points of the maximum shear stress on the critical plane, is proposed to describe multiaxial fatigue damage. By combining the maximum normal stress or the largest normal stress range with the maximum shear stress range on the critical plane, two axial equivalent stress modification factors, and , are proposed, which can account for the influence of non‐proportional additional hardening. The sensitivity of the proposed axial equivalent stress modification factors to multiaxial variable amplitude loading sequences is analyzed. Furthermore, two new multiaxial fatigue damage models based on the axial equivalent stress modification factors are proposed to estimate fatigue life. The applicability of the presented methodology was verified by the experimental data of En15R steel and 7050‐T7451 aluminum alloy, and the results showed that the predicted fatigue lifetimes agree well with the experimental data under variable amplitude multiaxial loading.

Data-driven bending fatigue life forecasting and optimization via grinding Top-Rem tool parameters for spiral bevel gears

To establish a bridge between grinding tool parameters and loaded tooth fatigue life, an innovative data-driven root flank bending fatigue life forecasting and optimization via Top-Rem tool parameters was proposed for grinding spiral bevel gears. The recent machine settings modification is extended into grinding Top-Rem tool parameters modification in case that geometric accuracy and root bending fatigue life are integrated into a collaborative optimization. The proposed Top-Rem modification includes three key steps: (I) arc-shaped blade, (II) top part, and (III) top fillet part. Then, while root bending stress is determined by using finite element method (FEM)-based simulated loaded tooth contact analysis (SLTCA), data-driven fatigue life forecasting is developed by correlating with the multiaxial fatigue damage model based assessment. Moreover, data-driven bending fatigue life optimization model is established by using Top-Rem tool parameters modification, where the important constraints in target flank determination includes: (i) root overcutting, (ii) geometric accuracy, and, (iii) fatigue life. For high accuracy and efficiency, two different strategies are proposed: (i) the different parameters modification types; and, (ii) sensitivity analysis of grinding Top-Rem tool parameters. Finally, proposed method can verify that bending fatigue life can be significantly improved by modifying the key Top-Rem tool parameters in early stage of the whole life product development for spiral bevel gears.

Crankshaft HCF Research Based on the Simulation of Electromagnetic Induction Quenching Approach and a New Fatigue Damage Model

In recent decades, the electromagnetic induction quenching approach has been widely applied in the surface treatment process of steel engine parts such as crankshafts. In this paper, the strengthening effect of this approach was selected to be the object of study. First, the multi-physics coupling phenomenon was established by a 3D finite element simulation approach. Then, the fatigue property of the crankshaft was predicted based on the combination of the residual stress field obtained in the previous step and a chosen multi-axial fatigue damage model. Finally, a corresponding experiment verification was carried out to check the accuracy of the prediction. The results showed that the method proposed by this paper can provide high enough accuracy in predicting the fatigue property of two types of commonly used steel crankshafts.

Design and fatigue analysis of diagonally reinforced structures with a negative Poisson’s ratio lattice material

In this paper, a typical negative Poisson’s ratio lattice structure was studied and several diagonally reinforced 3D lattice structures were designed and analysed using the finite element method. On this basis, the fatigue life of the unreinforced and reinforced structures was calculated using SIMULIA Fe-safe software. Meanwhile, the fatigue failure process of the lattice structure was systematically simulated and quantitatively analysed by combining the multiaxial fatigue damage model. Results show that the enhancement design from the cell structure can provide an anti-diagonal shear enhancement effect. The structure A, B, and C can decrease the maximum von Mises stress by 95.8, 97.1, and 94.66%, and increase the compressibility by 80%, 56%, and 127%, respectively. The structure A enhancement yields the best overall performance in terms of structural stress, compressibility, and negative Poisson’s ratio properties enhancement. Compared with the unreinforced structure, the lifetime distribution of the structure A reinforced structure changes in both position and level. The overall lifetime has been improved from 102.813 of the unreinforced structure to 107 of the reinforced structure. Quantitative calculation of the fatigue damage is consistent with the fatigue life prediction results, which further validate the effectiveness of the diagonal enhancement method and the enhancement structure of the negative Poisson’s ratio lattice structure.

Bending fatigue life oriented tooth flank dry-grinding tool modification for cleaner manufacturing of spiral bevel gear product

Gear tooth flank dry-cutting was beget with emergent and disruptive NC technology. This new technology is enabling ever-higher levels of production efficiency and sustainability. It also has the potential to dramatically influence sustainable development of spiral bevel gear product. Sufficient guidance, in this respect, is lacking in the scholarly or practitioner literature. In this work, focusing on spiral bevel gear production, we further examine dry-cutting technology in terms of application and sustainability implications. We introduce bending fatigue life design into gear dry-grinding by considering various economic, environmental and social attributes. We also develop bending fatigue life oriented tooth flank dry-grinding tool modification by incorporating a high life cycle assessment (LCA) and low life cycle cost (LCC). At first, data-driven tool modification design relating to dry-grinding tool parameters is developed. Then, finite element method (FEM) based root bending fatigue assessment is performed by using the multiaxial fatigue damage model. Here, with data-driven finite element modeling, simulated loaded tooth contact analysis (SLTCA) is employed to root bending stress determination. They were introduced into the multiaxial fatigue damage model based fatigue life assessment. Moreover, focusing on the minimum fatigue at dangerous point namely fatigue limit, bending fatigue life oriented dry-grinding tool modification model considering geometric accuracy is established. Then, data-driven adaptive feedback and optimization is performed by using tool modification. The final output tool modification parameters can be used to obtain the cleaner manufacturing of gear product both flank geometric accuracy and fatigue life. Finally, the numerical instance was given to verify the proposed method. By building a bridge between the tool parameters in early design and the fatigue life in actual transmission, the proposed method can get a significantly important access to cleaner manufacturing of spiral bevel gears product.

Multiaxial low cycle fatigue of notched 10CrNi3MoV steel and its undermatched welds

It is a fundamental step to quantify the multiaxial fatigue damage considering the complex service conditions for notched components or welded structures. In our study, multiaxial Low Cycle Fatigue (LCF) tests of notched specimens were conducted on 10CrNi3MoV high strength steel and related undermatched welds under proportional and non-proportional cyclic loadings. The characteristic states of normal/shear stress, strain and energy around notch roots are analyzed considering the elasto-plastic material behavior under low cyclic loadings by the cyclic plasticity model. The predicted fatigue life curves of the test data were constructed by five strain-based and energy-based parameters combining with the critical plane approach and notch Theory of Critical Distance (TCD). According to Smith-Watson-Topper (SWT) damage parameters definitions, the paper proposed a simplified SWT model incorporating the effect of non-proportional loading, notch energy concentration characteristics and cyclic hardening behaviors for the LCF assessment of notch specimens. The proposed model shows good agreements between predictions and test data by comparing different multiaxial fatigue damage models for notch specimens.

Life prediction of wind turbine blades using multi-scale damage model

Wind turbine blade life prediction is the most important parameter to estimate the power generation cost. Due to the price and importance of wind blade, many experimental and theoretical methods were developed to estimate damages and blade life. A novel multiaxial fatigue damage model is suggested for the life prediction of a wind turbine blade. Fatigue reduction of fiber and interfiber characteristics are separately treated and simulated in this research. Damage behavior is considered in lamina level and then extended to laminate; hence, this model can be used for multidirectional laminated composites. The procedure of fatigue-induced degradation is implemented in an ABAQUS user material subroutine. By applying the fatigue damage model, life is estimated by the satisfaction of lamina fracture criteria. This model provides a comprehensive idea about how damage happens in wind blades regarding a multi-axis fatigue loading condition.

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

AbstractThe numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

AbstractTo realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.

Multiaxial fatigue assessment of S355 steel in the high-cycle region by using Susmel’s criterion

Multiaxial fatigue is frequently present on engineering structures and is the cause of many mechanical failures. However, multiaxial fatigue analysis is full of questions and different points of view. Thus, throughout this study, Susmel’s criterion, a recent multiaxial fatigue damage model also known as the Modified Wöhler Curve Method, is presented, explained and assessed. Experimental data of axial, torsional and proportional (axial+torsional) fatigue tests conducted on S355 structural steel and under different stress ratios were analysed and evaluated according to this model. Mean fatigue design curves for each loading condition were obtained and plotted in the high cycle fatigue region. Finally, the ability of Susmel’s criterion to assess the multiaxial fatigue behaviour of S355 steel in the high cycle region was evaluated by determining the error index between the theoretically estimated and the experimental fatigue damage. Susmel’s model was found to be adequate to describe the fatigue behaviour of the steel under study in high cycle region.

Multiaxial fatigue of extruded ZK60 magnesium alloy

AbstractMultiaxial monotonic and cyclic behaviors of ZK60‐T5 magnesium extrusion are investigated. Strain‐controlled tests were performed at standard laboratory condition with fully reversed straining. Twinning‐detwinning deformation plays an important role in the cyclic axial behavior for tests that were performed under strain amplitudes higher than 0.4%. However, the hysteresis loop for the 0.4% was found symmetric and no sign of twinning‐detwinning deformation was observed. On the contrary, the cyclic shear behavior was found to be similar to conventional alloys and no significant asymmetric or twinning‐detwinning deformations were observed. The multiaxial fatigue tests suggest that multiaxiality and nonproportionality are not detrimental to fatigue life. Three multiaxial fatigue damage models were used: Smith‐Watson‐Topper, Fatemi‐Socie, and Jahed‐Varvani. While Fatemi‐Socie and Jahed‐Varvani models show comparable estimation, Smith‐Watson‐Topper overestimates shear and nonproportional lives.

Multiaxial creep–fatigue Life Prediction Under Variable Amplitude Loading at High Temperature

Based on the time–temperature parameter method, a modified von Mises stress is proposed to calculate the multiaxial creep damage at high temperature. By employing the strain-based multiaxial fatigue damage models, the modified von Mises stress is used to predict the creep–fatigue life under variable amplitude multiaxial loading at high temperature. The experimental data of GH4169 superalloy and 304 stainless steel conducted under both constant and variable amplitude loadings at high temperature are used to verify the proposed method, and a good agreement is obtained with the experimental data.

Recent progress in the application of multiaxial fatigue criteria to lifetime calculations

This paper presents the concept of life-dependent material parameters applied to multiaxial fatigue damage models. Every multiaxial fatigue limit criterion based on the history of the stress tensor components is defined by a scalar parameter that is compared with the fatigue limit. The defined damage parameter is usually also a function of some characteristic material parameters. These material parameters are usually derived from fatigue limits obtained under uniaxial and torsion loading. Attempts to extend this classic form of the damage parameter beyond the fatigue limit domain, i.e. to lifetime calculations, fail even within the high cycle fatigue domain. The aim of this paper is to demonstrate that the material parameters derived from fatigue limits should not be applied in multiaxial fatigue criteria for lifetime calculations. A definition of these material parameters based on applying fatigue uniaxial and torsion characteristics instead of fatigue limits implies that the resulting parameters are functions of the fatigue life. Applying a life-dependent material parameter to the Matake multiaxial fatigue criterion leads to a remarkable improvement in the fatigue life prediction for 2124-T851 aluminium alloy.

A synthesis of cracking directions in tension-torsion multiaxial low cycle fatigue at high and room temperatures

Cracking direction in multiaxial low cycle fatigue is an important research subject because cracking direction is a physical basis for developing an appropriate multiaxial low cycle fatigue damage model. However, there are still many open questions about cracking direction in multiaxial low cycle fatigue. Maximum shear and maximum principal cracks are reported in tension-torsion low cycle fatigue, depending on stress/strain multiaxiality, stress/strain range, notch, and type of materials. The reason for two crack directions has not been well investigated. This paper overviews and discusses a couple of factors that influence the cracking direction, including strain multiaxiality, notch/precrack and strain range for low alloy steels and nickel base superalloys.

Life prediction approach based on the isothermal fatigue and creep damage under multiaxial thermo-mechanical loading

Based on the isothermal fatigue and creep damage, a life prediction approach under multiaxial thermo-mechanical loading was proposed in this investigation. In the proposed method, the multiaxial thermo-mechanical fatigue damage during one cycle period was divided into the isothermal fatigue damage and the creep damage. In order to evaluate conservatively, the isothermal fatigue damage during one cycle period was calculated by using multiaxial fatigue damage model at the maximum temperature during the whole period, and the creep damage during one cycle period was calculated by accumulating the creep damage of all portions originated from the divided time history for the axial load component and temperature history. The life prediction results by the proposed model showed a good agreement with experimental data for nickel-base alloy GH4169 and cobalt-base Haynes188 under axial-torsional thermo-mechanical loading.

Fatigue life predictions of metal structures based on a low-cycle, multiaxial fatigue damage model

A modeling strategy is developed accounting for the simulation of fatigue in metallic structures subjected to multiaxial, cyclic loading conditions. Cyclic plastic deformations are assumed to cause microcrack nucleation and growth, which in turn, lead to a deterioration of the mechanical and thermal properties. Microcrack nucleation and growth are modeled by a continuum damage mechanics formulation which accounts for a progressive loss of material integrity. The formulation utilizes a critical plane method for the prediction of microcrack nucleation. The emerging microcracks are assumed to be aligned with the critical plane orientation causing an anisotropic damage behavior. A second-order damage tensor is defined to approximate the damage behavior by an orthotropic material response. Damage evolution caused by microcrack growth is obtained from an empirical energy criterion based on the inelastic strain energy density. This way, the isotropic material response of a pristine material becomes orthotropic during damage evolution causing a direction dependent loss of material integrity. The continuum damage mechanics formulation in combination with the nonlinear Finite Element Method enables the simulation of structural deterioration caused by a propagating region of material failure. The approach is implemented into the Finite Element Method and extended by a cycle jump technique to reduce the computational time. The modeling strategy is exemplified on micrometer-sized cantilever beams under low-cycle fatigue conditions.

A non-linear multiaxial fatigue damage model for the cervical intervertebral disc annulus

A significant portion of the military population develops severe neck pain in the course of their duties. It has been hypothesized that neck pain is a consequence of accelerated degeneration of the intervertebral discs in the cervical spine, but more occupational and mechanistic-based tools and research are needed to positively confirm the link between neck pain and accelerated disc degeneration. Heavy head-supported mass including helmets and accessories worn by military personnel may subject the intervertebral discs of the cervical spine to complex cyclic loading profiles. In addition, some military operational travel which includes riding on high speed planing boats has also been reported to result in high magnitude cyclic loading on cervical spine discs. In this article, we present a methodology to computationally predict fatigue damage to cervical intervertebral discs over extended periods of time, by integrating kinematics-based biomechanical models with a continuum damage mechanics-based theory of disc degeneration. Through this computational approach, we can gain insights into the relationship between these military activities and possible accelerated fatigue degeneration of cervical intervertebral discs and provide a quantitative prediction tool for decade-long time ranges. The four significant improvements this computational framework adds to the area of modeling intervertebral disc degeneration are the following: (a) it addresses the non-linear nature of fatigue damage evolution, (b) it includes the effect of aging and damage recovery to accurately simulate biological phenomena, (c) it computes fatigue damage taking into account the multiaxial stress state in the disc, and (d) it correlates the computational damage parameter with established clinical grading systems for disc degeneration.

A method for assessing critical plane‐based multiaxial fatigue damage models

AbstractFatigue failure is a complex phenomenon. Therefore, development of a fatigue damage model that considers all associated complexities resulting from the application of different cyclic loading types, geometries, materials, and environmental conditions is a challenging task. Nevertheless, fatigue damage models such as critical plane‐based models are popular because of their capability to estimate life mostly within ±2 and ±3 factors of life for smooth specimens. In this study, a method is proposed for assessing the fatigue life estimation capability of different critical plane‐based models. In this method, a subroutine was developed and used to search for best estimated life regardless of critical plane assumption. Therefore, different fatigue damage models were evaluated at all possible planes to search for the best life. Smith‐Watson‐Topper (normal strain‐based), Fatemi‐Socie (shear strain‐based), and Jahed‐Varvani (total strain energy density‐based) models are compared by using the proposed assessment method. The assessment is done on smooth specimen level by using the experimental multiaxial fatigue data of 3 alloys, namely, AZ31B and AZ61A extruded magnesium alloys and S460N structural steel alloy. Using the proposed assessment method, it was found that the examined models may not be able to reproduce the experimental lives even if they were evaluated at all physical planes.