Non-proportional Loading Conditions Research Articles

Fatigue behaviors and life evaluation of AISI304 stainless steel under non-proportional multiaxial random loading

Fatigue tests on AISI304 stainless steel under non-proportional multiaxial random loading conditions were conducted with uniform hollow specimens at room temperature. The results revealed initial hardening and subsequent cyclic softening under uniaxial loadings and additional hardening under non-proportional multiaxial loadings. This shift from softening to additional hardening significantly reduced the failure life. Fractographic analysis and Electron Backscatter Diffraction (EBSD) observations identified planar slip as the dominant deformation mechanism under uniaxial loading. Multiple slip system activations, strong slip interactions, and martensitic transformation were key factors influencing changes in cyclic deformation behavior under non-proportional loadings. A novel life evaluation method based on the Itoh–Sakane (IS) method was established, demonstrating accurate evaluations for both uniaxial and non-proportional multiaxial fatigue life under random loading conditions.

Biaxial Testing of Thin Metal Sheets under Non-Proportional Loading Conditions

During the manufacturing and service of thin metal sheets, different stress states occur, often caused by non-proportional loading conditions. They can lead to localization of inelastic deformations as well as to damage and failure processes. In the present paper, a series of experiments with newly designed biaxially loaded specimens is presented to analyze the damage and failure behavior of thin ductile metal sheets under non-proportional load paths. Bands of holes with different orientation have been milled in critical regions of the specimens to localize stresses and strains. In compression tests, a special downholder is used to avoid buckling. During the loading processes, strain fields in critical regions of the specimens are monitored by digital image correlation technique. After the experiments, fracture surfaces are investigated by scanning electron microscopy showing different damage and fracture modes depending on the loading history. The experiments clearly demonstrate the efficiency of the thin specimens and the experimental program.

Elastic-Gap Free Formulation in Strain Gradient Plasticity Theory

Abstract This article presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong–Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type nonincremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under nonproportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the nonincremental isotropic strain gradient plasticity theory without introducing any stress jump.

Study on ductile fracture behavior of hydrogen-charged API pipeline steel

With the increasing focus on reducing carbon emissions, hydrogen has emerged as a promising alternative energy source. However, the safe transportation of hydrogen poses challenges due to its potential impact on the integrity of pipeline materials. This study aims to investigate the effect of hydrogen charging time on the plastic behavior and ductile fracture characteristics of API 5L X42 pipelines, which are commonly used for transporting hydrocarbons. Tensile tests were conducted on various types of hydrogen-charged specimens at room temperature to assess different fracture modes. Hydrogen was introduced into the specimens using a cathodic electrolytic method, and 24-h charging time durations were considered. Finite element analyses were performed on standard dog-bone and notched tension specimens to evaluate the plastic behavior, employing the Swift hardening law to model the flow stress. Numerical analyses were conducted to determine the loading path leading to fracture initiation. A damage framework based on the Hosford–Coulomb model was utilized to predict ductile fracture under non-proportional loading conditions. The findings of this study provide insights into the fracture behavior of pipelines under hydrogen exposure, aiding in the design and assessment of safe and reliable hydrogen transport systems.

Numerical Study on a Ductile Fracture Model in Pre-Cracked Tension Tests of SUS304L.

The effectiveness of a ductile fracture model in accurately predicting fracture initiation has been demonstrated. In this study, we concentrate on applying the ductile fracture model to pre-cracked structures constructed from SUS304L stainless steel with experimental and numerical analyses. The Swift hardening law was employed to extend the plastic behavior beyond the onset of necking. Additionally, the Hosford-Coulomb model, integrated with a damaged framework, was utilized to predict ductile fracture behavior, particularly under non-proportional loading conditions. Tension tests were conducted on various specimens designed to illustrate various fracture modes resulting from geometric effects. Numerical analyses were conducted to explore the loading histories, utilizing an optimization process to calibrate fracture model parameters. The proposed fracture model is validated against pre-cracked structures detailed in a reference paper. The results convincingly demonstrate that the fracture model effectively predicts both fracture initiation and propagation in pre-cracked structures.

Stress-strain Deformation Analysis of Conventional Vehicle Shock Absorber Materials under In-service Multi-translated Non-proportional Loading Conditions

Stress-strain Deformation Analysis of Conventional Vehicle Shock Absorber Materials under In-service Multi-translated Non-proportional Loading Conditions

Comparison of critical plane models for multiaxial fatigue life prediction

Background. The operation of numerous machines and units takes place under conditions of multi-axial cyclic loading, which, as a rule, is non-proportional. Evaluating the fatigue durability of metal alloys under conditions of multi-axial non-proportional loading is a relevant task in modern engineering. Solving this problem requires fatigue calculation methods that would consider operating conditions and properties of structural materials, including factors such as the type of stress state, loading trajectory, material sensitivity to non-proportional loading, and so on.Objective. To conduct a comparative analysis of a range of fatigue life models based on the concept of the critical plane, including the Fatemi-Socie, Wang-Brown, Smith-Watson-Topper, Liu I, and Liu II approaches, and to identify the limits and peculiarities of their application.Methods. The fatigue lives calculated using the selected models were compared with experimental results obtained for various metal alloys subjected to uniaxial tension-compression, alternating torsion, and proportional and non-proportional multiaxial loading.Results. The applicability limits of fatigue life models based on the critical plane concept were analyzed for different metal alloys under conditions of proportional and non-proportional multiaxial loading.Conclusions. The research results demonstrated that models requiring the use of material constants obtained from tests in both tension-compression and alternating torsion provide reliable fatigue life estimates for various types of metal alloys. Calculations based solely on fatigue curves from alternating torsion better correlate with the results of tests on ductile materials, while calculations based on criteria utilizing fatigue curves from tension-compression align more closely with results from tests on brittle materials.

Fatigue assessment of a FSAE car rear upright by a closed form solution of the critical plane method

Material fatigue is extensively discussed and researched within scientific and industrial communities. Fatigue damage poses a significant challenge for both metallic and non-metallic components, often resulting in unexpected failures of in-service parts. Within multiaxial fatigue assessment, critical plane methods have gained importance due to their ability to characterize a component's critical location and detect early crack propagation. However, the conventional approach to calculate critical plane factors is time-consuming, making it primarily suitable for research purposes or when critical regions are already known. In many real-world scenarios, identifying the critical area of a component is difficult due to complex geometries, varying loads, or time limitations. This challenge becomes particularly crucial after topological optimization of components and in the context of lightweight design. Recently, the authors proposed an efficient method for evaluating critical plane factors in closed form, applicable to all cases that necessitate the maximization of specific parameters based on stress and strain components or their combination. This paper presents and validates the proposed methodology, with reference to a rear upright of a FSAE car, which is characterized by a complex geometry and is subjected to non-proportional loading conditions. The efficient algorithm demonstrated a substantial reduction in computation time compared to the standard plane scanning method, while maintaining solution accuracy.

Numerical analysis of non-proportional biaxial reverse experiments with a two-surface anisotropic cyclic plasticity-damage approach

This paper deals with the numerical analysis of ductile damage and fracture behavior under non-proportional biaxial reverse loading conditions. A two-surface anisotropic cyclic elastic–plastic-damage continuum model is adequately presented, which takes into account the Bauschinger effect, the stress-differential effect, and the change of hardening rate after reverse loading. An efficient Euler explicit numerical integration algorithm, based on the inelastic (plastic or plastic-damage) predictor-elastic corrector approach, is utilized to analyze the stress and finite strain loading histories. Detailed discussions are provided on different numerical integration-related consistent tangent operators that achieve convergence within the global Newton–Raphson scheme. The proposed continuum model is implemented into the commercial software Ansys as a user-defined subroutine (UMAT). Furthermore, the novel non-proportional biaxial tensile reverse experiments are performed to validate the proposed continuum model. The associated numerical simulations investigate the stability and accuracy of the proposed algorithm and material model.

A novel approach to multiaxial fatigue life prediction using the critical plane and phase difference angle

Multiaxial loads are the main cause of fatigue failure in engineering applications, where this failure affects the components and structure of these applications directly. The probability of failures can be decreased by using multiaxial fatigue analysis to assess the service life of components. This study proposes a simple and effective approach for measuring fatigue life in the presence of multiaxial loading. The proposed damage parameter includes terms such as the critical plane and phase difference angles. Calculating fatigue life using this model under proportional and nonproportional loading conditions is possible. The accuracy and validity of the model were tested by comparing the experimental results of four experimental datasets with the life estimation results. The analysis results of four metal materials show that the predicted life correlated well with the experimental observations. In addition to the proposed model, five famous fatigue prediction models were used, and the results of the proposed model were compared with these models. The suggested damage parameter is better for predicting fatigue life under different loads. This was shown through model comparison and prediction error analysis. The findings show good agreement between the suggested model's life estimation results and the experimental findings. Predicting fatigue life becomes more realistic with the suggested approach for any angle between 0 and 90°. The proposed model showed the highest accuracy among the tested models. Afterwards, the Fatemi and Socie FS, Kandil Brown and Miller (KBM), Smith Watson and Topper (SWT), maximum share stress (MSS), and ES models demonstrated lower levels of prediction error, respectively.

Ductile fracture of anisotropic QP980 steel sheet by using the isotropic/anisotropic modified Mohr-Coulomb models

The modified isotropic Mohr-Coulomb (iso-MMC) fracture model, which utilizes the Mises yield function and isotropic hardening law, was calibrated through tensile tests on various specimens. The resulting calibrated model was constructed in (η, L, ε¯f) space to represent the isotropic fracture locus of QP980 steel sheet. Subsequently, this calibrated model was utilized to predict the ductile fracture behavior of QP980 steel sheet loaded along rolling direction under different stress states. To comprehensively consider the impact of anisotropic properties on fracture evolution, an anisotropic MMC (aniso-MMC) ductile fracture model was developed in terms of strain space. Under the assumption of plane stress, the Mohr-Coulomb (MC) criterion was converted from stress space to strain space through an anisotropic constitutive model in order to characterize ductile fracture in QP980 steel sheet. The quadratic yield function of Hill's 48 yield function with the isotropic hardening law was employed to characterize the plastic behavior during loading. The anisotropic fracture loci of QP980 steel sheet were obtained in various loading directions. The scanning electron microscope (SEM) was utilized to characterize the microscopic morphology of the fracture surfaces of QP980 steel sheet, investigating the fracture mechanism of anisotropic ductility under different stress states. The results of both tensile experiments and simulations have confirmed that the plastic anisotropy of materials plays a critical role in determining ductile fracture behavior. The aniso-MMC fracture model was ultimately validated through hole expansion tests and equi-biaxial tensile tests, demonstrating its capability to predict ductile fracture behavior under both proportional and non-proportional loading conditions.

Multiaxial non-proportional fatigue behaviour and microstructural deformation mechanisms of 9%Cr steel at elevated temperature

High-temperature components utilised in practical service are often subjected to multiaxial non-proportional loading due to their complex geometry. In the present study, a set of strain-controlled fatigue tests were conducted on P92 steel at 600 °C, including uniaxial, multiaxial proportional, and multiaxial non-proportional loading conditions. Results reveal that the axial and shear stresses exhibit varied responses to the different non-proportionalities, with proportional loading resulting in the shortest fatigue life when the strain ratio is small. The non-proportional loading induces accelerated cyclic softening at axial direction while the shear stress is enhanced. Electron backscatter diffraction (EBSD) and transmission electron microscope (TEM) analysis indicate that the increased role of shear stress promotes the dislocation motion from the planar slip to cross-slip under non-proportional loading, which in turn facilitates the microstructure evolution. It is also important to note that the evident development of microstructure and the combined effect of more crack initiations and more secondary cracks contribute to the lowest fatigue life under proportional loading.

Path-dependent multiaxial fatigue behavior of A319 aluminum alloy under non-proportional loading conditions

Abstract In the multiaxial low fatigue test study, four multiaxial non-proportional fatigue loading paths were used including rectangular, square, rhombic and circular. The effect of loading condition changes on the fatigue behavior and cyclic damage characteristics of A319 aluminum alloy was investigated by means of stress response curves, stress–strain hysteresis lines, fatigue fracture morphology, and dislocation substructure morphology in combination with material microstructure. The non-proportional hardening behavior exhibits strong loading path dependence, and the fatigue plastic deformation in the torsional direction is greater in the circular and rhombic paths, and the fatigue damage is more severe, resulting in a shorter fatigue life of A319 aluminum alloy. The axial directions under non-proportional multiaxial loading all have tensile and compressive asymmetric behavior. The differences in loading paths result in different fatigue crack expansion modes. The non-proportional additional hardening behavior under different loading paths is closely related to the dislocation substructure. In the rhombic and circular paths, the alloys have higher dislocation density and strong interaction between dislocations and precipitation phases, which is macroscopically expressed as stronger non-proportional hardening ability in the rhombic and circular loading paths.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation

Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension–compression–passivation, bending–passivation and tension–bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall–Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2μm to 15μm and different orientations.

Mesoscopic unit cell analysis of ductile failure under plane stress conditions

Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

Multiaxial fatigue life prediction for various metallic materials based on the hybrid CNN‐LSTM neural network

AbstractA new algorithm optimization‐based hybrid neural network model is proposed in the present study for the multiaxial fatigue life prediction of various metallic materials. Firstly, a convolutional neural network (CNN) is applied to extract the in‐depth features from the loading sequence composed of the critical fatigue loading conditions. Meanwhile, the multiaxial historical loading information with time‐series features is retained. Then, a long short‐term memory (LSTM) network is adopted to capture the time‐series features and in‐depth features of the CNN output. Finally, a full connection layer is used to achieve dimensional transformation, which makes the fatigue life predictable. Herein, the hyperparameters of the LSTM network are automatically determined using the slime mold algorithm (SMA). The test results demonstrate that the proposed model has pleasant prediction performance and extrapolation capability, and it is suitable for the life prediction of various metallic materials under uniaxial, proportional multiaxial, nonproportional multiaxial loading conditions.

Failure Strength of Automotive Steering Knuckle Made of Metal Matrix Composite

This article presents the static performance of composite steering knuckle due to drive on an equivalent road, including different types of roughness and maneuvers. To achieve this purpose, the driving of a full-vehicle model was simulated using the multi-body dynamics (MBD) method, and the imposed loads on connection points of the steering knuckle to different components of the suspension system were extracted considering various maneuvers. Next, CATIA software was used to prepare a smooth model of the steering knuckle by employing coordinate measuring machine (CMM) data. Stress analysis was performed under the maximum value of the loading history in finite element (FE) software. Eventually, the safety factor was calculated based on some well-known criteria for static failure of the composite materials. Moreover, the optimum value of tungsten carbide as a reinforcing substance in aluminum composite was estimated to increase failure strength. The results show that an increase in tungsten carbide leads to an increase in the strength of the steering knuckle under purely axial loads (normal stress criterion) and also that an increase in this substance leads to a decrease in the strength of the part under shear loads (shear stress criterion). Therefore, based on the nature of the loads (i.e., multi-axial non-proportional random amplitude loading conditions) applied to the automotive steering knuckle due to actual conditions, this metal matrix composite (aluminum matrix and tungsten carbide as reinforcement) is not practical.

Multiaxial creep-fatigue constitutive modeling and damage evaluation for type F82H steel under non-proportional loading conditions

In this study, the deformation behaviors of F82H steel at 823 K under uniaxial and non-proportional loading conditions were described using a unified viscoplasticity model. The multiaxial creep–fatigue life was predicted using a strain energy damage parameter in collaboration with cycle-by-cycle concept. The creep–fatigue tested conditions includes tension holding and slow strain rate strain waveforms. Our findings showed that the cyclic deformation behaviors were well described using the unified viscoplasticity model. The creep–fatigue life was well predicted by the proposed energy-based model within a factor of 2.

Comparison of some selected time-domain fatigue failure criteria dedicated for multi input random non-proportional loading conditions in industrial components

This paper presents time-domain procedure to evaluate High-Cycle Fatigue (HCF) life of industrial components with complicated geometries and subjected to multi-input random loading conditions. To this end, the authors discuss some well-known equivalent stress criteria which can consider the orientation of critical plane changes with the time in non-proportional loading conditions to estimate the time history of equivalent stress. This task is successfully accomplished by knowing time histories of local stress tensor components in a critical area of the part that is prone to failure. Next, two different categories were used to predict fatigue life of component: 1- Linear Damage Accumulation (LDA) rule by employing Rain-flow cycle counting and 2- probabilistic approach by utilizing level crossing counting method. To apply these methodologies and awareness of their challenges, a case study was performed on the automotive steering knuckle. Finally, the predicted lives were compared to experimental results, and the accuracies of different fatigue life assessment techniques were reported. The obtained results show that combination of Rain-flow cycle counting with the Liu-Zenner criterion and especially, with the Energy-based instant fatigue damage tracing proposed by Shariyat lead to the highest accuracies. However, using the probabilistic approach, we will get the response in a much shorter time compared to another category. Therefore, the choice which method to use also depends on the parameters of the research situation, and the interaction of the two factors of prediction accuracy and prediction time in the industry.