Multiaxial Non-proportional Loading Research Articles

Dealing with multiaxial non-proportional fatigue with varying mean stress: Invariant and critical plane approaches for component-like structural adhesive joints

A comparative investigation between an invariant-based approach using the signed Beltrami-stress and critical-plane approach using the Findley-stress is carried out for the fatigue lifetime prediction of an epoxy structural adhesive under multiaxial non-proportional loading with varying mean stress. Fatigue experiments with uniaxial and multiaxial loading (proportional and non-proportional) are done at stress ratios of −1 and 0.1. Two adhesive joints are evaluated: a hollow-cylinder butt-joint (HCBJ, sample with homogeneous stresses distribution), and a flange-rod-joint (FRJ, component-like specimen with complex stress state). For both geometries, multiaxial loading and an increasing mean stress lead to fatigue strength reduction, whereas the phase-shift effect is less pronounced. A systematic procedure for parameter determination is implemented for both approaches. For predictions of the HCBJ-sample, stresses are analytically obtained. For validation with the FRJ-sample, FEA-based stress calculation is used. For both joints, the critical plane approach results in more accurate predictions than the invariant-based approach. In comparative terms, the invariant-based approach is experimentally more complex, by requiring a mean stress correction, but its numerically simpler with lower calculation time. The critical-plane approach requires fewer experiments for parameter determination and provides more accurate results for non-proportional loading. However, it is more numerically demanding with larger computing time.

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.

Effect of non-proportional stress states caused by varying phase shifts on the fatigue life of welded joints

In this paper, the effect of multiaxial non-proportional stress states on the fatigue life of welded joints is investigated. The non-proportional stress states are caused by various phase shifts between the normal and shear stresses. In total 45, welded tube-to-tube specimens are tested under multiaxial proportional and non-proportional loading. The increase in fatigue damage caused by non-proportional stresses, compared to proportional stresses, is quantified by penalty factors. A set of penalty factors are derived from the fatigue experiments for use with the governing multiaxial fatigue criteria by the International Institute of Welding (IIW) and Det Norske Veritas (DNV). The experimental results show that phase shifts decrease the fatigue life. However, this reduction is not to the extend proposed by the governing guidelines. Furthermore, the results indicate that different degrees of phase shift do not induce varying levels of fatigue life degradation.

Assessing Fatigue in Materials with Small Defects: A New Multiaxial Model Based on Principal Stress Amplitudes

A new multiaxial fatigue model for materials containing small defects proposed by the authors is presented, which one can be considered as a modification of the SWT model. This new model relates the fatigue limit of the material obtained from the √area parameter with values associated with the principal stresses. These values are the amplitude of the principal stresses and the maximum principal stress observed. The amplitude value associated with the principal stresses is defined by using the Maximum Variance Method. This amplitude only can be easily obtained under uniaxial loading conditions, but its calculation for torsion, proportional and non-proportional multiaxial loadings is not trivial. Therefore, the calculation of the principal stress amplitude posed a challenge not yet addressed by other authors. The multiaxial fatigue model was evaluated with experimental data from AISI 4140 steel, with several different loading conditions, including uniaxial loading, combined loads in in-phase and out-of-phase configurations. In addition, two types of specimens were used: smooth cylindrical specimens and specimens with a surface micro hole. Comparing the experimental data with the prediction of the new model it was observed that the predictions are slightly conservative with average error not exceeding 6%.

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.

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.

Fretting fatigue crack propagation under out-of-phase loading conditions using extended maximum tangential stress criterion

In this paper, a numerical crack growth analysis is conducted by using the Maximum Tangential Stress (MTS) criterion and its extension, which considers the contact stress between the crack surfaces. Moreover, fretting fatigue is a multiaxial non-proportional loading problem, and most components are subjected to asynchronous loads. Therefore, this paper mostly focuses on the influence of loading phase difference (Φ) on the crack propagation behavior. Meanwhile, for the fretting fatigue problem, as there is a relationship between the crack initiation and propagation, the effect of initiation characteristics, including crack initiation position and direction is studied under different loading phase differences using Linear Elastic Fracture Mechanics (LEFM) theory. It is observed that the predicted crack path and lifetime by using the extended MTS criterion and Paris’ law is in good agreement with the experimental results in the literature. It is found that the phase difference has a strong effect on the crack propagation behavior. Furthermore, we found that the crack initiation position has a greater influence on crack propagation behavior than the crack initiation direction.

Theoretical and experimental investigations of crack propagation behavior and delamination in GLARE specimens affected by non-proportional fatigue loadings

In actual operation conditions, the structural parts of automotive, aerospace and other significant industrial applications undergo the multi axial fatigue loading with non-proportionality states. Fiber metal laminates (known as FML) are the best options to manufacture these structural parts. The current study examines the effects of a specific condition of multi-axial fatigue loadings (repeated tension with static shear stresses) on the behaviors of crack growth and delamination in GLARE specimens (abbreviated of glass laminates aluminum reinforced epoxy). Analytical model with idea of maximum tangential stress criterion modification has been adopted to represent the non-proportionality state of fatigue loading. Paris equation, equivalent stress intensity factor range, fiber-bridging effects and delamination shape were included in this model. The current idea was compared with a previous idea that depends on the principal stresses in representation of non-proportional multi-axial fatigue loadings. Specimens have coding GLARE_2A 2/1 were fabricated by VARTM technique (vacuum assisted resin transfer molding technique). Special treatments have been done on the aluminum surfaces before specimen fabrication to increasing delamination resistance. Novel fatigue apparatus was manufactured to guarantee apply the under study conditions for multi axial fatigue loading and to introduce experimental investigation of crack and delamination growths in GLARE specimens. The obtained results of the current idea were in a considerable agreement with that of the previous idea of the principal stresses. The maximum deviations between analytically extracted results were less than 1% for crack growth, 5.4% for bridging stress, 4.8% for crack opening and 6.3% for delamination growth. Experimentally, the measured results have been compared with analytical results for the purpose of validation. Acceptable matching between results with maximum difference of 7.65% was the important outcome of this study.

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.

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.

Improvement of the Adjustable Localization Operator identification based on the confined plasticity zone shape for multiaxial elasto-plastic cyclic predictions

Simplified methods for elasto-plastic calculations are a cost and time savings solution to obtain mechanical state at the notch tip. The Adjustable Localization Operator (ALO) method has been proven to be a robust and inherently multiaxial method. This study aims to propose an alternative strategy for identifying its parameters. The principal idea is to consider the shape of the confined plastic zone in order to adapt the various parameters of the adjustable localization operator. The proposed approach has been validated on notched structures with plane strain assumption as well as on a new design structure for multiaxial proportional and non-proportional loadings. The results obtained have shown the interest of considering the shape of the confined plastic.

Multiaxial fatigue prediction and uncertainty quantification based on back propagation neural network and Gaussian process regression

Engineering structures are often suffering multiaxial stress which leads to multiaxial fatigue failures. Accurate and reliable multiaxial life prediction is a challenging issue in fatigue analysis due to the intricate deterioration mechanisms of the fatigue failure and the large uncertainty in the material parameters at the microscopic scale. Moreover, conventional multiaxial fatigue life prediction models are empirical or semi-empirical. To tackle this problem, a data-driven method is presented, which combines the back propagation neural network (BPNN) and the Gaussian process regression (GPR). The BPNN-GPR method can predict the multiaxial fatigue life and quantify the uncertainty simultaneously. This method is validated using six materials including the uniaxial, multiaxial proportional and multiaxial nonproportional loading cases. All the predicted lives fall within a life factor of ± 3, which indicates that the BPNN-GPR method has the satisfactory capability for multiaxial fatigue life prediction. In addition, results also show the prediction capability of the BPNN-GPR method for unknown multiaxial nonproportional loading paths.

Glass laminate aluminum reinforced epoxy under non-proportional multiaxial fatigue loading: Experimental testing and new fatigue apparatus development

Predominately, the structures and components in aeronautic, automotive and other important implementations suffer from non-proportional multi-axial fatigue loading. One of the best selected materials to fabricate these structures and components are fiber metal laminates (FML). In this research, fatigue crack-propagation in glass-laminate aluminum reinforced-epoxy (GLARE) specimen under the effect of special case of multi-axial fatigue loading (constant shear with repeated tensile stresses) has been studied analytically, numerically and experimentally. GLARE_2 A 2/1 specimen was fabricated using vacuum assisted resin transfer molding technique after special preparation aluminum surface procedure. New multi-axial fatigue apparatus including mechanical, hydraulic and control systems was manufactured to investigate crack growth experimentally. Analytical model using Paris relation was adopted to predict crack growth through aluminum layers of GLARE specimen. The rate of crack propagation is related to the mixed-mode equivalent stress intensity factor, which is estimated by the superposition for both fiber-bridging and far-field stress intensity factors. The crack opening contour, distribution of fiber-bridging stress, delamination growth and its shape were evaluated in simultaneous manner to find the fiber-bridging stress intensity factor. ABAQUS 2021 software has been used to simulate crack and delamination growth in GLARE specimen with the aforementioned fatigue loading. The extracted results from analytical and numerical models such as crack growth, crack opening, delamination shape and crack angle have been compared with that measured experimentally. The comparison indicates that there is good agreement between the calculated and measured results (with maximum deviation of 8.74% for crack growth).

Multiaxial fatigue behavior of a 2198-T8 Al–Li alloy under proportional and nonproportional loading

Abstract 2198-T8 Al–Li alloy was examined under different loading path. Uniaxial and multiaxial proportional and nonproportional loading tests were conducted to determine the material fatigue constant, and to study the multiaxial fatigue behavior, respectively. The multiaxial fatigue life was estimated by various criteria. The results show that, the torsional fatigue performance is better than the tension–compression fatigue performance. The fatigue life of nonproportional loading increases firstly and then decreases with the increase of phase difference from 0° to 90°. Shear Findley model and SWT model were modified by introducing shear damage parameters. The modified models provide fine results which are all within a factor of two.

Prediction of fatigue damage and spalling in a multilayered journal bearing shell

A 3D nonlinear approach for predicting the fatigue damage of plain journal bearings is proposed. The criterion selected, among several models, is inspired by Dang Van’s but is modified through an ascending slope in tensile direction. This criterion is consistent with the stresses seen on the bearing shells through hydrodynamic oil pressure and allows to reflect the severity of the compressive multiaxial non-proportional loading. From a fatigue test campaign, a modified Dang Van criterion is calibrated. Then, the simulation on the engine bench structure predicts a lifetime mapping consistent with the imposed loading and the experimental observations.

A comparison of uniaxial and multiaxial non-proportional fatigue properties in cast Al-Si-Cu-T6 alloys solidified at two cooling rates: Fatigue behavior, fracture characteristics and dislocation evolution

The cyclic deformation behavior and fatigue fracture characteristics of cast Al-Si-Cu-T6 (A319-T6) alloys solidified at two cooling rates under uniaxial and multiaxial non-proportional loading conditions were investigated. The A319-T6 alloy exhibited cyclic hardening and additional non-proportional hardening effects during cyclic loading. The cyclic hardening rate and non-proportional loading sensitivity coefficient improved by 2.8% and 5.1%, respectively, when the solidification cooling rate was increased from 0.1 to 10 °C/s. To account for the hardening effects, the dislocation evolution and interaction between dislocations and other microstructures were analyzed. Based on the asymmetry parameter, the tension-compression symmetries of A319-T6 alloys subjected to uniaxial and multiaxial non-proportional loading were discussed. The presence or absence of a steady crack propagation area was considered to be the primary difference in the cross-section caused by cooling rates, leading to varied fracture flatness. Multiaxial non-proportional loading yielded reciprocating wear marks and a significant quantity of wear debris on the fracture surface. The majority of wear debris was identified as matrix oxide. The reciprocating wear process removed fatigue striation and secondary cracks that emerged on the uniaxial fracture, further increasing fracture flatness.

Multi-axial fatigue life assessment of additively manufactured nickel-based superalloys

In the present work, the microstructures and mechanical properties of additively manufactured IN718 alloy were studied and the dendritic columnar microstructures elongated along the building direction are related to macroscopic mechanical properties. Detailed experiments under both proportional and non-proportional multi-axial loading conditions indicate that the influence of the building orientation from manufacturing on mechanical property and fatigue performance is negligible. Fractography analysis reveals that fatigue crack initiates from carbide and oxygen phases. The shear energy-based models reasonably predict the fatigue life and shear failure is the dominant failure mode for the laser melting material.

An Anisotropic Continuum Damage Mechanics Model for the Simulation of Yield Surface Evolution and Ratcheting

A new anisotropic continuum damage model was presented on the basis of irreversible thermodynamics. Second rank symmetric damage tensor, kinematic hardening tensor, and damage potential surface were introduced. The yield surface in this study has been modeled to distort in the stress space by the evolution of the damage tensor. The new model was applied in yield surface characterization and led to a well description of the subsequent yield surfaces. This model is then applied to predict experimental results of the cyclic nonproportional loading paths obtained by Kang et al. [2004], Hassan et al. [2002] and Taleb and Cailletaud [2011]. It is demonstrated that the new model can predict the yield surface distortion and the ratcheting strains of multiaxial nonproportional cyclic loading with acceptable accuracy and by using less material constants with respect to the previous models.

Multiaxial fatigue life prediction for metallic materials considering loading path and additional hardening effect

PurposeA large number of data have proved that under the same von Mises equivalent strain condition, the fatigue life under multiaxial non-proportional loading is often much lower than the life under multiaxial proportional loading. This is mainly due to the influence of the non-proportional loading path and the additional hardening effect, which lead to a sharp decrease in life.Design/methodology/approachThe modulus attenuation effect is used to modify the static hardening coefficient, and the predicted value obtained is closer to the additional hardening coefficient obtained from the experiment. A fatigue life model can consider non-proportional paths, and additional hardening effects are proposed. And the model uses multiaxial fatigue test data to verify the validity and adaptability of the new model. The life prediction accuracy and material application range are satisfactory.FindingsBecause loading path and additional hardening of the material affect fatigue life, a new multiaxis fatigue life model based on the critical plane approach is proposed. And introducing a non-proportional additional damage coefficient, the joint influence of the load path and the additional hardening can be considered. The model's life prediction accuracy and material applicability were verified with multiaxial fatigue test data of eight materials and nine loads compared with the prediction accuracy of the Kandil–Brown–Miller (KBM) model and Fatemi–Socie (FS) model.Originality/valueThe physical meaning of the new model is clear, convenient for practical engineering applications.