Complex Multiaxial Loading Research Articles

A frequency domain enhanced multi-view neural network approach to multiaxial fatigue life prediction for various metal materials

Fatigue damages and failure widely exist in engineering structures, particularly in industries such as aerospace, automotive, and construction, where components are often subjected to complex multiaxial loading conditions. Accurate prediction of fatigue life is critical for ensuring the safety and longevity of these structures. In this study, a novel multi-view deep learning model incorporating frequency domain analysis for fatigue life prediction is proposed. The proposed model integrates a Convolutional Neural Network (CNN), a Long Short-Term Memory Network (LSTM), and FNet that combines frequency domain analysis, in a parallel structure to extract features from the loading paths of materials. These extracted features are then connected to a fully connected neural network to predict fatigue life. The model was validated using fatigue data collected from 6 different materials, encompassing 17 loading paths and 336 samples. Additionally, ablation experiments were conducted, and the extrapolation capabilities were evaluated using specifically designed test sets. The results demonstrate that the proposed model exhibits excellent predictive performance and extrapolation capabilities. We anticipate that the multi-view approach, along with its accuracy and applicability, can offer potential applications in engineering fields that require reliable, data-driven models to assess material durability under complex loading scenarios.

Multiscale 3D displacement field measurement using stereo digital image correlation on a fractal speckle pattern

AbstractEven though the simulations used to predict failure are becoming increasingly predictive, complex multiaxial loading tests are still required to validate the design of structural components in a wide range of industries. Large specimen testing often requires two different scales. A global Far Field to obtain boundary conditions and a local Near Field to evaluate strain gradients around discontinuities such as bolts, notches… The main goal of this study is to provide a continuous displacement over the whole specimen surface integrating data from multiple cameras. In this paper, we propose a new methodology that generates 3D displacements determined by finite‐element stereo digital image correlation in the Near Field and in the Far Field using a unique fractal speckle pattern and an off‐line determined texture. The displacements are obtained in the same coordinate system and on the same mesh. Satisfactory data fusion from both Near Field and Far Field images of a biaxial test on a notched laminate composite was obtained with a refined mesh at the notch tip. This methodology can be applied to any tests requiring multiple camera systems and will support the use of the finite‐element digital image correlation framework as an experimental‐numerical efficient technique.

Multiaxial low cycle fatigue behavior and life prediction of wire arc additive manufactured 308L stainless steel

Wire arc additive manufacturing (WAAM) is a technique that has gained popularity in various industrial sectors due to its high productivity and flexibility. However, the comprehension of cyclic deformation and fatigue behaviors in WAAM austenitic stainless steel (SS), particularly under complex multiaxial loading conditions, is much less advanced compared to conventional manufacturing methods. This study aims to fill some of these gaps by performing fatigue tests of WAAM 308L SS under axial, torsional and axial–torsional multiaxial loadings. Similar tests were carried out on the hot-rolled 308L SS as a basis for comparison. WAAM 308L SS exhibits notable distinctions in cyclic deformation, fatigue life, cracking mode and fatigue failure mechanisms compared to its hot-rolled counterparts as a result of its distinct manufacturing technologies and resulting microstructures. To assess all fatigue life data, three critical plane criteria, namely FS, SWT and CXH criteria, were employed. The CXH model, which considers the effects of both tensile and shear damage on fatigue properties, has the ability to predict the fatigue life of both hot-rolled and WAAM 308L SS.

Bounding surface plasticity model modification for ratcheting of metals

The Bounding Surface (BS) plasticity model for metals is modified according to the proposition introduced in the works of Burlet and Cailletaud (1986) and Delobelle (1993) for the kinematic hardening of a classical Armstrong/Frederick (AF) model, called the BCD modification from the initials of the foregoing authors. The BCD modification was introduced in the relative kinematic hardening between Yield Surface (YS) and BS, unlike its introduction in the absolute and single kinematic hardening of YS for an AF model, hence, achieving two objectives: first, maintaining the inherent feature of BS for decoupling plastic modulus and direction of kinematic hardening, and, second, allowing a flexibility as to the relative kinematic hardening direction without altering the value of the plastic modulus, a property of BCD modification. In addition, the introduced BCD modification for the BS is significantly modified itself, by introducing a properly varying modification parameter instead of the fixed one used in the original works. This simple feature of the novel BCD modification provides a dramatically improved capability to simulate multiaxial ratcheting (MR), because it affects directly the changing flow rule direction, due to the relative kinematic hardening, during complex multiaxial loading, without sacrificing accurate simulations under uniaxial ratcheting (UR) since the plastic modulus is not affected. An additional significant contribution to successful UR simulations is provided by the free-to-choose kinematic hardening of the BS, since the BCD modification is applied only to the relative kinematic hardening between BS and YS. The new model, named SANIMETAL-BCD, is shown to yield superior or equal simulations of UR and very complex MR experimental data for three Carbon Steel specimens, in comparison with other models, within a much simpler constitutive framework. Shortcomings and future necessary improvements are discussed in details.

Physiological and degenerative loading of bovine intervertebral disc in a bioreactor: A finite element study of complex motions

Intervertebral disc (IVD) degeneration and regenerative therapies are commonly studied in organ-culture experiments with uniaxial compressive loading. Recently, in our laboratory, we established a bioreactor system capable of applying loads in six degrees-of-freedom (DOF) to bovine IVDs, which replicates more closely the complex multi-axial loading of the IVD in vivo. However, the magnitudes of loading that are physiological (able to maintain cell viability) or mechanically degenerative are unknown for load cases combining several DOFs. This study aimed to establish physiological and degenerative levels of maximum principal strains and stresses in the bovine IVD tissue and to investigate how they are achieved under complex load cases related to common daily activities.The physiological and degenerative levels of maximum principal strains and stresses were determined via finite element (FE) analysis of bovine IVD subjected to experimentally established physiological and degenerative compressive loading protocols. Then, complex load cases, such as a combination of compression + flexion + torsion, were applied on the FE-model with increasing magnitudes of loading to discover when physiological and degenerative tissue strains and stresses were reached.When applying 0.1 MPa of compression and ±2–3° of flexion and ±1–2° of torsion the investigated mechanical parameters remained at physiological levels, but with ±6–8° of flexion in combination with ±2–4° of torsion, the stresses in the outer annulus fibrosus (OAF) exceeded degenerative levels.In the case of compression + flexion + torsion, the mechanical degeneration likely initiates at the OAF when loading magnitudes are high enough. The physiological and degenerative magnitudes can be used as guidelines for bioreactor experiments with bovine IVDs.

A moment quadrature method for uncertainty quantification of three-dimensional crack propagation via extremely few model runs

The finite element-based three-dimensional crack propagation analysis has increasingly been used in many design assessment applications, particularly those high reliability-demanding structures subject to complex multi-axial fatigue loading. Such analysis is computationally intensive and poses a great challenge to current uncertainty quantification methods, which normally require a substantial number of finite element model runs. This study proposes a new method for uncertainty quantification of finite element-based three-dimensional crack propagation analysis under material uncertainty via extremely few, normally 2d, model runs, and d is the number of uncertain variables. When the classical two-parameter Paris’ equation is employed as the fatigue crack growth rate model, a total number of 4 model runs are sufficient. The method employs the Hankel matrix of moments associated with the uncertainty variables to determine the optimal nodes and weights in the variable space for Gauss quadrature under prescribed distributions. A two-step time integration scheme is employed to further reduce the number of propagation steps within an individual finite element model run. The accuracy of the proposed method is validated using a practical case with realistic fatigue testing data and analytical solutions. The holistic method is applied to two three-dimensional crack propagation problems to demonstrate the effectiveness. It is shown that using 4 model runs the mean and variance of the crack front can be accurately captured under material uncertainty.

Multiaxial fatigue life prediction of an aero-engine turbine shaft with a modified critical plane-basedmodel

For aero-engine components subjected to complex multiaxial loadings, estimating their fatigue damage and life accurately is important to ensure structural integrity and safety of the engine. To make up for the deficiency that results obtained through uniaxial fatigue life prediction models is sometimes unable to satisfy the requirements of engineering accuracy under practical loading conditions, this research carries out the fatigue life prediction of an aero-engine turbine shaft with a multiaxial fatigue approach, which can better reflect the fatigue damage evolution of the shaft. What's more, considering the influence of multi-critical sections on structure, this research modified the SWT model when predicting the fatigue life of turbine shaft. An actual engineering case is completed to validate the feasibility of the proposed approach, and the predicted result is consistent with practice.

A COMPREHENSIVE STUDY OF FATIGUE CRACK INITIATION AND GROWTH UNDER VERY HIGH CYCLE TORSIONAL FATIGUE LOADING

This paper investigates the fatigue behavior of smooth specimens made of VT3-1 titanium alloy under fully reversed loading conditions. Mathematical modeling results are presented for the fatigue fracture of smooth specimens under high cycle torsional fatigue loading. The fatigue quasi-crack initiation and growth are calculated using a multimode two-parameter model of fatigue damage accumulation. The surface and subsurface quasi-crack initiation under torsional loading is studied. The numerical results are in good agreement with experimental data and can be used to predict the change in crack growth mechanisms under complex multiaxial loadings such as torsion.

Fatigue life calculation of notched specimens by modified Wöhler curve method and theory of critical distance under multiaxial random loading

AbstractReformulation of a critical plane‐based multiaxial fatigue criterion named as Modified Wöhler Curve Method (MWCM) in the frequency domain is proposed; moreover, it is combined with the theory of critical distance (TCD) to implement vibration fatigue lifetime prediction of notched specimens subjected to complex multiaxial random loading. Firstly, a frequency‐domain formulation of the maximum variance method (MVM) is proposed for determining the critical plane with high computational efficiency. Then, a reference fatigue curve is defined through the frequency‐domain formulation of the reference stress ratio corresponding to the critical plane. Finally, the power spectral density (PSD) function of the resolved shear stress along the maximum variance direction is applied with the Bendat/Tovo–Benasciutti (TB) method to implement fatigue damage estimation of mechanical components. Both the time‐domain formulation and the proposed frequency‐domain formulation of the MWCM combined with the TCD are applied to the experimental results from the literature, concerning notched specimens made of 2024‐T4 aluminum alloy tested under various nonproportional bending‐torsion random vibration fatigue loading.

On the Issue of Determining Relative Rail Rolling Contact Fatigue Damageability

Adoption of heavy haul traffic on many railroads, comprising Russian railways, has highlighted the relevance of assessing the effect of increased axial loads on the contact fatigue life of rails.The article describes a set of theoretical studies carried out to create a scientifically substantiated method for predicting the contact fatigue life of rails depending on the values of axial loads. The stress-strain state of the contact area has been determined using the finite element model of wheel rolling on a rail. It has been found that the wheel-rail rolling contact area undergoes complex multiaxial loading with the simultaneous action of normal and shear strains. Based on the analysis of models describing multiaxial fatigue damage, the Brown–Miller model was chosen, which considers the simultaneous action of normal strains at the contact area and of maximum shear strains, which most fully describes the stress-strain state of the wheel-rail rolling contact area. To apply the Brown–Miller model, fatigue stress-strain curves for rail steel have been identified. Based on the analysis of methods for determining the parameters of stress-strain curves carried out by V. A. Troschenko, a modified Roessle– Fatemi hardness method has been applied. Based on the experimentally determined values of hardness on the rolling surface, the parameters of the curves of elastic and plastic fatigue have been revealed by calculation and experiment. To establish the damaging effect of the load from wheel rolling on a rail, the concept of relative damage per rolling cycle had been assumed which is the value inverse to the number of cycles preceding formation of a contact-fatigue crack at a given value of the axial load.Calculations of the relative damage rate of the rolling surface of rails caused by contact fatigue defects were carried out with the Fatigue software package considering mean values of the indicators of the degree of fatigue strength and plasticity of rail steel and the calculated stresses in the wheel-rail contact area, as well as the plasticity correction using Neuber method. The polynomial dependence of relative damageability of the rolling surface of rails is obtained. The established functional dependence of relative damageability of the rolling surface of rails on the values of vertical forces can be used as the basis for the developed methodology for predicting the contact fatigue life of rails.

Effect of Including Periodic Boundary Condition on the Fatigue Behaviour of Cancellous Bone

Trabecular bone consists of complex webbing of plates and struts, in which the properties vary across anatomical sites. The substantial constraint is the reduction on discretization error will reduce time in computation. So it is significant to consider carefully the boundary condition effects when utilizing such a complex multiaxial loading mode. Additionally, multiaxial loading gives distinct effects towards boundary condition compare to uniaxial whereas percentage prediction of fatigue failure is lower and applying of periodic boundary reflect a more precise real loading condition. 3D models of trabecular samples were constructed for FE simulations. The response of the models towards simulated mechanical loading was investigated. Preparation of the models begins with 3D reconstruction of micro-CT stacked images, follows by segmentation, meshing and refurbishing process. The resistance of trabecular bone deformation to loading in both uniaxial and multiaxial modes improved the fatigue life and failure with application of periodic boundary conditions.

Omnidirectional stretchability of freestanding interconnects for stretchable electronics

Advanced stretchable electronics applications, such as health monitoring patches, high-density curvilinear detectors etc, not only require the interconnects in these devices to accommodate large uniaxial strains vvvvbut they should also be able to withstand complex multiaxial loading such as in-plane and out-of-plane shear loading for reliable and optimal device operation. However, only uniaxial stretchability of these stretchable interconnects is typically characterised and reported in the literature. Here, we compare three relatively similar and relatively simple freestanding interconnect geometries on the basis of their multiaxial stretchability to evaluate their feasibility for typical stretchable electronics applications. The three geometries include: (1) the (traditional) serpentine structure, that has been studied most extensively in the literature (2) the rotation out-of-plane elongation (ROPE) interconnect, designed to exploit buckling and out-of-plane rotation to enhance stretchability (Shafqat et al 2017 Micromachines 8 277) and the (3) the non-buckling in-plane elongation (IPE) interconnect, designed to fit a maximum number of beam members within the footprint area. To evaluate the multiaxial stretchability of the three designs finite element (FE) simulations were performed by loading the interconnects in the xy-, yz- and xz- planes under a range of loading angles. Furthermore, multiaxial loading experiments were performed on the ROPE interconnect samples by loading the samples in uniaxial in-plane stretching, in-plane shear and out-of-plane shear loading cases and compared with the FE simulations.

Modeling multiple damage mechanisms via a multi-fiber multi-layer representative volume element (M2RVE)

This paper is aimed at incorporating all possible micro-scale damage mechanisms, namely, fiber failure, matrix cracking, fiber-matrix debonding and delamination in multi-fiber multi-layer representative volume element (M2RVE) subjected to multi-axial loading. Different loading conditions have been selected to induce a particular or combined damage mechanism/s to study the damage evolution. The predicted constitutive material responses for tensile and in-plane shear loading by M2RVE are in reasonably good agreement with the experimental results. M2RVE then used for capturing all the microscale damage mechanisms even for complex multi-axial loading. The stress–strain responses have been effectively captured for different combinations of dominant damage mechanisms.

Validating generality of recently developed critical plane model for fatigue life assessments using multiaxial test database on seventeen different materials

AbstractThe present studies are aimed at validation of a newly developed critical plane model with respect to large variety of engineering materials used for different applications. This newly developed model has been recently reported by present authors. To strengthen general applicability of this model, multiaxial test database consisting of a wide variety of multiaxial loading paths have been considered. The strain paths include pure axial, pure torsion, in‐phase axial‐torsion, out‐of‐phase axial‐torsion with phase shift angles varying from 30° to 180° having sine/trapezoidal/triangular strain waveforms, with/without mean axial/shear strains and asynchronous axial‐torsion strain paths of different frequency ratios etc.The materials covered in present study are mainly categorized as ferrous and nonferrous alloys. In ferrous alloy category, material grades from plain carbon steel (mild steel, 16MnR, SA333 Gr. 6, E235 and E355), low‐alloy steel (1Cr‐Mo‐V and S460 N) and austenitic stainless steel (SS304, SS316L and SS347) have been considered. In nonferrous alloy category, aluminium alloys (2024T3‐Al, 7075T651‐Al, and PA38‐T6‐Al), titanium (pure titanium and TC4 alloy), cobalt base super‐alloy (Haynes 188), and nickel alloy (Inconel‐718) have been considered.The predicted and test fatigue lives are found in good agreement for all these materials and complex multiaxial loading paths.

Multiaxial low cycle fatigue assessment of notch specimens for 10CrNi3MoV steel and its welds

Due to the complex multiaxial loading service conditions for welded structures, it is a fundamental step to accurately compute the fatigue damage under complex stress states. Multiaxial low cycle fatigue behaviors of notch specimens considering geometry variations and strength heterogeneity for 10CrNi3MoV high strength steel and weldments under proportional and non-proportional loading modes were investigated in our study. The experimental results show that the crack initiates from the notch tip. The characteristic states of normal stress, shear stress and energy are analyzed to express the notch gradient behaviors. Furthermore, a new simplified fatigue damage parameter is proposed to predict the multiaxial low cycle fatigue life of notch components. This damage parameter is combined with Smith-Watson-Topper (SWT) damage parameter and notch stress concentration factor in the proximity of the notch tip. Finally, the proposed model gives more satisfactory estimations than other notch energy damage models for low cycle multiaxial fatigue life.

A CPFEM based study to understand the void growth in high strength dual-phase titanium alloy (Ti-10V-2Fe-3Al)

High strength titanium alloys are generally used in widespread applications ranging over, but not limited to biomedical, aerospace, automotive, marine, oil and gas, and energy. Besides other manufacturing processes, forming is one of the common manufacturing process used to produce components out of these alloys. Forming processes generally involve significant plastic deformation of material under complex multiaxial loading conditions. Titanium alloys undergo considerable plastic deformation before failure while later is governed by the mechanisms of void nucleation, growth and coalescence. A number of titanium alloys used for high strength applications are multiphase alloys having α and β phases. It has been reported in the past that the voids tend to nucleate on the phase boundaries. This study is focused on understanding the growth of the nucleated voids at two selected locations in a dual phase titanium alloy (Ti-10V-2Fe-3Al); globular α phase (hexagonal closed pack, HCP) and at the interface of lamellar α and β phases (α - HCP and β – body centred cubic, BCC). This is one of the very few 3D representative volume element (RVE) study of void growth in single crystal titanium (HCP), carried out using crystal plasticity finite element modelling (CPFEM) at higher triaxialities (ranging 1/3-3) and the first one on the interface of bicrystals with different crystal symmetry. The effects of initial porosity, crystal orientation and the Lode parameter on void growth in single crystal (α-HCP) has been studied and it is found that they affects void growth considerably. An effort has been made to explain the physics behind it. In the second part, growth in a void at the interface of two distinct single crystals (α - HCP and β –BCC) was studied. The effects of Burgers orientation relationship (BOR) variant of the two phases, initial porosity, and phase boundary inclination (PBI) on void growth is investigated. It is found that the PBI has a very strong impact on the void growth. The effect of initial porosity is similar to the void growth in single crystals. Choice of BOR variant affected the void growth in moderate triaxialities.

Equivalent Strain and Stress Models for the Effect of Mechanical Loading on the Permeability of Ferromagnetic Materials

An equivalent strain/stress approach is proposed for modeling permeability change in ferromagnetic materials due to mechanical loadings. The model can be used for transforming complex multiaxial mechanical loadings into equivalent uniaxial loadings parallel to the magnetic field, such that the permeability can be predicted only based on uniaxial measurements. Contrary to earlier approaches, the new definition of the equivalent strain/stress also accounts for shear strain/stress with respect to the magnetic field. The results are shown to match well measurements under multiaxial stresses.

Fatigue damage behavior in carbon fiber polymer composites under biaxial loading

An investigation into the damage accumulation and propagation behavior in carbon fiber reinforced polymer (CFRP) composites under complex in-phase biaxial fatigue loading has been conducted. The goal is to capture early stage damage and obtain an improved understanding of damage propagation and associated degradation in material properties. Both cross ply and quasi isotropic laminate configurations have been studied and the tests were conducted under constant amplitude in-phase biaxial loading. An optimization technique was used to design the cruciform specimens for each stacking sequence. To understand the propagation of damage from the micro-to the macroscale, the fractured surfaces were analyzed, during various stages of fatigue, using electron microscope assisted fractography and a high-resolution camera. Material property degradation was determined by measuring the change in specimen stiffness to analyze the progression of fatigue damage and is correlated to the micro- and macroscale damage mechanisms and the biaxial fatigue loading parameters. The results provide insight into the initiation and propagation of damage mechanisms in CFRP composites which is essential to understanding the fatigue behavior of composite materials under complex multiaxial loadings.

Crack paths in additive manufactured metallic materials subjected to multiaxial cyclic loads including surface roughness, HIP, and notch effects

Additive Manufacturing (AM) has recently gained much attention due to its many advantages. Nevertheless, design of critical load carrying parts via AM is still at its infancy because the damage mechanism and evolution of AM metals under cyclic loading are not yet understood, particularly under complex multiaxial loading conditions. This work investigates fatigue cracking behavior of two AM metals including Ti-6Al-4V and 17-4 PH Stainless Steel and their wrought counterparts using both unnotched and notched tubular specimens. Cracking mechanisms and paths under a variety of conditions including annealing and HIPing processes, surface roughness, and build orientation are evaluated.

Flexible identification procedure for thermodynamic constitutive models for magnetostrictive materials.

We present a novel approach for identifying a multiaxial thermodynamic magneto-mechanical constitutive law by direct bi- or trivariate spline interpolation from available magnetization and magnetostriction data. Reference data are first produced with a multiscale model in the case of a magnetic field and uniaxial and shear stresses. The thermodynamic model fits well to the results of the multiscale model, after which the models are compared under complex multiaxial loadings. A surprisingly good agreement between the two models is found, but some differences in the magnetostrictive behaviour are also pointed out. Finally, the model is fitted to measurement results from an electrical steel sheet. The spline-based constitutive law overcomes several drawbacks of analytical approaches used earlier. The presented models and measurement results are openly available.