Multiaxial Loading Research Articles

Capability of different multiaxial fatigue evaluation approaches on adhesively butt-bonded hollow cylinders under multiaxial loading with variable amplitudes

Capability of different multiaxial fatigue evaluation approaches on adhesively butt-bonded hollow cylinders under multiaxial loading with variable amplitudes

Failure criterion and damage evolution of high-strength geopolymer concrete under compression-shear composite loading after high temperatures

Geopolymer concrete (GPC) holds significant potential for building fire safety design due to its green, low-carbon, and high-temperature resistant properties. In practical applications, concrete structures often face multiaxial composite loads. Therefore, investigating the composite stress performance of high-strength geopolymer concrete (HGPC) after exposure to high temperatures is crucial for assessing structural damage and enhancing fire prevention measures. This paper examines the compressive shear performance of HGPC at various temperatures T (20°C, 200°C, 400°C, 600°C) and stress ratios k (0.15, 0.3, 0.45, 0.6). The study analyzes failure patterns, shear load-displacement curves, shear strengths and their components, and peak shear deformation. Failure criteria are proposed to describe the damage patterns of HGPC under compressive shear loading after high temperatures. Additionally, the damage evolution process is evaluated using the energy method. The results show that HGPC damage surfaces penetrate the coarse aggregate at room temperature under compression-shear composite loading but shift to the aggregate-mortar interface at 600°C. Shear stiffness, peak shear strength, and residual strength increase with higher stress ratios but decrease with rising temperatures. Temperature affects peak shear strength by over 95 %, significantly more than the stress ratio. The shear strength decreases more slowly than compressive strength up to 400°C but more rapidly beyond 400°C. The cohesive strength of HGPC decreases with increasing stress ratio under different temperatures, while contact friction strength exceeds 50 % of peak shear strength. Shear dilation strength generally increases, then decreases, peaking at k = 0.45. The failure criterion based on the modified twin shear unified strength theory aligns best with experimental results. Furthermore, an increased stress ratio retarded the development of damage evolution, which was first accelerated and then slowed with rising temperature.

Characterization of woven composite material under multiaxial loading regimes using FE-based stereocorrelation

In this paper, woven glass fiber composite samples were subjected to three different cyclic loading histories (i.e., tensile, shear and combined loading at 45° via the Modified Arcan Fixture. During the experiments, the samples were monitored by a stereovision system. Finite Element based stereocorrelation was used to measure the displacement and strain fields. The analysis of the experiments revealed different damage mechanisms. Furthermore, for the 45° experiment, the highest strain levels were reached, whereas for the tensile test, the highest stress levels were achieved.

Stress fracture of bone under physiological multiaxial cyclic loading: Activity-based predictive models

While it is known that excessive accumulation of fatigue damage from daily activities contributes to fracture, a model of bone failure under physiologically relevant multiaxial cyclic loading needs to be developed in order to develop effective management strategies for stress or fatigue fractures. The role of strain-induced damage from repetitive loading is a strong candidate for such a model, as cycles of mechanical loading leading to failure can be measured directly. However, this approach has been limited by the restrictions of uniaxial loading models, which often overestimates the fatigue life of bone and suggests that bone will only break well beyond the realistic limits of exercise. To address this gap and develop a physiologically relevant model, our study leverages the power of four commonly used engineering failure criteria as a model for multiaxial loading using a cohort of human tibiae from cadaveric donors (age range 21–85 years old). Four failure criteria (Von Mises, Tsai-Wu, Findley critical plane, and maximum shear strain) were found to be effective in vitro models of tibial fracture when age groups of donors were combined (r2 > 0.84) and stratified (younger: 21–52-years-old versus older: 57–85-years-old) (r2 > 0.83) (p < 0.001). Each failure criterion displayed distinctly lower fatigue curves for the older age group. The maximum shear strain model was used to determine the efficacy of this approach to predict fatigue fractures in humans using published in vivo data from human volunteers. Consistent with in vivo observations in general population, the model demonstrated failure at 5000 to 200,000 loading cycles depending on activities such as jumping, sprinting, and walking, with a 3-fold reduction of fatigue life in older donors. These findings dramatically improve estimates of fatigue life under repetitive loading and demonstrate how age-related changes in bone significantly increase its propensity for fatigue-induced fractures.

Is suture-based cerclage biomechanically superior to traditional metallic cerclage for fixation of periprosthetic femoral fractures: A matched pair cadaveric study

BackgroundWhile traditional metallic cerclage remains the primary method in clinical application, non-metallic cerclage systems have recently gained popularity due to low risks of soft tissue irritation and bone intrusion. The objective of this study was to assess the performance of a novel non-metallic suture-based cerclage in comparison to traditional metallic cerclage cables for fixation of periprosthetic femoral fractures. MethodsAn extended trochanteric osteotomy was performed on eight pairs of cadaveric femora, followed by reduction using either metallic cerclages (Group I) or the suture-based cerclage (Group II). A modular tapered fluted stem was then implanted in each specimen. The fragment translation during canal preparation and stem implantation was quantified using laser-scanning. Subsequently, each specimen underwent 500 cycles of multiaxial loading, with fragment translation and stem subsidence measured using a motion capture system. FindingsFollowing stem implantation, specimens in Group II exhibited a significantly greater lateral fragment translation (466 μm vs 754 μm, p = 0.017). However, there were no significant differences in anterior and distal translation between groups (p > 0.05). During multiaxial loading, the average stem subsidence in Group I was 0.36 mm (range, 0.04–1.42 mm), compared to 0.41 mm (range, 0.03–1.29) in Group II (p > 0.05). No significant difference was found in fragment translations between the two groups (p > 0.05). InterpretationThe suture-based cerclage system exhibited comparable biomechanical performance in fixation stability to conventional metallic cerclage cables. Yet, it was associated with a larger residual lateral gap between the fragments following stem implantation. Ultimately, the choice of fixation method should account for multiple factors, including patient characteristics, surgeon preference, and bone quality.

Nonlinear behavior simulation of ceramic-matrix composites using constituent-volume homogenization method

The nonlinear behavior of ceramic-matrix composites is affected by interface debonding and fiber pull-out. In this paper, we propose the constituent-volume homogenization method (CVHM) to replace the conventional bundle homogenization method, in order to model the behavior of trans-element debonding in woven structures using finite element method. Based on the CVHM, we establish the elastic relation of the relative motion between the fiber and the matrix, and the elastic constitutive relations for the constituents. Methods have also been developed to calculate the microscopic local stress of bundle under pull-out and multiaxial loads. Based on the above studies, we develop a procedure to analyze the stress-strain relation of braided composites using the CVHM. To validate the proposed method, we estimate the nonlinear behavior of the 2D plain-weave ceramic-matrix composites and compare the results with experimental data. The influence of interface shear strength (ISS) and the fiber ultimate tensile strength (UTS) on the nonlinear behavior is investigated.

The Role of Polarization in Multiaxial Mechanical Loadings Sensing Using Fiber Bragg Gratings

The Role of Polarization in Multiaxial Mechanical Loadings Sensing Using Fiber Bragg Gratings

A new approach on constitutive modeling for quasi-brittle materials under multiaxial loading

Abstract This work introduces a new method for expanding unidimensional models to predict material behavior under multiaxial loading. The concept of six-dimensional mechanical space is adopted, and in each basis direction of the space, there is one fiber-bundle model (FBM), so these six FBMs are independent amongst one another but follow the same damage evolution rule. Under triaxial loading, these FBMs have different stress and strain states, so six corresponding damage variables have different values. The anisotropic damage is thus represented by the six damage variables. When it is under uniaxial loading, the six-dimensional space reduces to one-dimensional space, so the proposed model can be calibrated using uniaxial loading test data, and the calibrated model can predict the material behavior under multiaxial loading conditions. Biaxial loading and triaxial loading test data are used to verify the proposed model, and parametric analyses are performed to analyze model predictions under different loading conditions. It shows that model predictions agree well with the test data and are consistent with experimental observations.

Enhanced Cyclically Stable Plasticity Model for Multiaxial Behaviour of Magnesium Alloy AZ31 under Low-Cycle Fatigue Conditions.

Magnesium alloys, particularly AZ31, are promising materials for the modern automotive industry, offering significant weight savings and environmental benefits. This research focuses on the challenges associated with accurate modelling of multiaxial cyclic plasticity at small strains of AZ31 under low-cycle fatigue conditions. Current modelling approaches, including crystal plasticity and phenomenological plasticity, have been extensively explored. However, the existing models reach their limits when it comes to capturing the complexity of cyclic plasticity in magnesium alloys, especially under multiaxial loading conditions. To address this gap, a cyclically stable elastoplastic model is proposed that integrates elements from existing models with an enhanced algorithm for updating stresses and hardening parameters, using the hyperbolic tangent function to describe hardening and ensure a stabilised response with closed hysteresis loops for both uniaxial and multiaxial loading. The model is based on a von Mises yield surface and includes a kinematic hardening rule that promises a stable simulation of the response of AZ31 sheets under cyclic loading. Using experimental data from previous studies on AZ31 sheets, the proposed model is optimised and validated. The model shows promising capabilities in simulating the response of AZ31 sheet metal under different loading conditions. It has significant potential to improve the accuracy of fatigue simulations, especially in the context of automotive applications.

Cemented sand under hollow cylinder multiaxial loading

Improvement of granular soils mechanical properties can be achieved by the addition of bonding agents. In this research, low amount of Portland cement was added to a sand and its beneficial shear strengthening effects were evaluated under a range of multiaxial stress paths. The influence of the orientation of the principal axes of stress and strain on the stress-strain response and failure of cemented sand has only been scarcely investigated. Therefore, this experimental investigation reports the results of a series of consolidated drained hollow cylinder torsional tests with constant principal stress path direction, ασ, varying from 0° to 90° Results were compared with the shear behaviour of the uncemented sand tested under similar loading conditions. Results show that the addition of cement to the sand matrix increases the soil strength for all multiaxial stress path directions. The suitability of two multiaxial strength criteria for reproducing the shape of the failure envelope as a function of the orientation of principal stress axis ασ has also been analysed.

A multiscale modeling for progressive failure behavior of unidirectional fiber-reinforced composites based on phase-field method

The effective macroscopic properties of composites are determined by the intricate interactions among the individual components within their microstructure. Preserving these microscopic details during the failure simulation of macrostructures presents significant challenges. This work proposes a multiscale modeling framework to numerically predict the macroscopic fracture properties of unidirectional fiber-reinforced composites based on micromechanical analysis. In this study, 2D representative volume elements (RVEs) combined with the phase-field method are utilized to simulate fiber-reinforced composites under transverse loadings. A series of representative loading conditions are employed to investigate cracking patterns and to construct failure strength envelopes of the composites subjected to different multiaxial proportional loadings. By extracting the softening curve from the uniaxial tensile simulation of the RVE and fitting it with a tenth-order polynomial, the homogenized cohesive law, combined with the phase-field method, is applied to the damage analysis of macroscopic heterogeneous materials. The homogenized model of unidirectional fiber reinforced composites is numerically validated through simulations of a 2D flat plate. The simulation results demonstrate the excellent potential of the proposed multiscale modeling framework to accurately and efficiently predict the progressive failure and fracture behavior of fiber-reinforced composites in engineering applications.

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.

Using physics-informed neural networks to predict the lifetime of laser powder bed fusion processed 316L stainless steel under multiaxial low-cycle fatigue loading

Axial-torsional Low-Cycle Fatigue (LCF) tests were conducted under strain control on Additively Manufactured (AM) 316L stainless steel using laser powder bed fusion. The tests covered various strain amplitudes under tension-compression, proportional, and pure shear loading paths. The AM 316L stainless steel exhibited cyclic softening and transgranular cracking under all the investigated loading conditions. The presence of deposition defects, predominantly the lack of fusion type, was identified as the main factor influencing the crack initiation and propagation, as well as the scatter in the fatigue lifetime. Therefore, to account for the damaging effects of these deposition related defects on fatigue lifetime, a novel physics-informed neural network was proposed. Subsequently, this neural network was combined with the critical plane approach, based on the tensile mode of failure, in order to predict the lifetime of AM 316L stainless steel. The predicted data exhibited a good correlation with the experimental results.

Acoustic emission-based delamination investigation in drilled GFRP under mixed tensile and bending cyclic loading

The drilling process can cause various defects in glass fiber-reinforced polymer (GFRP), such as delamination, which ultimately leads to damage progression, especially under fatigue loading. Therefore, the current study aims to investigate the progression of failure in drilled composites subjected to cyclic bending and tensile loads using acoustic emission (AE), image processing, and mechanical behavior monitoring. The results show tyhat the fatigue diagram consists of three stages associated with resistance of fibers and matrix against delamination propagation, stable delamination progression, and ultimate spread of failure which are accurately identified by AE and mechanical methods. Additionally, the pattern and procedure of all fatigue diagrams under all loading conditions were similar and independent of loading parameters. Results from this study provide a strategy for real-time structural health monitoring (SHM) of delamination propagation in GFRPs under multi-axial fatigue loading.

Experimental investigation and computational modelling of 304LN stainless steel under constant and variable strain path multiaxial loading conditions

This study investigates the fatigue behavior of 304LN stainless steel under constant and variable strain path multiaxial loading conditions. Experimental methods and computational modelling were used to analyze the response of the material to different loading scenarios. Experimental investigations were conducted to gather empirical data, which were subsequently validated using a modified Ohno-Wang and Tanaka cyclic plasticity framework. Two models were used for the analysis: the MOT model and a modified model that incorporated a weighted function and fractional functions for hardening and softening. In contrast, the modified model offers significant improvements, accurately capturing primary hardening and secondary softening across all loading scenarios. Furthermore, the modified model effectively simulates transient behavior, including load alteration and recovery effects, due to the integration of load history memory regulating functions. Overall, this study emphasizes the importance of considering the complexities of cyclic loading and the sensitivity of the material behavior to the loading history.

Experimental investigation and probabilistic analysis of the buckling load of isotropic cylinders under multiaxial loading

This paper presents a multitude of experimental results for cylindrical shells under combined loading. The loading is a combination of axial compression and bending moment. These are accompanied with numerical simulations. The load ratio itself is subject to scatter, a direct comparison and application of results for the sizing of shells is not straight forward. Therefore, a new approach is presented, which transfers the results to normalized load factors.

Classification of damage modes in scaled open-hole composite laminates under combined tension-shear loading using acoustic emission technique

The damage initiation and evolution of carbon fiber-reinforced polymer (CFRP) composite under multi-axial loading is of fundamental interest. This study investigates intra- and interlaminar damage modes induced in open-hole quasi-isotropic (QI) carbon/epoxy composite laminate under combined tension-shear loading using the acoustic emission (AE) technique. The effect of layer thickness is studied using three types of laminates with stacking sequences PL-1: [−452/452/902/02]s, PL-2: [−453/453/903/03]s (ply blocked), and SL-1: [−45/45/90/0]2s (a sub-laminate blocked or distributed). Clustering of acquired AE signals is carried out using hierarchical methods. Damage modes evolution for the open hole QI CFRP is captured using the clustered AE signal data. It is observed that the thickness scaling significantly affects the open-hole strength and the critical failure mechanisms. Dominant damage mechanisms are identified based on AE cumulative energy. Ply-level blocked (PL-1 and PL-2) laminates exhibit lower strength than the SL-1 blocked laminate. The findings from this experimental investigation indicate that the AE technique in conjunction with the clustering approach is a prospective tool for the structural health monitoring of composite structures under combined loading.

Fatigue life prediction of rubber suspension bushings based on virtual road load spectrum pulses

Rubber suspension bushings have mainly been studied under single- or multi-axis load cycling, while research on rubber suspension bushings under random load cycling is not deep enough. This study conducted uniaxial tensile and fatigue tests on N60 rubber dumbbell-shaped plate samples to obtain stress–strain curves and S–N curves. Using the uniaxial tensile test data, a Mooney–Rivlin hyperelastic constitutive model was fitted using Abaqus software, and a finite element model of the rubber suspension bushing was established. A 3D virtual road surface was constructed using Adams software, and characteristic features of typical road surfaces were extracted for statistical analysis, resulting in the generation of a load spectrum showing variations in force over time. Based on the Miner linear damage accumulation theory, finite element fatigue life prediction of the rubber suspension bushing was conducted using pulses from the 232 s region of the load spectrum. The predicted fatigue life was compared to the results from benchtop fatigue testing, resulting in a relative error of less than 6.443 %. The findings suggest that the method is effective in predicting the fatigue life of rubber suspension bushings under random loads.

Bayesian-informed fatigue life prediction in shallow shell structures with the dual boundary element method

This study introduces an innovative approach for statistically inferring the Equivalent Initial Flaw Size Distribution (EIFSD) in shallow shell structures with the aim of predicting fatigue life. The proposed approach integrates Bayesian inference and surrogate modelling techniques, and utilizes a long crack growth model. The EIFSD is crucial for estimating fatigue life and ensuring structural durability. To showcase the proposed methodology, a numerical example featuring a fuselage window structure under multi-axial loading, employing the Dual Boundary Element Method (DBEM) for crack growth modelling, is presented. Efficiency gains in the inference of the EIFSD are achieved through the development of surrogate models, notably a Co-Kriging model that significantly reduces computational time and outperforms a Kriging model in error reduction. The study explores two assumptions for inspection data sourcing, leading to enhanced methodological effectiveness across varying uncertainty levels. It considers the separate effects of Paris Law constants and loading conditions under increased uncertainty, presenting cases that demonstrate the Co-Kriging model’s high accuracy and computational efficiency. The proposed methodology’s robustness is further validated by assessing the impact of prior distribution quality on Bayesian inference, showing the method’s adaptability to high uncertainty while maintaining a good level of accuracy. This study also demonstrates an approach for fatigue life estimation of structures using the inferred EIFSD. By evaluating the structure up to a critical crack length, the methodology allows for the accurate estimation of fatigue life, which, in turn, facilitates the determination of optimal inspection intervals. Notably, under conditions of high uncertainty, the method showcased a maximum difference of 1.51% in the estimated fatigue life when compared to the true EIFSD, underscoring the technique’s high accuracy and reliability.

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.