Multiaxial Loading Research Articles

Study on the behavior of small cracks in PA38-T6 (6060-T6) aluminum alloy under multiaxial fatigue loadings

This study investigated the effects of multiaxial cyclic loading on the initiation and propagation of fatigue cracks in an industrial-grade aluminum alloy. Four different loading cases, including 90° out-of-phase and asynchronous loading, were used under the control of strain. The study used cellulose acetate film replication and SEM fractography techniques to increase the understanding of the evolution of fatigue damage on specimen surfaces. The material exhibited a shear damage mechanism with a significant amount of small cracks coalescence. It was explained why, despite a high agreement with the assumptions of the critical plane approach, the predicted fatigue life was overestimated at high loading levels. A correlation between the crack initiation period and overall fatigue life, regardless of loading case, was presented, which has a potential for practical applications.

Multiaxial fatigue life prediction using an improved Smith‐Watson‐Topper model

AbstractIn this paper, the SWT model was improved by incorporating the Walker equation into the strain–life curve. The established model takes into account the material's sensitivity to mean stress by introducing the Walker exponent, w. Under uniaxial loading condition, the proposed model can reduce to the SWT model, Manson‐Coffin equation, and Walker model for w values of 0.5, 1, and 0, respectively. Under multiaxial symmetric loading, when w = 0.5, the proposed model can be simplified as another SWT correction model (CXH) proposed by Chen et al. The prediction accuracy of the established model was validated using about 200 data points collected from literature. These data points were obtained from tests conducted on eight different kinds of metals under various multiaxial loading paths. The verification results indicate that 96.8% and 97.9% of the data points fall within the factor‐of‐three boundary for the loading paths without and with mean stresses, respectively.

Study on biaxial tensile failure behavior of ultra-thin-ply carbon fiber reinforced composites

The superior mechanical properties of ultra-thin-ply carbon fiber reinforced composites under uniaxial stress have been widely recognized. However, composite structures are often subjected to multiaxial loading in practical applications. Therefore, this study focuses on investigating the mechanical properties of ultra-thin-ply carbon fiber reinforced composites under biaxial stress conditions. Firstly, the geometric structure of a cruciform biaxial test specimen for composites is designed, and its rationality is demonstrated. Subsequently, cruciform biaxial test specimens with ply thicknesses of 24 μm and 100 μm are prepared for quasi-isotropic laminated plates, and biaxial tensile experiments with stress ratios of 0:1, 1:1, and 2:1 are conducted. This study establishes the failure envelope of ultra-thin-ply composites under biaxial tensile conditions and compare it with the experimental results of standard-ply composites. Finally, the fracture surfaces of the specimens and acoustic emission signals are analyzed to reveal the failure mechanisms of the composites under biaxial stress conditions. The results indicate that ultra-thin-ply carbon fiber reinforced composites exhibit higher interaction degree under biaxial stress, and their ability to suppress delamination is stronger.

Design of A Highly Sensitive, Low-cost Underwater Force Plate to Record Substrate Reaction Forces.

The study of underwater walking presents major challenges because the small forces applied during underwater walking are difficult to measure due to the lack of a sufficiently sensitive force plate that functions underwater. Understanding the force interaction between the underwater walker and the substrate may lead to better understanding of the evolution, ecology, and biomechanics of underwater walking. The shift from aquatic to terrestrial life was a crucial transition in animal evolution where, underwater walking preceded the invasion of land and combines mechanics from terrestrial locomotion (substrate reaction forces) and aquatic swimming (buoyancy and drag). In this work, we describe our design of a low-cost underwater force plate made using 3D printed multi axis load cells equipped with commercial strain gauges amplified with a custom circuit board, and custom code to gather force data. The use of 3D printed sensors allows customization of the material and thickness of the shear beam load cell to accommodate the loads for a wide range of study species. We show that our design can detect loads as small as 1 mN (filtered) with minimal noise and present sample live animal trials of several species. The 3D multiaxial load cells, circuit design, and custom code are open-source and available online.

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.

Mechanical Behaviors and Precursory Characteristics of Coal-Burst in Deep Coal Mining for Safety-Sustainable Operations: Insights from Experimental Analysis

Coalburst, a frequent and severe dynamic disaster, poses significant challenges to the safety and sustainable development of coal mines during deep excavation. To investigate the mechanical behaviors and precursory characteristics of coalburst subjected to in situ stress conditions, multiaxial cyclic loading experiments were conducted on cubic coal specimens, and the effects of different confining pressures on the mechanical parameters and energy evolution were analyzed. Acoustic emission (AE) technology was utilized to study the accumulation process of stress-induced damage and identify the source modes of microcracks. Then, nonlinear fractal theory and critical slowing theory were used to investigate the time-varying precursory characteristics of catastrophic failure in coalburst. The results show that as the confining pressure increases, the coal samples exhibit higher levels of elastic strain energy and dissipative energy, indicating an enhancement of plasticity. The AE count and accumulated energy show a strong correlation with cyclic loads. With an increasing number of cycles, the AE Felicity ratio gradually decreases, indicating a progressive increase in irreversible damage. Shear-mode microcracks also become more prominent with applied stress and confining pressures, as supported by varying AF/RA values of AE signals. The AE signals also follow the Hurst statistical law, and increasing applied stress and confining pressure strengthen this statistical pattern with a higher Hurst index. Throughout the cyclic loading process, certain AE varying trends were observed: the autocorrelation coefficient increased, the fractal dimension gradually decreased, and the variance suddenly increased. These trends serve as early, middle, and short–imminent warning signals, respectively, for the catastrophic failure of the loaded coal sample. These research findings contribute to a deeper understanding of coal failure evolution and provide a basis for early detection and warning of coalburst disasters, which are also essential for promoting the safe and sustainable development of deep coal mining operations.

Experimental investigation of probabilistic failure of SiC/SiC composite tubes under multiaxial loading

This paper presents an experimental investigation of the failure behavior of SiC fiber-reinforced SiC matrix (SiC/SiC) composite tubes under multiaxial loading. A new testing apparatus is designed to independently apply axial stress and internal pressure to SiC/SiC tubes. Acoustic emission (AE) is used to monitor the damage growth in the specimen. Based on the measured stress–strain response, a strain-based criterion is proposed to determine the proportional limit stress (PLS). The proposed strain-based criterion is compared with the PLS determined by the AE measurement. The PLS is determined for different loading ratios to form a multiaxial failure surface. By testing multiple replicates, the statistical variations of the PLS are determined. Based on the experimental results, a mathematical model is developed to characterize the probability distribution of the PLS of SiC/SiC composites under multiaxial loading.

Multiaxial failure behavior and fatigue life prediction of unidirectional composite laminates

Complex coupling mechanisms exist between longitudinal and shear stress on the multiaxial fatigue behavior of composites. A thorough reanalysis of matrix shear failure mechanism under multiaxial fatigue loading is presented. Longitudinal single splitting fracture were analyzed and validated as an independent failure mode under multiaxial loading by analogy to the failure mechanism of natural composites. A new multiaxial fatigue life prediction model was established by double projection on the critical and subcritical fracture planes. Experiments on unidirectional tubular specimens were carried out under combined tension-torsion loadings to separate and identify the multiaxial fatigue failure behavior of composites. The proposed model has been verified using unidirectional laminates subjected to cyclic tension-torsion and off-axis loading, and the results showed that the predicted life is in good agreement with the experimental ones. Applications of three-dimensional digital image correlation (3D-DIC) and microscopy regarding verification in multiaxial damage mechanism are also addressed.

Testing the properties of cemented tailings backfill under multiaxial compressive loading

The engineering design of cemented paste backfill (CPB) typically relies on technical data obtained from tests conducted on CPB samples cured under conventional laboratory conditions. However, these methods often fall short in capturing the complex multiaxial stress curing conditions that CPB masses experience in many underground mines, particularly in deep underground mines. In these mining environments, CPB is subjected to multi-axial stress conditions during the curing process that are challenging to replicate in a controlled laboratory setting. No lab-scale apparatus can currently accurately reproduce these actual field multiaxial stress conditions, especially the intricate interplay of horizontal rockwall closure stresses, vertical self-weight stress, and overburden stresses from upper layers. Moreover, the impact of these conditions on the key engineering properties of CPB is unknown. To address this significant challenge and technology gap, this study has developed a new apparatus for curing and monitoring CPB under realistic multiaxial compressive loading conditions, simulating the complex stress environment encountered in underground mines. The developed apparatus was then utilized to assess the impact of multiaxial stress curing conditions, including vertical stress and horizontal stresses induced by rockwall closures, on key engineering properties (strength, deformation behaviour, self-desiccation) of CPB at early ages. The research results clearly indicate that the application of multiaxial stresses leads to a significant enhancement in the mechanical and physical properties of CPB. This enhancement is supported by observable densification of the pore structure in CPB subjected to multiaxial compressive stresses. In addition, a comprehensive analysis of deformation and strain patterns establishes a direct correlation between multiaxial stresses and the progressive increase in stiffness and hardness of CPB over time. Furthermore, the evolution of matric suction and degree of saturation provides compelling evidence of the significant impact of multiaxial stresses on pore water consumption or self-desiccation. The development of this new apparatus fills a substantial void in CPB research capabilities. Furthermore, the results obtained provide a better understanding of the complex behavior of CPB in multi-stress loading environments, paving the way for the design and optimization of backfill solutions that effectively address the unique challenges posed by deep underground mining operations.

Critical Plane Approach-Based Fatigue Life Prediction for Multiaxial Loading: A New Model and its Verification

Critical Plane Approach-Based Fatigue Life Prediction for Multiaxial Loading: A New Model and its Verification

A crystal plasticity model for multiaxial cyclic deformation of U75V rail steel

The theoretical investigations of cyclic deformation behavior and deformation mechanism of the rail steels under multiaxial loadings are of great significance to the study of rolling contact fatigue. Based on the classical crystal plasticity framework, a new nonproportional parameter at the mesoscale is proposed, and the isotropic and kinematic hardening models are modified. A series of finite element simulations of U75V rail steel under uniaxial and multiaxial cyclic loading are carried out using the proposed model. The simulation results show that the proposed model can reasonably reflect the cyclic softening under strain-controlled uniaxial cyclic loading, cyclic hardening under strain-controlled multiaxial cyclic loadings, and ratcheting behavior under stress-controlled uniaxial and multiaxial cyclic loadings of U75V rail steel. Moreover, the influence of multiaxial loading paths on the plastic strain is explained from a mesoscopic perspective. The values of nonproportional parameters of different slip systems under uniaxial and multiaxial paths are compared, and the difference of nonproportional parameters at the macroscale and mesoscale are discussed. Finally, the simulation results of the proposed model and the existing model with modified kinematic hardening rules are compared. The results show that the proposed model has better predictions on the evolution of ratcheting strain and nonproportionally additional hardening effect caused by nonproportionally multiaxial loadings.

Stress-Based Model for Calculating the Opening Angle of Notch Cracks in a Magnesium Alloy under Multiaxial Fatigue

This paper presents a model to calculate the opening angle of crack initiation in notched fractures subjected to multiaxial loading. To validate the proposed model, a study was performed on polished AZ31B-F magnesium alloy specimens under multiaxial high-cycle fatigue loading. The specimens exhibited a notch in the smaller cross-sectional area, which was created with a special drilling jig to promote the formation of fatigue cracks in this localized area of the specimen. The load paths used in the experiments and numerical analyses were proportional and non-proportional, resulting in different stress states in the crack front opening, which were determined by finite element analysis to validate the proposed model. To obtain more accurate numerical results for these estimates, these finite element analyses were performed using the nonlinear Chaboche plasticity model of ABAQUS® 2021 software. A sensitivity analysis was also performed to determine which load component—axial or torsional—has a greater influence on the fatigue strength and contributes significantly to the crack opening process. The results show that the type of load path and the stress level of each load component—axial and torsional—has a strong influence on the opening angle of the notch crack and the fatigue lifetime of the specimen. This result is confirmed not only by the experimentally determined fatigue strength, but also by a fractographic analysis performed on the surface of the specimens for both load paths. Moreover, the results show an acceptable correlation between the experimental results and the estimates obtained with the proposed model and the stresses obtained with the finite element analysis.

Finite Element Model of the Shoulder with Active Rotator Cuff Muscles: Application to Wheelchair Propulsion.

The rotator cuff is prone to injury, remarkably so for manual wheelchair users. To understand its pathomechanisms, finite element models incorporating three-dimensional activated muscles are needed to predict soft tissue strains during given tasks. This study aimed to develop such a model to understand pathomechanisms associated with wheelchair propulsion. We developed an active muscle model associating a passive fiber-reinforced isotropic matrix with an activation law linking calcium ion concentration to tissue tension. This model was first evaluated against known physiological muscle behavior; then used to activate the rotator cuff during a wheelchair propulsion cycle. Here, experimental kinematics and electromyography data was used to drive a shoulder finite element model. Finally, we evaluated the importance of muscle activation by comparing the results of activated and non-activated rotator cuff muscles during both propulsion and isometric contractions. Qualitatively, the muscle constitutive law reasonably reproduced the classical Hill model force-length curve and the behavior of a transversally loaded muscle. During wheelchair propulsion, the deformation and fiber stretch of the supraspinatus muscle-tendon unit pointed towards the possibility for this tendon to develop tendinosis due to the multiaxial loading imposed by the kinematics of propulsion. Finally, differences in local stretch and positions of the lines of action between activated and non-activated models were only observed at activation levels higher than 30%. Our novel finite element model with active muscles is a promising tool for understanding the pathomechanisms of the rotator cuff for various dynamic tasks, especially those with high muscle activation levels.

Biaxial compressive capacity of textile-reinforced concrete

The structural behaviour of textile-reinforced concrete (TRC) components under uniaxial compressive loading has already been studied. However, for practical applications, multi-axial loading conditions are often of great importance. It is well known from steel-reinforced concrete that multiaxial compressive stresses lead to increased compressive strength. The extent to which this assumption can be transferred to TRC components should be investigated. This paper investigates the influence of textile carbon grid reinforcement on the compressive capacity of disc-shaped concrete specimens. The specimens were subjected to a biaxial compressive load in the plane of the reinforcement. Emphasis was placed on the influence parameters of production type of the disc specimens (laminated or poured), impregnation material of the carbon textile (polystyrene or epoxy resin) and number of reinforcement layers. It was found that the general presence of a textile reinforcement as a two-dimensional interference plane had the greatest influence on the compressive capacity of the specimens, while the other parameters investigated played a minor role. Depending on the load ratio in the two compression axes, there were increases or decreases in capacity compared to the uniaxial tests. This has to be taken into account in the design of the corresponding components. Finally, an outlook is given on future investigations planned to support and extend the results presented in this paper.

Uncertainty quantification in multiaxial fatigue life prediction using Bayesian neural networks

In practical engineering scenarios, unforeseen failures may result in significant costs and risks. Assessing the uncertainty related to multiaxial fatigue life prediction is crucial for engineering applications. However, establishing a reliable multiaxial fatigue life prediction model remains challenging due to uncertainties in physical models, material properties, and measurement data. This paper proposes an effective Bayesian Neural Network (BNN) model for quantifying the uncertainty in multiaxial fatigue life prediction. Fatigue parameters in the multiaxial fatigue life prediction model are used as inputs for the BNN. The BNN method utilizes No-U-turn Sampler (NUTS) and Automatic Differentiation Variational Inference (ADVI) to address the inference problem in the model and perform life predictions for unknown non-proportional loading paths and different materials. Validation using experimental data from six different materials confirms the effectiveness of the BNN model. Experiments show that the performance of BNN models is beneficial in most cases compared to classical ML models, assessed through different error standards, statistical tests, Taylor diagrams, uncertainty analysis, and scatter index analysis. The proposed method provides a clear understanding of the uncertainty in multiaxial fatigue life prediction, offering a promising approach for simulating fatigue life under multiaxial loading in engineering applications.

Probabilistic fatigue evaluation of notched specimens considering small sample properties under multiaxial loading

Probabilistic fatigue evaluation is the key to ensure the service integrity of large-sized mechanical equipment, but in practical engineering, the probabilistic fatigue models coupled with multiaxial stress conditions and small sample information characteristics are still insufficient. Accordingly, the virtual subsample augmentation method is effectively coupled with the improved Bootstrap method to propose a general probabilistic fatigue evaluation process. Specifically, the random sample regeneration method is first used to expand the small sample fatigue data, and then life distribution information under different stress levels is fused based on the backwards statistical inference method, the P-S-N curve is fitted with the integrated life dispersion information. Secondly, a new fatigue damage parameter based on the inhibition function is proposed to modify the P-S-N curve and predict fatigue life. Meantime, the multiaxial fatigue test of Q355(D) alloy steel with different notch sizes is carried out, and the model is verified in conjunction with existing fatigue test data of TC4-DT alloy and TC4 alloy. The results show that the proposed model has a certain universality for notched specimens, the modified stress field intensity method can accurately characterize the impact of notch and size effects on fatigue damage of specimens.

A new adjustable localization operator method to compute local stresses and strains at notched bodies under multiaxial cyclic loading

Simplified methods for elastoplastic calculations offer a cost-effective and time-saving solution to determine the mechanical state at the notch tip of a structure. Recently, a method using an Adjustable Localization Operator (ALO) has been developed, drawing inspiration from Eshelby’s inclusion problem. This method has demonstrated its efficiency in addressing various engineering challenges owing to its robustness and inherent ability to handle multiaxial conditions. This paper aims to propose an alternative non-linear formulation of the ALO method to improve the accuracy of mechanical state predictions. To achieve this goal, Buczynski–Glinka’s heuristic, which provides a non-linear plasticity correction, is expressed within the framework of the ALO method to highlight the ingredients required for a non-linear plastic correction. Subsequently, the parameters of the ALO method are adjusted based on these findings. To validate the approach, two cases are studied: a notched structure under plain strain conditions, and a more complex saddle notched structure subjected to local multiaxial proportional loadings. In both cases, the non-linear ALO method has shown a greater capability to reproduce the finite element reference results compared to the linear version of the method or to energetic methods.

Notch approximation methods for components under thermomechanical stresses

In this paper two different kinds of notch approximation methods are presented. The proposed methods are known as the incremental notch approximation method (e. g. Neuber method [1] or ESED [2, 3]) and the structural yield surface approach (SFF) (after Köttgen et al. [3]), while two different approaches of the SFF are used. All methods are capable to handle multiaxial cyclic loading. For a validation, the methods are compared to the results of a finite element analysis (FEA) of a notched component. The presented comparison is made for a non-proportional loading case. One objective of the work is to find out, which is suitable to extend it to thermomechanical loads as a next step.

High-cycle and low-cycle fatigue life prediction under random multiaxial loadings without cycle counting

A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers.

Energy harvesting using magnetostrictive materials: Effects of material anisotropy and stress multiaxiality

Low-frequency vibrations are common as background noise in urban and industrial environments. They originate from natural or artificial sources: road vehicles, industrial machinery, wind, etc., and constitute a ubiquitous energy source. In the framework of energy harvesting, magnetostrictive materials are an attractive alternative solution to the brittleness and geometrical limitations of piezoelectric materials. While numerous previous works dealt with uniaxial stress on selected materials, the exploration of the effects of multiaxial loadings and material anisotropy has not yet been investigated as a way to improve the performance of low-frequency vibration energy harvesting systems. In this work, we investigated the capability of grain-oriented electrical steel in an energy-harvesting context. This material has been selected as a model material, notably as it is abundant and cost-effective. It shows limited magnetostriction but significant elastic, magnetic, and magnetostrictive anisotropy. We combined experimental and predictive simulation results to discuss the possibility of increasing the levels of harvested energy by playing with the orientation of magnetic and mechanical stimuli. Various orientations of magnetic field and mechanical stress were considered with regard to the rolling direction of the material. Unexpectedly high energy density amounts, up to 10 mJ·cm−3, were obtained, competing with giant magnetostrictive materials like Terfenol-D or Galfenol.