Multiaxial Loading Research Articles

Ultimate resistance and fatigue performance predictions of woven-based fiber reinforced polymers using a computational homogenization method

PurposeIn order to achieve the desired macroscopic mechanical properties of woven fiber reinforced polymer (FRP) materials, it is necessary to conduct a detailed analysis of their microscopic load-bearing capacity.Design/methodology/approachUtilizing the representative volume element (RVE) model, this study delves into how the material composition influences mechanical parameters and failure processes.FindingsTo study the ultimate strength of the materials, this study considers the damage situation in various parts and analyzes the stress-strain curves under uniaxial and multiaxial loading conditions. Furthermore, the study investigates the degradation of macroscopic mechanical properties of fiber and resin layers due to fatigue induced performance degradation. Additionally, the research explores the impact of fatigue damage on key material properties such as the elastic modulus, shear modulus and Poisson's ratio.Originality/valueBy studying the load-bearing mechanisms at different scales, a direct correlation is established between the macroscopic mechanical behavior of the material and the microstructure of woven FRP materials. This comprehensive analysis ultimately elucidates the material's mechanical response under conditions of fatigue damage.

Numerical study on the influence of cell gas on the compression behavior of expanded polypropylene

AbstractExpanded polypropylene (EPP) bead foam mainly consists of entrapped gas within closed polymer cells. This numerical study presents a method to account for the influence of this entrapped gas on the compression behavior of EPP foam. The method developed combines a finite element (FE) model of the foam structure with a smoothed particle hydrodynamics model to simulate the effect of the cell gas. The foam structure is modeled using the open‐source software neper, the FE simulations are conducted using the explicit FE solver of LS‐Dyna. Numerically obtained stress–strain curves for the investigated foam materials, both with and without considering the cell gas, are compared with experimental data from tests using a specially designed vacuum test chamber. The comparison shows a good agreement between numerical and experimental results, indicating that entrapped cell gas increases the structural stiffness under compression. However, in load‐hold‐unload tests, the numerical model fails to accurately capture the stress relaxation behavior observed during the hold phase of the experiment. This study highlights the significant impact of cell gas on the compression behavior of EPP foam and the need for further refinement in simulation strategy to capture effects like the stress relaxation and multiaxial loading.

Fatigue life prediction considering conversion of mean stress for titanium alloy under multiaxial thermo-mechanical random loading

This paper presents a thermo-mechanical fatigue (TMF) life prediction method for titanium alloy TA15 under multiaxial random amplitude loading. Through strain-controlled TMF tests, it was found that under full-reversed cyclic loading, there was a significant presence of mean stress in the stress response. The induced mean stress led to the anomalous phenomenon where the fatigue life of thermal phase angle out-of-phase (TOP) was shorter than that of thermal phase angle in-phase (TIP). Therefore, a new damage calculation model was proposed, which can take into account the pure fatigue damage considering mean stress conversion and the cumulative environmental damage. Uniaxial TMF tests, constant amplitude multiaxial TMF tests, and random amplitude multiaxial TMF tests are conducted to verify the proposed method. The predicted results for all types of tests are in a good agreement with the experimental data.

A 3D thermo-mechanical damage model for concrete including Short-Term Thermal Creep Strain (STTCS)

In the current study, a Short-Term Thermal Creep Strain (STTCS) model of concrete was innovatively developed. This model can predict the time-dependent deformation of concrete subjected to wide applied load level ranging from 20 % to 60 % and temperatures up to 900 °C. A creep compliance function was developed to study the nonlinear creep characteristics of concrete with creep parameters. The definition and sensitivity of the creep parameters were investigated. In order to comprehensively predict the performance of concrete subjected to multiaxial compressive loads in fire, an orthotropic triaxial compression thermo-mechanical damage model for concrete is developed. The influence of STTCS on the multiaxial stress-strain behaviors was taken into account in the multiaxial model. The coupling thermo-mechanical contributions containing the development of STTCS with thermal effect, stress confinement, plastic damage and hardening evolution were creatively considered in the potential function within thermodynamics framework. The sensitivity of yield surface was discussed. The numerical operations of this proposed model were conducted for validation. The nonlinear stress-strain responses of concrete were accurately captured at temperatures ranging from 20 °C to 800 °C through the comparative study with test results in literatures, which indicates the accuracy and applicability of the proposed model.

Probabilistic fatigue life prediction of notched specimens based on modified stress field intensity method under multiaxial loading

In practical engineering components, due to the existence of non-uniform stress and strain field near the notch, it brings severe challenges to fatigue life prediction when evaluating the integrity of notched components. In this study, a probabilistic fatigue life prediction model for notched specimens was established by coupling the stress field intensity (SFI) method and Weibull distribution. Firstly, the position of the dangerous point is determined by finite element calculation, and the maximum strain energy density plane through the dangerous point is defined as the critical plane. Secondly, from the perspective of 2D features, the traditional SFI method is modified based on the stress distribution on the critical plane, and a new concept of effective stress is proposed to predict the fatigue life of notched specimens by the experimental data of smooth specimens. Finally, a new non-proportional additional hardening factor is established to characterize the influence of material properties and loading path on fatigue life. The experimental data of Q345 low alloy steel and GH4169 nickel base alloy are used to compare and analyze the proposed model. The results show that the predicted life of the proposed model is in good agreement with the experimental life.

Neural networks for critical load factors of unstiffened plates according to the reduced stresses method of EN 1993-1-5

The critical load factor resulting from the complete stress field is the main input parameter for the verification against plate buckling according to the reduced stresses method (RSM) from Eurocode EN 1993-1-5. Currently, the code provides just a simple and often conservative interaction formula with a limited application range. Realistic values can only be obtained by numerical methods, like the FEM, which is tedious for many load cases. To enhance the ease of use of the RSM, simple-to-use but accurate methods are needed, which can be automated and implemented into EN 1993-1-5. The current research deals with this problem by applying artificial neural networks (ANN) to predict the critical load factors of unstiffened plates under longitudinal, shear, and patch loading stresses, including their interaction behaviour. ANNs were used because approximated solutions with polynomials (as actual in the standard) are not suitable due to the complexity of the problem. The developed ANNs are highly accurate (as shown by an independent verification), can be implemented into the Eurocode, and can easily be used, even without in-depth programming skills. Moreover, a simple Python code is provided to demonstrate the ease of use. Still, the code can also be implemented into other software packages (like Excel), as only basic matrix operations are needed. The interaction surfaces are visualized, gaining a deeper understanding of plates under multiaxial loading situations. Finally, recommendations are given for generating ANNs for plate buckling problems.

Influence of proportional multiaxial fatigue loading on the residual mechanical properties of glass-reinforced plastic pipes

This work is dedicated to the experimental investigation of multiaxial cyclic loading influence on the residual mechanical properties of glass-reinforced plastic pipes (GRP pipes). Static, cyclic and combined (static after the preliminary cyclic loading) tests have been carried out on tubular specimens under tension with torsion. Residual stiffness curves have been made, their approximation has been carried out, using previously developed model, damage accumulation stages’ boundaries have been calculated. A specimen’s individual fatigue life prediction method, based on the initial parts of stiffness degradation curves, has been proposed. Influence of the preliminary multiaxial cyclic loading on residual Young’s modulus and tensile strength has been studied. Patterns of deformation and fracture processes have been studied, using digital image correlation method and acoustic emission method. A significant influence of fatigue damage on the residual properties of GRP pipes has been concluded.

Dynamic biaxial loading of vascular smooth muscle cell seeded tissue equivalents

An intricate reciprocal relationship exists between adherent synthetic cells and their extracellular matrix (ECM). These cells deposit, organize, and degrade the ECM, which in turn influences cell phenotype via responses that include sensitivity to changes in the mechanical state that arises from changes in external loading. Collagen-based tissue equivalents are commonly used as simple but revealing model systems to study cell–matrix interactions. Nevertheless, few quantitative studies report changes in the forces that the cells establish and maintain in such gels under dynamic loading. Moreover, most prior studies have been limited to uniaxial experiments despite many soft tissues, including arteries, experiencing multiaxial loading in vivo. To begin to close this gap, we use a custom biaxial bioreactor to subject collagen gels seeded with primary aortic smooth muscle cells to different biaxial loading conditions. These conditions include cyclic loading with different amplitudes as well as different mechanical constraints at the boundaries of a cruciform sample. Irrespective of loading amplitude and boundary condition, similar mean steady-state biaxial forces emerged across all tests. Additionally, stiffness-force relationships assessed via intermittent equibiaxial force–extension tests showed remarkable similarity for ranges of forces to which the cells adapted during periods of cyclic loading. Taken together, these findings are consistent with a load-mediated homeostatic response by vascular smooth muscle cells.

Near real-time calculation of the critical plane in all surface nodes of large metallic structures under multiaxial fatigue loading by visualization of the solution space

Applications of critical-plane-based fatigue criteria on large FE meshes remain uncommon, primarily due to the absence of a search scheme capable of identifying the critical plane for multiaxial loading scenarios in a way that is both reliable and fast enough. To address this gap, we introduce a three-module optimization scheme based on the Maximum Variance Method (MVM), guided by insights learned from visualizing the solution space. These visualizations not only validate the MVM strategy but also reveal a symmetry axis, which in turn assists in selecting the most critical among reciprocal solutions. Through iterative refinement of optimization parameters on automatically generated loading signals, our algorithm achieves a significant speedup over existing methods, while improving accuracy. The potential that comes with a processing speed of 10k nodes per CPU minute is demonstrated on a design challenge involving an additively manufactured Ti–6Al–4V bearing house subjected to non-proportional loading. A full critical-plane-based fatigue analysis on the 100k surface nodes takes 75 s with C++ PPL across 16 threads, which is fast enough to enable integration into iterative procedures such as topology optimization, promising substantial advancements in both academic research and engineering practices.

Yield locus and texture evolution of AA7475-T761 aluminum alloy under planar biaxial loading: An experimental and analytical study

AA7475 aluminum alloy is used as a structural material in aerospace and automobile applications where complex loading conditions are applicable. The material properties under multi-axial loading are recommended for efficient component design. Hence, the mechanical behaviour of AA7475-T761 aluminium alloy was investigated through planar biaxial tensile tests. The yield locus evolution and plastic strain direction were measured at higher plastic strain values (up to 7 %) at various load ratios. The yield loci were constructed and compared with existing yield criteria. Yld2000–2d yield criterion demonstrated accurate predictions with a deviation of approximately 1 %, highlighting its effectiveness in capturing the yield behavior of AA7475. Microstructure analysis using Electron Backscatter Diffraction (EBSD) was conducted to understand the misorientation evolution under the multi-axial loading. Bulk-texture analysis was performed using X-ray diffraction method. Texture analysis revealed that uniaxial deformation favoured the development of Cube and Inverse-Copper textures, while biaxial deformation yielded split Inverse-Goss texture formation. Fractography study shows very different fracture surfaces of biaxial samples compared to uniaxial samples. Overall, this study contributes to a comprehensive understanding of the yield behavior, microstructure, and texture evolution of AA7475-T761 aluminium alloy under different loading conditions at very large strains.

Multiaxial creep–fatigue failure mechanism and life prediction of a turbine blade based on a unified numerical solution approach

AbstractExposure of turbine blades to cyclic torsional loading at high temperature, stemming from pre‐torque installation and the aerodynamic forces during operation, has the potential to induce substantial creep–fatigue damage, thereby contributing to the likelihood of premature failure. Investigating the deformation mechanisms and proposing a reliable life prediction method aiming at torsional loading is critical to ensure the structural integrity of turbine blades. This study conducted strain‐controlled fatigue and creep–fatigue tests on Inconel 718 superalloy, employing a multiaxial servo‐hydraulic testing machine. Electron backscattering diffraction elucidated deformation and damage mechanisms, forming a basis for subsequent constitutive modeling and life prediction. The lack of creep–fatigue mechanical behavior and microscopic failure mechanism when stress triaxiality equal to 0 is filled, which provides the theoretical basis and data support for the life design and damage assessment of this material under extreme service conditions. The unified viscoplasticity constitutive model effectively characterized macroscopic deformation under torsional loading. Prediction of creep–fatigue life under torsional loading, utilizing the multiaxial ductility factor‐modified strain energy density exhaustion model, demonstrated excellent alignment with experimental findings. Finally, parametric analyses of stress distribution and damage assessment under different conditions were carried out for the example of a turbine blade with relatively rarely considered aerodynamic loading as a variable. It is expected to be popularized and applied in life design and damage assessment of high‐temperature structures under multiaxial loading in engineering.

The anisotropic and region-dependent mechanical response of wrap-around tendons under tensile, compressive and combined multiaxial loads

The present work reports on the multiaxial region and orientation-dependent mechanical properties of two porcine wrap-around tendons under tensile, compressive and combined loads based on an extensive study with n=175 samples. The results provide a detailed dataset of the anisotropic tensile and compressive longitudinal properties and document a pronounced tension-compression asymmetry. Motivated by the physiological loading conditions of these tendons, which include transversal compression at bony abutments in addition to longitudinal tension, we systematically investigated the change in axial tension when the tendon is compressed transversally along one or both perpendicular directions. The results reveal that the transversal compression can increase axial tension (proximal-distal direction) in both cases to orders of 30%, yet by a larger amount in the first case (transversal compression in anterior-posterior direction), which seems to be more relevant for wrap-around tendons in-vivo. These quantitative measurements are in line with earlier findings on auxetic properties of tendon tissue, but show for the first time the influence of this property on the stress response of the tendon, and may thus reveal an important functional principle within these essential elements of force transmission in the body. Statement of significanceThe work reports for the first time on multiaxial region and orientation-dependent mechanical properties of wrap-around tendons under various loads. The results indicate that differences in the mechanical properties exist between zones that are predominantly in a uniaxial tensile state and those that experience complex load states. The observed counterintuitive increase of the axial tension upon lateral compression points at auxetic properties of the tendon tissue which may be pivotal for the function of the tendon as an element of the musculoskeletal system. It suggests that the tendon’s performance in transmitting forces is not diminished but enhanced when the action line is deflected by a bony pulley around which the tendon wraps, representing an important functional principle of tendon tissue.

Structural Analysis of Deck Reinforcement on Composite Yacht for Crane Installation

The crane installation on the deck of a yacht redistributes the stress field and affects the local structural integrity and performance. The safe operation of the yacht is associated with the optimal placement of the crane on the deck and the proper local structural reinforcement. Here, the structural analysis of the bow part of a yacht made of composite materials is studied, considering the retrofit installation of a crane, in three different cases of reinforcing the deck: (a) without any reinforcement, (b) with a T-type reinforcement, and finally, (c) with a longitudinal beam. The T-type connects the longitudinal bulkhead and the deck, reinforced locally with overlamination skin and adhesive-filler. The longitudinal beam works as a local longitudinal stiffener attached to the deck and connects the second, third, and fourth transverse frames. The structural analysis is performed using the finite element method following the classification societies’ rules. The local reinforcements are made from the same composite materials as the unreinforced deck. The maximum deformations, the principal stresses, and the safety factors following Tsai-Wu and Hashin criteria are calculated and compared for the three different cases. The T-type and longitudinal reinforcements reduce deck stresses by 33%, with longitudinal reinforcement reducing deck deformation by 17%. Composite failure analysis shows the structure was near failure, and the reinforcements enhance safety; T-type is better for multiaxial loads (Tsai-Wu), and longitudinal is superior for micromechanical failure (Hashin). By considering the structural performance and safety aspects, designers and engineers can make optimal decisions regarding yacht crane installation and proper reinforcement, leading to safer and more efficient structures.

Reliability modeling of pre-stressed composite structures subject to interlayer slip failure under multi-axial random impact and vibration loads

A time-dependent reliability model for pre-stressed metal/polymer/metal composite structures subject to interlayer slip failure is developed in this study, allowing for predicting the probability of failure of the whole structure under multi-axial random multi-peak impact loads and transport vibration. A multi-Gaussian envelope model with uniform modulations is proposed to model random multi-peak impact loads, and the inverse sampling method is employed to model random transport vibration. An interlayer slip physics model is developed based on the contact surface friction mechanism under multi-axial vibration load and the stress-relaxation constitutive model. By implementing the interlayer slip physics model in the finite element method framework via the user-material routine, the geometry effect of the structure can be dealt with, and the reliabilities at an arbitrary location of the structure can be obtained. The proposed method is demonstrated using engineering examples. The results show that the proposed reliability assessment method provides a viable and systematical procedure of computing the time-dependent reliability of composite structures as a whole under multi-axial impact loads and vibrations.

Cartilage tissue engineering using decellularized biomatrix hydrogel containing TGF-β-loaded alginate microspheres in mechanically loaded bioreactor

Physiochemical tissue inducers and mechanical stimulation are both efficient variables in cartilage tissue fabrication and regeneration. In the presence of biomolecules, decellularized extracellular matrix (ECM) may trigger and enhance stem cell proliferation and differentiation. Here, we investigated the controlled release of transforming growth factor beta (TGF-β1) as an active mediator of mesenchymal stromal cells (MSCs) in a biocompatible scaffold and mechanical stimulation for cartilage tissue engineering. ECM-derived hydrogel with TGF-β1-loaded alginate-based microspheres (MSs) was created to promote human MSC chondrogenic development. Ex vivo explants and a complicated multiaxial loading bioreactor replicated the physiological conditions. Hydrogels with/without MSs and TGF-β1 were highly cytocompatible. MSCs in ECM-derived hydrogel containing TGF-β1/MSs showed comparable chondrogenic gene expression levels as those hydrogels with TGF-β1 added in culture media or those without TGF-β1. However, constructs with TGF-β1 directly added within the hydrogel had inferior properties under unloaded conditions. The ECM-derived hydrogel group including TGF-β1/MSs under loading circumstances formed better cartilage matrix in an ex vivo osteochondral defect than control settings. This study demonstrates that controlled local delivery of TGF-β1 using MSs and mechanical loading is essential for neocartilage formation by MSCs and that further optimization is needed to prevent MSC differentiation towards hypertrophy.

Multiaxial fatigue life prediction based on modular neural network pretrained with uniaxial fatigue data

PurposeData-driven models are increasingly being used to predict the fatigue life of many engineering components exposed to multiaxial loading. However, owing to their high data requirements, they are cost-prohibitive and underperforming for application scenarios with limited data. Therefore, it is essential to develop an advanced model with good applicability to small-sample problems for multiaxial fatigue life assessment.Design/methodology/approachDrawing inspiration from the modeling strategy of empirical multiaxial fatigue models, a modular neural network-based model is proposed with assembly of three sub-networks in series: the first two sub-networks undergo pretraining using uniaxial fatigue data and are then connected to a third sub-network trained on a few multiaxial fatigue data. Moreover, general material properties and necessary loading parameters are used as inputs in place of explicit damage parameters, ensuring the universality of the proposed model.FindingsBased on extensive experimental evaluations, it is demonstrated that the proposed model outperforms empirical models and conventional data-driven models in terms of prediction accuracy and data demand. It also holds good transferability across various multiaxial loading cases.Originality/valueThe proposed model explores a new avenue to incorporate uniaxial fatigue data into the data-driven modeling of multiaxial fatigue life, which can reduce the data requirement under the promise of maintaining good prediction accuracy.

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.

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.

Fatigue behavior analysis and life evaluation method of building steel under the influence of multiple factors

The paper aims to analyze the stress–strain response of building steel under low-cycle multiaxial fatigue and to accurately evaluate the fatigue life of specimens by selecting the more important relevant factors that affect fatigue behavior. Based on this, low-cycle multiaxial fatigue experiments of Q355D notched specimens under different multiaxial loading are carried out. Firstly, the fatigue behavior of notched specimens under different loadings and the relationship between the biaxial strain amplitude ratio and fatigue life are analyzed. Secondly, Grey correlation analysis, Pearson correlation analysis, and Random Forest importance analysis are used to screen out the important factors affecting fatigue life. Finally, the grey MGM (1, N) model is used to predict the fatigue life of notched specimens, and the results show that the predicted life based on Random Forest importance analysis is in good agreement with the experimental life. In this paper, the multiaxial fatigue problem is decoupled into two sub-problems, i.e. screening out related factors and life prediction based on the related factors, which can be used as a reference for life prediction in structural design.

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.