Combined Loading Modes Research Articles

Experimental Assessment of the Adequacy of Numerical Modeling of the Interlayer Crack Resistance of a Laminate Glass-Epoxy Composite under Combined Loading Mode I/II

Experimental Assessment of the Adequacy of Numerical Modeling of the Interlayer Crack Resistance of a Laminate Glass-Epoxy Composite under Combined Loading Mode I/II

Damage investigation in steel pipe under pressure and combined bending moment: Application in structure connected by elbow and reduced tee

Steel tubular structures in pipelines, or those connections such as concentric reductions, reduced tees, and elbows, all differ in their response to loading, they are sometimes solicited to complex and combined loads, which accumulate with the internal pressure to their solicitation cause in certain situation their damage, the objective in this analysis is to numerically predict the mechanical behavior until damage of a complete tubular structure, which contains the connecting elements of an elbow and a reduced tee attached to each other by straight tubular parts, this structure, by its standardized dimensions presents a real design of a main pipeline spigot for a possible supply line, this tubular structure is analyzed in this work under these real pressure conditions, and combined loads probably coming from the weight of a valve, or a pipe flanged to this spigot element or other, in X60 steel This structure is solicited under different combined modes of loading. The elastic-plastic behavior is under Voce’s model and Von Mises’ equivalent stress flow theory, the damage of the structure by crack initiation and propagation is ensured by using the XFEM technique, the response up to damage of the structure is evaluated under the effect of the parameters of the combined loading mode, we present by angular bendingrotation moment curves that these parameters clearly condition the response and the level of damage.

Graphene Oxide-Based Nanocomposites for Stereolithography (SLA) 3D Printing: Comprehensive Mechanical Characterization under Combined Loading Modes.

Additive manufacturing, particularly Stereolithography (SLA), has gained widespread attention thanks to its ability to produce intricate parts with high precision and customization capacity. Nevertheless, the inherent low mechanical properties of SLA-printed parts limit their use in high-value applications. One approach to enhance these properties involves the incorporation of nanomaterials, with graphene oxide (GO) being a widely studied option. However, the characterization of SLA-printed GO nanocomposites under various stress loadings remains underexplored in the literature, despite being essential for evaluating their mechanical performance in applications. This study aimed to address this gap by synthesizing GO and incorporating it into a commercial SLA resin at different concentrations (0.2, 0.5, and 1 wt.%). Printed specimens were subjected to pure tension, combined stresses, and pure shear stress modes for comprehensive mechanical characterization. Additionally, failure criteria were provided using the Drucker--Prager model.

ON THE RECONSTRUCTION OF PRESTRESS FIELDS IN A HOLLOW CYLINDER

The present research is devoted to the development of the theoretical foundations of nondestructive acoustic method for identifying inhomogeneous prestress fields in a hollow cylinder, depending on the probing loading type. A linearized model of steady oscillations of an elastic body in the presence of an inhomogeneous prestress field of arbitrary nature is considered in the standard and weak formulations. On the basis of this model, we formulate a problem for a cantilever-clamped prestressed hollow cylinder that performs steady axisymmetric vibrations under three types of probing loading. A corresponding weak formulation of the problem in the cylindrical coordinate system is presented, in which six independent components of the prestress tensor are taken into account. At that, a case of prestress fields obtained by applying some initial mechanical external static load is considered. In the presence and absence of prestresses of various types, amplitude-frequency dependences are analyzed, and resonant and natural frequencies are found in a wide frequency range. Numerical calculations were carried out using the FEM on a non-uniform grid; mesh refinement is carried out in the vicinity of the boundary points, where the type of boundary conditions changes. Based on the numerical solution of an auxiliary set of direct problems, seven types of prestress fields are constructed, differing in the types of initial loading, most often encountered in practice. To assess the possibility of implementing the procedure for reconstructing prestresses of each of the considered types, a sensitivity analysis was additionally performed, which showed that for some prestress types there are frequencies and types of probing loading for which the presence of prestress is practically not manifested. The sensitivity analysis performed made it possible to implement the optimal method of probing loading when solving the inverse coefficient problem. The statement of the new inverse problem on the restoration of arbitrary inhomogeneous prestress fields in the considered finite hollow cylinder is formulated. When restoring the prestress of a given structure, the inverse problem is reduced to finding a set of parameters from an ill-conditioned algebraic system, which was studied with the help of the A.N. Tikhonov regularization method. Additional data for solving the inverse problem was obtained on the basis of probing both via a single load and via combined probing modes. It has been found that it is most effective to use a combined loading mode and use a sufficiently wide frequency range when selecting sounding frequencies. The results of computational experiments on the reconstruction of six components of the prestress tensor are presented and analyzed, and recommendations are proposed for choosing the optimal modes of acoustic sounding.

Development and validation of lumbar spine finite element model.

The functional biomechanics of the lumbar spine have been better understood by finite element method (FEM) simulations. However, there are still areas where the behavior of soft tissues can be better modeled or described in a different way. The purpose of this research is to develop and validate a lumbar spine section intended for biomechanical research. A FE model of the 50th percentile adult male (AM) Total Human Model for Safety (THUMS) v6.1 was used to implement the modifications. The main modifications were to apply orthotropic material properties and nonlinear stress-strain behavior for ligaments, hyperelastic material properties for annulus fibrosus and nucleus pulposus, and the specific content of collagenous fibers in the annulus fibrosus ground substance. Additionally, a separation of the nucleus pulposus from surrounding bones and tissues was implemented. The FE model was subjected to different loading modes, in which intervertebral rotations and disc pressures were calculated. Loading modes contained different forces and moments acting on the lumbar section: axial forces (compression and tension), shear forces, pure moments, and combined loading modes of axial forces and pure moments. The obtained ranges of motion from the modified numerical model agreed with experimental data for all loading modes. Moreover, intradiscal pressure validation for the modified model presented a good agreement with the data available from the literature. This study demonstrated the modifications of the THUMS v6.1 model and validated the obtained numerical results with existing literature in the sub-injurious range. By applying the proposed changes, it is possible to better model the behavior of the human lumbar section under various loads and moments.

PRESTRESSED MULTILAYER DESIGNS OF POLYMER COMPOSITES FOR THE VIBRATION AND NOISE CONTROL OF AIRCRAFTS

This paper presents an approach for designing the compact and miniature infra- and low-frequency vibration isolation systems based on the layered composite elastic elements with adjustable negative and quasi-zero stiffness. New problems of modeling the specified parameters of stiffness and bearing capacity of the elements of a certain geometry under combined mode loading are solved by varying the structure, elasticity and configuration of the layers, and by controlling the local mobility of the binder. The approach is valid with the results of experimental designing and studying the system models. Application of the approach makes a qualitatively change in solving a number of critical issues of vibration and noise control in the aerospace and other promising engineering.

Hygrothermal degradation of MWCNT/epoxy brittle materials under I/II combined mode loading conditions: An experimental, micro structural and theoretical study

The effects of carboxylated multi-walled carbon nanotubes (MWCNTs) are studied experimentally and theoretically on mixed-mode (I/II) fracture behavior of epoxy resin at the presence of hygrothermal aging conditions. In this paper, the mixed-mode fracture of MWCNT/epoxy is experimentally measured using Short Beam Bending (SBB) samples with different crack inclination angles (α) ranging from pure mode I (i.e., α = 0°) to pure mode II (i.e., α = 39°). To examine the effects of hygrothermal aging conditions and water barrier properties of MWCNTs, four groups of samples including a group of neat epoxy specimens, and three groups of MWCNT/epoxy specimens (with 0.1, 0.3, and 0.5 wt% of MWCNTs) were manufactured and immersed into hot deionized water for 15 days at 60 °C temperature and similarly four groups were placed at room temperature conditions (26 °C and 25–35% relative humidity) for 15 days. According to the experimental results, toughening the epoxy resin by incorporating nanotubes with 0.1, 0.3, and 0.5 wt% of MWCNTs improved the fracture toughness at both environmental conditions, but the highest fracture toughness was obtained for composition containing 0.3 wt% nanoparticles. The variations of fracture loads were dependent on the ambient environment, MWCNTs content, and mode mixity. The relationship between the obtained experimental results, microstructure and morphology of fracture in the tested samples was also investigated. In addition, the load-carrying capacity of the SBB samples made of the neat and MWCNTs modified epoxy material was also predicted well using a two-term based fracture model called Generalized Maximum Tangential Stress (GMTS) criterion.

Calculation of fatigue fracture in structural elements using a multimode damage model

The problem of nucleation and development for the fatigue fracture process in element of aircraft structure is solved using previously developed cyclic damage model. The model contains the evolution equation for the damage function depending on stress state and amplitudes of the cyclic loads. On this basis, calculations of the initiation and development of crack-like fracture zones are carried out for an aircraft structure element of a disk with a blade in a flight loading cycle (HCF mode). The damage function was calculated based on the elastic solution for the element of structure loaded by centrifugal forces in disk and blade and aerodynamical pressure on blade. An alternative cyclic loading regime associated with high-frequency vibrations of the blades was investigated. Fatigue fracture in this process corresponds to the VHCF mode. Simulation of the combined cyclic loading mode was also carried out. In all these modes, the real time of the nucleation and development of quasi-cracks was estimated up to reaching the observed disk surface.

Providing a Prediction Model for Stress Intensity Factor of Fiber- Reinforced Asphalt Mixtures under Pure Mode III Loading Using the Edge Notched Disc Beam (ENDB)

The use of Edge Notched Disc Beam (ENDB) sample has been proposed as a suitable geometry in performing fracture tests in different loading modes. The most important features of the ENDB samples include easy making, quick and easy sampling, simple testing, and the ability to examine a wide range of pure and combined loading modes. Using a wide range of fracture tests, a statistical model is proposed to predict the stress intensity factors of asphalt mixtures in terms of the pure torsion mode (mode III) loading in this study. To this end, the experiments were carried out at different temperature conditions (-5, -15 and -25 °C), different loading conditions (0.5, 1 and 5 mm/min), and on control and modified asphalt mixtures with different percentages of polyolefin-aramid fibers. The results showed that, with increasing the fiber content and loading rate, the fracture strength increased with average 25%, while an increase in fracture toughness due to lower temperature had an effect of less than 5%. Using the Response Surface Method (RSM), the prediction model of stress intensity coefficients of asphalt mixtures was presented in the pure torsion mode. The results of the proposed models had a good correlation with the results of the conducted fracture tests.

Analysis of foundation bearing capacity and structural stability of suction bucket for offshore wind power

The large-scale wide and shallow bucket foundation of offshore wind power has a unique bucket top bearing mode, and the bucket foundation is provided with partition plates, which has greater bearing capacity as a whole. By numerical method, the solid and structural elements such as bucket body, rib plate connector and silo plate, as well as bucket-soil contact element are established, and the real three-dimensional complex model of bucket foundation and foundation soil is constructed in detail. The nonlinear contact calculation of bucket foundation under the combined loading modes such as horizontal load, wave force, vertical load and bending moment are simulated, and the deformation, bearing characteristics and safety of suction bucket are analyzed. The ultimate bearing capacity of foundation under horizontal load, vertical load and bending moment are calculated by Flac3d finite difference method, which provide reference for the foundation structure selection, bucket foundation design, implementation and safety evaluation of offshore wind farm projects.

Calibration and validation of a novel hybrid model of the lumbosacral spine in ArtiSynth-The passive structures.

In computational biomechanics, two separate types of models have been used predominantly to enhance the understanding of the mechanisms of action of the lumbosacral spine (LSS): Finite element (FE) and musculoskeletal multibody (MB) models. To combine advantages of both models, hybrid FE-MB models are an increasingly used alternative. The aim of this paper is to develop, calibrate, and validate a novel passive hybrid FE-MB open-access simulation model of a ligamentous LSS using ArtiSynth. Based on anatomical data from the Male Visible Human Project, the LSS model is constructed from the L1-S1 rigid vertebrae interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, and facet joints. A mesh convergence study, sensitivity analyses, and systematic calibration were conducted with the hybrid functional spinal unit (FSU) L4/5. The predicted mechanical responses of the FSU L4/5, the lumbar spine (L1-L5), and the LSS were validated against literature data from in vivo and in vitro measurements and in silico models. Spinal mechanical responses considered when loaded with pure moments and combined loading modes were total and intervertebral range of motions, instantaneous axes and centers of rotation, facet joint contact forces, intradiscal pressures, disc bulges, and stiffnesses. Undesirable correlations with the FE mesh were minimized, the number of crisscrossed collagen fiber rings was reduced to five, and the individual influences of specific anatomical structures were adjusted to in vitro range of motions. Including intervertebral motion couplings for axial rotation and nonlinear stiffening under increasing axial compression, the predicted kinematic and structural mechanics responses were consistent with the comparative data. The results demonstrate that the hybrid simulation model is robust and efficient in reproducing valid mechanical responses to provide a starting point for upcoming optimizations and extensions, such as with active skeletal muscles.

Mechanical fatigue of whole rabbit-tibiae under combined compression-torsional loading is better explained by strained volume than peak strain magnitude

The mechanical fatigue behavior of whole bone is poorly defined, particularly for the combined loading modes that occur in vivo. The purpose of this study was to quantify the fatigue life of whole rabbit-tibiae under cyclic uniaxial compression and biaxial (compression and torsion) loading, and to explore the relationship between fatigue life and specimen-specific finite element (FE) predictions of stress/strain. Twelve tibiae were tested cyclically until failure across a range of uniaxial-compressive loads. Another twenty-two tibiae were separated into three groups and loaded biaxially; peak compressive load was constant in all three groups (50% ultimate force) but torsion was varied (0%, 25%, or 50% of ultimate torque). FE models with heterogeneous linear-elastic material properties were developed from computed tomography. We assessed peak stress/strain and stressed/strained volume based on principal stress/strain, as well as von Mises and pressure modified von Mises criteria. A logarithmic (r2 = 0.68; p < 0.001) relationship was observed between uniaxial-compressive load and fatigue life. Biaxial tests demonstrated that fatigue life decreased with superposed torsion (p = 0.034). Strained volume, based on a maximum principal strain or pressure modified von Mises strain criteria, were strong predictors of fatigue life under both uniaxial (r2 = 0.73–0.82) and biaxial (r2 = 0.59–0.60) loads, and these outperformed equivalent peak stress- and strain-based measures. Our findings highlight the importance of evaluating strain distributions, rather than peak stress or strain, to predict the fatigue behavior or whole bone, which has important implications for the study of stress fracture.

Investigation of damage accumulation and delamination propagation in polymer composite materials based on two-level fracture models

The work is devoted to the study of deformation and fracture processes occurring in layered composites under combined loading modes. The aim of the work is numerical analysis of different modes of fracture, which are simultaneously realized in the samples of laminated composite material. Models of laminated composite material with imitation of technological defects in the form of material debonding are constructed. The delamination process is implemented using the virtual crack closure technique. The processes of damage accumulation and fracture of laminated composites are set on the basis of the models for reduction of stiffness properties using the Hashin criterion and Matzemiller model. The models are based on the laws corresponding to brittle and plastic fracture. Several models of fracture and degradation of elastic properties have been compared. A multiscale approach was used to solve the difficulties related to the precise description of the composite's internal structure. The essence of the approach is that the analysis of a laminated composite can be performed on three different scales: macro level, meso level and micro level. At the macro level, an equivalent material is used for which the effective properties are determined by homogenization methods, in particular by the mean field method. The multiscale finite element modeling is implemented, in the course of which macroscopic parameters of material sample at each step depend on characteristics and properties of components at the micro-level. The behavior of two samples of laminated polymer composite material was studied with different configuration of embedded defects under the load of two types: uniaxial compression and torsion, and only uniaxial compression. The influence of internal defects on the processes of damage accumulation and material delamination has been established.

Fatigue device driven by a three degree of freedom tripodal piezoelectric actuator.

A miniature piezoelectric-driven fatigue device with three degrees of freedom is developed. The device integrates two fatigue testing functions, including uniaxial tensile fatigue and tensile-bending combined loading modes. The synchronous tensile-bending loading principle is described, which is applicable for calculating the vector displacements along two orthogonal directions and investigating the anisotropic fatigue properties. Regarding the combined loading mode, maximum load/displacement amplitudes for tensile and bending vector components that could be achieved are 16.9 N/22.8 µm and 3.3 N/5.6 µm, respectively. Based on tensile and tensile-bending combined fatigue loading modes, the displacement responses and fatigue lives at loading frequencies ranging from 1 Hz to 100 Hz are valuated experimentally to indicate the validation.

Model of the brittle crack growth under the combined mode loading.

The modified model for dynamic crack growth in viscoelastic material has been proposed. The model based on the structural approach that includes Zhurkov’s thermokinetical concept and Neiber-Novozhilov’s criterion of brittle fracture. The structural approach describes the microstructure inhomogeneity of material and staging of crack propagation revealing by optical and electronic fractography as changing the scale of damage accumulation and fracture. The main parameters of the physical model approved by experimental data on the pulse hit action of striker to a notch of the permanently hardly loaded single edge-notched specimen in wide range of environment temperatures has been analyzed in the paper. The proposed model of brittle crack growth under the dynamic blow influence based on physical representations of the fluctuation nature of the fracture process and enables a description of the transition from discrete experimental data under combined loading to a set of continuous numerical data sufficient to calculate the values of the crack tip energy flow in a wide range of external loading and extreme environment, including the low temperatures.

Towards Reliability-Enhanced Mechanical Characterization of Non-Crimp Fabrics: How to Compare Two Force-Displacement Curves against a Null Material Hypothesis

Detailed characterization of fabric reinforcements is necessary to ensure the quality of manufactured composite parts, and subsequently to prevent structural failure during service. A lack of consensus and standardization exists in selecting test methods for the mechanical characterization of fabrics. Moreover, in reality, during any experimentation there are sources of uncertainties which may result in inconsistencies in the interpretation of data and the comparison of different testing methods. The aim of this article is to show how simple statistical data analysis methods may be used to enhance the characterization of composite fabrics under individual and combined loading modes while accounting for inherent material/test uncertainties. Results using a typical glass non-crimp fabric (NCF) show that, statistically, there are significant differences between the warp and weft direction responses of a presumably balanced NCF under all deformation modes, with weft yarns being generally stiffer. Moreover, the statistical significance of warp-weft couplings under both simultaneous and sequential biaxial-shear loading modes became statistically evident, when compared to a pure biaxial deformation.

Effect of complex combined loading mode on the fracture toughness of titanium alloys

This paper presents new experimental data concerning the effect of the complex combined loading mode on changes in the mechanical properties of titanium alloys of different classes subjected to static stretching. The complex combined loading mode consists in the application of additional pulse loads for given degrees of static pre-loading followed by quenching of titanium alloys at a temperature of liquid nitrogen under a pre-set scheme. The authors used a new method for studying the material fracture kinetics, the so-called method of complete stress-strain diagrams, to explore a full range of mechanical properties of titanium alloys subjected to the combined loading mode, including the crack resistance.

Injury mechanisms of the ligamentous cervical C2–C3 Functional Spinal Unit to complex loading modes: Finite Element study

The cervical spine sustains high rate complex loading modes during Motor Vehicle Crashes (MVCs) which may produce severe injuries accompanied with soft and/or hard tissue failure. Although previous numerical and experimental studies have provided insights on the cervical spine behavior under various loading scenarios, its response to complex impact loads and the resulting injury mechanisms are not fully understood. A validated Finite Element (FE) model of the ligamentous cervical C2–C3 Functional Spinal Unit (FSU) was utilized to assess the spinal response to six combined impact loading modes; flexion–extension combined with compression and distraction, and lateral bending and axial rotation combined with distraction. The FE model used time and rate-dependent material laws which permit assessing bone fracture and ligament failure. Spinal load-sharing, stresses in the spinal components, intradiscal pressure (IDP) change in the nucleus as well as contact pressure in the facet joints were predicted. Bone and ligaments failure occurrence and initiation instants were investigated. Results showed that spinal load-sharing varied with loading modes. Lateral bending combined with distraction was the most critical loading mode as it increased stresses and strains significantly and produced failure in most of the spinal components compared to other modes. The facet joints and surrounding cancellous bone as well as ligaments particularly the capsular (CL) and flavum (FL) ligaments were the most vulnerable structures to rapid flexion–extension, axial rotation and lateral bending combined with distraction or compression. The excessive stress and strain resulted from these loading modes produced rupture of the CL and FL ligaments and failure in the cancellous bone. The detection of failure initiation as well as fracture assessment demonstrated the vulnerability of ligaments to tensile combined loads and the major contribution of the bony structures in resisting compressive combined loads. Findings of this study may potentially assist in the development of injury prevention and treatment strategies.

On the notch sensitivity of cast iron under multi-axial fatigue loading

This work deals with the notch sensitivity of sharp notches under multi-axial fatigue loading. The main discussion concerns the differences in notch sensitivity at high cycle fatigue regime, between tensile, torsional and combined loading. For this comparison, this paper considers a large set of fatigue experimental tests and several computing simulations analyzed with several notch theories for predicting fatigue life of a component. The considered experimental data, taken from literature, deal with the fatigue behavior of cast iron circumferentially V-notched specimens under tension, torsion, and combined loading mode. This paper tries to apply several techniques for theoretical strength assessment and to compare different procedures. The examined procedures need the computation of many parameters, focusing on the importance of using the tensile resistance to set these parameters or using both tensile and torsion resistances. However, the improvements obtained by means of the more complex procedures are not noteworthy, compared to the overall scatter. In author’s opinion, the differences in notch sensitivity under tensile and torsional loading remain questionable.

Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values.Eight well-established FE models of the lumbar spine (L1-5) of different research centers around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces.Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values.In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.