Off-axis Loading Research Articles

A nonlinear homogenized finite element analysis of the primary stability of the bone-implant interface.

Stability of an implant is defined by its ability to undergo physiological loading-unloading cycles without showing excessive tissue damage and micromotions at the interface. Distinction is usually made between the immediate primary stability and the long-term, secondary stability resulting from the biological healing process. The aim of this research is to numerically investigate the effect of initial implantation press-fit, bone yielding, densification and friction at the interface on the primary stability of a simple bone-implant system subjected to loading-unloading cycles. In order to achieve this goal, human trabecular bone was modeled as a continuous, elasto-plastic tissue with damage and densification, which material constants depend on bone volume fraction and fabric. Implantation press-fit related damage in the bone was simulated by expanding the drilled hole to the outer contour of the implant. The bone-implant interface was then modeled with unilateral contact with friction. The implant was modeled as a rigid body and was subjected to increasing off-axis loading cycles. This modeling approach is able to capture the experimentally observed primary stability in terms of initial stiffness, ultimate force and progression of damage. In addition, it is able to quantify the micromotions around the implant relevant for bone healing and osseointegration. In conclusion, the computationally efficient modeling approach used in this study provides a realistic structural response of the bone-implant interface and represents a powerful tool to explore implant design, implantation press-fit and the resulting risk of implant failure under physiological loading.

Strain rate-dependent mechanical behavior of quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading

To make a better use of quasi-unidirectional fabrics in structural application, the strain rate-dependent tensile behavior of quasi-unidirectional E-glass fabric reinforced polypropylene composites was studied. Monotonic tensile tests were firstly performed on 10°, 20° and 90° off-axis samples of composites. The experimental results show that both mechanical properties and nonlinear stress-strain behavior of composites are dependent of strain rate. A regression function is adopted to describe the variation in overall mechanical properties with the imposed strain rate. A strain rate-dependent coupled damage-plasticity model is built for quasi-unidirectional composites. The damage variables and plastic parameters in the proposed model are determined through cyclic loading-unloading tensile tests and can be represented as a function of the imposed strain rate. In addition, the damage mechanism of composites is observed to evolve with strain rate. Increasing strain rate can hinder the initiation and evolution of damage in composites.

Temperature-dependent response of quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading

Abstract The temperature-dependent off-axis tensile behavior of quasi-unidirectional E-glass fabric reinforced polypropylene composites has been investigated both experimentally and constitutively in this paper. The nonlinearity in composites under off-axis loading is shown to be a combination of damage and plasticity regardless of temperature. A nonlinear constitutive model is established to predict the temperature-dependent nonlinear stress-strain curves of composites, in which the accumulation of plastic strain and evolution of damage in composites are described by the plasticity and damage theories, respectively. A full suite of temperature-dependent plastic and damage parameters in the model are determined through cyclic loading-unloading tests.

A multiscale experimental approach for correlating global and local deformation response in woven composites

A multiscale experimental approach is introduced that facilitates correlating globally applied stress to the local material response at yarn scale. Using a high-resolution optical digital image correlation, low and high strain zones in off-axis woven composite samples loaded in uniaxial tension are identified and the corresponding full-field strains are quantified. The local strain response quantified over low and high strain domains are used along with the continuum scale deformation to establish a correlation between global and local deformation behavior as a function of fiber orientation. In addition, global stress-local strain curves are extracted for low and high strain domains at different fiber orientation angles. A simple plasticity model in conjunction with the obtained stress-strain curves is implemented and utilized to develop a phenomenological model that enables correlating global stress with the locally developed strain at different locations in a composite specimen subjected to off-axis tensile load.

Experimental and numerical investigation on mechanical behaviors of woven fabric composites under off-axial loading

A mesoscale finite element model was developed to investigate the progressive damage behaviors of twill woven composites under off-axial tension and compression. The anisotropic damage model based on the Murakami-Ohno damage theory was adopted to characterize the composites failure process, and a combined elastoplastic damage model was developed for modeling the mechanical behavior of the matrix. Effective tow properties were obtained based on micromechanical characterization of the fiber bundles, and the failure mechanisms at the tow constituent scale were also investigated. Moreover, experimental tension and compression tests were carried out on the woven specimens to obtain their mechanical responses under various off-axial loading conditions. The fracture surfaces of the test specimens were characterized by optical microscopy and the corresponding failure mechanisms were identified. The numerical predictions showed good agreement with the experimental result.

On crashing behaviors of aluminium/CFRP tubes subjected to axial and oblique loading: An experimental study

Abstract Thin-walled energy-absorbing structures rarely experience in pure axial loading in real crash events, but rather a combination of axial and off-axial loads. In this perspective, it is critical to understand the oblique crushing process of thin-walled structures. To address this issue, circular aluminum and carbon fiber reinforced plastics (CFRP) tubes were experimentally investigated for characterizing their crashworthiness subject to quasi-static axial and oblique compression in this study. The tests were conducted at five different loading angles (θ) of 0°, 5°, 10°, 20° and 30° to the tubal axis. Five sets of specific fixtures were fabricated to apply the desired axial and off-axial loads onto the aluminum and CFRP specimens, respectively. The failure modes, load-displacement curves, crushing force and energy absorption of all the specimens were analyzed; and the effects of loading angle were explored. It is found from the experiments that with the increase in loading angle, aluminum tubes were more prone to collapse in an irregular diamond mode (Id) instead of axisymmetric concertina mode (Ac), while the CFRP tubes collapsed in much more complex failure modes which included splaying mode (Sp), tearing mode (Te), socking mode (So), micro-fragmentation mode (Mf) and catastrophic failure (Cf). As for the energy absorption characteristics, the loading angle (θ) ranged from 0° to 10° had little impact on the energy absorption for the both aluminum and CFRP tubes, nevertheless, the energy absorption of the CFRP tubes decreased more significant from θ = 10° to 30°, while that of aluminum tubes declined fairly steadily.

A novel basic cell modeling method for elastic-viscoplastic homogenization analysis of plain-woven laminates with nesting

In this study, a novel basic cell modeling method is developed for the elastic-viscoplastic homogenization analysis of plain-woven laminates with nesting. For this, based on the periodicity and point-symmetry of internal structures of plain-woven laminates with nesting, a hexagonal prism-shaped basic cell and its boundary conditions are proposed. The basic cell and boundary conditions are then introduced into the homogenization theory for nonlinear time-dependent composites developed by the authors. Using the present method, elastic-viscoplastic behavior of a plain-woven glass fiber-reinforced plastic (GFRP) laminate with nesting subjected to on- and off-axis loading is analyzed. In the analysis, the present method is successful in significantly reducing the analysis domain, and in achieving the modeling of a high volume fraction of fiber bundles. It is shown from the analysis results that the present method accurately predicts experimentally observed macroscopic elastic-viscoplastic behavior of the plain-woven GFRP laminate with nesting. In addition, the elastic-viscoplastic analysis of plain-woven GFRP laminates without nesting is also conducted, showing that the nesting affects elastic-viscoplastic behavior of plain-woven GFRP laminates.

Macro-mechanical damage modeling of fibrous composite materials accounting for non-linear material behavior

In the present paper, a new macro-mechanical model for tracing damage-evolution in composite materials is proposed. The present model represents a new extension and a new approach to a previous model (Ghazi-Farid model), which can be applied for a general state of stress. The model is verified by comparing its results with those corresponding to Ghazi-Farid model for different composite materials and it seems to give very close correlations. The proposed model can be applied to both elastic and inelastic materials as well as generally orthotropic fibrous composite nonlinear-materials.It was concluded that shear damage is always higher than any other damage types due to the high nonlinear-material shear behavior, which causes high plastic strain-energy density. Damage in a composite lamina causes a reduction in its stiffness. Therefore, a new quantum-damage variable is proposed: '' tangential quantum-damage variable '' to quantify the overall-damage in a composite lamina. Percentage reduction of composite stiffness depends mainly on the amount of resulting damage irrespective of fiber-orientation angle. So, a new trend for the behavior of composite materials is introduced which states that the relation between damage-evolution and corresponding stiffness-reduction follows a certain behavior and it is independent of fiber-orientation. Each composite material has a unique trend which is verified using three different composite materials; Boron-Epoxy-Narmco 5505, Graphite-Epoxy 4617/Modmore-II, and Carbon-Epoxy AS4/3501–6.A new damage-term is introduced as: "directional damage-variable", to simplify tracing damage in the case of a uniaxial off-axis loading. The new damage-variable was used to predict damage-evolution in the three laminas made of the indicated composite materials. It is concluded that, Graphite-Epoxy 4617/Modmore-II has the minimum damage at all stress levels and Boron-Epoxy-Narmco 5505 has the maximum damage. The importance of the new damage-term makes it easier to predict damage and make preferences between several composite materials subjected to uniaxial off-axis loading.

Laminate Tailoring of Composite Tubular Structures to Improve Crashworthiness Design at Off-Axis Loading

This paper presents experimental and numerical investigation on the parameters effecting energy absorption capability of composite tubular structures at oblique loading to improve crashworthiness performance. Various inclined angles of 5°, 10°, 20° and 30° were selected for the study of off-axis loading. The results indicate that by increasing the lateral inclination angle the mean crushing force and also energy absorption capability of all tested sections decreased. From design perspective, it is necessary to investigate the parameters effecting this phenomenon. The off-axis loading effect that causes significant reduction in energy absorption was investigated and the effected parameters were improved to increase energy absorption capability. To establish this study, 10° off-axis loading was chosen to illustrate the obtained improvement in energy absorption capability. Five cases were studied with combinations of ply-orientation and flat trimming with 45° chamfer. This method was applied to the integrated 10° off-axis loading and the final results showed significant improvement in energy absorption capability of composite absorbers. Finite element model (FEM) was developed to simulate the crushing process of axial and off-axis composite section in LS-DYNA and the results were in good agreement with the experimental data.

Modeling & Simulation of Interface Stability in Metal Matrix Composites Subjected to off-axis loading using Cohesive Zone Model under Elevated Temperature: A Review

A three-dimensional, finite element, the micro-mechanical model is used to study the damage initiation and the inelastic behavior of SiC/Ti composites subjected to a generally complicated off-axis loading using a three-dimensional representative volume element (RVE). The imperfect interface between the fiber and matrix is to be defined by using cohesive zone model. Due to low bonding strength between fiber and matrix interface, the effects of manufacturing process thermal residual stresses together with interface damage and fiber coating. In this review paper, different researchers have been cited the effect of debonding of the fiber and matrix, friction between fiber and matrix due to the presence of residual stress. The effects of stress relaxation, interface damage together with fiber coating are considered. The recrystallization of the matrix materials played a great role in refining the matrix grain size, improving the diffusion bonding of the matrix and matrix interface as well as the fiber and matrix interface.

Experimental and theoretical investigation of a unidirectional glass/epoxy composites under tensile and impact loading

Impact resistance (energy absorption) is the needful information for any engineering material which has been used for vehicles to reduce the fatal accidents. The present study focuses to investigate the behavior of unidirectional glass fiber reinforced plastic (GP) composites of different orientations [0°, 45°, [45°/-45°/45°]s, [±45°/0°/90°]s and 90°] under tensile and impact loading. The new laminate orientation ([45°/-45°/45°]s) is introduced in contrast to [±45°]s laminate for improving the energy absorption of the composites. The notched impact tests have conducted to obtain the energy absorption of a material using the Izod impact machine. The classical laminate theory [CLT] is employed for determining the theoretical tensile properties. The properties obtained from the theoretical model and experimental studies match well. The significant results obtained from this study indicate that the tensile strength and modulus are decreasing with increasing off-axis loading angle. The attempt is interpreted to elucidate the comparison of experimental studies and theoretical modelling in alliance with the fractography analysis in tensile and impact damaged specimens using the scanning electron microscopy is discussed.

Observation and modeling of loading–unloading hysteresis behavior of unidirectional composites in compression

The loading–unloading hysteresis behavior of unidirectional HTS40/PA6 carbon/polyamide laminates under off-axis compression has been examined both experimentally and constitutively in the present study. Monotonic compressive tests are first performed on unidirectional laminates to identify the basic properties of off-axis deformation. Then, five cycles of compressive loading and unloading tests are carried out with a gradually increasing peak stress for each specimen, followed by testing to failure. Significant nonlinear unloading behavior is observed after the material has been loaded into the nonlinear deformation region, and apparent plastic strain is seen after full unloading. The reloading curve also exhibits nonlinearity and conduces to a slightly open hysteresis loop with unloading. An approach is developed to predict the nonlinear hysteresis behavior of unidirectional composites by assuming an anelastic strain component in the nonlinear compressive deformation. The assumption of anelastic strain is a modification of Sun–Chen’s one-parameter plasticity model that considers the nonlinear deformation completely as plastic strain from monotonic tests. The modified model has been validated by the off-axis loading–unloading test results on unidirectional laminates. Results verify that the model accurately captures not only the plastic strain but also the complex nonlinear hysteresis behavior in the observed off-axis loading–unloading stress–strain curves.

Characterizing the off-axis dependence of failure mechanism in notched fiber metal laminates

Fiber metal laminates (FMLs) are usually more complicated in the failure aspect as compared to their constituents, especially when complex load is applied. In this paper, notched FMLs and the constituents, i.e., the aluminum and glass fiber reinforced plastic (GFRP) were subjected to off-axis tensile loading to evaluate the failure mechanism. Initial attention was paid on the off-axis dependence of mechanical responses, especially on its relation to the notch size. As expected, off-axis dependence of notched strength and notch sensitivity were closely related to the notch size, but different for GFRP laminates and FMLs due to their different damage behavior. Finite element model was employed to predict accurately the mechanical responses of FMLs, particularly for elucidating the damage mechanism. Failure of notched FMLs under off-axis loading was a combined transverse fracture and shear-off, while it was shear-dominated in notched GFRP laminates. Transverse fracture in aluminum appeared first, followed by the fiber breakage, which was postponed by the extensive subcritical damage. Thereafter, shear-failure in fiber and aluminum layers were encountered instantaneously at the descending part. Thus, the critical failure of off-axis notched FMLs was still tension-dominated as that in the on-axis case, but aluminum played the critical role.

Characterization of nonlinear response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading

The present paper addressed the nonlinear stress-strain response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading. A series of monotonic and cyclic loading-unloading tensile tests were carried out. Both irreversible strains and stiffness degradation were observed in cyclic loading-unloading tests, which indicate that the nonlinear response of composites was induced by a combination of damage and plasticity. A coupled damage-plasticity model was employed to describe the nonlinear off-axis tensile stress-strain relation of materials. In this model, a plastic potential function together with associated plastic flow rule were adopted to assess the evolution of plastic strains. The damage variables in forms of stiffness degradation were expressed as a Weibull function of the effective stress. A full suite of model parameters was experimentally determined from cyclic loading-unloading tensile tests. The stress-strain curves predicted by this model agreed well with experimental results.

Off-axis fatigue behaviour of unidirectional laminates based on a microscale fatigue damage model under different stress ratios

A fatigue damage micro-model is developed for two-phase composite materials. Constitutive law is derived at the level of fibre and matrix and extended for a damaged lamina using the reformulation of Mori-Tanaka model. A new non-dimensional effective local stress based on a failure criterion which is rewritten in term of average stress of fibre and matrix is coupled with a fatigue damage model for prediction of fatigue damage and fatigue life. The proposed model is able to distinguish between damage in fibre and matrix and also stiffness reduction of the matrix and transverse direction during fatigue loading using three different damage variables. The fatigue behaviour of unidirectional carbon/epoxy and glass/epoxy laminates are studied under off-axis loading conditions. Fatigue life of unidirectional composites is predicted at different stress levels, stress ratios and fibre orientations under tension-tension and tension-compression fatigue. The obtained numerical results from the proposed model are in good agreement with the experimental data.

Coupling coefficients of glass/epoxy laminates under off-axis tensile conditions: Experimental verification

A comprehensive experimental study on the coupling coefficients of unidirectional (UD) and woven fabric glass/epoxy laminates under off-axis tensile loading was conducted in comparison with the theoretical prediction. The capability of the off-axis test to evaluate the elastic constants in the loading direction was reported. Four coupling coefficients were obtained from tests and discussed in comparison with the theoretical prediction. A further comparison of coupling compliance coefficients in compliance matrix was made in order to generalize the influence of off-axis angle on the compliance coefficients. The theoretical prediction agreed well with the experimental data. It is shown that non-monotonic and symmetry phenomena can be observed in the curves of the coupling and compliance coefficients. The results of this experimental study provide a data base of the coupling coefficients of glass/epoxy laminates for engineering application.

Application of energy dissipation approach for notched behavior in fiber metal laminates

Characterization of the complicated failure behavior in fiber metal laminate (FML) depends on well understanding of the contributions from metal and composite layers. It seems to be very cumbersome to deal with this by conventionally collecting the stress, strain and damage patterns through experiments or numerical simulations, especially when complicated load (e.g., off-axis load) or a more hybrid degree is adopted. Since all mechanical responses in nature are governed by energy principles, in the present study an energy dissipation approach was introduced in FML. Analyses were carried out with employing the available history outputs in Abaqus, where four kinds of energy variables in terms of internal or total strain energy (Eint), elastic or recoverable strain energy (Eelast), energy dissipated by plastic deformation (Eplast) and damage (Edam) were requested for both the constituents and the laminates. Two issues were clarified by this energy approach: off-axis dependence of mechanical response and damage behavior in notched glass fiber reinforced aluminum laminate (Glare), and the reinforced effect of titanium on notched Glare (a more hybrid case). Results have shown the potentiality of energy approach in straightforwardly and effectively characterizing the failure behavior of FMLs.

Wall Pressure and External Velocity Field Relation in Overexpanded Supersonic Jets

Truncated ideal contour nozzles operating at offdesign conditions encounter offaxis loads for which the exact origin remains unclear. Although these loads are usually attributed to the nonaxisymmetric motion of the adaptation shock wave, the unsteady pressure field in the downstream separated region may also be of importance: as the distance from the nozzle’s structural attachment increases, small wall pressure fluctuations can generate undesired torque. Experiments are conducted on a truncated ideal contour nozzle operated at overexpanded conditions. The study investigates the unsteady characteristics of the pressure fluctuations in the downstream separation region and their links with the downstream developing jet flow dynamics. The analysis of the pressure fluctuations inside the nozzle reveals the existence of highly organized structures, both in time and in the azimuthal direction. It is shown that these organized fluctuations dominate the pressure signals in the separated region and that they correspond to an azimuthal mode responsible for the side-load generation. Moreover, it is shown that these specific pressure modes have a clear signature in the exiting jet flowfield. A discussion is given in the paper on the possible origins of these organized structures.

Peri-implant biomechanical responses to standard, short-wide, and double mini implants replacing missing molar supporting hybrid ceramic or full-metal crowns under axial and off-axial loading: an in vitro study

BackgroundThe aim of this study was to evaluate the biomechanical response of the peri-implant bone to standard, short-wide, and double mini implants replacing missing molar supporting either hybrid ceramic crowns (Lava Ultimate restorative) or full-metal crowns under two different loading conditions (axial and off-axial loading) using strain gauge analysis.MethodsThree single-molar implant designs, (1) single, 3.8-mm (regular) diameter implant, (2) single, 5.8-mm (wide) diameter implant, and (3) two 2.5-mm diameter (double) implants connected through a single-molar crown, were embedded in epoxy resin by the aid of a surveyor to ensure their parallelism. Each implant supported full-metal crowns made of Ni-Cr alloy and hybrid ceramic with standardized dimensions. Epoxy resin casts were prepared to receive 4 strain gauges around each implant design, on the buccal, lingual, mesial, and distal surfaces. Results were analyzed statistically.ResultsResults showed that implant design has statistically significant effect on peri-implant microstrains, where the standard implant showed the highest mean microstrain values followed by double mini implants, while the short-wide implant showed the lowest mean microstrain values. Concerning the superstructure material, implants supporting Lava Ultimate crowns had statistically significant higher mean microstrain values than those supporting full-metal crowns. Concerning the load direction, off-axial loading caused uneven distribution of load with statistically significant higher microstrain values on the site of off-axial loading (distal surface) than the axial loading.ConclusionsImplant design, superstructure material, and load direction significantly affect peri-implant microstrains.

Improvement in Offaxis Neuromuscular Control Under Slippery Conditions Following Six-Week Pivoting Leg Neuromuscular Training.

Knee injuries are usually associated with offaxis loadings in the transverse and frontal planes. Thus, improvement of lower limb offaxis neuromuscular control is important in knee injury prevention and post-injury rehabilitation. The goal of this paper was to investigate the effects of six-week pivoting offaxis intensity adjustable neuromuscular control training (POINT) using a custom-made offaxis elliptical trainer on lower limb offaxis neuromuscular control performance in trained and untrained functional tasks under slippery conditions. Twenty-six subjects participated in 18 sessions of POINT (three sessions per week for six weeks) and 25 subjects served as controls who did a regular workout. Offaxis neuromuscular control performance measures in terms of pivoting instability, sliding instability, and time-to-peak offaxis EMG entropy were evaluated on both groups under slippery conditions including a trained free pivoting task and untrained free sliding task and free pivoting and sliding task. Compared with the control group, the training group significantly decreased pivoting instability and the time-to-peak offaxis EMG entropy in lower limb muscles, indicating improvement in offaxis neuromuscular control performance. Furthermore, the training group showed reduced pivoting instability and sliding instability during the untrained free pivoting and sliding task. This paper may help us develop more focused and effective offaxis training programs to reduce knee injuries associated with offaxis loadings.