Off-axis Loading Research Articles

A dimensionless analysis of Poisson’s ratio and stress distribution for anisotropic materials

The effect of various offaxis angles and lamina material properties on the Poisson’s ratio and the stress distribution of a circular cutout in an orthotropic composite plate under off-axis loading are presented. Based on the generalized Hook’s law, the generalized plane stress condition and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12, and ν12on the Poisson’s ratio and the stress distribution along the boundary of the circular cutout under various off-axis loadings. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

Anisotropic elastic properties of common ash (Fraxinus excelsior L.)

Abstract Hardwoods in principle show a similar orthotropic behavior as softwoods; however, the ratios of the mechanical parameters between the three anatomical directions and their magnitudes are different and depend strongly on the individual microstructure of the species. The aim of the current study was to characterize the 3-D elastic behavior of common ash (Fraxinus excelsior L.) by tensile, compression, and shear tests in the three anatomical directions and stepwise in between, by means of a universal testing machine in combination with a digital image correlation technique. Young’s moduli, shear moduli, and Poisson’s ratios have been determined for the different load directions. From studies on the radial-tangential plane of other wood species, it is known that the elastic moduli in the principal directions and the off-axis elastic moduli vary in a nonlinear correlation, depending on density gradients between earlywood and latewood. This angular dependency has been experimentally and theoretically proven for ash. Furthermore, the dependency of mechanical parameters on the fiber-load angle has been experimentally determined. The measurements for principal and off-axis load directions provide a sound basis for modeling of hardwood structures.

Damage occurrence at edges of non-crimp-fabric thin-ply laminates under off-axis uniaxial loading

Thin-ply based laminates are a promising development in composite materials and are expected in the near future to outperform conventional laminates in mechanical performance. A rational design with thin plies requires understanding the effect of ply thickness on each damage mechanism. This paper presents an experimental investigation into damage occurrence in a quasi-isotropic laminate made from thin-ply, bi-axial, Non-Crimp-Fabric (NCF), under different off-axis uniaxial loadings. The NCF layers are positioned through the laminate thickness creating two regions, namely THICK and THIN (with and without ply clustering). Then, the onset and progress of three damage mechanisms (transverse matrix cracking, matrix crack induced delamination and free-edge delamination) for both regions are analyzed by monitoring the specimen’s free-edge. The results show that the critical region where damage occurs is that with ply clustering (THICK), whereas delamination originating from matrix cracks or free edge effects are delayed or even suppressed in the THIN region.

Anisotropic unilateral damage with initial orthotropy: A micromechanics-based approach

A micromechanics-based damage model able to describe the brittle response of initially anisotropic materials is presented. A special emphasis is put on the account of damage-induced anisotropy and unilateral behaviour related to microcracks closure effects. These both features clearly influence the inelastic deformation of microcracked materials and lead to even more complex consequences in the context of initial anisotropy. The aim of this work is then to derive a new strain-based formulation which allows representing the related interactions between all these phenomena. This is achieved through a recent two-dimensional energy-based micromechanical analysis that accounts for the fully anisotropic multilinear response of orthotropic materials weakened by arbitrarily oriented microcracks. On the other hand, the thermodynamics framework gives a standard procedure for the development of the damage evolution law. Throughout the paper, attention is put on the mathematical and thermodynamical consistency of the model to avoid difficulties usually associated to the simultaneous description of damage-induced anisotropy and unilateral effects. In addition to elastic constants, the model requires the identification of only two parameters related to damage evolution. The model has been implemented within the commercial finite-element code ABAQUS, and various numerical simulations are presented to illustrate its capabilities. Especially, evolution of the material symmetry and influence of opening-closure states of microcracks on the damage process are illustrated in the case of brittle matrix composites subjected to different loading cases (axis and off-axis loads, tension and compression, tension followed by compression).

Modeling Free Shock Separation Induced Side Loads in Overexpanded Rocket Nozzles

While operating in an overexpanded condition, rocket nozzles exhibit dynamic off-axis loads caused by asymmetric internal flow separation. It has been demonstrated that topologies, which only display free shock separation, produce side-load magnitudes lower than those that can transition to restricted shock separation. It is therefore suggested that geometries such as truncated ideal contour nozzles could be used on launchers with large-area-ratio designs providing improved vacuum performance. Part of the challenge of designing nozzles to operate in the overexpanded regime is characterizing and quantifying associated side loads. This paper presents the methodology and results of an analytical model that simulates side loads induced by free shock separation. The pressure distribution within a separated rocket nozzle is produced using free interaction theory, and a spring–damper analogy is used to model shock fluctuations in response to external pressure disturbances. Good agreement has been found between simulated side loads and experimentally measured forces on four conical and one truncated ideal contour nozzle.

Prophylactic vertebroplasty can decrease the fracture risk of adjacent vertebrae: An in vitro cadaveric study

Adjacent level vertebral fractures are common in patients with osteoporotic wedge fractures, but can theoretically be prevented with prophylactic vertebroplasty. Previous tests on prophylactic vertebroplasties have been performed under axial loading, while in vivo changes in spinal alignment likely cause off-axis loads. In this study we determined whether prophylactic vertebroplasty can also reduce the fracture risk under off-axis loads.In a previous study, we tested vertebral bodies that were loaded axially or 20° off-axis representing vertebrae in an unfractured spine or vertebrae adjacent to a wedge fracture, respectively. In the current study, vertebral failure load and stiffness of our previously tested vertebral bodies were compared to those of a new group of vertebral bodies that were filled with bone cement and then loaded 20° off-axis. These vertebral bodies represented adjacent-level vertebrae with prophylactic bone cement filling.Prophylactic augmentation resulted in failure loads that were comparable to those of the 0° group, and 32% greater than the failure loads of the 20° group. The stiffness of the prophylacticly augmented vertebrae was 21% lower than that of the 0° group, but 27% higher than that of the 20° group. We conclude that prophylactic augmentation can decrease the fracture risk in a malaligned, osteoporotic vertebra. Whether this is enough to actually prevent additional vertebral fractures in vivo remains subject of further study.

The effects of off-axial loading on periimplant marginal bone loss in a single implant

A discrepancy between crown width and implant width may contribute to potential bending overload. The purpose of this study was to evaluate the influence of the crown width-fixture width ratio on crestal bone loss around single dental implants placed in the first molar area. Seventy-six participants (37 men and 39 women; age range, 25-83 years; mean age [standard deviation], 56.3 ±10.6 years) were selected from individuals who were treated with single tooth implants between May 2004 and December 2009 at the Department of Periodontology, Gangnam Severance Dental Hospital. The marginal bone-level change and gingival parameters (modified plaque index and modified sulcus bleeding index) of the periimplant soft tissue were assessed 1 year after functional loading. The perpendicular distances from the vertical axis of each fixture to the most distal aspect of the crown and most mesial aspect of the crown were measured in the periapical radiographic view. No statistically significant relationship was found between crown width-fixture width ratio and the 1-year bone-level change (Pearson correlation, P=.06; Spearman rank test, P=.14). No statistically significant differences in marginal bone-level change were found between axial and nonaxial loading implants (2 independent samples t test; P=.19). The bone-level change for the surface adjacent and distant to the cantilever was not statistically significant (paired t test; P=.10). From this study, it may be concluded that off-axial loading that results from a high crown width-fixture width ratio does not increase the risk for periimplant marginal bone loss after 1-year functional loading.

Off-axis tensile properties of multistitched plain woven E-glass/polyester composites

The aim of this study was to understand the ±45 ° directional off-axis tensile properties of the developed two dimensional (2D) multistitched multilayer E-glass/polyester woven composites. It was found that the off-axis tensile strength of the unstitched structure was slightly higher than those of the multistitched structures. The reason was that the multistitching process caused the filament breakages. It was also found that when the stitching direction and stitching density in structures increased, their off-axis tensile modulus decreased. Therefore, stitching directions, stitching density and stitching yarn on the composite structures were considered as important parameters. All structures under the off-axis tensile load had normal deformation, or angular deformation or shrinkage in width. In addition, both the normal deformation and the shrinkages in width occurred in most of the two and four directional stitched structures. On the other hand, four directional Kevlar® 129 yarn dense stitched E-glass/polyester structure showed only shrinkage in width after angular deformation. This could be considered as a new failure mode because of the multistitching. These results indicated that the stitching directions and density generally influenced the off-axis tensile properties of the multistitched E-glass/polyester woven composites.

Experimental off-axis tensile characterization of multistitched woven nano composites

The aim of this study was to understand the off-axis tensile properties of the developed two dimensional multistitched multilayer E-glass/polyester woven nano composites. It was found that the specific off-axis tensile strength of unstitched structure was higher than that of the machine stitched structure due to stitching caused filament breakages. But it was slightly lower than that of the machine stitched/nano structure. In addition, the specific off-axis tensile strength of machine stitched/nano composite structure was slightly higher than that of the machine stitched structure. When the nano silica material in the unstitched E-glass/polyester composite structure increased, the off-axis specific tensile strength and the modulus of the unstitched/nano structures increased whereas, the off-axis specific tensile strain of the unstitched/nano structures decreased. The damaged areas of the unstitched/nano structures increased, when the nano silica material in the unstitched E-glass/polyester woven composite structures increased. The failures under the off-axis tensile load of the stitched or stitched/nano structures were confined at narrow area due to the multistitching. On the other hand, it was observed that the off-axis failure of unstitched/nano or stitched/nano woven E-glass/polyester composite structures showed more brittle behavior.

Mechanical characterization and modeling of poly (β-hydroxybutyrate)-co-poly(β-hydroxyvalerate)-Alfa fiber-reinforced composites

The mechanical properties of biobased composites of poly(β-hydroxybutyrate)-co-poly(β-hydroxyvalerate) biopolymer continuously reinforced with unidirectional Alfa fibers are investigated via tensile testing of oriented composite laminates. Simple mechanical models for the elastic stiffness, strength, and nonlinear hardening of the biobased composites are proposed with an emphasis on techniques that only require the independent properties of the fiber and matrix to facilitate composite design. Rule of mixtures (ROM) approaches are found to effectively predict the elastic properties of the composites but generally overestimate strength. Modified ROM approaches that discount the contribution of the matrix in the fiber loading direction and the contribution of the fiber in the transverse loading direction provide the most accurate strength predictions. Apparent elastic properties for composites with varying fiber orientations are predicted using a modified orthotropic laminate plate method which was found to overestimate composite stiffness in off-axis loading directions. Postyield nonlinear hardening is modeled using a calibrated continuum yield and plasticity model and demonstrated to provide a close match of the experimental results. POLYM. COMPOS., 35:1758–1766, 2014. © 2014 Society of Plastics Engineers

Structural performance of a hybrid FRP-aluminum modular triangular Truss system subjected to various loading conditions.

A novel hybrid FRP-aluminum truss system has been employed in a two-rut modular bridge superstructure composed of twin inverted triangular trusses. The actual flexural behavior of a one-rut truss has been previously investigated under the on-axis loading test; however, the structural performance of the one-rut truss subjected to an off-axis load is still not fully understood. In this paper, a geometrical linear finite element model is introduced and validated by the on-axis loading test; the structural performance of the one-rut truss subjected to off-axis load was numerically obtained; the dissimilarities of the structural performance between the two different loading cases are investigated in detail. The results indicated that (1) the structural behavior of the off-axis load differs from that of the on-axis load, and the off-axis load is the critical loading condition controlling the structural performance of the triangular truss; (2) under the off-axis load, the FRP trussed members and connectors bear certain out-of-plane bending moments and are subjected to a complicated stress state; and (3) the stress state of these members does not match that of the initial design, and optimization for the redesign of these members is needed, especially for the pretightened teeth connectors.

A Dimensionless Analysis of Young's Modulus and Stress Distribution for Orthotropic Materials

The effect of various offaxis angles and lamina material properties on the axial and transverse modulus of the orthotropic lamina under off-axis loading is studied. Also, the stress distribution of the orthotropic composite plate containing a circular cutout with normal pressure distributed uniformly along the opening edge is investigated. Through the generalized Hooke’s law and plane stress condition, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the axial and transverse modulus of the orthotropic lamina under various off-axis loadings. Moreover, based on the generalized Hooke’s law, the generalized plane stress and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the stress distribution along the boundary of the circular cutout of the orthotropic plate with normal pressure distributed uniformly along the opening edge. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

平織積層板のマクロ/メゾ/ミクロ非弾性解析手法の開発と実験的評価

In this study, macro/meso/micro inelastic analysis method for plain-woven laminates is developed based on a homogenization theory for nonlinear time-dependent composites. For this, a three-scale modeling of plain-woven laminates is performed by considering a plain-woven laminate as a macrostructure, fiber bundles (yarns) and a matrix in the laminate as a mesostructure, and fibers and a matrix in the yarns as a microstructure. Then, a macroscopic constitutive equation of the laminate is derived by dually applying the homogenization theory for nonlinear time-dependent composites to not only the meso/micro scale but also the macro/meso scale. Using the present analysis method, the elastic-viscoplastic analysis of a plain-woven glass fiber/epoxy laminate subjected to on and off-axis loading is performed. Moreover, the analysis results are compared with the experimental data. It is shown that the present analysis method successfully takes into account the effects of inelastic properties of the epoxy not only around the fiber bundles but also inside of the fiber bundles. It is also shown that the results of analysis are in good agreement with experimental data.

A Three-Dimensional Finite Element Analysis of Short Dental Implants in the Posterior Maxilla

This study evaluated the biomechanical behavior of short dental implants with different heights of residual bone and compared it with that of standard dental implants in 13 mm or less of residual bone by means of finite element analysis. It was assumed that the maxillary first and second molars had been replaced with splinted cast gold crowns supported by two implants. A total of five posterior edentulous maxilla models were fabricated with various residual bone heights (13 mm, 7 mm, 6 mm, 5 mm, and 4 mm). Residual bone height was 13 mm in the group 1 model (control) and 7, 6, 5, and 4 mm in group 2-1, group 2-2, group 2-3, and group 2-4 models, respectively. In the group 1 model, two identical implants (4.5 × 11 mm) and abutments (6 × 2.5 mm) were placed. In the group 2 models, two identical wide/short implants (6 × 5.7 mm) and abutments (6 × 5 mm) were placed. Off-axis (30 degrees) loading of 187 N was applied to the central fossae of the two implant-supported crowns. Maximum von Mises stresses in crestal cortical bone were lower in group 2 models than in the group 1 model. This numeric simulation confirmed that, without maxillary sinus bone graft, more effective stress distribution could be obtained in 4, 5, 6, or 7 mm of residual bone with short dental implants than in 13 mm of residual bone with standard dental implants.

Off-Axis Crushes Simulation of Thin-walled Tapered Tubes Inserted with Foam-filled Structures

In this study deal with numerical analysis of the impact dynamic effects of crush performance of the tapered cross-section tubes, containing straight, single taper, double taper, taper triple and fourth tapered lightweight polyurethane foam filled alloy steel thin-walled tube. Foam-filled thin-walled tubes have been examined numerically. Off-axis angle load dynamic effects in front of crash were examined at an angle of 0, 5, 10, 15 and 20 degrees. Numerical analysis has been verified by experimental studies in place to validate the data. The results show that the energy absorption capacity has been significantly affected tube with various oblique angle, impact velocity and wall thickness. It was found that the foam filling in a thin-walled tubes increase the amount of energy absorbed compared with empty tubes.

Strain Rate Dependent Deformation of a Polymer Matrix Composite with Different Microstructures Subjected to Off-Axis Loading

This paper aims to investigate the comprehensive influence of three microstructure parameters (fiber cross-section shape, fiber volume fraction, and fiber off-axis orientation) and strain rate on the macroscopic property of a polymer matrix composite. During the analysis, AS4 fibers are considered as elastic solids, while the surrounding PEEK resin matrix exhibiting rate sensitivities are described using the modified Ramaswamy-Stouffer viscoplastic state variable model. The micromechanical method based on generalized model of cells has been used to analyze the representative volume element of composites. An acceptable agreement is observed between the model predictions and experimental results found in the literature. The research results show that the stress-strain curves are sensitive to the strain rate and the microstructure parameters play an important role in the behavior of polymer matrix.

806 クロスプライCFRP積層板のプライベース疲労寿命予測法の開発(OS8-(2),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

A ply-by-ply basis fatigue life prediction method for multi-directional composite laminates that can be applied to fatigue loading at any stress ratio has been developed, taking into account the inelastic deformation and in-situ strength of plies embedded in the laminates. Fatigue failure in embedded plies is evaluated using a quasi-static failure criterion based on the residual principal strengths. The residual principal strengths of unidirectional plies are predicted using the anisomorphic constant fatigue life diagrams that are identified for loading in the principal directions, respectively. The fatigue failure criterion for plies takes into account not only the in-situ principal strengths of plies embedded in a general laminate, but also the progressive reduction in in-situ constraint effect due to the growth of fatigue damage. The actual stress components in the plies embedded in a laminate are evaluated using a laminate constitutive model based on the classical lamination theory, in which the nonlinear plastic deformation of inclined plies under in-plane off-axis loading is taken into account. It is demonstrated that the proposed ply-by-ply basis fatigue model can successfully be used for prediction of on-axis and off-axis fatigue lives of cross-ply CFRP laminates that are subjected to fatigue loading at different stress ratios, respectively.

Crush Force Efficiency of Composite Square Profile under Off-Axis Loading

The present paper determines the effect of crush force efficiency on laminate glass wrapped on aluminum cross-section square tubes under quasi-static loading. The analysis was examined via experimentally. The wall-thicknesses aluminum square of 1.6 mm was investigated on wrapped woven composite type of E-glass fiber reinforced polyester resin. Two different numbers of layers woven E-glass were investigated and examined. Result obtained from experimental analysis such that initial peak load, mean load, versus displacement curves were compared for each specimen. Results showed that the tubes energy absorption was affected significantly by different number of layers wrapped on wall aluminum square profile and also that the effect of crushing behaviors and failure modes was discussed.

Gender differences in offaxis neuromuscular control during stepping under a slippery condition

Females are at greater risks of musculoskeletal injuries than are males, which may be related to decreased neuromuscular control in axial and/or frontal planes, offaxis neuromuscular control. The objective of this study was to investigate gender differences in offaxis neuromuscular control during stepping under a slippery condition. Forty-three healthy subjects (21 males and 22 females) performed different stepping tasks under a slippery condition, namely, free pivoting task (FPT) to control axial plane pivoting, free sliding task (FST) to control frontal plane sliding, and free pivoting and sliding task (FPST) to control axial pivoting, and frontal sliding on a custom-made offaxis elliptical trainer. Compared to males, females showed significantly higher pivoting instability, higher max internal and external pivoting angles, higher mean max medial and lateral sliding distance, and higher entropy of time to peak EMG in the medial and lateral gastrocnemius muscles during the FPST and higher entropy of time to peak EMG in the lateral gastrocnemius muscle during the FPT and FST. The findings may help us understand potential injury risk factors associated with gender differences, and provide a basis for developing targeted neuromuscular training to improve offaxis neuromuscular control, and reduce musculoskeletal injuries associated with excessive offaxis loadings.

Multi-scale finite element analysis of 2.5D woven fabric composites under on-axis and off-axis tension

The stress–strain behaviors and progressive damage processes of 2.5D woven fabric composites under uniaxial tension are analyzed using a two-step, multi-scale progressive damage analysis method. The collision algorithm is used to construct the representative volume cell (RVC) of the yarn, with random fiber arrangement. Based on the RVCs of the yarn and the composite, the failure behaviors in the monofilament scale and the tow scale are investigated, respectively. The simulated stress–strain curves of the 2.5D woven fabric composites under on-axis uniaxial tension both in the weft and warp directions show good agreements with the experimental results. Furthermore, the relationship between the decrease of tensile strength and the deflection of the loading direction is obtained. The characteristic failure modes at different off-axis loading angles are analyzed, subsequently.