Off-axis Loading Research Articles

Large strain zero Poisson’s ratio spring cell metamaterial with critical defect analysis and variable stiffness distributions

This paper presents novel metamaterial skins formed by 3D Spring Cells exhibiting zero Poisson’s ratio in two directions with no stress concentration on joints. Precise CAD models are generated to perform numerical and experiment analysis. High-fidelity Finite element models are developed to assess the homogenisation study of zero Poisson’s ratio. Moreover, the analytical method is also used to present for normalised Young’s modulus. Parametric study for the effect of parameter on normalised Young’s modulus and Poisson’s ratio is demonstrated based on analytical method. Pure shear analysis is demonstrated to show the off-axis loading behaviour. Structural defect analysis is investigated with regarding to its deformation mechanism under tensile strain. Furthermore, variable stiffness distribution of Spring Cell metamaterials is demonstrated while maintaining large strain zero Poisson’s ratio. The frequency and buckling analysis of metamaterials formed by spring cells are investigated and compared with equivalent shell. Moreover, their mechanical behaviours including buckling and frequency are investigated. Experiment analysis is performed to validate the force–displacement, Poisson’s ratio and deformation mechanisms discussed in numerical simulations. Finally, construction material analysis is taking to investigate the relations between metamaterial Poisson’s ratio and Young’s modulus and variety types of construction material.

Thin-ply thermoplastic composites: From weak to robust transverse performance through microstructural and morphological tuning

Thin-shell carbon fiber composites have great potential for structures that require large recoverable deformations, high stiffness and low weight, as in deployable space structures, biomedical devices and robotics. Despite being astonishingly flexible in fiber direction, such thin shells are highly sensitive to off-axis loading. This relates to the high manufacturing complexity and sensitivity to imperfections, revealing the need for in-depth understanding and enhancement of their transverse response. This paper provides crucial insights into influencing factors of thin-shell composites’ transverse strength using a highly controllable manufacturing technique to create novel thermoplastic thin-ply (35μm) carbon fiber-PEEK laminas. The effects of fiber type, microstructure and polymer morphology as well as their interactions, are addressed towards a drastic increase in performance. A combination of microstructure tuning and isothermal crystallization can provide thin-shell composites with a more than 150% improved transverse performance compared to the state-of-the-art. The conducted analysis reveals the sensitivity to all related processing conditions and highlights the effect of their accurate control.

In search of the quasi-isotropic laminate with optimal delamination resistance under off-axis loads

Delamination is one of the most feared failure modes in laminated composites and yet there is a lack of well established procedures to find the ply configuration with the highest delamination resistance for a given geometry of the component and a set of elastic and strength constraints. This paper presents a methodology for determining the quasi-isotropic ply sequence more resistant to delamination under off-axis uniaxial tension. Delamination is considered to be triggered by interlaminar stresses at free-edges or by matrix cracks. Two different ply thicknesses (standard and thin) and two sets of ply orientations (multiples of π/4 or π/8) are considered. The results show that the use of thin plies enlarges the design domain by up to 70% and generates a practically isotropic safe space. The methodology presented is also suitable for optimizing the delamination resistance of other load cases with stress singularities.

Numerical investigation on the mechanical behaviors of 2D woven composites under complex in-plane stress states

Using finite element method (FEM), the mechanical behaviors of 2D woven composites with different weave structures are investigated with considering the complex in-plane stress states. Periodic boundary conditions for arbitrary off-axis loading scenarios are established, and a progressive damage model based on Linde criterion is proposed, which is subsequently validated by the previous experiments. In addition, the failure envelopes predicted by classical failure criteria are compared to the results obtained by FEM. The effects of woven structures on elastic properties and failure behavior are also discussed, which demonstrates that the plain woven composites have inferior mechanical performance than twill and satin woven composites. Based on the assessment of the failure criteria, this study provides recommendations for selecting relevant failure criteria to anticipate mechanical properties under various loading conditions. The findings in this paper are expected to encourage the development of damage constitutive models and their engineering applications for 2D woven composites.

Life assessment of thermomechanical fatigue in a woven SiC/SiC ceramic matrix composite with an environmental barrier coating at elevated temperature

In this work, the tension–tension fatigue behavior of a woven SiC/SiC ceramic matrix composite with an environmental barrier coating is investigated under elevated temperatures up to 1300 °C. Experimental investigations reveal the fatigue failure mechanism for SiC/SiC CMCs with EBCs under on-axis and off-axis loading conditions, and the materials undergo cyclic softening throughout the loading history. A mechanism-based framework is proposed to interpret the fatigue behavior of CMCs through detailed fatigue experiment observations. Based on the decrease in the elastic modulus of the composites, a new fatigue damage model is developed to characterize the fatigue damage evolution and assess the fatigue life of woven SiC/SiC CMCs with EBCs. The good agreement between the proposed model and experimental data indicates that the damage model has the potential to describe complex thermomechanical damage of SiC/SiC CMCs with EBCs under thermomechanical loading.

The Off-Axis Embedment Performance of Bamboo Panels Used for Glubam Structures

The off-axis embedment behaviors of unidirectional and multidirectional laminated engineered bamboo panels used for glued-laminated bamboo (glubam) structures under dowel-type bolts with three different diameters, 12, 14, and 16 mm, were experimentally studied in this research. The half-hole loading method given by current standards was adopted to perform the embedment tests. Seven different off-axis loading directions from 0° to 90° related to the main bamboo fiber direction at an interval of 15° in the panel plane were considered. The different failure patterns, stress-displacement curves, and the corresponding full-field surface strain measured through the digital image correlation (DIC) method are reported. The loading angles significantly influenced the embedment performance of unidirectional bamboo panel specimens, and the strength values decreased with the increasing off-axis loading angles. A difference of 35% in the strength values between 0° and 90° loading specimens was observed. However, quasi-isotropic embedment properties were noticed for the multidirectional laminated engineered bamboo panels. The capacity functions were provided to predict the mean off-axis embedment strength and characteristic strength values by inputting the characteristic density values into the functions. Compared with the characteristic strength values estimated through the statistical method, with a 95% probability of exceedance and 75% significant level, the conventional capacity-function method underestimated the off-axis embedment strength values, and thus may leading to an overconservative design. The statistical characteristic embedment strength values are suggested to be used to calibrate the safety factor of capacity equations given by wood standards. Results from this research can be used to predict the ultimate strength of glubam joints under complex loading conditions and obtain reliable design values for engineering applications.

Effects of bone type and occlusal loading pattern on bone remodeling in implant-supported single crown: A finite element study.

To assess the influence of bone types and loading patterns on the remodeling process over 12 months according to the variations in stress, strain, strain energy density (SED), and density allocation in the bone of implant-supported single crown. A three-dimensional finite element of a single crown implant was modeled in five different bone types (D1-D4, and grafted bone). A 200N load was applied on an implant crown with three occlusal loading patterns (nonfunctional contact, functional contact at center, and at 2-mm offset loading). During the first 12 months after implant placement, the SED was employed as a mechanical stimulus to simulate cortical and cancellous bone remodeling. Functional contact at 2-mm offset loading led to a higher bone remodeling rate and stress compared to functional contact at center and nonfunctional contact. Under 2-mm offset loading, the greatest remodeling rate after 12 months was achieved with D3 and D4, D2, grafted, and D1 cortical bone with an average peri-implant density of 1.95, 1.77, 1.56, and 1.50g/cm3 , respectively. Meanwhile, the highest von Mises stresses were found in D4 (22.2MPa) and D3 (21.9MPa) bones. A greater stress concentration and remodeling rate were found when an off-axial load was applied on an implant placed in low bone density. Although the fastest remodeling processes resulting in increased bone density and strength were found in D3 and D4 bone types with greater off-axial loading that may provide greater bone engagement, it could increase stress concentrations that are susceptible to inducing implant failure.

Modeling fracture of multidirectional thin-ply laminates using an anisotropic phase field formulation at the macro-scale

An equivalent single layer approach to model fracture events of multidirectional balanced thin-ply laminates via the use of the Phase Field method is explored. The inherent anisotropic nature of a multidirectional laminate is taken into account through the use of a structural tensor, defined from scaled directional vectors, which can account for the variation in fracture toughness of the laminates in varying directions. The scaling constants are defined using the lay-up of the laminate and the intra-laminar fracture toughness of the lamina, minimizing the number of input parameters required while also alleviating the structural tensor of a pure numerical and geometric meaning. They have a significant effect in the solution, and are here related to materials properties, not only providing a new perspective on their definition but also allowing the reduction of the number of numerical parameters used to calibrate the anisotropic PF model. The numerical implementation of the proposed formulation is performed using a simple and robust thermal analogy in Abaqus by exploiting the use of an anisotropic conductivity matrix that plays the role of the structural tensor in the anisotropic phase field formulation, which reduces the complexity of the simulations. Experimental results, based on open-hole tension and double edge-notched tension, are reproduced via simulation validating the model for size effects and for the response to off-axis loading. Successful prediction of notch size effects in multidirectional composite laminates is achieved by means of an equivalent single layer approach, incl. the off-axis open-hole tension strengths of a directional thin-ply laminate. All numerical strength predictions were well within acceptable errors of the respective experimental values.

Experimental and numerical investigation on the failure behavior of Bouligand laminates under off-axis open-hole tensile loading

The Bouligand structure is a fibrous laminate with uniaxial layers assembled periodically into a helicoidal pattern. Compared to other types of laminates, its resistance to in-plane damage still lacks clarification. The failure behavior of Bouligand laminates under off-axis open-hole tensile (OHT) loading was investigated compared to cross-ply and quasi-isotropic structures using experiment and numerical simulation. After verifying the progressive damage model based on Hashin criteria, the numerical predictions from various off-axis loadings were compared between these three structures. The results show that Bouligand laminates exhibit low but nearly stable OHT strength. In comparison, the cross-ply structure exhibits high OHT strength variation when loaded in different directions. With the change of off-axis angle, the OHT strength of the Bouligand structure changes by 10.1 % from 405.2 MPa to 364.1 MPa, while it changes by 69.1 % from 533.8 MPa to 165.1 MPa for the cross-ply structure. Besides, the Bouligand structure exhibits higher OHT strength when the off-axis angle exceeds 5°. It also exhibits a more stable OHT strength than the quasi-isotropic structure. It is shown that the failure of fiber and matrix is the primary factor affecting the OHT strength of the laminate, while the delamination has little effect on the OHT strength.

Off-Axis Tension Behaviour of Unidirectional PEEK/AS4 Thermoplastic Composites

An experimental method for non-standard off-axis tension tests of unidirectional composites is developed. A new oblique end-tab is designed to eliminate stress concentration and in-plane bending moment induced by off-axis tension loading. Finite element analysis and experiments on Polyetheretherketone (PEEK)/AS4 unidirectional thermoplastic composites (CFRTP) were conducted to evaluate the effectiveness of the proposed testing method. Simulation and test results demonstrate that the use of oblique end-tabs eradicates stress concentration and bending movements. The digital image correlation (DIC) method was used to help investigate the full-field tension/shear coupling deformation response of the off-axis specimen. Test results show significant nonlinear behaviour and inhomogeneous strain distribution under tension/shear combined stresses. A fractographic study was carried out to study the damage mechanisms under a tension/shear combined stress state. Specimens with 30°, 45° and 60° off-axis angles, fail in tension/shear mixed failure mode. Fracture surface morphology indicates that matrix plastic deformation and ductile drawing under tension/shear coupled stress state induced the nonlinear stress-strain response.

Development of a Fully Compliant Bistable Mechanism Based on Circular Beams with Enhanced Pitch Stiffness

Compliant bistable mechanisms with planar configurations demonstrate two in-plane stable states through the nonlinear deformations of in-plane flexible segments, which are widely used in the field of shock sensors and threshold sensors. In these mechanisms, consistent dynamic and static bistable behaviors are difficult to maintain under the influence of an out-of-plane load. This is limited in some applications where precise displacement is required. To this end, we developed a bistable mechanism with circular beams instead of conventional straight beams, such that enhanced robustness against external loads in the out-of-plane region is obtained. An analytical kinetostatic model is established to predict the bistable behavior of the proposed mechanism, which is further verified using finite element simulations and experimental results. Compared with the prototype of the straight-beam-based bistable mechanism, the developed circular-beam bistable mechanism demonstrates improved pitch stiffness along the out-of-plane rotation and robustness against off-axis load conditions. The proposed bistable mechanism design can be extended to applications of sensors subjected to out-of-plane loads.

Open hole tensile behavior of plain woven carbon/glass hybrid composites

Hybrid composites are increasingly attractive for advanced engineering applications. In this study, the open-hole tensile (OHT) properties and failure mechanism of plain woven carbon fiber, glass fiber, and carbon/glass hybrid fiber composites under on-axis (0°) and off-axis (45°) loads were investigated through experimental and numerical approaches. The progressive damage was characterized by high-speed infrared thermography. The numerical simulation presented a good explanation on the damage development. It indicates that the carbon/glass hybrid composites exhibited significant improvement in failure strain and toughness compared to pure carbon fiber composite. With the insertion of glass fiber layers, the failure modes of hybrid structures were modified and quick propagation of cracks was prevented. Once the cracking on their carbon layers had initiated there was an increase in damage to glass fiber layers showing the transfer of stress from carbon layers to glass layers. Similar mechanical properties were reached among sandwich-like hybrid samples in on-axis tension, but much greater properties can be achieved when the carbon fiber at the interior layers of the hybrid specimens under off-axis load. Since glass fiber with great ductility was laminated as the surface layers in hybridization, resulting in less delamination and higher ultimate strength in 45○ off-axis tension.

Compressive failure and kink-band formation modeling

To increase the use of polymeric structural composites, a major issue is to properly account for intra-laminar failure mechanisms, such as fiber kinking induced under compression. We propose a new continuum damage model that can predict the fiber kinking response at the ply level. The model is based on a previous structure tensor-based model for the response of UD-plies. A novel feature is that the compressive UD-ply response at the macroscale includes the effect of the fiber misalignment shaped as a kink-band that is resolved at the sub-scale. Concepts of computational homogenization are used to include the fiber-shear of the kink-band at the sub-scale. The model calibration is adapted to account for either kink-band formation or shear-splitting depending on the off-axis loading. Finally, the model is validated at the laminate level against experimental data for OHC-tests available in the literature. A good agreement is found for predicted strength values and observed fracture patterns of the laminates. The size effect experienced when different hole sizes are tested is also addressed.

Multiscale modelling of material degradation and failure in plain woven composites: A novel approach for reliable predictions enabled by meta-models

In this paper a multiscale method for modelling damage evolution at meso and macro scales with application to plain woven composites is presented for the first time. The method couples the macro and micro-scale simulations using an averaging theorem in which the computations in the two scales are performed simultaneously. Unlike the local–global approach, the developed multiscale analysis is carried out over the entire macro domain rather than a predefined segment. To address the computational challenges in multiscale damage analysis, the proposed method a) employs a non-local approach in constructing the macro–micro interface to avoid the pathological localisation effect introduced by microdamage at the macro continuum; b) reduces the considerable computing effort incurred by the non-linear behaviours in multiscale damage analysis by the introduction of machine learning meta-models. Experimental tensile tests conducted are shown to be in good agreement with the proposed method for both on-axis and off-axis load directions. The biaxial loading cases are also investigated with the results illustrated by the failure envelopes and compared with the existing damage criteria. Finally, an example of open-hole tension test is presented to demonstrate an application of the proposed method to model progressive damage and crack propagation in composite plates.

Characterisation of mechanical behaviour of fibre reinforced thermoplastic composites subjected to off-axis compressive loading

This paper presents an experimental and numerical investigation on the mechanisms of damage onset and evolution in unidirectional carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting and end collapsing of specimens during test. A series of compression tests were conducted with specimens of various off-axis angles. Different failure mechanisms and nonlinear stress-strain responses were observed and studied. The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented using finite element analysis and compared to experimental results. It is shown that the LaRC05 criterion can provide accurate predictions for matrix cracking failure mode of unidirectional thermoplastic composites controlled by compression-shear combined stresses.

A micromechanics based model for rate dependent compression loaded unidirectional composites

Strain-rate effects in a unidirectional non-crimp fabric carbon/epoxy composite are addressed. To allow for kink-band formation including strain-rate effects and damage in such composites, the paper advances a recent model focused on compression loading at small off-axis angles. The model is based on computational homogenization with a subscale represented by matrix and fibre constituents at finite deformation. The fibre constituent is assumed to be elastic transversely isotropic and the matrix is viscoelastic–viscoplastic with damage degradation. Novel model improvements of special importance to small off-axis loading relate to the isostress formulation of the homogenized response in transverse shear. In this context, an enhanced homogenized elastic response is proposed based on Halpin–Tsai corrections to account for the nonuniform stress distribution on the microscale. The model captures the strongly rate sensitive kink-band formation due to localized matrix shearing and fibre rotation, confirming the experimentally observed increase in compressive strength for high strain rates.

Numerical study on off-axis tensile behavior of 3D braided composites at elevated temperature

3D braided composites consolidated by heat-resistant resin are expected to become essential structural material of new generation aerospace vehicles. In this work, the thermo-mechanical behavior of 3D braided composites subjected to general off-axis tensile loadings at room and elevated temperatures is evaluated based on the meso-scale finite element (FE) model. A user-material subroutine UMAT is adopted to implement the thermal stress analysis, temperature-dependent failure initiation criteria and material properties degradation scheme of both fiber yarns and matrix. The meso-scale damage evolutions under thermal-mechanical coupling loads are simulated based on ABAQUS/Standard and the corresponding detailed failure mechanisms are revealed. The off-axial elastic moduli and strengths of 3D braided composites under elevated temperatures are also predicted. The numerical results indicate that high temperature affects the material properties mainly by weakening the matrix properties while off-axis loading affects the damage mechanisms by changing the load distribution of fiber yarn in each direction. The present work provides routine support for the numerical study of structural properties and damage behavior of other textile composites in service temperature environment.

Microscale modeling of rate-dependent failure in thermoplastic composites under off-axis loading

In this paper we develop a finite deformation micromechanical framework for modeling rate-dependent failure in unidirectional composites under off-axis loading. The model performance is compared with original experiments on thermoplastic carbon/PEEK composites tested at different strain-rates and off-axis angles. To achieve quantitative agreement with the experiments, a microcrack initiation criterion based on the local stress and the local rate of deformation state in the polymer matrix is proposed. Microcracking is represented by a cohesive zone model, with special attention to the inclusion of geometric nonlinearity in the formulation. In this regard, the cohesive geometric nonlinearity is based on extension of an existing formulation to three-dimensional space. Beside microcracking, the Representative Volume Element (RVE) also accounts for viscoplasticity in the polymer matrix. A recently introduced dedicated arclength control method is utilized to impose a strain-rate on the micromodel. Accordingly, kinematic relations governing the RVE deformation allow for the change in orientation of the micromodel in the loading process. This change in orientation of the microstructure has an important implication on the apparent material strength.

The Biomechanical Profile of an Osseo-Integrated Rectangular Block Implant: A Pilot In Vivo Strain Analysis

Aim: To load-test the osseo-integrated rectangular block implant (RBI), measure the generated cortical peri-implant strains, and relate these findings to known human physiological parameters. Materials and methods: Two RBIs were placed into the posterior mandibular saddle in a mature greyhound dog and allowed to osseo-integrate. The half mandible (implants in situ) was mounted in a servohydraulic system. Four triple-stacked rosette gauges were placed cortically (mesial, distal, buccal, and lingual). A modified ISO-14801 protocol was used (1000 N, 300, 2 Hz, 1 h) and the generated principal strains (ep, eq) and their angular orientations (F), were calculated. Results: (1) Bucco-lingual “horizontal” dimension: dominant “horizontal” compressive stresses were on the lingual aspect and “horizontal” tensile stresses on the buccal aspect. The buccal cortex was elastically tensile-stretched, while the lingual cortex was elastically compressed. (2) Bucco-lingual “vertical” dimension: dominant vertical torsional stresses were oriented buccally and apically, with an overall buccally inclined torsional effect. This was also evidenced on the lingual aspect, where there remained high torsional rotation elements (high F and e2). (3) Mesio-distal “horizontal” dimension: dominant torsional stresses oriented as a distal-lingual “counter-clockwise” rotation. Conclusions: The applied off-axial loads generated a heterogeneous pattern of bucco-lingual and mesio-distal cortical strains, both vertically and horizontally. The short dimensioned osseo-integrated RBI design appeared to biomechanically withstand the applied loads and to maintain the strains generated to levels that were within physiological limits. More studies and statistical analyses are needed to confirm these findings.

Off-Axis Compressive Behaviour of Fibre Reinforced Thermoplastic Composites.

This paper presents an experimental investigation on the mechanisms of damage onset and evolution in unidirectional PEEK/AS4 carbon fibre reinforced thermoplastic (CFRTP) composites subjected to off-axis compressive loadings. A test fixture was designed to prevent buckling, splitting, and end collapsing of the specimens during the test. A series of compression tests were conducted with specimens of various off-axis angles. The displacement and strain fields of all specimens during the tests were evaluated by the digital image correlation (DIC) method. In combination with the DIC results, the influence of the off-axis angles on the failure mechanisms and nonlinear stress–strain responses were analysed. The corresponding failure mechanisms were examined by scanning electron microscopy (SEM). The fracture angles of the tested specimens were evaluated and analysed according to Puck’s theory. The off-axis compression failure envelope based on LaRC05 and Hashin criteria was presented and compared to the experimental results. It was shown that the LaRC05 criterion can provide accurate predictions when the off-axis angle is larger than 15°. The complex failure mechanisms were analysed to better understand the effect of ductility of the thermoplastic matrix to the composites. The series of tests provide an experimental failure envelope in combined stress states and can be used for the evaluation of failure theories and the criteria of thermoplastic composites.