In-plane Material Properties Research Articles

Characterization and modelling of the microstructural and mechanical properties of additively manufactured continuous fiber polymer composites

The additive manufacturing of continuous fiber reinforced polymer composites is a technology showing great potential for the production of end-use functional and structural components. The reasons for its still limited use are primarily related to an insufficient knowledge of the mechanical behavior of these composites, especially when considering the features that distinguish the printed components from conventional composite parts. Among these peculiar features, their bead-based architecture has been experimentally and analytically investigated in this study. Following an analysis of the process-morphology correlation, carbon fiber (CF)/polyamide 12 (PA12) specimens were tested to characterize the in-plane quasi-static material properties. Then, a modelling framework has been proposed for assessing the composite elastic properties and average bead stresses. This framework holds the potential to scale up to a structural level, accommodating various fiber trajectories.

Thermal postbuckling and thermally induced postbuckled flutter of tri-directional functionally graded plates in yawed supersonic flow

The current work examines the thermal postbuckling, aero-elastic flutter and thermally induced postbuckled flutter about a static equilibrium state of tri-directional functionally graded (TFGM) rectangular and tapered plates in yawed supersonic flow. Based on the von Kármán nonlinear strains, the general higher-order shear deformation theory (GHSDT) and the first-order piston theory, the governing equations of motion for TFGM plates in yawed supersonic flow are established via the Hamilton's principle. The isogemetric analysis (IGA), the load continue strategy associated with the Newton Raphson iterative technique are exploited synthetically to capture the postbuckling paths, and then the postbuckled flutter behaviors are acquired with the static equilibrium state being obtained. Comparative and convergence studies are provided to improve reliabilities of the present material model, formulae and code implementations. Subsequently, detailed parametric investigations are carried out to evaluate the influences of material volume fractions, boundary conditions and airflow angles on the thermal postbuckling, aero-elastic flutter and postbuckled flutter behaviors of TFGM plates. The results show that it is the in-plane volume fractions, rather than the thickness volume fraction, that exert a greater influence on the thermal postbuckling and flutter behaviors of TFGM plates. Furthermore, TFGM plates exhibit more diverse postbuckling paths and more complex deformations due to the inhomogeneity of the in-plane material properties compared with z-directional FGM plates.

Experimental Characterization and Analysis of the In-Plane Elastic Properties and Interlaminar Fracture Toughness of a 3D-Printed Continuous Carbon Fiber-Reinforced Composite.

The use of continuous fiber as reinforcement in polymer additive manufacturing technologies enhances the mechanical performance of the manufactured parts. This is the case of the Carbon-Fiber reinforced PolyAmide (CF/PA) used by the MarkForged MarkTwo® 3D printer. However, the information available on the mechanical properties of this material is limited and with large variability. In this work, the in-plane mechanical properties and the interlaminar fracture toughness in modes I and II of Markforged’s CF/PA are experimentally investigated. Two different standard specimens and end-tabs are considered for the in-plane properties. Monolithic CF/PA specimens without any additional reinforcement are used for the interlaminar fracture toughness characterization. Two different mode I specimen configurations are compared, and two different test types are considered for mode II. The results show that prismatic specimens with paper end-tabs are more appropriate for the characterization of the in-plane material properties. The use of thick specimens for mode I fracture toughness tests complicates the characterization and can lead to erroneous results. Contrary to what has been reported in the literature for the same material, fracture toughness in mode I is lower than for mode II, which agrees with the normal tendency of traditional composite materials.

Identification of printed circuit boards mechanical properties using response surface methods

PurposeThis study aims to discuss the determination of the unknown in-plane mechanical material properties of printed circuit boards (PCBs) by correlating the results from dynamic testing and finite element (FE) models using the response surface method (RSM).Design/methodology/approachThe first 10 resonant frequencies and vibratory mode shapes are measured using modal analysis with hammer testing experiment, and hence, systematically compared with finite element analysis (FEA) results. The RSM is consequently used to minimize the cumulative error between dynamic testing and FEA results by continuously modifying the FE model, to acquire material properties of PCBs.FindingsGreat agreement is shown when comparing FEA to measurements, the optimum in-plane material properties were identified, and hence, verified.Originality/valueThis paper used FEA and RSMs along with modal measurements to obtain in-plane material properties of PCBs. The methodology presented here can be easily generalized and repeated for different board designs and configurations.

Effects of Shear Deformation of Struts in Hexagonal Lattices on their Effective In-Plane Material Properties

Two-dimensional lattices are widely used in many engineering applications. If 2D lattices have large numbers of unit cells, they can be accurately modeled as 2D homogeneous solids having effective material properties. When the slenderness ratios of struts in these 2D lattices are low, the effects of shear deformation on the values of the effective material properties can be significant. This study aims to investigate the effects of shear deformation on the effective material properties of 2D lattices with hexagonal unit cells, by using the homogenization method based on equivalent strain energy. Several topologies of hexagonal unit cells and several slenderness ratios of struts are considered. The effects of struts’ shear deformation on the effective material properties are examined by comparing the results of the present study, in which shear deformation is neglected, with those from the literature, in which shear deformation is included.

Effects of water saturation and low temperature coupling on the mechanical behavior of carbon and E-Glass epoxy laminates

An experimentally based study has been conducted to quantify the effects of coupled water saturation and low temperatures on the quasi-static and dynamic mechanical behavior of E-Glass and Carbon Epoxy laminates. The relative performance of the materials as a function of water saturation and decreasing temperature was characterized through detailed experiments, specifically in-plane (tensile/compressive) and shear material properties, static and dynamic Mode-I fracture, and impact/flexure after impact strength. In the investigation temperatures from Room Temperature (20 °C) down to arctic seawater and extreme ocean depth conditions (−2 °C) were evaluated. The materials utilized in the study, Carbon/Epoxy and E-glass/Epoxy, are chosen due to their primary interest to the underwater vehicle and marine industry communities. The results of the quasi-static and dynamic material experiments show that all properties are affected by both water saturation and decreasing temperature, although the trends are specific to the property under consideration.

Effect of negative poisson's ratio on the axially compressed postbuckling behavior of FG-GRMMC laminated cylindrical panels on elastic foundations

Auxetic materials are one of the metamaterials that have potential applications in many scientific and engineering fields. In this paper, an investigation is presented on the postbuckling responses of axially loaded graphenereinforced metal matrix composite (GRMMC) laminated cylindrical panels with in-plane negative Poisson's ratio (NPR). The panels are made of GRMMC laminates and rest on an elastic foundation in thermal environments. The graphene volume fraction in GRMMC layer may vary across the panel thickness in order to achieve a piece-wise functionally graded (FG) pattern. The GRMMC layers have in-plane NPR and temperature dependent material properties. The governing differential equations for the GRMMC laminated cylindrical panels are formulated based on the Reddy's third order shear deformation shell theory and are solved by using a singular perturbation technique along with a two-step perturbation approach. Numerical investigation is carried out to study the influence of the in-plane NPR, the FG patterns, the thermal environmental conditions and the foundation stiffness on the postbuckling responses of the GRMMC laminated cylindrical panels under axial compressive load. The results reveal that the in-plane NPR can lead to a substantial change of the postbuckling behaviors of the GRMMC laminated cylindrical panels.

Low temperature effects on the mechanical, fracture, and dynamic behavior of carbon and E-glass epoxy laminates

An experimental investigation through which the effects of low temperatures on the mechanical, fracture, impact, and dynamic properties of carbon- and E-glass-epoxy composite materials has been conducted. The objective of the study is to quantify the influence of temperatures from 20 °C down to −2 °C on the in-plane (tensile/compressive) and shear material properties, static and dynamic Mode-I fracture characteristics, impact/residual strength, and the storage and loss moduli for the materials considered. The low end of the temperature range considered in the study is associated with Arctic seawater as well as conditions found at extreme ocean depths (2 °C–4 °C). In the investigation, both carbon/epoxy and E-glass/epoxy laminates are evaluated as these materials are of keen interest to the marine and undersea vehicle community. The mechanical characterization of the laminates consists of controlled tension, compression, and short beam shear testing. The Mode-I fracture performance is quantified under both quasi-static and highly dynamic loading rates with additional flexure after impact strength characterization conducted through the use of a drop tower facility. Finally, dynamic mechanical analysis (DMA) testing has been completed on each material to measure the storage and loss moduli of the carbon fiber- and E-glass fiber reinforced composites. The findings of the study show that nearly all characteristics of the mechanical performance of the laminates are both material and temperature dependent.

An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates

Two assumptions have been made based on by this proposed theory, which come from recently developed exponential–trigonometric shape function for transverse shear deformation effect and a simple higher order shear deformation theory for plate, based on a constraint between two rotational displacements of axis parallel to the plate midplane, about the axes x, y Cartesian coordinates system, which caused fewer unknown number. For the application of this method, a displacement field extended as only bending membrane for transverse displacement is used, a governing equations of motion as a result are determined according to Hamilton’s principle, and simplified using Navier analytical solutions, as well as the transverse shear stresses effect that satisfied the stress-free boundary conditions on the simply supported plate free faces as a parabolic variation along the thickness are taken into account. A functionally graded materials plates are chosen for the parametric study, where the plates are functionally graded continuously in materials through the plate thickness as a function of power law or exponential form. The aim of this study is to analyze the bending, free vibration as well as the buckling mechanical behaviors, where the results are more focused on the investigation of different parameters such as the volume fraction index, geometric ratios, frequency modes, in-plane compressive load parameters and material properties effects on the deflection, stresses, natural frequencies, and critical buckling load, which are validated in terms of accuracy and efficiency with other plate theories results found in the literature.

Strain-engineering the in-plane electrical anisotropy of GeSe monolayers.

As a representative in-plane anisotropic two-dimensional (2D) material, germanium monoselenide (GeSe) has attracted considerable attention recently due to its various in-plane anisotropic material properties originating from the low symmetry of a puckered honeycomb structure. Although there have been plenty of reports on the in-plane anisotropic vibrational, electrical and optical properties of GeSe, the strain effect on those appealing anisotropies is still under exploration. Here we report a systematic first-principles computational investigation of strain-engineering of the anisotropic electronic properties of GeSe monolayers. We found that the anisotropic ratio of the effective mass and mobility of charge carriers (electrons and holes) of GeSe along two principle axes can be controlled by using simple strain conditions. Notably, the preferred conducting direction of GeSe can be even rotated by 90° under an appropriate uniaxial strain (>5%). Such effective strain modulation of the electronic anisotropy of GeSe monolayers provides them abundant opportunities for future mechanical-electronic devices.

An elasto-plastic damage model for functionally graded plates with in-plane material properties variation: Material model and numerical implementation

The paper presents an elasto-plastic damage model based on irreversible thermodynamics for the analysis of functionally graded (FG) plates with in-plane material properties variations. The model considers a simple power law function to describe the FG plates as continua with smooth variation of material properties, such as Young’s Modulus, yield stress, plastic material constants and damage parameters. By introducing two independent plastic and damage multipliers, the model is applicable to different types of materials. Employing the operator splitting methodology, a three-step predictor/multi-corrector algorithm is developed that includes an elastic predictor, a plastic corrector, and a damage corrector. Then, the damage finite element (FE) solutions are obtained using linear hexahedral solid elements with spatially graded property distribution (at different Gauss points), and subsequently implemented by a user material subroutine (UMAT) in the ABAQUS FE software. Good agreement is shown between the analytical damage models, the FE solutions and experimental results sourced from the literature. Several numerical examples establish that the present model is not only accurate, but provides a simple approach to predicting damage of different types of materials, including those that demonstrate both elastic-brittle damage and elasto-plastic damage behaviours. Moreover, the presented model effectively describes the continuum damage of FG plates, capturing variation of the damage variable throughout the plane of the plate.

画像相関法による変位分布の測定値を用いた一方向CFRPの弾性係数の同定

Identification of in-plane and through-thickness material properties of a unidirectional carbon fiber reinforced plastics (CFRP) plate from displacement fields is performed using a virtual fields method. The displacement fields are obtained through the measurement using digital image correlation. In order to obtain appropriate identification results, the measured displacements are reasonably smoothed and the optimized virtual displacement fields are determined for minimizing the influence of the measurement errors. The material properties are determined by applying this method to the displacement fields obtained for the beam specimen under three-point bending. Results show that the orthotropic material properties can be identified from the measured displacement fields. As the orthotropic material properties are obtained from measured displacement distributions, this method is expected to be applied to various materials.

New Two-Dimensional Polynomial Failure Criteria for Composite Materials

The in-plane damage behavior and material properties of the composite material are very complex. At present, a large number of two-dimensional failure criteria, such as Chang-Chang criteria, have been proposed to predict the damage process of composite structures under loading. However, there is still no good criterion to realize it with both enough accuracy and computational performance. All these criteria cannot be adjusted by experimental data. Therefore, any special properties of composite material cannot be considered by these criteria. Here, in order to solve the problem that the criteria cannot be adjusted by experiment, new two-dimensional polynomial failure criteria with four internal parameters for composite laminates are proposed in the paper, which include four distinct failure modes: fiber tensile failure, fiber compressive failure, matrix tensile failure, and matrix compressive failure. In general, the four internal parameters should be determined by experiments. One example that identifies parameters of the new failure criteria is given. Using the new criteria can reduce the artificialness of choosing the criteria for the damage simulation of the failure modes in composite laminates.

Experimental methods to determine in-plane material properties of polyurethane-coated nylon fabric

Experimental procedures have been developed to obtain the mechanical stiffness and strength properties of an orthotropic polyurethane-coated nylon fabric for use in a finite element analysis of an inflatable, deployable structure. A method that utilizes a specialized material test fixture and photogrammetry to collect the linear and angular displacement data has been employed. Different material holding methods were compared with the objective of producing strength values not influenced by gripping and that allow for use of machine displacement to estimate longitudinal strains during cyclic testing. A series of tension and bias tension tests provided material properties such as Young’s modulus in both warp and fill directions, Poisson’s ratios in plane and through the thickness, and shear modulus. Results obtained from the photogrammetry method show good correlation to machine readings using a pinched gripping method. Additionally, cyclic tests gave the continuous load–unload response and the hysteresis characteristics of the stress–strain in plane and indicated the degree of material degradation. The shear stress–shear strain behavior and shear modulus values are acquired using bias tension tests on 45° skewed specimens.

Transversely isotropic mechanical properties of PVC foam under cyclic loading

Cyclic material tests were done on Divinycell PVC H100 foam to obtain out-of-plane and in-plane compression and shear material properties after foam yielding. The compression and shear stress–strain behaviors were very similar to each other except that a plateau (flow) stress occurred after yielding in compression, while the foam underwent mild strain hardening after shear yielding. The ratio of out-of-plane to in-plane stiffness and yield strength for the PVC H100 was found to be approximately 3/2 in both the compression and shear modes. After viscoplastic yielding, the foam underwent permanent damage and exhibited hysteresis, mainly in the form of viscoelasticity. Damage that occurred in the foam after it yields followed the pattern of Mullins damage, i.e., the damage was essentially fixed at a given strain amplitude, and more damage occurred with increasing the strain amplitude. Hysteresis was much more pronounced as the damage grew, suggesting that viscoelastic properties of the foam could be changing with the amount of damage.

On the in-plane properties and capacities of infilled frames

The important contribution of infill walls in the resistance of earthquake loads is documented along with a presentation of the behavior modes of the infill and the bounding frame. Equations for quantifying the in-plane stiffness, strength and deformation capacity of infills are given as well as simplified methods for predicting the in-plane failure mode of mainly solid panels. A parametric study is performed to compare these methods and check them against experimental results whenever this was possible. Based on the above material, recommendations are made for the in-plane material properties, failure modes, strength and stiffness as well as deformation characteristics of infilled frames.

Design of a Biomimetic Skin for an Octopus-Inspired Robot – Part I: Characterising Octopus Skin

Octopus skin samples were tested under quasi-static and scissor cutting conditions to measure the in-plane material properties and fracture toughness. Samples from all eight arms of one octopus were tested statically to investigate how properties vary from arm to arm. Another nine octopus skins were measured to study the influence of body mass on skin properties. Influence of specimen location on skin mechanical properties was also studied. Material properties of skin, i.e. the Young's modulus, ultimate stress, failure strain and fracture toughness have been plotted against the position of skin along the length of arm or body. Statistical studies were carried out to help analyzing experimental data obtained. Results of this work will be used as guidelines for the design and development of artificial skins for an octopus-inspired robot.

Response of a laterally vibrating nanotip to surface forces

The torsional eigenmodes of atomic force microscope (AFM) cantilevers are highly sensitive toward in-plane material properties of the sample. We studied the effect of viscosity and lateral contact stiffness on the detuning, amplitude, and phase response numerically. To verify the theoretical considerations, a torsion mode AFM was operated in frequency modulation. During approach and retract cycles, we observed a negative detuning of the torsional resonant frequency close to the sample surface depending on the tilt angle between the tip and the sample. Thus, the tilt has a significant effect on the imaging process in torsional resonance mode.

Micromechanics of fabric reinforced composites with periodic microstructure

A model to predict the effective stiffness of woven fabric composite materials is presented. Taking advantage of the inherent periodicity of woven fabric architecture, periodic microstructure theory is used at the mesoscale for the case of a two-phase heterogeneous material with multiple periodic inclusions. For plain weave fabrics, the representative volume element (RVE) is discretized into fiber/matrix bundles and the pure matrix regions that surround them. The surfaces of the fiber/matrix bundles are fit with sinusoidal equations using two approaches. The first is based on measurements taken from photomicrographs of composite specimens and the second is based on an idealized representation of the plain weave structure. Three-dimensional sinusoidal surfaces are generated from the face equations and weave shape for the real and idealized cases in order to mathematically describe the fiber/matrix bundle regions, which are treated as unidirectional composites. Model results from the idealized geometry are compared to experimental data from the literature and show good agreement, including interlaminar material properties. From a comparison of the real and idealized geometry results for similar material RVE dimensions, it is seen that the model is capable of predicting significant changes in the in-plane material properties from slight mismatch in the fiber/matrix bundle shape and crimp, which can be captured using the geometric surfaces generated from photomicrograph measurements.

Static Indentation of Anisotropic Biomaterials Using Axially Asymmetric Indenters—a Computational Study

Indentation has historically been used by biomechanicians to extract the small strain elastic or viscoelastic properties of biological tissues. Because of the axisymmetry of indenters used in these studies however, analysis of the results requires the assumption of material isotropy and often yields an "effective" elastic modulus. Since most biological tissues such as bone and myocardium are known to be anisotropic, the use of conventional indentation techniques for estimating material properties is therefore limited. The feasibility of using an axially asymmetric indenter to determine material directions and in-plane material properties for anisotropic tissue is explored here using finite element analysis. The load versus displacement curves as would be measured by an indenter depend on the orientation of the indenter cross section relative to the in-plane material axes, thus suggesting a method for determining the underlying material directions. Additionally, the stiffness of the tissue response to indentation is sensitive to the values of the in-plane anisotropic material properties and prestretches, and thus test results can be used to back out relevant constitutive parameters.