Effective Young Modulus Research Articles

An Empirical Approach for the Determination of Skin Elasticity: Finger pad Friction against Textured Surfaces

Surface topography significantly influences tactile friction and perception. While friction forces can be reduced by surface texturing, selection of pattern dimensions is challenging due to the highly variable elastic modulus of the skin. This work proposes an empirical approach for the evaluation of the skin elasticity through surface transition from asperity to full contact state. To highlight the contact transition, two textures with evenly distributed identical micro asperities, but varying density, were moulded with several grades of silicone rubber. Dynamic friction coefficient measurements were performed during finger pad sliding against the textured samples with a range of normal loads up to 5 N. A combination of analytical and numerical contact models is used to explain the observed friction behaviour, estimate the development of contact area and calculate the effective elastic modulus of the skin at the micro-scale. Low density textures clearly indicate the transition to the full contact state, which is reflected in friction coefficient development, while high density textures remain in an asperity contact state, with significantly lower friction values. The effective Young's modulus is hereby estimated in the range of 0.2–0.5 MPa. Observed frictional behaviour is explained by the change in the apparent and real contact areas. The presented approach allows to study the influence of individual surface parameters on effective skin elastic modulus, which is essential for the development of functional surfaces with improved tactile perception.

Cálculo simplificado de vidrio laminado: determinación de desplazamientos en vigas y placas ante cargas estáticas utilizando modelos monolíticos

In the calculation of laminated glass elements, glass layers are commonly considered as linear-elastic whereas the polymeric interlayers present viscoelastic behavior. Consequently, the mechanical behavior of laminated glass elements depends on time and temperature. Many finite elements are needed to calculate these elements because the thickness of the glass layers (and above all that of polymeric interlayers) are much smaller than the other two dimensions of the element (with and length). For this reason, the calculation of these elements is very high time consuming. Recently, several authors have proposed the effective stiffness concept (alternatively effective thickness or effective Young's modulus) for the simplified calculation of laminated glass elements. In this work, a methodology is proposed to predict the deflection of laminated beams and plates under static loadings using a linear elastic monolithic model (analytical or numerical) and the equations of the effective stiffness for the laminated glass. The equations proposed in this work have been validated by experimental tests carried out in simply-supported beams and in a plate supported at the four corners, the maximum error being less than 10%.

Research on one-dimensional ubiquitiformal constitutive relations for a bimaterial bar

A one-dimensional ubiquitiformal constitutive model for a bimaterial bar is proposed in this paper. The explicit analytical expression for the effective Young modulus is then obtained, which, unlike the fractal one, leads to a continuous displacement distribution along the bar. Moreover, the numerical results for concretes are calculated and found to be in agreement with previous experimental data. In addition, some previous empirical and semi-empirical constitutive models are also examined, which shows that each of these models can corresponding well to a ubiquitiformal one under a certain complexity.

A brittle material with tunable elasticity: Crêpe paper

We study the mechanical response, and tearing features of crêpe paper, a two-dimensional, very anisotropic material, with one direction much less stiff than the other one. Depending on how the soft direction has been pre-stretched or not, the apparent Young modulus of the material can be varied over a broad range, while its fracture energy remains unaltered. The classical tearing concertina problem shows that a macroscopic measurement (the shape of the teared region) provides a direct access to the fracture properties of the material (effective Young's modulus, and fracture energy). The overall discussion is conducted in the frame of Griffith's theory of fracture.

Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets

For the first time, forced resonance vibration of Graphene Nano-Platelets (GNPs) reinforced Functionally Graded Polymer Composite (FG-PC) nanoplates is studied. The effective Young's modulus is determined using the Halpin–Tsai model while the rule of mixture is used to compute the effective Poisson's ratio and mass density. The governing equations, classical and non-classical boundary conditions are obtained through Hamilton's principle for nonlocal strain gradient Kirchhoff plate theory. Employing Navier solution procedure, a closed form solution is introduced for forced resonance vibration of the nanoplate. The influences of the GNPs distribution schemes, nonlocal and strain gradient length scale parameters, weight fraction and the total number of layers of GNPs as well as geometrically parameters are discussed in detail. The results show that the impact of layer's number on the resonance position depends on the reinforcement patterns.

Effective modulus of biological staggered nanocomposites with interface stress effect

Biological composites with staggered matrix–platelet nanostructures, such as bone, teeth and nacre, possess superior mechanical properties. The interface property between mineral platelets and protein matrix at nanoscale is one of the key factors influencing effective properties of such nanocomposites. In this study, based on the Gurtin-Murdoch model, two tension-shear chain models (TSCMs) considering the interface stress effect are established to analyse the influence of interface stress effect on the effective Young's modulus of the staggered nanocomposites. One is the TSCM without tension region between two adjacent hard platelets, while another is with tension region. Two explicit formulae of effective Young's modulus of the nanocomposites are derived based on the two TSCMs. Meanwhile, an interface factor reflecting the combined influence of the platelet thickness and interface-platelet modulus ratio is also abstracted. The validity and accuracy of the two TSCMs are verified by comparing with the finite element simulations. Both the explicit formulae and the finite element simulations show that the interface stress effect has significant influence on the effective modulus, when the absolute value of the interface factor is large. For a given interface modulus, the interface effect on the effective modulus becomes more significant with decreasing the internal structure size of the nanocomposites to nanoscale.

Size dependent free vibration analysis of multilayer functionally graded GPLRC microplates based on modified strain gradient theory

In this study, for the first time, a size dependent computational model based on the modified strain gradient theory (MSGT) and higher-order shear deformation theory (HSDT) for free vibration analysis of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) microplates is proposed. To capture size effects of microstructures, three material length scale parameters (MLSPs) are considered and used. The effective Young's modulus for each layer of the FG GPLRC microplate is computed according to the Halpin–Tsai model, while the effective density and Poisson's ratio are computed by the rule of mixtures. Four different types of graphene platelets (GPLs) distributions, which are either uniform or functionally graded (FG), are considered. The principle of virtual work is used to derive discretize governing equations which are then solved by an isogeometric analysis (IGA). In addition, thank to continuous higher-order derivatives of NURBS basis functions in IGA, it is suitable for a numerical implementation of the present size dependent model within required third-order derivatives in the weak form. Besides, the present size dependent model can be recuperated into the modified couple stress theory model (MCST) or classical HSDT model when two or all MLSPs in the theory are taken equal to zeros, respectively. The rectangular and circular FG GPLRC microplates with different boundary conditions, distributed types of GPLs and MLSPs are exampled to evaluate natural frequencies. Numerical results have shown that the difference of the natural frequency predicted by the MSGT, the MCST and classical HSDT are large when the plate thickness approaches the MLSPs, however, this difference decreases with a rise of the plate thickness.

Multiscale simulation of the interlaminar failure of graphene nanoplatelets reinforced fibers laminate composite materials

ABSTRACTThis article presents a multiscale approach to derive the interlaminar properties of graphene nanoplatelets (GNPs)‐based polymeric composites reinforced by short glass fibers (SGFs) and unidirectional carbon fibers (UCFs). The approach accounts for the debonding at the interface of a 2‐phases GNPs/polymer matrix using a cohesive model. The resulting composite is used within a 3‐phases nanocomposite consisting either of a GNPs/polyamide/SGFs or a GNPs/epoxy/UCFs nanocomposite. Experiments are performed for determining the interlaminar fracture toughness in mode I for the GNPs/epoxy/UCFs. Results show that the aspect ratio (AR) of GNPs influences the effective Young modulus which increases until a threshold. Also, the addition of the GNPs increases up to 10% the transverse Young modulus and up to 11% the shear modulus as well as up to 16% the transverse tensile strength useful in crashworthiness performance. However, the nanocomposite behavior remains fiber dominant in the longitudinal direction. This leads to a weak variation of the mechanical properties in that direction. Due to the well‐known uniform dispersion issues of GNPs, the interlaminar fracture toughness GIC has decreased up to 8.5% for simulation and up to 2.4% for experiments while no significant variation of the interlaminar stress distribution is obtained compared to a nanocomposite without GNPs. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47664.

Compressive response of high-strength [001]-oriented single crystals of a Co35Ni35Al30 shape memory alloy

The effects of stress-free and stress-assisted aging at 673 K on microstructures, thermoelastic stress-induced B2-L10 martensitic transformation and superelasticity were investigated in [001]B2-oriented Co35Ni35Al30 (at. %) single crystals in compression. The aging of quenched crystals results in the formation of high-strength nanostructured composites containing spherical nanosized particles and elongated ε-Co (HCP structure) particles, which do not undergo martensitic transformation. The stress-free and stress-assisted aged at 673 K for 0.5 h Co35Ni35Al30 crystals, oriented along [001]B2-direction, demonstrate high-yield stress levels for the B2-phase of 1360÷1630 MPa and a wide superelasticity temperature range from 193 K to 563 K with good cyclic stability and narrow stress hysteresis of Δσ = 50–60 MPa. It has been shown experimentally that a difference in the effective Young's modulus of austenite and martensite determinates a decrease in the reversible strain with a test temperature in both quenched and aged crystals. The tensile two-way shape memory effect with a reversible strain of εTWSME = +2.2% along the [001]B2-direction is induced due to the oriented growth of elongated ε-Co-particles in stress-assisted aged crystals. These results provide a clear demonstration of the potential of aged CoNiAl single crystals for applications involving high stresses and temperatures.

Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements

This research presents an analytical approach for nonlinear static responses and stability analysis of functionally graded porous (FGP) arches with graphene platelets (GPLs) reinforcements (i.e., FGP-GPLRC arches). The constitutive material composition of the FGP-GPLRC arch varies along the radial direction of the cross section specifically, so that the mechanical performance of the arch such as buckling strength and weight can be well controlled for various engineering design purposes. The effective Young's modulus of the FGP-GPLRC arch is determined by the volume fraction distribution of materials. Based on the Euler-Bernoulli hypothesis, the structural responses of the arch considering the geometric nonlinearity are derived by using the virtual work method. Two boundary conditions are considered which are including the pinned-pinned and the fixed-fixed supports. The loading condition is defined as uniformly distributed load in the radial direction of the arch. Different buckling modes are discussed by the illustration of the equilibrium paths. By adopting the developed analytical solution, the relationship between the structural response, buckling load, self-weight, porosity level and the percentage of content of the GPLs can be investigated efficiently. The applicability and effectiveness of the proposed analytical approach for the geometric nonlinear analysis of FGP-GPLRC arch structures are demonstrated through numerical examples.

Tribological properties and oxidation resistance of tungsten and tungsten nitride films at temperatures up to 500 °C

Abstract The paper reports on the structure, microstructure, mechanical and tribological properties and oxidation resistance of WNx films with a stoichiometry x = [N]/[W] ranging from 0 to 1.5 prepared by magnetron sputtering. It was found that (i) films with x ≤ 0.20 exhibit α-W structure and columnar microstructure, while films with x ≥ 0.27 exhibit β-W2N or δ-WN structure and fine-grained microstructure, (ii) the hardness H and hardness to effective Young's modulus H/E∗ strongly affect the tribological properties of the films. Furthermore, we investigate and discuss how the tribological properties are affected by the humidity and by the film oxidation. The oxidation is expressed in terms of the thickness of the WO3 scale, and is shown to be significantly different for x ≤ 0.20 and x ≥ 0.27 WNx films.

Double-Negative Pillared Elastic Metamaterial

Elastic metamaterials exhibiting negative values of both effective mass density and Young's modulus in certain frequency ranges are important for controlling the propagation and path of elastic waves. However, a description of the vibrations involved in this ``double negativity'' is still needed. In this numerical study, the authors bring to light the microscopic mechanisms that lead to the double negativity of a double-sided metamaterial with pillars. The results will promote the computational design of devices to control waves guided in membranes and plates, such as acoustic lenses and ``inaudibility'' cloaks.

Simulation of bone ingrowth into bone substitutes on implant level length scale

AbstractComputational modelling is a promising and ethical reasonable method in implant development. A computational model for bone ingrowth on implant level length scale has been implemented and applied for an open‐pored space‐filling bone substitute. First numerical simulations showed reasonable results for the average bone density and the effective Young's modulus of the bone‐implant‐compound.

Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets

The paper presents a large parametric investigation on the bending response of Functionally Graded (FG) polymer composite curved beams reinforced by graphene nanoplatelets resting on a Pasternak foundation. The theoretical framework is based on the First-order Shear Deformation Theory (FSDT) and the nonlocal elasticity theory. The governing equations are obtained by means of the principle of virtual works. Four different patterns are considered to describe the through-the-thickness distribution of the reinforcing phase. The effective Young's modulus and Poisson's ratio are evaluated through the application of the Halpin-Tsai model and the rule of mixture, respectively. The numerical results are presented in terms of some significant parameters, such as the weight fraction and geometrical features of the graphene nanoplatelets, the total number of layers, the foundation properties and the nonlocal parameter. The effect of these quantities on the kinematic and static behavior is discussed.

Ultrahigh-Strength AISI-316 Austenitic Stainless Steel Foils Through Concentrated Interstitial Carbon

This research explores intrinsic properties of the carbon-rich subsurface zone (case) that low-temperature carburization generates in austenitic stainless steel (AISI-316). Foils of this steel were carburized to obtain concentrated interstitially dissolved carbon distributed uniformly throughout their thickness. Compared to the as-received AISI-316 foils, carburization increases the ultimate tensile strength to 3 times, the yield strength to 4 times, and the effective Young modulus to 1.5 times, respectively. On the other hand, the strain to failure decreases to (9 ± 1) 10-3. For comparison, foils with larger thickness were carburized as well. Those foils retained a core of low carbon level. Decreasing the ratio of mean carbon depth to foil thickness was found to decrease the ultimate tensile strength, yield strength, and elastic modulus, while increasing the strain to failure. Tensile testing partially carburized foils to failure confirmed ductility in the core, but revealed reduced ductility in the carbon-rich zone near the surface. On the surface, intergranular cracks were observed to propagate perpendicular to the tensile direction, indicating brittle fracture initiated by cracks nucleating at grain boundaries. The isolated concentrated solid solution of interstitial carbon in austenite can be regarded as a new material with exceptional properties, particularly ultrahigh tensile strength, high yield strength, and high Young's modulus.

Elastic constants of graphene: Comparison of empirical potentials and DFT calculations

The capacity of popular classical interatomic potentials to describe elastic properties of graphene is tested. The Tersoff potential, Brenner reactive bond-order potentials REBO-1990, REBO-2000, REBO-2002 and AIREBO as well as LCBOP, PPBE-G, ReaxFF-CHO and ReaxFF-C2013 are considered. Linear and non-linear elastic response of graphene under uniaxial stretching is investigated by static energy calculations. The Young's modulus, Poisson's ratio and high-order elastic moduli are verified against the reference data available from experimental measurements and ab initio studies. The density functional theory calculations are performed to complement the reference data on the effective Young's modulus and Poisson's ratio at small but finite elongations. It is observed that for all the potentials considered, the elastic energy deviates remarkably from the simple quadratic dependence already at elongations of several percent. Nevertheless, LCBOP provides the results consistent with the reference data and thus realistically describes in-plane deformations of graphene. Reasonable agreement is also observed for the computationally cheap PPBE-G potential. REBO-2000, AIREBO and REBO-2002 give a strongly non-linear elastic response with a wrong sign of the third-order elastic modulus and the corresponding results are very far from the reference data. The ReaxFF potentials drastically overestimate the Poisson's ratio. Furthermore, ReaxFF-C2013 shows a number of numerical artefacts at finite elongations. The bending rigidity of graphene is also obtained by static energy calculations for large-diameter carbon nanotubes. The best agreement with the experimental and ab initio data in this case is achieved using the REBO-2000, REBO-2002 and ReaxFF potentials. Therefore, none of the considered potentials adequately describes both in-plane and out-of-plane deformations of graphene.

On the effective elastic properties of isotactic polypropylene

Calculating the effective elastic properties of semi-crystalline polymers is challenging due to a pronounced phase stiffness contrast, complex micro-structures and extreme anisotropies of the crystalline phases. To estimate the effective Young modulus of isotactic polypropylene depending on the crystallinity, we construct complex and simple homogenization schemes that unify the micro-scale interaction mechanisms that have been identified by Bartenev and Valishin [4], Bédoui et al. [5], Parenteau et al. [38]. This is achieved by a two-step homogenization approach, namely a local laminate stiffness that is then subjected to orientation averaging. The resulting estimates show good agreement to experimental results. They further suggest that the relatively high effective stiffness of isotactic polypropylene when compared to polyethylene may in part be a result of the stronger lateral confinement effect on the laminate level.

Unilateral and bilateral buckling of functionally graded corrugated thin plates reinforced with graphene nanoplatelets

This paper deals with the buckling behavior of corrugated thin plates made of multilayer functionally graded (FG) graphene nanoplatelets (GPLs) reinforced nanocomposites (FG-GPLRC) within the framework of classical plate theory. The GPLs are uniformly dispersed in each individual layer with its weight fraction following a layer-wise variation along the thickness direction. The effective Young modulus of each layer is determined by the modified Halpin-Tsai model while the Poisson’s ratio is predicted based on the rule of mixture. It is assumed that the plate is subjected to either compression or shear or both on the edge. Analytical critical buckling solutions are obtained for both unilateral buckling when the plate is resting on a rigid foundation and bilateral buckling without the constraint of the foundation. A parametric study is conducted to investigate the influences of distribution pattern, geometry, size, and weight fraction of GPL nanofillers as well as the corrugated profile and rigid foundation on the buckling performance of the plate. It is found that the buckling resistance of the corrugated plate can be effectively enhanced by adding a small amount of GPLs into the matrix according to FGX distribution pattern and when the inclination angle is 45 degrees.

Micromechanical analysis of bioresorbable PLLA/Mg composites coated with MgO: Effects of particle weight fraction, particle/matrix interface bonding strength and interphase

Magnesium (Mg) particle has been recently introduced in a poly-l-lactic acid (PLLA) matrix to enhance to its mechanical properties. The coating of Mg particle could also regulate its degradation rate. In this work, the mechanical behavior of PLLA/Mg composite was characterized using a three-dimensional representative volume element (RVE) model. The influences of Mg weight fraction, imperfect bonding between particle and polymer matrix, and the interphase layer on the mechanical behaviors of the composites were quantified. Results clearly demonstrated that the effective Young's modulus and yield strength of the composite were enhanced by the Mg particles, as well as its MgO coating. In addition, the imperfect interfacial bonding between the Mg particle and PLLA weakened the mechanical advantage of the composite, which was in good agreement with the documented experimental observations. This work might shed some light on the optimal design and manufacturing of the bioresorbable composites.

Compressive characteristics and low frequency damping of aluminium matrix syntactic foams

Al99.5 and AlSi12 matrix syntactic foams were produced by pressure infiltration of Globocer grade ceramic hollow spheres. The produced aluminium matrix syntactic foams (AMSFs) were investigated by compressive tests, dynamic mechanical analysis (DMA), finite element methods (DMA) and elasticity based analytical calculations. The aim of the investigations was (i) to map the compressive properties of the AMSFs, (ii) to determine and compare the effective Young's modulus of the AMSFs determined by compressive tests, DMA, FEM and analytical calculations and (iii) to determine the low frequency damping capability of the AMSFs. The compressive tests showed pronounced differences between the two matrix materials, characterized by higher compressive strength, compressive strain and absorbed mechanical energy in the case of AlSi12 matrix, however, the energy absorption efficiency due to the different failure mechanism of AMSFs (homogeneous densification in the case of Al99.5 and cleavage in the case of AlSi12 matrix, respectively). The DMA tests confirmed the effective Young's moduli values, measured by compression and proved higher damping capability in the case of AlSi12 matrix. FEM and analytical calculations also confirmed the measured effective Young's moduli within a reasonable error band.