Independent Material Properties Research Articles

Hygrothermal buckling analysis of thin rectangular FGM plate with variable thickness

PurposeThis paper aims to contribute novel insights into the analysis of thin functionally graded material (FGM) plates with variable thickness, considering both temperature-dependent and independent material properties, focusing on critical linear buckling temperature rise and the effect of critical linear moisture for various moisture concentrations.Design/methodology/approachThe study derives stability and equilibrium equations for thin rectangular FGM plates under hygrothermal loading, employing classical plate theory (CPT). Buckling behavior is examined using Galerkin’s method to obtain pre-buckling force resultants.FindingsThe findings highlight significant increases in critical buckling temperature with aspect ratio, distinct temperature sensitivity between materials and increasing moisture susceptibility with larger aspect ratios. These insights inform material selection and design optimization for FGM plates under hygrothermal loading, enhancing engineering applications.Research limitations/implicationsThis research primarily focuses on hypothetical scenarios and mathematical model development and analysis.Originality/valueThis paper presents original contributions in the field by addressing the hygrothermal buckling analysis of thin FGM rectangular plates with variable thickness, utilizing CPT, thereby enriching the understanding of structural behavior in varying environmental conditions.

Temperature-Dependent Vibration Characteristics of Porous FG Material Plates Utilizing FSDT

This study focuses on the vibration characteristics of the functionally graded materials (FGMs) porous plate. The plate is to be supported on different boundary constraints with linearly varying thicknesses. Existence of different porosity (void) pattern, within the materials, are taken into consideration using the power (P-FGM) and sigmoidal (S-FGM) gradation laws. The current methodology was developed utilizing the FSDT (first-order shear deformation theory) under thermal environmental conditions. Variations of temperature like as uniform, linearly varying, and nonlinear distribution patterns were examined by including temperature-dependent and independent material properties. The equations of motion including all the effects are derived from Hamilton’s principle and, subsequently solved using the Galerkin’s Vlasov method for various plate boundary conditions. Finally, the analytical outcomes are verified numerically, with the existing works. Furthermore, the study demonstrates that the fundamental frequency of porous FGM tapered plate is very close to the result obtained by the other researchers. Moreover, a detailed examination has been carried out to reveal the effect of various factors such as volume exponent index ([Formula: see text], side-to-thickness ratio ([Formula: see text]/[Formula: see text], and temperature effect ([Formula: see text]. In addition to this, some new benchmark results are obtained for free vibration analysis of tapered plates under a thermal environment.

Interfacial cavitation.

Cavitation has long been recognized as a crucial predictor, or precursor, to the ultimate failure of various materials, ranging from ductile metals to soft and biological materials. Traditionally, cavitation in solids is defined as an unstable expansion of a void or a defect within a material. The critical applied load needed to trigger this instability -- the critical pressure -- is a lengthscale independent material property and has been predicted by numerous theoretical studies for a breadth of constitutive models. While these studies usually assume that cavitation initiates from defects in the bulk of an otherwise homogeneous medium, an alternative and potentially more ubiquitous scenario can occur if the defects are found at interfaces between two distinct media within the body. Such interfaces are becoming increasingly common in modern materials with the use of multimaterial composites and layer-by-layer additive manufacturing methods. However, a criterion to determine the threshold for interfacial failure, in analogy to the bulk cavitation limit, has yet to be reported. In this work, we fill this gap. Our theoretical model captures a lengthscale independent limit for interfacial cavitation, and is shown to agree with our observations at two distinct lengthscales, via two different experimental systems. To further understand the competition between the two cavitation modes (bulk versus interface), we expand our investigation beyond the elastic response to understand the ensuing unstable propagation of delamination at the interface. A phase diagram summarizes these results, showing regimes in which interfacial failure becomes the dominant mechanism.

Crack nucleation and propagation in the phase-field cohesive zone model with application to Hertzian indentation fracture

Hertzian indentation fracture (Hertz, 1896) is an intriguing problem with no pre-defects. Recent studies indicated that those popular phase-field models for brittle fracture might be restrictive in dealing with this problem — crack nucleation can be considered only for the failure strength within a rather limited range. In this work, this problem is analyzed by the phase-field cohesive zonde model (PF-CZM), focusing on the whole failure process of crack nucleation and propagation. Analytical and numerical results show that for any realistic failure strength, the ‘spontaneous’ crack nucleation in an initially defect-free surface, the subsequent small but rapid vertical extension and finally the stable cone-shaped crack propagation, etc., can all be qualitatively and quantitatively captured by the PF-CZM with no modification. This competence is credited to treating the failure strength and the fracture energy (toughness) as two independent material properties. Accordingly, the phase-field length scale is a numerical parameter of no further constraint, which can be made as small as possible such that the convergence to the Barenblatt (1959) cohesive zone model is guaranteed even for short cracks. Moreover, the seamless incorporation of the strength-based crack nucleation criterion and the energy-based crack propagation criterion endows the PF-CZM with the capability of tackling crack nucleation and propagation in pristine solids.

Planar orientation of hydrophilic channels by biaxial deformation of perfluorinated sulfonic acid membranes for vanadium redox flow batteries

Commercially available perfluorosulfonic acid (PFSA) membranes are used as cation exchange membranes for vanadium redox flow batteries (VRFBs) due to their outstanding chemical stability and proton conductivity. However, high vanadium crossover, and expensive production cost of PFSA membranes are considered as limitations for the further commercialization of VRFBs. Here, in order to overcome the issues, PFSA membranes are biaxially stretched for planar orientation of hydrophilic channels with the expanded membrane area over 800%. The area stretching ratio (γ) of PFSA membranes is controlled by water bath temperature, and by the degree of biaxial stretching. As γ increases, vanadium permeability and proton conductivity, known as thickness independent material properties, decrease, and then reach constant values over γ ~1.25. Thus, both of the hydrophilic channel orientation and the membrane thickness matter for the VRFB cell performance. With thick PFSA membranes, a VRFB cell is not operated at high current density, but with the biaxially 827% area expanded Nafion 117, a VRFB cell shows stable efficiencies even at high current density and better capacity retention (82.9%) than a thin Nafion 211 (57.8%) during the long-term cycling. This planarly oriented morphology by biaxial stretching offers an efficient way to utilize the expansive PFSA membranes.

Numerical Modelling of Foamed Concrete Beam under Flexural Using Traction-Separation Relationship

The aim of the current project is to carry out the FEA framework for predicting the flexural strength of notched foam concrete tested under three-point bending following the conducted experimental set-up. The investigated testing series have a variation of notch size opening in the foamed concrete beam. The Traction-separation relationship was used as a constitutive model to incorporate independent material properties and used in the modelling framework. Modelling techniques of 2D XFEM and CZM were adopted and later expanded to 3D XFEM models. Good agreement was found between the predicted structure response and experimental observation for all the investigated models. Crack was initiated at the crack tip and propagated to the beam edge under the applied load. It was found that the average discrepancies below 20% were found within XFEM techniques. Less agreement was found using the CZM models, partly due to the simplification of the adopted failure path. The modelling framework implemented in this project is potentially used as a predictive tool in estimating the flexural strength of the concrete beam with notches.

Temperature evolution in disc brakes during braking of train using finite element analysis

Axle mounted disc brake system is used in LHB (Linke Hofmann Busch) coaches of Indian railways for braking of the train. In the present work, temperature evolution during braking process is analyzed. Heat dissipation during braking process is estimated by considering the dissipation of kinetic energy. The variation of heat dissipation with respect to braking time is assumed to be linear. Three-dimensional finite element model is used for estimation of temperature. Heat distribution in the disc surface is taken as axis-symmetric and dissipated heat is uniformly distributed on the disc surface. Temperature independent material properties are assumed for analysis. Heat loss to environment due to convection and radiation is taken into consideration. Maximum peak temperature rise of 215 °C is observed on the disc at 290 mm in the radial direction at about 60% of braking time while stop braking from 160 kmph.

Enriched analytical solutions for additive manufacturing modeling and simulation

Recent developments in additive manufacturing (AM) technologies involving heat and mass deposition have exposed the need for computationally efficient modeling of thermal field histories. This is due to the effect of such histories on resulting morphologies and quantities of interest, such as micro- and meso-structure, residual strains and stresses, as well as on material and structural properties and associated functional performance at the macro-scale. Limiting undesirable manifestations of these phenomena has motivated the development of both feed-forward and feedback loop control methodologies. However, up to now the computational cost of existing methods for predicting thermal fields and associated aspects, have allowed only feed-forward control methods. Consequently, in this paper, analytic solutions are enriched and then used to model the thermal aspects of AM, in a manner that demonstrates both high computational performance and fidelity required to enable “in the loop” use for feedback control of AM processes. It is first shown that the utility of existing analytical solutions is limited due to their underlying assumptions, some of which are their derivation based on a homogeneous semi-infinite domain and temperature independent material properties among others. These solutions must therefore be enriched in order to capture the actual thermal physics associated with the relevant AM processes. Enrichments introduced herein include the handling of strong nonlinear variations in material properties due to their dependence on temperature, finite non-convex solution domains, behavior of heat sources very near domain boundaries, and mass accretion coupled to the thermal problem. The enriched analytic solution method (EASM) that implements these enrichments is shown to produce results equivalent to those of numerical methods (such as Finite Elements and Finite Differences) that require six orders of magnitude greater computational cost.

Direct measurement and master curve construction of viscoelastic Poisson's ratio with digital image correlation

AbstractA simple procedure for measuring two independent material properties of a viscoelastic material is proposed. Poisson's ratio is directly measured using digital image correlation during dynamic viscoelasticity test. Therefore, the complex Poisson's ratio as well as the complex modulus is simultaneously obtained from same specimen under same condition. The effectiveness of the proposed method is demonstrated by measuring the material properties of a soft epoxy resin. The measurement example shows that the master curves of the time‐dependent Poisson's ratio as well as other material properties for the wide range of the reduced time can be obtained by the proposed procedure.

Possibility of useful mechanical energy from noise: the solitary wave train problem in the granular chain revisited

A momentary velocity perturbation at an edge of a granular chain with the grains barely touching one another and held between fixed walls propagates as a solitary wave whereas a long lived perturbation, even if it is noisy, ends up as a solitary wave train. Here, we extend our earlier work but with a force instead of a velocity perturbation. Such a perturbation can propagate an extended compression front into the system. We find that a snapshot of the distribution of grain compressions in the solitary wave train shows parabolic as opposed to an approximate exponential decay with the leading edge at the front of the traveling pulse and the trailing edge following it. The system’s time evolution depends on three independent parameters-the material properties, duration of perturbation and the characteristic amplitude of the perturbation. Hence, the coefficients used to describe the parabolic decay of the grain compressions in the solitary wave train depend on these three parameters. When a random finite duration force perturbation is applied we find that the randomness is smoothed out by the system, which in turn suggests that long granular chains (or equivalent systems, such as circuits) can be potentially useful in converting random noisy signals to organized solitary wave trains and hence to potentially usable energy.

Stochastic nonlinear bending response of elastically supported nanotube-reinforced composite beam in thermal environment

This paper presents the second-order statistics of the nonlinear bending response of elastically supported single-wall carbon nanotube reinforced composite (CNTRC) beam composed of uniformly distributed (UD) and functionally graded (FG) reinforcements in thermal environments with uncertain system properties. The uncertain system properties such as material properties of matrix and SWCNTs, foundation parameters, thermal expansion coefficients are be modeled as uncorrelated Gaussian random variables. The material properties of FG-CNTRCs are assumed to be graded in the beam thickness direction and are evaluated through a micromechanical model. The higher order shear deformation theories (HSDT) with von-Karman nonlinear strain kinematics are used for the mathematical formulation of CNTRCs beam. The thermal effects are also included in the material properties of CNTRCs which are assumed to be temperature dependent and independent. The second-order perturbation technique (SOPT) and Monte Carlo simulation (MCS) via [Formula: see text] nonlinear finite element method (FEM) through Newton–Raphason method are proposed to examine the mean, COV and probability density function (PDF) of transverse deflection of the beam. Typical numerical results are presented for the different volume fraction of carbon nanotube, slenderness ratios, boundary conditions, foundation parameters, load parameters, CNTRC distribution, temperature dependent and independent material properties with random system properties. The present outlined approach is validated with the results available in the literature and by employing MCS.

Thermal Buckling Behaviour of Functionally Graded Plates

Functionally Graded Materials (FGM) are those materials which have continuous variation of material properties from metal phase to ceramic phase. Due to the continuous change in material properties of FGMs, the stress singularity at the interface between the two different materials is eliminated and thus the bonding strength is enhanced. They are widely used in high temperature environment such as nuclear reactors and rocket heat shields. The material property of FGM plate varies along the thickness direction and the variation is idealised by different mathematical idealisation techniques. This paper deals with the buckling behaviour of clamped PFGM plate under uniform temperature field. Thermal buckling behaviour of FGM plate has been obtained numerically through ANSYS software. The convergence study of the results is optimized by changing the mesh size. The critical buckling temperature rise obtained for functionally graded plates using ANSYS software are compared with the available literature. The effect of different parameters such as power-law index, thickness ratio, and aspect ratio on critical buckling temperature rise for temperature independent and dependent material properties of each constituent is also discussed. It is found that the critical buckling temperature rise decreases with the increase in power-law indices and thickness ratio and increases with increase in aspect ratio.

Evaluation of material properties of incompressible hyperelastic materials based on instrumented indentation of an equal-biaxial prestretched substrate

It is well known that instrumented indentation tests are useful tools in probing mechanical properties of materials such as metals and ceramics. Instrumented indentation of hyperelastic materials such as rubbers, bio-materials, tissues etc has not been examined in depth, especially the inverse problem of material characterization from instrumented indentation response. The difficulty of the inverse problem for such materials is that the unknown property is a function, the elastic energy density function. There are several such functions and each function is often characterized by more than one parameter. If the maximum indentation depth is low, we have shown that instrumented indentation of initially unstretched hyperelastic materials can only resolve a combination of the material parameters. If the maximum indentation depth is high, the indentation can provide independent material properties, however not in a unique way. Moreover, high indentation loads could lead to surface puncturing and so blur the test results. In this work, we show that we can use spherical indentation of a substrate at different but known prestretch levels to obtain the involved material properties of the energy density function. The present methodology can also incorporate a limit energy failure criterion and instrumented indentation can incorporate this behavior which we may call indentation strength.

Effective Fatigue Stress and Criterion for High-Cycle Multi-axial Fatigue

Multi-axial fatigue criterion corresponding to the limiting condition of complicated multi-axial stress state is very important in application. Stresses and deformations are usually elastic if cyclic loadings are near to the limiting condition. A definition of effective fatigue stress has been proposed. Adopting the effective fatigue stress, a multi-axial fatigue criterion has been proposed by considering the equivalence of multi-axial stresses to a uni-axial problem. To clarify the fatigue criterion for a uni-axial problem with arbitrary mean stress, a quantitative relationship between fatigue limit and mean stress has also been proposed and examined. To verify the multi-axial fatigue criterion, examinations have been carried out for the cases of pure shear, shear and axial, and two-axial fatigue by experimental results. It is found that the criterion agrees well with experimental results, even for the cases with various multi-axial mean stresses and phase differences. It is also found that the shear fatigue limit is not an independent material property in common metals.

Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment

An analytical approach on the nonlinear response of thick functionally graded circular cylindrical shells with temperature independent material property surrounded on elastic foundations subjected to mechanical and thermal loads is presented. Material properties are graded in the thickness direction according to a Sigmoid power law distribution in terms of the volume fractions of constituents (S-FGM). The formulations are based on the third order shear deformation shell theory taking into account von Karman nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method and using stress function, explicit relations of thermal load–deflection curves of the S-FGM shells are determined. Detailed parametric studies are carried out to investigate effects of volume fraction index, material properties and geometrical shapes, axial compressions and thermal load, foundation stiffness and imperfection on nonlinear buckling behaviors of S-FGM thick circular cylindrical shells. The present analysis is validated by comparing results with other publications.

Stochastic Nonlinear Free Vibration Analysis of Functionally Graded Beam Subjected to Thermal Loading with Random Material Properties

This paper deals with the stochastic nonlinear free vibration response of functionally graded materials (FGMs) beam subjected to thermal loadings with uncertain material properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituents material and volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C0 continuity. A direct iterative based nonlinear finite element method in conjunction with first order perturbation technique (FOPT) is used for FGMs beam to compute the second order statistics (mean and coefficient of variation) of the nonlinear fundamental frequency. The present outlined approach has been validated with the results available in literatures and independent Monte Carlo simulation (MCS).

Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading

An improved third-order shear deformation theory is employed to investigate free and forced vibration responses of functionally graded plates. A power law distribution is used to describe the variation of material compositions across the plate thickness. The governing equations for vibration analysis obtained using an energy approach are then solved using the Ritz method. Two types of solutions, temperature independent and dependent material properties, are considered. Many effects of the volume fraction index, temperature, material pairs, thickness, plate aspect ratio, etc., which have significant impact on dynamic behaviour of the plates, are considered in the numerical illustrations of free and forced vibration results. At high temperatures, it is observed that the maximum deflections of the functionally graded plates subjected to the dynamic loading increase with the increase of frequency ratio and temperature.

Using regression models to determine the poroelastic properties of cartilage

The feasibility of determining biphasic material properties using regression models was investigated. A transversely isotropic poroelastic finite element model of stress relaxation was developed and validated against known results. This model was then used to simulate load intensity for a wide range of material properties. Linear regression equations for load intensity as a function of the five independent material properties were then developed for nine time points (131, 205, 304, 390, 500, 619, 700, 800, and 1000s) during relaxation. These equations illustrate the effect of individual material property on the stress in the time history. The equations at the first four time points, as well as one at a later time (five equations) could be solved for the five unknown material properties given computed values of the load intensity. Results showed that four of the five material properties could be estimated from the regression equations to within 9% of the values used in simulation if time points up to 1000s are included in the set of equations. However, reasonable estimates of the out of plane Poisson's ratio could not be found. Although all regression equations depended on permeability, suggesting that true equilibrium was not realized at 1000s of simulation, it was possible to estimate material properties to within 10% of the expected values using equations that included data up to 800s. This suggests that credible estimates of most material properties can be obtained from tests that are not run to equilibrium, which is typically several thousand seconds.

Thermal Buckling and Free Vibration Analysis of Heated Functionally Graded Material Beams

The effect of temperature dependency of material properties on thermal buckling and free vibration of functionally graded material (FGM) beams is studied. The FGM beam is assumed to be at a uniform through thickness temperature, above the ambient temperature. Finite element system of equations based on the first order shear deformation theory is developed. FGM beam with axially immovable ends having the classical boundary conditions is analysed. An exhaustive set of numerical results, in terms of buckling temperatures and frequencies, is presented, considering the temperature independent and temperature dependent material properties. The buckling temperature and fundamental frequency obtained using the temperature independent material properties is higher than that obtained by using the temperature dependent material properties, for all the material distributions, geometrical parameters in terms of length to thickness ratios and the boundary conditions considered. It is also observed that the frequencies of the FGM beam will reduce with the increase in temperature. This observation is applicable for the higher modes of vibration also. The necessity of considering the temperature dependency of material properties in determining thermal buckling and vibration characteristics of FGM beams is clearly demonstrated.Defence Science Journal, 2013, 63(3), pp.315-322, DOI:http://dx.doi.org/10.14429/dsj.63.2370

Thermomechanical Elastic Post-Buckling of Functionally Graded Materials Plate with Random System Properties

This paper presents the stochastic post-buckling response of elastically supported FGM plate with random system properties subjected to uniform and nonuniform temperature change with temperature-dependent and -independent material properties. The FGMs plate is supported with two parameters of Pasternak foundation with Winkler cubic nonlinearity. The basic formulation is based on higher-order shear deformation theory (HSDT) with von-Karman nonlinearity using modified C0 continuity. A direct iterative-based nonlinear finite element method combined with first-order perturbation technique is used to compute the second-order statistics (mean and coefficient of variation) of post-buckling response of FGM plates.