Effective Thermomechanical Properties Research Articles

Experimental investigation and micromechanical analysis of glass fiber reinforced polyamide 6

Achieving process stability in the thermoforming of fiber reinforced polymer materials (FRPs) for aerospace or automotive manufacturing is usually associated with a costly trial-and-error process, where experimental boundary conditions and other influencing factors, such as, for example, material composition, need to be adjusted over time. This is especially true when material phenomena on the microlevel, such as the crystallization kinetics of the polymer matrix or resulting stresses from temperature gradients, are the cause of the process instability. To reduce the experimental effort and reliably predict the material behavior during thermoforming, finite element simulation tools on multiple scales are a useful solution. Hereby, incorporating micromechanical phenomena into the model approaches is crucial for an accurate prediction by further reducing the deviation between simulation and experiment, in particular with regard to the underlying nonlinear material behavior. In this work, unit cell simulations on the microscale of a unidirectional glass fiber reinforced polymer (UD GFRP) are conducted to predict effective thermomechanical properties of a single material ply and ascertain the effect of individual ply constituents on the homogenized material behavior. The polymeric matrix material model used was identified in a prior publication with experimental data at various temperatures for polyamide 6 blends with varying degrees of crystallinities. Various randomization methods are tested to generate the unit cells and replicate the composites’ random fiber distribution, with a focus on process automation. The simulative results are successfully compared to an experimental study on glass fiber reinforced polyamide 6 tested at various temperatures, demonstrating the potential of the approach to reduce both time and cost required for material characterization. Finally, the unit cells are used to generate a database to predict untested load cases that will be used in future work to characterize a homogenized macroscopic material model.

Correction: Finite element modeling of effective thermomechanical properties of Al–B4C metal matrix composites

Correction: Finite element modeling of effective thermomechanical properties of Al–B4C metal matrix composites

Effects of oxidation on the effective thermomechanical properties of porous ultra-high temperature ceramics in compression via computational micromechanics and MPM

Due to the harsh flight environment of hypersonic platforms, Ultra-High Temperature Ceramics (UHTCs) imbued with macroscale porosity have been introduced as candidates for providing thermal insulation of sensitive on-board components. This study employs an oxidized state approach for modeling the coupled effects of surface oxidation and continuum damage in the effective thermomechanical response of such materials within the framework of computational micromechanics. Using an in-house Material Point Method (MPM) computational tool, two-dimensional plane strain simulations were performed on representative hexagonal structures of TiB2 with 10%, 40% and 70% macroporosity. Oxide layers ranging from 5 to 50 μm were applied to the structures in place of a transient, diffusion-based oxidation solver. Simulations with applied compressive strains of up to 30% were then performed on hexagonal structures with and without the oxide layer present. A range of dynamic thermal gradients were also applied to investigate the damage due to thermal expansion coefficient mismatch. Finally, the oxidized state modeling approach was applied to large porous structures derived from micro computed tomography images of TiB2 foam.

Three-dimensional analytical model for composite laminate with transverse cracks by assuming parabolic crack opening

In this study, a model for the three-dimensional effective compliance of composite laminates with transverse cracks is developed based on continuum damage mechanics. Three-dimensional laminate theory is used to reproduce all the thermoelastic properties of the damaged laminate. The damage variable, which describes the degree of stiffness reduction caused by transverse cracking, is formulated based on a three-dimensional micromechanical model, with a loose boundary condition and assuming parabolic crack opening. These assumptions contribute to the analytical accuracy of the stiffness reduction model, while simplifying the damage variable expression. The effective thermomechanical properties of various composite laminates are predicted using the proposed model and compared with finite element analysis (FEA) and experimental results. We found that the proposed model with derived damage variable successfully reproduces the FEA and experimental results of stiffness degradation of damaged composite laminates.

A dual‐scale three‐dimensional thermo‐viscoelastic model for the hot stamping simulation of thermoplastic composites

AbstractExisting hot stamping simulations are performed at the macroscopic scale, making optimizing process parameters for a new composite system time‐consuming. This paper develops a dual‐scale three‐dimensional thermos‐viscoelastic model based on a numerical homogenization approach to accurately predict the structural deformation of thermoplastic composite laminates during hot stamping. The viscoelastic homogenization model is developed on representative volume elements using temperature‐dependent viscoelastic parameters determined from thermo‐mechanical tests. The effective properties of the composites are identified from the homogenization results, which are then combined with the experimentally measured thermal behavior into a numerical model of the hot stamping process. The developed model is validated by the agreement between the finite element homogenization results and the predictions made using the determined parameters. The simulated warpage of the molded part also agrees well with the experimental measurements. The developed dual‐scale model can be used to predict the effective thermomechanical properties of composites. Moreover, it can also be integrated into numerical tools for structural design and process optimization of thermoplastic composites.

Effect of 3D aggregate shape on thermo-mechanical properties of asphalt concrete using a mesostructure-based homogenisation method

ABSTRACT Morphological characteristics of aggregates have long been recognised as an essential factor influencing the thermo-mechanical behaviour of asphalt concrete. However, studies on accurate quantification of this influence are still very limited. For this reason, the present study developed a mesoscale finite element method to investigate the effects of three-dimensional (3D) aggregate shape on the complex modulus, thermal expansion coefficient, thermal conductivity, and mesoscale responses of asphalt concrete. An upscaling homogenisation method was adopted to predict the effective thermo-mechanical properties of asphalt concrete. The 3D true sphericity (3DTS) was used as an index to characterise the aggregate shape. The computational results showed that the temperature and loading frequency significantly affect the role of aggregate shapes in determining the effective dynamic modulus of asphalt concrete. The high-angularity aggregates can increase the deformation resistance of asphalt concrete under thermal load, and thus reduces the thermal contraction coefficient of asphalt concrete. However, aggregate shape has no significant effect on the thermal conductivity of the asphalt concrete. In addition, the asphalt concretes with less angular aggregates have stronger low-temperature damage resistance, while the aggregates with high angularity can improve the rutting resistance of asphalt pavements.

Application of Chebyshev-based GDQ and Newmark methods to viscothermoelasticity responses of FG composite annular systems

This study explores the thermo-viscoelasticity response of annular disks made of a functionally graded graphene platelet reinforced composite (FG-GPLRC). Random orientation is considered for GPL nanofillers. A power-law model with a controller index is also used to determine the GPL volume fraction distribution along the radial direction. The effective thermomechanical properties of the nanocomposite medium are calculated through the one-point and two-point correlation homogenization processes. The Kelvin-Voigt technique is employed to design the viscosity nature of the system. Coupled thermoelasticity is considered to attain the governing formulation because the considered disk is subjected to a sudden high temperature. Furthermore, by incorporating generalized thermoelasticity based on the Lord-Shulman concept, the physical structure of the problem is altered. The transient governing equations are solved based on a hybrid approach. The spatial dependency is solved using a Chebyshev-based generalized differential quadrature (GDQ) method, while the time dependency is calculated using an average acceleration-based Newmark technique. After confirming the described formulation and method with previous research, different parametric samples are given to explain more about the behavior of viscoelastic nanocomposite disks that are heated quickly and rotated at a constant rate.

Architected cellular fiber-reinforced composite

Advances in 3D printing have enabled fabrication of rationally-designed cellular architectures out of fiber-reinforced composites, offering a new class of low-density high-performance materials with multifunctional properties unattainable with either of their constituent composites or the underlying cellular architectures. In this study, efficacy of the hierarchical material design approach is investigated by creating various periodic fiber-reinforced representative cells and evaluating effects of fiber volume fraction , fiber length , fiber orientation, and cell topology on their effective thermo-mechanical properties using multiscale standard mechanics homogenization with periodic boundary conditions. The incorporated approach is finally corroborated by comparing the numerical and experimental data for the Young's moduli of cellular metamaterials with tunable isotropic/anisotropic thermo-mechanical properties, 3D printed out of pure and carbon-fiber-reinforced PETG polymer.

Thermal hysteresis of stress and strain in spin-crossover@polymer composites: towards a rational design of actuator devices

Polymer composites of molecular spin crossover complexes have emerged as promising mechanical actuator materials, but their effective thermomechanical properties remain elusive. In this work, we investigated a series of iron(ii)-triazole@P(VDF-TrFE) particulate composites using a tensile testing stage with temperature control. From these measurements, we assessed the temperature dependence of the Young's modulus as well as the free deformation and blocking stress, associated with the thermally-induced spin transition. The results denote that the expansion of the particles at the spin transition is effectively transferred to the macroscopic composite material, providing ca. 1–3% axial strain for 25% particle load. This strain is in excess of the ‘neat’ particle strain, which we attribute to particle-matrix mechanical coupling. On the other hand, the blocking stress (∼1 MPa) appears reduced by the softening of the composite around the spin transition temperature.

Thermo-mechanical analysis of wood through an asymptotic homogenisation approach

In the last decades the use of wood as a construction material has been steadily increasing. Among the main reasons behind this, are its renewable resource nature and its low environmental footprint. In this context, one of the main challenges faced by engineers during the design process is the knowledge and characterization of wood’s thermo-mechanical properties. This is related to the large morphological variations present at the microstructural level, that lead to a wide scatter of the macroscopic properties. To circumvent this issue, in this work a multiscale modelling strategy based on asymptotic homogenisation is proposed. The model is based on the hierarchical nature of wood and incorporates the three material scales generally identified in soft woods: (i) the microfibril scale, (ii) the wood cell scale, and (iii) the growth ring scale. The effective thermo-mechanical macroscopic properties are obtained by sequentially applying the homogenisation procedure from the microfibril scale all the way up to the macroscopic scale. The model is employed here to investigate the thermo-mechanical response of radiata pine grown in Chile. To determine values of the microstructural parameters that yield macroscopic properties consistent with those observed experimentally, a parameter identification strategy is proposed. The latter considers four elements: an existing experimental database on timber boards density and bending tests, the multiscale model, a timber board bending test finite element model and a genetic algorithm for the optimization procedure. With the resulting microstructural parameters the model is then used to estimate the effective elastic, thermal, and thermo-mechanical properties of radiata pine wood. When compared with measured experimental data and typical experimental values found in the literature, the numerical estimates demonstrate the model predicting capabilities.

Size-dependent vibration analysis of fluid-infiltrated porous curved microbeams integrated with reinforced functionally graded graphene platelets face sheets considering thickness stretching effect

Size-dependent vibration analysis of three-layered fluid-infiltrated porous curved microbeams, which are integrated with nanocomposite face sheets, is provided in this work. The effect of the fluids within the pores of the core is taken into consideration and the core’s thermomechanical properties vary across the thickness based on three different patterns. Also, the face sheets are made from epoxy, which are reinforced by graphene platelets as lightweight and high-stiffness reinforcements. Graphene platelets dispersion patterns are also considered, which obey three different functions, namely parabolic, linear, and uniform. Moreover, effective thermomechanical properties of the face sheets are determined with the aid of ERM and Halpin–Tsai micromechanical models. The microstructure is under thermal load and it is rested on Pasternak elastic foundation. In the polar coordinate system, the strains are determined for deep curved beams that lead to more accurate results. Based on a refined higher-order shear deformation theory, which includes four variables and considers the thickness stretching effect, and employing the modified couple stress theory for accounting the size effect, the differential motion equations are derived and via an analytical method, they are solved. A verification study is conducted by neglecting some parameters and after that, the results are presented and discussed in detail. It is seen that the porous core and nanocomposite face sheets material properties have significant effects on the vibrational response of the under consideration model. Up to now, no similar work in the available literature has been found, therefore, the results of this study can be considered as a benchmark for future ones. The outcomes of this study may help to design more efficient structures with the desired properties.

A two-dimensional random aggregate structure generation method: Determining effective thermo-mechanical properties of asphalt concrete

This study presents a 2D random aggregate structure generation algorithm for asphalt concrete. It involves two steps: first, the “convex-concave surface method” is proposed to generate random aggregate particles; second, the “double background grid method” is developed to place the generated aggregates and form the asphalt concrete mesostructure. The convex-concave surface method can produce aggregate particles randomly with both irregular convex and concave surfaces, enabling the generated aggregates to look realistic. Very few parameters are required during the particle generation, significantly simplifying the operation of input parameters. The double background grid method employs two types of background grids: the coarse grids are used to determine the placing position of the particle, whereas the fine grids are used to inspect if the particle overlaps with the placed ones; in this way, it effectively improves the placing efficiency. Besides, it allows for a predefined minimum gap between the adjacent particles, successfully guaranteeing the quality of finite element meshing. Based on the developed 2D random aggregate structure of asphalt concrete, a unified computational methodology for determining the effective thermo-mechanical properties is presented. The effectiveness of these methods is demonstrated using experimental data and typical values reported in the literature.

Predicting the overall response of an orthogonal 3D woven composite using simulated and tomography-derived geometry

Effects of two meso-scale geometry generation approaches on predicting effective elastic properties and thermal conductivity of an orthogonal 3D woven composite are studied in this paper. The two approaches used are fabric mechanics simulation (DFMA software, Kansas State University) and direct processing of X-ray microtomography (µCT) data. Two models are created in DFMA using two different sets of cross-sectional areas as input: nominal (based on the initial weave pattern) and adjusted (informed by volume fraction measurements obtained from microscopy data). In addition, one conformal mesh and three voxel mesh models are created from µCT data. Experimental measurements of transverse Young’s moduli are used to evaluate the accuracy of the predicted results.In each case, a unit cell with in-plane periodic boundary conditions is modeled, which has not been previously done in the case of µCT-based models. The effect of high frequency oscillations in local material orientations imparted by a wavy centerline (artifact of µCT image processing) on the elastic and thermal conductivity properties is studied. The differences in volume fractions and shapes of bundles of fibers (tows) between µCT-based and DFMA-based models are also investigated to determine sensitivity of effective thermo-mechanical properties to each of these factors.

Multiscale stochastic computational homogenization of the thermomechanical properties of woven Cf/SiCm composites

This paper demonstrates a set of two-scale asymptotic computational homogenization formalisms of Cf/SiCm thermomechanical properties and proposes a 3D micro-to-mesoscale stochastic bridging methodology considering the uncertainties of the constituents’ properties and geometries. For multiscale thermomechanical analyses, the thermal conductivity (TC), the coefficient of thermal expansion (CTE) and the elastic stiffness (ES) properties are homogenized at the microscale within the fiber tow. The proposed consistent multiscale bridging method models spatial random fields using the three-dimensional Karhunen-Loève (KL) expansion method with integration with a 3D FE-based computational homogenization model. We compare effects of two different uncertainties (i.e., geometric and spatial material randomness) to statistical variations of the effective thermomechanical properties at the microscale. By comparing with threshold COV values, we determine the thermomechanical properties to be modeled as random fields. At the mesoscale RVEs, we randomize the key twelve thermomechanical properties, perform two-scale computational homogenization and draw statistical variations at the mesoscale.

Thermo-mechanical bending of architected functionally graded cellular beams

This article investigates the effect of cell architecture on the bending behavior of architected cellular beams subjected to a thermo-mechanical load. The architected functionally graded cellular (FGC) beam is made of porous cells whose properties vary across the thickness or length of the beam. The FGC beam is modeled according to Reddy's third-order shear deformation theory (TSDT), and the effective thermo-mechanical properties are obtained by standard mechanics homogenization. The governing equations are solved by a finite element method, and deflection curves are presented for the architected cellular beams with relative density gradients, subjected to thermal and mechanical loads. Numerical results demonstrate that tailoring relative density through the thickness of an FGC beam can reduce the lateral deflection of lightweight beams to less than half; consequently, tuning the flexural stiffness of cellular structures without changing their total weight. Interestingly, numerical results reveal that the flexural deformation of an FGC beam subjected to a thermo-mechanical load can be controlled by means of the variation function of cell architectures. We also present the optimized architectural variation and cell topologies leading to the least flexible architected cellular beams for alternative thermo-mechanical loading conditions. This paper sheds light on the application of cellular-based mechanical metamaterials for programming the multifunctional behavior of lightweight meta-structures.

Thermoelastic analysis of FG-GPLRC spherical shells under thermo-mechanical loadings based on Lord-Shulman theory

The transient thermoelastic behavior of functionally graded graphene platelets reinforced composite (FG-GPLRC) spherical shells under thermo-mechanical loadings is studied based on the Lord-Shulman thermoelasticity theory, which includes the coupled as well as the nonlinear terms. The problem formulation is so prepared that both types of commonly used FG-GPLRC in the literature (i.e., multilayer FG-GPLRC, for which the material properties vary in a layerwise or piecewise continuous manner and those with continuously varying material properties) can be analyzed. The modified Halpin-Tsai micromechanical model, rule of mixture and a newly introduced micromechanical model are employed to estimate the effective thermo-mechanical properties of FG-GPLRC shells. The governing equations are discretized in the spatial domain using the layerwise differential quadrature method (LW-DQM). Then, a novel multi-step time integration scheme based on non-uniform rational B-spline (NURBS) in conjunction with Newton-Raphson algorithm are employed to solve the resulting system of nonlinear ordinary differential equations iteratively. In addition, the Laplace transform is employed to obtain the solution in the time domain. The method is validated by performing the convergence study and comparing the obtained results with available solutions in the limit cases. Afterward, the effects of the GPL distribution pattern, GPLs weight fraction and dimensions ratios, the shell thickness-to-outer radius ratio and suddenly applied thermo-mechanical loadings on the thermoelastic behavior of FG-GPLRC spherical shells are investigated. The results show that adding a very small amount of GPLs into polymer matrix significantly increase the shell stiffness and heat wave speed, and considerably changes the temperature and displacement distributions of the FG-GPLRC spherical shells.

Coupled Thermo-mechanical Behavior of Weakening Geo-Materials

In this paper, the overall effective thermo-mechanical properties of limestone samples are estimated using a micro–macro mechanical approach. A mathematical framework is proposed to estimate the overall properties based on local geometrical considerations using Mori–Tanaka’s scheme. In addition, a homogenization-based mathematical formulation is proposed to predict the effective thermal conductivity of composite materials subjected to periodic micro-scale heat fluxes and governed by Fourier’s law and steady state balance equations. Moreover, Coussy’s approach is used to derive the expression of heat capacity. In order to take into account the degradation of heterogeneous rock materials, a damage based numerical model that uses the homogenized thermo-mechanical properties and Griffith’s criterion is proposed. The model is implemented as an external user material subroutine to the multi-purpose finite element software Abaqus, to assess the damage of a limestone rock sample under normal percussion drilling conditions. Moreover, a model parameter identification procedure is performed to calibrate the necessary parameters using a simple indentation test. The obtained results show that the numerical model can reproduce the elastic damaged behavior of rocks, such as limestone, subjected to a simple indentation that mimic the conditions of rock drilling. Finally, the proposed analysis proves that effect of temperature on the overall behavior of limestone can be investigated using multi-physics upscaling.

A numerical homogenization of E-glass/acrylic woven composite laminates: Application to low velocity impact

For recyclability purposes, an acrylic resin (Elium 150) has been recently developed for the elaboration of laminated composites at room temperature. This new resin is endowed with some interesting mechanical properties that allow it to replace some epoxies in some industrials applications where a high strength is required. In this paper, the Mechanics of Structure Genome (MSG) and a finite element based micromechanics approaches were conducted to evaluate the effective thermomechanical properties of a plane woven glass fiber/acrylic resin composite laminate. Through a two-step and the asymptotic homogenization approach, the present investigation aims to predict the elastic properties of the glass fiber/Acrylic resin laminated composites. Prior to numerical simulations, some experimental observations have been performed on the laminate samples in order to accurately represent the geometry of a periodic representative volume element (RVE). The obtained numerical results were compared with those issued from some previous experimental investigations on laminated composites. A satisfactory agreement was observed between the numerical predictions and experimental data. In order to test the relevance of the proposed numerical procedure, the effects of the strain rate and the temperature on the predicted results were then discussed. Finally, a finite element model has been implemented for the simulation of low velocity impacts on the studied laminated composite.

Micromechanical Constitutive Equations for the Effective Thermoelastic Properties of Carbon Nanotube-Reinforced Composites

Predicting thermomechanical properties of composites containing carbon nanotubes (CNTs) is significantly depending on the assumed microstructural parameters (MSPs) of CNTs and CNT/matrix morphology. These MSPs include geometry, dispersion and orientation. On the other hand, CNT/matrix morphology refers to two microstructural observations. The first is whether or not an interphase exists between CNTs and matrix, whereas the second is whether or not voids exist due to, for example, debonding of CNTs. In this work, the aim is to propose micromechanical constitutive equations, which are based on the micromechanics principles of Eshelby and Mori-Tanaka models, for considering all of these MSPs altogether in addition to the other well-known MSPs. Accordingly, these equations can be used for modeling realistic nanocomposites to predict their effective thermomechanical properties in different directions. The obtained computational results are compared with other results of both experimental and theoretical investigations found in the literature, and good agreement is obtained.

Modeling of thermomechanical properties of polymeric hybrid nanocomposites

This article reports modeling of effective thermomechanical properties of multifunctional carbon nanotube (CNT)‐reinforced hybrid polymeric composites (hereafter, it is referred as “fuzzy fiber composite”). The novel constructional feature of fuzzy fiber composite (FFC) is that nanoscale CNTs are radially grown on the circumferential surfaces of microscale carbon fibers. Several micromechanical models were developed to predict the effective thermomechanical properties of FFC. The waviness of CNTs is intrinsic to many manufacturing processes and it influences thermomechanical behavior of two‐phase CNT‐reinforced composites. Therefore, an endeavor was also made to investigate the effect of wavy CNTs on the effective thermomechanical properties of FFC. The proposed modeling approach was applied to a heat exchanger made of FFC to determine its effective thermal conductivities. The findings of our study suggest that FFC containing nano‐ and micro‐scale fillers show improved thermomechanical properties and are promising next‐generation polymeric composites for advanced structural applications. POLYM. COMPOS., 39:4148–4164, 2018. © 2017 Society of Plastics Engineers