The temperature field induced by the dynamic stresses of a transverse crack in periodically layered composites

The temperature field induced by the dynamic application of a far-field mechanical loading on a periodically layered material with an embedded transverse crack is investigated. To this end, the thermoelastically coupled elastodynamic and energy (heat) equations are solved by combining two approaches. In the first one, the dynamic representative cell method is employed for the construction of the time-dependent Green’s functions generated by the displacement jumps along the crack line. This is performed in conjunction with the application of the double finite discrete Fourier transform on the thermomechanically coupled equations. Thus the original problem for the cracked periodic composite is reduced to the problem of a domain with a single period in the transform space. The second approach is based on wave propagation analysis in composites where full thermomechanical coupling in the constituents exists. This analysis is based on the coupled elastodynamic-energy continuum equations where the transformed time-dependent displacement vector and temperature are expressed by second-order expansions, and the elastodynamic and energy equations and the various interfacial and boundary conditions are imposed in the average (integral) sense. The time-dependent thermomechanically coupled field at any observation point in the plane can be obtained by the application of the inverse transform. Results along the crack line as well as the full temperature field are given for cracks of various lengths for Mode I and Mode II deformations. In particular the temperature drops (cooling) at the vicinity of the crack’s tip and the heating zones at its surroundings are generated and discussed.     

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro–macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation.     

Time-dependent response of active composites with thermal, electrical, and mechanical coupling effect

The mechanical and physical properties of materials change with time. This change can be due to the dissipative characteristic of materials like in viscoelastic bodies and/or due to hostile environmental conditions and electromagnetic fields. We study time-dependent response of active fiber reinforced polymer composites, where the polymer constituent undergoes different viscoelastic deformations at different temperatures, and the electro-mechanical and piezoelectric properties of the active fiber vary with temperatures. A micromechanical model is formulated for predicting effective time-dependent response in active fiber composites with thermal, electrical, and mechanical coupling effects. In this micromechanical model limited information on the local field variables in the fiber and matrix constituents can be incorporated in predicting overall performance of active composites. We compare the time-dependent response of active composites determined from the micromechanical model with those obtained by analyzing the composites with microstructural details. Finite element (FE) is used to analyze the composite with microstructural details which allows quantifying variations of field variables in the constituents of the active composites.     

Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

Constitutive relations for the thermomechanical behavior of fiber-reinforced inelastic laminates

The thermomechanical behavior of laminated composites in which every lamina is unidirectional fiber-reinforced thermoinelastic material is determined by a micromechanical analysis followed by a macromechanical one. In the micromechanical analysis, effective constitutive relations are derived for unidirectional fibrous materials in which the matrix and fiber phases are thermoelastic in the linear region and thermoinelastic in the nonlinear region. The derivation is based solely on the material properties of fibers and matrix and amount of reinforcement. By a macromechanics analysis the gross behavior of the laminated composite in stretching and bending deformation is determined. Applications are given for the deformation field developed in cooling and reheating of graphite/aluminium laminated plates.     

Modelling of the Mechanical Properties of Composite Materials at High Temperatures: Part 2. Properties of Unidirectional Composites

In this paper, with the help of the the four-level model developed in Part 1 for charring unidirectional composites at high temperatures, the analytical relations between, on the one hand, thermo-elastic constants and thermostrength of the composite and, on the other hand, thermomechanical characteristics of its fibre and matrix are derived. It is shown that defects in the internal structure of unidirectional composites, such as misalignment and breakage of fibres, surface defects in fibres, cracking and delamination of the matrix, and also the thermal degradation of the properties of the matrix and fibres, define a thermomechanical behaviour of composites at high temperatures. Comparison of the the theoretical calculations and experimental data on thermomechanical behaviour of different polymer composites is conducted.     

形状记忆合金短纤维增强弹塑性基体复合材料的力学行为

基于Eshelby等效夹杂方法和Mori-Tanaka的平均化理论推导了针对SMA短纤维增强弹塑性基体复合材料的细观力学模型。利用此模型,分析了这种复合材料的力学行为,讨论了材料温度、纤维体积分数和纤维特征形状等参数对复合材料残余应力和残余应变的影响。这对复合材料的分析和设计都有重要的意义。      

Micromechanical parameters from macromechanical measurements on glass reinforced polypropylene

In recent years many elegant techniques have been developed for the quantification of composite micromechanical parameters. Unfortunately most of these techniques have found little enthusiastic support in the industrial product development environment. We have developed an improved method for obtaining the micromechanical parameters, interfacial shear strength, fibre orientation factor, and fibre stress at composite failure using input data from macromechanical tests. In this paper we explore this method through its application to injection moulded glass-fibre-reinforced thermoplastic composites. We have measured the mechanical properties and residual fibre length distributions of glass fibre reinforced polypropylene containing different levels of glass fibre. The level of fibre-matrix interaction in these composites was varied by the addition of maleic anhydride modified polypropylene “coupling agent”. This data was used as input for the model. The trends observed for the resultant micromechanical parameters obtained by this method were in good agreement with values obtained by other methods. Given the wealth of microstructural information obtained from this macroscopic analysis and the low level of resources employed to obtain the data we believe that this method deserves further investigation as a screening tool in composite system development programmes.     

Micromechanical model of 3D cross-ply copper matrix composite reinforced with SiC fibres

A 3D cross-ply micromechanical model is used to analyse the thermomechanical behaviour of copper matrix composite reinforced with SiC fibres, when subjected to cyclic loadings at high temperature. The copper matrix composite is reinforced with 45% fibre volume fraction. A cohesive model is employed to capture the influence of the debonding interface in the composite, during the consolidation and subsequent thermal and mechanical loading.     

A micromechanical model for the mechanical degradation of natural fiber reinforced composites induced by moisture absorption

This paper develops a micromechanical model to study the mechanical degradation of natural fiber reinforced composites (NFRCs) induced by moisture absorption. Since the moisture absorption and the mechanical degradation of the composite are correlated, a modified Mori–Tanaka method with a damage variable is proposed. A set of micromechanical equations are established to describe the modulus loss of NFRCs. After specifying this model with different inclusion shapes, the overall swelling deformation and the mechanical degradation of the randomly oriented and the unidirectional straight natural fiber reinforced composites are studied in detail. Theoretical predicted results of the randomly oriented straight fiber reinforced composite are compared with experimental ones from literature and a good agreement is obtained. Further numerical results demonstrate that a stiffer matrix can reduce both the moisture absorption and the mechanical degradation of natural fibers.     

Continuum Models for the Thermomechanical Behavior of Discontinuously Reinforced Materials

Continuum micromechanical models have become important tools for understanding the thermomechanical behavior of composite materials. This work presents the most important continuum‐level approaches for modeling the thermomechanical behavior of discontinuously reinforced composites. Analytical and numerical models are covered, special emphasis being put on multi‐inclusion unit cell methods. The fields of application of the different models are discussed and selected applications are demonstrated.     

A coupled thermomechanical nonordinary state‐based peridynamics for thermally induced cracking of rocks

A novel coupled thermo‐mechanical nonordinary state‐based peridynamics is proposed to study thermally induced damage in rocks. The thermal expansion characteristics of solid material are introduced into the coupled thermomechanical model to consider the influence of temperature. The deformation gradient tensor is obtained by the temperature fields, which is solved by peridynamic heat conduction theory. By introducing the deformation gradient tensor into the force state function of the nonordinary state‐based peridynamics, the coupling of thermal and mechanical is realized. A failure criterion is developed to investigate the thermally induced cracking of rocks. Then, the validity of the coupled thermo‐mechanical model is demonstrated by a numerical simulation. The correctness of the coupled model is validated by a benchmark example with analytic solution. Moreover, the thermal cracking progress in rocks is simulated using the proposed coupled nonordinary state‐based peridynamic model, and it is found that the numerical results are in good agreement with the previous experimental observations.     

Effect of fiber arrangement on shape fixity and shape recovery in thermally activated shape memory polymer-based composites

In the present study, we conducted periodic-cell simulations of the thermomechanical cycle of thermally activated shape memory polymer (SMP)-based composites. The present simulation utilizes a micromechanical model for reproducing the discontinuous fibers and SMP. We analyzed the effect of fiber volume fraction, fiber aspect ratio, and fiber end position on the shape fixity and shape recovery of the composite. The simulated results revealed that fiber elasticity is a key factor for the shape fixity of the composite, while both strain concentration near the fiber ends and fiber elasticity play important roles in the shape recovery properties of the composite.     

Effect of moisture absorption on the mechanical behavior of carbon fiber/epoxy matrix composites

A carbon fiber/epoxy unidirectional laminated composite was exposed to a humid environment and the effect of moisture absorption on the mechanical properties and failure modes was investigated. The composites were exposed to three humidity conditions, namely, 25, 55, and 95 % at a constant temperature of 25 °C. The carbon fiber–epoxy laminated composites for two different carbon fiber surface treatments were used. The results showed that the mechanical properties differ considerably for each fiber surface treatment. The application of a coupling agent enhanced the fiber-matrix adhesion and reduced dependence of the properties on humidity. The damage mechanism observed at micromechanical level was correlated to acoustic emission signals from both laminated composites. The untreated carbon fiber failure mode was attributed to fiber-matrix interfacial failure and for the silane-treated carbon fiber reinforced epoxy laminate attributed to matrix yielding followed by fiber failure with no signs of fiber-matrix interface failure for moisture contents up to 1.89 %.     

Phenomenological description of thermomechanical behavior of shape memory alloy

On the basis of a thermomechanical phenomenological model, we analyze the thermomechanical behavior of polycrystalline NiTi. Pseudoelastic response and strain-temperature response under fixed stress are studied by using finite element simulation. Calculated mechanical and thermal hysteresis behaviors of NiTi sheet are in good agreement with those observed experimentally. Hardening in stress–strain hysteresis loop and sharp change of strain in strain-temperature hysteresis loop are described by numerical simulation. The result from thermomechanically coupled calculation shows the phenomenon that phase transition occurs by nucleation and propagation of transformation fronts.     

Classical estimates of the effective thermoelastic properties of copper–graphene composites

Significant research effort is concentrated worldwide on development of graphene-based metal-matrix composites with enhanced thermomechanical properties. In this work, we apply two classical micromechanical mean-field theories to estimate the effective thermoelastic properties that can be achieved in practice for a copper–graphene composite. In the modelling, graphene is treated as an anisotropic material, and the effect of its out-of-plane properties, which are less recognized than the in-plane properties, is studied in detail. To address the severe difficulties in processing of graphene-based metal-matrix composites, the copper–graphene composite is here assumed to additionally contain, due to imperfect processing, particles of graphite and voids. It is shown quantitatively that the related imperfections may significantly reduce the expected enhancement of the effective properties. The present predictions are also compared to the experimental data available in the literature.     

A new method for evaluation of mechanical properties of glass/epoxy composites at low temperatures

The analytical models based on micromechanical properties of composites are applied to predict the behavior of unidirectional (UD) composite under different types of loadings at room temperature and -60°C. In this study, unlike conventional methods which characterize UD composite via experimental tests on UD specimens under tensile, compressive and shear loadings, micromechanical properties of glass fiber and epoxy matrix at room temperature and -60°C are measured. Then by using various analytical models four elastic moduli and strengths at room temperature and -60°C are calculated. To investigate the validity of the results, experimental tests are performed and compared with analytical results. Results show that elasticity model is the best analytical method to predict four elastic moduli at room temperature and -60°C. Good fits are also found between experimental and analytical results for composite mechanical properties at the room temperature and -60°C.     

Effective thermal properties of viscoelastic composites having field-dependent constituent properties

This study introduces a micromechanical model for predicting effective thermal properties (linear coefficient of thermal expansion and thermal conductivity) of viscoelastic composites having solid spherical particle reinforcements. A representative volume element (RVE) of the composites is modeled by a single particle embedded in the cubic matrix. Periodic boundary conditions are imposed to the RVE. The micromechanical model consists of four particle and matrix subcells. Micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the subcells. Perfect bonds are assumed along the subcell’s interfaces. Stress and temperature-dependent viscoelastic constitutive models are used for the isotropic constituents in the micromechanical model. Thermal properties of the particle and matrix constituents are temperature dependent. The effective coefficient of thermal expansion is derived by satisfying displacement and traction continuity at the interfaces during thermo-viscoelastic deformations. This formulation leads to an effective time–temperature–stress-dependent coefficient of thermal expansion. The effective thermal conductivity is formulated by imposing heat flux and temperature continuity at the subcells’ interfaces. The effective thermal properties obtained from the micromechanical model are compared with analytical solutions and experimental data available in the literature. Finally, parametric studies are also performed to investigate the effects of nonlinear thermal and mechanical properties of each constituent on the overall thermal properties of the composite.     

Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

A computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two‐phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two‐phase framework is cast within a self‐consistent iterative scheme that acts as a first‐order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar‐based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non‐uniform rational B‐spline basis functions. Overall, the two‐phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures. Copyright © 2013 John Wiley & Sons, Ltd.     

Coupled thermomechanical analysis of transformation-induced plasticity in multiphase steels

The thermomechanical response of low-alloyed multiphase steels assisted by transformation-induced plasticity (TRIP steels) is analyzed taking into account the coupling between the thermal and mechanical fields. The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation that occurs during mechanical loading is accompanied by the release of a considerable amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The internal generation of heat associated with the martensitic phase transformation and the plastic deformation are modeled explicitly in the balance of energy. The momentum and energy equations are solved simultaneously by using a fully-implicit numerical scheme. The simulations are conducted using a micromechanical formulation for single crystals of austenite and ferrite. The characteristics of the model are illustrated by means of simulations for a single crystal of austenite and an aggregate of austenitic and ferritic grains. For a single crystal of austenite, it is found that the increase in local temperature due to transformation actually hinders further transformation and, instead, promotes plastic deformation. However, for an aggregate of austenitic and ferritic grains in a multiphase steel, the increase in temperature due to transformation is limited since the heat generated in the austenite is conducted to the ferritic matrix, effectively lowering the temperature in the austenitic phase.