Thermoviscoelastic Response Research Articles

Thermo-mechanical behavior of elastomers with dynamic covalent bonds

Natural and synthetic rubbers (networks of polymer chains connected by irreversible chemical cross-links) cannot be repaired after damage, while discarded rubbers cannot be economically recycled and reprocessed. To avoid this shortcoming, a number of elastomers with dynamic covalent bonds have recently been synthesized that demonstrate recyclability, malleability and capability of autonomous self-healing due to thermally triggered bond-exchange reactions.A constitutive model is developed for the thermo-viscoelastic and thermo-viscoplastic responses of elastomers whose chains are bridged by adaptive bonds with the associative mechanism of rearrangement. Material parameters in the governing equations are determined by fitting observations in tensile tests, cyclic tests, relaxation tests and creep tests in a wide range of temperatures on covalently cross-linked rubber, thermoplastic elastomer, several elastomers and elastomer nanocomposites with dynamic covalent bonds, and epoxy vitrimers. Characteristic features are discussed of the thermo-mechanical behavior of elastomers with dynamic bonds and structure–property relations are established for these materials.

Thermo-viscoelastic analysis of biological tissue during hyperthermia treatment

Although viscoelastic properties of biological tissue has been reported in many articles, no effort has been made to investigate the coupled thermal and mechanical behavior of biological tissue based on the viscoelastic theory. This provides us a motivation to study the transient thermoelastic coupling response in the context of generalized thermo-viscoelastic model. The dual phase lag thermo-viscoelastic model is established to capture the micro-scale responses of biological tissue. The governing equations are solved by Laplace transformation. The effects of relaxation times and viscoelastic property on the responses of the tumor and normal tissues are discussed and illustrated graphically. According to the numerical results, we can obtain (1) the viscoelastic parameter has a significant effect on the distributions of displacement and stress; (2) the lagging thermo-viscoelastic responses depend not only on the ratio of τt/τq, but also on the absolute values of τt and τq.

Thermoviscoelastic response of an axially loaded beam under laser excitation and resting on Winkler’s foundation

PurposeThe purpose of this paper is to investigate the response of viscoelastic beam resting on a Winkler’s foundation and subjected to an axial initial stress, thermal load and an ultra-fast laser heating.Design/methodology/approachIn this introduced model, the authors considered the interaction design between the vertical springs only. The beam is considered as an Euler–Bernoulli beam exposed to sinusoidal varying heat.FindingsThe deflection and the temperature response of the beam are obtained using Laplace transform and its numerical inversion method. In the numerical example, the effect of the laser pulse duration and viscous damping coefficient on the transverse displacement response of the beam is discussed. The thermoelastic interactions of the beam due to the axial load are also illustrated.Originality/valuePhysical views of this paper may be useful for the design and vibration analysis of micro-resonators and micro-sensors applications. In addition, the utilization of laser-ultrasonic technology has found wide applications in lab environments, and in an expanding number of cases, it is extending to the industrial field and realm application.

Generalized thermoviscoelastic analysis with fractional order strain in a thick viscoelastic plate of infinite extent

Viscoelastic materials (e.g. rubber, resin, concrete skeleton, etc.) serve as one of the most promising candidate for new multifunctional materials due to their excellent rheological properties, as they are widely used in biology, petroleum industry, chemical and civil engineering, and other areas. The interaction of high-heat-flux loads (e.g. ultrafast pulsed lasers) with viscoelastic materials is a hot topic of numerous theoretical and experimental studies. Nevertheless, classical and extended generalized thermoviscoelasticity models available in literatures cannot characterize the strain relaxation behavior for viscoelastic materials. In this work, the time-based fractional thermoviscoelasticity model is further extended with a new consideration of fractional order strain. The governing equations involving strain and thermal relaxation times as well as fractional order parameters of strain and heat flux are formulated and are also applied to investigate thermal shock problem of a transient heated thick viscoelastic plate of infinite extent. With the aids of Laplace transformation methods, the transient solutions are also obtained. Finally, the effects of fractional order parameters of strain and heat flux on the transient thermoviscoelastic responses are studied and discussed.

Thermo-mechanical coupling of a viscoelastic-viscoplastic model for thermoplastic polymers: Thermodynamical derivation and experimental assessment

In this paper, a new constitutive model is proposed for the behavior of thermoplastic polymers under non-isothermal conditions. The model couples linear viscoelasticity, viscoplasticity and thermal effects. It is formulated within the framework of irreversible thermodynamics. The total strain is the sum of viscoelastic, viscoplastic and thermal strains. General hereditary integrals describe the thermo-viscoelastic response. The viscoplastic part accounts for both isotropic and kinematic hardenings. The stress-strain response and the material self-heating are predicted and compared to experimental data on Polyamide 66 (PA66) and Polypropylene (PP). Good agreement between the numerical simulations and experimental data was obtained for the two materials.

Thermo-viscoelastic response of a cracked, functionally graded half-plane under a thermal shock

In this paper, a thermo-viscoelastic model is developed for the crack problem in an infinite, functionally graded half plane under a thermal shock. The moduli are assumed to be separable forms of both spatial coordinates and time, and two types of relaxation function of viscoelasticity are considered in this paper. By employing the Fourier transform and Laplace transform, coupled with the singular integral equations, the governing partial differential equations under mixed thermo-mechanical boundary conditions are solved numerically. The results show that the variations of stress intensity factors (SIFs) in viscoelastic functionally graded materials (FGMs) are significantly different than those in the elastic ones, which cannot be neglected in designing FGMs.

A magneto-thermo-viscoelastic problem with fractional order strain under GN-II model

In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magneto-thermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation.

Thermoviscoelastic dynamic response for a rectangular steel plate under laser processing

The thermoviscoelastic dynamic response of a simply supported rectangular steel plate under laser processing is studied in this paper. Three-dimensional transient temperature field of the laser processing thermoviscoelastic rectangular steel plate is solved by the method of separation of variables. Meanwhile, based on von Karman nonlinear strain–displacement relationships and classical thin plate theory, a list of nonlinear dynamic equilibrium equations for a rectangular thermoviscoelastic steel plate are deduced. Then the entire problem is solved by utilizing the Newmark method and the iterative method. Finally, numerical results show that laser moving speed, laser power density and thickness-to-length ratio have a great influence on the thermoviscoelastic response of the rectangular DP980 steel plate.

Thermo-viscoelastic analysis of GLARE

Abstract In this paper, the study of residual stresses in Fibre Metal Laminates (FMLs) is improved using a thermo-viscoelastic model developed for composites which have an orthotropic viscoelastic response. Prepreg layers of GLARE consist of epoxy adhesive that has temperature dependent and viscoelastic response in thermal environments such as the curing cycle. Thermal and viscoelastic response of the adhesive is already characterised using thermo-mechanical methods. In order to get the response for unidirectional fibre-epoxy composite (prepreg) layers, the Correspondence principle is utilised with self-consistent micromechanics equations in the Laplace domain. By reverting, the thermo-viscoelastic response of the composite layer is obtained in the time domain. A user defined material model is added to ANSYS able to analyse the orthotropic thermo-viscoelastic behaviour. Using the developed model, residual stresses of GLARE are calculated. Comparison to the curvature measurements of manufactured non-symmetric laminates, shows the accuracy of the modelling and the improvements with respect to the thermo-elastic analyses.

A new procedure for thermo-viscoelastic modelling of composites with general orthotropy and geometry

In this paper, a solution procedure is presented for thermo-viscoelastic analysis of composites in a general form which can be used for general orthotropic materials with simple flat to complicated geometries with thickness change and curvature. Small deformation problems in which the prediction of thermal stresses and/or deformations is of interest, are considered. The incremental solution already available in FE packages is extended to the orthotropic case using available formulations in the literature, making it more general in the sense of having different relaxations in each orthogonal direction. Only the viscoelastic response of the polymeric part of the material should be obtained as input and characterisation tests on the composite material are not needed. The linear orthotropic viscoelastic response of the composite layer is obtained using self-consistent micromechanics equations in the Laplace domain. The material model is implemented in the ANSYS subroutine to define the time-dependent thermo-viscoelastic response of the composite layer. Numerical results are presented which verify the accuracy and applicability of the modelling procedure. The proposed approach can be used later for the residual stress analysis of anisotropic materials including full composites and also complex fuselage panels made of hybrid Fibre Metal Laminates (FMLs).

Three-Dimensional Microstructural Modeling Framework for Dense-Graded Asphalt Concrete Using a Coupled Viscoelastic, Viscoplastic, and Viscodamage Model

This paper presents a three-dimensional (3D) image-based microstructural computational modeling framework to predict the thermoviscoelastic, thermoviscoplastic, and thermoviscodamage response of asphalt concrete. X-ray computed tomography is used to scan dense-graded asphalt concrete (DGA) to obtain slices and planar images, from which the 3D microstructure is reconstructed. Image process- ing techniques are used to enhance the quality of images in terms of phase identification and separation of particles. This microstructure is divided into two phases: aggregate and matrix. The aggregate phase is modeled as an elastic material and the matrix phase is modeled as a thermoviscoelastic, thermoviscoplastic, and thermodamage material. Stress-strain response, damage propagation, and the distributions of the viscoelastic and viscoplastic strains are predicted by performing virtual uniaxial and repeated creep-recovery tests of the developed 3D model of asphalt concrete. The effects of loading rate, temperature, and loading type on the thermomechanical response of asphalt concrete are investigated. In addition, the microscopic and macroscopic responses of DGA are compared with those of stone matrix asphalt (SMA). The results demonstrate that SMA can sustain higher strain levels at the microscopic level and higher macroscopic ultimate strength. The damage in SMA is more localized than in DGA. The microstructure-based framework presented in this paper can be used to offer insight on the influence of the distribution and properties of microscopic constituents on the macroscopic behavior of asphalt concrete. DOI: 10.1061/ (ASCE)MT.1943-5533.0000860. © 2014 American Society of Civil Engineers. Author keywords: X-ray computed tomography; Three-dimensional microstructure; Finite element method; Dense-graded asphalt concrete; Damage mechanics.

An implicit thermomechanical theory based on a Gibbs potential formulation for describing the response of thermoviscoelastic solids

The aim of this paper is to develop an implicit constitutive for the thermoviscoelastic behavior of polymers, based on a thermomechanical framework. The core idea is to assume that the response of the material can be modeled as that of multiple superposed networks whose stresses are additive. The thermomechanical response is then developed based on the Gibbs potential of the networks (which is assumed to be a function of the individual network stresses and the temperature) and a rate of dissipation function. The approach results in a set of implicit rate equations for the stresses (without the need for explicitly postulating viscoelastic or inelastic strain as a primitive variable) that is easily amenable to analysis. We demonstrate how certain “internal clock” models as well as anisotropic integral type models can be derived within the context of such an approach. We compare the predictions of the model with the published experimental results concerning the thermoviscoelastic response of FM 13 Adhesive and demonstrate both the simplicity of the approach as well as the efficacy of the model in predicting the complex behavior of such adhesives.

How to Compare the Frequency Dependent Adiabatic Compressibility with Other Thermoviscoelastic Response Functions

How to Compare the Frequency Dependent Adiabatic Compressibility with Other Thermoviscoelastic Response Functions

Considering Viscoelastic Micromechanics for the Reinforcement of Graphene Polymer Nanocomposites.

There has been much recent work investigating the reinforcement of glassy polymers with nanoparticles, and much excitement has been generated by some apparent synergies that suggest reinforcements greater than expected from elastic bound models. Here we show that it is necessary to consider the thermoviscoelastic response of the polymer matrix in nanocomposites (PNCs) to fully understand the reinforcement of the filler. This is especially so because polymer nanocomposites are frequently used at high fractions of the glass transition temperature Tg, where the time dependence of the polymer is significant. Therefore it is a conceptual error to examine the modulus behavior of PNCs via only elastic micromechanics. When the glass transition temperature increases due to the interactions between reinforcement and polymer, it is more reasonable to use a viscoelastic micromechanics approach to estimate the bounds on modulus behavior of PNCs. Here we use new results for grapheme oxide reinforced poly(ethyl methacrylate) (PEMA) and literature results for reinforced poly(methyl methacrylate) (PMMA) and show that the ultralow loading of graphene oxide raises the Tg of PEMA and PMMA significantly and leads to a large shift of the frequency-temperature properties of the polymer matrix. Our thermoviscoelastic approach shows that apparent extreme reinforcements can be attributed to the changing Tg of the polymer, and the corrected mechanical reinforcement from graphene oxide is much weaker than previously reported.

Mesomechanical modeling of the thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamage response of asphalt concrete

This paper focuses on the meso-scale computational modeling of the thermo-mechanical response of asphalt concrete mixes using for the first time a compressive coupled thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamage constitutive model. Asphalt concrete is represented by two-dimensional images of the microstructure that consist of three phases: aggregate, matrix, and interfacial transmission zone (ITZ). The matrix and ITZ are considered as thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamaged materials, while the aggregate is considered to be elastic. The effects of variation in aggregate shape, distribution, volume fraction, ITZ strength, strain rate, and temperature on the degradation and micro-damage patterns in asphalt concrete are investigated under uniaxial tension, compression, and repeated creep-recovery loading conditions. It is concluded that the aggregate volume fraction and distribution significantly influence the micromechanical response of asphalt concrete. Additionally, the results indicate that the constitutive model presented in this paper can provide a computational tool for predicting the overall macroscopic behavior of asphalt concrete based on the distribution of the microstructure constituents and the properties of these constituents. As such, the results of this computational model can be used to guide the design of asphalt concrete mixtures.

Studying the thermoviscoelastic response of the Redux 312 adhesive—Part 2: Modeling

The aim of this work is to propose a numerical model of a bonded joint that takes into account the thermoviscoelastic response of the adhesive to compute the stress distribution in the adhesive as well as in the adherends. The adhesive is assumed to obey a generalized Maxwell model. The effect of temperature is taken into account by considering that the branches of the model change with temperature. The numerical solution is obtained iteratively. The particular case of the Redux 312 adhesive is then considered as an example. The procedure is applied in various cases exhibiting an increasing complexity. Some significant differences are observed with the usual solution obtained within the framework of elasticity if the effects of both temperature and time are taken into account.

Studying the thermoviscoelastic response of the Redux 312 adhesive—Part 1: Experimental characterization

The aim of this study is to investigate the thermoviscoelastic behaviour of the Redux 312 structural adhesive. Two types of tests are performed on bulk specimens: dynamic tests over a wide range of temperature and stress–relaxation tests for five temperatures ranging between −50 and 70 °C. Dynamic tests clearly show that the shear modulus of the adhesive decreases with temperature. The parameters governing the Maxwell model used to model the viscoelastic properties of the adhesive are identified with the curves obtained with the stress–relaxation tests for the five different temperatures. The procedure used to identify these parameters takes into account the evolution of these parameters with temperature. Results obtained are presented and discussed throughout the paper.

A combined measurement of thermal and mechanical relaxation

In order to describe relaxation the thermodynamic coefficient 1 β S = ( ∂ V ∂ S ) p can be generalized into a complex frequency-dependent cross response function. We explore theoretically the possibility of measuring 1 β S ( ω ) for a supercooled liquid near the glass transition. This is done by placing a thermistor in the middle of the liquid which itself is contained in a spherical piezoelectric shell. The piezoelectric voltage response to a thermal power generated in the thermistor is found to be proportional to 1 β S ( ω ) but factors pertaining to heat diffusion and adiabatic compressibility κ S ( ω) do also intervene. We estimate a measurable piezoelectric voltage of 1 mV to be generated at 1 Hz for a heating power of 0.3 mW. Together with κ S ( ω) and the longitudinal specific heat c l ( ω) which may also be found in the same setup a complete triple of thermoviscoelastic response functions may be determined when supplemented with shear modulus data.

Thermoviscoelastic Analysis and Creep Testing of Ambient Temperature Cure Epoxies Used in Adhesive Anchor Applications

Thermoviscoelastic properties and creep response of two commercial ambient temperature cure epoxy structural adhesives were analyzed and compared. The adhesives were formulated by the same manufacturer and appeared to be chemically similar; however, one system contained accelerators to shorten its cure time. In the laboratory, dynamic mechanical temperature/frequency sweeps were performed on both systems to generate dynamic mechanical and creep compliance master curves using time-temperature superposition principles. Differences were observed in the dynamic mechanical properties of the two adhesive systems as well as in their calculated creep compliance, which have been attributed to differences in their curing agent(s) and accelerator(s). Full-scale creep tests were carried out on anchors installed in concrete slabs and subjected to sustained loads for 82 days. These results were in good agreement with the creep compliance estimated using time-temperature superposition, suggesting that dynamic mechanical...

A micromechanical model for predicting thermal properties and thermo-viscoelastic responses of functionally graded materials

This study introduces a micromechanical model for predicting effective thermo-viscoelastic behaviors of a functionally graded material (FGM). The studied FGM consists of two constituents with varying compositions through the thickness. The microstructure of the FGM is idealized as solid spherical particles spatially distributed in a homogeneous matrix. The mechanical properties of each constituent can vary with temperature and time, while the thermal properties are allowed to change with temperature. The FGM model includes a transition zone where the inclusion and matrix constituents are not well defined. At the transition zone, an interchange between the two constituents as inclusion and matrix takes place such that the maximum inclusion volume contents before and after the transition zone are less than 50%. A micromechanical model is used to determine through-thickness effective thermal conductivity, coefficient of thermal expansion, and time-dependent compliance/stiffness of the FGM. The material properties at the transition zone are assumed to vary linearly between the two properties at the bounds of the transition zone. The micromechanical model is designed to be compatible with finite element (FE) scheme and used to analyze heat conduction and thermo-viscoelastic responses of FGMs. Available experimental data and analytical solutions in the literature are used to verify the thermo-mechanical properties of FGMs. The effects of time and temperature dependent constituent properties on the overall temperature, stress, and displacement fields in the FGM are also examined.