Thermoviscoelastic Materials Research Articles

The quasi-homogenized Bakhvalov–Eglit model of a thermoviscoelastic material beyond the periodic setting

The one-dimensional model of dynamics of a thermoviscoelastic Kelvin–Voigt material provided with rapidly oscillating initial distributions of specific volume, velocity, and specific internal energy is considered. It is allowed that the rapidly oscillating initial distributions do not have any ordered microstructure: periodic, quasi-periodic, random homogeneous, and so on. We rigorously justify the homogenization procedure as the frequency of rapid oscillations tends to infinity. As the result, we construct a closed limit effective model of a thermoviscoelastic material motion. This model contains an additional kinetic equation that carries complete information on the evolution of the limit oscillation regimes. We show that if the initial data are periodic, then the constructed limit model can be reduced to a system of the classical quasi-homogenized Bakhvalov–Eglit equations.

A thermo-viscoelastic analysis using the eigenvector expansion method

A novel eigenvector expansion method under the symplectic system is introduced for boundary condition problems of thermo-viscoelastic materials. On the basis of the state space formalism and the use of the Laplace integral transform, the general solutions of the governing equations, zero and non-zero-eigenvalue eigenvectors, are obtained analytically. Since the eigenvectors are expressed in concise analytical forms, the adjoint symplectic relation in the Laplace domain is generalized to the time domain. Using this method, various boundary conditions and the particular solution of non-homogeneous governing equations can be conveniently described by combinations of the eigenvectors.

Spatial behavior in the vibrating thermoviscoelastic porous materials

In this paper we study the spatial behavior of the amplitude of the steady-state vibrations in a thermoviscoelastic porous beam. Here we take into account the effects of the viscoelastic and thermal dissipation energies upon the corresponding harmonic vibrations in a right cylinder made of a thermoviscoelastic porous isotropic material. In fact, we prove that the positiveness of the viscoelastic and thermal dissipation energies are sufficient for characterizing the spatial decay and growth properties of the harmonic vibrations in a cylinder.

On the uniqueness and analyticity of solutions in micropolar thermoviscoelasticity

This paper deals with the linear theory of isotropic micropolar thermoviscoelastic materials. When the dissipation is positive definite, we present two uniqueness theorems. The first one requires the extra assumption that some coupling terms vanish; in this case, the instability of solutions is also proved. When the internal energy and the dissipation are both positive definite, we prove the well-posedness of the problem and the analyticity of the solutions. Exponential decay and impossibility of localization are corollaries of the analyticity.

Time harmonic waves in a thermo-viscoelastic material with voids

In the present work, we study the propagation of time harmonic waves in an infinite thermo-viscoelastic material with voids. Four basic waves traveling with distinct speeds are found, out of which, one is a shear wave, and the remaining three are dilatational waves. All the dilatational waves are found to be coupled due to the presence of voids and thermal properties of the material, while the shear wave is found to be uncoupled and travels independently with the speed that exists in a linear viscoelastic medium. The speeds of propagation of all the waves are found to be complex valued and frequency dependent. Reflection phenomena of these waves from a mechanically stress-free and thermally insulated plane boundary of a thermo-viscoelastic half-space with voids have been investigated. Formulae for amplitudes and energy ratios corresponding to various reflected waves have been obtained and are presented in closed form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.

Energy approach for the fatigue of thermoviscoelastic materials: Application to asphalt materials in pavement surface layers

This paper focuses on a study of the dissipated energy approach according to two methods, i.e. cumulative energy and the ratio of dissipated energy. An experimental investigation has been performed, with a double shear cyclic test of asphalt material HMA 0/6 being chosen at a 10Hz frequency, 10°C and 20°C and at various force or displacement loading levels. A comparison between the two fatigue characterization methods shows that cumulative energy yields an intrinsic fatigue law that can be further developed to obtain other relations between different loading modes: displacement or force loading. Thanks to this paper, users are able to define the fatigue law in other loading-controlled modes than those introduced during the tests analyzed to identify fatigue parameters. The possibility is available to obtain a fatigue law independent of loading mode and representative of a real loading evolution in the field.

Investigation of the thermoviscoelastic material behaviour of adhesive bonds close to the glass transition temperature

In the present contribution, a phenomenological material model is presented describing the viscoelastic behaviour of polyurethane bonds under finite deformations. The model includes the temperature dependency of the material behaviour close to the glass transition temperature. Experimentally observed size effects can also be described. It is known from previous investigations that the bonds show an effective behaviour that is influenced by the layer thickness. The physical reason for this behaviour can be found in the formation of boundary layers in the polymer which are located close to the substrate. In these boundary layers, the material behaviour differs from the bulk behaviour. The effective properties of bonds of different thickness are experimentally investigated in isothermal shear tests performed at different temperatures. In order to model the observed effects, a previously developed approach of viscoelasticity is extended including the temperature dependency. Furthermore, a supplementary parameter field is introduced, taking the formation of the boundary layers into account. This field is determined by a partial differential equation in form of a reaction–diffusion equation containing the boundary conditions. The local properties of the polymer are linked to the distribution of this additional field. It is shown that the model parameters can be identified and that the model is able to describe the complex experimentally observed behaviour.

On a Theory of Thermoviscoelastic Materials with Voids

In this paper we extend the theory of elastic materials with voids to the case when the time derivative of the strain tensor and the time derivative of the gradient of the volume fraction are included in the set of independent constitutive variables. First, the basic equations of the nonlinear theory of thermoviscoelastic materials with voids are established. Then, the linearized version of the theory is derived. We establish a uniqueness result and the continuous dependence of solution upon the initial data and supply terms. A solution of the field equations is also presented.

Simulation Strategy of the Final Dimension in the Glass Pressing Process

The simulation of the final dimension in the glass pressing process is presented in this paper, in which the part contraction and mold deformation are considered as important factors. A thermorheologically simple thermoviscoelastic material model is used to calculate the residual stress. The model for the analysis of contraction is proposed based on the theory of shells, as an assembly of flat elements. The numerical model for the mold deformation is based on a three‐dimensional thermoelastic boundary element formulation. Finally, an application example of the picture tube panel is used to verify the presented models and simulation methods.

Modelling of thermo‐viscoelastic material behaviour of polyurethane close to the glass transition temperature

AbstractIn this contribution a viscoelastic elastomer is examined with respect to its thermo‐mechanical behaviour. Therefore uniaxial tension tests and relaxation tests are performed at different constant temperatures up to the glass transition region. Hence an experimental data pool is provided. On the theoretical side a finite viscoelastic and incompressible material model is used and enhanced by temperature dependency in order to model the experimentally observed effects. The material parameters are strategically identified by means of biologic evolution strategies. Thereby it turned out that the investigated material cannot be modelled as a thermo‐rheologically simple material. Quite the contrary, a new ansatz is chosen.

Fracture Mechanics of Composite Solid Rocket Propellant Grains: Material Testing

Following a detailed literature survey on the fracture-mechanics properties of solid rocket propellants, this paper reports on an innovative set of fracture tests performed on a composite solid propellant based on ammonium perchlorate hydroxyl-terminated polybutadiene. After a short summary on standard linear–viscoelastic mechanical characterization, results on both linear–elastic fracture-mechanics (characterized by the fracture toughness KIC) and nonlinear fracture-mechanics (characterized by GF) tests are reported. Test results for linear–elastic fracturemechanics simulations have been obtained usingmiddle-tension specimens. A practical methodology to separate the amount of strain energy lost through viscous processes from other sources is given and provides an effective method to apply the toughness-test validity criteria of the American Society for Testing and Materials E399 norm to propellants and other thermoviscoelastic materials. Measurements to determine the linear fracture-mechanics properties of the propellant have been carried out applying the wedge-splitting test methodology. Master curves for the toughness, the critical crack-opening displacement, and the fracture energy have been generated to correlate test data. Results are coherent with Shapery’s theory of fracture for viscoelastic materials. Results can be used within finite element simulations to assess the safety and integrity of a solid-propellant rocket motor under various loads, such as thermal cycling and ignition, assuming stationary conditions.

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature ϑ, an evolution equation for the phase change parameter χ, including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable u. The main novelty of the model is that the equations for χ and u are coupled in such a way as to take into account the fact that the properties of the viscous and of the elastic parts influence the phase transition phenomenon in different ways. However, this brings about an elliptic degeneracy in the equation for u which needs to be carefully handled.

Modelling of materials with long memory

We deduce the Lagrangian motion and energy conservation equations for thermoviscoelastic materials with long memory and with strongly dependent temperature stresses. For this purpose, the Eulerian conservation equations are written in terms not only of the classical thermodynamical variables such as the deformation gradient and the temperature, but also of an internal variable which gives the viscoplastic history of the material. For these materials, we also obtain some linearized conservation equations. As example of this type of materials we present the Maxwell–Norton ones.

Analysis of a nonlinear degenerating PDE system for phase transitions in thermoviscoelastic materials

We address the analysis of a nonlinear and degenerating PDE system, proposed by M. Frémond for modelling phase transitions in viscoelastic materials subject to thermal effects. The system features an internal energy balance equation, governing the evolution of the absolute temperature ϑ, an evolution equation for the phase change parameter χ, and a stress–strain relation for the displacement variable u. The main novelty of the model is that the equations for χ and u are coupled in such a way as to take into account the fact that the properties of the viscous and of the elastic parts influence the phase transition phenomenon in different ways. However, this brings about an elliptic degeneracy in the equation for u which needs to be carefully handled. In this paper, we first prove a local (in time) well-posedness result for (a suitable initial–boundary value problem for) the above mentioned PDE system, in the (spatially) three-dimensional setting. Secondly, we restrict to the one-dimensional case, in which, for the same initial–boundary value problem, we indeed obtain a global well-posedness theorem.

Well-posedness results for a model of damage in thermoviscoelastic materials

This paper deals with a phase transitions model describing the evolution of damage in thermoviscoelastic materials. The resulting system is highly non-linear, mainly due to the presence of quadratic dissipative terms and non-smooth constraints on the variables. Existence and uniqueness of a solution are proved, as well as regularity results, on a suitable finite time interval.

Dynamic deformation of a thermoviscoelastic rod of triangular cross section in a coupled formulation

For the coupled model of a thermoviscoelastic rod of equilateral triangular cross section, two exact solutions are obtained for the cases where a normal displacement and a shear stress or a tangential displacement and a normal stress are specified on the lateral surface of the rod. A dimensionless parameter R0 is introduced to judge the appropriateness of taking into account the coupling in the formulation of the problem. Formulas are given for the velocities and lengths of the temperature, shear, and longitudinal waves, which can be used in experiments to determine the physical properties of thermoviscoelastic materials.

Prediction of Fracture Initiation in Thermo-Viscoelastic Material

In this study, we propose a method to predict fracture initiation time for thermo-viscoelastic material by using master curves of stress intensity factors and fracture toughness, which are derived according to the time-temperature equivalence principle. As a concrete example, we analyzed a problem concerning a thermo-viscoelastic cylinder with a crack under steady or transient-isothermal temperature and crack length conditions. We show the process for predicting fracture initiation time. Based on the analysis results, we conclude that this method is useful for estimating crack propagation and is also available to solve various fracture problems dealing with thermo-viscoelastic materials.

Modeling and simulation of residual stresses during glass bulb pressing process

The residual stresses accumulated in the forming process have great effects on the product quality of the glass bulb. Based on the characteristics analysis of glass bulb forming, a mathematical model has been established for calculating residual stresses of glass pressing process. The material is assumed as thermorheologi-cally simple thermoviscoelastic material, and the flow-induced stress is neglected. The consequences of equilibrium and compatibility equations are discussed in detail, and the boundary conditions are specified for various stages of the forming process. The numerical solution is based on the theory of thin layers, combined with finite difference method in the time and layer difference in the thickness di-rection. The presented model and solution method could easily be extended to general pressing process of glass, and applied to problems relative to glass pressing, providing extensive reference values.

Residual Thermal Stresses Simulation of Television Panel in the Forming Process. Part 1: Modelling

Internal residual stresses in glass-pressed components such as television panel are mainly frozen in thermal stresses because of inhomogeneous cooling when surface layers stiffen sooner than the core region as in free quenching. Additional factors in pressing are the effects of melt pressure history and mechanical restraints of the mould. The solidification of a molten layer of glass between cooled parallel plates is used to model the mechanics of the buildup of residual stresses in the pressing process. Flow effects are neglected, and a thermorheologically simple thermoviscoelastic material model is assumed. The equilibrium thermomechanical properties of the material and the shift function can be temperature- and pressure-dependent. The finite-element method employed in the numerical simulation is based on the theory of shells, as an assembly of flat elements. The approach allows the prediction of residual deformations and residual stresses layer by layer like a truly three-dimensional calculation while reducing the computational cost significantly.

Numerical study of solid propellant grains subjected to unsteady state thermal loading

For an air-to-air missile system, the work environment contains steady and unsteady state thermal loading condition during shipment, storage and firing. Traditionally, the unsteady state thermal loading of solid propellant grains was not considered for simplifying the analytical task, and a steady state thermal loading assumption was analysed for structural integrity. But it does not mean that the unsteady state thermal loading is not useful and could be neglected arbitrarily, and this effect usually plays a very important role for determining the real critical area and obtaining a more reasonable result. In order to simulate the correct failure mode of thermoviscoelastic and incompressible polymer material design, concepts of transient heat transfer, time-temperature shift principle, cumulative damage theory and reduced integration were used. Under unsteady state thermal loading case, transient thermal and structural responses of solid rocket motor could be obtained, and one can see that those are dependent on time and location because of transient thermal loading. Results show that the unsteady state thermal loading case is important for structural integrity of solid propellant grains and improper negligence may obtain the incorrect failure mode and cause structural failure of missile system.