Theory Of Thermoviscoelasticity Research Articles

Numerical Simulation of Glass Imprinting for Molding Temperature Prediction

For optimizing the conditions of glass imprinting, many researchers commonly use the trial-and-error method. Therefore, it is advantageous to carry out a preliminary analysis of glass imprinting. The viscoelastic property of glass is necessary for MEMS-ONE in which a viscoelastic model is used. Assuming glass materials to be viscoelastic boies, the relaxation share modulus was measured by the creep test based on traditional thermo-viscoelastic theory. The Williams–Landel–Ferry (WLF) equation is applied using the temperature dependence of liquid viscosity. We compared experimental results with the analytic results of MEMS-ONE simulation under the conditions of fixed pressure (3.56 MPa) and time (10 min). The object of evaluation is the height of the central position prong. The molding temperature can be predicted within 10 °C error by the simulation.

The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory

In this paper, a model of the generalized thermoviscoelasticity for a saturated porous media is used. Taking the rheological properties of the volume into consideration, it is developed on the basis of the thermo-hydro-elastodynamic model proposed by the authors. The formulation is applied to the generalized porous thermoviscoelasticity theories: coupling theory, Lord–Shulman theory and Green–Lindsay theory. The general characteristic equations for arbitrary coordinate system are derived using a semi-analytical approach in the Laplace domain. Exact solutions of the saturated porous thermoviscoelastic media, with a cylindrical cavity that is subjected to a time dependent thermal load, are obtained in the absence of heat sources. Numerical results are illustrated graphically employing numerical method for inverting the Laplace transform. Comparisons are made with the results predicted by these theories and the classical theory. In addition, the influence of rheological parameters on the thermoviscoelastic property is analyzed.

ガラスマイクロプレス成形に関する数値シミュレーション

In the present paper, some experiments for press molding and numerical simulation about micro press molding of glass devices using finite element method is investigated. Thermo-viscoelastic properties of the glass materials were estimated using unidirectional compression creep test based on traditional thermo viscoelastic theory. In this study, Pyrex and D263 were used as glass materials. Glass micro press molding was carried out with Glass-like Carbon (GC) mold given to Line & Space patterns machined by dicing. The adaptive condition of the molding temperature which given appropriate transcription profile of the glass was investigated. Moreover, numerical simulation for micro press molding of the glass was carried out by finite element method using universal FEM code (ANSYS ver. 11.0). As a result of comparing experimental results with numerical ones, the cross section shape and the height of groove profile obtained by FEM simulation approximately agree with experimental value.

Deliberation of Effect to Glass Imprinting Analysis by Williams-Landel-Ferry Equation

The Mems-ONE is well known software which simulates thermo-viscoelastic properties in the conduct of nanoimprinting. Assuming the glass materials to be viscoelastic body, the relaxation shear modulus was measured by the creep test, Williams-Landel-Ferry (WLF) equation is applied for expressing the temperature dependence of liquid viscosity. We compared experimental with analytic results used by Mems-ONE with the condition of fixed pressure and time. Thermo-viscoelastic properties of the glass materials were estimated using unidirectional compression creep test based on traditional thermo viscoelastic theory. Glass was Borosilicate Glass (D263, Schott). Glass imprinting was carried out on Glassy Carbon (GC) mold with line & space10 μm patterns fabricated by dicing saw. The machining accuracy is most important thing as the evaluation mold. The glass imprinting temperature consulted thermo-viscoelastic properties of the glass materials. The numerical simulation was carried out on the small portion of mold and glass. The constant value of WLF equation fitting in high temperature translates the master curve of D263 with a high degree of accuracy. It caused the accuracy improvement of analysis result. In addition, we confirm that WLF equation intended to resin can use to the glass imprinting.

Numerical Simulation and Press Molding of Glass Micro Devices

Many kinds of optical glass devices are needed in various fields such as optics, biotechnology, medical care and so on. If an optical device such as an aspheric lens does not have a simple shape, and/or its size is micro-/nanometer scale, press molding should be carried out at a higher temperature than the glass transition temperature (Tg) to reduce cost and increase productivity. However, the most suitable conditions for glass molding are generally determined by performing many experiments. Consequently, it is useful to be able to predict the most suitable molding condition by numerical simulation. Press molding experiments and numerical simulation using finite element analysis, in relation to micro press molding of the borosilicate glasses Pyrex and D263, were carried out. Thermo-viscoelastic properties of the glasses were estimated using unidirectional compression creep testing according to traditional thermo-viscoelastic theory. Glass micro press molding was carried out with a glassy carbon die with a line and space pattern machined by a dicing saw. The optimum molding temperatures for accurate transcription of the die profile to the glass were investigated. Numerical simulation of micro press molding of the glass was carried out by the finite element method using universal FEM code (ANSYS ver.11.0). Experimental and numerical simulation results for the cross-section shape and the height of the groove profile were in approximate agreement.

Lp – Lq time decay estimate to the solution of the Cauchy problem for the system of equations describing nonlocal model of the thermoviscoelastic body

AbstractThe aim of this paper is to present a new system of equations describing nonlocal model of thermoviscoelastic theory. We used the Papkin and Gurtin approach based on the constitutive relations for stress tensor σ(x), internal energy e(x) and heat flux q(x), with integral terms. Using the modified Cagniard‐de Hoop's method we constructed the matrix of fundamental solutions for this system of equations in three‐dimensional space. Basing on this matrix we represent in the explicit formula the solution of the Cauchy problem to this system of equations. Next, applying the method of Sobolev spaces, we proved the Lp–Lq time decay estimate to the solution of the Cauchy problem. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermo-Viscoelastic Analysis of Warp for Laminated Body Consisting of Epoxy Resin and Steel with Thermal Deterioration by Thermal Load

The mechanical and thermal properties of epoxy resin used for electronic parts are changed by thermal load in manufacturing processes and prolonged use, and these properties make defective of electronic devices. In this report, warp behavior of a two-layer-laminated body consisting of epoxy resin and steel caused by thermal load were examined from both sides of experiment and theory. As a result, it was clarified that viscoelastic properties of epoxy resin, such as storage modulus, loss modulus, loss tangent and glass transition temperature were changed by thermal load, and that warp behavior could be predicted by thermo-viscoelastic analysis based on linear thermo-viscoelastic theory by using these viscoelastic properties.

Numerical Simulation and Characterization of Press Molding of Thermo-Plastic Resin Reinforced by Carbon Nanofiber

In the present paper, press molding for thermo-plastic resin toughened by carbon nanofiber were discussed. Polycarbonate (PC) and vapor grown carbon nanofiber (VGCF) are used for the resin matrix and the reinforcement. In order to investigate and simulate the process molding process of the PC/VGCF composite by finite element method, the thermo-viscoelastic property of the composites are estimated using unidirectional compression creep test. The creep functions were converted into relaxation function based on the convolution integral form of the basic equation using Laplace transform. Experimental testing for press molding of the PC/VGCF composites using V-shape die has been carried out. The results of the V-shape profiles and those obtained by FEM analysis were compared to confirm the validity of the present analysis method based on thermo-viscoelastic theory. The effect of the carbon nanofiber for the formability improvement of the PC/VGCF composites was discussed in detail.

1225 境界要素解析によるCFRP積層板の冷却過程における熱粘弾性残留応力解析(J10-2 マイクロ・ナノ材料システムの力学と強度・機能評価(2) 熱伝導・粘弾性特性評価,ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

In this study, analysis of residual stress and deformation in CFRP which is anisotropic thermoviscoelasticity is discussed. The analysis is calculated, according to thermoviscoelastic theory which is based on time-temperature superposition, and using Laplace transformation for 2-dimensional and 3-dimensional BEM. Thermoviscoelastic model is approximated by Maxwell model.

Reflection and refraction of thermo-viscoelastic waves at the interface between two micropolar viscoelastic media without energy dissipation

Reflection and refraction of a plane harmonic wave at the interface between two viscoelastic media are studied under generalized thermo-viscoelastic theory. Using potential function, the governing equations reduce to two fourth-order ifferential equations. Coefficient ratios of reflection and refraction of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection and refraction with the angle of incidence are illustrated graphically for aluminium–epoxy and magnesium crystal micropolar viscoelastic materials. Also, the effects of viscous and micropolar elastic are illustrated by numerical results in the theory of thermo-viscoelasticity without energy dissipation. PACS No.: 62.20.Dc

2756 カーボンナノファイバー強化熱可塑性樹脂のプレス成形性評価(S17-2 複合材料(2),S17 複合材料の動向とその加工技術)

In the present paper, press molding for thermo-plastic resin toughened by carbon nanofiber were discussed. Polycarbonate (PC) and vapor grown carbon nanofiber (VGCF) are used for the resin matrix and the reinforcement. In order to investigate and simulate the process molding process of the PC/VGCF composite by finite element method, the constitutive equation, namely thermo-viscoelastic property of the composites are required. The relaxation modulus (Master curve) and shift factor to characterize it's thermo-viscoelastic behavior were estimated by unidirectional compression creep test in this paper. The relaxation modulus for the composite were approximated by the discretized series form using generalized Maxwell model. Demonstrations for press molding using V-shape die has been carried out. Experimental results of the height of the V-shape and those obtained by FEM analysis were comparead and disscussed in detail to confirm the validity of the present numerical method based on thermo-viscoelastic theory.

On the phenomenological representation of curing phenomena in continuum mechanics

To simulate curing phenomena, for example for the purpose of optimising the manufacturing processes or to calculate the stress distribution in adhesive seams, constitutive models representing the thermomechanically-coupled behaviour of adhesives are required. During the curing reaction, the adhesive changes its thermomechanical material behaviour from a viscous fluid to a viscoelastic solid. This phase transition is an exothermal chemical reaction which is accompanied by thermal expansion, chemical shrinkage and changes in temperature. In this essay we develop a physically-based theory of finite strain thermoviscoelasticity to represent these phenomena. To this end, we introduce a multiplicative split of the deformation gradient into a thermal, a chemical and a mechanical part. We define the coordinate of chemical reaction determined by an evolution equation to describe the temporal behaviour of the curing reaction. The free energy of the model contains an additional term, the chemically-stored free energy, which depends on this internal variable. The mechanical behaviour of the adhesive is modelled using a constitutive approach of finite thermoviscoelasticity and the viscosities are functions of the coordinate of chemical reaction. We show that the model is compatible with the Clausius–Duhem inequality, derive the equation of heat conduction and illustrate the physical properties of the theory by a numerical example.

Modelling of length scale effects in viscoelastic materials

A length scale dependent linear viscoelastic constitutive model is developed. First, a generalized Maxwell model that can describe standard linear viscoelasticity is considered. The model is then generalized to include effects of viscous strain gradients. The formulation of additional boundary conditions resulting from the strain gradient terms is discussed. It is shown that the boundary conditions can be formulated in terms of a surface energy. As an example, the thermal expansion of a thin polymeric film on an elastic substrate is analyzed. It is shown that the relative thermal expansion in the thickness direction of the film decreases for sufficiently small film thicknesses, in accordance with experimental observations. This effect cannot be captured by a standard thermo-viscoelastic theory, which gives a constant thermal expansion independent of film thickness.

Magneto-thermoviscoelastic wave propagation at the interface between two micropolar viscoelastic media

Problems of a plane harmonic wave at the interface between two viscoelastic media are studied under generalized thermoviscoelastic theory when the media permeate into a uniform magnetic field. Using potential function, the governing equations reduced to two four-order differential equations. Amplitude ratios of reflection and refraction of different waves with the angle of incidence are obtained using continuous boundary conditions. Some special cases are considered in the absence of effects of micropolar or viscous. By numerical calculation, the variations of amplitude ratios of reflection and refraction with the angle of incidence are shown graphically for aluminium-epoxy and magnesium crystal micropolar viscoelastic materials. Comparison among CD, LS and GL theories and effects of magnetic field, viscous and micropolar are given by numerical results in this paper.

熱サイクルを受けるCSP実装体のたわみと応力の解析(J01-3 熱変形と衝撃,J01 エレクトロニクス実装における熱制御および信頼性評価)

In the present paper, a deformation induced in a new bonding technology of Chip Size Package (CSP) using resin encapsulation sheets is examined numerically and experimentally. Deflections after cooling from a bonding temperature are measured experimentally for various kinds of substrate and the thickness of an integrated circuit using a laser beam. In particular, a simple theory on the basis of a multilayered plate theory considering a viscoelastic property in the substrate and encapsulation are presented, arid the thermo-viscoelastic analysis for the deflection of CSP is performed. We could show that the simple formula for multilayered plates based on the thermo-viscoelastic theory can estimate fairly well the deflection of CSP in experiment.

On the boundary integral formulation of thermo-viscoelasticity theory

A formulation of the boundary integral equation method for generalized thermo-viscoelasticity is given. Fundamental solutions of the corresponding differential equations are obtained. An outline of the implementation of the boundary element method is discussed for the solution of the above boundary equations. Special emphasis is given to the representation of the primary fields, namely, temperature and displacement.

Prediction of the generation of acoustic waves due to the penetration of pulsed microwaves in multilayer media.

The acoustic wave generation in a body irradiated by a pulsed microwave is predicted theoretically. The irradiated body is a viscoelastic multilayer rod inserted into a waveguide or an uniformly irradiated viscoelastic plate. The model is based on Maxwell's equations, the heat equation, and thermoviscoelasticity theory. It is validated experimentally by means of four tests performed on three different specimens. The two first specimens are homogeneous rods used to evaluate and verify the mechanical and electromagnetic characteristics of two different materials. The third specimen is a composite rod made up of these materials. Two tests are performed with this specimen. The comparison between the experimental results and the theoretical computations leads to the validation of the theoretical model.

Thermoviscoelastic analysis for a polymeric composite plate with embedded shape memory alloy wires

The deflection of the polymeric-matrix composite plate with embedded shape memory alloy (SMA) wires and subjected to uniform lateral pressure is studied using the finite element method. The behavior of the polymeric composite plate under electrical heating of SMA is analyzed with thermoviscoelastic theory. The actuation of SMA is modeled by Brinson’s one-dimensional constitutive equation. The influences of the boundary conditions, the ply orientations and the pre-strains of SMA wires on the deflection of composite plate are discussed. It is found that the effect of thermoviscoelasticity of the polymeric matrix on the actuation of SMA is significant.

Acoustic waves generated by pulsed microwaves in viscoelastic rods: modeling and experimental verification.

The acoustic wave generation in a specimen irradiated by a pulsed microwave is predicted theoretically. The specimen is a viscoelastic rod inserted into a wave guide. The model is based on Maxwell's equations, heat equation and thermoviscoelasticity theory. Computations show the presence of temperature oscillations due to the electromagnetic interferences in the irradiated rod if its electromagnetic absorption is low. An experimental method to infer indirectly the detailed behavior of microwave-generated acoustic waves in polymer rods, including the influence of electromagnetic wave reflection at the rod ends, is presented. The method consists of measuring the oscillations in the particle acceleration detected at the end of the rod that are induced by variations in the polymer rod length. The oscillations are caused by changing electromagnetic standing-wave conditions within the rod. It is found that these oscillations are in agreement in period, amplitude, and phase, with independent values of the complex dielectric constant and complex acoustic slowness of the polyvinyl chloride samples used in the study.

Further development in thermodynamic approach for thermoviscoelastic materials

In this paper we derive linear and nonlinear theories ofthermoviscoelasticity for thermorheologically simple materials. Thisderivation is based on two theories: the Thermodynamic of IrreversibleTheory and the Generalized Viscoelastic Standard Theory. These twotheories, along with other assumptions, lead to three-dimensionalthermoviscoelastic models. The derivation we give here is an extensionof Schapery's models. We will soon state the relations expressing thebalance of energy, i.e., the specific heat capacity and the heatconduction equation.