The closed form solutions for axisymmetric modeling of thermal stress due to repetitive pulse laser heating

Repetitive pulse laser heating is increasingly being used in the laser processing industry such as laser welding, laser cutting and laser drilling due to its energy accumulation effect. Modeling of thermo-mechanical coupling effect of repetitive pulse laser heating can enhance the understanding of its thermo physical process. In this paper, an axisymmetric modeling of thermal stress for repetitive pulse laser heating solid materials is introduced, and its closed form solutions are obtained based on a semi-analytical method. The accuracy and efficiency of the closed form solutions are verified by comparison with the existing numerical modeling software based on the finite element method. Distributions of thermal stress for different radial locations, axial locations and duty cycles are calculated, and effects of these parameters on temporal profile of the thermal stress distributions are analyzed. In the region of laser irradiation, three components of thermal stress are all shown as compressive stress. And outside the region of laser irradiation, the hoop component is shown as tensile stress. On the material surface, the change of thermal stresses is very sharp as a result of direct absorption of incident laser energy. With the increasing of the depth, the rises and decreases of thermal stresses become smooth gradually. The duty cycle has a significant effect on the profiles of thermal stresses. In the same conditions, the maximum value of thermal stresses gets higher as the duty cycle decreases. Results of this study can provide some theoretical basis for parameter inversion and optimization of repetitive pulse laser heating, as well as some corresponding experimental research.     

Ohmic heating of foods during aspetic processing

The problem of heating food by applying a large electrical currentacross it is considered. Various aspects of the problem areconsidered, with emphasis on the electrical and thermal behaviourdue to variations in electrical conductivity of the food. Suchvariations are due to variations in temperature within the foodand differences in material properties of the food. The stabilityof ohmic heating as a method used for processing is consideredfor the simple case of a homogeneous food. The heating of ahomogeneous food in a shear layer close to a wall is analysed.The case of a single spherical solid food particle with temperature-dependentconductivity surrounded by a liquid sauce is considered to modelthe behaviour of a multiphase food.     

Stability Analysis for maxwell’s Equation with a Thermal Effect in one Space Dimension

In this paper we study the asymptotic behavior of a system modeling heating of material by microwaves. Various assumptions have been made, concerning complexity (nonhomogeneous structure) and the two-phase state of the material. The mathematical model includes Maxwell’s and heat–transfer equations. Stability of solutions of the system is shown.     

Towards Phase Field Modeling of Ductile Fracture in Gradient-Extended Elastic-Plastic Solids

The modeling of failure in ductile metals must account for complex phenomena at a micro-scale as well as the final rupture at the macro-scale. Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model with a concept for the modeling of macroscopic crack discontinuities. In this context, it is important to account for material length scales and thermo-mechanical coupling effects due to dissipative heating. This can be achieved by the construction of non-standard, gradient-enhanced models of plasticity with a full embedding into continuum thermodynamics [1,2]. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture based on regularized crack discontinuities. This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns within a pure continuum formulation. Moreover, the phase field modeling of fracture is related to gradient theories of continuum damage mechanics, and fits nicely the structure of constitutive models for gradient plasticity. The main focus of this work is the extensions to gradient thermoplasticity and phase field formulation of ductile fracture, conceptually in line with the work [3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cellular automata study of high burn-up structures

We propose a new approach, based on the cellular automata, for processing and modeling the structure dynamics of UO₂ at different cross-section averaged burn-ups. Micrographs of the material surface, subjected to both “as-polished” and “as-etched” treatments, with a magnification of 1250× have been used in our study. It has been shown that this approach provides efficient tools for investigation of the surface structure dynamics both at local and global levels.     

Effects of Moisture and Stresses on the Structure and Properties of Polyester Resin

The results of a complex study of structural changes in a cured Norpol 440 polyester resin under the action of damp environment and mechanical loading are presented. A considerable effect of absorbed moisture on the structure and some characteristics of the material is revealed by using thermophysical methods and X-ray diffractometry. The joint effect of moisture and mechanical stress is estimated by investigating the creep in stationary and nonstationary moisture conditions. The anisotropy of the material structure formed during creep is evaluated from the results of dilatometric measurements. It is found that the degree of anisotropy of the material after creep accompanied by moisture sorption is higher than that after creep in the conditions of moisture equilibrium with atmosphere. It is established that the aftercure and relaxation of the residual creep deformation come to an end at heating to 80-85°C. At a further rise in temperature and repeated heating, changes in the material structure are not observed.     

Vibrocreep of polymer materials

The vibrocreep of low-density polyethylene (LDP) in uniaxial tension has been investigated in the presence of vibration in the direction of action of the constant load. The material was deformed under nonisothermal conditions owing to heating caused by the dissipation of vibrational energy. Superimposing vibrations leads to a considerable increase in creep rate. It is shown that this increase can not be explained solely in terms of the rise in temperature due to heating of the material; there is also a dynamic creep acceleration effect. Avariant of the vibrocreep approximation with allowance for the dynamic and temperature creep acceleration effects is proposed.Mekhanika Polimerov, Vol. 4, No. 3, pp. 413–420, 1968     

Modeling of microscopic failure in heterogeneous materials

The proper modeling of state-of-the-art engineering materials requires a profound understanding of the nonlinear macroscopic material behavior. Especially for heterogeneous materials the effective macroscopic response is amongst others driven by damage effects and the inelastic material behavior of the individual constituents [1]. Since the macroscopic length scale of such materials is significantly larger than the fine-scale structure, a direct modeling of the local structure in a component model is not convenient. Multiscale techniques can be used to predict the effective material behavior. To this end, the authors developed a modeling technique based on representative volume elements (RVE) to predict the effective material behavior on different length scales. The extended finite element method (XFEM) is used to model discontinuities within the material structure independent of the underlying FE mesh. A dual enrichment strategy allows for the combined modeling of kinks (material interfaces) and jumps (cracks) within the displacement field [2]. The gradual degradation of the interface is thereby controlled by a cohesive zone model. In addition to interface failure, a non-local strain driven continuum damage model has been formulated to efficiently detect localization zones within the material phases. An integral formulation introduces a characteristic length scale and assures the convergence of the approach upon mesh refinement [3]. The proposed method allows for an efficient modeling of substantial failure mechanisms within a heterogeneous structure without the need of remeshing or element substitution. Due to the generality of the approach it can be used on different length scales. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Group theoretical modeling of thermal explosion with reactant consumption

Today engineering and science researchers routinely confront problems in mathematical modeling involving nonlinear differential equations. Many mathematical models formulated in terms of nonlinear differential equations can be successfully treated and solved by Lie group methods. Lie group analysis is especially valuable in investigating nonlinear differential equations, for its algorithms act as reliably as for linear cases. The aim of this article is to provide the group theoretical modeling of the symmetrical heating of an exothermally reacting medium with approximations to the body’s temperature distribution similar to those made by Thomas [17] and Squire [15]. The quantitative results were found to be in a good agreement with Adler and Enig in [1], where the authors were comparing the integral curves corresponding to the critical conditions for the first-order reaction. Further development of the modeling by including the critical temperature is proposed. Overall, it is shown, in particular, that the application of Lie group analysis allows one to extend the previous analytic results for the first order reactions to nth order ones.     

Finite Element Models of Hyperelastic Materials Based on a New Strain Measure

To construct constitutive equations for hyperelastic materials, one increasingly often proposes new strain measures, which result in significant simplifications and error reduction in experimental data processing. One such strain measure is based on the upper triangular (QR) decomposition of the deformation gradient. We describe a finite element method for solving nonlinear elasticity problems in the framework of finite strains for the case in which the constitutive equations are written with the use of the QR-decomposition of the deformation gradient. The method permits developing an efficient, easy-to-implement tool for modeling the stress–strain state of any hyperelastic material.     

A Green’s function model for the analysis of laser heating of materials

An analytical model based on Green’s function method is developed to analyze the temperature distribution and heated regions in a material irradiated by a high-energy laser beam. The model is multi-dimensional, transient and incorporates different types of beam characteristics and boundary conditions. The multi-dimensional integration formulas in the Green’s function solution equation are evaluated using an adaptive numerical integration algorithm. A parametric study is conducted to show the effect of various laser beam parameters and material properties on the laser heating process.     

Numerical modeling of the active damping of forced thermomechanical resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric inclusions

We consider the problem of active damping of forced resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric sensors and actuators. Here, the interaction of electromechanical and thermal fields is taken into account. For modeling of vibrations, we use the Kirchhoff–Love hypotheses as well as hypotheses adequate to them and describing the distribution of temperature and electric field quantities. The shell temperature increases as a result of dissipative heating. For the active damping of vibrations, piezoelectric sensors and actuators are used. It is supposed that the electromechanical characteristics of materials depend on the temperature. The solution of this complex nonlinear problem has been obtained by the iterative method and finite element method. We have investigated the influence of temperature of dissipative heating on the efficiency of active damping of vibrations of a viscoelastic cylindrical panel with rigid restraint of its edges.     

Effect of radiation losses on hotspot formation and propagation in microwave heating

The use of microwaves for the rapid heating of materials hasfound widespread industrial use. However, a number of potentialproblems are inherent in this rapid heating, including the hotspotphenomenon. A hotspot is a type of thermal instability whicharises because of the nonlinear dependence of the electromagneticand thermal properties of the material on temperature. The evolutionof a hotspot in a cylindrical material is studied. The propagationof the microwaves is treated in the Wentzel-Kramers-Brillouin(WKB) limit (geometric optics), and the thermal behaviour isstudied in the limit of small thermal diffusivity. The resultingtemperature distributions are in excellent agreement with fullnumerical solutions of the governing equations, even outsidethe strict range of the asymptotic validity of the WKB approximation.     

Stress-optimal local heating during welding of unlike plates with variable thicknesses

A method is proposed and is used to solve the problem of determining the stress-optimal temperature fields of the local heating during welding of unlike plates with variable thicknesses. Computational modelling was carried out for plates of M-40 material and St. 3 steel, with thickened edges, depending on the width of the heating zone and the beginning of the region of elastic deformation.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 53–56, 1987.     

The equations of the thermodynamic model of magnetoelasticity of dielectric ferromagnetic bodies

We develop a thermodynamic approach to the mathematical modeling of magnetoelastic processes in dielectric ferromagnetic bodies that are subject to the action of force loading, heating, and an external electromagnetic field. The basis for the construction of the physical relations is the principle of local thermodynamic state. In the computations of the momentum balance equation of the magnetization process account is taken of its tensor character.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 30–34.     

Optimization of the heating of a heat-sensitive layer under constraints on the stresses in the plastic region of deformation of the material

We study the problem of optimal control for rapidity of the heating of a heat-sensitive layer under constraints on the control (the temperature of the heating medium or the heat flux) and maximal values of the stress intensity in the plastic region of deformation of the material. We propose an algorithm for solving the problem that presumes it has been reduced to the inverse problem of thermoplasticity. For the case of one-sided heating we give a numerical analysis of the direct and inverse problems of thermoplasticity. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Heating of large parts prior to steeling

The article deals with the nonsteady temperature field of a large part with a cylindrical cavity with special boundary conditions. A simple formula is obtained for evaluating the minimal time of heating the material of the part to the required depth when heat is supplied by a liquid heat carrier flowing through the cavity.Translated from Dinamicheskie Sistemy, No. 4, pp. 77–80, 1985.