Severino P. C. Marques

Transient Thermomechanical Analysis of a Layered Cylinder by the Parametric Finite-Volume Theory

The recently developed parametric finite-volume theory for functionally graded materials is employed to investigate the response of a layered cylinder under transient thermal loading that simulates a cyclic thermal shock durability test. The results reveal a potential for the occurance of two distinct failure modes that may be activated due to two different stress components reaching critical values during different portions of the thermal cycle at different locations. These are delamination of the ceramic top coat from the bond coat, and radial cracking of the top coat that potentially initiates at the outer surface subjected to concentrated transient thermal load. Steady-state analysis substantially underestimates the magnitude of the radial and hoop stresses and, moreover, does not predict the stress reversals during cooldown that likely initiate radial cracks at the outer surface. The fidelity with which local stress fields are captured provides a convincing evidence that the parametric finite-volume theory is an attractive alternative to the finite-element analysis for this class of problems.

Transient Finite-Volume Analysis of a Graded Cylindrical Shell Under Thermal Shock Loading

A major failure mechanism in thermal barrier coatings involves delamination of the ceramic top coat from the substrate, which is accompanied and/or aided by transverse cracks that initiate at the outer surface. Techniques to mitigate these failure modes include grading the transition region between the ceramic top coat and the metallic bond coat by gradually varying the content of the two phases. This concept is explored herein for a graded cylinder subjected to transient thermal cyclic loading, that simulates a thermal shock durability test, using the parametric finite-volume theory for functionally graded materials. Previous investigation into the transient response of a three-layer cylinder under the considered thermal shock loading revealed two potential failure modes, one of which was a direct result of transient effects. Herein, examination of average phase-level stress fields indicates that grading influences the initiation of delamination and potential radial cracking through redistribution of the radial and hoop stress components in the thermal coatings graded region upon rapid heating. The large hoop stress reversal responsible for radial crack initiation at the outer surface, however, is not reduced upon rapid cooling, pointing to the importance of accurately modeling transient effects in thermal shock testing as well as crack-growth management through grading.

Analysis of conduction‐radiation problem in absorbing and emitting nongray materials

Purpose – The purpose of this paper is to present a computationally efficient model to solve combined conduction/radiation heat transfer problems in absorbing, emitting, non‐scattering, non‐gray materials.Design/methodology/approach – The model is formulated for steady‐state condition and based on an iterative approach where the medium is discretized into finite strips and the extinction spectrum is divided into finite bands to consider the extinction coefficient variation with the wavelength.Findings – Temperature fields and heat flux distributions are presented to demonstrate the capability of the formulation. It is shown that the model is quite accurate and efficient even for the cases of pure radiation. Differently from other models, the number of iterations required by the model for convergence is very low, even in the cases dominated by radiation.Originality/value – The model has great potential to contribute with the evaluation and design of materials for thermal insulation, where radiation heat tr...

Rheological Models: Integral and Differential Representations

Viscoelastic relations may be expressed in both integral and differential forms. Integral forms are very general and appropriate for theoretical work. Differential forms are related to rheological models that provide a more direct physical interpretation of viscoelastic behavior. In this chapter we describe the most usual rheological models, deduce their differential equations and, by solving them, we find the corresponding integral representations. These relations will be set in a more computational friendly form in Chap. 3 and extended to three-dimensional situations in Chap. 4 and then used in analytical and computational solutions.

A MODEL FOR HOMOGENIZATION OF LINEAR VISCOELASTIC PERIODIC COMPOSITE MATERIALS WITH IMPERFECT INTERFACE

IN THIS PAPER, A MICROMECHANICAL EXTENSION OF THE FINITE-VOLUME DIRECT AVERAGING MICROMECHANICS THEORY (FVDAM) IS PRESENTED FOR EVALUATION OF THE HOMOGENIZED RELAXATION MODULI OF LINEAR VISCOELASTIC UNIDIRECTIONAL FIBER REINFORCED COMPOSITES WITH PERIODIC MICROSTRUCTURES. SUCH MATERIALS ARE ASSUMED AS COMPOSED OF REPEATING UNIT CELL WITH ARBITRARY INTERNAL ARCHITECTURAL ARRANGEMENTS OF FIBERS COATED BY THIN FLEXIBLE INTERPHASES. THESE INTERPHASES ARE REPLACED BY EQUIVALENT IMPERFECT INTERFACE ELEMENTS WITH IMPOSED CONTINUITY IN TRACTIONS AND DISCONTINUITY IN DISPLACEMENTS. INDEED, THE PROPOSED COMPUTATIONAL PROCEDURE ALLOWS AN EASY AND EFFICIENT TREATMENT OF THE DISPLACEMENT DISCONTINUITY CONDITION ACROSS THE INTERFACES. THE VISCOELASTIC BEHAVIOR OF THE CONSTITUENT PHASES IS MODELED USING THE GENERALIZED MAXWELL MODEL. THE FORMULATION OPERATES DIRECTLY IN THE TIME DOMAIN USING A NUMERICAL INCREMENTAL TIME-STEPPING PROCEDURE BASED ON THE CONCEPT OF INTERNAL STRESS VARIABLES. THE PERFORMANCE OF THE PROPOSED APPROACH IS DEMONSTRATED THROUGH HOMOGENIZATION OF VISCOELASTIC FIBER REINFORCED COMPOSITES AND PERIODIC MULTILAYER MATERIALS WITH FLAT AND WAVY ARCHITECTURES.

A model for evaluation of effective thermal conductivity of periodic composites with poorly conducting interfaces

This paper presents a new micromechanical extension of the parametric finite-volume theory for evaluation of effective thermal conductivities of periodic unidirectional fiber reinforced composites. Such materials are assumed as composed of repeating unit cells with arbitrary internal architectural arrangements of fiber coated by thin interphase with low thermal conductivity. The parametric homogenization approach uses quadrilateral subvolumes for discretization of the repeating unit cell microstructure, thereby allowing an efficient modeling of the details of fibers with arbitrarily shaped cross sections. The interphases are replaced by imperfect interface elements with continuity in normal heat flux and discontinuity in temperature. The performance of the homogenization model is demonstrated for several numerical examples, including two-and three-phase composites with regular squared and hexagonal arrays of fibers. The ability of the model to accurately predict the effective thermal conductivity of those composites is demonstrated by means of comparisons of results obtained using finite-element and analytical solutions.

Solutions with Abaqus

To help the reader to practice with a professional computer code, we use Abaqus to solve a few problems in viscoelasticity (small and large strains). First we relate Abaqus procedure to the general formulation given in this book and then we provide detailed instructions to run the code.

A Model for Viscoelastic Heterogeneous Materials Based on the Finite-Volume Theory

This article presents a new numerical model for the analysis of structures of heterogeneous materials with linear viscoelastic constituents. The model is based on the recently developed parametric finite-volume theory that has produced a paradigm shift in the finite-volume theorys development. This parametric formulation is here extended to model linear viscoelastic behavior. The present model employs the state variables approach for the computation of the time-dependent strains. Several examples, including both homogeneous and heterogeneous situations, are analyzed. Comparison between the numerical and analytical results shows the excellent performance of the proposed model.

A Parametric Finite-Volume Formulation for Linear Viscoelasticity

This chapter of contribution presents a new numerical model for the analysis of structures of heterogeneous materials with linear viscoelastic constituents. The model is based on the recently developed parametric finite-volume theory. The use of quadrilateral subvolumes made possible by the mapping facilitates efficient modeling of microstructures with arbitrarily shaped heterogeneities, and eliminates artificial stress concentrations produced by the rectangular subvolumes employed in the standard version. The parametric formulation is here extended to model viscoelastic behavior. Several examples, including both homogeneous and heterogeneous situations, are analyzed. Comparison between numerical and analytical results has shown an excellent performance of the proposed model.

Materials with Aging

We call aging the change in the mechanical properties of a given material with age which is the time period between some origin more or less arbitrarily established and the time of observation. Concrete is a material that may be used as an example: from the moment of casting (taken usually as age zero) it begins to increase its strength and to decrease its deformability. In the case of polymers both physical (reversible) and chemical (irreversible) aging are observed. In the present chapter we introduce the equations for viscoelasticity with aging for situations in which compliance diminishes (“hardening”) and for situations in which compliance increases (“softening”) with age in integral form and through rheological models and state variables equations. The time-age equivalence model applied to the physical aging of polymers is also discussed.