On the Thermoplasticity Constitutive Relations for Isoptopic and Transversely Isotropic Materials

Abstract

The widely used engineering construction materials such as fiber and laminated composite materials are usually under the thermomechanical forces and undergoes thermoplastic deformations. These composites may be considered as a transversely isotropic or orthotropic materials. In this paper, the plasticity constitutive relations for isotropic and transversely isotropy materials proposed in [33]are developed taking into account the temperature and written up the strain and stress space thermoplasticity constitutive relations for aforementioned materials. For simplicity, thermoplasticitytheories are restricted to a small deformations. The usefulness and privileges of the strain space thermoplasticity constitutive relations for the formulation the coupled thermomechanical boundary value problems are discussed.It is found that the strain space thermoplasticity constitutive relations are more convenient for numerical solution of the coupled thermoplasticity boundary value problems as compared to stress space theory. INTRODUCTIONDespite the advances made in the theory of plasticity and thermoplasticity for small and large deformations, the construction of adequate constitutive relations for isotropic and anisotropic materials remains relevant.The investigation of the plastic deformations of transversely isotropic materials under the thermomechanical forces is important in analyzing the material structures. It is well known that fiber and laminated composites may be considered as a transversely isotropic or orthotropic materials. In recent years, in conjunction with the development of composite materials, researchers have proposed various types of plasticity theories for fiber reinforced, laminated and other composite materials. Aboudi [1] proposed the thermomechanical continuum theory for the prediction of the average behavior of unidirectional fiber reinforced graphite-aluminum composite under various types of mechanical and thermal changes. It should be noted that the theory of plasticity for orthotropic bodies was first proposed by Hill [2]. For fiber reinforced composites, Dvorak and Bahei-EL-Din [3] proposed the constitutive relation for transversely isotropic materials. Constitutive relations of inelasticity for anisotropic materials based on tensor function representations was considered in Boehler and Sawczuk [4], Murakami and Sawczuk [5] and Pobedria [6]. In the literature, there are many works on the thermoplasticity constitutive relations for isotropic, anisotropic and Impact Factor (JCC): 7.6197 SCOPUS Indexed Journal NAAS Rating: 3.11 Y < S J + $% and S J = % J M M .The notations and ℎ depend on hardening functions L( , ) and N( , ) which are defined from the experimental stress-strain curves constructed at different temperatures. Note that a set of stress-strain curves at different temperatures makes up the deformation surface for temperature dependent materials (Figure 1). The hardening functions L( , ) and N( , ) for strain space and stress space thermoplasticity theories, are obtained by generalizing the...

Numerical Modeling of Partially Coupled Problems of Thermoelasticity

“…In [8], electromagnetic voltages were investigated. A.A. Khaldjigitov and his students studied the issues of anisotropic plasticity taking into account temperature [9]- [10]. In many applied engineering and technical problems, the process of deformation of structures and their elements, taking into account temperature effects, can be described by model equations of two types, namely, in the form of a coupled or not coupled thermo mechanical problem.…”