Unsteady Thermal Plasticity

  • Boris F. ShorrEmail author
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)


A topic of this chapter is the general approach to computation analysis of unsteady elastoplastic deformations in machine parts and mechanical systems under non-isothermal loading, based on modern experimental data and theoretical developments. It is shown that widespread variants of theories of plasticity, including strain hardening model, enable satisfactory evaluation of the plastic strain rate, associated with transient processes, only provided that strains increase along an invariable direction. The theory of stabilized anisotropic hardening (SAH theory) developed over the last few decades is outlined. This theory takes into consideration loading history and material adaptability along with separation of stresses into so-called active and residual micro-stress parts. A comparison with numerous experimental results demonstrates efficiency of the SAH theory for calculating the plastic strain rate under sign-varying multi-axial proportional loading. An experimentally justified extension of the SAH theory proposed by the author for analyzing more elaborate case of non-proportional (out-of-phase) non-isothermal loading and conditionally named “the model of stabilized anisotropic-ray hardening” (the SARH theory) is described in detail. The theory starts from the concept of the evolvement of anisotropy deformation along a “hardening axis,” which is collinear to a varying vector of the aforementioned active stresses, and also relies on separation of residual micro-stresses into steady (isotropic) and unsteady (anisotropic) parts; in doing so, unsteady micro-stresses vary under rotation of the hardening axis. The constitutive relations written in the form of the projections of micro-stresses, plastic strains, and their increments onto this axis govern arbitrary non-isothermal deformations. A step-by-step procedure of numerical solution of a thermal plasticity problem using the SARH model is also described. Numerical examples illustrate the applicability of the proposed fairly simple model for restoring the plastic strain rate and direction of plastic strain observed for specimens loaded over a wide range of magnitudes and orientations of the stress vector. The possibility of estimating damage accumulation and failure conditions is addressed for general elastoplastic non-isothermal process. A brief survey of the publications (both in Russian and English) on the SAH theory of elastic plastic deformations of solids subject to sign-varying loading is presented.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Central Institute of Aviation Motors (CIAM)MoskvaRussia

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