Growth of Yield Front of Functionally Graded Non-uniform Bars Under Thermal Load

  • Priyambada NayakEmail author
  • Kashi Nath Saha
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)


This study concentrates on the yield front propagation of functionally graded material (FGM) non-uniform bars subjected to thermal loads. Under the action of thermal load, the bar is considered to be axisymmetric and the axisymmetry persists with plane cross sections of the bar. The modelling of FGM is done for continuous distributions of constituents of ceramic and metal along length of the bar by utilizing variation of power law for volume fraction. Moreover, the FGM bar is modelled by assuming the metal’s material behaviour to be linear elastic and linear strain hardening whereas the ceramic to be linear elastic. The problem is solved through a variational method, taking modulus of elasticity and yield stress of the metallic part, being a function of temperature, whereas the ambient temperature value for elasticity modulus is considered for the ceramic part. The post-elastic investigation is carried out on the basis of deformation theory of plasticity and von Mises yield criterion by a series approximation assumption for the unknown displacement field. The governing differential equation is solved through Galerkin’s principle. The propagation of yield front is located by applying an iterative process for the approximate solution and for the prescribed temperature field. MATLAB® computational simulation software is used to implement the solution algorithm. Clamped–clamped FGM bars of various geometries subjected to different temperature distributions are considered, and their effect on the thermo-elasto-plastic performance is emphasized through some results in graphical form. The parametric study reveals the nature of temperature field distribution, the effect of geometry parameters and material parameters on the elasto-plastic deformation of FG bars under thermal loading.


Functionally graded materials Thermal load Yield front Volume fraction Variational method Deformation theory 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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