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Title: Finite element analysis of thick sheet superplastic forming
Author: Bhargava, P.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1994
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This thesis deals with the numerical techniques required to simulate the superplastic forming of three dimensional thick sheet components. Superplastic behaviour is characterised by the dependence of the flow stress upon the strain rate and the constitutive equations are established on the basis of a viscoplastic potential. An 8-noded hexahedron element along with a mean quadrature integration scheme is employed for the purpose of finite element discretisation and the subsequent formulation. A well documented consequence of the mean quadrature integration scheme is the existence of zero energy modes which are prevented by introducing artificially hourglass control forces. The numerical framework for the simulation of SPF process, using the finite element methodology, is first set in the context of the standard flow formulation. Nodal velocities, the main unknown variables of the problem, are integrated using a full implicit integration scheme to obtain a geometry update during the forming process. The solution of the non-linear equilibrium equations is achieved by linearising them and using a Newton-Raphson iterative procedure. These linearised equations are expressed in terms of a tangent matrix which is unsymmetric on account of the dependency of the equilibrium equation on nodal positions. However, due to the several limitations those were experienced during the course of the study and computation involving flow formulation, an alternative formulation entitled the incremental flow formulation is proposed. Within the framework of this formulation, the rate type of constitutive equations are approximated over a timestep to yield a material description that enables the stresses to be obtained in terms of the geometry changes of this time period. The resulting non-linear equations are the functions of the nodal positions instead of velocities and unlike the flow formulation their linearisation leads to symmetric tangent matrix.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available