Kinematics of large deformations and continuum mechanics

3. Kinematics of large deformations and continuum mechanics 3.1 Introduction The strains, be they elastic or plastic, which most engineering components undergo in service are usually small, that is, <0.001 (or 0.1%). At yield, for example, a nickel alloy may have undergone a strain of about σ y /E ∼ 0.002 and it is hoped that this occurs rarely in nickel-based alloy aero-engine components in service! During man- ufacture, however, the strains may be much bigger; the forging of an aero-engine compressor disc, for example, requires strains in excess of 2.0 (i.e. >200%). This is three orders of magnitude larger than the strain needed to cause yield. In manu- facturing processes, another very important feature is material rotation. Deformation processing leading to large plastic strains often also leads to large rigid body rotations. The bending of a circular plate, to large deformation, is an example which shows the rigid body rotation. Figure 3.1 shows the result of applying a large downward dis- placement at the centre of an initially horizontal, simply supported circular disc. Only one half of the disc section is shown. While the displacements and rigid body rotations can be very large, the strains remain quite small. × × Fig. 3.1 Simulated large elastic–plastic deformation of an initially horizontal, simply supported circular plate. Only one half of the plate section is shown. Dunne, Fionn, and Nik Petrinic. <i>Introduction to Computational Plasticity</i>, Oxford University Press, 2005. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/unc/detail.action?docID=422467. Created from unc on 2019-08-30 11:20:33. Copyright © 2005. Oxford University Press. All rights reserved.

Kinematics of large deformations and continuum mechanics

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linear deformation

strain

stresses

nickel

alloy

material rotation