ELASTICITY. Elasticity Elasticity of Composites Viscoelasticity. Elasticity: Theory, Applications and Numerics Martin H. Sadd Elsevier Butterworth-Heinemann, Oxford (2005). Revise modes of deformation, stress, strain and other basics (click here) before starting this chapter etc. .
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Elasticity: Theory, Applications and Numerics
Martin H. Sadd
Elsevier Butterworth-Heinemann, Oxford (2005)
Revise modes of deformation, stress, strain and other basics (click here) before starting this chapter etc.
Propagation of cracks in a material
Elongation at constant load at High temperatures
Note: above is a ‘broad’ classification for ‘convenience’. E.g. Creep is also leads to plastic deformation!
E.g. Al deformed at small strains
E.g. deformation of an elastomer like rubber
The plots of these functions is shown in the next slide
A,B,m,n → constantsm > n
Force (F) →
Potential energy (U) →
Elastic modulus is the slope of the Force-interatomic spacing curve (F-r curve), at the
Near r0 the red line (tangent to the F-r curve at r = r0)coincides with the blue line (F-r) curve
For displacements around r0→ Force-displacement curve is approximately linear THE LINEAR ELASTIC REGION
** Young’s modulus is not an elastic modulus but an elastic constant
T due to uncoilingof polymer chains
Due to efficient filling of space
Elastic modulus in design
► First transition series → good combination of ductility & modulus (200 GPa)► Second & third transition series → even higher modulus, but higher density
◘ the nature of secondary bonds- Van der Walls / hydrogen◘ presence of bulky side groups◘ branching in the chains Unbranched polyethylene E = 0.2 GPa, Polystyrene with large phenyl side group E = 3 GPa, 3D network polymer phenol formaldehyde E = 3-5 GPa◘ cross-linking
► By suitably alloying the Young’s modulus can be increased
► But E is a structure (microstructure) insensitive property the increase is fraction added► TiB2 (~ spherical, in equilibrium with matrix) added to Fe to increase E
Modulus parallel to the direction of the fiberes
For a given fiber fraction f, the modulii of various conceivable composites lie between an upper bound given by isostrain conditionand a lower bound given by isostress condition
Volume fraction →