Page 52 - Engineering Plastics Handbook

26 Introduction

To calculate the shear modulus for the elastic portion (below the elas-
tic limit), use
∆τ
G =
∆γ
where G is the slope of the curve.

Formulas for linear viscoelastic models can be applied to tensile defor-
mation as well as shear deformation by replacing the shear stress τ
with tensile stress σ, shear strain γ with tensile strain ε, shear modu-
lus G with Young’s tensile modulus E, and newtonian shear viscosity η
with Trouton’s tensile viscosity η [11–13].
e
Shear viscosity and shear modulus
Shear viscosity with the dashpot depicting a linear newtonian fluid is
calculated by
τ
η =
γ*
where η= shear viscosity of a newtonian fluid in dashpot, Pa⋅s (cP)
τ= shear stress, MPa (psi)
−1
γ* = shear strain rate, s
10 P = 1000 centipoise (cP)
Two conditions are that (1) a constant stress is suddenly applied, and
(2) strain is assumed to be zero when the stress is applied. Shear mod-
ulus G from a linear elastic model depicting a hookean solid is deter-
mined by G =τ/γ [11].

Poisson’s Ratio
Poisson’s ratio ν is the ratio of transverse contraction to longitudinal
extension in the stretching direction. For the purposes of visualization
only, picture a tough rubbery sheet, push a dull thin rod into the sheet,
and you have transverse contraction and longitudinal extension. In a
practical mode, Poisson’s ratio is about 0.33 for many solid plastics and
just under 0.5 for elastomers.
− ε
ν = transverse
ε
longitudinal
The transverse strain −ε transverse is defined as negative, and the longitudi-
nal strain ε longitudinal is defined as positive so that ν has a positive value.