Page 49 - Engineering Plastics Handbook

Products and Design 23

Elastic Region

Stress-to-strain proportionality
Stress-to-strain proportionality is limited to the elastic region, for very
low strains where Hooke’s law applies.
To calculate the modulus of elasticity E in the elastic region, use the
following [7–9]:

σ FA
/
Young's modulus E = = MPa (psi)
/∆
ε LL
where σ= stress, MPa (psi)
ε= strain, cm/cm (in/in) %
F = applied force (load), N (lb)
2 2
A = area of applied force, cm (in )
L = unit length, cm (in)
∆L = change in length due to stress, cm (in)

Beyond the Elastic Limit (Beyond the
Proportional Region)
In the proportional (elastic) region, Hooke’s law applies, and Young’s mod-
ulus E =σ/ε. Beyond the elastic limit there is no stress-to-strain propor-
tionality, and Hooke’s law does not apply. Beyond the elastic limit, stress
can be constant while strain continues to increase. A viscoelastic solid
plastic has viscous fluid characteristics beyond the elastic limit.

Spring-and-Dashpot Models

Hookean spring element
The simplest mechanical model, the hookean spring element, has an
elastic response. The spring is an energy storage element. It releases its
energy when it returns to its original form. When subjected to an instan-
taneous stress σ , the spring has a response with a strain ε [10]:
0
0
Young’s modulus E = σ 0 /ε 0

Newtonian dashpot element
The simplest linear viscous model is Newton’s model. This is shown by
a piston-dashpot element [10]. The dashpot is an energy dissipation
element, and it represents a viscous damping force. It relates the trans-
lational and rotational velocity of a fluid (oil) between two points, and
an applied load, by using a damping constant.