Page 54 - Engineering Plastics Handbook

28 Introduction

is used to predict mechanical characteristics of the thermoplastic beyond
the range of the available data. The equation is suitable for thermo-
plastics at temperatures near the glass transition temperature T g [16].

Dynamic Mechanical Analysis

DMA calculations are applied to data in the linear region of a stress-to-
strain curve. The calculations are most suited for low-amplitude sinu-
soidal strain when the sinusoidal strain is out of phase with sinusoidal
stress. Design considerations for dynamic mechanical applications use
values for the stress, strain, phase angle, storage modulus, and loss
modulus [14, 15, 17, 18].
To calculate strain,
sinωt
ε=ε 0
where ε= applied strain at time t, %
ε = applied initial strain, %
0
ω= frequency of applied strain, Hz
t = selected time for calculating applied strain

To calculate stress,
σ=σ sin (ωt + δ)
0
where δ = phase angle between stress and strain.
Stress can be expressed with two components:

cosδsinωt +σ sinδcosωt
σ=σ 0 0
Component 1 is in phase with strain:
cosδ
σ 0
Component 2 is 90° out of phase with strain:
σ sin δ
0
where σ= stress at time t and σ = initial stress.
0
Information on dynamic mechanical analysis and properties is found
in Chap. 3, “Properties,” and Chap. 4, “Processes.”

Beam Equations
To return to beam equations, the same equations used for steel are used
for plastic beams. Steel is an elastic material and thermoplastics are vis-
coelastic. The solutions of beam equations for plastic beams are based