Introduction
Students usually have trouble comprehending strain coordinate transformation. An experiment was developed at the University of Missouri-Rolla in 1997 to help demonstrate this fundamental concept for a mechanics of materials course. Squares drawn in different orientations on a clear polymer specimen are labeled with different coordinate systems but are exposed to the same strain field. Students can then visually comprehend and experimentally measure the results of applying a finite permanent strain to the specimen, thereby proving to themselves that the strain in the different coordinate systems is equivalent.
Objective
The objective for this experiment is to provide a physical explanation for the concepts of plane stress and strain coordinate system transformation.
Theory
Uniaxial Tension Test
Plane Stress
Normal Strain Definition
elongation or contraction of a line segment per unit of length,
Shear Strain Definition
change in angle that occurs between two line segments that were originally perpendicular to one another,
"Small" Strain Analysis
In-Plane Principal Directionsnormal strains are assumed "very small" compared to 1 (
<<1)
In-Plane Principal Strains
Maximum In-Plane Shearing Strain
Summary
- This experiment provides a good
introduction to experiments involving tension tests
and/or strain gages.
- It also introduces students to polymer
materials.
- Transparency film is an inexpensive and convenient choice because it is easily run through a copier and cut to the desired size, thereby greatly reducing the time needed to prepare specimens.