TABLE OF CONTENTS Stress is defined as force per unit area with units of psi or MPa. In a part subjected to some forces, stress is generally distributed as a continuously varying function within the continuum of material. Every infinitesimal element of the material can conceivably experience different stresses at the same time. Thus, we must look at stresses as acting on vanishingly small elements within the part. These infinitesimal elements are typically modeled as cubes, shown in Figure 12-7. The stress components are considered to be acting on the faces of these cubes in two different manners. Normal stresses act perpendicular (i.e., normal) to the face of the cube and tend to either pull it out (tensile normal stress) or push it in (compressive normal stress). Shear stresses act parallel to the faces of the cubes, in pairs (couples) on opposite faces, which tends to distort the cube into a rhomboidal shape. This is analogous to grabbing both pieces of bread of a peanut-butter sandwich and sliding them in opposite directions. The peanut butter will be sheared as a result. These normal and shear components of stress acting on an infinitesimal element make up the terms of a tensor. [4]
Stress is a tensor of order two [5] and thus requires nine values or components to describe it in three dimensions. The 3-D stress tensor can be expressed as the matrix:
| (12.2a) |  |
where each stress...
