Page 189 - Mechanical Behavior of Materials

5

Stress–Strain Relationships and

Behavior

5.1 INTRODUCTION
5.2 MODELS FOR DEFORMATION BEHAVIOR
5.3 ELASTIC DEFORMATION
5.4 ANISOTROPIC MATERIALS
5.5 SUMMARY

OBJECTIVES

• Become familiar with the elastic, plastic, steady creep, and transient creep types of strain, as
well as simple rheological models for representing the stress–strain–time behavior for each.
• Explore three-dimensional stress–strain relationships for linear-elastic deformation in
isotropic materials, analyzing the interdependence of stresses or strains imposed in more
than one direction.
• Extend the knowledge of elastic behavior to basic cases of anisotropy, including sheets of
matrix-and-fiber composite material.

5.1 INTRODUCTION

The three major types of deformation that occur in engineering materials are elastic, plastic, and
creep deformation. These have already been discussed in Chapter 2 from the viewpoint of physical
mechanisms and general trends in behavior for metals, polymers, and ceramics. Recall that elastic
deformation is associated with the stretching, but not breaking, of chemical bonds. In contrast, the
two types of inelastic deformation involve processes where atoms change their relative positions,
such as slip of crystal planes or sliding of chain molecules. If the inelastic deformation is time
dependent, it is classed as creep, as distinguished from plastic deformation, which is not time
dependent.
In engineering design and analysis, equations describing stress–strain behavior, called
stress–strain relationships, or constitutive equations, are frequently needed. For example, in

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