PLASTIC DEFORMATION

AND

STRESS-STRAIN CURVES

Background Unit: Plastic Deformation and Stress-Strain Curves

Introduction

In the last unit we studied the elastic response of materials to externally applied loads. All the loads applied were well below the elastic limit of the materials so no permanent deformation occurred in the sample.
In this unit we will continue our study of the effects of externally applied forces and will apply loads large enough to cause permanent deformation and eventually fracture .

Objectives

After studying this unit and completing the lab assignment you should be able to perform the following tasks:

1. Write definitions for the following terms, including SI and English units when appropriate.
a. Pascal
b. offset yield strength
c. ultimate tensile strength
d. plastic strain
e. hardness
2. Given specific dimensions and load-elongation data from a metal tensile test, calculate stresses and strains, plot an appropriate stress-strain curve, and determine the yield strength (by the 0.2% offset method when appropriate or by the sudden change in slope of the stress-strain curve when appropriate), the elastic modulus, and the ultimate tensile strength.
3. Given the dimensions of a tensile test specimen before and after testing calculate the percent elongation and the percent reduction in area.
4. With the assistance of a classmate, run a tensile test on a metal sample obtaining load and elongation data.

Plastic Deformation

After a material has reached its elastic limit, or yielded, further straining will result in permanent deformation. After yielding not all of the strain will be recovered when the load is removed. Plastic deformation is defined as permanent, non-recoverable deformation. Plastic deformation is not linear with applied stress.
Recall if a material experiences only elastic deformation, when the stress is removed the elastic strain will be recovered. If a material is loaded beyond its yield point it experiences both elastic and plastic strain. After yielding the rate of straining is no longer linear as the applied stress increases. When the stress is removed, only the elastic strain is recovered; the plastic strain is permanent.
Elastic deformation occurs as the interatomic bonds stretch, but the atoms retain their original nearest neighbors and they "spring back" to their original positions when the load is removed. Clearly in order to have permanent deformation there must be permanent movement in the interatomic structure of the material. Although some of the atoms move away from their original nearest neighbors not all of the interatomic bonds are broken (this is evident because we can achieve permanent deformation without fracture of the material). The mechanism for permanent deformation is called slip. Slip occurs when planes of densely packed atoms slide over one another: individual bonds are broken and reformed with new atoms in a step-wise fashion until the desired deformation is achieved.

Stress-Strain Curves

Again we will use stress-strain curves to investigate the mechanical behavior of materials. Recall most of the properties aren't dependent on the specimen size, and the elastic modulus is the same whether we use a tensile test or a compression test to find it. Since

the strain will be positive for tensile testing. A tensile stress will also be positive and

And during the initial deformation of the material when the strain is elastic, the stress and strain are related linearly by the elastic modulus.
Stress-strain curves for metals come in several basic types (Fig. 1). The linear portion of the stress-strain curve indicates elastic, or recoverable, deformation. The non-linear portion indicates plastic deformation. Plastic strain is defined as permanent, non-recoverable deformation. Curve A is for a metal which broke while still showing linearly elastic behavior.