1. Lecture 4: Plastic Deformation
MATSE 259
Lecture 4: Plastic Deformation
Christopher L. Muhlstein, Ph.D.
Department of Materials Science and Engineering
The Pennsylvania State University
University Park, PA

2. Last Lecture Elastic behavior of materials
Trends in elastic properties
Elastic deformation calculations

3. Lecture 4: Key Concepts and References
Plastic deformation
Yielding
Tensile strength
Ductility
elongation
reduction in area
Resilience
Toughness
True stress and strain
Reference: Chapter 6 of Callister

4. Tensile Deformation Proportional limit (onset of plastic deformation)
Yield strength, sy
0.2% offset
Callister, Materials Science and Engineering: An Introduction (2003)

5. Anatomy of an Engineering Stress-Strain Curve
Elastic modulus
Yielding behavior
Ultimate strength
Fracture/failure strain
Stress-strain diagram for a ductile steel. (after Balan et al., J. Eng. Struct., No. 3 March 1998, Vol. 124).
Popov, Engineering Mechanics of Solids (1991)

6. True Stress and Strain True stress, st True strain, et
Plastic deformation
Constant volume (isochoric)
Constitutive law

7. Tensile Deformation Ultimate tensile stress/strength (sUTS or TS)
Necking Fracture stress/strength (sF)
Callister, Materials Science and Engineering: An Introduction (2003)

8. Tensile Behavior of Steels
Features
Elastic response
Yielding behavior
Ultimate strength
Failure
Influence of alloy chemistry
Popov, Engineering Mechanics of Solids (1991)

9. Resilience and Toughness
Resilience, Ur
Ductility
Percent elongation, %EL
Percent reduction in area, %RA
“Toughness”

10. Example Problem Cylindrical specimen Tensile force 10,000 N
10 mm diameter
101.6 mm long
Tensile force 10,000 N
E = 93.8 GPa
n = 0.35
Specimen elongation?
Reduction in diameter?
Elastic or plastic deformation?
Tensile behavior of brass.
Callister, Materials Science and Engineering: An Introduction (2003)

11. Example Problem
Cylindrical metal specimen pulled in tension to failure
d0 = 12.8 mm
l0 = 50.8 mm
df = 6.6 mm
lf = mm
What are %EL, %RA, and true strain to failure?