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

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

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

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

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)

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

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

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

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

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)

Example Problem Cylindrical metal specimen pulled in tension to failure d0 = 12.8 mm l0 = 50.8 mm df = 6.6 mm lf = 72.14 mm What are %EL, %RA, and true strain to failure?