MATSE 259 Properties and Processing of Engineering Materials

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MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

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MATSE 259

Lecture 4: Plastic Deformation


Christopher L. Muhlstein, Ph.D.



Department of Materials Science and Engineering

The Pennsylvania State University

University Park, PA

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

2

Last Lecture


Elastic behavior of
materials


Trends in elastic
properties


Elastic deformation
calculations


MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

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

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

4

Tensile Deformation


Proportional limit
(onset of plastic
deformation)


Yield strength,
s
y


0.2% offset

Callister,
Materials Science and Engineering:
An Introduction

(2003)

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

5

Anatomy of an Engineering Stress
-
Strain Curve

Popov,
Engineering Mechanics of Solids

(1991)

Stress
-
strain diagram for a ductile steel. (after Balan et al.,
J. Eng. Struct.
, No. 3 March 1998, Vol. 124).


Elastic modulus


Yielding behavior


Ultimate strength


Fracture/failure
strain


MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

6

True Stress and Strain


True stress,
s
t


True strain,
e
t


Plastic deformation


Constant volume (isochoric)


Constitutive law

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

7

Tensile Deformation


Ultimate
tensile
stress/strength
(
s
UTS

or TS)


Necking
Fracture
stress/strength
(
s
F
)


Callister,
Materials Science and Engineering:
An Introduction

(2003)

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

8

Tensile Behavior of Steels


Features


Elastic response


Yielding behavior


Ultimate strength


Failure


Influence of alloy
chemistry

Popov,
Engineering Mechanics of Solids

(1991)

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

9

Resilience and Toughness


Resilience,
U
r


Ductility


Percent elongation,
%EL


Percent reduction in
area, %RA


“Toughness”

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

10

Example Problem


Cylindrical specimen


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)

MATSE 259 Spring 2007, C. Muhlstein

©

C. Muhlstein, 2007

11

Example Problem


Cylindrical metal specimen pulled in tension to
failure


d
0

= 12.8 mm


l
0

= 50.8 mm


d
f
= 6.6 mm


l
f

= 72.14 mm


What are %EL, %RA, and true strain to
failure?