P4 Stress and Strain
Dr. A.B. Zavatsky
HT08
Lecture 6
Mohrs Circle for Plane Stress
Transformation equations for plane stress.
Procedure for constructing Mohrs circle.
Stresses on an inclined element.
Principal stresses and maximum shear stresses.
Introdu

Lecture 1:
Course overview
Assignment: Read Chapter 1 of Dieter
Materials Science is a disciplinary field to correlate the properties (e.g. physical, chemical, thermal,
electrical, magnetic, optical, and mechanical .) of a material with its microstructure

STRESS-STRAIN CURVES
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
August 23, 2001
Introduction
Stress-strain curves are an extremely important graphical measure of a materials mec

Methods to measure elastic constants
To accurately measure elastic constants is not trivial. The test machine must be rigid (i.e., with
negligible compliance). In uniaxial tension, Hookes law gives
E=
total
where total is the the total measured strain. I

The criterion for plastic instability in engineering materials, which are strain-hardened and follow the
Hollomon equation ( = A N ), is
d
=
d
necking = N
Substitute = S (1 + e) and = ln(1 + e) into the instability equation,
Sde + (1+ e)dS = d = d = S(1+

Lecture 3 Tensors, Coordinate Transformation, Mohrs Circle
A generalization method to transform from one coordinate system to another TENSOR
TRANSFORMATION
Consider the general 2D (plane stress) case
yy
y
y
yx
y
y
y
x
xy
x
x
xx
x
x
xx xy
=
yx yy
=
x '

9
Strain rate effect and strain rate sensitivity
4
3
T ~ 0.3Tm
2
stress
Conventional tensile tests are carried out at
a constant strain rate.
The strength of a material usually increases
with strain rate. On the other hand, strain to
failure usually de

LECTURE
Third Edition
FAILURE CRITERIA: MOHRS
CIRCLE AND PRINCIPAL STRESSES
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
22
Chapter
7.4
by
Dr. Ibrahim A. Assakkaf
SPRING 2003
ENES 220 Mechanics of Materials
Departme