FAILURE CRITERIA: MOHRS
CIRCLE AND PRINCIPAL STRESSES
A. J. Clark School of Engineering Department of Civil and Environmental Engineering
Dr. Ibrahim A. Assakkaf
ENES 220 Mechanics of Materials
P4 Stress and Strain
Dr. A.B. Zavatsky
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.
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
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
August 23, 2001
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
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
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
Consider the general 2D (plane stress) case
Strain rate effect and strain rate sensitivity
T ~ 0.3Tm
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