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Mechanical Behavior of Materials
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AIN SHAMS UNIVERSITY
FACULTY OF ENGINEERING
NEW PROGRAMS IN MATERIALS ENGINEERING
NEW PROGRAMS IN MANUFACTURING ENGINEERING
Mechanical Behavior of Materials MATL 362 1/2
Nahid 1
Question 1
ex = (1/E)[σx - ν (σy + σz)] = (1/E)( σx - ν σx) = (σx /E)(1-ν) (1)
ey = (1/E)[σy - ν (σz + σx)] = (1/E)( σx - ν σx) = (σx /E)(1-ν) (2)
ez = (1/E)[σz - ν (σx + σy)] = (1/E)(-2ν σx) (3)
By dividing 2 over 1 ez/ex = -2ν/ (1-ν)
Substituting in 2 1.0 x 10-3
= (σx/70) (1-0.3) σx = 0.1 GPa
Substituting in 3 ez = 0.00086 mm/mm
Question 2
The area under the stress-strain curve is a measure of the work done or energy
required to deform unit volume of the metal. Generally,
Work done = Force x distance moved
. .
dW F dl
dlBut d i e dl ld
l
F A
AIN SHAMS UNIVERSITY
FACULTY OF ENGINEERING
NEW PROGRAMS IN MATERIALS ENGINEERING
NEW PROGRAMS IN MANUFACTURING ENGINEERING
Mechanical Behavior of Materials MATL 362 2/2
Nahid 2
dW Ald V d
Elastic Work Done
In elastic portion:
Ee
edW VEede
2 2
2 2e
VEe VW VE ede
E
Work done per unit volume
Plastic Work Done
Over the plastic portion:
n
tK
1
1 1
nn t
p
VVKW VK d
n n
Work done per unit volume Wp/V
2 2
/2 2
e
EeW V
E
1
1 1
n
tK
n n