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