Winter 2014
MATLS 3Q03
Assignement 2
Deadline: 10-2-2014
(Dropbox, MSE wing, JHE third oor)
TA: Sheikh Jamil Ahmed, JHE A204, Ext: 27326
email: ahmedsj@mcmaster.ca
Consultation: Thrusdays 3-5 PM
1. a) The interaction energy between two atoms may be phenom
Eng. 4J03, 2013-2014, Tutorial VI SOLUTIONS
Eng. 4J03, Tutorial VI SOLUTIONS
Question1:
The roof of automobiles could be made of (i) DQSK steel (Y=160 MPa, E=200GPa,
=0.3) (ii) HSLA steeel (Y=310 MPa, E=200 GPa, =0.3), or (ii) an aluminum alloy
6111-T4 (Y
1
Open Die Forging
(Chapter 7, Lecture 14)
h0
h1
h2
Friction forces
h0
h1
h2
Barreling
Cracks
2
Direct compression in plane strain of a block slab analysis
Pressure is applied normal to the surface of the block
P
P
x
x + d x
P
h
x + d x
X
x
dx
Y
dx
P
P
1
Axisymmetric compression
(Chapter 7, Lecture 15)
Slab analysis is similar to previous cases (strip
drawing, axisymmetric wire drawing and plane strain
compression of a block).
Element analyzed is a ring of differential thickness,
dr , and height, h , an
1
Slab Analysis Force Balance (Chapter 7)
(Lecture 12)
Slab analysis provide a more accurate analysis of
forming processes compared to the ideal work
method. It accounts for friction and redundant work.
Friction: Coulombs or Amontons law:
Consider two sol
1
Wire or Rod Drawing
(Chapter 7, Lecture 13)
2
Analysis of wire drawing process by slab method:
d=
Fd
A1
Fd
A0
A1
Consider forces acting on a conical element:
Drawing die or
extrusion chamber (container)
p
p
dD
2
D0
dx
dD
2
p
D
D1
x
p
x + dx
x
dx
p
p
Ba
1
Ideal work or uniform Energy
(Chapter 6, Lecture 11)
[1]. One fundamental problem in metal forming
involves prediction of applied loads needed to do
a forming operation.
[2]. Several methods are available accuracy is
dependent upon the assumptions invol
1
Stress
(Chapter 1, Lecture 1)
A typical engineering stress-strain curve:
TS
YS
Fracture
Plastic
Stress
Elastic
Strain
Engineering Stress,
=
P
A0
True Stress,
=
P
A
2
Stress at a point
F
A
P
P
F
Normal stress components, n
A
where F is normal force over
1
Strain (Lecture 2)
l0
l
l l0 l
Engineering Strain, e =
=
l0
l0
True Incremental strain,
d =
(1-18)
dl
l
(1-19)
dl
dA
Incremental strain, d =
=
l
A
Total true strain,
= d =
o
d
= [ln
]
o
= ln
o
2
Two-Dimensional or Plane Strain Deformation
ABCD : small
Eng. 4J03 (2013/14 class) Tutorial III-Hooks Law-, 2014 January.
Eng. 4J03 (2013/14 class) Tutorial III Hooks Law
Question 1
A steel part is under load and the following elastic strains have been measured:
ex = 0.005 , ey = 0.002 , ez = 0.003 , exy = 0.0
1
Mechanics of Pure Bending
(Chapter 12, Lecture 19)
2
Bend Characteristics
3
Mechanics of Pure Bending
Assumptions:
[1]. The material is homogeneous no internal
cavities, edge defects etc.
[2]. The material is isotropic.
[3]. Bending is carried out by th
1
Plastic Anisotropy
(Chapter 13, Lecture 21)
Anisotropy means that properties of a material
depend upon the direction in which the property is
tested.
Most metals display anisotropic behaviour in
electrical, magnetic, thermal and mechanical
properties.
R
1
Bending and Springback of a
Work Hardening Material
(Chapter 12, Lecture 20)
= K n
Power law,
z
= K ' n = K '
x
x
r
and
where
4
K '= K
3
n
(A)
( n + 1) / 2
K ' plane strain strength coefficient
K and n come from uniaxial tension test.
t
r
r
(12-2)
1
Flat Rolling (Lecture 17)
Determination of Neutral Point
Previous lecture gives roll pressure distribution as:
Entry:
Exit:
where
(
)
P = Y h / h 0 exp[ (H 0 H )]
h
P = Y
h
f
(11)
R
R
tan 1
h
h
f
f
(5)
R
R
, P =Y
tan 1
h
hf
f
(A)
def n
H = 2
1
Rolling
(Chapter 7, Lecture 16)
Perhaps the largest amount of metal is processed by
rolling a primary metal forming process for
subsequent sheet forming (or stamping) operations.
2
Flat Rolling
Rolling can be assumed as a plane strain compression
proble