Problem 1
#
Area
1
l
2
l
Displacement
2
!
2
2
!
2
3
l
4
l
2!
2!
5
l
6
l
2
!
2
2
!
2
Area number denotation is referring to previous solution.
Thus, total internal work(pay special attention to the displacement of areas 5,6,7 and 8).
2
" ! l ! k + 2 ! 2" !
The puzzler answers
Nov 1st, 2011
Stress applied
Dislocation sort themselves
out, get stuck in twin
boundaries
Forming twin boundaries with
superimposed small angle grain
boundaries
TEM measures tilt angle which gives
dislocation content of original grain
MSE 4020 HW2SOLUTION 09/05/2011
Problem 1
(a)
0
!(a) =
0
0
F0
A0
(b)
y
Fx
x
Fy
F
F= !
2
F
20
!
2
F
20
(c)
F
y
x
Force along x direction Fx = F0 cos, and Fy= F0 sin
1
! xx =
! yy =
F cos "
F
Fx
=0
= 0 cos2 "
A x A 0 / cos " A 0
Fy
Ay
=
! xy = ! yx =
F0 si
MSE 4020 HW3SOLUTION 09/27/2011
Problem 1
Fail if the following conditions are satisfied,
N
N
!1 + ! N + ! N
!1 + ! N
2
3
2
=
" Pyield #
3
3
!
N
1
3pyield
SAFE
3pyield
3pyield
!
N
2
3pyield
1
Problem 2
Fail if the following conditions are satisfied,
N
MSE 4020 HW4SOLUTION 09/27/2011
Problem 1
(a)
!yy =
"0
E
&
"
( ! = $ #! = $ # 0
yy
( xx
!xx
!zz
E
#=$
=$
%'
!yy
!yy
"0
(
( !zz = $ #!yy = $ # E
)
where , E, and 0 are Poissons ratio, Youngs modulus, and the tensile stress
along y direction, respectively.
MSE 4020 HW6SOLUTION 10/05/2011
Problem 1
(a)
Displacement
2
1
2
3
4
7
5
6
8
2
Contact area
2l
l
l
Totally, there are 8 contact areas(see sketch above), which can be separate into
two groups:
Group 1: Areas 1~6;
Group 2 : Areas 7~8;
Focus on only one are
MSE 4020 HW7SOLUTION 11/10/2011
Problem 1
Force applied on the shank is,
!D2
!D2K
2K =
4
2
!D2K
!D " # " K = FSN =
2
D
$#=
2
D 1 D"n
$#=#= / =
2n
2
FSN =
()
1
Problem 2
First, divide the whole system into blocks A, B, C and D (see sketch above), and
anal
Designation: D882 10
Standard Test Method for
Tensile Properties of Thin Plastic Sheeting1
This standard is issued under the xed designation D882; the number immediately following the designation indicates the year of
original adoption or, in the case of
Designation: D638 10
Standard Test Method for
Tensile Properties of Plastics1
This standard is issued under the xed designation D638; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the
Chapter4
Imperfections: Point and Line
Defects
Dimensional Ranges for Different Classes of Defects
Stress Required to Shear a Crystal
Point Defects
Atomic point defects.
Two most common
point defects in compounds:
Schottky and Frenkel defects.
Point Defec
Twinning
Dislocation Reactions
Deformation by Twinning
The second important mechanism by which metals
deform is the process known as twinning.
Twinning results when a portion of the crystal takes up
an orientation that is related to the orientation of t
Fatigue Life is a Statistical
Quantity
Introduction to the Weibull
distribution
Consider 2 competing Spring Designs, called A and B.
10 Samples of each spring are tested in fatigue
The number of cycles to failure are recorded.
Spring A:
Spring B
726000
52
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Self Assessment of Prelim Exam Preparation
MSE 4020 Fall 2011
1. Can you write down the stress and strain tensor for simple loading
conditions (such as uniaxis tensile and simple shear etc)?
2. How the stress and strain tensor change in different coordina
Designation: D1708 10
Standard Test Method for
Tensile Properties of Plastics by Use of Microtensile
Specimens1
This standard is issued under the xed designation D1708; the number immediately following the designation indicates the year of
original adopti
MSE 4020 HW9SOLUTION 10/26/2011
Problem 1
1.
y
Fy
Fx
r
B
x
A
For two parallel edge dislocations with antiparallel Burgers vectors (shown in the
figure above), the force F(Glide force Fx and Climing force Fy) can be written as:
Fx = !
Gb2 x( x 2 ! y 2 )
2
Mechanical Properties of Materials, Processing, and Design
MSE 4020

Spring 2014
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Mechanical Properties of Materials, Processing, and Design
MSE 4020

Spring 2014
4020 F 2011
HOMEWORK # 15
Due Dec 8 th
1. A cylindrical pressure vessel with a diameter of 4 and wall thickness of 0.35 is made of A533B steel (K 1c = 45
KSI inch1/2). The vessel is made by rolling the steel first into a cylinder and welding the longitud
Mechanical Properties of Materials, Processing, and Design
MSE 4020

Spring 2014
Fatigue Life is a Statistical
Quantity
Introduction to the Weibull
distribution
Consider 2 competing Spring Designs, called A and B.
10 Samples of each spring are tested in fatigue
The number of cycles to failure are recorded.
Spring A:
Spring B
726000
52