Ae/ME/CE/AM 102c Spring 2013
Mechanics of Solids and Structures  Homework 3
Due April 25,9:00AM,in class.
Instructor;G.Ravichandran,205Firestone,ravi@caltech:edu,x4525
Oce Hours:
Bharat Penmecha,bharat@caltech:edu,SFLGroup Study 23,Mondays 56.00 PM
Pinaky Bhattacarya,pinaky
b@caltech:edu,TOM 014,Wednesdays,5.306.30 PM
Problem 1
Consider a SingleEdged Notched Panel under tension (SENT) made of an aircraft aluminium alloy Al
2024T351.For SENT,the stress intensity factor (SIF) is of the form
K
I
=
1
p
aF
a
W
(1)
where shape factor,F(a=W) is of the form
F(a=W) =
h
1:12 0:23
a
W
+10:55
a
W
2
21:71
a
W
3
+30:38
a
W
4
i
(2)
The nominal critical stress intensity factor for the material is K
Ic
= 30MPa
p
m.The yield stress is 324
MPa and the ultimate tensile strength is 469 MPa.Young's modulus and Poisson's ratio are,73 GPa
and 0.33 respectively.
Figure 1:Problem 1
1.If the panel width (W) is 60mm and the crack length,a,is 20mm,estimate the critical stress at
the crack initiation.What is the critical stress (
c
) as fraction of the ultimate stress.
2.If the design stress is 20% of the ultimate stress,estimate the critical crack length (a
c
) the panel
can tolerate?
Problem 2
Consider a center crack of length (2a) in a large plate made up of linearly elastic material subject to
antiplane shear loading (mode III) with a far eld stress
1
.
Derive the stress and displacement elds,u
3
= w(x
1
;x
2
).Formulate the governing equation in
terms of w and use the traction free boundary conditions in terms of displacement.
1
Using these elds derive the asymptotic stress and displacement elds around the crack tip and
the Stress Intensity factor K
III
.(Use the approximation r=a << 1)
Problem 3
Consider a crack of length 2a that makes an angle with the yaxis in an innite plane subject to far
eld stresses and along the y and x directions as shown.Derive the expressions for the singular
stress components.
Figure 2:Problem 3
2
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