Ae/ME/CE/AM 102c Spring 2013

Mechanics of Solids and Structures - Homework 3

Due April 25,9:00AM,in class.

Instructor;G.Ravichandran,205-Firestone,ravi@caltech:edu,x4525

Oce Hours:

Bharat Penmecha,bharat@caltech:edu,SFL-Group Study 2-3,Mondays 5-6.00 PM

Pinaky Bhattacarya,pinaky

b@caltech:edu,TOM 014,Wednesdays,5.30-6.30 PM

Problem 1

Consider a Single-Edged Notched Panel under tension (SENT) made of an aircraft aluminium alloy Al

2024-T351.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

anti-plane 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 y-axis 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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