NAME:____________________

MAE 543

Fracture Mechanics

NC State University

Homework #1

DUE: Tues Jan 25th Spring Semester 2011

1.) Describe two real-world examples of failures involving fracture, one from your own

experience and one found using the World-Wide-Web. Write up a one paragraph

summary for each of your examples. These should not be examples previously discussed

in class or found on the class website.

2.) Two steels are being considered for the construction of a 30 in. diameter pressure tank

to hold compressed gas at 1000 psi. The properties of the two steels are: Steel A: ys=50

ksi and KIc=90 ksi in1/2

, and Steel B: ys=130 ksi and KIc=55 ksi in1/2

. For a desired safety

factor against yield of 2.0 and against fracture of 6.0, select the optimal steel for this

application and determine the minimum wall thickness required. For the fracture

mechanics analysis use the following stress intensity factor: KI= hoop( a)1/2

, where hoop

is the hoop stress and 2a is the total crack length for an assumed longitudinal flaw.

Assume the total crack length 2a is equal to twice the wall thickness.

3.) In a fracture toughness test, the load and corresponding crosshead displacement at

which cracking commenced were P1 and u1, respectively. After the load had fallen to P2

(with displacement u2), by which time the crack had propagated some distance, the test

piece was unloaded. The unloading line went back to the origin. Prove that the critical

energy release rate Gc is given by

12

1221

cAA

uPuP2

1

G)(

where A1 is the initial crack area and A2 is the final crack area.

4.) Problems in textbook: 7.1a,b, 7.2.

P1u1

P2u2

Crosshead Movement (u)

Load (P)