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5.1 Fatigue and Endurance
Problem 1 - It is desired to construct a 75 mm gun for a pressure of 43,000 psi. The chamber
diameter has been chosen to be 3.1 inches. If we use AISI 4340 steel with a yield strength (SY)
of 100,000 psi, determine the outer diameter of the weapon over the chamber. Assume that the
tube is NOT autofrettaged and the endurance limit (S’n) for 4340 is 0.875SY for the amount of
cycles desired. Assume the following factors from our cyclic loading discussion: CR = 0.93, CG
= 0.95 and CS = 0.99. Assume the chamber is open ended as a conservative measure.
Problem 2 - A shotgun is to be modified so that it can be rigidly mounted to a vehicle. The recoil
force is estimated to be 800 lbf. There are two failure points: a weld on the barrel and two 10-32
screws connecting the receiver to the barrel. If we assume that each point of failure (the two
screws act together) must individually take the full load, determine how many firings can be
achieved using the curve for steel provided in the text and the data below:
Both materials:
CR = 0.8
CG = 0.85
Screws:
CS = 0.78
Shear Area = 0.019 in2 each
Welds (1/8” Fillet):
CS = 0.5
Shear Area = 0.247 in2
( )
( )( )( )
=
==
22 in
lbf
292,11
in
lbf
5.085.08.0
839,3
SGR
n
nCCC
S
S
This tells us the weld will survive infinite numbers of cycles. The weak link is clearly the
screws.
5.2 Tube Design
Problem 3 - The gun in problem P 5.1.1, is sized to a 20 inch O.D. The manufacturer decides to
autofrettage the weapon with 75,000 psi of hydraulic fluid. Assuming the material behaves
elastic-perfectly-plastic:
a.) Approximately to what radial distance does the compressive layer extend into the
tube wall?
( )
=
−
+
=222
22
2in
lbf
910,68
80.110
80.110
in
lbf
584,64
2
( )( ) ( )( ) ( )
=
−+−−+−−
=22
222
in
lbf
630,115
in
lbf
2
584,6400910,68584,64910,68
2
E
