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Flavin, Daniel
Finite Element Stress Analysis of a 1903 Springfield Rifle Bolt
by
Daniel J. Flavin
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Professor Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2014
© Copyright 2014
by
Daniel Flavin
All Rights Reserved
ii
CONTENTS
CONTENTS ..................................................................................................................... iii LIST OF TABLES ............................................................................................................ iv LIST OF FIGURES ........................................................................................................... v GLOSSARY ..................................................................................................................... vi KEY WORDS .................................................................................................................. vii ABSTRACT ................................................................................................................... viii 1. BACKGROUND ......................................................................................................... 1 1.1 PROBLEM DESCRIPTION .............................................................................. 3 2. METHODOLOGY ...................................................................................................... 5 2.1 GEOMETRY ..................................................................................................... 5 2.2 MATERIALS ..................................................................................................... 6 2.3 FEA .................................................................................................................... 7 3. RESULTS AND DISCUSSION ................................................................................ 10 3.1 TWO DIMENSIONAL EXAMPLE ................................................................ 10 3.2 THREE DIMENSIONAL RESULTS .............................................................. 11 3.2.1 Displacement ........................................................................................ 12 3.2.2 Peak Stress ........................................................................................... 12 3.2.3 Plastic Deformation.............................................................................. 14 4. CONCLUSION.......................................................................................................... 17 REFERENCES ................................................................................................................ 19 Appendix A: Material Properties, SAE 2340 Steel ......................................................... 20 Appendix B: COMSOL Report ....................................................................................... 21 iii
LIST OF TABLES
Table 1: Material Properties of Heat Treated SAE 2340 ................................................... 6 iv
LIST OF FIGURES
Figure 1: Bolt Action Rifle Nomenclature and Cross Section (Brophy 67) ...................... 2 Figure 2: Bare Rifle Bolt ................................................................................................... 2 Figure 3: Outline Diagram ................................................................................................. 4 Figure 4: Bolt Model in CAD (exploded view) ................................................................. 5 Figure 5: FEA Geometry ................................................................................................... 7 Figure 6: Boundary Load ................................................................................................... 8 Figure 7: Fixed Constraint ................................................................................................. 8 Figure 8: Model Mesh ....................................................................................................... 9 Figure 9: Two Dimensional FEA Sample (Von Mises Stress) ........................................ 10 Figure 10: Calculated Values of Displacement ............................................................... 11 Figure 11: Surface Stress Values (Von Mises) ................................................................ 12 Figure 12: Surface Stress Values (Von Mises), Peak ...................................................... 13 Figure 13: Calculated Areas of Failure ............................................................................ 14 Figure 14: Calculated Areas of Failure (Cross Section) .................................................. 15 Figure 15: Percentage of Yield ........................................................................................ 16 Figure 16: Barrel Rupture Due to Obstructed Barrel (Hatcher 195) ............................... 17 v
GLOSSARY
Action: the mechanical parts of a firearm, which manipulate the cartridge and seal the
breech.
Barrel: a metal tube, through which the projectile is propelled by a controlled explosion
and the resulting rapid expansion of gas.
Bolt: the part of the firearm action which blocks the rear of the chamber (sealing the
breach) during firing, but is moved to allow a new cartridge to be loaded.
Bolt action: a specific form of firearm action in which the bolt is manipulated by hand
between each round fired.
Bolt thrust: the amount of rearward force exerted by the cartridge during firing. The
force is transmitted into the bolt, which must be strong enough to contain it.
Breech: the end of the barrel closest to the operator, where the chamber is found.
Cartridge: a unit of ammunition consisting of a bullet, gunpowder, casing, and primer
assembled into a single piece.
Chamber: The portion of the barrel in which the cartridge is inserted prior to firing. The
shape of the chamber will closely match the shape of the cartridge.
Firearm: a portable weapon which launches projectiles through an explosive force
Lug: a projecting portion of the assembly for the purpose of transferring forces between
two parts
Muzzle: the end of the barrel from which the projectile exits
Proof Load: a cartridge loaded to a higher than standard pressure, used for safety testing
of newly manufactured firearms
Receiver: a portion of the firearm action which houses the operating pieces and connects
to the stock and barrel assemblies.
Stock: the portion of the firearm used by the operator for support and aiming by holding
against the shoulder
Trigger: the mechanical lever used to actuate the firing mechanism
vi
KEY WORDS

Bolt action

COMSOL

Finite Element Analysis (FEA)

Locking lug

M1903 Springfield

Receiver

Rifle

Stress
vii
ABSTRACT
This study analyzed the worst-case scenario loading and resulting stressed of the bolt
lugs in a M1903 Springfield bolt action rifle. The load-carrying portion of the bolt head
and the corresponding portion of the receiver were modeled in Solidworks, using legacy
drawings and surviving examples of spare bolts. The model was then loaded into
COMSOL finite element analysis software using material properties of the now obsolete
steel. Using the static solid mechanics module with plasticity, the loading and internal
stresses of the bolt lugs were calculated. Results showed that the stresses in the bolt lugs
approached, but did not exceed, the yield strength of the material.
viii
1. BACKGROUND
At its simplest, a firearm can be thought of as a tube strong enough to resist the forces of
an explosion, which is plugged at one end and open at the other. In modern cartridge
firearms, the plug must be mobile in order to allow loading and removal of cartridges.
This mobile plug is called the bolt, and must be capable of withstanding many thousands
of pounds of pressure during firing. To do so, some low pressure firearms will use the
inertia of the bolt, but most will require the bolt to interlock with the receiver, the main
structural component of a rifle. Locking methods, and the methods of operating them,
vary widely amongst different types of firearms. One common method is the manually
operated bolt, or bolt action, rifle. First developed in the mid-1800s, and used by both
military and civilians, it is still a popular method of achieving power and accuracy in
sporting and hunting applications.
Many modern bolt action rifles are "Mauser-style" rifles, based off a design
developed for the German military in 1898. This action uses two large locking lugs at
the front of the bolt to engage with the receiver. The operational portions of a rifle of this
style are shown in Figure 1, with important portions of the assembly color-coded. A bare
bolt of this style is shown in Figure 2. The chamber, with the loaded cartridge, would be
to the right of the bolt face.
While any individual rifle is capable of firing a specific cartridge, a
family of rifles may share identical receivers and bolts with only minor modifications
required to fire a variety of different cartridges. Each unique caliber of cartridge has a
specified peak pressure, which until recently was a "best guess" due to the difficulty in
measuring pressures upwards of 50 ksi in a matter of milliseconds. In order to ensure
strength, designs were often very conservative. Some designs, such as the Japanese Type
99 Arisaka, have been known to regularly withstand pressure well above the design
cartridge values (Hatcher 210). Less conservative designs, particularly for military arms
which saw high firing counts, would occasionally have to be recalled and rebuilt in order
to ensure the safety of the user. Modern measuring methods have resulted in much more
accurate measurements of peak pressure, and these values are regulated and published by
two organizations, the Sporting Arms and Ammunition Manufacturers' Institute
(SAAMI) in the United States, and the Commission Internationale Permanente pour
1
Figure
F
1: Boltt Action Rifle Nomenclatur e and Cross S
Section (Broph
hy 67)
Red: Bolt Bo
ody
Orange:
O
Receiv
ver
Blue: Barrel
Yeellow: Cartridgge
Figu
ure 2: Bare Riffle Bolt
1: Bolt face 2: Locking lu
ugs 3: Extracttor grooves 4 : Bolt body 5: Backup lug 6: Bolt handlee
2
l'Epreuve des Armes à Feu Portatives (Permanent International Commission for
Firearms Testing, or CIP) in Europe. By knowing the maximum cartridge pressure and
the size of the base of the cartridge, the force imparted by the cartridge on the bolt face
can be calculated. Called the “bolt thrust”, this value is the maximum loading which the
bolt may be expected to withstand during firing. Any given firearm action has a
maximum bolt thrust value; as long as each cartridge chosen for use remains below the
calculated bolt thrust, the action is safe to operate.
To test the level of safety, manufacturers are required to proof test their firearms,
under both SAAMI and CIP regulations. Proof testing usually consists of firing “proof
rounds,” cartridges loaded at approximately 130% of the standard peak pressure of the
firearm being tested. The firearm is then disassembled and examined for any sign of
fracture or plastic deformation. Particular attention must be paid to the locking
mechanism, such as the bolt lugs described previously.
In older firearms, with less advanced manufacturing techniques, this testing
procedure was particularly important to ensure safety. Despite the testing, issues would
occasionally arise. For example, in the period leading up to the First World War, the
United States army used the M1903 Springfield rifle, a bolt action built on the Mauser
pattern (so closely, in fact, that the Mauser company later sued the US government and
won royalties for patent infringement (Brophy 323)). Inconsistent heat treatment of the
rifle receivers, built of high-carbon steel, resulted in some rifles in the field suffering
catastrophic failures of the receiver during firing, at times severely injuring the
individual holding the rifle. To solve this problem, better heat treat procedures were
implemented. During the build-up to the Second World War, the raw materials were
changes to a nickel-bearing steel known as WD 2340, with the heat treatment altered to
reflect the requirements of the new steel.
1.1 PROBLEM DESCRIPTION
The most dangerous failure of a bolt action rile is the failure of the locking lugs, as this
will both release the high pressures normally contained with the chamber, and propel the
bolt rearwards, into the face of the firer. The sensible engineering approach, then, is to
design the bolt-to-receiver interface with a large factor of safety, particularly in military
3
firearms
f
which are expected to hav
ve a long sservice life despite harssh environm
ments,
careless
c
han
ndling, and potentially
p
inconsistent
i
ammunitionn. Historicaally, these ddesign
calculations
c
have been done with pencil
p
and ppaper, but m
modern techhnology alloows a
more
m
advancced and acccurate appro
oach. Utiliziing computeer aided deesign (CAD)) and
finite
f
elemen
nt analysis (FEA), a design
d
can bbe analyzedd electronicaally to deterrmine
failure
f
points and modess. In this rep
port, the M1903 Springffield rifle boolt was meassured,
modeled,
m
and
d analyzed for
f stress loaads under firring conditioons. A schem
matic view oof the
bolt
b cross seection is giv
ven in Figu
ure 3, whichh includes thhe primary parts and fforces
involved.
i
Figu
ure 3: Outline Diagram
4
2. METHODO
M
OLOGY
2.1
2
GEOMETRY
The
T model was
w built in SolidWorks
S
computer aiided design ((CAD) softw
ware. Dimennsions
were
w pulled from a goveernment draw
wing of a fieeld guage (B
Brophy 596), used to estaablish
safe
s
headspaace in a riflee. This was compared
c
too a vintage M
M1903 bolt, to ensure thhat all
critial
c
dimen
nsions on thee field guagee matched th e critcal dim
mension of thhe “live” bollt. All
dimensions
d
were
w
modeled as least material tollerance limitts, in order to take the most
conservative
c
e case.
Figure 4: Boltt Model in CA
AD (exploded vview)
1: Cartrridge Base
2: Bolt Heaad
5
3: Reeceiver Ring
Only the head of the bolt, the bolt face to the rear of the locking lugs, was considered for
the FEA. This was done in order to reduce calculation time, as the remaining portions of
the bolt are not stressed to any significant factor. Portions of the bolt forward of the front
bolt face were not modeled for similar reasons. All units were done in US customary
units (inch/pounds/seconds), rather than metric, to match source material.
Models were also created for the base of the cartridge, using the SAAMI
standard sizing, and a receiver ring. By modeling the base of the cartridge, known load
pressures could be directly input into the model, reducing the likelihood of a calculation
error. The receiver ring is a stand in for the main body of the receiver. Clearance hole
sizing on the reaction ring was taken from the machining plan for the receiver (Brophy
549), but other dimensional values may be approximate due to the difficulty in locating
an accurate dimensional drawing of the finished receiver.
2.2 MATERIALS
Both the bolt and the receiver are made from a now-obsolete steel known as WD 2340
(Hatcher 224). This is the War Department’s designation for Society of Automotive
Engineering (SAE) 2340 steel (Hatcher 231), which was taken off the SAE standards in
the early 1950s. The bolt material was hardened to a Rockwell Hardness C of 33-44
HRC (Hatcher 226), equal to approximately 280 – 400 on the Brinell scale of hardness.
Using the lower end of the hardness scale, aproximately 300 Brinell, results in the
material properties shown in Table 1, taken from the material available in Appendix A.
Property
Value
Young’s Modulus, elastic (typical to steels)
29,700 ksi
Young’s Modulus, plastic (estimated)
300 ksi
Poisson’s Ration (typical to steels)
0.29
Density
0.284 lb/in3
Yield Stress
128 ksi
Terminal Stress
150 ksi
Table 1: Material Properties of Heat Treated SAE 2340
6
2.3
2
FEA
The CAD model
m
was im
mported into COMSOL F
Finite Elemeent Analysiss (FEA) softw
ware,
using
u
the sttationary (sttatic) solid mechanics m
module. Thhis was chosen in lieu of a
dynamic
d
anaalysis to red
duce the eff
ffect of the high strain rate on thee strength oof the
materials.
m
As the strain rate increasses, the valuues for yieldd and terminnal strenegthh will
also
a rise. By
y utilizing a static analyssis, the resullts are more conservativve than the vvalues
given
g
by the dynamic mo
odule.
del is show
w in Figure 5. The maaterial properties
The orientation of the mod
described
d
in section 2.2 were input for
f the receivver ring andd bolt. Materrial propertiees for
C26000
C
anneealed cartrid
dge brass werre used for tthe base of thhe receiver ((MatWeb, LL
LC).
Figure 5: FEA G
Geometry
Modeel loading was
w determin
ned through examinatioon of worst-ccase scenariios of
bolt
b thrust lo
oading. The cartridge
c
fireed by the M 1903 rifle iss the .30-06, with a maxiimum
SAAMI
S
presssure rating of 60,000psi (SAAMI)) . Proof tessting of the rifle occurrred at
7
75,000psi (Hatcher 198). Under normal firing conditions, full pressure would be
contained with the case, and friction between the case sides and the rifle chamber would
decrease the bolt thrust. However, abnormal conditions, including excess lubricant in the
chamber or the structural failure of the cartridge, can result in the full thrust being
transmitted to the bolt. Therefore, the maximum proof loading pressure of 75,000 psi
was applied to the area of the cartridge base, as shown by the area highlighted blue in
Figure 6. This is considered the worst case loading condition.
The leading face of the receiver ring was fixed in position, as shown by Figure 7.
By modeling the receiver ring in this way instead of having the bolt anchored against an
unmoving ring, reactive forces of the receiver are more closely approximated. Failing to
allow some displacement of the receiver locking surfaces would result in artificially high
stress loads at the points of contact between the bolt and the receiver.
Figure 6: Boundary Load
Figure 7: Fixed Constraint
Loaded surface is highlighted in blue.
Constrained surface is highlighted in blue
In order to insure that the flexibility of the lugs would be properly simulated,
plasticity with strain hardening was added to the model. While increasing calculation
time, it ensures a more accurate result due to localized portions of the model undergoing
plastic deformation in areas of high stress (such as the root fillets of the locking lugs). As
strain hardening data was not available for WD2340 steel, the strain hardening curve for
8
SAE 4340 was used. The material properties of SAE 4340 are very similar to WD2340,
and SAE 4340 is a material commonly used for modern rifle bolt actions.
Meshing was done with the "Physics Controlled Mesh" option in COMSOL, with
the sizing set to "Fine." The resulting mesh was reviewed, with very fine elements in the
areas of most concern. Finer meshes were attempted, but very quickly reached the limits
of the computer hardware available. The final acceptable mesh is shown in Figure 8,
with just fewer than 117,000 tetrahedral elements ranging from 0.015 to 0.12 inches.
More information on the meshing values can be found in Appendix B.
Figure 8: Model Mesh
9
3.
3 RESUL
LTS AND D
DISCUSS
SION
3.1
3
TWO
O DIMENS
SIONAL EXAMPL
E
LE
Some
S
difficu
ulty was had
d in attaining
g reliable reesults from tthe FEA anaalysis, due tto the
inherent
i
com
mplexity of the geom
metry. Thiss was partticularly truue at pointts of
discontinuou
d
us loading where
w
some increase
i
in lloading wouuld be expeccted due to shear
effects,
e
but not
n to the exttent often sh
hown by the model. To ddemonstrate this effect, a two
dimensional
d
cross section of the boltt was modeleed and analyyzed.
Figure 9: Two Dimen
nsional FEA S
Sample (Von M
Mises Stress)
10
The results are shown in Figure 9. The topmost picture shows the bolt head, with the bolt
thrust loading being applied from the top. The central image shows the extreme ends of
the contact area between the bolt and receiver have areas of stress significantly higher
than the surrounding areas. The bottom image illustrates how these high stress
concentrations are the result of a single node, at the edge of the contact point. The
extreme peak values are representative of the limits of the FEA software to handle edge
conditions.
3.2 THREE DIMENSIONAL RESULTS
The three dimensional model took approximately ten minutes to calculate on an
3.30GHz Intel Core I5 machine with 8 gigabyte of RAM. The results were then plotted
for several different values: displacement, areas of peak stress, and areas of plastic
deformation.
Figure 10: Calculated Values of Displacement
11
3.2.1
Displacement
The displacement values are shown in Figure 10, where the bolt face is show as moving
0.00002 inches under firing load. While these values do not directly affect the factor of
safety inherent in bolt design, they are important to help determine areas which will be
expected to undergo greater values of strain hardening. The displacement is also of
interest when considering the overall stretching of the bolt and receiver, as higher
rigidity is often correlated to a more accurate firearm.
Figure 11: Surface Stress Values (Von Mises)
3.2.2
Peak Stress
The peak calculated stress for the model was 4.2x105 psi, which is significantly higher
than the terminal strength of the material, shown in Table 1 as 1.5x105 psi. However,
examining Figure 11 will show that the bulk of the model is well below the peak value,
with higher stresses at the contact points and several points on the bolt lugs. The peak
values are in fact nearly invisible on the model, unless careful use of the zoom function
12
is
i used, as shown in Figure
F
12. These
T
peak loads appeear to be a function oof the
calculation
c
liimits at the edges
e
of the mesh at tho se points, ass demonstratted in sectionn 3.1.
Fig
gure 12: Surfa
ace Stress Valu
ues (Von Misees), Peak
In
I order to determine
d
th
he exact locaation of the peak loadinng, the Von Mises stresss was
compared
c
to
o the termin
nal strength
h of the maaterial. This highlightedd every nodde or
element
e
wheere the calcullated stress would
w
resultt in a materiaal failure durring firing. T
These
results
r
are sh
hown in Figu
ure 13. The black
b
coloraation in this figure highliights areas w
which
exceed
e
the teerminal stren
ngth of the material.
m
As expected froom previous results, the areas
are
a all edgee discontinuiities in the mesh. Whi le it is possible that soome of the high
stresses
s
at th
he root of thee bolt lugs would
w
be conncerning to a designer, tthe relativelyy low
stresses
s
of th
he surroundiing area sug
ggest that thhe bolt would not underrgo failure dduring
firing,
f
which
h real world testing
t
has borne
b
out.
13
Figure 13:: Calculated A
Areas of Failurre
Blacck areas exceed the terminal strength of thee material
3.2.3
3
Plasttic Deforma
ation
As
A entering the plastic range
r
is gen
nerally consiidered a failuure for a staatic structuree, the
examination
e
of plastic deeformation was
w the mosst important result of thee analysis. D
Due to
the
t tight toleerance requirrements of fiirearms actioons, plastic ddeformation of the bolt m
might
easily
e
result in an unsaffe or unusablle firearm. A
As shown inn Figure 11, the stress vvalues
appear
a
to app
proach and possibly
p
excceed the yieldd strength of 1.28x105 sshown in Tabble 1.
However,
H
th
hat value caan be expected to rise with the innclusion of strain hardeening.
Figure
F
14 deemonstrates that differen
nce betweenn the yield ccalculation w
with and wiithout
strain
s
harden
ning. In the left-hand im
magine of thhe figure, a ccross sectionn of the bollt and
14
receiver, the areas in red are where the calculated Von Mises stress exceeds the initial
yield strength of the material. This image would suggest that the bolt lugs are too small,
as large portions of them enter the plastic range of the material. However, the right-hand
picture shows the same cross section with the inclusion of strain hardening effects. In
this image, several isolated and disjoint nodes appear to have entered the plastic range,
suggesting the material is on the cusp of deformation, but most portions of the bolt lugs
are not yet ready to yield.
Figure 14: Calculated Areas of Failure (Cross Section)
Left: Without strain hardening
Right: With strain hardening
Having determined that the bolt lugs are nearing the yield point, but not yet entering
it when the effects of strain hardening are accounted for, Figure 15 shows the results of
dividing the Von Mises stress by the yield stress, and plotting is surfaces. In this
diagram, each surface identifies a ten percent increase in stress ratio. The maximum
stress is 95.05% of the yield stress. This suggests that the bolt lugs will not undergo
plastic deformation in the worst-case conditions modeled here. However, any higher
loading will probably result in a factor of safety less than one, indicating the imminent
failure of the bolt.
15
Figure 15: Percentage of Yield
16
4. CONCLU
USION
During
D
the modeling
m
an
nd FEA porttions of thiss analysis, eevery effort was taken to be
conservative
c
e in calculatiions. To anaalyze the bollt under worrst possible ffiring condittions,
three
t
areas were
w
consid
dered. First, the dimenssions of thee model werre taken in least
material
m
con
ndition, resullting in the weakest
w
boltt allowed byy drawing tollerances. Seccond,
the
t maximum
m possible bolt
b loading was utilizedd, which greeatly exceedds anything llikely
to
t be seen during
d
the seervice life of
o the rifle. F
Finally, desppite conditioons which w
would
result
r
in high
h strain ratess, the effect of strain ratte on yield sstrength was ignored. Deespite
these
t
handiccaps, the bolt stress waas limited too around 95% of the yiield stress oof the
material,
m
tho
ough only du
ue to the effeects of strainn hardening. This suggessts that the bbolt is
at
a the very liimits of its ability
a
to witthstand the fforce of firinng, and that m
minor changges to
material
m
prop
perties or calculation meethods may sshow failuree of the bolt llugs.
Moree accurate calculation of bolt sttress wouldd require a more thorrough
understandin
u
ng of the matterial properrties. While tthis analysiss used the beest available data,
a modern tessting of WD 2340 steel to
t understannd the effectss of heat treatment and sstrain
hardening
h
would
w
result in
i more accu
urate FEA innputs. Effortts to refine tthe FEA meshing
and
a analysis to help remo
ove the mesh
h discontinuuities would also reduce spurious datta.
Figure 16: Barrel Ruptu
ure Due to Obsstructed Barrrel (Hatcher 1995)
The mo
odel method
ds used heree may also be extendedd to other pparts of the rifle.
Modeling
M
thee chamber an
nd barrel, in
ncluding the friction coeffficient betw
ween the carttridge
17
and chamber walls, would result in a more accurate measure of the bolt thrust. Including
the barrel in the analysis could also demonstrate which would fail first, the hoop strength
of the barrel or the shear strength of the bolt locking lugs. This question is raised by
images such as the one shown in Figure 16, where a rifle was fired with the barrel filled
with preservative grease, destroying the barrel and stock of the rifle. However, the bolt
and receiver did not fail. This suggests that the maximum loading of the bolt and
receiver are not the weakest link in this particular rifle design. By extending this analysis
performed in this report to all pressure containing parts of the rifle, a good balance of
economy and safety can be obtained. Each part can be more accurately made to the ideal
safety level, without overbuilding any single part significantly beyond the strength of its
neighbors.
18
REFERENCES
Al, Varmint. Stolle Panda Bolt Stress and Deflection Analysis. 8 February 2013.
Website. 9 September 2014. <http://www.varmintal.com/abolt.htm>.
Brophy, William S. The Springfield 1903 Rifles (The Illustrated, Documented Story of
the Design, Development, and Production of all the Models of Appendages, and
Accessories). Mechanicsburg, PA: Stackpool Books, 1985. Book.
Hatcher, Julian S. Hatcher's Notebook : A Standard Reference Book For Shooters,
Gunsmiths, Ballisticians, Historians, Hunters, And Collectors. Harrisburg, PA:
Stackpole Co., 1957. Book.
Iron and Steel Division Report. "Iron and Steel Specifications." The Journal of the
Society of Automotive Engineers IX.6 (1921): 392-422. Journal Article.
Lilja, Dan. A Look at Bolt Lug Strenght. 2002. Website. 8 September 2014.
<http://www.riflebarrels.com/articles/custom_actions/bolt_lug_strength.htm>.
MatWeb, LLC. Cartridge Brass, UNS C26000 (260 Brass), OS025 Temper tubing. 2014.
Web Site. 02 10 2014.
Ozmen, Dogan, et al. "Static, dynamic and fatigue analysis of a semi-automatic gun
locking block." Engineering Failure Analysis 16.7 (2009): 2235-2244.
SAAMI. "Maximum Cartridge / Minimum Chamber, 30-06 Springfield." Technical
Paper.
2012.
PDF
Document.
24
September
2014.
<http://www.saami.org/pubresources/cc_drawings/Rifle/3006%20Springfield.pdf>.
—. "Velocity and Piezoelectric Transducer Pressure: Centerfire Rifle." Industry
Standard.
2013.
Digital
Docutment.
<http://www.saami.org/specifications_and_information/specifications/Velocity_
Pressure_CfR.pdf>.
Yu, V.Y., et al. "Failure Analysis of the M-16 Rifle Bolt." Engineering Failure Analysis
12.5 (2005): 746-754. Web.
19
Appendix A: Material Properties, SAE 2340 Steel
The following information is taken from the Journal of the Society of Automotive
Engineers, Volume 9, 1921.
Material Composition, in Percentage:
Carbon
0.35-0.45
Manganese
0.50-0.80
Phosphorus
0.04 max
Sulfur
0.045 max
Nickel
3.27-3.75
Material Properties, taken from tensile tests:
20
Appendix B: COMSOL Report
The following pages contain the COMSOL output report, including all major inputs and
values used in the analysis.
21
Appendix B: FEA Report from COMSOL
1 of 28
FEA Locking Stackup Rev06
Date Oct 16, 2014 9:50:13 PM
Contents
1.
Model 1 (mod1)
1.1.
Definitions
1.2.
Geometry 1
1.3.
Materials
1.4.
Solid Mechanics (solid)
1.5.
Mesh 1
2.
Study 1
2.1.
Stationary
2.2.
Solver Configurations
Results
3.
3.1.
Plot Groups
1.1. Definitions
1.1.1. Coordinate Systems
Boundary System 1
Coordinate system type Boundary system
Identifier
sys1
Settings
Name
Coordinate names
Value
{t1, t2, n}
Create first tangent direction from Global Cartesian (spatial)
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1.2. Geometry 1
Geometry 1
Units
Length unit in
Angular unit deg
Geometry statistics
Property
Space dimension
Value
3
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Number of domains
3
Number of boundaries 109
Number of edges
276
Number of vertices
170
1.2.1. Import 1 (Imp1)
Selections of resulting entities
Name
Value
Geometry import 3D CAD file
Filename
R:\Private\Documents\School\Master's Project\CAD\LockupStack_REV04.SLDASM
1.3. Materials
1.3.1. WD2340
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WD2340
Selection
Geometric entity level Domain
Selection
Domains 1–2
Material parameters
Name
Value
Unit
Density
7850[kg/m^3] lb/in^3
Young's modulus
205e9[Pa]
lb/(in*s^2)
Poisson's ratio
0.28
1
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Initial yield stress
1.28e5
lb/(in*s^2)
Isotropic tangent modulus 205e7[Pa]
lb/(in*s^2)
Basic Settings
Description
Value
Relative permeability
{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Electrical conductivity
{{4.032e6[S/m], 0, 0}, {0, 4.032e6[S/m], 0}, {0, 0, 4.032e6[S/m]}}
Coefficient of thermal expansion {{12.3e-6[1/K], 0, 0}, {0, 12.3e-6[1/K], 0}, {0, 0, 12.3e-6[1/K]}}
Heat capacity at constant pressure 475[J/(kg*K)]
Relative permittivity
{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
Density
7850[kg/m^3]
Thermal conductivity
{{44.5[W/(m*K)], 0, 0}, {0, 44.5[W/(m*K)], 0}, {0, 0, 44.5[W/(m*K)]}}
Young's modulus and
Poisson's ratio Settings
Description
Value
Young's modulus 205e9[Pa]
Poisson's ratio
0.28
Elastoplastic material model Settings
Description
Value
Initial yield stress
1.28e5
Isotropic tangent modulus
205e7[Pa]
Kinematic tangent modulus
Hill's coefficients
{0, 0, 0, 0, 0, 0}
Initial tensile and shear yield stresses {0, 0, 0, 0, 0, 0}
1.4. Solid Mechanics (Solid)
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Solid Mechanics
Selection
Geometric entity level Domain
Selection
Domains 1–3
Equations
Used products
COMSOL Multiphysics
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Geomechanics Module
1.4.1. Linear Elastic Material 1
Linear Elastic Material 1
Selection
Geometric entity level Domain
Selection
Domains 1–3
Equations
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Settings
Settings
Description
Value
Solid model
Isotropic
0
Force linear strains
0
No descr used; This is a dummy resource for controlling
anisotropic damping.
Standard (XX, YY, ZZ, XY, YZ, XZ)
Nearly incompressible material
0
Specify
Young's modulus and Poisson's ratio
Calculate dissipated creep energy
0
Young's modulus
From material
Poisson's ratio
From material
Elasticity matrix
{{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0,
0, 0}, {0, 0, 0, 0, 0, 0}}
Elasticity matrix, Voigt notation
{{0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0,
0, 0}, {0, 0, 0, 0, 0, 0}}
Density
From material
Properties from material
Property
Material
Property group
Young's modulus WD2340
Young's modulus and Poisson's ratio
Poisson's ratio
WD2340
Young's modulus and Poisson's ratio
Density
WD2340
Basic
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Young's modulus UNS C26000 (UNS C26000) [solid] Young's modulus and Poisson's ratio
Poisson's ratio
UNS C26000 (UNS C26000) [solid] Young's modulus and Poisson's ratio
Density
UNS C26000 (UNS C26000) [solid] Basic
Shape Functions
Name
Shape function
Unit
Description
Shape frame
Selection
u
Lagrange (Quadratic) in
Displacement field, X component Material
Domains 1–3
v
Lagrange (Quadratic) in
Displacement field, Y component Material
Domains 1–3
w
Lagrange (Quadratic) in
Displacement field, Z component Material
Domains 1–3
Weak Expressions
Weak expression
-solid.Sl11*test(solid.el11)-2*solid.Sl12*test(solid.el12)-2*solid.Sl13*test(solid.el13)-solid.Sl22*test(solid.el22)2*solid.Sl23*test(solid.el23)-solid.Sl33*test(solid.el33)
Integration
frame
Material
Selection
Domains
1–3
Plasticity 1
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Plasticity 1
Selection
Geometric entity level Domain
Selection
Domains 1–3
Equations
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Settings
Settings
Description
Initial yield stress
Value
From material
Isotropic tangent modulus From material
Plasticity model
Small plastic strains
Yield function F
von Mises stress
Hardening model
Isotropic
Isotropic hardening
Use tangent data
Properties from material
Property
Initial yield stress
Material
Property group
WD2340
Elastoplastic material model
Isotropic tangent modulus WD2340
Elastoplastic material model
Initial yield stress
UNS C26000 (UNS C26000) [solid] Elastoplastic material model
Isotropic tangent modulus UNS C26000 (UNS C26000) [solid] Elastoplastic material model
1.4.2. Free 1
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Free 1
Selection
Geometric entity level Boundary
Selection
Boundaries 1–10, 13–58, 60–64, 66–79, 81–106, 108–109
Used Products
COMSOL Multiphysics
1.4.3. Initial Values 1
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Initial Values 1
Selection
Geometric entity level Domain
Selection
Domains 1–3
Settings
Settings
Description
Displacement field
Value
{0, 0, 0}
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Structural velocity field {0, 0, 0}
Used Products
COMSOL Multiphysics
1.4.4. Boundary Load 1
Boundary Load 1
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Selection
Geometric entity level Boundary
Selection
Boundary 59
Equations
Settings
Settings
Description
Value
Load type
Load defined as force per unit area
Load
User defined
Load
{0, -75000, 0}
Used Products
COMSOL Multiphysics
Weak Expressions
Weak expression
Integration
frame
solid.bndl1.FAx*test(solid.bndl1.ux)+solid.bndl1.FAy*test(solid.bndl1.uy)+solid.bndl1.FAz*test(solid.bndl1.uz) Material
Selection
Boundary
59
1.4.5. Fixed Constraint 1
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Fixed Constraint 1
Selection
Geometric entity level Boundary
Selection
Boundary 80
Equations
Settings
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Settings
Description
Value
Apply reaction terms on All physics (symmetric)
Use weak constraints
0
Used Products
COMSOL Multiphysics
Constraints
Constraint Constraint force
Shape function
Selection
-u
test(-u)
Lagrange (Quadratic) Boundary 80
-v
test(-v)
Lagrange (Quadratic) Boundary 80
-w
test(-w)
Lagrange (Quadratic) Boundary 80
1.5. Mesh 1
Mesh statistics
Property
Value
Minimum element quality 0.07294
Average element quality
0.6912
Tetrahedral elements
98444
Triangular elements
15512
Edge elements
2481
Vertex elements
170
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Mesh 1
1.5.1. Size (Size)
Settings
Name
Value
Maximum element size
0.12
Minimum element size
0.015
Resolution of curvature
0.5
Resolution of narrow regions
0.6
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Maximum element growth rate 1.45
Predefined size
Fine
1.5.2. Free Tetrahedral 1 (Ftet1)
Selection
Geometric entity level Remaining
Problems 1 (Prob1)
Warning 1 (Warning1)
Selection
Geometric entity level Edge
Selection
Edges 73, 264
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Warning 1
Settings
Name
Value
Warning message Edge_is_much_shorter_than_specified_minimum_element_size
2.1. Stationary
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Study settings
Property
Value
Include geometric nonlinearity Off
Mesh selection
Geometry
Mesh
Geometry 1 (geom1) mesh1
Physics selection
Physics
Discretization
Solid Mechanics (solid) physics
2.2. Solver Configurations
2.2.1. Solver 1
Compile Equations: Stationary (St1)
Study and step
Name
Value
Use study
Study 1
Use study step Stationary
Dependent Variables 1 (V1)
General
Name
Value
Defined by study step Stationary
Initial values of
variables solved
for
Name Value
Solution Zero
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Values of
variables not
solved for
Name Value
Solution Zero
Displacement Field (Material) (Mod1.u) (Mod1_u)
General
Name
Value
Field components {mod1.u, mod1.v, mod1.w}
Stationary Solver 1 (S1)
General
Name
Value
Defined by study step Stationary
Log
Stationary Solver 1 in Solver 1 started at 16-Oct-2014 21:39:26.
Nonlinear solver
Number of degrees of freedom solved for: 439911 (plus 7580188 internal DOFs).
Symmetric matrices found.
Scales for dependent variables:
Displacement field (Material) (mod1.u): 1
Iter
ErrEst Damping Stepsize #Res #Jac #Sol
1
0.15 1.0000000
0.9 2 1 2
2
1.3 0.1000000
1.5 3 2 4
3
0.9 0.2976185
1.2 4 3 6
4
0.64 0.3219917
0.86 5 4 8
5
0.73 0.2776389
0.94 6 5 10
6
0.7 0.3064251
0.94 7 6 12
7
0.3 0.4948157
0.51 8 7 14
8
0.034 1.0000000
0.24 9 8 16
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9
0.0033 1.0000000
0.053 10 9 18
10 6.6e-005 1.0000000
0.0038 11 10 20
Stationary Solver 1 in Solver 1: Solution time: 586 s (9 minutes, 46 seconds)
Physical memory: 5.85 GB
Virtual memory: 6.41 GB
Fully Coupled 1 (Fc1)
General
Name
Value
Linear solver Direct
Information 1 (Prob1)
Warnings 1 (Warning1)
Log
Inverted mesh element near coordinates (-1.95115, 0.785932, 1.31662).
Warnings 2 (Warning2)
Log
Inverted mesh element near coordinates (-1.95115, 0.785932, 1.31662).
Warnings 3 (Warning3)
Log
Inverted mesh element near coordinates (-1.95115, 0.785932, 1.31662).
Warnings 4 (Warning4)
Log
Inverted mesh element near coordinates (-1.95115, 0.785932, 1.31662).
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3.1. Plot Groups
3.1.1. Surface Stress
Surface: von Mises stress (lb/(in*s2)) Mesh
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Isosurface: von Mises stress (lb/(in*s2))
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Mesh
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Volume: Total displacement (in)
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Isosurface: solid.mises/solid.sY (1)
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