ANALYTICAL

FATIGUE
by Kelly
All images scanned by T. Schmierer

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Visual example of axial stress

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Visual example of torsional stress

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Visual example of flexural stress

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An S-N plot for an aluminum alloy

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A diagram showing location of the three steps in a fatigue fracture under axial stress

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A diagram showing the surface of a fatigue fracture.
The rough surface indicates brittle failure, while the smooth surface represents crack propagation

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An example of beachmarks or "clamshell pattern" associated with stress cycles that vary in magnitude and time as in factory machinery

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An example of the striations found in fatigue fracture.

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Equation 1

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Equation 2

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Equation 3

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Equation 4

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A case hardened steel gear

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Example of pits formed by corrosion on the surface of LiF



STRESS INTENSITY
by Kim
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Schematic representations of
(a) an interior crack in a plate of infinite width, and
(b) an edge crack in a in a plate of semi-infinite width

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Schematic representation showing the effect of plate thickness on fracture toughness

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Basic modes of loading involving different crack surface displacements

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Graph showing distribution of stresses in vicinity of crack tip

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Picture of the Liberty Bell



STRESS CONCENTRATION
by Noble
All images scanned by T. Schmierer

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img1.jpg
Diagram showing
(a)The geometry of surface and internal cracks.
(b) Schematic stress profile along the line X-X' in (a),
demonstrating stress amplification at crack tip positions

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Equation 1

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Equation 2

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img4.jpg
Diagrams showing stress concentration factor plots for three different macroscopic flaw situations



ENERGY METHODS
by Yue
All images scanned by M. Gallagher

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img00001.jpg
Diagram of a plate with a crack growing with an applied stress

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Fractograph of ductile cast iron showing a transgranular fracture surface

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Fractograph of an intergranular fracture surface

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Three modes of crack surface displacements

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A cracked body with a force (F) and (a) is the crack length

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A graph of the increase of growth rate with crack size

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Illustration of Charpy and Izod Impact Tests

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A graph of the temperature dependence on the Charpy V-notch impact energy
(curve A) and percent shear fracture (curve B)



NUMERICAL

THEORY
by Midkiff
All images scanned by J. Midkiff

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midkiff1.jpg
Structure of a three-member truss

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Single truss member

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Equation 1

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Equation 2

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Force diagram of single truss member

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Equation 3

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Equation 4

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Equation 5

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Three member truss

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diagram showing displacements and external forces
on a three member truss

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Equation 6

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Equation 7

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Equation 8

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midkif14.jpg
Nodal forces on a three member truss

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Equation 9

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Equation 10

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Equation 11



EXAMPLES
by Schultz
All images preprocessed in Patran and processed in
Abaqus by J. Schultz on an ESM workstation

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rmin.gif
FEA results of stresses in a plate with an elliptical crack

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rmed.gif
FEA results of stresses in a plate with an elliptical crack

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FEA results of stresses in a plate with a circular crack

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mesh.gif
Mesh with boundary conditions for one of the models

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GEOM.gif
Geometry of FEA drawn in Autocad

SIMPLE COMPUTER PROBLEM
by Tingler
All images scanned by T. Schmierer

Tingler8-1.jpg
Equation 8.1

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Equation 8.2

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Equation 8.5 a,b,c

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Equation 8.6

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Equation 8.7

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Equation 8.8

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Equation 8.9

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Equation 8.10



HISTORY/INTRODUCTION
by Widas
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widas1.jpg
Figure 1 from http://www.noraneng.com

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Mesh diagram of a van

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widas3.jpg
Figure 3 from http://umass.edu/mie/labs/mda/fea/fealib/goldstein/PROJECT.html

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Non-linear model of a bicycle frame

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widas5.jpg
Fatigue analysis of a train



EXPERIMENTAL

DUCTILE FRACTURE
by Bailey
All images scanned by T. Schmierer

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bailey1.jpg
A tensile stess-strain curve

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A scanning electron fractograph of ductile cast iron, examining a transgranular fracture surface

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Figure showing the macroscopic differences between two ductile specimens(a,b)
and the brittle specimen (c)

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Figure demonstrating the microscopic qualities of ductile fracture surfaces

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Figure demonstrating the microscopic qualities of ductile fracture surfaces

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bailey6.jpg
Sheared aluminium specimen showing cup and cone, and brittle fracture

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Graph that determines brittle to ductile transition
through an impact test for a 1018 hot-rolled steel



BRITTLE FRACTURE
by Ballard
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chevrons.gif
Chevron fracture surface

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Diagram showing intergranular fracture

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radiate.gif
Radiating ridge fracture surface

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Diagram showing transgranular fracture



DESIGN
by Gordon
All images scanned by T. Schmierer

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cf-1.gif
Graph showing aluminum oxide's modulus of elasticity as a function of porosity

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Graph showingaluminum oxide's modulus of rupture as a function of porosity

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Diagram of a ceramic material before sintering

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Diagram of a ceramic material during sintering

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Diagram of a ceramic material after sintering

pe-1.jpg
Equation showing the minimum fiber length for a continuous fiber composite

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Equation showing the tensile strength of a discontinous
fiber composite with fiber length greater than lc

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Equation showing the tensile strength of a discontinous
fiber composite with fiber length less than lc

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rf-1.gif
Figure showing the tenile and compressive stress on tempered glass

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Equation for factor of safety

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sf-1.gif
A poor design that will create a stree concentration

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A good design that will minimise stress concentration

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Equation for the minimum thickness of material before plane strain behavior occurs

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Equation for the fracture toughness of a material with a thickness less than B

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Equation for the fracture toughness of a material with a thickness equal to or greater than B;
when it fractures in mode I

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Equation for the critical applied stress required to cause failure in a material

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Equation for the critical crack length required to cause failure in a material

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tf-2.gif
Diagram of a mode I fracture

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Diagram of a mode II fracture

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Diagram of a mode III fracture

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Graph showing composite performance in relation to stress alignment



FRACTOGRAPHY
by Halahan and Mutter
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Stainless steel showing transgranular cleavage
Scanned by M. Gallagher

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TiB2 showing cleavage
Scanned by M. Gallager

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Ni base alloy showing cleavage
Scanned by M. Gallagher

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Silicon carbide showing small cleavage
Scanned by M. Gallagher

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Obvious decohesion
Scanned by R. Halahan

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Stainless steel showing hydrogen embrittlement
Scanned by R. Halahan

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Stainless steel showing decohesive rupture
Scanned by M. Gallagher

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Carbon-Magnesium steel showing stress corrosion cracking
Scanned by M. Gallagher

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Low carbon steel with a layer of oxide
Scanned by R. Halahan

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Gray cast iron with sulfate deposites
Scanned by R. Halahan

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Nickel based alloy with fatigue striations
Scanned by M. Gallagher

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Enlarged picture of fatig1.jpg
Scanned by M. Gallagher

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fatig3.jpg
Nickel based alloy with jagged fatigue striations
Scanned by M. Gallagher

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Titanium alloy with fatigue striations
Scanned by M. Gallagher

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void1.jpg
High carbon steel with an elongated dimple
Scanned by M. Gallagher

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AISI 10B21 Steel with well defined microvoid coalescence
Scanned by M. Gallagher

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Aluminum alloy with microvoids
Scanned by M. Gallagher

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Titanium alloy with equiaxed and elongated dimples
Scanned by M. Gallagher

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Nitralloy 135 M with microvoid coalescence
Scanned by M. Gallagher



FRACTURE TOUGHNESS
by McMurtry
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fig1.jpg
A specimen with an internal crack

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A specimen with a through-thickness crack

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A specimen with a half circle surface crack

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A fracture toughness vs. thickness graph

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Three modes of crack surface displacement

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Two ASTM standard compact specimen of different b sizes

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Graph of fracture toughness vs. temperature for different steels

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fig8.jpg
A graph of fracture toughness vs. temperature for various strain rates
applied to A572 steel



EXPERIMENTAL FATIGUE
by Meyer
All images scanned by C. Meyer

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Fracture appearances of fatigue failures in bending

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Typical fatigue zone with identifying marks

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Graph showing the effect of hardness on the fatigue life
of threads rolled before and after heat treatment

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Graph of bending fatigue test results on sections from crankshafts:
endurance limit versus surface treatment

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Typical fatigue life curve

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Bending angle guide

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Graph of experimental data: angle vs. cycles to failure

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Graph of crack growth rates obtained from adjacent pairs of a vs. N data points

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figure showing completely reversed controlled strain test and
two possible stress responses, namely cycle-dependent
hardening and softening

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Diagram of a stable stress-strain hysteresis loop

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Elastic, plastic, and total strain vs. Life curves

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A tension fatigue failure of a helicopter rotor blade flapping link



MOVIES
by Luszcz and Mix

cyclic.mpg and cyclic2.mpg
Fracture of a Hercules Graphite fiber/vinyl ester matrix composite resulting from a completely reversed load
controlled fatigue test
(performed by Nikhil Verghese - Tech graduate student)

brittle.mpg
shows brittle fracture of a class 20 gray iron sample resulting from a constant strain tensile test (performed by J. Luszcz and J. Mix)

ductile.mpg
shows ductile fracture of a 4 wt% Cu in Al sample resulting from a constant strain tensile test (performed by J. Luszcz and J. Mix)

fractures.jpg
shows resulting fractures of gray iron (brittle fracture, round specimen), 4 wt% Cu in Al (ductile fracture, flat specimen), and polyethylene (extremely ductile fracture, white specimen) (taken by J. Luszcz and J. Mix)