ENGR 151
Professor Martinez

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Simple fracture is the separation of a body into two or more pieces in response to an imposed constant stress and at temperatures relatively low as compared to the material’s melting point

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Stress can be tensile, compressive, shear, or torsional
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For uniaxial tensile loads:
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Ductile fracture mode (high plastic deformation)
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Brittle fracture mode (little or no plastic deformation)

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“ductile” and “brittle” are relative (ductility is based on percent elongation and percent reduction in area)
Fracture process involves two steps:
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Crack formation & propagation
Ductile fracture characterized by extensive plastic deformation in the vicinity of an advancing crack
Process proceeds slowly as crack length is extended.

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Stable crack: resists further extension unless there is increase in applied stress
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Brittle fracture: cracks spread extremely rapidly with little accompanying plastic deformation (unstable)
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Ductile fracture preferred over brittle fracture
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Brittle fracture occurs suddenly and catastrophically without any warning
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Brittle (ceramics), ductile (metals)

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
Figure 8.4 (differences between highly, moderately, and brittle fracture)
Common type of fracture occurs after a moderate amount of necking
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After necking commences, microvoids form
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Crack forms perpendicular to stress direction
Fracture ensues by rapid propagation of crack around the outer perimeter of the neck (45 ° angle)
Cup-and-cone fracture

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Takes place without much deformation (rapid crack propagation)
Crack motion is nearly perpendicular to direction of tensile stress
Fracture surfaces differ:
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Lines/ridges that radiate from origin in fan-like pattern
Ceramics: relatively shiny and smooth surface

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Crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes
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Transgranular: fracture cracks pass through grains
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Intergranular: crack propagation is along grain boundaries (only for processed materials)

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Quantification of the relationships between material properties, stress level, crackproducing flaws, and propagation mechanisms

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Fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies.

Due to microscopic flaws that exist at surface and within the material (stress raisers)

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Assume that a crack is similar to an elliptical hole through a plate, oriented perpendicular to applied stress.
σ m
= 2σ o
(a/ρ t
) 1/2
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

σ o
= applied tensile stress
ρ t
= radius of curvature of crack tip a = represents the length of a surface crack
(pg. 167)

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Maximum stress at crack tip

T
K t
= σ m
/σ o
=2(a/ρ t
) 1/2
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Measure of the degree to which an external stress is amplified at the tip of a crack
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Stress amplification can also take place:
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Voids, sharp corners, notches
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Not just at fracture onset

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Critical stress required for crack propagation in a brittle material:
σ c
=(2 E γ s
/π a ) 1/2
E = modulus of elasticity
γ s
= specific surface energy a = one half the length of an internal crack

When magnitude of tensile stress at tip of flaw exceeds critical stress, fracture results

EXAMPLE PROBLEM:
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A relatively large plate of glass is subjected to a tensile stress of 40 MPa. If the specific surface energy and modulus of elasticity for this glass are 0.3 J/m 2 and 69 GPa, respectively, determine the maximum length of a surface flaw that is possible without fracture.

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The measure of a material’s resistance to brittle fracture when a crack is present
σ c
K
IC
= Yσ c
(πa) 1/2
= critical stress for crack propagation a = crack length
Y = parameter depending on both crack and specimen sizes and geometries

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For thin specimens, K
IC thickness depends on specimen
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Example 8.2
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Example 8.3

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Charpy V-notch (CVN) technique:
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Measure impact energy (notch toughness)
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Specimen is bar-shaped (square cross section) with a V-notch
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High-velocity pendulum impacts specimen
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Original height is compared with height reached after impact
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Izod Test
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Used for polymers

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Form of failure that occurs in structures subjected to dynamic and fluctuating stresses.
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Failure can occur at stress level considerably lower than tensile of yield strength
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Occurs after repeated stress/strain cycling
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Single largest cause of failure in metals

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Axial, flexural, or torsional
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Three modes
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Symmetrical
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Asymmetrical
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Random
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Mean stress:
σ m
= (σ max
+ σ min
)/2

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Range of stress:

Stress amplitude
σ a
= σ r
/2 = (σ max
– σ min
)/2
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Stress ratio
σ r
= σ max
– σ min
R = σ min
/ σ max

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Fatigue testing apparatus
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Simultaneous axial, flex, and twisting forces
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S-N curve (stress v. number of cycles)
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Fatigue limit
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Fatigue strength
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Fatigue life

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Evaluation of materials without impairing their usefulness
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X-radiography
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Produces shadowgraph
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Ultrasonic testing
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Pulse echo

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Midterm #2
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Tuesday, May 4 th
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Quiz on Thursday
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Creep