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ENGR 151 Professor Martinez Simple fracture is the

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Title: ENGR 151 Professor Martinez Simple fracture is the


1
Engineering materialslecture 14
  • ENGR 151
  • Professor Martinez

2
Failure analysis (Chapter 8)
  • 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 materials melting point

3
Fracture
  • Stress can be tensile, compressive, shear, or
    torsional
  • For uniaxial tensile loads
  • Ductile fracture mode (high plastic deformation)
  • Brittle fracture mode (little or no plastic
    deformation)

4
Fracture
  • ductile and brittle are relative (ductility
    is based on percent elongation and percent
    reduction in area)
  • Fracture process involves two steps
  • 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.

5
Fracture
  • Stable crack resists further extension unless
    there is increase in applied stress
  • Brittle fracture cracks spread extremely rapidly
    with little accompanying plastic deformation
    (unstable)
  • Ductile fracture preferred over brittle fracture
  • Brittle fracture occurs suddenly and
    catastrophically without any warning
  • Brittle (ceramics), ductile (metals)

6
Ductile Fracture
  • Figure 8.4 (differences between highly,
    moderately, and brittle fracture)
  • Common type of fracture occurs after a moderate
    amount of necking
  • After necking commences, microvoids form
  • 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

7
Brittle Fracture
  • Takes place without much deformation (rapid crack
    propagation)
  • Crack motion is nearly perpendicular to direction
    of tensile stress
  • Fracture surfaces differ
  • Lines/ridges that radiate from origin in fan-like
    pattern
  • Ceramics relatively shiny and smooth surface

8
Brittle Fracture
  • Crack propagation corresponds to the successive
    and repeated breaking of atomic bonds along
    specific crystallographic planes
  • Transgranular fracture cracks pass through
    grains
  • Intergranular crack propagation is along grain
    boundaries (only for processed materials)

9
Principles of Fracture Mechanics
  • Quantification of the relationships between
    material properties, stress level,
    crack-producing flaws, and propagation mechanisms

10
Stress Concentration
  • 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)

11
Maximum Stress at Crack Tip
  • Assume that a crack is similar to an elliptical
    hole through a plate, oriented perpendicular to
    applied stress.
  • sm 2so(a/?t)1/2
  • so applied tensile stress
  • ?t radius of curvature of crack tip
  • a represents the length of a surface crack
  • (pg. 167)

12
Example 6.4 (pg. 167)
  • Maximum stress at crack tip

13
Stress Concentration Factor (Kt)
  • Kt sm/so2(a/?t)1/2
  • Measure of the degree to which an external stress
    is amplified at the tip of a crack
  • Stress amplification can also take place
  • Voids, sharp corners, notches
  • Not just at fracture onset

14
Brittle Material
  • Critical stress required for crack propagation in
    a brittle material
  • sc(2E?s/pa)1/2
  • E modulus of elasticity
  • ?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

15
Example Problem
  • 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/m2 and 69 GPa, respectively,
    determine the maximum length of a surface flaw
    that is possible without fracture.

16
Fracture Toughness
  • The measure of a materials resistance to brittle
    fracture when a crack is present
  • KIC Ysc(pa)1/2
  • sc critical stress for crack propagation
  • a crack length
  • Y parameter depending on both crack and
    specimen sizes and geometries

17
Fracture Toughness
  • For thin specimens, KIC depends on specimen
    thickness
  • Example 8.2
  • Example 8.3

18
Impact Fracture Testing
  • Charpy V-notch (CVN) technique
  • Measure impact energy (notch toughness)
  • Specimen is bar-shaped (square cross section)
    with a V-notch
  • High-velocity pendulum impacts specimen
  • Original height is compared with height reached
    after impact
  • Izod Test
  • Used for polymers

19
Fatigue
  • Form of failure that occurs in structures
    subjected to dynamic and fluctuating stresses.
  • Failure can occur at stress level considerably
    lower than tensile of yield strength
  • Occurs after repeated stress/strain cycling
  • Single largest cause of failure in metals

20
Cyclic Stresses
  • Axial, flexural, or torsional
  • Three modes
  • Symmetrical
  • Asymmetrical
  • Random
  • Mean stress
  • sm (smax smin)/2

21
Cyclic Stresses
  • Range of stress
  • sr smax smin
  • Stress amplitude
  • sa sr/2 (smax smin)/2
  • Stress ratio
  • R smin / smax

22
The S-N Curve
  • Fatigue testing apparatus
  • Simultaneous axial, flex, and twisting forces
  • S-N curve (stress v. number of cycles)
  • Fatigue limit
  • Fatigue strength
  • Fatigue life

23
Nondestructive testing (NDT)
  • Evaluation of materials without impairing their
    usefulness
  • X-radiography
  • Produces shadowgraph
  • Ultrasonic testing
  • Pulse echo

24
Announcements
  • Midterm 2
  • Tuesday, May 4th
  • Quiz on Thursday
  • Creep
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