1. Engineering materials lecture #14
ENGR 151
Professor Martinez
Engineering materials lecture #14

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 material’s 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.
σm = 2σo(a/ρt)1/2
σo = applied tensile stress
ρt = 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 = σm/σo=2(a/ρt)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:
σc=(2Eγs/πa)1/2
E = modulus of elasticity
γs = 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. σc = critical stress for crack propagation
Fracture Toughness
The measure of a material’s resistance to brittle fracture when a crack is present
KIC = Yσc(πa)1/2
σc = 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 Mean stress:
Symmetrical
Asymmetrical
Random
Mean stress:
σm = (σmax + σmin)/2

21. Cyclic Stresses Range of stress: Stress amplitude Stress ratio
σr = σmax – σmin
Stress amplitude
σa = σr/2 = (σmax – σmin)/2
Stress ratio
R = σmin / σmax

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