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ENGR 151 Professor Martinez.  Simple fracture is the separation of a body into two or more pieces in response to an imposed constant stress and at temperatures.

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Presentation on theme: "ENGR 151 Professor Martinez.  Simple fracture is the separation of a body into two or more pieces in response to an imposed constant stress and at temperatures."— Presentation transcript:

1 ENGR 151 Professor Martinez

2  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  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  “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  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  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  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  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  Quantification of the relationships between material properties, stress level, crack- producing flaws, and propagation mechanisms

10  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  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  σ o = applied tensile stress  ρ t = radius of curvature of crack tip  a = represents the length of a surface crack (pg. 167)

12  Maximum stress at crack tip

13 K t = σ m /σ o =2(a/ρ 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  Critical stress required for crack propagation in a brittle material: σ c =(2Eγ s /πa) 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

15  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.

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

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

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

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

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

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

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

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