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

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

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)

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.

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)

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

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

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)

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

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)

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)

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

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

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

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.

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

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

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

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

Cyclic Stresses Axial, flexural, or torsional Three modes Mean stress: Symmetrical Asymmetrical Random Mean stress: σm = (σmax + σmin)/2

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

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

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

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