Engineering materials lecture #14

ENGR 151Professor Martinez

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

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)

“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.

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)

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

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

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)

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

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)

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)

Maximum stress at crack tip

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

Critical stress required for crack propagation in a brittle material:

σc=(2Eγs/πa)1/2

E = modulus of elasticityγs = specific surface energya = one half the length of an internal crack

When magnitude of tensile stress at tip of flaw exceeds critical stress, fracture results

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.

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 lengthY = parameter depending on both crack

and specimen sizes and geometries

For thin specimens, KIC depends on specimen thickness

Example 8.2 Example 8.3

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

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

Axial, flexural, or torsional Three modes

Symmetrical Asymmetrical Random

Mean stress:σm = (σmax + σmin)/2

Range of stress:σr = σmax – σmin

Stress amplitudeσa = σr/2 = (σmax – σmin)/2

Stress ratioR = σmin / σmax

Fatigue testing apparatus Simultaneous axial, flex, and twisting

forces S-N curve (stress v. number of cycles)

Fatigue limit Fatigue strength Fatigue life

Evaluation of materials without impairing their usefulness X-radiography

Produces shadowgraph Ultrasonic testing

Pulse echo

Midterm #2 Tuesday, May 4th

Quiz on Thursday Creep