Transcript 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, crackproducing 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.
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

 Symmetrical
 Asymmetrical
 Random

Mean stress:
σm = (σmax + σmin)/2
CYCLIC STRESSES

Range of stress:
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
 Ultrasonic
 Pulse
shadowgraph
testing
echo
ANNOUNCEMENTS

Midterm #2
 Tuesday,

May 4th
Quiz on Thursday
 Creep