1 Chapter 8: Mechanical Failure ISSUES TO ADDRESS... • How do cracks that lead to failure form? • How is fracture resistance quantified? How do the fracture resistances of the different material classes compare? • How do we estimate the stress to fracture? • How do loading rate, loading history, and temperature affect the failure behavior of materials? Ship-cyclic loading from waves. Computer chip-cyclic thermal loading. Hip implant-cyclic loading from walking. Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.) Adapted from Fig. 22.26(b), Callister 7e. Adapted from chapter-opening photograph, Chapter 8, Callister & Rethwisch 8e. (by Neil Boenzi, The New York Times.)
51
Embed
ISSUES TO ADDRESS - Eastern Mediterranean Universityme.emu.edu.tr/behzad/meng286/Mechanical Failure.pdf · ISSUES TO ADDRESS ... • How do ... 15 Ideal vs Real Materials ... ASM
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Chapter 8: Mechanical Failure ISSUES TO ADDRESS...
• How do cracks that lead to failure form?
• How is fracture resistance quantified? How do the fracture
resistances of the different material classes compare?
• How do we estimate the stress to fracture?
• How do loading rate, loading history, and temperature
affect the failure behavior of materials?
Ship-cyclic loading
from waves.
Computer chip-cyclic
thermal loading.
Hip implant-cyclic
loading from walking. Adapted from Fig. 22.30(b), Callister 7e.
(Fig. 22.30(b) is courtesy of National
Semiconductor Corporation.)
Adapted from Fig. 22.26(b),
Callister 7e. Adapted from chapter-opening photograph,
Chapter 8, Callister & Rethwisch 8e. (by
Neil Boenzi, The New York Times.)
Fracture mechanisms • Ductile fracture
– Accompanied by significant plastic deformation
2
• Brittle fracture
– Little or no plastic deformation
– Catastrophic
Ductile vs Brittle Failure
3
Very
Ductile
Moderately
Ductile Brittle
Fracture
behavior:
Large Moderate %AR or %EL Small
• Ductile fracture is
usually more desirable
than brittle fracture!
Adapted from Fig. 8.1,
Callister & Rethwisch 8e.
• Classification:
Ductile:
Warning before
fracture
Brittle:
No
warning
DUCTILE FRACTURE
• Highly ductile materials – Pure gold and lead at room temperature, and other metals,
polymers, and inorganic glasses at elevated temperatures.
– They neck down to a point fracture
– Showing virtually 100% reduction in area.
4
• Moderate ductile fracture • The most common type of tensile fracture profile for ductile
materials
• Brittle fracture • Happens without any appreciable deformation and by rapid
crack growth
• The direction of crack growth is very nearly perpendicular to the
direction of the applied stress and yields a briefly flat surface.
5
Example: Pipe Failures
• Ductile failure: -- one piece
-- large deformation
Figures from V.J. Colangelo and F.A.
Heiser, Analysis of Metallurgical Failures
(2nd ed.), Fig. 4.1(a) and (b), p. 66 John
Wiley and Sons, Inc., 1987. Used with
permission.
• Brittle failure: -- many pieces
-- small deformations
6
Moderately Ductile Failure
• Resulting
fracture
surfaces
(steel)
50 mm
particles
serve as void
nucleation
sites.
50 mm
From V.J. Colangelo and F.A. Heiser,
Analysis of Metallurgical Failures (2nd
ed.), Fig. 11.28, p. 294, John Wiley and
Sons, Inc., 1987. (Orig. source: P.
Thornton, J. Mater. Sci., Vol. 6, 1971, pp.
347-56.)
100 mm
Fracture surface of tire cord wire
loaded in tension. Courtesy of F.
Roehrig, CC Technologies, Dublin,
OH. Used with permission.
• Failure Stages: necking
s
void nucleation
void growth and coalescence
shearing at surface
fracture
Moderately Ductile vs. Brittle Failure
7
Adapted from Fig. 8.3, Callister & Rethwisch 8e.
cup-and-cone fracture brittle fracture
Moderately Ductile Failure
8
– Occurs in several stages: 1) initial necking, 2) small cavity
formation, 3) coalescence of cavities to form a crack, 4)
crack propagation, 5) final shear fracture at a 45 angle
relative to the tensile direction
– 45° with the tensile axis is the angle at which the shear
stress is maximum
Fractography-Ductile materials
9
– In a cop-and-cone fracture, the central interior region of the
surface has an irregular and fibrous appearance, which is
indicative of plastic deformation
– High magnification: consists of numerous spherical
“dimples”. Each dimple is one half of a microvoid that formed
and then separated during fracture process (elongated and
C-shaped).
Figure 8.4
Fractography-Brittle materials
10
– In brittle fracture, the sign of gross plastic
deformation is absent. A series of V-shaped
“chevron” marking may form near the center of the
fracture cross section that point back toward the
crack initiation site.
– Other brittle fracture surfaces contain lines or ridges that
radiate from the origin of the crack in a fanlike pattern
– Brittle fracture in amorphous materials, such as
ceramic glasses, yields a relatively shiny and
smooth surface
Brittle Failure
Arrows indicate point at which failure originated
11 Adapted from Fig. 8.5(a), Callister & Rethwisch 8e.
CLEAVAGE FRACTURE
12
– For most brittle crystalline materials, crack
propagation corresponds to the successive and
repeated breaking of atomic bonds along specific
crystallographic planes (Cleavage).
– This type of fracture is transgranular (or
transcrystalline), as the fracture cracks pass
through the grains.
– Macroscopically, the fracture surface may have a
grainy or faceted texture, because the orientation
of the cleavage planes were changed from grain
to grain.
13
Brittle Fracture Surfaces • Intergranular (between grains) 304 S. Steel
(metal) Reprinted w/permission
from "Metals Handbook",
9th ed, Fig. 633, p. 650.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
J.R. Keiser and A.R.
Olsen, Oak Ridge
National Lab.)
Polypropylene
(polymer) Reprinted w/ permission
from R.W. Hertzberg,
"Defor-mation and
Fracture Mechanics of
Engineering Materials",
(4th ed.) Fig. 7.35(d), p.
303, John Wiley and
Sons, Inc., 1996.
4 mm
• Transgranular (through grains)
Al Oxide
(ceramic) Reprinted w/ permission
from "Failure Analysis of
Brittle Materials", p. 78.
Copyright 1990, The
American Ceramic
Society, Westerville, OH.
(Micrograph by R.M.
Gruver and H. Kirchner.)
316 S. Steel
(metal) Reprinted w/ permission
from "Metals Handbook",
9th ed, Fig. 650, p. 357.
Copyright 1985, ASM
International, Materials
Park, OH. (Micrograph by
D.R. Diercks, Argonne
National Lab.)
3 mm
160 mm
1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol.
3, ICF4, Waterloo, CA, 1977, p. 1119.)
INETRGRANULAR FRACTURE
14
– Normally results subsequent to the occurrence of
processes that weaken or embrittle grain
boundary regions.
15
Ideal vs Real Materials • Stress-strain behavior (Room T):
TS << TS engineering
materials
perfect
materials
s
e
E/10
E/100
0.1
perfect mat’l-no flaws
carefully produced glass fiber
typical ceramic typical strengthened metal typical polymer
• DaVinci (500 yrs ago!) observed... -- the longer the wire, the
smaller the load for failure.
• Reasons:
-- flaws cause premature failure.
-- larger samples contain longer flaws!
Reprinted w/
permission from R.W.
Hertzberg,
"Deformation and
Fracture Mechanics
of Engineering
Materials", (4th ed.)
Fig. 7.4. John Wiley
and Sons, Inc., 1996.
STRESS CONCENTRATION
16
– Theoretical calculations of fracture strength is
based on atomic bonding energies.
– The measured fracture strengths of materials are
significantly lower than the theoretical values,
because of the presence of microvoid flaws or
cracks that always exist under normal conditions.
– The applied stress is amplified or concentrated at
the crack tips.
– The flaws are called stress risers
Flaws are Stress Concentrators!
• Griffith Crack
where t = radius of curvature
so = applied stress
sm = stress at crack tip
17
t
Adapted from Fig. 8.8(a), Callister & Rethwisch 8e.
ott
om Ks
ss2/1
2a
Concentration of Stress at Crack Tip
18
Adapted from Fig. 8.8(b),
Callister & Rethwisch 8e.
ENGINEERING FRACTURE DESIGN
19
– Stress amplification is not restricted to these
microscopic defects, and may occur at
macroscopic internal discontinuities (e.g., voids or
inclusions), at sharp corers, scratches, and
notches.
– When the magnitude of a tensile stress at the tip
of one of the flaws exceeds the value of critical
stress, a crack forms and then propagate, which
result in fracture.
ENGINEERING FRACTURE DESIGN
20
Engineering Fracture Design
21
r/h
sharper fillet radius
increasing w/h
0 0.5 1.0 1.0
1.5
2.0
2.5
Stress Conc. Factor, K t =
• Avoid sharp corners! s
Adapted from Fig.
8.2W(c), Callister 6e.
(Fig. 8.2W(c) is from G.H.
Neugebauer, Prod. Eng.
(NY), Vol. 14, pp. 82-87
1943.)
r , fillet
radius
w
h
s max
smax
s0
Crack Propagation
22
Cracks having sharp tips propagate easier than cracks
having blunt tips • A plastic material deforms at a crack tip, which
“blunts” the crack.
deformed region
brittle
Energy balance on the crack
• Elastic strain energy- • energy stored in material as it is elastically deformed
• this energy is released when the crack propagates
• creation of new surfaces requires energy
ductile
Criterion for Crack Propagation
23
Crack propagates if crack-tip stress (sm) exceeds a critical stress (sc)
where – E = modulus of elasticity
– s = specific surface energy
– a = one half length of internal crack
For ductile materials => replace s with s + p
where p is plastic deformation energy
2/12
sas
cE
i.e., sm > sc
Example – Brittle Fracture • Given Glass Sheet with
– Tensile Stress,
s = 40 Mpa
– E = 69 GPa
– = 0.3 J/m
• Find Maximum Length
of a
Surface Flaw
• Plan
• Set sc = 40Mpa
• Solve Griffith Eqn for
Edge-Crack Length
2
2
applied
sEa
s
Solving
µm2.8m102.8
N/m1040
N/m3.0N/m10692
6
226
29
a
a
Fracture Toughness Ranges
25
Based on data in Table B.5,
Callister & Rethwisch 8e. Composite reinforcement geometry is: f