Transcript SM3-05_FM 3 - Fracture 0

SM3-03: Fracture
Linear Fracture Mechanics
(LFM)
3. Mechanics of cracks growth
M.Chrzanowski: Strength of Materials 3
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SM3-03: Fracture
1,2,3
Typical stages of fatigue failure development, and its fraction
of failure process
– nucleation
- small area - up to 80% of the life-time
4,5,6
– fatigue deterioration
7
- large area
- up to 20% of the life-time
– instantaneous fracture - large area
- below 1 % of the life-time
Sub-critical
Linear Fracture
propagation
Mechanics
of micro-ckracs
(LFM)
Post-critical
Dynamicalpropagation
Fracture
Mechnaics
of a main crack
(DFM)
SPACE
DOMAIN
TIME DOMAIN
Continuum
Damage
Initial cumullation
of
Mechanics
(CDM)
damages
SPACE
PROCESS
OF FATIGUE
MATERIAL
DETERIORATION
DETERIORATION
IN TIME SPACE
M.Chrzanowski: Strength of Materials 3
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SM3-03: Fracture
SS Schenctady T2 transporter cracked on 16.01.1943, Portland, OR
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SM3-03: Fracture
Production
-1949
Catastrophic
failures 10.01.1954 8.04.1954
Introduced to
the service 1952
De Havilland „Comet” the first passenger jet – analysis of 10.01.1954 disaster
M.Chrzanowski: Strength of Materials 3
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SM3-03: Fracture
Stress-based approach
q[Pa]
G.Kirsch, 1898 – Thin plate of unlimited width
containing a circular hole
http://www.britannica.com/EBchecked/topic/553306/mechanics-ofsolids/77450/Stress-concentrations-and-fracture?anchor=ref611555
y
σy= 3q
x
M.Chrzanowski: Strength of Materials 3
q[Pa]
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SM3-03: Fracture
G.V. Kolosow 1910 & C.E.Inglis, 1913 – Thin plate of
unlimited width containing an elliptical hole
q[Pa]
 2a 
 y  q 1  
b

y
b
a
b0
σ 
ab
INDEPENDENT OF THE
MAGNITUDE OF a !!!
σ 3q
M.Chrzanowski: Strength of Materials 3
q[Pa]
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x
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SM3-03: Fracture
H.M.Westergaard, 1939, N.I.Muskhelischvili, 1943 –
2D analysis of the stress field around the notch tip
0
A
y
 y  0

a


3

cos 1  sin  sin  ...
2r
2
2
2

x
Dla
a
r  0,  0
 A  0
 A  0
a
K

2r
2r
M.Chrzanowski: Strength of Materials 3
y A
a
2r
Singularity !
K   0 a
Stress intensity factor
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SM3-03: Fracture
Stress intensity factors for different orientation of crack plane and loading has
been calculated around 1960 (G.Sih)
To stystemise above, three cases are distinguished:
KI
KII
KIII
Mode I - Tearing; crack surfaces open perpendicular to the planes of its movement
Mode II – Out-of-plane shear; crack surfaces slide perpendicular to the planes of its
movement
Mode III - Out-of-plane shear; crack surfaces slide paralell to the planes of its
movement
M.Chrzanowski: Strength of Materials 3
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SM3-03: Fracture
Stress-based approach
Safe design requires following conditions to be fulfilled:
KI < KIc
where
KII < KIIc
KIII < KIIIc
KIc , KIIc , KIIIc
are critical values of responsible stress intensity factors, experimentally
determined
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Simple example showing importance of Facture Mechanics
SM3-03: Fracture
(after J.Hult, Bära Brista, Almqvist&Wiksell, 1975)
q
What is the length of central crack which
can be introduced without dimintion of load
carrying of the specimen (no interaction
between cracks is assumed)
For edge crack:
K Iedge  1,12q c
c
c
For central crack:
KIcentr  KIedge
2l
q
KIcentr  q l
q l  1,12q c
E.g. if c = 2 cm
l  1,122 c
l  2,5 cm
2l  5 cm
l  1,25c
M.Chrzanowski: Strength of Materials 3
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