Physical Aspects of Dynamic Fracture

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Physical Aspects of Dynamic Fracture

• K. Ravi-Chandar
• Department of Aerospace Eng and Eng Mechanics
• 2003 Applied Mechanics and Materials Conference
• June 2003
• Scottsdale, Arizona

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Outline

• Motivation
• Review continuum dynamic fracture
• Experiments, physical aspects
• Mode I
• Mode II
• Mode III
• Conclusion

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Motivating problems

• Pipelines and pressure vessels
• Nuclear reactor containment vessels
• Airplanes
• Armor penetration and protection
• Earths crust
• Scientific curiosity

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Pipelines
National Transportation Safety Board
http//www.ntsb.gov
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Pan Am 103
UK Air Accidents Investigation Report , N739PA at
Lockerbie, Scotland on 21 December 1988
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San Andreas
Aerial view of the San Andreas fault slicing
through the Carrizo Plain in the Temblor Range
east of the city of San Luis Obispo. (Photograph
by Robert E. Wallace, USGS.) http//pubs.usgs.gov
/publications/text/San_Andreas.html
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Curious phenomena
Crack path oscillations
Crack branching and fragmentation
Crack surface roughening
Ravi-Chandar, Comprhensive Struct Integrity
Handbook, 2003
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Continuum Theory of Dynamic Fracture

• Key Assumptions
• Medium is elastic, isotropic, homogenous
• Small scale process zone
• Rate independent material behavior
• Outer problem is to be analyzed decouple the
  failure criterion from the elastic problem

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Loading symmetries
Mode I
Mode II
Mode III
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Analysis of mode I cracks
KI dynamic stress intensity factor
Enegry Flux Integral
Freund, Dynamic Fracture Mechanics, Cambridge,
1990
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Crack Tip Equation of Motion
G is the dissipation in the fracture process per
unit extension

• Consequences
• Dynamics of crack growth crack speed and crack
  path - is governed completely by the wave
  propagation in the continuum
• Limiting crack speed is the Rayleigh wave speed

Freund, Dynamic Fracture Mechanics, Cambridge,
1990
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Electromagnetic Loading
Homalite-100, electromagnetic loading
Ravi-Chandar and Knauss, Int J Fract, 1982
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Photoelasticity
Polycarbonate, quasi-static loading Taudou,
Potti and Ravi-Chandar, Int J Fract, 1992
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Caustics
Homalite-100, electromagnetic loading Ravi-Chandar
and Knauss, Int J Fract, 1984
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Mode I dynamic fracture
v0.41CR
v0.22CR
Homalite-100, electromagnetic loading
Ravi-Chandar and Knauss, Int J Fract, 1984, J
App Mech, 1987
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Dynamic crack growth criterion
v0.4CR
Doll, 1975 Kobayashi et al 1980, 1985 Dally et
al., 1979, 1985 Ravi-Chandar and Knauss, 1984,
1987 Kalthoff, 1985 Hauch and Marder, 1998
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Experimental observations

• For vlt0.2 CR, elastodynamic fracture theory works
  quite well
• Limiting speed v0.5 CR, is not predicted by the
  theory
• Rapid increase in fracture toughness in nominally
  brittle materials
• Crack branching cannot be predicted

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Physical models - MD
Farid F. Abraham, D. Brodbeck, R.A. Rafey and
W.E.Rudge, Phys. Rev. Lett. 73, 272 (1994) MPEG
version can be viewed at http//www.almaden.ibm.c
om/st/Simulate/
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Physical Models - Lattice Dynamics
http//chaos.ph.utexas.edu/marder/
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Physical Models Cohesive zone
Xu and Needleman, J Mech and Phys Solids,
1994 Falk, Needleman and Rice, Eur J Phys, 2001
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Surface roughening
Ravi-Chandar and Knauss, Int J Fract, 1984
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Fractography
Polymethylmethacrylate Ravi-Chandar, Int J Fract,
1998
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Physical Models Damage Mechanics
Johnson, Int J Fracture, 1992
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Dynamic Cracks under Mode II Loading
Sub-Rayleigh Crack Speeds
Intersonic Crack Speeds
KII dynamic stress intensity factor
Freund, J Geophys Res, 1979, Broberg, Int J
Fract, 1989
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In-Plane Shear or Mode II

• Crack Compression
• Broberg, 1987
• Ductility
• Kalthoff, Optical Eng, 1989
• Rosakis et al., J Mech and Phys of Solids, 1992
• Ravi-Chandar, Int J Solids and Struct, 1995
• Rittel, Mech of Materials, 1999
• Weak plane
• Rosakis et al., Science, 2000
• Shukla, J Mech and Phys of Solids, 2001
• Groove
• Ravi-Chandar et al, Int J Fracture 2000, 2003

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Mode II cracks along weak planes
X2
r
q
X1
l
Bondline
Homalite-100 specimens, bonded with an epoxy and
impacted asymmetrically with a projectile
Rosakis et al., Science, 2000
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Grooved specimen
X2
X2
X3
r
d
q
X1
l
Critical fracture energy in pure mode II is
significantly greater than the critical fracture
energy in pure mode I For PMMA, KIIC gt 2 KIC
Ravi-Chandar, Int J Fract, 2003
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Influence of the groove on the stress field
Grooved specimen
Homalite-100, Ravi-Chandar, 1997
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Mode I and Mode II crack in PMMA
PMMA, Lu et al., Int J Fract, 2000
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Crack speed
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Intersonic crack in the groove
Homalite-100
Crack Speed v1.414Cs
Ravi-Chandar, Int J Fract, 2003
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Mode II fracture mechanisms
B. Linkage of Brittle Cracks Cs lt v lt Cd

• Ductile Mechanism
• v CR

Ravi-Chandar, Int J Fract, 2003
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Echelon cracks under mode II
10 mm
Echelon cracks
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Dynamic Cracks under Mode III Loading
KIII dynamic stress intensity factors
Freund, Dynamic Fracture Mechanics, 1990
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Anti-Plane Shear or Mode III
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Mode III loading perturbations
Wavelength 180 mm lt l lt 5 mm Duration 50 ns lt t
lt 2 ms
12.7 mm
Bonamy and Ravi-Chandar, Int J Fract, 2003
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Crack speed measurements
Bonamy and Ravi-Chandar, 2003
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Crack-ultrasonic pulse interaction
Crack front
v
Shear wave
l
q
Cs
vl/Cs
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Shadowgraphy
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Wallner lines
Glass Bonamy and Ravi-Chandar, Int J Fract, 2003
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Measurement of surface profiles
Bonamy and Ravi-Chandar, 2003
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Surface undulation due to mode III perturbation
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Attenuation of Wallner lines
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Mode III perturbations

• Wavelength of surface undulations is the same as
  the wavelength of the perturbation lack of
  inherent length scale
• Amplitude decay follows attenuation behavior of
  glass
• Small amplitude mode III perturbations do not
  produce crack break-up

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Multiple Wallner lines
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Dominant mode III loading
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Echelon cracks in mode III
Echelon cracks
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Conclusion
Macroscale Outer Problem Lengths mm Time ms
Microscale link - Inner problem
Nanoscale atomistic problem Lengths nm Time
ps
http//chaos.ph.utexas.edu/marder/
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Physical Aspects of Dynamic Fracture
Echelon cracks
Cavitation
Microcracking