Role of Experiments in Mechanics

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Role of Experiments in Mechanics

• K. Ravi-Chandar
• Murray Lecture
• Society for Experimental Mechanics, June 2004

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Phases of Investigations

• DISCOVERY
• observation
• understanding
• CHARACTERIZATION
• measurement
• description
• VERIFICATION
• recreation
• scaling

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Linear Elasticity

• DISCOVERY
• Hooke 1676, Mariotte 1700
• CHARACTERIZATION
• Theoretical 100 year gap
• Euler 1767, Young 1807, Cauchy, Poisson
• Experimental - Wertheim 1842
• VERIFICATION
• Continues to the present

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Verification?

• Marie Alfred CORNU - 1869
• interferometry
• photography
• accurate, but...
• Adolf Theodore KUPFFER - 1848
• enormous resources
• vast collection of inaccurate results

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Method of Caustics

• DISCOVERY
• Crack tip shadow spots or stress coronas
  Schardin 1937
• CHARACTERIZATION
• Mannog 1965, Kalthoff, Theocaris, Rosakis
• VERIFICATION
• Rosakis and Ravi-Chandar (static), Ravi-Chandar
  and Knauss (dynamic)

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Serendipity

• My intended optical experiment was therefore
  dropped.....This was a case where pertinacity of
  purpose would not have been good tactics.
• ... Percy Williams BRIDGMAN

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Role of Experiments?

• DISCOVERY
• CHARACTERIZATION
• VERIFICATION

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Role of Experiments?

• It is a fact that Galilean science, not
  Aristotelian logic and metaphysics, made our
  material civilization what it is.
• - E.T. Bell,
• The Development of Mathematics, 1943

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Dynamic Fracture

• Schardins experiments in glass (1937)
• Limiting crack speed
• Crack branching
• Motts analysis of energy balance (1944)
• Consideration of kinetic energy
• Yoffes analysis of stress field (1951)
• Inertial rearrangement of the stress field

Discovery phase 1937 - 1951
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Dynamic Fracture

• Achenbach, Broberg, Eshelby, Freund, Kostrov,
  Nikitin, Rice, Willis,
• Dally, Fineberg, Irwin, Kalthoff, Knauss,
  Kobayashi, Post and Wells, Ravi-Chandar, Rosakis,
  Shukla,
• Abraham, Gao, Marder, Needleman, Ortiz,

Characterization phase 1957 present!
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Analysis of mode I cracks
KI dynamic stress intensity factor
Energy Flux Integral
See for example 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 - are governed completely by the wave
  propagation in the continuum
• Limiting crack speed is the Rayleigh wave speed

See for example, Freund, Dynamic Fracture
Mechanics, Cambridge, 1990
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Electromagnetic Loading
Ravi-Chandar and Knauss, Int J Fract, 1982
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Method of Caustics
Homalite-100, electromagnetic loading Ravi-Chandar
and Knauss, Int J Fract, 1984
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Stationary crack under dynamic loading
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Dynamic crack initiation toughness
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Dynamic propagating crack
Homalite-100, electromagnetic loading
Ravi-Chandar and Knauss, Int J Fract, 1984, J
App Mech, 1987
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Dynamic crack growth criterion
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 vlt0.25 CR, elastodynamic fracture theory
  works quite well
• Limiting speed v0.5 CR, is not predicted by the
  theory
• Dynamic square root singular filed not
  established for high crack speeds
• Crack branching appears

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Crack Branching
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Surface roughening
Ravi-Chandar and Knauss, Int J Fract, 1984
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Fractography
Polymethylmethacrylate Ravi-Chandar and Yang,
JMPS, 1997
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Dynamic crack growth mechanism
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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) movie
version can be viewed at http//www.almaden.ibm.c
om/st/computational_science/msmp/fractures/
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Surface roughening Crack front waves
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Characterization
Sharon, Cohen and Fineberg, Nature, 2001
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Mode III loading perturbations
12.7 mm
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Ultrasonic wave profile
Wavelength and duration for glass
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Ultrasonic attenuation in glass
Attenuation -0.1 dB/mm
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Crack speed measurements
Thin film coating
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Shadowgraphy
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Interaction of shear waves with the growing crack
Specimen K v 480 m/s f 5 MHz
12.7 mm
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Crack-wave interaction
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Specimen P v 890 m/s f 5 MHz
10 mm
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12.7 mm
Specimen AC v 440 m/s f 5 MHz
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Specimen AI v 440 m/s f 20 MHz
10 mm
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Measurement of surface profiles
Bonamy and Ravi-Chandar, 2003
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Surface undulation due to mode III perturbation
Parameters of surface undulation
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Attenuation of undulations
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Characteristic marks from a surface imperfection
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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Attenuation of Wallner lines
Bonamy and Ravi-Chandar, Phys Rev Letters, 2003
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The Tension Test

• The tensile test is very easily and quickly
  performed, but it is not possible to do much with
  its results, because one does not know what they
  really mean. They are the outcome of a number of
  very complicated physical processes.
• Emil OROWAN

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Tension response of polycarbonate
Discovery phase
Buisson and Ravi-Chandar, Polymer, 1990
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Tension response of polycarbonate
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Tensile response of polycarbonate
Characterization phase
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Measurement what is measurable!
Buisson and Ravi-Chandar, Polymer, 1990
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Buisson and Ravi-Chandar, Polymer, 1990
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Interpretation
Stress-induced birefringence
Form birefringence
Buisson and Ravi-Chandar, Polymer, 1990
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Stress-strain relationship
Buisson and Ravi-Chandar, Polymer, 1990
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Verification phase
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Numerical Simulation
Lu and Ravi-Chandar, IJSS, 1999
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Lu and Ravi-Chandar, IJSS, 1999
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Confined Compression
Ma and Ravi-Chandar, Exp Mech, 2000
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Analysis of the test configuration
IMPOSED AXIAL STRAIN
CONTINUITY Requires the specimen should have the
same displacement and radial strain as the
cylinder. EQUILIBRIUM Requires that the hoop
stress in the specimen should be equal to the
radial stress, assuming homogeneity of stresses.
DEFORMATION OF A CYLINDER UNDER INTERNAL PRESSURE 
Ma and Ravi-Chandar, Exp Mech, 2000
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Strain and stress in the specimen
The state of the deformation and stress in the
specimen is completely determined. It should be
possible to extract constitutive information from
such an experiment.
Ma and Ravi-Chandar, Exp Mech, 2000
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Interpretation of measurements
SHEAR RESPONSE
BULK RESPONSE
Ravi-Chandar and Ma, MTDM, 2000
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Volumetric response
Ravi-Chandar and Ma, MTDM, 2000
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Shear response
Ravi-Chandar and Ma, MTDM, 2000
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Role of Experiments

• DISCOVERY
• CHARACTERIZATION
• VERIFICATION

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Thanks
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AcknowledgmentsWolfgan
g KnaussCalifornia Institute of
TechnologyStelios Kyriakides, Ken Liechti, Mark
Mear, Greg RodinThe University of Texas at
AustinAres RosakisCalifornia Institute of
TechnologyKamel Salama, Ken White,
VipulanandanUniversity of HoustonDaniel
BonamyCEA Saclay, FranceJohn DempseyClarkson
UniversityDimitris LagoudasTexas AM
UniversityEckhardt SchneiderInstitut fur
zerstorungsfrie prufverfahrenL.
MahadevanHarvard University National Science
FoundationAir Force Office of Scientific
ResearchArmy Research OfficeOffice of Naval
ResearchTexas Center for SuperconductivityInst
itute for Advanced TechnologyFraunhofer
Institut fur zerstorungsfreie Prufverfahren
Graduate Students Terapat Apicharttabrut Marc
BalzanoGerard Buisson Bharathi
ChandrakarAbhijit Dhumne Hui FangPaul
Foltyn William HoffmanHwai-Jiang Jong Zaitao
LiJaeyoung Lim Bisen Lin Kuen-der Lin Hanfei
LuJinyang Lu Zhonghui MaRavi Mahajan John
OlivasJames Piedra Deva PonnusamyShyam
Potti Dan QvaleShriram Ramanathan K.P.
ReddyFrank Richter Tin-Jong ShueChristophe
Taudou Renjun WangRick Watkins Yan XiaBo
Yang Yanqui Zhang
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Discovery

• This work has not been done as a result of
  preconceived ideas and as an end we proposed to
  reach from the first. It has presented itself to
  us only in consequence of varied experiments
  realized in the first place in complicated
  circumstances which we have striven to reduce
  more and more to conditions which are simple and
  such as to permit the laws of the phenomena to be
  studied easily.
• ....Henri Edouard TRESCA, 1868

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Characterization

• Measure what is measurable, and make measurable
  what is not so.
• - Galileo GALILEI

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Verification

• it is obvious that an experimentist does not
  verify theories. ... it is fallacious to
  presume that a correlation between data and
  prediction implies the validity of any one set of
  such assumptions.
• - James F. BELL, Encyclopedia of Physics, 1973