Fracture of solids is considered from the viewpoint of wave dynamics derived from a field theory. Based on the principle known as the symmetry of physical laws, the present field theory describes deformation and fracture on the same theoretical basis. From experimental observations, fracture is classified into two types; the first type characterized by decaying displacement waves that initially travel and eventually become stationary, and the second type characterized by shear-bands that are initially dynamic and eventually become stationary. The field theory interprets that the decaying displacement wave represents elasto-plastic deformation dynamics and that the shear band indicates solitary wave dynamics associated with strain concentration. In either case, the theory explains that the termination of wave propagation causes infinite volume expansion that generates material discontinuity. From the wave dynamical viewpoint, fracture is a self-driving phenomenon where the decrease in the elastic constant in a late stage of deformation induces instability in oscillatory dynamics which leads to exponential increase in the volume expansion with time. The theory indicates that in this mechanism fast pulling rate enhances the instability. Simple numerical analysis with finite element modeling supports this argument of instability and its association with the pulling rate.

1.
S. P.
Timoshenko
and
J. N.
Goodier
,
Theory of Elasticity
(
McGraw-Hil
,
New York
,
1951
).
2.
L. D.
Landau
and
E. M.
Lifshitz
,
Theory of Elasticity
(
Butterworth-Heinemann
,
Oxford
,
1986
), 3rd edn.
3.
E.
Orowan
(
1934
)
Zür Kristallplastizitt I-III
,
Z. Physik
89
,
605
613
, 614–633, 634–659.
4.
M.
Polanyi
(
1934
)
Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte
,
Z. Physik
89
,
660
664
.
5.
G. I.
Taylor
(
1934
)
The mechanism of plastic deformation of crystals. Part I. Theoretical
,
Proc. R. Soc. A
145
,
362
387
.
6.
J.
Lubliner
,
Plasticity Theory
(
Courier Dover
,
New York
,
2008
).
7.
D. A.
Gokhfeld
and
O. S.
Sadakov
, “A unified mathematical model for plasticity and creep under variable-repeated loading,” in
Creep in Strucutures
,
M.
Zyczkowski
(ed),
1991
, pp.
23
28
.
8.
R.
Hill
,
The Mathematical Theory of Plasticity
(
Oxford University Press
,
Oxford
,
1998
).
9.
A. A.
Griffithl
(
1920
)
The phenomena of rupture and flow in solids
,
Philos. Trans. A
221
,
163
198
.
10.
G. R.
Irwin
,
Fracture Dynamics
(
Fracturing of Metals
,
American Society for Metals, Cleveland
,
1948
).
11.
J. P.
Elliot
and
P. G.
Dawber
,
Symmetry in Physics
, Vol.
1
(
Macmillan
,
London
,
1984
).
12.
S.
Yoshida
, Deformation and Fracture of Solid-State Materials – Field Theoretical Approach and Engineering Applications (
Springer
,
New York
,
2015
).
13.
V. E.
Egorushkin
(
1990
)
Gauge dynamic theory of defects in nonuniformly deformed media with a structure, interface behavior
,
Sov. Phys. J.
33
,
135
149
.
14.
D. G. B.
Edelen
(
1996
)
A correct, globally defined solution of the screw dislocation problem in the gauge theory of defects
,
Int. J. Eng. Sci.
34
,
81
86
.
15.
M.
Lazar
(
2011
)
On the fundamentals of the three-dimensional translation gauge theory of dislocations
,
Math. Mech. Solids
16
,
253
264
.
16.
R. S.
Sirohi
(ed),
Speckle Metrology
(
Marcel Dekker
,
New York
,
1993
).
17.
C. A.
Sciammarella
and
F. M.
Sciammarella
,
Experimental Mechanics of Solids
(
Wiley
,
Hoboken
,
2012
).
18.
S.
Yoshida
,
M. H.
Pardede
,
N.
Sijabat
,
H.
Simangunsong
,
T.
Simbolon
, and
A.
Kusnowo
(
1999
)
Observation of plastic deformation wave in a tensile-loaded aluminum alloy
,
Phys. Lett. A
251
,
54
60
.
19.
S.
Yoshida
,
Suprapedi
,
R.
Widiastuti
,
M.
Pardede
,
S.
Hutagalon
,
J.
Marpaung
,
A.
Faizal
, and
A.
Kusnowo
(
1996
)
Direct observation of developed plastic deformation and its application to nondestructive testing
,
Jpn. J. Appl. Phys. Part 2
35
,
L854
L857
.
20.
S.
Yoshida
(
2015
)
Wave nature in deformation of solids and comprehensive description of deformation dynamics
,
Proc. Estonian Acad. Sci.
64
,
438
448
.
21.
T.
Nakamura
, (private communication),
2012
.
22.
T.
Sasaki
, (private communication),
2008
.
23.
S.
Yoshida
(
2015
)
Comprehensive description of deformation of solids as wave dynamics
,
Math. and Mech. of Comp. Sys.
3
, .
24.
I. J. R.
Aitchson
and
A. J. G.
Hey
,
Gauge Theories in Particle Physics
(
IOP Publishing
,
Bristol
,
1989
).
25.
M. D.
Todorov
, Nonlinear Waves: Theory, Computer Simulation, Experiment,
IOP Series on wave phenomena in the physical sciences
,
S.
Yoshida
(ed) (
Morgan & Claypool
,
San Rafael, CA
,
2018
).
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