Statistical damage mechanics in this work establishes the connection between damaged random heterogeneous micromaterial and the system macroparameter. Renormalization group theory provides the bridge from the microscale to the macroscale. Delaunay lattices, which simulate and capture the role of the disordered microstructure in damage process, substitute a polycrystal specimen assuming that microcracks are grain-boundaries cracks. The macroparameters of the system, in the form of algebraic functions, are obtained applying the Family–Vicsek scaling relation on simulation data.

Issue Section:
Technical Papers
Keywords:
failure (mechanical), fracture mechanics, renormalisation, lattice theory, ceramics, random media, inhomogeneous media, microcracks, grain boundaries
Topics:
Damage, Microcracks, Failure, Damage mechanics, Phase transitions
1.
Billington, E. W., and Tate, A., 1981, The Physics of Deformation and Flow, McGraw–Hill Inc., NY.
2.
Kellogg, O. D., 1953, Foundations of Potential Theory, Dover, NY.
3.
Kunin, I. A., 1982, Elastic Media with Microstructure I—One-Dimensional Models, Springer-Verlag, Berlin.
4.
Kunin, I. A., 1983, Elastic Media with Microstructure II—Three-Dimensional Models, Springer-Verlag, Berlin.
5.
Bazant, Z. P., and Planas, P., 1998, Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton.
6.
Torquato, S., 2002, Random Heterogeneous Material, Microstructure and Macroscopic Properties, Springer, NY.
7.
Chaikin, P. M., and Lubensky, T. C., 1995, Principles of Condensed Matter Physics, Cambridge University Press, Cambridge, Great Britain.
8.
Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice–Hall, Inc., Englewood Cliffs, NJ.
9.
Mura, T., 1982, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague.
10.
Nemat-Nasser, S., and Hori, M., 1993, Micromechanics: Overall Properties of Heterogeneous Material, North–Holland, Amsterdam, The Netherlands.
11.
Krajcinovic, D., 1996, Damage Mechanics, North-Holland, Amsterdam, The Netherlands.
12.
Kachanov
,
L. M.
,
1958
, “
On the Time to Failure Under Creep Conditions
,”
Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Metall. Topl.
,
8
, pp.
26
–
31
.
13.
Lemaitre, J., and Chaboche, J.-L., 1985, Mecanique des Materiaux Solides, Dunod, Paris.
14.
Krajcinovic
,
D.
, and
Silva
,
M. A. G.
,
1982
, “
Statistical Aspects of the Continuous Damage Theory
,”
Int. J. Solids Struct.
,
18
, pp.
551
–
562
.
15.
Krajcinovic
,
D.
,
Lubarda
,
V.
, and
Sumarac
,
D.
,
1993
, “
Some Fundamental Aspects of the Brittle Cooperative Phenomena—Effective Continua Models
,”
Mech. Mater.
,
15
, pp.
99
–
115
.
16.
Janson
,
J.
, and
Hult
,
J.
,
1977
, “
Fracture Mechanics and Damage Mechanics—A Combined Approach
,”
J. Mec. Theor. Appl.
,
1
, pp.
S18–S28
S18–S28
.
17.
Budiansky
,
B.
, and
O’Connell
,
R. J.
,
1976
, “
Elastic Moduli of a Cracked Solid
,”
Int. J. Solids Struct.
,
12
, pp.
81
–
97
.
18.
Kachanov, M., 1993, “Elastic Solids With Many Cracks and Related Problems,” in Advances in Applied Mechanics, edited by Hutchinson, J. and Wu, T., Academic Press, NY, Vol. 29, pp. 259–445.
19.
Lubarda
,
V.
, and
Krajcinovic
,
D.
,
1994
, “
Tensorial Representation of the Effective Elastic Properties of the Damage Material
,”
Int. J. Damage Mech.
,
3
, pp.
38
–
56
.
20.
Chandler, D., 1987, Introduction to Modern Statistical Mechanics, Oxford University Press, NY.
21.
Garrod, C., 1995, Statistical Mechanics and Thermodynamics, Oxford University Press, NY.
22.
Cardy, J., 1996, Scaling and Renormalization in Statistical Physics, Cambridge University Press, Cambridge.
23.
Fujimoto, M., 1997, The Physics of Structural Phase Transitions, Springer, NY.
24.
Kadanoff, L. O., 2001, Statistical Physics—Statics, Dynamics and Renormalization, World Scientific, Singapore.
25.
Chowhury, D., and Stauffer, D., 2000, Principles of Equilibrium Statistical Mechanics, Wiley–VCH, Weinheim.
26.
Kardar, M., 1990, “Fluctuations of Interfaces and Fronts,” in Disorder and Fracture, edited by Charmet, J. C., Roux, S., and Guyon, E., Plenum Press, NY.
27.
Wilson
,
K. G.
, and
Kogut
,
J.
,
1974
, “
The Renormalization Group and the e Expansion
,”
Phys. Rep.
,
12
, pp.
75
–
200
.
28.
Barabasi, A.-L., and Stanley, H. E., 1995, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge.
29.
Rice
,
J. R.
,
1978
, “
Thermodynamics of the Quasi-Static Growth of Griffith Cracks
,”
J. Mech. Phys. Solids
,
26
, pp.
61
–
78
.
30.
Weiner, J. H., 1983, Statistical Mechanics of Elasticity, Wiley–Interscience John Wiley and Sons, NY.
31.
Rice, J. R., 1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” in Constitutive Equation in Plasticity, edited by A. S. Argon, MIT Press, Cambridge, MA.
32.
Weibull, W., 1939, “A Statistical Theory of the Strength of Materials,” Inst. Eng. Res., Stockholm, 151, pp. 1–45.
33.
Suresh, S., 1991, Fatigue of Materials, Cambridge University Press, Cambridge.
34.
Zallen, R., 1983, The Physics of Amorphous Solids, John Wiley and Sons, NY.
35.
Goodman, L. E., 1976, “Material Damping and Slip Damping,” in Shock and Vibration Handbook, edited by C. M. Harris and C. E. Crede, McGraw–Hill Book Company, NY, Vol. 36, pp. 1–28.
36.
Goranson, U. G., 1993, Damage Tolerance; Facts and Fiction, Commercial Airplane Group, Boeing Commercial Airplane Group, U.S.A.
37.
Hansen
,
A.
,
Roux
,
S.
, and
Herrmann
,
H. J.
,
1989
, “
Rupture of Central-Force Lattices
,”
J. Phys. (France)
,
50
, pp.
517
–
522
.
38.
Krajcinovic
,
D.
, and
Basista
,
M.
,
1991
, “
Rupture of Central-Force Lattices
,”
J. Phys. I
,
1
, pp.
241
–
245
.
39.
Bunde, A., and Havlin, S., eds., 1994, Fractals in Science, Springer-Verlag, Berlin.
40.
Reches
,
Z.
, and
Lockner
,
D. A.
,
1994
, “
Nucleation and Growth of Faults in Brittle Rock
,”
J. Geophys, Res.
,
99
(B9), pp.
159
–
18
.
41.
Turcotte, D. L., 1992, Fractal and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge.
42.
Krajcinovic
,
D.
, and
Vujosevic
,
M.
,
1998
, “
Strain Localization—Short to Long Correlation Length Transition
,”
Int. J. Solids Struct.
,
35
, pp.
4147
–
4166
.
43.
Hansen, A., and Roux, S., 2000, “Statistics Toolbox for Damage and Fracture,” in Damage and Fracture of Disordered Materials, edited by D. Krajcinovic and J. V. Mier, Springer, Wien, pp. 17–102.
44.
Hemmer
,
P. C.
, and
Hansen
,
A.
,
1992
, “
The Distribution of Simultaneous Fiber Failures in Fiber Bundles
,”
ASME J. Appl. Mech.
,
59
, pp.
909
–
915
.
45.
Barenblatt
,
G. I.
,
1962
, “
Mathematical Theory of Equilibrium Cracks in Brittle Fracture
,”
Adv. Appl. Mech.
,
7
, pp.
590
–
129
.
46.
Anderson, T. L., 1995, Fracture Mechanics, 2nd ed., CRC Press, Boca Raton, FL.
47.
Gouyet, J.-F., 1996, Physics and Fractal Structures, Masson, Paris.
Copyright © 2005
 by ASME
You do not currently have access to this content.