Dynamic fracture in two-phase Al2O3/TiB2 ceramic composite microstructures is analyzed explicitly using a cohesive finite element method (CFEM). This framework allows the effects of microstructural heterogeneity, phase morphology, phase distribution, and size scale to be quantified. The analyses consider arbitrary microstructural phase morphologies and entail explicit tracking of crack growth and arbitrary fracture patterns. The approach involves the use of CFEM models that integrate cohesive surfaces along all finite element boundaries as an intrinsic part of the material description. This approach obviates the need for any specific fracture criteria and assigns models the capability of predicting fracture paths and fracture patterns. Calculations are carried out using idealized phase morphologies as well as real phase morphologies in actual material microstructures. Issues analyzed include the influence of microstructural morphology on the fracture behavior, the influence of phase size on fracture resistance, the effect of interphase bonding strength on failure, and the effect of loading rate on fracture.

1.
Tomar, V., Zhai, J., and Zhou, M., 2004, “Bounds for Element Size in a Variable Stiffness Cohesive Finite Element Model,” to appear in Int. J. Numer. Methods Eng.
2.
Needleman
,
A.
,
1987
, “
A Continuum Model for Void Nucleation by Inclusion Debonding
,”
ASME J. Appl. Mech.
,
38
, pp.
289
324
.
3.
Tvergaard
,
V.
,
1990
, “
Effect of Fibre Debonding in a Whisker-Reinforced Material
,”
Mater. Sci. Eng., A
,
125
, pp.
203
213
.
4.
Shabrov
,
M. N.
, and
Needleman
,
A.
,
2002
, “
An Analysis of Inclusion Morphology Effects on Void Nucleation
,”
Modell. Simul. Mater. Sci. Eng.
,
10
, pp.
163
183
.
5.
Needleman
,
A.
,
1990
, “
An Analysis of Decohesion Along an Imperfect Interface
,”
Int. J. Fract.
,
42
, pp.
21
40
.
6.
Needleman
,
A.
,
1990
, “
Analysis of Tensile Decohesion Along an Interface
,”
J. Mech. Phys. Solids
,
38
, pp.
289
324
.
7.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
,
1992
, “
The Relation Between Crack Growth and Fracture Process Parameters in Elastic-Plastic Solids
,”
J. Mech. Phys. Solids
,
40
, pp.
1377
1397
.
8.
Xu
,
X. P.
, and
Needleman
,
A.
,
1994
, “
Numerical Simulations of Fast Crack Growth in Brittle Solids
,”
J. Mech. Phys. Solids
,
42
, pp.
1397
1434
.
9.
Pandolfi
,
A.
,
Guduru
,
P. R.
,
Ortiz
,
M.
, and
Rosakis
,
A. J.
,
2000
, “
Three Dimensional Cohesive-Element Analysis and Experiments of Dynamic Fracture in C300 Steel
,”
Int. J. Solids Struct.
,
37
(
27
), pp.
3733
3760
.
10.
Ruiz
,
G.
,
Pandolfi
,
A.
, and
Ortiz
,
M.
,
2001
, “
Three-Dimensional Cohesive Modeling of Dynamic Mixed-Mode Fracture
,”
Int. J. Numer. Methods Eng.
,
52
, pp.
97
120
.
11.
Xu
,
X. P.
, and
Needleman
,
A.
,
1995
, “
Numerical Simulations of Dynamic Interfacial Crack Growth Allowing for Crack Growth Away From the Bond Line
,”
Int. J. Fract.
,
74
, pp.
253
275
.
12.
Xu
,
X. P.
, and
Needleman
,
A.
,
1996
, “
Numerical Simulations of Dynamic Crack Growth Along an Interface
,”
Int. J. Fract.
,
74
, pp.
289
324
.
13.
Siegmund
,
T.
, and
Needleman
,
A.
,
1997
, “
A Numerical Study of Dynamic Crack Growth in Elastic-Viscoplastic Solids
,”
Int. J. Solids Struct.
,
34
, pp.
769
787
.
14.
Rosakis, A. J., Samudrala, O., Singh, R. P., and Shukla, A. 1998, “Intersonic Crack Propagation in Bimaterials,” J. Mech. Phys. Solids-Special Volume on Dynamic Deformation and Failure Mechanics of Materials, 46, pp. 1789–1813.
15.
Camacho
,
G. T.
, and
Ortiz
,
M.
,
1996
, “
Computational Modeling of Impact Damage in Brittle Materials
,”
Int. J. Solids Struct.
,
33
, pp.
2899
2938
.
16.
Miller
,
O.
,
Freund
,
L. B.
, and
Needleman
,
A.
,
1999
, “
Modeling and Simulation of Dynamic Fragmentation in Brittle Materials
,”
Int. J. Fract.
,
96
(
2
), pp.
101
125
.
17.
Espinosa
,
H.
,
Zavattieri
,
P.
, and
Emore
,
G.
,
1998
, “
A Finite Deformation Continuum/Discrete Model for the Description of Fragmentation and Damage in Brittle Materials
,”
J. Mech. Phys. Solids
,
46
(
10
), pp.
1909
1942
.
18.
Espinosa
,
H.
,
Zavattieri
,
P.
, and
Emore
,
G.
,
1998
, “
Adaptive FEM Computation of Geometrical and Material Nonlinearities With Application to Brittle Materials
,”
Mech. Mater.
,
29
, pp.
275
305
.
19.
Zhai, J., and Zhou, M., 1998, “Micromechanical Modeling of Dynamic Fracture in Ceramic Composites,” Special Technical Publication 1359 ASTM, pp. 174–200.
20.
Zhai
,
J.
, and
Zhou
,
M.
, 1999, “Finite Element Analysis of Micromechanical Failure Modes in Heterogeneous Brittle Solids,” Int. J. Fract. (special issue on Failure Mode Transition), pp. 161–180.
21.
Geubelle
,
P.
, and
Baylor
,
J.
,
1998
, “
Impact-Induced Delamination of Composites: A 2D Simulation
,”
Composites, Part B
,
29
, pp.
589
602
.
22.
Minnaar, K., and Zhou, M., 2000, “Real-Time Detection and Explicit Finite Element Simulation of Delamination in Composite Laminates Under Impact Loading,” in AMD ASME IMECE, Orlando, FL, USA.
23.
Minnaar, K., and Zhou, M., 2001, “Experimental Characterization and Numerical Simulation of Impact Damage in Composite Laminates,” in ASME IMECE, ASME NY.
24.
Espinosa
,
H. D.
,
Dwivedi
,
S.
, and
Lu
,
H.-C.
,
2000
, “
Modeling Impact Induced Delamination of Woven Fibre Reinforced Composites With Contact/Cohesive Laws
,”
Comput. Methods Appl. Mech. Eng.
,
183
, pp.
259
290
.
25.
Zou
,
Z.
,
Reid
,
S. R.
, and
Li
,
S.
,
2003
, “
A Continuum Damage Model for Delaminations in Laminated Composites
,”
J. Mech. Phys. Solids
,
51
, pp.
333
356
.
26.
Xuan
,
W.
,
Curtin
,
W. A.
, and
Needleman
,
A.
,
2003
, “
Stochastic Microcrack Nucleation in Lamellar Solids
,”
Eng. Fract. Mech.
,
70
, pp.
1869
1884
.
27.
Rahul-Kumar
,
P.
,
Jagota
,
A.
,
Bennison
,
S. J.
,
Saigal
,
S.
, and
Muralidhar
,
S.
,
1999
, “
Polymer Interfacial Fracture Simulations Using Cohesive Elements
,”
Acta Mater.
,
47
(
15–16
), pp.
4161
4169
.
28.
Rahul-Kumar
,
P.
,
Jagota
,
A.
,
Bennison
,
S. J.
,
Saigal
,
S.
, and
Muralidhar
,
S.
,
2000
, “
Cohesive Element Modeling of Viscoelastic Fracture: Application to Peel Testing of Polymers
,”
Int. J. Solids Struct.
,
37
(
13
), pp.
1873
1897
.
29.
Rahul-Kumar
,
P.
,
Jagota
,
A.
,
Bennison
,
S. J.
,
Saigal
,
S.
, and
Muralidhar
,
S.
,
2000
, “
Interfacial Failures in a Compressive Shear Strength Test of Glass/Polymer Laminates
,”
Int. J. Solids Struct.
,
37
(
48–50
), pp.
7281
7305
.
30.
Roychowdhury
,
S.
,
Arun Roy
,
Y. D.
,
Dodds
,
J.
, and
Robert
,
H.
,
2002
, “
Ductile Tearing in Thin Aluminum Panels: Experiments and Analyses Using Large-Displacement, 3-D Surface Cohesive Elements
,”
Eng. Fract. Mech.
,
69
(
8
), pp.
983
1002
.
31.
Zavattieri
,
P. D.
,
Raghuram
,
P. V.
, and
Espinosa
,
H. D.
,
2001
, “
A Computational Model of Ceramic Microstructures Subjected to Multi-Axial Dynamic Loading
,”
J. Mech. Phys. Solids
,
49
, pp.
27
68
.
32.
Scheider
,
I.
, and
Brocks
,
W.
,
2003
, “
Simulation of Cup-Cone Fracture Using the Cohesive Model
,”
Eng. Fract. Mech.
,
70
, pp.
1943
1961
.
33.
Gomez
,
F. J.
, and
Elices
,
M.
,
2003
, “
Fracture of Components With V-Shaped Notches
,”
Eng. Fract. Mech.
,
70
, pp.
1913
1927
.
34.
Yuan
,
H.
, and
Chen
,
J.
,
2003
, “
Computational Analysis of Thin Coating Layer Failure Using a Cohesive Model and Gradient Plasticity
,”
Eng. Fract. Mech.
,
70
, pp.
1929
1942
.
35.
Jin
,
Z.-H.
,
Paulino
,
G. H.
, and
Dodds
, Jr.,
R. H.
,
2003
, “
Cohesive Fracture Modeling of Elastic-Plastic Crack Growth in Functionally Graded Materials
,”
Eng. Fract. Mech.
,
70
, pp.
1885
1912
.
36.
Carpinteri
,
A.
,
Cornetti
,
P.
,
Barpi
,
F.
, and
Valente
,
S.
,
2003
, “
Cohesive Crack Model Crack Description of Ductile to Brittle Size-Scale Transition: Dimensional Analysis Versus Renormalization Group Theory
,”
Eng. Fract. Mech.
,
70
, pp.
1809
1839
.
37.
Pandolfi, A., Yu, C., Corigliano, A., and Ortiz, M., 1997, “Modeling Dynamic Fracture in Transversely Isotropic Composites: A Cohesive Approach,” California Inbstitute of Technology, caltechASCI/2000.097.
38.
Yu, C., 2001, “Three-Dimensional Cohesive Modelling of Impact Damage of Composites,” Ph.D. Thesis, Caltech, Pasadena, CA.
39.
Pandolfi
,
A.
, and
Ortiz
,
M.
,
2002
, “
An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations
,”
Eng. Comput.
,
18
, pp.
148
159
.
40.
Spearot, D. E., Jacob, K. I., and McDowell, D. L., 2004, “Nonlocal Separation Constitutive Laws for Interfaces and Their Relation to Nanoscale Simulations,” to appear in Mech. Mater.
41.
Falk, M. A., Needleman, A., and Rice, J. R., 2001, “A Critical Evaluation of Dynamic Fracture Simulations Using Cohesive Surfaces,” in Fifth European Mechanics of Material Conference, Delft, The Netherlands.
42.
Papoulia, K. D., and Vavasis, S. A., 2002, “Time-Continuous Cohesive Interface Finite Elements in Explicit Dynamics,” in 15th ASCE Engineering Mechanics Conference, Columbia University, New York, NY.
43.
Prado
,
E. P.
, and
van Mier
,
J. G. M.
,
2003
, “
Effect of Particle Structure on Model-I Fracture Process in Concrete
,”
Eng. Fract. Mech.
,
70
, pp.
1793
1807
.
44.
Sorensen
,
B. F.
, and
Jacobsen
,
T. K.
,
2003
, “
Determination of Cohesive Laws by the J Integral Approach
,”
Eng. Fract. Mech.
,
70
, pp.
1841
1858
.
45.
Nguyen
,
O.
, and
Ortiz
,
M.
,
2002
, “
Coarse-Graining and Renormalization of Atomistic Binding Relations and Universal Macroscopic Cohesive Behavior
,”
J. Mech. Phys. Solids
,
50
(
8
), pp.
1727
1741
.
46.
Klein, P., Foulk, J., Chen, E., Wimmer, S., and Gao, H., 2000, “Physics-Based Modeling of Brittle Fracture: Cohesive Formulations and the Application of Meshfree Methods,” SAND2001-8099, Sandia National Laboratories, USA.
47.
Logan, K. V., 1996, “Composite Ceramics, Final Tehnical Report,” USSTACOM DAAEO7-95-C-R040.
48.
Ortiz
,
M.
, and
Pandolfi
,
A.
,
1999
, “
Finite Deformation Irreversible Cohesive Elements for Three-Dimensional Crack-Propagation Analysis
,”
Int. J. Numer. Methods Eng.
,
44
(
9
), pp.
1267
1282
.
49.
Shet
,
C.
, and
Chandra
,
N.
,
2002
, “
Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes
,”
J. Eng. Mater. Technol.
,
124
, pp.
440
450
.
50.
Lin, Y. K., 1967, Probabilistic Theory of Structural Dynamics, McGraw-Hill.
51.
Nguyen
,
O.
,
Repetto
,
E. A.
,
Ortiz
,
M.
, and
Radovitzky
,
R. A.
,
2001
, “
A Cohesive Model of Fatigue Crack Growth
,”
Int. J. Fract.
,
110
, pp.
351
369
.
52.
Krieg
,
R. D.
, and
Key
,
S. W.
,
1973
, “
Transient Shell Response by Numerical Integration
,”
Int. J. Numer. Methods Eng.
,
7
, pp.
273
286
.
53.
Belytschko
,
T.
,
Chiapetta
,
R. L.
, and
Bartel
,
H. D.
,
1976
, “
Efficient Large Scale Non-Linear Transient Analysis by Finite Elements
,”
Int. J. Numer. Methods Eng.
,
10
, pp.
579
596
.
54.
Tomar, V., and Zhou, M., 2004, “Deterministic and Stochastic Analyses of Dynamic Fracture in Two-Phase Ceramic Microstructures With Random Material Properties,” manuscript in preparation.
55.
Tomar, V., and Zhou, M., 2004, “Deterministic and Stochastic Analyses of Fracture Processes,” in International Conference on Heterogeneous Material Mechanics, Chongqing University, China.
56.
Johnson
,
E.
,
1992
, “
Process Region Changes for Rapidly Propagating Cracks
,”
Int. J. Fract.
,
55
, pp.
47
63
.
57.
Ravi-Chandar
,
K.
, and
Knauss
,
W. G.
,
1984
, “
An Experimental Investigation Into Dynamic Fracture-I. Crack Initiation and Arrest
,”
Int. J. Fract.
,
25
, pp.
247
262
.
58.
Ravi-Chandar
,
K.
, and
Knauss
,
W. G.
,
1984
, “
An Experimental Investigation Into Dynamic Fracture II. Microstructural Aspects
,”
Int. J. Fract.
,
26
, pp.
65
80
.
59.
Ravi-Chandar
,
K.
, and
Knauss
,
W. G.
,
1984
, “
An Experimental Investigation Into Dynamic Fracture III. Steady-State Crack Propagation and Crack Branching
,”
Int. J. Fract.
,
26
, pp.
141
154
.
60.
Ravi-Chandar
,
K.
, and
Knauss
,
W. G.
,
1984
, “
An Experimental Investigation Into Dynamic Fracture IV. On the Interaction of Stress Waves With Propagating Cracks
,”
Int. J. Fract.
,
26
, pp.
192
203
.
61.
Keller
,
A. R.
, and
Zhou
,
M.
,
2003
, “
Effect of Microstructure on Dynamic Failure Resistance of TiB2/Al2O3 Ceramics
,”
J. Am. Ceram. Soc.
,
86
(
3
), pp.
449
57
.
You do not currently have access to this content.