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ASTM Selected Technical Papers
Fractography of Modern Engineering Materials: Composites and Metals
By
JE Masters
JE Masters
1
Senior Research Engineer
,
American Cyanamid Co.
,
Stamford, CT 06904
;
symposium cochairman and coeditor
.
Search for other works by this author on:
JJ Au
JJ Au
2
Sundstrand Corp.
,
editor
Search for other works by this author on:
ISBN-10:
0-8031-0950-4
ISBN:
978-0-8031-0950-6
No. of Pages:
470
Publisher:
ASTM International
Publication date:
1987

A general constitutive theory is formulated for a short-fiber metal matrix composite. The constitutive theory is based on continuum mechanics with constraints provided by fracture mechanics and thermodynamics. The basic premise of the constitutive theory is that load-induced microstructural damage associated with the inclusion of the fibers in the metal matrix results in a loss of material stiffness.

The concept of the damage-dependent constitutive theory was evaluated by an experimental investigation of the microstructural damage in an Aluminum 6016-T6 matrix with silicon carbide (SiC) whiskers. The primary objective of the investigation was the identification of microstructural damage such as voids or cracks that were associated with the presence of the SiC whiskers.

The results of the experimental investigation include measured reductions in the elastic modulus of tension specimens which were loaded beyond yield and unloaded. Also, there was an associated change in the extent of the microstructural damage. These results lead to the conclusion that the effect of microstructural damage must be included in the constitutive relationship in order to fully describe the behavior of a metal matrix composite.

1.
Vinson
,
J. R.
and
Chow
,
T.
,
Composite Materials and Their Use in Structures
,
John Wiley & Sons
,
New York
,
1975
, Chap. 2.5.
2.
Renton
,
W. J.
,
Hybrid and Select Metal-Matrix Composites: A State of the Art Review
,
American Institute of Aeronautics and Astronautics
,
New York
,
1977
, Chap. 1.
3.
Hancock
,
J. R.
and
Shaw
,
G. G.
, “
Effect of Filament-Matrix Interdiffusion on the Fatigue Resistance of Boron-Aluminum Composites
,” in
Composite Materials: Testing and Design (Third Conference)
, ASTM STP 546,
American Society for Testing and Materials
,
Philadelphia
,
1974
, pp. 497-506.
4.
Nielsen
,
L. E.
, “
Mechanical Properties of Particulate-Filled Systems
,”
Journal of Composite Materials
, Vol.
1
,
1967
, pp. 100-119.
5.
Martin
,
J. W.
,
Micromechanics in Particle-Hardened Alloys
,
Cambridge University Press
,
London
,
1980
.
6.
Herakovich
,
C. T.
,
Davis
,
J. G.
, and
Dexter
,
H. B.
, “
Reinforcement of Metals with Advanced Filamentary Composites
,” in
Composite Materials: Testing and Design (Third Conference)
, ASTM STP 546,
American Society for Testing and Materials
,
Philadelphia
,
1974
, pp. 52.
7.
Divecha
,
A. P.
,
Fishman
,
S. G.
, and
Karmarkar
,
S. D.
, “
Silicon Carbide Reinforced Aluminum—A Formable Composite
,”
Journal of Metals
 0148-6608,
09
1981
, pp. 12-17.
8.
Maclean
,
B. J.
and
Misra
,
M. S.
, “
SiC Reinforced Alloys for Aeorspace Applications
,”
Martin Marietta Aeorspace
,
Denver, CO
,
1983
.
9.
Parry
,
C. W.
, Ed., “
Aluminum Metal Matrix Composites Outperform Unreinforced Alloys
,”
Aluminum Developments Digest
, Winter 1984–85, p. 3.
10.
Pipes
,
R. B.
,
Ballintyn
,
N. J.
, and
Carlyle
,
J. M.
, “
Acoustic Emission Response Characteristics of Metal Matrix Composites
,” in
Composite Materials: Testing and Design (Fourth Conference)
, ASTM STP 617,
American Society for Testing and Materials
,
Philadelphia
,
1977
, pp. 153-169.
11.
Ulman
,
D. A.
and
Henneke
E. G.
 II
Nondestructive Evaluation of Damage in FP/Aluminum Composites
,” in
Composite Materials: Testing and Design (Sixth Conference)
, ASTM STP 787,
Daniel
I. M.
, Ed.,
American Society for Testing and Materials
,
Philadelphia
,
1982
, pp. 323-342.
12.
Hoover
,
W. R.
, “
Crack Initiation in B-Al Composites
,”
Journal of Composite Materials
, Vol.
10
,
04
1976
, p. 106.
13.
Awerbuch
,
J.
and
Hahn
,
H. T.
, “
Hard Object Damage of Metal Matrix Composites
,”
Journal of Composite Materials
, Vol.
10
,
07
1976
, pp. 231-257.
14.
Awerbuch
,
J.
and
Hahn
,
H. T.
, “
K-Calibration of Unidirectional Metal Matrix Composites
,”
Journal of Composite Materials
, Vol.
12
,
07
1978
, pp. 222-237.
15.
Johnson
,
W. S.
, “
Mechanisms of Fatigue Damage in Boron/Aluminum Composites
,” in
Damage in Composite Materials
, ASTM STP 775,
Reifsnider
K. L.
, Ed.,
American Society for Testing and Materials
,
Philadelphia
,
1982
, pp. 83-102.
16.
Dvorak
,
G. J.
and
Johnson
,
W. S.
, “
Fatigue of Metal Matrix Composites
,”
International Journal of Fracture
, Vol.
16
,
1980
, pp. 585-607.
17.
Hancock
,
J. P.
and
Swanson
,
G. D.
, “
Toughness of Filamentary Boron/Aluminum Composites
,” in
Composite Materials: Testing and Design (Second Conference)
, ASTM STP 497,
American Society for Testing and Materials
,
Philadelphia
,
1972
, pp. 299-310.
18.
Sun
,
C. T.
and
Prewo
,
K. M.
, “
The Fracture Toughness of Boron Aluminum Composites
,”
Journal of Composite Materials
, Vol.
11
,
04
1977
, p. 164.
19.
Awerbuch
,
J.
and
Hahn
,
H. T.
, “
Crack-Tip Damage and Fracture Toughness of Boron/Aluminum Composites
,”
Journal of Composite Materials
, Vol.
13
,
04
1979
, pp. 82-107.
20.
Stüwe
,
H. P.
, “
The Work Necessary to Form a Ductile Fracture Surface
,”
Engineering Fracture Mechanics
 0013-7944, Vol.
13
,
1980
, pp. 231-236.
21.
Aboudi
,
J.
, “
A Continuum Theory for Fiber-Reinforced Elastic-Viscoplastic Composites
,”
International Journal Engineering Science
, Vol.
20
, No.
5
,
1982
, pp. 605-621.
22.
Aboudi
,
J.
, “
Effective Constitutive Equations for Fiber-Reinforced Viscoplastic Composites Exhibiting Anisotropic Hardening
,”
International Journal of Engineering Science
, Vol.
21
, No.
9
,
1983
, pp. 1081-1096.
23.
Bodner
,
S. R
and
Partom
,
Y.
, “
Constitutive Equations for Elastic-Viscoplastic Strain-Hardening Materials
,”
Journal of Applied Mechanics
, Vol.
42
, No.
2
,
1975
, pp. 385-389.
24.
Bodner
,
S. R.
, “
Representation of Time Dependent Mechanical Behavior of Rene 95 by Constitutive Equations
,” AFML-TX-79-4116,
Air Force Materials Laboratory, Wright-Patterson Air Force Base
,
Dayton, OH
,
1979
.
25.
Bodner
,
S. R.
,
Partom
,
I.
, and
Partom
,
Y.
, “
Uniaxial Cyclic Loading of Elastic-Viscoplastic Materials
,”
Journal of Applied Mechanics
,
1979
, pp. 805-810.
26.
Stouffer
,
D. C.
and
Bodner
,
S. R.
, “
A Relationship Between Theory and Experiment for a State Variable Constitutive Equation
,” AFWAL TR-80-4194,
Air Force Materials Laboratory, Wright-Patterson Air Force Base
,
Dayton, OH
,
1981
.
27.
Krieg
,
R. D.
,
Swearengen
,
J. C.
, and
Rohde
,
R. W.
, “
A Physically-Based Internal Variable for Rate-Dependent Plasticity
,”
Proceedings ASME/CSME PVP Conference
,
1978
,
American Society of Mechanical Engineers
,
New York
, pp. 25-27.
28.
Miller
,
A. K.
, “
An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytic Procedures and Part II—Application to Type 304 Stainless Steel
,”
ASME Journal of Engineering Materials and Technology
,
98-H
,
1976
, p. 97.
29.
Miller
,
A. K.
, “
Modelling of Cyclic Plasticity with Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects
,”
Journal of Engineering Materials and Technology
, Vol.
102
,
04
1980
, pp. 215-220.
30.
Hart
,
E. W.
, “
Constitutive Relations for the Nonelastic Deformation of Metals
,”
ASME Journal of Engineering Materials and Technology
,
98-H
,
1976
, p. 193.
31.
Walker
,
K. P.
, “
Representation of Hastelloy-X Behavior at Elevated Temperatures With a Functional Theory of Viscoplasticity
,” presented at the
ASME Pressure Vessels Conference
,
San Francisco
,
12
08
1980
,
American Society of Mechanical Engineers
,
New York
.
32.
Krempl
,
E.
, “
On the Interaction of Rate and History Dependence in Structural Metals
,”
Acta Mechanica
, Vol.
22
,
1975
, pp. 53-90.
33.
Cernocky
,
E. P.
and
Krempl
,
E.
, “
A Theory of Viscoplasticity Based on Infinitesimal Total Strain
,”
Acta Mechanica
, Vol.
36
,
1980
, pp. 263-289.
34.
Cernocky
,
E. P.
and
Krempl
,
E.
, “
A Theory of Thermoviscoplasticity Based on Infinitesimal Total Strain
,”
International Journal of Solids and Structures
 0020-7683, Vol.
16
,
1980
, pp. 723-741.
35.
Liu
,
M. C.
,
Krempl
,
E.
, and
Nairn
,
D. C.
,
Transactions of ASME, Series H
, and
Journal of Engineering Materials and Technology
, Vol.
98
,
1976
, pp. 322-329.
36.
Cernocky
,
E. P.
and
Krempl
,
E.
, “
A Nonlinear Uniaxial Integral Constitutive Equation Incorporating Rate Effects, Creep, and Relaxation
,”
International Journal of Nonlinear Mechanics
, Vol.
14
,
1979
, pp. 183-203.
37.
Liu
,
M. C.
and
Krempl
,
E.
, “
A Uniaxial Viscoplastic Model Based on Total Strain and Overstress
,”
Journal of the Mechanics and Physics of Solids
, Vol.
27
,
1979
, pp. 377-391.
38.
Zienkiewicz
,
O. C.
and
Cormeau
,
I. C.
, “
Visco-Plasticity—Plasticity and Creep in Solids—A Unified Numerical Approach
,”
International Journal for Numerical Methods in Engineering
 0029-5981, Vol.
8
,
1974
, pp. 821-845.
39.
Allen
,
D. H.
and
Haisler
,
W. E.
, “
A Theory for Analysis of Thermoplastic Materials
,”
Computers and Structures
, Vol.
13
,
1981
, pp. 124-135.
40.
Horii
,
H.
and
Nemat-Nasser
,
S.
, “
Overall Moduli of Solids with Microcracks: Load-Induced Anisotropy
,”
Journal of the Mechanics and Physics of Solids
, Vol.
31
, No.
2
,
1983
, pp. 155-171.
41.
Eshelby
,
J. D.
, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems
,”
Proceedings of the Royal Society
, A241,
1957
, pp. 376-396.
42.
Margolin
,
L. G.
, “
Elastic Moduli of a Cracked Body
,”
International Journal of Fracture
, Vol.
22
,
1980
, pp. 65-79.
43.
Laws
,
N.
,
Dvorak
,
G. J.
, and
Hejazi
,
M.
, “
Stiffness Changes in Unidirectional Composites Caused by Crack Systems
,”
Mechanics and Materials
, Vol.
2
,
1983
, pp. 123-127.
44.
Min
,
B. K.
and
Crossman
,
F. W.
, “
Analysis of Creep for Metal Matrix Composites
,”
Journal of Composite Materials
, Vol.
16
,
05
1982
, pp. 188-203.
45.
Johnson
,
W. S.
, “
Modelling Stiffness Loss in Boron/Aluminum Laminates Below the Fatigue Limit
,” in
Long-Term Behavior of Composites
, ASTM STP 813,
O'Brien
T. K.
, Ed.,
American Society for Testing and Materials
,
Philadelphia
,
1983
, pp. 160-176.
46.
Schapery
,
R. A.
, “
On Viscoelastic Deformation and Failure Behavior of Composite Materials with Distributed Flaws
,” in
Advances in Aerospace Structures and Materials
, AD-01,
American Society of Mechanical Engineers
,
New York
,
1981
, pp. 5-20.
47.
Schapery
,
R. A.
, “
Models for Damage Growth and Fracture in Nonlinear Viscoelastic Particulate Composites
,” in
Proceedings
,
Ninth U. S. National Congress of Applied Mechanics, American Society of Testing and Materials
,
Philadelphia
,
1982
.
48.
Talreja
,
R.
, “
A Continuum Mechanics Characterization of Damage in Composite Materials
,”
Proceedings of the Royal Society London
,
1984
.
49.
Allen
,
D. H.
,
Groves
,
S. E.
, and
Harris
,
C. E.
, “
A Thermomechanical Constitutive Theory for Elastic Composites with Distributed Damage Part I: Theoretical Development
,” MM-5023-85-17,
Mechanics and Materials Center, Texas A & M University
,
College Station, TX
,
10
1985
.
50.
Allen
,
D. H.
,
Harris
,
C. E.
, and
Groves
,
S. E.
, “
A Thermomechanical Constitutive Theory for Elastic Composites with Distributed Damage Part II: Model Applications
,” MM-5023-85-15,
Mechanics and Materials Center, Texas A & M University
,
College Station, TX
,
10
1985
.
51.
Allen
,
D. H.
, “
Thermodynamic Constraints on the Constitution of a Class of Thermoviscoplastic Solids
,” Report No. MM-12415-82-10,
Mechanics and Materials Center, Texas A & M
, College Station, TX,
12
1982
.
52.
Wren
,
G.
and
Allen
,
D. H
, “
Development of a Theoretical Framework for Constitutive Equations for Metal Matrix Composites with Damage
,” Report No. MM-4875-85-9,
Mechanics and Materials Center, Texas A & M
, College Station, TX,
06
1985
.
53.
Samuels
,
L. E.
,
Metallographic Polishing by Mechanical Methods
,
American Society for Metals
,
Metals Park, OH
,
1982
.
54.
McCall
,
J. L.
and
Mueller
,
W. H.
,
Metallographic Specimen Preparation
,
Plenum Press
,
N.Y.
,
1974
.
55.
Rostoker
,
W.
and
Dvorak
,
J. R.
,
Interpretation of Metallographic Structures
,
Academic Press
,
N.Y.
,
1965
, Chap. 5.
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