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Failure of Composite Materials
Isaac M. Daniel
Robert R. McCormick School of Engineering and Applied Science
Northwestern University
Evanston, IL 60208,
USA
The failure of composites has been investigated extensively from the micromechanical and macromechanical points of view. On the micromechanical scale, failure mechanisms and processes vary widely with type of loading and are intimately related to the properties of the constituent phases, i. e., matrix, reinforcement, and interface-interphase. Failure predictions based on micromechanics, even when they are accurate with regard to failure initiation at critical points, are only approximate with regard to global failure of a lamina and failure progression to ultimate failure of a multi-directional laminate. For these reasons a macromechanical approach to failure analysis is preferred.
Numerous failure theories have been proposed and are available to the
composite structural designer[1].They are classified into three groups, limit or noninteractive theories
(maximum stress, maximum strain); interactive
theories (Tsai-Hill, Tsai-Wu); and partially
interactive or failure mode based theories (Hashin-Rotem, Puck). The
validity and applicability of a given theory depend on the convenience of
application and agreement with experimental results. The plethora of theories is accompanied by a
dearth of suitable and reliable experimental data, which makes the selection of
one theory over another rather difficult.
Considerable effort has been devoted recently to alleviate this
difficulty. The problem can be divided in two parts, one being the prediction
of failure of a single lamina and the second dealing with prediction of
first-ply-failure and damage progression leading to ultimate failure of a
multi-directional laminate.
C. T. Sun [2] reviewed six failure theories and showed comparisons of
theoretical predictions with experimental results for six different composite
material systems and various loading conditions. The latter included uniaxial (normal and
shear) loading, off-axis loading and biaxial (normal and shear) loading. It was found, as observed before, that most
theories differed little from each other in the first quadrant
(tension-tension). The biggest
differences among theories occurred under combined transverse compression and
shear. In this case predictions of the
Tsai-Wu interactive theory were in better agreement with experimental results
than other theories.
A round robin exercise was initiated by Hinton, Soden, and Kaddour for
the purpose of assessing the predictive capabilities of current failure
theories [3]. One observation of this exercise was that, even for the
unidirectional lamina, predictions of the various theories differed by up to
200-300% from each other. Overall evaluation and conclusions were
presented by the initiators of the exercise.
Regarding failure of the unidirectional lamina, based on eighteen test
cases, best agreement with experimental results was shown by the fully
interactive Tsai-Wu theory and Puck and Schürmann’s theory.
The difficulty
in evaluating failure theories is much greater in the case of a
multidirectional laminate. The scope of the proposed laminate failure analysis
comprises the following [1]:
1. A selected or adapted lamina failure theory
for prediction of failure initiation, i.e., first-ply-failure (FPF) in the
laminate.
2. A failure mode discrimination rule and a scheme
of ply discounting and failure progression in the laminate after FPF.
3.
A criterion or definition of ultimate
laminate failure (ULF).
In general, a wide variation has been observed in the prediction of laminate failures by the various theories. The divergence in the predictions is greater for FPF than for ULF; also is greater for matrix dominated failures than for fiber dominated ones. The divergence observed may be attributed primarily to the following factors:
1. The different ways in which curing
residual stresses are introduced in the predictions, especially in the case of
first-ply-failure.
2. The
concept of in-situ behavior of a lamina within the laminate which is still
debated.
3. The different methods of modeling the
progressive failure process and the definition of ultimate laminate failure.
4.
The nonlinear behavior of matrix-dominated laminates, e.g., angle-ply laminates.
Under uniaxial loading of a
laminate the deciding factor in predicting ultimate failure is whether it is
fiber or matrix dominated. Under uniaxial loading of a laminate the deciding
factor in predicting ultimate failure is whether it is fiber or matrix dominated.
In the case of matrix dominated angle-ply laminates, predictions by the limit
or interactive theories are not usually in agreement with each other and with
experimental results. Failure is
governed by the lamina transverse normal stress
and the in-plane shear stress
. When
, as in the case of
and the limit theories
predict higher strengths in agreement with the experiment [1]. When
, as in the case of the
laminate under tension,
the Tsai-Wu criterion comes closer to the experimental results [1]. In the more
general cases of biaxial loading it is not easy to establish fiber or matrix
dominance in failure as that varies with the loading biaxiality.
It is
difficult to reach definitive conclusions on the applicability of the various
theories based on comparison with the limited experimental data available,
especially in the cases of FPF and under biaxial compression or compression and
shear. Theories based on the maximum
stress criterion, a partly interactive approach (Puck et al.), or a totally
interactive criterion (Tsai-Wu), give reasonable predictions of ultimate
failure in fiber-dominated laminates if the first fiber failure (FFF) is used
as the definition of ULF. In the case of
matrix dominated failure, a distinction must be made between cases of
transverse tensile stress
and transverse
compressive stress
in the lamina. In the
former case limit theories (maximum stress) agree better with experimental
results, whereas interactive theories (Tsai-Wu) underestimate the
strength. In the second case
the opposite is true.
In view of the multitude of failure theories, the divergence of their predictions and the lack of definitive general conclusions regarding their applicability, a practical approach is recommended as follows [1]:
1. Select
a classical representative theory from each category, i.e., non-interactive
(maximum stress), fully interactive (Tsai-Wu), and partly interactive
(Hashin-Rotem).
2. Compute and plot stress-strain relations of
the laminate under representative mechanical and hygrothermal loading.
3. Use a newly proposed failure mode discrimination
rule and define ULF
4. Compute safety factors for FPF and ULF and
compute and plot failure envelopes for the selected failure theories for the
two failure levels (FPF and ULF).
5. Select prediction according to degree of
conservatism desired. For the most
conservative approach, limit the state of stress (loading) to within the common
domain of the selected failure envelopes.
All
computations and plots can be performed by a newly developed computer program
[4]. The approach above is adequate for conservative structural design. More
sophisticated theories and approaches exist as discussed before incorporating
nonlinear behavior and in-situ effects.
References
1. I.
M. Daniel and O. Ishai, Engineering
Mechanics of Composite Materials, Second Edition, Oxford University Press,
2005.
2.
C. T. Sun, “Strength Analysis of Unidirectional Composites and Laminates,” in Comprehensive Composite Materials, ed.
by A. Kelly and C. Zweben, Ch. 1.20, Elsevier Science, Ltd., Oxford, UK, 2000.
3. M. J. Hinton, P. D. Soden,
and A. S. Kaddour, Failure Criteria in Fibre-Reinforced-Polymer Composites,
Elsevier, Oxford, 2004.
4. J. J. Luo and I. M. Daniel, “Webcomp: Stress and Failure Analysis of Laminate Composites,”http:www.composites.northwestern.edu/~webcomp, 2004.
Isaac M. Daniel
Walter P. Murphy Professor
Northwestern University Departments of Civil and Environmental
Engineering and Mechanical Engineering
2137 Tech Drive
Evanston, IL 60208-3020
E-mail: imdaniel@northwestern.edu
Phone: 847-491-5649
Fax: 847-491-5227
Web pages:
http://www.composites.northwestern.edu
http://www.ipc.northwestern.edu
Isaac M. Daniel was born and raised in Greece where he attended the
National Technical University of Athens. He obtained his BS, MS, and Ph. D.
degrees from the Illinois Institute of Technology (1957, 1959, 1964). He was
employed at the IIT Research Institute (IITRI) serving as Section Manager and
Science Advisor. He was appointed Professor at IIT and served as Director of
the Mechanics of Materials Laboratory (1982-1986). He joined Northwestern
University in 1986 where he is currently Walter P. Murphy Professor of Civil
and Mechanical Engineering, Director of the Center for Intelligent Processing
of Composites, and Director of the Theoretical and Applied Mechanics program.
Selected honors
include:
Symposium on “Recent Advances in Experimental Mechanics” in honor of
Isaac M. Daniel held in conjunction with 14th U.S. National Congress of
Theoretical and Applied Mechanics, Blacksburg, VA (2002).
Fellow, American Society of Mechanical Engineers (1999)
William M. Murray Medal and Lecture, Society for Experimental Mechanics (1998)
Distinguished Research Award, American Society for Composites (1996)
Fellow, American Academy of Mechanics (1994)
Associate Editor, ASME Journal of Applied Mechanics, (1993-1999)
Keynote speaker at 2nd International Conference on Composites Engineering (1995)
B. J. Lazan Award, Society for Experimental Mechanics (1984)
Keynote speaker at 7th International Conference on Experimental Stress Analysis (1982)
Fellow, Society for Experimental Mechanics (1981)
Professional activities include:
Committee
on "Characterization of Organic Matrix Composites" of the National Materials
Advisory Board of the National Research Council, 1978-1980.
Associate
Editor of Journal of Applied Mechanics
(1993-1999).
Member
of the Editorial Board of Composites A (Elsevier) (current)
Member
of Editorial Board of the Journal of
Composite Materials (current)
Member
of the Editorial Board of Strain.
(current)
Organized
and chaired the Sixth ASTM Conference on Composite Materials in Phoenix, AZ,
May 1981.
Publications
He has published
over 300 papers, 10 chapters of books, and three books, one of which is a
widely used textbook on composites. He has six patents, two issued and four
pending.
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