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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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