Research Papers

A Three-Phase Shear-Lag Model for Longitudinal Cracking of a Ceramic Matrix Composite Ply With Thick Fiber Coatings

[+] Author and Article Information
Lucas R. Hansen

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: lrhansen@umich.edu

Anthony M. Waas

Felix Pawlowski Collegiate Professor of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: awaas@aa.washington.edu

1Present address: Boeing-Egtvedt Chair, William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, WA, 98195.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 7, 2015; final manuscript received October 6, 2015; published online November 9, 2015. Assoc. Editor: Daining Fang.

J. Appl. Mech 83(1), 011009 (Nov 09, 2015) (8 pages) Paper No: JAM-15-1305; doi: 10.1115/1.4031762 History: Received June 07, 2015; Revised October 06, 2015

During progressive cracking of cross-ply ceramic matrix composites (CMCs), load is transferred from the fiber to the matrix in the longitudinal (0 deg) ply via shear through a compliant interphase layer, also referred to as the coating. In the material system of interest, this coating has significant thickness relative to the fiber diameter. The damage process in the cross-ply CMC is observed to be as follows: (1) elastic deformation, (2) cracking of the transverse plies, (3) matrix cracking within the longitudinal plies, (4) failure of longitudinal fibers, and (5) pullout of the cracked fibers from the matrix. In this paper, the focus is on the longitudinal (0 deg) ply. Existing shear-lag models do not fully represent either the stress transfer through the coating or the true accumulations of shear and normal stresses in the matrix. In the current study, a model is developed that takes into account both of these factors to provide a more accurate, analytical representation of the stress distribution and progressive damage accumulation in a longitudinal CMC ply.

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Fig. 1

Tractions acting on differential chunks of length dx of the three constituents

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Fig. 2

Matrix cracks in the composite. Note that the problem is periodic in the axial direction.

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Fig. 3

The partially debonded composite is decomposed into a bonded region and a debonded region. The bonded region acts as a shortened version of the fully bonded composite. The debonded region acts as though there is only fiber, as there is no frictional force to transmit shear to the matrix.

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Fig. 4

Comparison between current model and ACK [4] model for a unidirectional SiC/SiC laminate for various levels of strain-mismatch between the fiber and matrix. Solid lines denote the current model and dashes denote ACK. Stress and strain scale bars removed at the request of the material provider.

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Fig. 5

The effects of increased friction (enhanced load transfer and reduced debond length) have competing effects on the effective stress–strain curve of the lamina

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Fig. 6

Equivalent stiffness at a given crack density for the current model, compared with HVM with a thin coating (25% volume fraction)

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Fig. 7

Equivalent stiffness at a given crack density for the current model, compared with HVM with a thick coating (25% volume fraction)

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Fig. 8

Stress–strain curves predicted by the Marshall model and the current model for a composite with a thin coating (25% volume fraction)

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Fig. 9

Stress–strain curves predicted by the Marshall model and the current model for a composite with a thick coating (25% volume fraction)

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Fig. 10

A differential length of elastic bushing, representing the coating, between a rigid boundary (matrix) and post (fiber)



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