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Research Papers

# Model for the Effect of Fiber Bridging on the Fracture Resistance of Reinforced-Carbon-Carbon

[+] Author and Article Information
K. S. Chan

Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238kchan@swri.org

Y.-D. Lee, S. J. Hudak

Southwest Research Institute, 6220 Culebra Road, San Antonio, TX 78238

J. Eng. Mater. Technol 133(2), 021017 (Mar 22, 2011) (10 pages) doi:10.1115/1.4003344 History: Received December 17, 2009; Revised July 14, 2010; Published March 22, 2011; Online March 22, 2011

## Abstract

A micromechanical methodology has been developed for analyzing fiber bridging and resistance-curve behavior in reinforced-carbon-carbon (RCC) panels with a 3D composite architecture and a SiC surface coating. The methodology involves treating fiber bridging traction on the crack surfaces in terms of a weight function approach and a bridging law that relates the bridging stress to the crack opening displacement. A procedure has been developed to deduce material constants in the bridging law from the linear portion of the K-resistance curve. This approach has been applied to analyzing R-curves of RCC generated using double cantilever beam and single cantilever bend specimens to establish a bridging law for RCC. The bridging law has been implemented into a micromechanical code for computing the fracture response of a bridged crack in a structural analysis. The crack geometries considered in the structural analysis include the penetration of a craze crack in SiC into the RCC as a single-edge crack under bending and the deflection of a craze crack in SiC along the SiC/RCC interface as a T-shaped crack under bending. The proposed methodology has been validated by comparing the computed R-curves against experimental measurements. The analyses revealed substantial variations in the bridging stress ($σo$ ranges from 11 kPa to 986 kPa, where $σo$ is the limiting bridging stress) and the R-curve response for RCC due to the varying number of bridging ligaments in individual specimens. Furthermore, the R-curve response is predicted to depend on crack geometry. Thus, the initiation toughness at the onset of crack growth is recommended as a conservative estimate of the fracture resistance in RCC. If this bounding structural integrity analysis gives unacceptably conservative predictions, it would be possible to employ the current fiber bridging model to take credit for extra fracture resistance in the RCC. However, due to the large scatter of the inferred bridging stress in RCC, such an implementation would need to be probabilistically based.

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## Figures

Figure 1

Craze cracks in SiC coating and delamination cracks along SiC/RCC interface detected in the RCC leading edges of the wings of an orbiter. From Opila (1).

Figure 2

Specimen geometry and measured R-curves in RCC: (a) DCB specimen, (b) schematic of the DCB specimen, and (c) energy release rate, G, as a function of crack extension. (a) and experimental data are from Reeder (4).

Figure 3

Experimental setup for performing interface fracture toughness testing of SiC/RCC using SCB specimens: (a) test setup, (b) closed-up view SCB specimen with a machined crack near the SiC/RCC interface, and (c) schematic of the SCB specimen. The scale shows 1 mm/division. (a) and (b) are from O’Brien (5).

Figure 4

(a) Typical load-displacement curve and (b) energy release rate, G, versus crack extension for RCC generated using SCB specimens. From O’Brien (5).

Figure 5

Flow diagram of the micromechanical approach utilized to develop a fiber bridging model for RCC using DCB data

Figure 6

Schematic of a DCB specimen with bridged crack surfaces

Figure 7

KR-curves in RCC showing linear relationship between K and Δa

Figure 8

Bridging stress as a function of distance behind the crack tip for DCB specimens

Figure 9

Bridging stress as a function of crack opening displacement for DCB specimens

Figure 10

Comparison of bridging stress for RCC against bridging laws from the literature (12-14) and the present study

Figure 11

Experimental values of bridging stresses compared against computed curves based on the bridging law proposed in this study

Figure 12

Bridging stress as a function of (a) distance behind the crack tip and (b) crack opening displacement for RCC 2b series SCB specimens

Figure 13

Bridging stress as a function of (a) distance behind the crack tip and (b) crack opening displacement for RCC 6L series SCB specimens

Figure 14

Bridging stress normalized by the limiting stress, σo, as a function of distance behind the crack tip: (a) RCC 6L series and (b) RCC 2b series

Figure 15

Schematics of an edge crack and a T-shaped crack subjected to combined bending and tension: (a) an edge crack penetrating into the RCC and (b) a T-shaped crack deflecting along the SiC/RCC interface

Figure 16

Computed KR-curves compared against experimental data of RCC measured using SCB specimens: (a) RCC 2b series and (b) RCC 6L series

Figure 17

Computed GR-curves compared against experimental data for RCC measured using DCB specimens

Figure 18

Comparison of computed GR-curves for DCB and T-shaped cracks in RCC

Figure 19

Comparison of computed GR-curves for SCB and edge cracks in RCC under bending

Figure 20

(a) Schematic and (b) actual bridging zone with bridging ligaments observed in RCC fracture mechanics specimens (5)

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