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TECHNICAL PAPERS

# Kinking of Transversal Interface Cracks Between Fiber and Matrix

[+] Author and Article Information
Federico París

School of Engineering, Group of Elasticity and Strength of Materials, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spainparis@esi.us.es

Elena Correa

School of Engineering, Group of Elasticity and Strength of Materials, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spaincorrea@esi.us.es

School of Engineering, Group of Elasticity and Strength of Materials, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spainmantic@esi.us.es

J. Appl. Mech 74(4), 703-716 (Sep 27, 2006) (14 pages) doi:10.1115/1.2711220 History: Received July 25, 2005; Revised September 27, 2006

## Abstract

Under loads normal to the direction of the fibers, composites suffer failures that are known as matrix or interfiber failures, typically involving interface cracks between matrix and fibers, the coalescence of which originates macrocracks in the composite. The purpose of this paper is to develop a micromechanical model, using the boundary element method, to generate information aiming to explain and support the mechanism of appearance and propagation of the damage. To this end, a single fiber surrounded by the matrix and with a partial debonding is studied. It has been found that under uniaxial loading transversal to the fibers direction the most significant phenomena appear for semidebonding angles in the interval between $60deg$ and $70deg$. After this interval the growth of the crack along the interface is stable (energy release rate (ERR) decreasing) in pure Mode II, whereas it is plausibly unstable in mixed mode (dominated by Mode I for semidebondings smaller than $30deg$) until it reaches the interval. At this interval the direction of maximum circumferential stress at the neighborhood of the crack tip is approximately normal to the applied load. If a crack corresponding to a debonding in this interval leaves the interface and penetrates into the matrix then: (a) the growth through the matrix is unstable in pure Mode I; (b) the value of the ERR reaches a maximum (in comparison with other debonding angles); and (c) the ERR is greater than that released if the crack continued growing along the interface. All this suggests that it is in this interval of semidebondings $(60–70deg)$ that conditions are most appropriate for an interface crack to kink. Experiments developed by the authors show an excellent agreement between the predictions generated in this paper and the evolution of the damage in an actual composite.

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## Figures

Figure 1

Figure 2

Local coordinate systems at the interface crack tip

Figure 3

Angular distribution of σθ for β=0.229 and β=0.136 following Comninou (14)

Figure 4

Angle of maximum σθ as a function of β

Figure 5

Model of the single fiber debonded from the matrix

Figure 6

Model of the single fiber after kinking of the debonding crack

Figure 7

Values of ERR for the fiber–matrix interface crack under remote tension from BEM (open model) and from Toya’s analytical model

Figure 8

Distribution of the radial stress between fiber and matrix with no damage at the interface

Figure 9

Values of ERR for the fiber–matrix interface crack under remote tension for two bimaterial systems: carbon–epoxy and glass–epoxy

Figure 10

Evolution of the fracture mode mixity with the semidebonding angle

Figure 11

Evolution of G and Gc as a function of the semidebonding angle

Figure 12

Configuration of circumferential stresses at the neighborhood of the interface crack tip

Figure 13

Value of the angle φ defining the MCS direction as a function of the semidebonding angle

Figure 14

Graphical description of the evolution of the angle of MCS with the semidebonding angle

Figure 15

Distribution of the circumferential stresses around the crack tip of the interface crack

Figure 16

Distribution of circumferential stresses at the neighborhood of the crack tip, for different semidebondings

Figure 17

Values of the ERR and its components for a kinked crack

Figure 18

Values of ERR for the shortest kinked cracks corresponding to different semidebondings

Figure 19

Comparison between ERR of an interface crack and kinked cracks growing normal to the load and along the direction of MCS

Figure 20

Schematic development of the damage: (a) damage in the form of the small cracks originated by the radial stress, Fig. 8; (b) unstable growth of the crack until a semidebonding of 60–70deg is reached, Fig. 1; (c) kinking of the interface crack, Figs.  13141518; (d) unstable growth of the kinked crack, Fig. 1, originating a macrocrack; and (e) actual damage in a fibrous composite under transversal load

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