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TECHNICAL PAPERS

The Bridged Crack Model for the Analysis of Brittle Matrix Fibrous Composites Under Repeated Bending Loading

[+] Author and Article Information
Alberto Carpinteri1

Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italyalberto.carpinteri@polito.it

Simone Puzzi

Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

1

Corresponding Author.

J. Appl. Mech 74(6), 1239-1246 (Mar 07, 2007) (8 pages) doi:10.1115/1.2744042 History: Received January 16, 2006; Revised March 07, 2007

In this paper, we present a fracture-mechanics based model, the so-called bridged crack model (Carpinteri, A., 1981, “A Fracture Mechanics Model for Reinforced Concrete Collapse,” Proc. of IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft, I.A.B.S.E., Zürich, pp. 17–30; Carpinteri, A., 1984, “Stability of Fracturing Process in R.C. Beams,” J. Struct. Engng. (A.S.C.E.), 110, pp. 544–558) for the analysis of brittle matrix composites with discontinuous ductile reinforcements under the condition of repeated bending loading. In particular, we address the case of composites with very high number of reinforcements (i.e., fiber-reinforced composites, rather than conventionally reinforced concrete). With this aim, we propose a new iterative procedure and compare it to the algorithm recently proposed by Carpinteri, Spagnoli, and Vantadori (2004, “A Fracture Mechanics Model for a Composite Beam with Multiple Reinforcements Under Cyclic Bending,” Int. J. Solids Struct., 41, pp. 5499–5515), showing the advantages in terms of computational efficiency. Furthermore, we analyze the combined effects of crack length, brittleness number, and fiber number on the cyclic behavior of the composite beam, showing the conditions enhancing the energy dissipation in the composite system. Eventually, we analyze crack propagation and propose, consistently with the model premises, a fracture-mechanics-based crack propagation criterion that allows one to simulate cyclic bending tests under the fixed grip condition.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 2

Decomposition of the load history into monotonic parts

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Figure 3

Typical moment-rotation response, with evidence of elastic (2) and plastic (3–5) shakedown

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Figure 4

Moment versus rotation relation for a specimen with n=50 reinforcements: complete loading-unloading cycle. The continuous line with circles represents the outcome of the exact algorithm proposed in (3), whereas the dotted one reports results of the iterative procedure.

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Figure 5

Effect of fiber number n and brittleness number NP on the system response type and energy dissipation: (A) very brittle to (E) very ductile. Graph (a) presents the whole diagram and (b) shows a zoomed view of the portion near the axes origin.

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Figure 6

Repeated loading (fixed grip condition) of a composite beam with two reinforcements and initial crack length ξ=0.30; NP=0.05 and NP=0.15 in (a) and (b), respectively. Large hysteresis loops are visible only in (b).

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