MODELLING THE PULLOUT OF HOOKED STEEL FIBERS FROM CEMENTITIOUS

MATRIX

Edmunds Zīle, Olga Zīle

Institute of Polymer MechanicsRiga, Latvia

Introduction

Concrete is brittle material with low fracture toughness in tension

Addition of short, randomly distributed fibers greatly improve the fracture toughness. The fibers bridge discrete cracks and thereby provide increased control of the fracture process

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What affects performance of FRC?

Fiber material

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Fiber volume fraction

Fiber shape

Fiber aspect ratio

Fiber strength

Objectives

1. Testing of some commercially available hooked-end steel fibers.

2. Development of simple analytical model for the effect of fiber geometry on the pullout behavior suitable for practical use.

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Single fiber pullout specimens

HE+ 1/60 and HE 75/50 hooked steel fibersproduced by ArcelorMittal

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Properties of the fibers

Fiber type σY (MPa) r (mm) le (mm) l (mm) ρ (mm) θ (rad)

HE 75/50 1100 0.35 2.0 2.1 1.7 0.62

HE+ 1/60 1450 0.45 1.9 1.4 2.2 0.66

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Experiment: pullout of straight fibers

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Experiment: pullout of hooked fibers

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Modeling of the fiber pullout process

Pullout load P of mechanically deformed fiber can be split into two components:

Component due to the plastic bending of the fiber in the curved matrix ducts

Component due to the frictional slidingof fiber through straight matrix ducts

where Ls is total lenght of straight matrix ducts andτ is frictional shear stress

Frictional shear stress can be obtained from straight fiber pullout tests

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Bending of fiber under tension

2Y YT T r

The following assumptions are made:

1.The material is isotropic and strain-rate independent.

2.The elastic strains are small in comparison with the plastic strains and can be neglected. Hence, the material is assumed to be rigid, perfectly plastic.

3.The damage of cementitious matrix around the mechanically deformed fiber during the pullout is neglected.

If fiber is subjected to a tension force less than the yield tension

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Increase of the tension

1. As the fiber bends at A and unbends at B there will be an increase in tension.

2. The tension will increase as the fiber slides against friction between A and B.

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Increase of the tension

The plastic work done on the fiber element by deforming it at A:

The external work:

Increase of the tension at A: The tension in the fiber after bending at A:

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Friction in the curved matrix duct

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B AT T e

Due to friction the tension in the fiber before unbending at B:

where μ is coefficient of friction

Tension in the fiber after curved matrix duct

Tension in the fiberafter unbending at B:

in

out in T T T T

T

T T T e T

1

1i

i i T T T T

T

T T T e T

or Tension in the fiber after ith curved duct:

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Pullout of hooked-end fibers: stage 1

Length of embedded part of the fiber without hook before pullout process

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Fiber segments in curved ducts C1 and C2 subjected to plastic bending.

Fiber segments in straight ducts S1, S2 and S3 subjected to frictional sliding.

Pullout of hooked-end fibers: stage 2

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Length of the fiber segment in the curved duct C1 decreases, which causes gradual reduction of pullout force component due to plastic bending.

Fiber segment in curved duct C2 subjected to plastic bending.

Fiber segments in straight ducts S2 and S3 subjected to frictional sliding.

Pullout of hooked-end fibers: stage 3

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Fiber segment in curved duct C2 subjected to plastic bending.

Fiber segments in straight ducts S2 and S3 subjected to frictional sliding.

Pullout of hooked-end fibers: stage 4

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Length of the fiber segment in the curved duct C2 decreases, which causes gradual reduction to zero of pullout force component due to plastic bending.

Fiber segment in straight duct S3 subjected to frictional sliding.

Pullout of hooked-end fibers: stage 5

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Pullout force is only due to frictional sliding of fiber segment in straight duct S3.

Comparison with experiment

Model proposed by Alwan et al.*

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Proposed model

* J.M. Alwan, A.E. Naaman, P. Guerrero, Concrete Science and Engineering, 1 (1999) 15-25.

Conclusions

1.A simple model is developed to simulate the mechanical contribution of fiber geometry to the pullout response. It is assumed that fiber geometry is composed of straight and curved segments. The mechanical contribution depends on the amount of plastic work required to straighten the fiber during pullout and friction in the curved ducts. The plastic work is a function of geometrical parameters and yield stress of the fiber. The damage of cementitious matrix during pullout is neglected.

2.The model provides a reasonably good description of experimental pullout data of hooked-end steel fibers.

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This work was supported by ERAF via project Nr. 2010/0293/2DP/2.1.1.1.0/10/APIA/VIAA/073