Keywords: fracture, quasi-brittle, fracture process zone, work of fracture, material property, boundary effect.

This paper focuses on the development of an efficient technique for the determination of fracture material properties of quasi-brittle materials from experimental tests on laboratory specimens as independent as possible of a specimen's size and geometry or a specimen's free boundaries, respectively. The approach is motivated by observations and analyses reported in the literature [1,2] and based on findings from numerical simulations conducted by the authors [3] from which it is obvious that the dependence of apparent fracture energy on a specimen's geometry and size is caused mainly by the change in the size and shape of the fracture process zone (FPZ) during fracture propagation. This change is governed by the location of the FPZ in relation to the free surfaces of the body and causes the alteration of the amount of energy dissipated in the zone. Therefore, the possibilities of specification of the energy dissipated within the FPZ (a portion of the entire work-of-fracture) according to the volume of the FPZ rather than to the cracked ligament area, as is usual, are investigated in this paper. An amalgamation of the equivalent elastic crack approach, the cohesive crack approach and multi-parameter fracture mechanics is employed for a reconstruction of the volume of the FPZ by which the amount of energy consumed within the FPZ during the fracture process is specified.

In this paper an attempt is made to separate the energy amounts consumed via different energy dissipation mechanisms during quasi-brittle fracture and to specify them using the spatial characteristics of the propagating crack and the FPZ evolving at its tip. The portion of energy consumed in order to create new crack surfaces is specified by the area of the projection of the surfaces to the crack plane resulting in a critical energy release rate referred to as fracture energy, the value of which is assumed to be a material property. The other part of the entirely dissipated energy is consumed in the failure mechanism taking place in the FPZ. This value is specified by the volume of the FPZ, resulting in the spatial energy dissipation density. The progress of this quantity during the fracture is the subject of this paper.

The proposed concept was verified using the results of numerically simulated fracture tests of notched beams under three point bending conducted using the ATENA 2D software [4]. The method provided satisfactory results concerning the estimation of the extent of the FPZ. The other part of the proposed procedure, i.e. the specification of the energy dissipated in the FPZ by its volume, has not lead to unambiguous results so far. Alternative approaches for this part of the procedure are under consideration. It is also intended that the conclusions will be confirmed by both numerical simulations and experimental data.

1

Z.P. Bazant, "Analysis of work-of-fracture method for measuring fracture energy of concrete", J. Eng. Mech., 122(2), 138-144, 1996. doi:10.1061/(ASCE)0733-9399(1996)122:2(138)

2

X.-Z. Hu, K. Duan, "Influence of fracture process zone height on fracture energy of concrete", Cem. Concr. Res., 34, 1321-1330, 2004. doi:10.1016/j.cemconres.2003.12.027

3

V. Veselý, L. Routil, Z. Keršner, "Structural geometry, fracture process zone and fracture energy", In: A. Carpinteri, P. Gambarova, G. Ferro, G. Plizzari, (eds.), Proc. FraMCoS-6, Catania, Italy. Taylor & Francis/Balkema, 1, 111-118, 2007.

4

V. Cervenka, et al., "ATENA Program Documentation, Theory and User manual", Prague: Cervenka Consulting, 2005.

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