PSI - Issue 13

Lucie Malíková et al. / Procedia Structural Integrity 13 (2018) 1798–1803 Lucie Malíková & Jan Klusák / Structural Integrity Procedia 00 (2018) 000 – 000

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diagram containing the so-called tensile softening, see Karihaloo (1995). This kind of behavior can be explained by various kinds of toughening mechanisms, such as microcracking or others. It has been shown that an Interfacial Transition Zone (ITZ) develops at the boundary between the matrix (MTX) and aggregate (AGG), see Farran (1956) and Scrivener et al. (2004), and its influence on the fracture behavior of the whole system is important. The presence of the very thin porous ITZ at the MTX/AGG interface brings additional difficulties to analyzes of fracture response of cementitious composites. Several approaches have been proposed how to deal with this phenomenon, such as homogenization techniques, see Mori and Tanaka (1973), or generalized self-consistent scheme, see Hashin and Monteiro (2002). In this paper, the crack terminating at the interface between the MTX and AGG is modelled numerically by means of the Finite Element Method (FEM). The widely used three-point-bending (3PB) test, see RILEM (1985), is simulated and the effect of the ITZ on the crack behavior is investigated. Particularly, the level of the critical load is estimated by means of two generalized fracture criteria – criterion of the mean tangential stress value and criterion of the generalized strain energy density factor, see Náhlík et al. (2008).

Nomenclature a

crack length

B

specimen thickness

d

critical distance considered in the generalized fracture criteria ( d = t ITZ )

E AGG

Young's modulus of the AGG Young's modulus of the ITZ layer

E ITZ

E MTX Young's modulus of the MTX f ij ( p,  ) known function of bi-material parameters  and  F appl applied force F crit critical value of the applied force H I , H IC generalized stress intensity factor and its critical value, respectively K IC fracture toughness L half specimen length p stress singularity exponent r AGG radius of the AGG S half span between the supports in the 3PB test t ITZ thickness of the ITZ layer W specimen width  ,  bi-material parameters, see Lin and Mar (1976)  eigenvalue corresponding to an elastic mismatch for a crack with its tip at a bi-material interface,  = 1- p σ ij stress tensor component  Poisson's ratio (used for all the materials considered) The effect of the ITZ thickness, AGG radius and MTX/ITZ elastic mismatch is investigated via evaluation of critical applied load values calculated by means of selected fracture criteria for a crack terminating at the interface between the MTX and ITZ. Because the crack with its tip at a bi-material interface represents a general singular stress concentrator (in contrast to a crack in a homogeneous material, where the stress intensity exponent p = 1/2), generalized forms of the suggested criteria need to be applied. The basic idea of the both criteria is comparison of the generalized stress intensity factor (GSIF) value, H I , to its critical one, H IC (considering mode I of loading). Whereas the GSIF can be obtained by means of the direct method from numerical analysis, i.e. the formula for a selected 2. Stability fracture criteria