Stochastic matrix-cracking model for textile reinforced cementitious composites under tensile loading

When cementitious composites are loaded in tension, cracks initiate and propagate at very low stress levels, leading to a non-linear constitutive behaviour. A first attempt to model this behaviour (the well-known ACK-model) was done by Aveston et al. [1] and Aveston and gKelly [2]. However, according to several authors [3-10], the main limitation of this model is the stochastic nature of the strength of the cementitious matrix, which is not included in the ACK-model. Based on the work of Curtin et al. [7, 10], presenting a statistical treatment of matrix crack evolution in unidirectionally reinforced ceramic micro-composites with single fibres; a two-parameter Weibull model is proposed in this paper to describe the matrix strength. It was shown by Curtin et al. [7, 10] that one can determine the Weibull parameters on pure matrix specimens and transfer them to the matrix behaviour in the composite, if single fibre ceramic composites are used. However, it has been determined that this is not the case when textile reinforcement is used in a cementitious matrix. As will be shown in this paper, this stochastic cracking model cannot be simply transferred from single fibre ceramic composites to cementitious matrices with fibre bundles. The necessary modifications to make it useful for textile-reinforced cements are discussed.