Strain Rate, Volume Fraction and Notch Depth Effects on Fracture Properties of Fibrous Cementitious Composites

Abstract

It is known that concrete is weak in tension. Steel Fibre Reinforced Concrete (SFRC) is an alternative cementitious composite to increase the tensile strength, energy absorption capacity and durability of concrete structures. The variation of tensile stress (σ) developed in the Fracture Process Zone (FPZ) of SFRC with crack width (w) constitutes σ - w curves. The nonlinear tensile response of SFRC can be characterized using σ - w curves. Generally, the σ - w curves are obtained by direct method such as uniaxial tensile test or preferably by Three Point Bending (TPB) test using inverse analysis. However, the variation of tensile stress with crack width can be determined using Digital Image Correlation (DIC) technique and Acoustic Emission (AE) testing. The DIC technique was used to simulate the Olesen’s cracked hinge model to locate the position of neutral axis using displacement contours in x - direction. The crack initiation point was identified using Maximum strain component in x - direction. The deformation parameters such as crack width, Crack Mouth Opening Displacement (CMOD), nonlinear hinge displacement in x - direction, neutral axis depth, curvature, cracking tensile strain, tensile strain and compressive strain were determined using DIC technique. Thus, a DIC based method was introduced to obtain above mentioned deformation parameters to determine σ - w curves. An empirical relation was introduced between experimentally obtained tensile stress and crack width to generalize σ - w relation. Soranakom and Mobasher’s analytical model to obtain σ - ε relation of FRC in tensile and compressive region was used to determine σ - w relation for the validation of DIC based method. The strain related parameters such as µ, ω, β and 𝜆 were determined using DIC technique to obtain neutral axis depth ratio - normalized compressive strain response, normalized moment - normalized curvature response, Load (P) - CMOD response. The tensile strength was determined using DIC based method to compare with tensile strength predicted by Soranakom and Mobasher’s model. A damage based model was introduced where the variation of tensile damage indices corresponding to the cementitious matrix cracking and steel fibre bridging with normalized tensile strain was obtained from cumulative AE energy of hits corresponding to tensile cracking and shear cracking respectively. The parameter a and parameter b were introduced to study the influence of steel fiber volume fraction (Vf) on the increment of tensile stress corresponding to cementitious matrix cracking and steel fibre bridging respectively. The influence of Vf, strain rate, notch to depth ratio on the fracture energy, elastic modulus, ultimate peak load (Pu), midspan deflection and CMOD at Pu, fictitious crack tip displacement, crack propagation rate, parameter a, parameter b, tensile stress and damage indices corresponding to the cementitious matrix cracking and steel fibre bridging were studied under Mode I fracture. The σ - w curves were used to determine P - CMOD response using sigw - Concrete© to validate the DIC based method and damage based model.