Last modified: 2015-06-20
Abstract
High performance fiber reinforced cementitious composites (HPFRCC) are a special family of the fiber-reinforced cement-based composites, which are distinguished from the quasi-brittle fiber reinforced concrete (FRC) by a macroscopic pseudo strain-hardening behaviour in tension with sequential development of multiple cracking up to relatively high strain levels. The associated high ductility, large energy absorption capacity and high toughness are expected to significantly enhance the serviceability and sustainability of cementitious materials. Engineered cementitious composites (ECC) are a unique member of HPFRCC, featuring extraordinary tensile ductility and moderate fiber content. For example, ECC materials based on the polyethylene fiber or the polyvinyl alcohol (PVA) fiber have been reported to show a tensile strain capacity at a range of 3 – 6 % with fiber volume fraction no greater than 2 %. Additionally, ECC has been developed suitable for a regular casting and curing process, favorable for a high producing efficiency and low cost.
Although some theoretical models are available in the literatures to describe the tensile behaviour of HPFRCCs, few numerical analyses regarding the multiple-cracking fracture behaviour have been reported. In present work, the multiple-cracking fracture behaviour of ECC under uniaxial tensile loading is numerically modelled using the extended finite element method (XFEM), which has been proven to be a powerful numerical procedure for solving crack growth problems and generally acknowledged for its flexibility in dealing with cracks with arbitrary geometries. A representative volume element (RVE), the size of which should be significantly smaller than the structural dimensions so that it can be viewed as a material point yet big enough to accommodate a random number of cracks, is developed and employed. In this way, the tensile macroscopic constitutive law of the ECC material can be derived based on the relation between the overall tensile stress and the overall tensile strain of the RVE through the homogenization technique. The individual cracks are treated utilizing the cohesive crack concept, where the constitutive law in the cohesive zone in terms of the traction-separation law (TSL) is given by the crack bridging law of plain matrix plus the crack bridging law due to fibers. A simplified TSL based on the crack bridging law is adopted instead without loss of the accuracy. In addition, the effect of the RVE size on the macroscopic tensile stress-strain relation is investigated. To validate the presented work, the derived tensile stress-strain relation of a PVA-ECC will be compared against the experimental result.