Geometry-Dependent Of R-Curve,Construction Of Three Parameter Concrete R-Curve And Its Application

Fracture behavior of concrete-like quasibrittle materials should be described through nonlinear fracture models,among which cracking resistance or the R-curve represents the energy required for crack propagation in the material.Due to the existence of fracture process zone ahead of the crack,the R-curve of concrete-like quasibrittle materials often exhibits an ascending trend before attaining a stable value.An R-curve approach allowing for the fracture process zone can be used to predict the response of structures such as the load-displacement curve of the structures.Therefore,the determination of R-curve is an important content within the scope of concrete fracture mechanics,and has been one of the hot topics in the field of concrete fracture behaviors.Geometry-dependence of the R-curve is discussed in the paper,and a new R-curve is proposed by taking the crack initiation into account,which is then used to predict the cracking time of restrained concrete at early age and a comparison with the experimental results is made.Details of the present study are introduced as follows.(1)For concrete-like quasibrittle materials,an R-curve is defined as an envelope of the critical energy release rates from specimens with different sizes.For typical specimen geometries frequently used in fracture mechanics testing,it is possible to group R-curves into three types,i.e.type ?,type ? and type ?.R-curves for these three geometrical types are provided based on size effect law.The results show that for type ?,theR-curve proposed can be well used to describe the load-displacement of specimens made from concrete-like quasibrittle materials,and the R-curve can be regarded as one material property.Also,the R-curve determined for type ? can be definitely applied to type ? geometry.A special feature of the proposed R-curve is that the cracking resistance not only increases prior to the peak load but also increases after the peak load until reaching a steady value,which is assumed to be associated with the development of the fracture process zone.(2)A novel three parameter R-curve for concrete-like quasibrittle materials is established by considering the energy needed for cracking initiation in the pre-notched specimen.Only three material-related parameters are needed for constructing this R-curve,i.e.the initial fracture energy G0,fracture energy Gf and critical crack extension cf.The R-curve is therefore theoretically independent of specimen size.To explore the relationship between the R-curve and softening curve of the material,cracking resistance Rg is derived based on the linear and bilinear softening relations.The conclusion that the Rg from linear softening function agrees well with the propose three-parameter R-curve confirms that the softening function plays a vital role in determining the response of the specimen.(3)Mechanical and fracture tests are carried out on high performance concrete at early age,which are designed to construct three parameter R-curve and predict cracking time of restrained concrete.Variations of splitting tensile strength,Young's modulus and other mechanical properties with time are obtained through basic mechanical tests.Shrinkage tests involve free shrinkage and restrained shrinkage,among which cracks of three different lengths(15mm,30mm and 45mm)are tried.The results indicate the crack with length of 45mm is a better choice for testing cracking time of restrained concrete specimen.Three-point bending notched beam is then tested for deducing parameters necessary for constructing three parameter R-curve.(4)Three parameter R-curve approach is adopted to predict the cracking time of restrained concrete ring.Evolving Young's modulus and uniform temperature field are imposed on the restrained pre-notched concrete ring,and the stress intensity factor as well as energy release rate are then derived.An equivalent interfacial pressure pequ is defined according to the principle of crack driving force equation,and its fitting relation with crack length is established,thus theory of interfacial pressure in concrete without any crack can be extended to concrete with crack.Base on the current creep theory and active standard,a numerical simulation is performed by considering the influence of creep on pre-notched concrete ring.The cracking initiation time of concrete ring is determined by comparing the maximum allowable tensile strain from the relation between the cracking driving force and cracking resistance and the actual strain with creep considered.This approach is justified by the experimental results,and can be used to predict the cracking time of concrete ring on the condition that the precision requirement in engineering is satisfied.(5)Three parameter R-curve approach is used to predict the cracking time of restrained concrete ring with different geometries and strengths.A good agreement with the experimental results further indicates the validity of three parameter R-curve approach.