New G_R Crack Extension Resistance And Energy Transformation Analysis During The Whole Fracture Process In Concrete

For concrete or reinforced concrete structures,their failure process when subjected to external load is intimately associated with the appearance and propagation of crack and hence is regarded as a process of crack development.Fracture mechanics,where the strength of cracked solid and the general rules of crack development in cracked solid are major-cared, should be an effective and reasonable tool to analyze the mechanical response of cracked structures.However,owing to the heterogeneity of concrete and non-linear behavior exhibited in concrete,different from the ideal brittle materials,the fracture process of concrete material is complex and shows the typical three stages:crack initiation,crack stable propagation and unstable propagation.It had been commonly accepted that the bridging cohesive property of aggregate reinforcements is primary governing mechanism which results in the presence and development of fracture process zone(FPZ) and thereby resulting non-linear fracture behavior. So far,after considering the influence of fracture process zone on concrete fracture behavior, many fracture models applicable for concrete had been proposed in last several years. However,most of models were based on stress intensity factor approach not energy approach. It is very reason that the researches on the crack resistance determined using energy approach as well as studies regarding the transformed relationship between different energy consumption patterns during the whole fracture process in concrete are rather lack.As a consequence,in this paper the energy approach is attempted with the major purpose of obtaining further deeper understanding of fracture behaviors exhibited in concrete.1.Crack extension resistance curve better describes the change of crack resistance capacity of material with crack development and is used as a criterion to judge whether crack is stable at certain crack propagation.In this paper,firstly,a state-of-the-art retrospection on the conception of traditional crack extension resistance curve proposed by Irwin in 1960s and two different semi-analytical and semi-experimental methods to construct R-curve are made.Then,combining with the phenomenology observations from fracture experiments of concrete,and based on the two basic assumptions,new G_R crack extension resistance curve model which describes the change of crack resistance with crack propagation is constructed from the view of the composite materials.In this model, the crack extension resistance is composed of two parts.One part is contribution produced by hardening cement-gel matrix and is called mitiation fracture toughness. Another part is contribution caused by bridging cohesive action of aggregates and is named as cohesive toughness.For the front,according to the Griffith's brittle fracture theory,the value is a constant and is assumed to be equal to the fracture toughness of cement paste.While for the latter,the value is changeable.To determine it,the calculation equation of local fracture energy is firstly deduced based on the Hillerborg's fictitious crack model.After this,using Reinhardt's non-linear softening curve,the two different equations for evaluating cohesive toughness are obtained respectively corresponding to two different cases defined in terms of the values of crack length a and crack characteristic length a_w0.Finally,the equations for crack extension resistance at any time during the whole fracture process are obtained.2.A total of 7m³ concrete fracture specimens are cast.Of which,two typical geometries,i.e. three-point bending beam(TPB) and wedge-splitting(WS),are used.The maximum dimension for TPB and WS is 2000mm×500mm×200mm and 1440mm×1200mm×200mm,respectively.Fracture tests are performed on the intact concrete specimens.Then, according to the proposed G_R crack extension resistance curve model,the detailed calculation steps and corresponding calculation equations are further introduced for two geometries,respectively.Using the obtained P-CMOD curve,G_R crack extension resistance curve and crack driving curve are determined for every tested specimen.The basic features shown on G_R crack extension resistance curve are pointed out.Moreover, the implied physical meaning behind the intersection points of crack resistance curve and crack driving curve is clarified by comparing them with the P-CMOD curve.At last,the size effect and geometry effect of new G_R crack extension resistance curve together with the correlation between it and used softening curve are discussed.3.Softening curve gives a description of physical mechanical behavior occurred in non-linear fracture process zone ahead of crack tip.It can be said that the bridging cohesive properties determined by the different softening curve are distinguished.Hence, the calculated G_R crack extension resistance curve will show some differences,too.In this paper,the bilinear softening curves and non-linear softening curve are adopted.Also, the fracture energy determined from them according to the definition by Hillerborg is assumed to be a constant in all used softening curves.In such case,G_R crack extension resistance curves for seven numerical simulated TPB are computed.The impact of different softening curves on the obtained G_R crack extension resistance curves is highlighted.4.Similar to ideal brittle materials,the fracture process of concrete is a process of energy transformation,too.During this process,the work done by external load is consumed in two prime manners,i.e.,elastic strain energy and fracture surface energy.However,last extensive studies put more interests in the finally completely fracturing time at which the external work caused by applied load is assumed to totally flow into fracture narrow zone. But,for others any crack propagation time,the related studies are seriously few.Because of this,in the present paper,the emphasis of the work is put on the whole fracture process. Then,two kinds of energy consumption of external force work,namely,elastic strain energy and fracture surface energy at any picked crack propagation are determined using the data obtained from wedge-splitting experiments.The calculated results provide new insights into the understanding of concrete fracture behavior.Meanwhile,the energy needed for creating unit area crack propagation at any crack propagation is computed,too. The corresponding discussions are made.