Research On Fictitious Crack Analytic Modelling And Concrete Fracture Process Zone Under Combined Stress Conditions

Concrete is one of the most common building materials,used in hydraulic engineering and civil engineering widely.The problem of crack in service process has always been the focus of scholars.The fracture properties of concrete are different from the brittle fracture of metals.The most important feature of the fracture properties of concrete materials is that they have strong nonlinearity,and the fracture process zone(FPZ/cohesive zone)is the best representation of non-linearity,so the problem of FPZ properties has been the priority among priorities of the research.However,the research on the FPZ analytical solution and the influence of combined stress condition on the FPZ properties are not enough.So this article researched the problem of FPZ under combined stress condition through theoretical analysis,fracture test and numerical simulation.The details are listed as follows:(1)Based on Duan-Nakagawa model,with the weighted integral method,a semi-analytical method to stress functions satisfying the crack opening displacement of fictitious crack is proposed.The weight function is determined by using the selected points method and the superposition of analytic functions with the same crack length but different fracture process zone length,to satisfy the given crack opening displacement in the fracture process zone,and then the final stress function and displacement function can be obtained by the weighted integral method.As an example,a special analytical solution for a double edge notched plate under mode-I loading is yielded out,the tensile strain softening curve and the fracture energy are obtained.The rationality and feasibility of this method are verified.(2)Taking the wedge-splitting test on a compact tension specimen with single fulcrum as the research object.The fracture properties of mode I crack under bending are studied.Based on the Williams stress function,the stress function expression in the form of series is solved by the boundary collocation method(BCM).And the stress intensity factor is yielded out according to the obtained stress function,and the results show that the obtained stress function and stress intensity factor have higher accuracy;The fictitious crack model approximate solution of the problem is obtained by weighted integral method.(3)Taking the wedge-splitting test on a compact tension specimen with double fulcrums as the research object.The fracture properties of mode I crack under compressive stress parallel crack are studied.The general solution of the stress function was obtained by using the BCM.Followed by the actual the wedge-splitting test on a compact tension specimen,the FPZ length and the crack opening displacement(COD)in FPZ are obtained by using the digital image correlation method(DICM).The effect of compressive stress parallel crack on the FPZ properties is analyzed.The results show that as the compressive stress parallel crack increases,the size of the FPZ gradually decreases,and the peak load gradually decreases.The effect of compressive stress parallel crack on the FPZ properties can't be neglected,and the cause of effect is analyzed preliminary.Finally,based on the general solution of stress function and the FPZ length and COD in FPZ,the fictitious crack model analytical solution is determined by semi-analytical method.And the tensile strain softening curve and the fracture energy are obtained.(4)Taking a concrete gravity dam as the research object,the problem of FPZ under compression-shear condition is studied.The stress function was solved by the BCM.The crack type is divided into compression-shear failure(mode II)and I-II mixed mode according to the strength of the material,and the fracture properties are analyzed respectively.When the crack type is mode II,the analytical solution that represent the shear softening characteristics is obtained by the weighted integral method,the shear stress-slip displacement curve is yielded out;When the crack type is I-II mixed mode,based on the maximum tangential stress criterion,the crack propagation angle is calculated,and it is very close to the result of numerical simulation.(5)Using the obtained tensile strain softening curve and fracture energy as the material parameters,the whole fracture process of wedge-splitting test on a compact tension specimen with double fulcrums is analyzed by numerical simulation and theoretical calculation,the results are close to the fracture test results,the accuracy of FPZ analytical solution is certified again.In addition,other wedge angle situations are performed,the conclusion of effect of compressive stress parallel crack on fracture properties is the same as the experimental conclusion.Finally,the size effect in FPZ properties is studied,it is found that the FPZ size gradually decreases with the increase of the crack height ratio,but the size effect on the COD is not obvious.