N2 an analytical and experimental investigation of mode i tensile and mixed mode combined tensile and shear fracture of concrete subjected to impact loading was conducted. Simulations illustrate that this concise approach can provide a reasonable estimation of peak load of the precracked plain concrete beams in mixed mode fracture. Jun 06, 2018 the results indicated that, once the initial fracture toughnesses for the rock, the concrete, and the rock concrete interface from the experimental work were obtained, the propagation of interfacial cracks and the corresponding fracture modes, including nonlinear characteristics of the materials and interface, could be predicted using the. This criterion has been used to simulate crack propagation in reinforced concrete 79 10, modei and mixedmode fracture 11, 12 and multiple cohesive crack propagation 80 in concrete. Barenblatt 1959, 1962 proposed an early cohesive model to study brittle fracture, and dugdale 1960 adopted a process zone concept to. Mixed mode fracture of concrete is encountered frequently in design of concrete structures. The concrete crack propagation process of mixed mode fracture and its corresponding variations of crack surface displacements before the peak load stage were experimentally studied using dic technique. The crack propagation criterion based on initial fracture toughness has been successfully utilized to investigate mode i and mixed mode crack propagation in concrete 43, 46. Modelling the fracture of concrete under mixed loading. The fracture toughness parameter of concrete appears to be unique and represented by the mode i fracture energy gf or the stressintensity factor k1c, even for.
General mixed mode crack problems can be solved with the dbem in a singleregion formulation, when the displacement boundary integral equation is applied on one of the crack surfaces and the traction boundary integral equation on the other. This criterion has been used to simulate crack propagation in reinforced concrete 79 10, mode i and mixed mode fracture 11, 12 and multiple cohesive crack propagation 80 in concrete. The dense crack pattern that results from the usual reinforcement detailing and element. Hence, an attempt has been made to use the acoustic emission technique to understand the mixed mode crack propagation in reinforced concrete. Influence of shear parameters on mixedmode fracture of concrete. Numerical method for mixedmode iii crack propagation in concrete. Taha department of civil engineering, kansas state university, manhattan, kansas, u.
T1 mixedmode fracture of concrete subjected to impact loading. Simulation of the mode i fracture of concrete beam with. In this criterion, crack propagation is initiated when the difference between the stressintensity factor at the crack tip caused by the external force and that by the cohesive stress. The work is limited to twodimensions, and therefore, the fracture modes of interest are mode i pure tension and mode ii pure shear. Analysis of crack propagation in asphalt concrete using. Simulation of crack propagation in asphalt concrete using an. Investigating the effect of aggregate characteristics on the. Numerical simulation on mixed mode iii crack propagation. T1 mixed mode fracture of concrete subjected to impact loading. Parametric analysis of dynamic crack propagation of concrete. To do this, the fracture behaviour is based on the work described in galvez et al, 11 which uses the hyperbolic expression proposed by cervenka 10 to.
Rockconcrete interfacial crack propagation under mixed mode. Analysis of mixedmode crack propagation using the boundary. Tests were performed on concrete beams with crack simulating notches, and two methods, which have been called the analytical and the direct experimental methods, were used to determine the critical strainenergyrelease rate associated with the rapid extension of the crack. Abstractesults of experiments using the losipescu test specimen in which. In reinforced concrete, mixed mode crack propagation is mainly addressed from a technological stand point. The stress transfer in the fracture process zone can be expressed by the crack closing stress and the crack opening displacement relation only and the shear stress along the crack interface did. Experimental study of mixedmode crack propagation in rc. Mixed mode crack initiation and propagation starting from the aggregate matrix interface in concrete under uniaxial compression was investigated using fracture mechanics approach, finite element modeling, and holographic interferometry techniques.
Abstract the object of this work is to model the propagation of fracture in mixedmode in lightly reinforced concrete beams. Similarly, it can be seen that, at the time of ms, no damage still occurs. A novel testing procedure for mixed mode crack propagation in concrete is presented. As a matter of fact, the mixed mode fracture energy is substantially equal to the mode i fracture energy gf, each crack growth step being produced by a mode i or opening mechanism. Mixed mode crack propagation and fracture in concrete. An experimental investigation into the behavior of concrete under mixed mode loading, undertaken in the light of fracture mechanics, is reported. Numerical results agree quite well with three experimental sets of mixed mode fracture of concrete beams. A model, which was originally proposed for mode i failure of concrete, is extended to characterized mixed mode crack propagation. To analyze the fpz evolution during the complete fracture process, a numerical method was employed to simulate the evolution of fpz under fps. Till now substantial work has been done on crack propagation under modei loading, and mixedmode fracture mechanics problems. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the materials resistance to fracture. Fracture process zone fpz is created with the mixed mode of tensile and shear cracks near the notchtip not on a plane but in a zone, according to sigma analysis.
Pdf mixedmode crack propagation through reinforced concrete. The size of fracture process zone and apparent fracture toughness k c were also evaluated as a function of sample size. Crack propagation and fracture of plain concrete beams. The mixed mode iii fracture of concrete is investigated by using a fourpoint combined discrete and finite elements method. To accurately analyzed and design a concrete structure, it is e a model, which was originally proposed for mode i failure of concrete, is extended to characterized mixedmode crack propagation. Analysis of mixedmode fracture in concrete using interface. Assume that, at a given time t, we are in the presence of a crack under mixedmode condition, and bot sifs are non zero. At least for proportional loading, at each mode mixity uniquely corresponds a crack propagation angle, whatever criteria one prefers. The model is based on the cohesive crack concept and uses the local mode i approach. In reinforced concrete, mixedmode crack propagation is mainly addressed from a technological stand point. Investigation on crack propagation is important to understand mechanical behaviors and fracture mechanism in concrete. A comparative study on two stress intensity factorbased.
Mixed mode fracture an overview sciencedirect topics. To accurately analyzed and design a concrete structure, it is essential to understand the failure mechanisms of concrete under mixedmode types of loading. Evaluation of size effect on mixedmode fracture behavior of. Mixedmode fracture of concrete is encountered frequently in design of concrete structures. Cohesive zone models have been used to simulate fracture of both homogeneous and nonhomogeneous materials. The main objective in this work is to provide a tool that predicts the crack propagation under mixed. General mixed mode crack problems can be solved with the dbem in a singleregion formulation, when the displacement boundary integral equation is applied on one of the crack surfaces and the traction boundary integral equation on. The macroscopic crack extension in concrete is successfully analyzed on the basis of lefm. Mixedmode crack propagation through reinforced concrete.
Numerical method for mixedmode iii crack propagation in. The griffith crack theory of fracture strength is discussed. Figures 5 and 6 show the crack propagation process and the contours of horizontal displacement field in the concrete slab with a preexisted iii mixed mode crack. Implementation of fictitious crack model using contact finite. Mixed mode crack propagation in mortar and concrete. The mixed freedom finite element method proposed for contact problems was extended to simulate the fracture mechanics of concrete using the fictitious crack model. N2 an analytical and experimental investigation of mode i tensile and mixed mode combined tensile and shear fracture. A previously developed lattice model is improved and then applied to simulations of mixed mode crack propagation in concrete. Therefore, the fpz evolution under mixed mode iii fracture also affects the crack propagation trajectory and failure mode of concrete structures.
In this criterion, crack propagation is initiated when the difference between the stressintensity factor at the crack tip caused by the external force and that by the cohesive stress satisfies the crackinitiation equation. In this criterion, crack propagation is initiated when the difference between the stressintensity. A previously developed lattice model is improved and then applied to simulations of mixedmode crack propagation in concrete. Baiant, elsevier applied science, london, 1140 reprinting of s25. In contrast to classical procedures, this method allows nonproportional loading and crack trajectory modifications by changing the action of one actuator. To investigate the effect of size on fracture toughness, a number of threepoint semicircular bending tests with different radii and four angles of edgecrack orientation were conducted and subjected to mixedmode loading.
The distribution of tbe stresses in front of a crack tip a11 only mode i tensile condition is considered here can be expressed by the following equation. Crack propagation modeling in quasibrittle materials such as concrete is essential for improving the reliability and loadbearing capacity assessment. The lowtemperature crack of asphalt concrete is considered to be one of the main deteriorations in asphalt pavements. For the mixed mode fracture in the reinforced concrete, the determination of crack trajectory for the crack instability is more dif. Additionally, a comparison was made between the experimental results and the estimations made by different theoretical criteria. Abstractesults of experiments using the losipescu test specimen in which axial compression has been introduced in addition to the shearing loads are reported here. Here, an intrinsic cohesive crack model is employed to study mixed mode fracture in a plain concrete beam with regular meshes. The tests were designed so that only one single mixedmode crack generates and propagates through the specimen, as opposed to the usual dense crack pattern found in most of the tests in scienti. The results indicated that, once the initial fracture toughnesses for the rock, the concrete, and the rockconcrete interface from the experimental work were obtained, the propagation of interfacial cracks and the corresponding fracture modes, including nonlinear characteristics of the materials and interface, could be predicted using the. In the present paper, the cohesive crack model is extended to mixed mode propagation and an experimental confirmation is provided by testing fourpoint shear.
Application of ae to fracture toughness and crack analysis by. The frames can move independent of one another along the axial and the lateral. Founded in 1904 and headquartered in farmington hills, michigan, usa, the american concrete institute is a leading authority and resource worldwide for the development, dissemination, and adoption of its consensusbased standards, technical resources, educational programs, and proven expertise for individuals and organizations involved in concrete. The potential fracture zone is simulated by the discrete elements des and the other zone by the finite elements fes. Mixedmode crack propagation in mortar and concrete. The crack propagation criterion based on initial fracture toughness has been successfully utilized to investigate modei and mixedmode crack propagation in concrete 43, 46. Different crack paths and fracture modes were obtained depending on the presence or absence of axial compression. Abstract in this paper, the finite element method is used to study mixed mode crack propagation in concrete and ma sonry. Simulations illustrate that this concise approach can provide a reasonable estimation of peak load of the precracked plain concrete beams in mixedmode fracture. Abstract two smeared crack approaches to fracture of con crete in mixed mode are implemented in two dimensional.
This paper evaluated mixed mode iii fracture toughness of fiberreinforced concrete using cracked semicircular bend scb specimens subjected to threepoint bending test. The specimens were threepointbend beams of three different sizes. Experimental and numerical investigations of rockconcrete. Founded in 1904 and headquartered in farmington hills, michigan, usa, the american concrete institute is a leading authority and resource worldwide for the development, dissemination, and adoption of its consensusbased standards, technical resources, educational programs, and proven expertise for individuals and organizations involved in concrete design. Mixedmode crack initiation and propagation starting from the aggregate matrix interface in concrete under uniaxial compression was investigated using fracture mechanics approach, finite element modeling, and holographic interferometry techniques. Mixedmode fracture of concrete subjected to impact loading.
As the maintenance of the cracked asphalt pavement is cost and time consuming, it is essential to reveal the cracking mechanisms from the view of materials and structures, to mitigate cracking propagation via the whole asphalt overlay 1,2. Pairs of contact points were set along the potential developing path of the crack. Simulation of crack propagation of concrete is carried out by the twodomain bem. The dense crack pattern that results from the usual reinforcement detailing and element geometry may somehow make it difficult to induce direct relations between causes and effects. A crackpropagation criterion is proposed in this paper for mixedmode iii fracture in concrete. Pdf this paper presents the results of a very recent experimental research program aimed at investigating mixedmode fracture of reinforced concrete find. Numerical study on mixedmode fracture in reinforced concrete. The shear load was applied first up to a shear force close to the force capacity. Modeling mixed mode fracture of concrete by using the. A bilinear cohesive zone model tailored for fracture of. Once the difference between the stress intensity factor at the crack tip caused by the external load and the one caused by the cohesive force attains the above kikii curve, the crack begins to propagate.
For mixed mode fracture problem, the influences of initial notch position on crack propagation path can be expressed as a competition between mode i fracture and mixed mode fracture, with offset parameter increasing from 0. Different experimental crack trajectories, under mixed mode and. The displacement of structure was chosen as the basic variable, and the nodal contact force in contact region under local coordinate system was. A model, which was originally proposed for mode i failure of concrete, is extended to characterized mixedmode crack propagation. Abstractesults of experiments using the losipescu test specimen in which axial. To better understand the crack propagation of mixed mode iii fracture in concrete, experimental and numerical studies have been conducted in previous decades. The concrete mesostructure is simulated by a threedimensional lattice system connecting nodes which represent the centers of aggregate particles. Introduction the interpretationof the fourpoint shear test of concrete fig. In constrast to more sophisticated models, this method offers two major advantages.
For this purpose a unique biaxial machine which consists of two independent stiff square loading frames was built. In reinforced concrete, mixedmode crack propagation is mainly addressed from a technological standpoint. The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasibrittle materials, such as concrete. Experimental study of mixedmode crack propagation in rc beams. The tests were designed so that only one single mixedmode crack generates and. The influence of natural and synthetic fibers on mixed mode i. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. When a notched beam does not have enough shear reinforcement, fracture can initiate and propagate unstably and lead to failure through diagonal tension. Acrackpropagation criterion is proposed in this paper for mixedmode iii fracture in concrete. Here, an intrinsic cohesive crack model is employed to study mixedmode fracture in a plain concrete beam with regular meshes. Mixed mode crack propagation in mortar and concrete, report 81, dpt. This figure depicts the setup of the mixedmode fracture test in which a double notched prismatic panel was loaded in tension t and shear s. Till now substantial work has been done on crack propagation under mode i loading, and mixed mode fracture mechanics problems, however, are more common for actual crack growth.
The fracture process zone characterizing the concrete fracture was represented by a discrete crack model with stress transfer along a cracked interface. The parameter, called generalized fracture toughness, is expressed in equation 20 and considers the effect of t. On crack propagation of iii mixed mode fracture in concrete. A crack propagation criteria is proposed for mixed mode iii fracture in concrete based on the initial cracking k. Much effort has since been made to extend the fictitious crack model to mixedmode fracture because most practical fracture problems in concrete are mixedmode, involving modes i and ii. Assume that, at a given time t, we are in the presence of a crack under mixed mode condition, and bot sifs are non zero. The fracture mechanics of bond in reinforced concrete. In reinforced concrete, mixed mode crack propagation is mainly addressed from a technological standpoint. On the basis of this criterion, a numerical method is developed to simulate mixedmode iii crack propagation in concrete. To accurately analyzed and design a concrete structure, it is essential to understand the failure mechanisms of concrete under mixed mode types of loading. Crack propagation explains many failure characteristics of concrete structures using the fracture mechanics approach. Nonlocal peridynamic modeling and simulation on crack. Mixed mode fracture of concrete under proportional and. Examples as to how the fracture morphology changes with increasing mode ii shear component can be seen in figs.
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