混凝土断裂能的边界效应确定法

从试件边界条件对断裂过程区的影响出发,研究了断裂特性在韧带上的分布特征,解释了根据断裂功原理测试得到的断裂能的尺寸效应现象。并以此为基础,通过引入局部断裂能的概念,推导出与尺寸无关的混凝土断裂能表达式。以不同韧带长度的楔入劈拉和三点弯曲梁试验进行了验证工作。结果表明,在试件的破坏状态,由于边界条件的限制,局部断裂能在韧带方向上的分布是不均匀的,从而引起测试断裂能的尺寸相关性。根据建立的模型计算得出的断裂能与试件尺寸无关,但反映边界影响的长度参数却随着试件尺寸的变化而变化。     

基于虚拟裂缝模型的混凝土等效断裂韧度

本文采用虚拟裂缝模型,将临界裂缝尖端张开位移ＣＴＯＤｃ作为控制参数,利用三点弯曲梁试件通过迭代求得了混凝土裂缝亚临界扩展量的临界值△ａｃ,据此求得了混凝土起裂断裂韧度ＫｉｎｉＩｃ、等效断裂韧度ＫｕｎＩｃ值。计算结果表明,随着试件尺寸的增大,△ａｃ增大,但ＫｉｎｉＩｃ、ＫｕｎＩｃ值却是与试件尺寸无关的断裂参数。这表明线弹性断裂韧度准则可应用于混凝土结构的裂缝评定。     

自重对混凝土三点弯曲梁断裂性能的影响

自重对三点弯曲梁试件的断裂性能有重要影响,而以往基于三点弯曲梁研究混凝土的断裂性能时,很少考虑自重引起的试件初始裂缝张口位移（CMOD_ini）的影响。为了研究CMOD_ini对三点弯曲梁断裂性能的影响规律,给出了CMOD_ini及考虑CMOD_ini影响的有效裂缝长度（a_c）和失稳断裂韧度（K_ICun）的计算公式,并用不同试件尺寸及不同初始缝高比的三点弯曲梁试验数据进行了对比分析。结果表明:当试件初始缝高比为0.4时,CMOD_ini受试件尺寸影响较小,即使试件尺寸达到2200 mm×550 mm×240 mm时,自重对其CMOD_ini、a_c及K_ICun的影响均小于5%。CMOD_ini受初始缝高比的影响较大,且随着初始缝高比的增大而增大,对于尺寸为1143 mm×305 mm×76 mm,初始缝高比为0.818的三点弯曲梁试件,自重对其CMOD_ini、ac及K_ICun的影响分别为24.26%、1.73%和17.31%。可见,当三点弯曲梁试件尺寸及初始缝高比均较大时应该考虑自重引起的CMOD_ini的影响。     

小尺寸混凝土试件双K断裂参数试验研究

采用最大尺寸为680mm×160mm×40mm的标准三点弯曲梁试件,利用在初始裂缝两侧粘贴电阻应变片并利用混凝土裂缝扩展到此处时其应变回缩的方法测得了起裂荷载Pini,在此基础上根据Pini及初始缝长a0得到了起裂断裂韧度KIiCni;根据在试验中测得的最大荷载Pmax及对应的裂缝口张开位移CMODC计算了混凝土等效裂缝长度aC,据此计算了失稳断裂韧度KIuCn。结果表明:采用电阻应变片法可准确测定混凝土的起裂荷载Pini,且方法简单。试验结果还表明:在本试验范围内,三点弯曲梁法测得的混凝土双K断裂参数KIiCni、KIuCn与试件高度无关,进一步说明了混凝土双K断裂参数可以作为描述混凝土裂缝扩展的断裂参数。     

基于裂缝扩展准则的K_R阻力曲线研究

根据混凝土I型裂缝扩展准则,将起裂断裂韧度作为材料参数,提出了一种新的计算混凝土结构裂缝扩展过程KR阻力曲线模型。该模型认为,裂缝扩展阻力由混凝土材料固有的抗裂能力和粘聚力提供的阻力组成并等于裂缝扩展的驱动力;应用该模型并借助有限元法计算了混凝土三点弯曲梁、楔入劈拉试件的裂缝扩展量、断裂过程区（FPZ）长度,在此基础上...     

超高韧性水泥基复合材料延性断裂性能评价准则的试验研究

该文研究了超高韧性水泥基复合材料的断裂性能评价准则。对纤维体积掺量为1。5%、2。0%与2。5%的超高韧性水泥基复合材料试件进行了弯曲断裂试验,基于非线性断裂力学,应用双J参数评价其断裂性能,并分析了其J_R阻力曲线。结果表明,该材料的弯曲断裂表现出延性特征。应用双J参数评价该材料的断裂性能,当流入裂缝塑性区的能量大于起裂断裂能J_IC时,裂缝出现;随后,裂缝稳定扩展;当流入塑性区能量大于失效断裂能J_IF时,局部裂缝出现,材料进入失稳发展阶段。该材料的J_R阻力曲线存在三阶段线性关系,分别以宏观裂缝出现点与主裂缝局部化点为分界点。在UHTCC的变形稳态发展阶段,相同面积的裂纹发展量消耗的能量相同。     

用实用解析法计算混凝土基于裂缝粘聚力的新KR阻力曲线

对三点弯曲梁混凝土试件,虚拟断裂过程区上粘聚力呈线性或双线性分布的,可以用实用解析法计算混凝土双K断裂参数及新KR阻力曲线。实用解析方法是用简单函数拟合Green函数,将粘聚力在裂缝尖端产生的应力强度因子积分算式转化为简单的算术表达式。该方法无需进行数值积分,简化了计算过程。采用不同尺寸的三点弯曲梁混凝土试件的试验结果...     

确定混凝土开裂与拉伸强度及双K断裂参数

该文考虑混凝土材料的非均质特性,发展了确定无尺寸效应的混凝土开裂强度与起裂韧度、拉伸强度与断裂韧度等材料参数的断裂理论与相应方法。基于三点弯曲、楔入劈拉、四点弯曲等不同类型混凝土试件的断裂试验,确定出对应的开裂强度与起裂韧度、拉伸强度与断裂韧度等材料参数,并与试验强度值及由双K断裂模型确定的双K断裂参数进行了比较,从而验证了所提模型与方法的合理性与适用性。基于确定的材料参数,分别建立了混凝土起裂与断裂破坏的全曲线,给出了确定无尺寸效应起裂韧度的混凝土试件最小理论尺寸。建立了起裂荷载与起裂韧度之间的解析公式,对三点弯曲、楔入劈拉、四点弯曲等不同类型混凝土试件的起裂荷载,以及不同混凝土的起裂韧度进行了成功预测。     

岩石-混凝土界面拉伸断裂性能的率相关性研究EI北大核心CSCD

该文弯曲断裂试验获得了不同应变率下界面的抗拉强度、荷载-加载点位移曲线、荷载-裂缝口张开位移曲线、起裂荷载和峰值荷载,通过夹式引伸计法和DIC法获得了临界裂缝扩展长度。并计算了界面断裂能及双K断裂参数,分析了不同应变率下界面断裂过程区演化规律及特征长度的变化。结果表明:随应变率的增大,断裂能和起裂韧度增大,临界裂缝长度和失稳韧度先增加后减小,断裂过程区长度及特征长度随应变率的提高而减小。该文从裂缝发展路径、自由水粘性、惯性效应三方面探讨了岩石-混凝土界面断裂参数的率效应。     

定向钢纤维水泥基复合材料断裂理论分析及试验

基于非线性铰模型研究了定向钢纤维水泥基复合材料的裂缝断裂全过程理论分析方法,结合不同尺寸试件的三点弯曲梁断裂试验对本文方法进行了验证。进而利用该方法预测了大尺寸三点弯曲梁试件的裂缝断裂全过程,并研究了试件尺寸对名义强度的影响。通过理论分析与试验结果对比,表明本文方法可较好地预测定向钢纤维水泥基复合材料的裂缝断裂全过程;此外,定向钢纤维水泥基复合材料的名义强度存在一定的尺寸效应,但尺寸效应表现不明显。     

Fracture mechanic modeling of fiber reinforced polymer shear-strengthened reinforced concrete beam

A numerical method is developed to model shear-strengthening of reinforced concrete beam by using fiber reinforced polymer (FRP) composites. Tensile crack is simulated by a non-linear spring element with softening behavior ahead of the crack tip to model the cohesive zone in concrete. A truss element is used, parallel to the spring element, to simulate the energy dissipation rate by the FRP. The strain energy release rate is calculated directly by using a virtual crack closure technique. It is observed that the length of the fracture process zone (FPZ) increases with the application of FRP shear-strengthening. The present model shows that the main diagonal crack is formed at the support in the control beam while it appears through the shear span in the shear-strengthened beam. Another important observation is that the load capacity increases with the number of CFRP sheets in the shear span.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Boundary effect on the softening curve of concrete

The apparent fracture energy of concrete experimentally determined on the basis of the work of fracture in bending or wedge splitting tests becomes larger with increasing specimen dimensions. This experimental observation may be attributed to the varying local fracture energy along the crack path. When the crack tip approaches the specimen boundary, the size of the fracture process zone will be reduced and, consequently, only a portion of the fracture energy is activated; i.e., the local fracture energy is getting smaller. The influence of this boundary effect diminishes with increasing specimen size resulting in the size dependence of the apparent fracture energy determined by the work-of-fracture method as an average value in the ligament. With varying local fracture energy, the local softening curve will also show variations. The latter are subject of the present study. Wedge splitting tests with different specimen sizes as well as inverse analyses of these experiments were carried out. For the inverse analyses, the cohesive crack model was adopted and an evolutionary optimization algorithm has been used. The boundary effect on the local fracture properties was taken into account and, as a result, the variation of the softening curve along the crack path could be determined. It was found that the tail of the softening curve is shortened and lowered due to the boundary effect whereas the initial slope of this curve appears to be not affected.     

Numerical characterization of the nonlinear fracture process in concrete

The growth and development of the fracture process zone in plain concrete has been investigated. A fictitious crack model based noniterative numerical scheme is developed to study the fracture characteristics of specimens of different sizes and geometries. Results from numerical studies on four different geometrically similar specimen sizes and two different specimen geometries are reported and discussed. The finite element program developed accommodates linear as well as nonlinear softening laws for the fracture process zone in concrete. It is observed that the process zone reaches a steady state length which is specimen size as well as specimen geometry dependent. As long as the process zone is allowed to develop to its steady state length, the energy absorbed in the process zone appears to be size and geometry independent. Results from tests on three-point bending specimens and compact tension specimens reported in the literature have been compared with the numerical solutions obtained in this investigation. Specimen size and geometry dependence generally observed in these fracture experiments have been duplicated. The numerical model also successfully reproduces many of the other experimentally observed characteristics in the fracture of plain concrete.     

Fracture energy and fracture process zone

The fracture energy G_f can be determined following a RILEM recommendation. However, it has been found that fracture energy depends on both size and geometry of the test specimen. The underlying fictitious crack model postulates that fracture energy, tensile strength, the critical opening of the fictitious crack, and the shape of the softening curve (softening factor) are constants for a given type of concrete. Here it is shown that a local fracture energy ccan be introduced. This local fracture energy varies with the width of the fracture process zone. As the crack approaches the back end of a specimen the fracture process zone becomes more and more confined and hence the local fracture energy decreases. Theoretical predictions are compared with experimental results obtained with the wedge splitting technique described earlier. It is shown that a local variation of the fracture energy leads to a size dependence of the global specific fracture energy.     

An experimental investigation on the FPZ properties in concrete using digital image correlation technique

This paper presents an experimental investigation on the properties of the fracture process zone (FPZ) in concrete using the digital image correlation (DIC) technique. Based on the experimental results, it is found that the FPZ length increases during crack propagation but decreases after the FPZ is fully developed. The FPZ length at the peak load and the maximum FPZ length increase with an increase in specimen height, but decrease by increasing the notch depth to specimen height ratio. It is also found that the crack extension length at the peak load is about 0.25 times the ligament length.     

Boundary effect on concrete fracture and non-constant fracture energy distribution

This paper extends the local fracture energy concept of Hu and Wittmann [29] and [30], and proposes a bilinear model for boundary or size effect on the fracture properties of cementitious materials. The bilinear function used to approximate the non-constant local fracture energy distribution along a ligament is based on the assumption of the proportionality of the local fracture energy to the fracture process zone (FPZ) height and characterises the FPZ height reduction when approaching a specimen back boundary. The bilinear function consists of a horizontal straight line of the intrinsic fracture energy G_F and a declining straight line that reduces to zero at the back boundary. It is demonstrated that using the bilinear model, the size-independent fracture energy G_F can be estimated from the fracture energy data measured on laboratory-size specimens, and the intersection of these two linear functions, defined as the transition ligament, represents the influence of the back boundary on the fracture properties. It is also demonstrated that the specimen size alone is not sufficient to characterise the size effect in the fracture properties observed on laboratory-size specimens.     

Size effect and quasi-brittle fracture: the role of FPZ

Fracture process zone (FPZ), or the crack-tip damage zone created by crack-bridging and micro-cracking activities, in a specimen of a concrete-like material is comparable to the crack size and un-cracked ligament, so fracture is typically quasi-brittle. Increasing or decreasing the specimen size, quasi-brittle fracture transition occurs towards the toughness-controlled or strength-controlled fracture, which is known as size effect (SE). In this study it is shown that the “size-dependent” quasi-brittle fracture transition is actually due to the interaction of FPZ with the nearest structure boundary rather than the size variation, and the widely-accepted SE for geometrically-similar specimens of different sizes is only a special case of quasi-brittle fracture controlled by the FPZ/boundary interaction. Relevant SE relations are critically reviewed and explained by emphasizing the key SE mechanism, FPZ/boundary interaction.     

Cohesive Crack with Rate-Dependent Opening and Viscoelasticity: I. Mathematical Model and Scaling

The time dependence of fracture has two sources: (1) the viscoelasticity of material behavior in the bulk of the structure, and (2) the rate process of the breakage of bonds in the fracture process zone which causes the softening law for the crack opening to be rate-dependent. The objective of this study is to clarify the differences between these two influences and their role in the size effect on the nominal strength of stucture. Previously developed theories of time-dependent cohesive crack growth in a viscoelastic material with or without aging are extended to a general compliance formulation of the cohesive crack model applicable to structures such as concrete structures, in which the fracture process zone (cohesive zone) is large, i.e., cannot be neglected in comparison to the structure dimensions. To deal with a large process zone interacting with the structure boundaries, a boundary integral formulation of the cohesive crack model in terms of the compliance functions for loads applied anywhere on the crack surfaces is introduced. Since an unopened cohesive crack (crack of zero width) transmits stresses and is equivalent to no crack at all, it is assumed that at the outset there exists such a crack, extending along the entire future crack path (which must be known). Thus it is unnecessary to deal mathematically with a moving crack tip, which keeps the formulation simple because the compliance functions for the surface points of such an imagined preexisting unopened crack do not change as the actual front of the opened part of the cohesive crack advances. First the compliance formulation of the cohesive crack model is generalized for aging viscoelastic material behavior, using the elastic-viscoelastic analog (correspondence principle). The formulation is then enriched by a rate-dependent softening law based on the activation energy theory for the rate process of bond ruptures on the atomic level, which was recently proposed and validated for concrete but is also applicable to polymers, rocks and ceramics, and can be applied to ice if the nonlinear creep of ice is approximated by linear viscoelasticity. Some implications for the characteristic length, scaling and size effect are also discussed. The problems of numerical algorithm, size effect, roles of the different sources of time dependence and rate effect, and experimental verification are left for a subsequent companion paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measurements and Calculations of the Width of the Fracture Process Zones on the Surface of Notched Concrete Beams

Abstract: The paper presents the results of experimental and theoretical investigations of the width of the fracture process zone (FPZ) on the surface of notched concrete beams during quasi‐static three‐point bending. To measure two‐dimensional deformations on the surface of beams, a Digital Image Correlation (DIC) technique was used. Laboratory tests were performed with different notched concrete beams. The experiments were simulated with two different isotropic continuum crack models under two‐dimensional conditions: an elasto‐plastic and a damage one with non‐local softening.