全级配混凝土I型裂缝扩展全过程数值模拟

该文将起裂断裂韧度作为裂缝扩展的判定依据,应用ANSYS软件,对全级配混凝土I型裂缝扩展过程进行数值模拟,分别计算了混凝土楔入劈拉试件的荷载-裂缝口张开位移曲线、临界裂缝长度和双K 断裂韧度,并与溪洛渡大坝的断裂试验结果进行比较,吻合良好。同时,结合试验数据,将该文计算结果与《水工混凝土断裂试验规程》规定的标准尺寸试件断裂参数计算结果进行对比。结果表明:规程规定的方法也适用于大尺寸非标准试件双K 断裂参数的计算,其误差率在5%以内。此外,对于全级配混凝土,只要通过试验测得其弹性模量、抗拉强度、抗压强度和起裂荷载,即可用该文提出的方法计算混凝土的双K 断裂韧度和裂缝扩展全过程。应用该方法还可以得到全级配混凝土的K_R阻力曲线。     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

混凝土Ⅰ型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

混凝土断裂过程区长度计算方法研究

该文基于粘聚裂缝概念,以起裂韧度作为裂缝起裂和扩展的准则,提出了混凝土断裂过程区长度的计算方法。以Ⅰ型裂缝为例,计算了不同初始缝长和起裂韧度情况下的断裂过程区长度值,结合以往大体积混凝土的试验数据对其进行了验证。进而分析了断裂过程区长度的影响因素,结果表明:断裂过程区长度随初始缝长的增大而逐渐增大,随起裂韧度的增大而逐渐减小。     

光弹贴片法研究混凝土Ⅰ-Ⅱ复合型裂缝扩展过程

该文采用光弹贴片方法对最大尺寸为2500mm×600mm×200mm的混凝土四点剪切梁,Ⅰ-Ⅱ复合型裂缝起裂、稳定扩展直至失稳破坏全过程进行了系统的研究,通过照相机拍摄光弹贴片所显示的裂缝扩展全过程,得到了混凝土裂缝稳定扩展阶段完整而直观的观测结果。根据光弹贴片所显示的彩色条纹序列,测得了四点剪切荷载作用下裂缝尖端附近主应变场分布,得到了荷载-裂缝扩展量曲线。根据光弹贴片所观察的裂缝扩展长度?a,借助有限元计算了裂缝扩展过程中尖端应力强度因子的变化,并模拟断裂过程。结果表明,对于混凝土Ⅰ-Ⅱ复合型断裂,裂缝在失稳扩展前存在着明显的亚临界扩展,采用光弹贴片方法可有效地记录这一过程,而以往不考虑裂缝扩展量得到的断裂准则是偏于保守的。试验结果还表明,在裂缝起裂后,虽然加载方式仍为Ⅰ-Ⅱ复合型,但断裂类型已由Ⅰ-Ⅱ复合型退化为纯Ⅰ型断裂。     

混凝土非线性断裂韧度G_(Ic)及其尺寸效应

就混凝土而言，在裂缝失稳扩展前，由于裂缝尖端的微裂区而产生非线性变形并伴有裂缝的亚临界扩展。这种非线性变形与亚临界扩展，使混凝土材料在断裂前吸收更多的能量。本文从试验得出的荷载－位移的非线性曲线出发，求得了材料抵抗裂缝扩展的非线性断裂韧度，并探讨了试件缝高比及高度对的影响。     

大初始缝高比混凝土试件双K断裂参数的试验研究

双K 断裂准则能够定量描述混凝土裂缝的起裂、稳定扩展和失稳断裂。该文采用混凝土三点弯曲梁试件,通过在试验中测得的起裂荷载P_ini、最大荷载P_max及临界裂缝口张开位移CMOD_C计算了初始缝高比为0.3~0.9共7组试件的起裂断裂韧度K_ICini 和失稳断裂韧度K_ICun 。结果表明,当初始缝高比为0.3~0.7时,混凝土裂缝扩展经历起裂、稳定扩展和失稳破坏3 个阶段,双K 参数均是与初始缝高比无关的材料参数;当初始缝高比大于或等于0.8 时,混凝土裂缝起裂后便进入失稳扩展阶段,起裂荷载即为最大荷载,且计算得到的K_ICini 仍与初始缝高比无关。因此,在确定K_ICini 时,仅需测得初始缝高比大于或等于0.8试件的P_max,将P_max作为P_ini直接计算得到K_ICini。同以往的试验方法相比,其结果更为准确且试验方法简单。     

混凝土裂缝扩展的断裂过程准则与解析

该研究工作对混凝土这一多相的复合材料,通过实验和理论相结合的科学手段,建立了一套完整的描述混凝土裂缝发展的断裂理论以及分析方法。根据实验观测结果提出了双K断裂参数,可以反映混凝土裂缝发展特性。在线形渐进叠加假定基础上,给出了双K断裂参数的解析表达式。根据分布于断裂过程区上粘聚力对裂缝扩展阻力的增强作用,得到了双K断裂参数适用的解析解,并通过实验分析了各种可能因素对双K断裂参数的影响。在考虑粘聚力影响条件下,提出了裂缝扩展阻力的新KR曲线,并将双K断裂参数与之对应起来。研究工作又通过能量的观点提出了与双K断裂参数相对应的以能量释放率为参数的双G断裂参数。通过数值计算和实验分析证实了能量法和应力场法在描述混凝土断裂性能方面的等效性。     

基于粘结单元的三维随机细观混凝土离散断裂模拟

开发MATLAB 和ABAQUS Python脚本程序,建立含随机三维多面体骨料的混凝土细观有限元模型。通过自编高效C++程序插设三维零厚度的粘结界面单元,以模拟复杂三维离散多裂缝的起裂与扩展。对典型混凝土试件单轴拉伸断裂的模拟,分析粘性界面单元的主要材料参数(抗拉强度与断裂能)对应力-位移曲线、断裂过程、裂缝面特征的影响。结果表明:宏观应力-位移曲线主要受砂浆、界面粘性裂缝单元的抗拉强度、断裂能绝对数值的影响;裂缝面的位置与形态决定于砂浆、界面粘结裂缝单元的抗拉强度相对比值以及断裂能相对比值;混凝土的力学响应反映其裂缝发展特征,二者既决定于断裂材料参数,也受到骨料大小、形状等细观结构因素的影响;建立的有限元模型能有效描述混凝土复杂三维断裂过程。     

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。     

Crack Extension Resistance and Fracture Properties of Quasi-Brittle Softening Materials like Concrete Based on the Complete Process of Fracture

The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss–Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (K_R-curves) were determined by combining the crack initiation toughness that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing K_R-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve(K_R-curve) is lower than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.     

Fracture stability and residual strength assessment of reinforced concrete beams

In conventional analysis and design procedures of reinforced concrete structures, the ability of concrete to resist tension is neglected. Under cyclic loading, the tension-softening behavior of concrete influences its residual strength and subsequent crack propagation. The stability and the residual strength of a cracked reinforced concrete member under fatigue loading, depends on a number of factors such as, reinforcement ratio, specimen size, grade of concrete, fracture properties, and on the tension-softening behavior of concrete. In this work, a method is proposed to assess the residual strength of reinforced concrete beams subjected to cyclic loading. The crack extension resistance based approach is used for determining the condition for unstable crack propagation. The effect of reinforcement is modeled as a closing force counteracting the effect of crack opening produced by the external moment. The effect of percentage reinforcement and specimen size on the failure of reinforced beams is studied. Finally, the residual strength of the beams are computed by including the softening behavior of concrete.     

Modelling multiple cohesive crack propagation using a finite element–scaled boundary finite element coupled method

This paper presents an extension of the recently-developed finite element–scaled boundary finite element (FEM–SBFEM) coupled method to model multiple crack propagation in concrete. The concrete bulk and fracture process zones are modelled using SBFEM and nonlinear cohesive interface finite elements (CIEs), respectively. The CIEs are automatically inserted into the SBFEM mesh as the cracks propagate. The algorithm previously devised for single crack propagation is augmented to model problems with multiple cracks and to allow cracks to initiate in an un-cracked SBFEM mesh. It also addresses crack propagation from one subdomain into another, as a result of partitioning a coarse SBFEM mesh, required for some mixed–mode problems. Each crack in the SBFEM mesh propagates when the sign of the Mode-I stress intensity factor at the crack tip turns positive from negative. Its propagation angle is determined using linear elastic fracture mechanics criteria. Three concrete beams involving multiple crack propagation are modelled. The predicted crack propagation patterns and load–displacement curves are in good agreement with data reported in literature.     

An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete*

An embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi‐brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well‐known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete.     

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.     

Mode I and mode II initiation fracture toughness and resistance curve of medium density fiberboard measured by double cantilever beam and three-point bend end-notched flexure tests

Using specimens of medium density fiberboard, double cantilever beam and three-point bend end-notched flexure tests were conducted to obtain the mode I and mode II initiation fracture toughness and resistance curve for in-plane and through-the-thickness systems. The mode I initiation fracture toughness was smaller than that of mode II for the in-plane crack systems, but this tendency was inverse for the through-the-thickness systems. The fracture toughness increased during the crack propagation because of the significant fiber bridgings induced between the crack surfaces, but the increase of the mode I propagation fracture toughness was moderated after the crack reached a certain length. In contrast, the mode II propagation fracture toughness continuously increased during the crack propagation.     

Crack growth in cement-based composites

A model that can be used to predict Mode I crack growth in cement-based composites is presented. The region ahead of a crack tip, where nonlinear deformations and aggregate interlock occur, is modeled as an extension of the actual stress-free crack subjected to a closing pressure that depends on the crack face displacements. In the case of concrete, crack propagation is assumed to occur when the crack opening displacement at the tip of the actual crack reaches a critical value. To predict results, the elastostatics problem of a layer containing a vertical edge crack was solved using a Green's function approach together with integral transform techniques. Stress intensity factors and crack opening displacements were obtained by numerically solving a singular integral equation. The closing pressure function and critical crack tip opening displacement were taken from experimental data for various materials, and the model was applied to the analysis of experiments performed on initially notched concrete and fiber-reinforced mortar beams.     

不同软化曲线形状对裂缝扩展阻力G_R曲线的影响

最近基于裂缝粘聚力提出了描述裂缝扩展全过程阻力变化的GR曲线,所发展的解析解相关于骨料桥联咬合作用造成的非线性断裂过程区的能量耗散,故与该区域材料使用的拉伸软化本构关系即应力-裂缝张开口位移软化曲线有密切联系。鉴于此,该文采用4种不同的软化曲线研究了软化曲线形状对裂缝扩展阻力GR的影响。结果发现,GR曲线对软化曲线敏感,GR曲线的合理性依赖于软化曲线的准确性。在使用准确软化曲线的前提下,GR曲线的特征点与软化曲线的特征点存在相对应关系。