基于虚拟裂缝模型求解混凝土等效断裂韧度的实用解析方法

主裂缝亚临界扩展所形成的虚拟裂缝区的粘聚力是影响混凝土断裂韧度尺寸相关性的重要因素。根据混凝土准脆性材料的断裂特性,建立了一种基于虚拟裂缝模型的求解混凝土等效断裂韧度的实用解析方法。首先根据复合材料力学和线弹性断裂力学的基本原理,将虚拟裂缝的粘聚力作为相应的边界条件,运用修正的剪滞理论,分区引入变异层,建立了分层剪滞模型;然后根据能量法则,推导出求解混凝土等效断裂韧度的解析计算模式;最后针对相关试验的数值解,得到了混凝土等效断裂韧度的解析解。结果表明,对于不同的子层数,体积系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0398和0.0384,高度系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0394和0.0363,从而证明了混凝土等效断裂韧度是与试件尺寸无关的断裂参数;且与数值解相比,解析解的均方差和变异系数更小,证明了本文解析方法具有更好的鲁棒性。由此得出结论,基于虚拟裂缝模型所建立的解析模式为求解混凝土等效断裂韧度提供了一种可靠的、实用的解析方法。     

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。     

采用无缝试件确定混凝土岩石的断裂韧度

该文建立了由无缝试件确定混凝土和岩石断裂韧度的理论模型及其解析表达式。该模型考虑了混凝土骨料粒径与岩石颗粒尺寸的重要影响,仅需小尺寸无缝试件的峰值荷载,即可直接确定出无尺寸效应的混凝土与岩石的断裂韧度。进一步,进行了含不同裂缝长度的岩石试件的系列断裂试验,研究结果表明:基于该文模型由无缝试件确定的岩石断裂韧度,与采用含1 mm预制浅裂缝试件的确定结果相吻合,与基于回归分析方法由含不同长度预制裂缝试件确定的断裂韧度基本一致。同时,基于所提模型,对其他学者完成的岩石与混凝土无缝与含缝试件的试验成果进行了深入分析,验证了所提模型与方法的合理性及适用性。该文研究为由实验室小尺寸无缝试件确定混凝土与岩石无尺寸效应的断裂韧度提供了新思路。     

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。     

权函数法计算的混凝土断裂韧度

在采用解析方法确定混凝土的双K断裂韧度时,粘聚断裂韧度计算的准确性直接影响起裂韧度断裂控制参数计算的准确性。根据权函数法,给出了基于CEB-FIP粘聚应力软化函数计算的粘聚断裂韧度的表达式。使用最大高度为1000mm的五组楔入劈拉紧凑拉伸试件测量的最大荷载和临界裂缝嘴张开口位移,计算了混凝土的双K断裂韧度,并与积分解析计算公式进行了对比。结果表明,两种解析计算方法较为吻合,最大误差不超过2%。     

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。     

几何与非几何相似试件确定混凝土韧度及强度

几何相似与非几何相似试件,分别为尺寸效应与边界效应模型的推荐试件型式。考虑尺寸效应和边界效应模型的各自特点与优势,提出了改进的混凝土离散颗粒断裂模型。基于几何相似与非几何相似两类试件的断裂试验,确定出混凝土的材料参数——断裂韧度与拉伸强度,并与试验强度值及由尺寸效应模型确定的断裂韧度进行了比较。结果表明:当韧带高度(W-a0)与骨料代表尺寸di的比值约为10时,对应的断裂韧度与拉伸强度的确定曲线的相关系数最佳,且与试验强度值、尺寸效应模型断裂韧度计算值吻合较好。采用几何相似、非几何相似、几何与非几何相似试件确定的混凝土材料参数,分别建立了不同情况下混凝土断裂破坏设计预测曲线,其±20%即可涵盖全部试验数据。基于统计归纳,可取虚拟裂缝扩展量Δafic=ndi和特征裂缝长度a*∞=0.5di,进而建立了峰值荷载与断裂韧度、峰值荷载与拉伸强度的解析关系式,实现了由实测峰值荷载直接确定出混凝土的断裂韧度与拉伸强度的目的,预测值的±15%可涵盖所有试验数据。基于解析公式,预测了满足线弹性断裂的大尺寸真实结构的峰值状态。     

低热水泥全级配混凝土断裂试验及尺寸效应分析

该文分析了低热水泥全级配混凝土断裂性能的尺寸效应规律。通过在大坝工程施工现场浇筑成型试件有效高度为0.75 m、1.5 m和2.25 m的楔入劈拉试件并开展试验,获得低热水泥全级配混凝土稳定的双K断裂参数。基于试验结果,采用理论方法推求全级配混凝土无尺寸效应的失稳和起裂韧度,预测任意尺寸试件的最大和起裂水平荷载。研究发现,当韧带高度与骨料最大粒径比值大于等于6.0后,双K断裂参数趋于稳定。尺寸效应模型及其演化形式可用于确定全级配混凝土无尺寸效应的起裂和失稳断裂韧度,定量分析强度与韧度对裂缝扩展的影响,并可通过引入等效几何参数,分别建立任意尺寸试件最大和起裂水平荷载的预测方程。     

同时确定钢纤维高强混凝土的断裂韧度及拉伸强度

考虑钢纤维高强混凝土试件细观非均质性对宏观断裂的影响机制,将钢纤维掺量、长度、直径及钢纤维抗拉强度等细观层面的钢纤维特征参数,引入钢纤维高强混凝土宏观断裂模型的虚拟裂缝扩展量的具体计算公式,从而发展了考虑钢纤维特性的可同时确定钢纤维高强混凝土的断裂韧度与拉伸强度的模型及方法。采用变化参数为钢纤维掺量和混凝土水灰比的三点弯曲试件,基于所提模型,同时确定了钢纤维高强混凝土的断裂韧度与拉伸强度,确定值与试验拉伸强度值以及尺寸效应模型计算的断裂韧度吻合良好。基于测试数据离散性为钢纤维高强混凝土固有属性的事实,采用确定的断裂韧度及拉伸强度,建立起钢纤维高强混凝土塑性——准脆性——线弹性不同结构断裂模式的±20%全曲线,其可涵盖实验室条件下的所有试验数据。该文所提模型及方法适用于钢纤维高强混凝土及高强混凝土,可为钢纤维高强混凝土等复合材料真实断裂韧度与拉伸强度的确定,及个性化结构断裂破坏的预测等关键科技问题提供依据。     

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。     

Fracture toughness of concrete determined on large specimens

It has often been questioned whether linear elastic fracture mechanics can be applied to describe crack propagation and failure of concrete. An important argument is that most test results are obtained on specimens too small to be representative of a material with a composite structure such as concrete. Large specimens with four different geometries have been prepared and tested. Crack length was increased under controlled conditions to at least 250 mm. It was found that fracture toughness increases initially as a crack propagates, but that a length-independent value is reached asymptotically. Within the range of accuracy, asymptotic values obtained with the four different geometries were the same. It is concluded that failure of large size concrete elements can be predicted realistically on the basis of linear elastic fracture mechanics. For comparatively small specimens, however, an approach which takes total fracture energy into consideration (for instance the fictitious crack model) is more appropriate. It is pointed out that the role of subcritical crack growth on fracture toughness needs further investigation.     

A comparative study on five approaches to evaluate double-K fracture toughness parameters of concrete and size effect analysis

The current paper presents a comprehensive comparison of double-K fracture toughness parameters of concrete evaluated using experimental method and four existing analytical methods. Fracture tests were carried out on compact tension wedge splitting specimens with various depths varying from 200 mm up to 1000 mm. In the analytical calculation, depending on the relationship between critical crack tip opening displacement and the abscissa value of turning point on bilinear softening curve, two different distributions of cohesive stress are considered along crack extension. Results show that four available analytical calculations yield almost the same values of double-K fracture toughness parameters and agree well with those obtained from the experiment, which confirms the consistency of five approaches. Size effect was discussed, including unstable fracture toughness, initiation fracture toughness, critical effective crack length, the length of critical fracture process zone and critical crack tip opening displacement.     

Deterioration of fracture toughness of concrete under acid rain environment

Deterioration of fracture toughness of concrete caused by acid rain attack was investigated through laboratory-accelerated corrosion tests. Fracture toughness of the corroded concrete with different corrosion period was obtained by three point bending tests, and meanwhile the P-COMD curves and elastic modulus E of the corroded specimens with different corrosion degrees were also obtained. The experimental results showed that the deterioration of concrete surface is large and the corrosion depth increases with corrosion duration. The observation by scanning electron microscopy showed that the microstructures of crack tip are porous and loose due to acid corrosion, and many crisscross cracks appear at corrosion layer. Based on the experimental results, equivalent crack length in the fracture process zone and the effective fracture toughness K_IC were also obtained by theoretical analysis. Under the impact of acid corrosion, the concrete material physical and chemical properties changed significantly, which made the corresponding resistance stresses to crack propagation decrease. The curves of fracture toughness versus corrosion depth were obtained in this study.     

Using numerical simulations to compare the fracture toughness values for concrete from the size-effect,two-parameter and fictitious crack models

The size-effect, two-parameter, and fictitious crack models were developed to predict crack growth in materials like concrete that experience tension softening. The three models must predict the same response for infinitely large structures. Therefore, this study evaluates the differences in response for smaller structures. The metric used to compare response is the fracture toughness value required by the model to generate a particular load versus crack mouth opening displacement graph for a single edge specimen loaded in bending. The graphs, including unloading response, were generated numerically using the fictitious crack model and seventeen different sets of property values. The size-effect and two-parameter data reduction methods were then applied to the graphs to determine the associated fracture toughness values. Results of the evaluation indicate that the fracture toughness values for the size-effect and two-parameter models tend to be less than those of the fictitious crack model. However, there is a range of simulated materials for which the models are in reasonable agreement for structures on the scale of standard laboratory specimens.     

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。     

Einfluß der Probengröße auf die bruchmechanischen Eigenschaften von Sinterstahl

Influence of Specimen Size on the Fracture Mechanical Behaviour of Sintered Steel Fracture mechanics testing was carried out with small and big specimens using high-temperature sintered Fe-2%Cu-2.5%Ni-alloys in the densities of ρ = 7.1 and 7.4 g/cm³. These steels are often used in the manufacturing of PM-parts. Due to the different dismensions the crack propagation is for the bigger sizes faster than for the smaller sizes. Also the conditional fracture toughness of the big specimens is superiour to the toughness of the small specimens. But under consideration of a plain strain state for the big specimens and of a plain stress state for the small specimens valid fracture toughness values being independent from the specimen size can be calculated applying linear-elastic fracture mechanics. These results were obtained for both densities investigated. The increase of the density delivers principally better fracture mechanical data. Hereby the relation of strength data with the microstructure is also discussed.     

考虑骨料尺寸的混凝土岩石边界效应断裂模型

该文比较了边界效应模型（BEM）和尺寸效应模型（SEM）在研究材料断裂性能方面的不同。提出了由处于准脆性断裂状态的三点弯曲试件的峰值荷载P_max,同时确定材料参数--断裂韧度K_IC与拉伸强度f_t的理论与方法。由于实验室条件下混凝土试件高度W与骨料最大粒径d_max的比例W/d_max约为5~20,试件的非均质性明显,破坏为准脆性断裂控制。因此,区别于以连续介质力学为基础的应用于准脆性断裂研究的力学模型,该文研究将骨料最大粒径d_max引入相应的断裂模型解析表达式中,由参数组合β d_max来计算结构峰值状态对应的裂缝扩展量,通过离散参数β的不同取值,实现了对材料参数--断裂韧度与拉伸强度的准确预测。基于不同学者的相同尺寸W而不同初始裂缝长度a₀,以及相同初始缝高比a₀/W而不同尺寸W的几何相似的砂浆、混凝土及岩石类材料试件的试验成果（骨料最大粒径d_max从1.2 mm~40 mm变化）,验证了所提理论与方法的合理性。     

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。