V形切槽巴西圆盘法测定岩石断裂韧度KIC的实验研究

采用国际岩石力学学会岩石断裂韧度建议测试方法(ISRM)[1]提出的V形切槽巴西圆盘试样(CCNBD),测试了一种泥质砂岩的I型断裂韧度值,给出了一套试样切割制备方案,从试验现象角度分析了该泥质砂岩的断裂力学特性,讨论了该试样类型的有效尺寸和断裂机制,并指出了该方法的特点和优劣性,得出如下结论：（1）该类岩石试样测得的I型断裂韧度值对CCNBD试样直径尺寸变化具有较大的敏感性,并且直径大于ISRM建议方法中最小有效直径（75 mm）的试样测试结果更为稳定;（2）CCNBD试样断裂机制表现为以拉张应力（间接拉伸）作用为主,兼有一定的韧带面内剪切作用的应力状态下I型裂纹扩展模式;（3）V形切槽巴西圆盘方法具有试样加工工艺简单、能承受较大临界载荷、测试的I型断裂韧度值较稳定等优点,但其没有考虑断裂过程区(FPZ)的非线性问题,建议对该方法进行非线性修正图解方案研究,以达到更准确测定岩石断裂韧度的目的。     

断裂韧度试样CCNBD宽范围应力强度因子标定

国际岩石力学学会（ISRM）在1995年提出了一种新型岩石断裂韧度试样--人字形切槽巴西圆盘试样CCNBD,但是,其断裂韧度计算公式中的重要参数（即无量纲应力强度因子的标定）仍存在问题。采用一种新的分片合成方法并结合有限元法,参照ISRM给出的CCNBD试样的尺寸限制,对该范围试样的应力强度因子进行了宽范围的标定,以便在试验中能因地制宜地选用不同几何参数的CCNBD试样。结果表明：分片合成方法的计算值有很高的精度,不但减少了工作量,也使标定的无量纲应力强度因子比现有文献值更加准确、可靠。     

CCNBD断裂韧度试样的SIF新公式和在尺度律分析中的应用

根据国际岩石力学学会于1995年推荐的一种测试岩石断裂韧度的新型试样－人字形切槽巴西圆盘试样,对其断裂韧度计算公式中的关键参数即无量纲应力强度因子（SIF）提出了一个改进的计算公式。采用分片合成方法结合有限元法对CCNBD试样的应力强度因子进行了宽范围标定,结果以表格的形式给出;并采用数据线性回归的方法,将标定结果以一个指数函数的形式给出。结果表明,与标定值相比,无量纲应力强度因子新公式的误差较小,并且囊括了CCNBD试样的较宽范围的尺寸,且查表使用方便,也为理论分析提供了条件。在此基础上,对岩石断裂韧度测试的尺度律进行了更进一步的探索,结果表明,利用新公式进行的尺度律分析是有效的。     

Recalibration and Clarification of the Formula Applied to the ISRM-Suggested CCNBD Specimens for Testing Rock Fracture Toughness

The cracked chevron-notched Brazilian disc (CCNBD) was proposed by the International Society for Rock Mechanics (ISRM) to test the mode I (opening mode) fracture toughness of rock. The test method has been vigorously discussed and debated, despite being the subject of intensive research for decades. The minimum (critical) dimensionless stress intensity factors affiliated with the formula for calculating the fracture toughness using CCNBD specimens with different geometric parameters remain elusive and complex. The matter cannot be resolved by simply replacing the diameter in the original formula with the radius, as claimed by several authors. In this paper, the formula is fundamentally improved, as wide-ranging minimum dimensionless stress intensity factors pertaining to diversified CCNBD geometries are recalibrated by three-dimensional finite element analysis, and an expression with tabulated coefficients is obtained through curve-fitting the data obtained from the numerical calibration. The present results are shown to be more accurate than those in the literature. Furthermore, the importance of the reasonability of the results is highlighted; a comprehensive comparison of different values shows that the upper bounds of minimum stress intensity factors are violated by the above claim. The confusion resulting from the claim is, thus, clarified conclusively.     

有限宽切槽对CCNBD断裂试样应力强度因子的影响

国际岩石力学学会（ISRM）在1995年提出一种新型的岩石断裂韧度试样--人字形切槽巴西圆盘试样（cracked chevron notched Brazilian disc--CCNBD）,对该试样的一个重要力学参数即最小无量纲应力强度因子的标定,以前的分析和计算都没有考虑切槽宽度的影响。然而试样切槽的宽度受切割刀具厚度所限,不能为零。当试样较小时,切槽宽度则相对较大。通过三维边界元计算分析表明,切槽宽度越大,无量纲应力强度因子的标定值就越大;对于ISRM推荐的CCNBD标准试样,得出其最小无量纲因子值为0.954,这比ISRM给出对应值0.84要大13.6 %。同时,小裂纹应力强度因子曲线的变化趋势也发生了质的变化,这可能会导致实验的失败。推荐最小无量纲应力强度因子的标定采用考虑切槽的三维分析。     

Numerical Observation of Three-Dimensional Wing Cracking of Cracked Chevron Notched Brazilian Disc Rock Specimen Subjected to Mixed Mode Loading

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by International Society for Rock Mechanics for measuring mode I fracture toughness of rocks. Subsequently, this specimen geometry has been widely extended to conduct mixed mode fracture tests on rocks as well. A straight through crack front during the fracturing process upon the root of the chevron notch is assumed in the testing principle, but has never been thoroughly evaluated before. In this study, for the first time, the progressive rock fracture mechanism of the CCNBD rock specimen under mixed mode loading is numerically simulated. Specimens under representative mixed mode loading angles are modelled; and the assumption of the straight through crack front growth is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments, yielding a prominent twisted front, far from being straight. The crack front never grows up to the root of the notch ligament and the straight through crack front assumption is never satisfied in the realistic rock fracture progress of this chevron notched specimen subjected to mixed mode loads. In contrast, the fracture progress features typical three-dimensional wing cracking towards the loading ends. The numerically observed progressive fracture mechanism reveals that the measuring principle of mixed mode fracture tests employing CCNBD specimens is significantly violated and the measures of both modes I and II fracture toughness are uncertain.     

基于P-CCNBD试样的岩石动态断裂韧度测试方法

预裂的人字形切槽巴西圆盘(Pre-cracked chevron notched Brazilian disc,简称P-CCNBD)是将人字形切槽巴西圆盘(cracked chevron notched Brazilian disc,简称CCNBD)的切槽尖端再稍加切削制成直裂纹前沿的试样。利用霍普金森压杆对P-CCNBD砂岩试样进行径向冲击,完成I型动态断裂试验后再做数值分析得到岩石的动态断裂韧度。为了验证数值模拟的可靠性,先进行了无限平面中一条有限尺寸裂纹表面受冲击拉伸作用的动态有限元分析,结果表明,数值模拟的结果与Shi得到的结果非常吻合。将试验-数值法和他人的准静态法分别确定的砂岩的动态起裂韧度进行对比,两种方法得到的结果有一定的差异。采用试验-数值法,将比较成熟的直裂纹巴西圆盘(cracked straight-through Brazilian disc,简称CSTBD)和P-CCNBD两种试样测得的结果进行对比,两者吻合较好。得到的动态起裂韧度都有随着加载率的增加而增大的加载率效应。分析了准静态法的缺陷,认为试验-数值法得到的结果更为合理。     

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.     

The effect of specimen size and stress rate for the Brazilian test—A statistical analysis

Summary The Brazilian test is a widely accepted method for the determination of the tensile strength of intact rock. Specifications for the Brazilian tensile strength test have been established by the American Society for Testing and Materials (ASTM), ASTM D 3967-86 and a suggested approach is provided by the International Society for Rock Mechanics (ISRM). The ASTM and ISRM allow a relatively wide range of values for specimen geometry defined in terms of length to diameter ratio and loading rates defined as either time to failure or stress rate.A statistical study was carried out on a coal measure sandstone to determine whether the tensile strength determined by the Brazilian test is independent of the specimen geometry and the stress rate.     

Fracture Toughness and Fracture Roughness in Anisotropic Granitic Rocks

In this paper we present an experimental approach aimed at assessing the correlation between fracture toughness (K _IC) and fracture roughness of two granitic rocks (Barre and Stanstead granites) exhibiting significant fracture toughness anisotropy. Roughness values have been estimated for fractured surfaces obtained from Chevron Cracked Notch Brazilian Disc samples failed under mode I along three orthogonal planes with respect to their microstructural fabrics. There exists a clear correlation between roughness and toughness within each rock examined along the three planes. Specific orientation of micro-crack alignment could result in preferred out-of-plane propagation of the test-crack irrespective of grain-size distribution. These experimental observations reinforce the hypothesis of the existence of a link among pre-existing petrofabric anisotropy, fracture toughness, fracture roughness, and the evolution and extent of the associated induced fractures within the process zone of granitic rocks along specific directions. This study also highlights the need for employment of pre-failure and advanced post-failure diagnostic techniques in quantifying these inter-relationships.     

Determination of Rock Fracture Toughness <Emphasis Type="Italic">K</Emphasis><Subscript>IIC</Subscript> and its Relationship with Tensile Strength

Hydraulic fracture propagation is greatly influenced by mode-II fracture toughness since this is one of the factors which determine whether a fracture diverts. Direct measurement of rock fracture toughness is constrained by high cost, limited number of available cores and long turn around time. Therefore, to overcome these constrains, it is necessary to develop an effective mode-II fracture toughness test which can be used in a prediction analysis for deep rock formations. Consequently, a mode-II fracture toughness test system was designed for rocks using the straight-notched Brazilian disc (SNBD) test methodology. In the experiment, this system was used to test 20 rock samples from the WG oilfield. This enabled a fracture toughness prediction model to be established, based on an analysis of the test data. H341 acoustic, density and gamma-ray logging data were used to predict horizontal stresses and rock tensile strength. When combined with the mode-II fracture toughness prediction model, continuous values were predicted, which were successfully confirmed by field fracturing practices. It was confirmed, therefore, that this successful method met the need of providing continuous fracture toughness data during field fracturing operations.     

动载确定方法对岩石动态断裂韧度测试的影响

为了考察不同方法确定的动态载荷对测试岩石动态断裂韧度的影响,在SHPB压杆系统上动态冲击直径80 mm的大理岩圆孔裂缝平台巴西圆盘,获得了弹性压杆上的应力波形,间接计算得到3种不同的作用在圆盘端部的动态载荷。将载荷输入ANSYS动态有限元模型中,求得了相应的动态应力强度因子,并根据试验-数值分析方法确定了岩石的动态断裂韧度测试值。结果表明,在加载速率约为4.0×104 MPa•m1/2/s的条件下,采用三波法确定的大理岩的平均动态断裂韧度为 3.92 MPa•m1/2,采用一波法比三波法计算的结果偏低11.22%,采用二波法比三波法计算的结果偏高20.15%,3种方法得到的结果差异较大。应力波在传播过程中,通过圆盘表面和预制裂缝面发生散射,部分能量不断发生释放是造成圆盘试件两端加载载荷不相等的主要原因。三波法是3种方法中比较理想的动态载荷确定方法,但需要考察试件的动态应力平衡性。     

Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials

Numerical and experimental studies were performed on a new fracture test configuration called the edge cracked triangular (ECT) specimen. Using several finite-element analyses, the fracture parameters (i.e., K _I, K _II, and T-stress) were obtained for different combinations of modes I and II. The finite-element results show that the ECT specimen is able to provide pure mode I, pure mode II, and any mixed-mode loading conditions in between. Also, a series of mixed-mode fracture experiments were conducted on Neiriz marble rock using the proposed specimen. Furthermore, the generalized maximum tangential stress (GMTS) criterion was used to predict the experimental results. The GMTS criterion makes use of a three-parameter model (based on K _I, K _II, and T) for describing the crack tip stresses. Due to the significant positive T-stresses that exist in the ECT specimen, typical minimum fracture toughness values were expected to be obtained when the ECT specimen is used. The direction of fracture initiation and the path of fracture growth were also obtained theoretically using the GMTS criterion, and good agreement was observed between the experimental fracture path and theoretical simulations. The fracture study of this specimen reveals that the ECT specimen can be also used in mixed-mode fracture studies of rock materials in addition to the conventional circular or rectangular beam test samples.     

A calibration methodology to obtain material parameters for the representation of fracture mechanics based on discrete element simulations

A micro-mechanical model is developed to study the fracture propagation process in rocks. The model is represented by an array of bonded particles simulated by the discrete based method. Experimental results of tests using Cracked Chevron Notched Brazilian Discs (CCNBD) with different inclination angles relative to the direction of loading are used to calibrate and validate the model. Dimensional analysis is used to identify and minimise the microscale parameters to be considered. The comparison between experimental and computational results shows a satisfactorily good agreement.     

Effect of Specimen Geometry and Testing Method on Mixed Mode I–II Fracture Toughness of a Limestone Rock from Saudi Arabia

Summary The effect of testing method and specimen geometry such as diameter, thickness, and crack length and type on measured fracture toughness was investigated using specimens collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Straight Edge Cracked Round Bar Bend (SECRBB), semicircular disk specimens under three point bending, and Brazilian disk specimens under diametrical compression were used in this investigation. SECRBB specimens were used for the Mode-I study, and notched Brazilian disk and semicircular specimens were used for the mixed Mode I–II study. The results show that specimen diameter and crack type have a substantial influence on the measured fracture toughness; however, loading rate, crack size, and specimen thickness seem to have a negligible effect on the fracture toughness. Mode-I fracture toughness is significantly influenced by specimen diameter and crack type, while their effects on Mode-II fracture toughness are generally negligible. The different specimens (SECRBB, Brazilian disk, and semicircular) can give comparable results only when the proper span to diameter ratio is used. The Brazilian disk with a straight notch was found to be the most convenient geometry to use for fracture toughness determination. A simple method of making a precise notch inside the disk is presented, using the combination of a drilling machine and a wire saw.     

岩石非理想裂纹圆盘试件动态断裂韧性测试的有限元分析及试验研究

采用中心裂纹圆盘-霍普金森压杆(CCCD-SHPB)试验系统对大理岩中心裂纹圆盘试件进行不同加载速率下的纯Ⅰ型加载试验,研究岩石材料动态断裂韧性的加载速率相关性。考虑到试验中所使用的圆盘试件是带有中心切口的非理想裂纹,结合试件的实际加工情况,提出采用切口尖端形状为小圆弧形的预制裂纹,介绍了试件的制作方法,并利用有限元计算论证了采用这种形状非理想裂纹试件的试验可行性。结果表明,采用圆弧形裂尖、裂纹宽度为1 mm的中心切口非理想裂纹圆盘试件来代替理想裂纹圆盘试件是可行的,误差不超过2.13%。分析试验数据得出：非理想裂纹圆盘试件在纯Ⅰ型加载条件下,其断裂韧度表现出明显的速率相关性,且随着加载速率的增大而增大。     

Crack stability analysis for rock fracture toughness tests

A stable crack extension is a precondition for fracture toughness tests using chevron-notched specimens. The paper analyses the stability problem for crack extension in two chevron-notched specimens suggested by ISRM. Stability factors are calculated with various compliances of testing machine under different loading conditions. It is pointed out that the loading manner, compliance of the testing machine, as well as the specimen configurations have great influence on crack growth stability.     

Mixed mode fracture analysis of semi-circular bend (SCB) specimen: A numerical study based on extended finite element method

Previous studies are mainly concentrated on the use of the semi-circular bend (SCB) specimen for determining the entire mixed-mode I-II fracture toughness of rock, while less attention has been paid to its mixed-mode fracture process. In this situation, this study investigated mixed-mode fracture behavior of the SCB specimen using the extended finite element method (X-FEM). The crack growth trajectory, crack initiation angle and onset of fracture were discussed in detail. This paper is expected to provide a better understanding of mixed-mode fracture process of the SCB specimen occurring during fracture initiation and propagation.     

Typical Upper Bound–Lower Bound Mixed Mode Fracture Resistance Envelopes for Rock Material

Mixed mode fracture experiments were conducted on Harsin marble using two disc-shape samples namely the Brazilian disc (BD) and the semi-circular bend (SCB) specimens. For each specimen, a complete fracture toughness envelope ranging from pure mode I to pure mode II was obtained. The experimental results indicate that the mixed mode fracture toughness depends on the geometry and loading conditions such that for any similar mode mixture, the BD test data were significantly greater than the SCB fracture toughness results. Therefore, the conventional fracture criteria which present a unique mixed mode fracture curve, fail to predict the test results. It is shown that a generalized criterion, which takes into account the effects of geometry and loading conditions, is able to provide individual fracture curves for theses specimens with very good estimates for the test results obtained from both BD and SCB specimens. The BD and SCB specimens can be suggested as appropriate specimens for obtaining typical upper bound and lower bound envelopes for mixed mode fracture toughness of rocks.     

原状冻土非线性断裂韧度测试与修正

在以往原状冻土现场试验方法的基础上,针对原状冻土的非线性断裂力学特性进行了Ⅰ型和Ⅱ型断裂力学试验。在不同深度的冻胀量、冻深与时间变化规律下严格控制试样制作及试验时的温度,利用动态数据采集系统测出试样加力点处位移与力的关系曲线,并计算出相应的非线性参数。提出了利用非线性修正因子计算原状冻土断裂韧度的方法,并算出Ⅰ型、Ⅱ型直裂纹加卸载试样的非线性断裂韧度,将其与岩石断裂力学中的塑性修正因子方法的计算结果进行了对比,二者基本一致,说明该方法可以用来计算、修正原状冻土非线性断裂韧度,从而为冻土非线性理论的研究拓宽了思路。