DEM investigation on fracture mechanism of the CCNSCB specimen under intermediate dynamic loading

The cracked chevron notched semi-circular bending (CCNSCB) method falls into a significant testing category of chevron notched specimens for measuring the mode I fracture toughness, of which the progressive fracture mechanism deserves to be further assessed under intermediate dynamic loading rate (IDLR). In this study, the discrete element method (DEM) is adopted to depict the three-dimensional fracture processes of the CCNSCB specimens subjected to different IDLRs considering different supporting spans. The results demonstrate that the crack front of the CCNSCB specimen with any loading condition is prominently curved, which violates the straight-through crack propagation assumption and may induce some errors in the fracture toughness measurements. For each IDLR, the peak force of the CCNSCB specimen evidently increases with decreased supporting span, and the effect of loading rate on this parameter is more prominent for a smaller supporting span. For a relatively large span, the crack grows restrictively in the notched ligament, which conforms to the ideal assumption of the fracture process and contributes to an accurate measurement of the mode I fracture toughness. Thus, a large supporting span is suggested for the semi-circular bend tests. Additionally, the critical crack length and peak force are found dependent on the loading rate, and they are larger for the higher loading rate. Thus, the critical crack length determined under quasi-static conditions is not strictly suitable for the specimens under different IDLRs, especially for the much higher IDLR. This study calls for more attention on how to accurately determine the fracture toughness via chevron notched samples.     

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.     

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。     

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.     

Effect of Thermal Treatment on the Dynamic Fracture Toughness of Laurentian Granite

The effect of thermal treatment on the dynamic fracture toughness of Laurentian granite (LG) was investigated in this work. Notched semi-circular bend (NSCB) LG specimens are heat treated at temperatures up to 850?°C. The micro-cracks in the rock samples induced by thermal treatment are examined by scanning electron microscope (SEM). The microscopic observations are consistent with the subsequent P-wave velocity measurements, which shows that the P-wave velocity decreases with the treatment temperature monotonically when the temperature is higher than 250?°C. Dynamic fracture toughness measurements are then carried out on these samples with the dynamic load exerted by a modified split Hopkinson pressure bar (SHPB) system. The relationship between fracture toughness and treatment temperature is investigated. Experimental results show that fracture toughness increases with the loading rate but decreases with the treatment temperature. However, when the heating temperature is below 250?°C and above 450?°C, the dependence of dynamic fracture toughness on the temperature is different from other temperatures, which can be explained by the physical processes at the microscopic level of the rock due to heating. At treatment temperatures below 250?°C, the thermal expansion of grains leads to an increase in the toughness of the rock. At treatment temperatures above 450?°C, the sources of weakness such as grain boundaries and phase transition of silicon are depleted, and as a result the decrease in fracture toughness is not as significant as other treatment temperature ranges.     

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.     

基于数字图像相关法的两类岩石断裂特征研究

岩石破坏时的临界断裂特征,如过程区长度,裂缝口张开位移是运用断裂力学解决岩石断裂问题的关键所在。传统测量方法,如应变片、直线位移传感器无法获得岩石破坏时的全场变形,因此,也无法准确地获得上述断裂特征。数字图像相关法是一种光学的变形测量方法,其通过试样表面的数字图像采集及相关计算,能够获得岩石破裂过程各个阶段的高精度全场变形特征。利用该试验手段,对两类岩石,即相对较硬的大理岩和相对较软的黄砂岩开展了一系列半圆盘三点弯曲断裂试验并获得了岩石断裂时的临界变形场,对变形场进行分析,从而确定了两类岩石破坏时临界特征、过程区长度及裂缝口张开位移。结果表明,大理岩的断裂过程区长度明显小于黄砂岩的断裂过程区长度,峰值时黄砂岩COD的值均大于相同裂纹长度的大理岩,而较软岩的力学行为更容易受边界效应的影响。上述研究有助于进一步了解不同类型岩石的断裂发展过程并采用相应的方法来解决岩石破裂问题。     

锦屏大理岩蠕变损伤演化细观力学特征的数值模拟研究

岩石的蠕变损伤和断裂是岩石流变效应的重要表现形式,但其损伤演化过程往往难以直观观测,为此,采用二维颗粒流数值模拟方法(PFC2D)对岩石的蠕变损伤和断裂的细观力学机制进行了分析。在锦屏大理岩室内试验基础上,利用颗粒流应力腐蚀模型(PSC),建立了能反映其短期和长期强度特征的柱状岩样数值模型,并开展了大量数值试验。结果表明,蠕变损伤的演化过程与暂态的损伤演化过程具有明显的差异。在岩样蠕变损伤过程中,其内部微裂纹多沿加载方向开裂且分布均匀,先快速增加再稳定扩展,最后则发生快速断裂。当荷载较小时,岩样宏观上呈现劈裂破坏特征,当荷载较大时,岩样呈现剪切破坏特征。在岩样蠕变损伤初始和稳定演化阶段的前期,荷载大小对岩样的损伤演化过程影响不大;在稳定演化阶段的后期至断裂过程中,低荷载下岩样的损伤增速比高荷载下快。     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。     

单轴压缩条件下锚杆对含三维表面裂隙试样的锚固效应试验研究

在岩石相似材料试件中设置三维表面裂隙,制作不同锚固方式的试件,对其进行单轴压缩试验,研究锚杆对试件强度以及预置裂隙扩展模式的影响。试验结果表明,与无锚试件相比,4种加锚试件的抗压强度和压缩弹性模量均有不同程度的提高,而且锚杆对压缩弹性模量的增强效果比对抗压强度的增强效果更显著。4种加锚试件的残余强度大体相等,比无锚试件的残余强度提高了2.0～2.5倍。加锚试件的破坏过程大致分4个阶段:孔隙裂隙压密阶段、弹性变形至微弹性裂隙发展阶段、非稳定破坏阶段和破裂后阶段,试件表面宏观裂纹均出现在破裂后阶段。由于锚杆的加固止裂作用,预置裂隙的扩展模式发生变化,加锚试件内部出现了弧形破裂面和剪切薄弱面。试验中共出现3种裂纹:张拉裂纹、剪切裂纹和拉剪复合裂纹。     

Experimental Calibration of ISRM Suggested Fracture Toughness Measurement Techniques in Selected Brittle Rocks

Summary A wide variety of specimen types and methods are employed in fracture toughness measurement of rocks, which result in scattered values for the same rock type. In order to provide some consistency to the values, the International Society for Rock Mechanics (ISRM) recommended three suggested methods using core based specimens, the Chevron Bend (CB) test, the Short Rod (SR) test and the Cracked Chevron Notch Brazilian Disc (CCNBD) test. This standardization helped obtain more consistent values but still a variation of 20–30% was observed in the values of fracture toughness obtained with the CB and SR methods. The values obtained with the CCNBD method were found to be consistently lower (30–50%) than those of the other two methods (CB and SR). Many reasons have been offered to explain this deviation. These include size of the specimen, anisotropy of rock, a dimensionless parameter in the fracture toughness calculation equation for the CCNBD test, etc. A comprehensive test program was initiated to identify the cause of these discrepancies between the CB and CCNBD methods. Three brittle rock types were selected for the study and more than 200 tests were conducted to measure the values of fracture toughness. A rigorous statistical analysis was carried out to determine the confidence level and find the significance of the test results. It was found that the CB and CCNBD methods were very comparable provided the correct equation for fracture toughness calculation was used for the CCNBD method and the size of the specimens was selected carefully. The error in the ISRM 1995 formula of fracture toughness for the CCNBD method could be the major factor responsible for the consistently lower values obtained with the method.     

Mixed mode crack propagation in low brittle rock-like materials

Mixed mode fracture is quite common in rock structures. Numerous investigators have used the Brazilian disk specimens with a central crack for investigating modes I, II, and mixed fracture toughness in brittle materials. In this study, analytical, experimental, and numerical investigations were planned and performed on Central Straight Through Crack Brazilian Disk (CSCBD) specimens. Ranking of geometrical parameters effective on the value of stress intensity factors (SIFs) of CSCBD specimens were obtained using stochastic analysis. Furthermore, experimental tests were undertaken in order to evaluate the crack propagation in rock-like material of low brittleness. Finally, numerical modeling was performed to assess the effect of crack length on the failure mode of CSCBD specimens. Analytical analyses revealed that the inclination angle of the crack with respect to the diametrical load has the most important impact on the SIFs among the geometrical parameters of CSCBD specimen. Performed experimental and numerical analyses also confirmed the effect of inclination angle and crack length and their impact on the mode of failure of the tested specimen.     

Ⅰ型断裂韧度模拟方法及细观影响因素研究

既有离散元参数敏感性分析大多集中在压缩试验及巴西劈裂试验,对I型断裂韧度 试验细观影响因素及3D破裂过程系统分析的报道较少。采用三维平节理模型（FJM3D）研究微观结构参数及黏结细观参数对不同切槽形状的I型断裂韧度试验的影响。微观结构参数包括晶粒平均半径的平方根 、模型分辨率Ψ和最大/最小晶粒直径 。黏结细观参数包括平均配位数CN、S类型单元比例 、黏结抗拉强度 、黏结内聚力 、摩擦系数 和摩擦角 。参数敏感性分析结果表明, 与 、CN及 正相关,与 、 负相关,而与 、 、 和 无明显的线性关系,此外为获得较低的 波动水平,给出了参数 和 的建议范围。根据参数敏感性分析结果,校核匹配了Kowloon花岗岩直切槽半圆盘（SCB）和人字形切槽半圆盘（CCNSCB）试样的宏观力学性质。从细观角度直观、深入分析不同切槽形状I型断裂韧度试验破裂机制,得出SCB试验曲线的峰前和峰后行为与室内试验更为吻合。     

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.     

岩石断裂韧度CCNSCB方法渐进破坏机制与无量纲应力强度因子宽范围标定

国际岩石力学学会建议了4种岩石I型断裂韧度（KIC）测试方法。将建议方法的人字形切槽巴西圆盘试样与直切槽半圆盘试样结合,可以得到具有诸多优点的人字形切槽半圆盘（CCNSCB）三点弯曲试样。近年来,CCNSCB方法受到许多关注,然而,其渐进破坏过程却尚未进行有效的评估。为此,对其进行了数值研究,其内容包括：进行细观损伤力学模拟,直观展现CCNSCB试样渐进断裂过程;考虑不同支撑跨距与直径之比（ ）的影响,发现 愈大,愈加符合测试原理,建议 取0.8;采用有限元子模型技术对CCNSCB方法（ 0.8）中计算KIC的关键参数-临界无量纲应力强度因子（ ）进行了宽范围标定,可供相关研究直接查取;细观损伤力学模拟峰值力对应的临界裂纹与有限元标定 对应的临界裂纹较为一致,证明CCNSCB方法测试原理的合理性,以及数值模拟与 标定结果的有效性。     

Experimental study on three-point bending of granite after cryogenic freeze-thaw cycles at -160 ℃北大核心CSCD

In order to study the effect of freeze-thaw cycles on the type I fracture toughness of granite under ultra-low temperature conditions,semi-circular bending（SCB）specimens were used in this study,and different freeze-thaw times（1,2 and 3 times）were selected. The granite in the natural state was treated with -160 ℃ ultra-low temperature freeze-thaw cycles,and the three-point bending test was carried out on the granite after the freeze-thaw cycle. and microstructure effects. The results show that with the increase of freeze-thaw cycles,the localized damage of I-type crack tip of granite is intensified,the fracture toughness is decreased,the number of microcracks and pores in the rock is increased,the length of cracks is increased,and the pore size is increased. Finally,the changes of rock frost heaving force and fracture toughness under low temperature and ultra-low temperature conditions are compared and analyzed. Compared with low temperature conditions,the frost heaving force produced by ultra-low temperature freezing and thawing is larger. When fracture toughness decreases by approximately the same amplitude,rocks need more cycles of freezing and thawing at low temperature. The research results can provide theoretical reference for underground storage of liquefied natural gas（LNG）in ultra-low temperature environment. © 2022 Science Press (China).     

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。     

模拟岩石中裂纹扩展连接的近场动力学方法

脆性岩石材料在压应力作用下常出现两类裂纹：翼型张拉裂纹和次生剪切裂纹。近场动力学是一种新型的无网格数值计算方法。在近场动力学理论中,采用积分形式的控制方程代替微分形式的控制方程使得该数值算法在断裂问题上具有独特的优势。将Mohr-Coulomb准则和最大主应力准则引入非普通“态”基近场动力学理论中,分别用于模拟材料常见的压剪和张拉破坏。这种扩展的非普通“态”基近场动力学可以有效地模拟脆性岩石材料在多种受力状态下的裂纹起裂、扩展和连接问题。通过5个不同的数值算例说明该数值算法在处理脆性岩石材料断裂问题的有效性和准确性。首先,通过模拟含圆孔的弹性板拉伸数值试验说明该数值算法的有效性和准确性。其次,数值模拟了简单三点弯曲试验以及不使用其他外部准则条件下动荷载作用下裂纹的分叉试验,所得结果与其他试验结果或数值结果相吻合,从而验证了该理论的有效性。然后,模拟了包含斜裂纹的巴西圆盘试验,裂纹扩展路径和计算所得的断裂韧度同样吻合于试验结果。最后,模拟了单轴压缩状态下,预制裂纹试样的裂纹扩展和连接问题。将该数值算法与试验结果对比表明,所提出的数值方法可以模拟和预测岩石类材料的张拉和压剪裂纹的起裂、扩展和连接行为。     

岩石三轴拉伸试验装置研制及其应用

为准确地测量岩石试样在不同围压作用下的拉伸强度与变形特性,对用于岩石三轴压缩试验的MTS815材料试验机为主体设备进行了一系列技术改造,一方面设计加工了一套试验机活塞与三轴室的随动连锁装置,使原本只能提供压缩载荷的MTS815试验机也能精确提供轴向拉伸荷载;另一方面设计开发一种多自由度岩石试样三轴拉伸夹具,解决岩石等脆性材料在拉伸过程中难以始终保持对中的技术难题。提出一套完整的测试技术方法,能实现0～140 MPa围压范围内各种岩石试件的复杂三轴直接拉伸测试研究,利用研发的配套装置与测试方法对页岩试样进行了三轴拉伸试验。结果表明,试验装置和试验方法完全能够进行不同围压条件下的岩石三轴拉伸试验,得到相应的三轴拉伸试验曲线;页岩在低围压和高围压下呈现不同的破坏特征和破坏形式,低围压下依然呈现脆性特征,高围压下则是由脆性向塑性转换。     

含充填节理岩体相似材料试件单轴压缩试验及断裂损伤研究

研究了单轴压缩条件下裂隙含充填与否对节理岩体力学性能的影响。以相似材料模拟脆性岩石材料制作含预置裂隙试件,在刚性试验机上对试件进行单轴压缩试验,研究了裂隙充填与否对节理岩体强度峰值及峰后塑性变形能力的影响;用有限元软件ABAQUS对试件进行断裂及损伤分析,研究了裂隙充填与否对节理岩体应力强度因子及损伤因子的影响。研究表明,在单轴压缩情况下,裂隙中含充填与不含充填相比,裂隙含充填岩体峰值强度提高、峰后塑性变形能力增强、总应变能释放率Gc降低,增大了节理岩体抵抗开裂的能力;裂隙含充填岩体环向拉应力场从分布区域及峰值都小于无充填裂隙试件;在同样外荷载作用下,裂隙含充填岩体损伤度小于无充填岩体。