平台巴西圆盘复合型加载下T应力计算法

平台巴西圆盘(CFBD)具有避免加载点处应力集中、保证破坏由预制裂纹尖端处起始的优点,成为研究脆性材料断裂性能的常用试件之一。最近的研究发现,T应力也会影响材料断裂性能,但平台巴西圆盘并没有计算T应力的解析公式。使用解析分析与有限元数值分析相结合的方法,对复合型加载条件下平台巴西圆盘试件的T应力进行了计算,并对误差进行了系统的分析。结果表明,在一定载荷分布角内相对裂纹长度 时,不管是纯I、纯II还是复合型加载条件下平台巴西圆盘计算的T应力都可以用中心裂纹巴西圆盘均布载荷下T应力计算公式来计算;T应力相对误差随着相对裂纹长度的增加而增加。     

围压对巴西裂纹圆盘应力强度因子影响分析

为了研究围压对巴西裂纹圆盘应力强度因子的影响,使用权函数方法得到了围压作用下巴西裂纹圆盘的应力强度因子,进而得到径向集中荷载与围压共同作用下的应力强度因子的计算公式。在此基础上,从理论上分析了围压对巴西裂纹圆盘应力强度因子的影响,分析结果表明：围压对II型应力强度因子无影响,纯围压作用下裂纹趋于闭合;围压和集中力共同作用下,I型应力强度因子随着围压的增大而减小。对比分析了数值分析与理论结果,分析表明,理论与数值结果吻合良好,从而表明了理论分析的正确性。此外,还研究了围压对纯II型裂纹加载条件的影响,结果表明,纯II型裂纹的临界加载角随着围压增大而减小,直至为0。因此,当围压较大时,加载角为0°左右所发生的断裂不一定全是纯I型断裂。     

复合型加载条件下锈岩断裂韧度试验研究

岩石断裂韧度表征其抵抗裂纹起裂和扩展的能力,作为其力学性能的一个重要指标,在岩石力学理论研究与岩体工程应用中有着不可替代的作用。由于岩石结构的复杂性,其破坏形式大多呈现为复合型断裂破坏,研究复合型加载条件下岩石断裂韧度具有重要的意义。为了研究锈岩的断裂力学性能,以便其在建筑工业中得到更为广泛的应用,通过18个中心裂纹圆盘（CSTBD）试件径向受压试验,进行了复合型加载条件下锈岩断裂韧度的试验研究。测得了锈岩在纯I型,纯II型以及复合型加载时的断裂韧度,并将试验结果与基于广义最大周向应力（GMTS）准则的理论值进行了对比分析,结果表明：锈岩的纯I型断裂韧度为1.01 MPa?m0.5,而纯II型断裂韧度为1.51 MPa?m0.5,是纯I型断裂韧度的1.49倍,这与基于GMTS准则的理论值1.34非常接近,而比基于最大周向应力（MTS）准则的理论值0.87大很多。裂纹尖端附近的T应力及断裂过程区裂纹尖端的临界距离rc对岩石类材料的开裂路径以及复合型断裂韧度都有较大的影响。考虑了T应力的广义最大周向应力（GMTS）准则能很好的预测试验结果。     

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。     

裂纹面接触对中心裂纹圆盘应力强度因子影响分析

从理论和数值两个方面进行分析,发现受径向集中力和围压作用的中心裂纹圆盘(CCBD)试件裂纹面接触会对II型应力强度因子产生较大的影响。通过理论研究,分析CCBD受集中力和围压作用裂纹面接触时圆盘内部的应力场,采用断裂力学权函数理论,推导得出在集中力和围压共同作用下,考虑裂纹面闭合时应力强度因子的解析解。然后,使用ANSYS软件建立了相应的数值模型计算应力强度因子,并与理论解和相关文献进行对比验证,证明了理论公式的正确性。无论裂纹张合与否,所提出的解析公式都能计算出不同裂纹长度、加载角、围压和摩擦系数的应力强度因子。最后,利用公式分析摩擦系数对应力强度因子的影响,结果表明:随着摩擦系数的增大,I型裂纹的应力强度因子不变,II型裂纹的应力强度因子随之显著减小;当加载角较大时,裂纹面产生更为复杂的二次裂纹,故压剪断裂测试的推荐加载角范围为30°~50°。     

平台巴西劈裂试验确定岩石抗拉强度的理论分析

为了完善平台巴西劈裂试验测定岩石抗拉强度的理论基础,基于二维弹性理论,建立对弦载荷下的平台巴西劈裂力学模型,采用应力场叠加法求得圆盘内的应力近似解析解。该应力理论解与有限元数值解一致,证明理论求解的合理性。在此基础上,对比研究了平台加载角对圆盘内应力大小及应力集中程度的影响,其结果表明：平台加载角越大,圆盘加载处的应力集中程度和压拉应力比都急剧降低,而圆盘内的拉应力值和拉伸区却只有一定程度减小;过大或过小的平台加载角都不利于平台巴西试样发生中心拉伸劈裂破坏,其最优平台加载角在20°~30°之间。最后,依据Griffith强度破坏准则,推得岩石抗拉强度的理论计算公式,其结果与已有抗拉强度经验公式及试验所得抗拉强度相符较好。     

冲击载荷作用下岩石动态断裂试验研究

以自行研制的可调速落锤冲击试验机进行加载,通过高速相机搭建数据采集系统,采用数字散斑相关方法作为试验的观测方法,开展5组不同预制裂纹长度的花岗岩试件在冲击载荷作用下的动态断裂试验。并对岩石I型裂纹在冲击载荷作用下的位移场演化、裂纹动态断裂的裂尖张开位移、裂纹尖端的扩展历史、动态断裂的应力强度因子进行了定量研究。试验结果表明：对于单一试件而言,在落锤开始与岩石试件的边界接触到试件的预制裂纹开始扩展整个过程中,裂纹尖端的应力强度因子KI呈递增趋势,KII与KI相比,相差1～2个数量级。对于不同预制裂纹试件,在落锤冲击加载作用下,总体表现为一定的预制裂纹长度范围内,随着预制裂纹的长度增加,裂纹尖端应力强度因子呈增加的趋势。     

加载方式及抗拉强度对巴西圆盘试验影响的连续-非连续方法数值模拟

研究了集中加载、加载板加载和平台加载3种不同加载方式对巴西圆盘的宏观力学行为、开裂过程以及材料的抗拉强度的影响。对于平台加载方式给出了不同平台加载角时抗拉强度的修正系数。在数值模拟中,采用了自主开发的连续-非连续方法,该方法将拉格朗日元、变形体离散元及虚拟裂纹模型耦合在一起,既可以很好地模拟弹性阶段的变形,又可以较好地模拟材料的真实开裂过程。研究发现,采用平台加载方式,有利于圆盘中心起裂,而采用集中加载和加载板加载方式,圆盘的加载部位容易发生剪破坏。在圆盘中心起裂时,集中加载方式的抗拉强度的数值解最接近于选取的抗拉强度,然后是加载板加载方式,最后是平台加载方式。无论对于哪种加载方式,在材料的抗拉强度较小时,圆盘易于中心起裂,否则圆盘的加载部位将发生剪破坏。圆盘中心起裂后,众多微裂纹汇聚成的裂纹带在垂直方向不断扩展,直至贯穿整个圆盘,同时伴有应力波产生并传播。     

T应力对岩石裂纹扩展路径及起裂强度的影响研究

经典断裂判据在分析岩石起裂角度及强度时,往往只选择裂尖应力场展开式中的r1/2奇异应力项,而将高阶的O(r1/2)项以及非奇异应力项（T应力）忽略,造成理论预测并不能完全吻合实际的试验结果。在充分考虑非奇异应力项对裂纹扩展影响作用的基础上,利用最大周向应力判据重新研究了岩石类材料脆性破坏的I、II及I-II复合型裂纹扩展。研究结果表明：（1）纯I型裂纹状态下,T应力为负时（压缩）,裂纹的扩展是稳定的;而当T 应力为正时（拉伸）,只有当 ,裂纹才沿着裂纹方向扩展（经典断裂判据所预测的方向）,而其他情况下裂纹的扩展将发生偏转;（2）纯II型裂纹时,不仅沿着裂纹方向的T应力影响起裂角度及强度,垂直裂纹面上的N应力也同样具有重要的影响作用;（3）对I-II型裂纹而言,修正后的最大周向应力准则与试验结果吻合良好,且正的T应力增大开裂角,而负的T应力降低开裂角。通过控制T应力的大小,可以对裂纹扩展方向加以控制,从而使得裂纹扩展偏离最危险的方向,最大地限度阻止或延缓结构整体断裂的发生。     

基于颗粒流的直切槽式巴西圆盘裂纹扩展分析

利用颗粒流程序（PFC) 对直切槽式圆盘试样进行巴西试验模拟,分析了不同的裂隙倾角和裂隙长度对直切槽式圆盘试样裂纹扩展规律的影响。根据起裂位置的不同,主裂纹可分为从裂隙尖端萌生的Ⅰ型主裂纹和从裂隙尖端一定距离处萌生的Ⅱ型主裂纹;次生裂纹可分为从加载点附近萌生的Ⅰ型次生裂纹和从远离加载点的一侧萌生的Ⅱ型次生裂纹。当裂隙长度保持不变而增大裂隙倾角时,主裂纹从Ⅰ型过渡为Ⅱ型,次生裂纹则从Ⅰ型转变为Ⅰ型和Ⅱ型共存,最后又变为Ⅰ型。当裂隙角度保持不变而增大裂隙长度时,主裂纹保持不变,次生裂纹则由Ⅰ型逐渐过渡为Ⅰ型和Ⅱ型共存。另外,当径向应力达到峰值应力之后,试样内会有大量的微裂纹萌生、扩展,造成了圆盘试样的破坏。从力链和能量角度来看,巴西圆盘试样的破裂过程是试样内部拉应力集中产生的颗粒间黏结破裂以及应变能释放的过程。     

热处理砂岩不同接触角巴西劈裂数值模拟研究

基于颗粒流程序（particle flow code,PFC）,对不同接触角（2a = 6º～30º）条件下25～1 000 ℃砂岩进行巴西劈裂模拟试验,研究其应力分布和破裂模式,并将巴西劈裂与直接拉伸进行对比。研究表明：（1）巴西劈裂中,面接触加载可以降低端部效应,加载过程中首先在圆盘中部产生拉裂纹,随着荷载的升高,拉裂纹汇集、扩展、贯通。（2）平板点接触巴西劈裂测得的抗拉强度小于直接拉伸强度,其抗拉强度计算公式的修正系数k随温度T的升高线性减小,满足k = −3.303×10⁻⁴T+1.468。随着接触角的增大,不同温度处理后巴西圆盘的抗拉强度均呈现出增大的趋势。（3）在2a≥18º时,巴西圆盘可以保证中心起裂;2a = 18º～24º时,圆盘在不同温度下破裂模式稳定;在接触角过大（2a = 30º）时,圆盘在较低温度（≤600 ℃）下会形成倾斜裂纹。（4）结合修正系数和破裂模式分析,推荐接触角为18º～24º时,修正系数在0.802 6～ 0.856 0之间,可以保证所有温度试样中心起裂且破裂模式稳定。     

Crack propagation trajectories for rocks under mixed mode I-II fracture

Propagation of a crack in engineering materials including rocks can cause failure. Knowledge of the stress state under which a crack can propagate, and the trajectory it may follow during its growth are thus very important for the stability of rock masses/materials and for the safe design of structures in/on rocks. In this paper, the crack initiation angle and subsequent crack propagation path are experimentally investigated for limestone rock specimens. This investigation was conducted under various mixed mode I-II loading conditions, including pure mode-I and pure mode-II.This study includes conducting diametrical compression tests on notched Brazilian disk specimens. Moreover, the effect of confining pressure and temperature on crack initiation and propagation were also studied. The experimental results were compared with theoretical predictions of crack initiation angle. The results showed that limestone behaves in brittle fashion, and the effects of confining pressure and temperature on failure trajectories were not significant. Generally, the crack initiation angle can be predicted by the maximum tangential stress criterion. However, for notched Brazilian disk with high value of crack orientation with respect to loading direction, crack does not propagate from the tip of the crack. This important observation indicated that the tensile-strength failure can become more critical than the fracture-toughness failure.     

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.     

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.     

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.