Analysis of brittle fracture due to compressive loading using center-cracked Brazilian disk

Ｄｅｔｅｒｍｉｎａｔｉｏｎｏｆｆｒａｃｔｕｒｅｔｏｕｇｈｎｅｓｏｆｂｒｉｔｌｅｍａｔｅｒｉａｌｓｉｓｏｆｇｒｅａｔｉｍｐｏｒｔａｎｃｅｉｎｍｉｎｉｎｇａｎｄｇｅｏｌｏｇｉｃａｌｅｎｇｉｎｅｒｉｎｇ．Ａｖａｒｉｅｔｙｏｆｓｐｅｃｉｍｅｎｇｅｏｍｅｔ...     

Mode II fracture analysis of double edge cracked circular disk subjected to different diametral compression

A detailed analysis of modeⅡstress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode Ⅱ SIFs at crack tips can be obtained by simply calculating an integral of the product of mode Ⅱ weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode Ⅱ SIF, fⅡ , is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10^。 to 75^。) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors‘ previous work on modeⅠfracture analysis, the new specimen geometry can be used to study fracture through any combination of mode Ⅰ and mode Ⅱ loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode Ⅱ crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.     

Mode Ⅱ fracture analysis of double edge cracked circular disk subjected to different diametral compression

A detailed analysis of mode Ⅱ stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode Ⅱ SIFs at crack tips can be obtained by simply calculating an integral of the product of mode Ⅱ weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode Ⅱ SIF, fⅡ , is derived for different crack lengths (from 0. 1 to 0.7) and inclination angles (from 10° to 75°) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors' previous work on mode Ⅰ fracture analysis, the new specimen geometry can be used to study fracture through any combination of mode Ⅰ and mode Ⅱ loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode Ⅱ crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.     

Semi-analytical weight function method for center-cracked circular disk subjected to diametral compression

Ｓｉｎｃｅｔｈｅｃｅｎｔｅｒ ｃｒａｃｋｅｄｃｉｒｃｕｌａｒｄｉｓｋｓｐｅｃｉ ｍｅｎｃａｎｂｅａｖａｉｌａｂｌｅｄｉｒｅｃｔｌｙｆｒｏｍｒｏｃｋｃｏｒｅ ,ａｎｄｍｉｘｅｄ ｍｏｄｅｆｒａｃｔｕｒｅｒａｎｇｉｎｇｆｒｏｍｐｕｒｅｍｏｄｅⅠｔｏａｎｙＫⅡ/ＫⅠ ｒａｔｉｏｃａｎｂｅｅａｓｉｌｙａｃｈｉｅｖｅｄｕｓｉｎｇｔｈｉｓｇｅｏｍｅｔｒｙ ,ｉｔｉｓｗｉｄｅｌｙｕｓｅｄｉｎｔｈｅｍｉｘｅｄ ｍｏｄｅｆｒａｃｔｕｒｅｉｎｖｅｓｔｉｇａｔｉｏｎｏｆｂｒｉｔｔｌｅｍａｔｅｒｉａｌｓ .Ｔｈｅｐｒｏｂｌｅｍｃｏ…     

Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure

To reveal the water inrush mechanics of underground deep rock mass subjected to dynamic disturbance such as blasting, compression-shear rock crack initiation rule and the evolution of crack tip stress intensity factor are analyzed under static-dynamic loading and seepage water pressure on the basis of theoretical deduction and experimental research. It is shown that the major influence factors of the crack tip stress intensity factor are seepage pressure, dynamic load, static stress and crack angle. The existence of seepage water pressure aggravates propagation of branch cracks. With the seepage pressure increasing, the branch crack experiences unstable extension from stable propagation. The dynamic load in the direction of maximum main stress increases type I crack tip stress intensity factor and its influence on type II crack intensity factor is related with crack angle and material property. Crack initiation angle changes with the dynamic load. The initial crack initiation angle of type I dynamic crack fracture is 70.5°. The compression-shear crack initial strength is related to seepage pressure, confining pressure, and dynamic load. Experimental results verify that the initial crack strength increases with the confining pressure increasing, and decreases with the seepage pressure increasing.     

Dynamic fracture behavior of rock under impact load using the caustics method

We studied the dynamic fracture mechanical behavior of rock under different impact rates. The fracture experiment was a three-point bending beam subjected to different impact loads monitored using the reflected caustics method. The mechanical parameters for fracture of the three-point bending beam specimen under impact load are analyzed. The mechanism of crack propagation is discussed. Experimental results show that the dynamic stress intensity factor increases before crack initiation. When the dynamic stress intensity factor reaches its maximum value the crack starts to develop. After crack initiation the dynamic stress intensity factor decreases rapidly and oscillates. As the impact rate increases the cracks initiate earlier, the maximum value of crack growth velocity becomes smaller and the values of dynamic stress intensity factor also vary less during crack propagation. The results provide a theoretical basis for the study of rock dynamic fracture.     

岩石在压应力作用下的裂纹扩展模型

在分析压应力作用下裂纹扩展模型的基础上,指出了目前几种常用的岩石中平面分支裂纹尖端应力强度因子的近似解析式所存在的问题,并给出了应力强度因子的较为简便且合理的近似表达式.     

Effect of specimen thickness on Mode II fracture toughness of rock

Anti-symmetric four-point bending specimens with different thickness, without and with guiding grooves, were used to conduct Mode II fracture test and study the effect of specimen thickness on Mode II fracture toughness of rock. Numerical calculations show that the occurrence of Mode II fracture in the specimens without guiding grooves (when the inner and outer loading points are moved close to the notch plane) and with guiding grooves is attributed to a favorable stress condition created for Mode II fracture, i.e. tensile stress at the notch tip is depressed to be lower than the tensile strength or to be compressive stress, and the ratio of shear stress to tensile stress at notch tip is very high. The measured value of Mode II fracture toughness K _{II C} decreases with the increase of the specimen thickness or the net thickness of specimen. This is because a thick specimen promotes a plane strain state and thus results in a relatively small fracture toughness. Foundation item: The National Natural Science Foundation of China (No: 49672164) Biography of the first author: RAO Qiu-hua, doctor of engineering, born in 1965, majoring in rock fracture mechanics.     

3-D distribution of tensile stress in rock specimens for the Brazilian test

It is claimed that the formula used for calculating the tensile strength of a disk-shaped rock specimen in the Brazilian test is not accurate, because the formula is based on the 2-dimensional elastic theory and only suitable for very long or very short cylinders. The Matlab software was used to obtain the 2-dimensional distribution of stress in the rock specimen for Brazilian test. Then the 2-dimensional stress distribution in Brazilian disk was analyzed by the Marc FEM software. It can be found that the results obtained by the two software packages can verify each other. Finally, the 3-dimensional elastic stress in the specimen was calculated. The results demonstrate that the distribution of stress on the cross section of the specimen is similar to that in 2-dimension. However, the value of the stress on the cross section varies along the thickness of the specimen and the stress is bigger when getting closer to the end of the specimen. For the specimen with a height-to-diameter ratio of 1 and a Poisson＇s ratio of 0.25, the tensile strength calculated with the classical 2-D formula is 23.3% smaller than the real strength. Therefore, the classical 2-D formula is too conservative.     

Microscopic characteristics of different fracture modes of brittle rock

Ａｓｕｒｖｅｙｏｆｆｒａｃｔｕｒｅｍｅｃｈａｎｉｃｓｌｉｔｅｒａｔｕｒｅｒｅ ｖｅａｌｓｔｈａｔｒｅｓｅａｒｃｈｗｏｒｋｏｎｒｏｃｋｆｒａｃｔｕｒｅｍｅｃｈａｎ ｉｃｓｈａｓｍａｉｎｌｙｆｏｃｕｓｅｄｏｎＭｏｄｅⅠｆｒａｃｔｕｒｅ (ｏｐｅｎ ｉｎｇｍｏｄｅ) ,ｉｎｐａｒｔｉｃｕｌａｒ,ｏｎＭｏｄｅⅠｆｒａｃｔｕｒｅｔｏｕｇｈｎｅｓｓｔｅｓｔｉｎｇ[1 2 ] .Ｈｏｗｅｖｅｒ,ｐｒｅ ｅｘｉｓｔｉｎｇｃｒａｃｋｓｉｎｒｏｃｋｍａｔｅｒｉａｌｓｏｒｄｉｓｃｏｎｔｉｎｕｉｔｉｅｓｉｎｒｏｃｋｍａｓｓｅｓａｒｅｓｅ…     

神经网络在研究岩石断裂韧度尺寸效应的应用

介绍了人工神经网络在预测人字形切槽巴西圆盘试样(CCNBD)断裂韧度时的应用，通过分析表明，神经网络得到的断裂韧度预测值比CCNBD尺度律公式得到的值更加接近实验值，神经网络直接基于实验数据进行训练，不需要作任何假设，对于构形比较复杂，试样制备时难以满足完全几何相似的CCNBD试样，研究其尺寸效应是比较有利的。     

试件几何尺寸和杆材对CCCD-SHPB试验系统测试结果影响的数值分析

为了分析CCCD-SHPB动态断裂试验系统试验结果的有效性,采用3维动态有限元方法分析了试件几何尺寸和入射杆、透射杆材料对实验结果的影响。分析结果表明,试件直径对CCCDSHPB动态断裂试验系统的试验结果有较大影响,而入射杆和透射杆的波阻抗与试件的波阻抗是否匹配会影响试验结果的精度,但在一定尺寸范围内,试件厚度对试验结果影响较小。进一步计算结果表明,在动态加载的初期阶段,由于试件两边载荷不平衡,导致CCCD-SHPB动态断裂试验系统中存在与试件尺寸相关的特征时间ΔT,且ΔT近似等于应力波在试件中来回往返两次的时间;动态断裂试验时,试件从加载至断裂的时间应大于特征时间ΔT,否则试验结果不可靠。     

岩石裂隙的法向蠕变及渗流的影响

法向蠕变是岩石裂隙的重要力学性质之一．通过分析岩石裂隙法向蠕变机理、进行干燥及渗流情况下岩石裂隙法向蠕变试验,探讨了岩石裂隙的法向蠕变及渗流的影响．研究表明,对于粗糙岩石裂隙来说,瞬时有效应力总等于裂隙凸起的压缩强度,因而初始法向蠕变明显,而后随接触面增加,蠕变速率逐渐降低;渗流过程中,岩石裂隙法向蠕变更加明显,且初次加栽应力水平下岩石裂隙法向蠕变远大于后续加载应力水平;岩石裂隙法向蠕变不能决定岩石裂隙渗流能力的降低,水力冲蚀作用明显时,可能产生裂隙渗流能力随裂隙法向压缩而增大的情况;岩石裂隙的蠕变闭合与岩石裂隙面粗糙度有关,粗糙度越大,岩石裂隙蠕变闭合量越大．研究结果对岩石裂隙法向蠕变的数值模拟及工程实践有一定参考价值．     

岩石压剪断裂及其强度特性分析

籍助于断裂力学的理论和有限元数值计算方法,分析了压剪断裂过程中裂纹尖端应力场的演变规律;修正了应力强度因子的有关计算式,建立了表征初裂的新的断裂准则;反映了裂纹几何尺寸、分布规律、裂纹面物理力学性质、岩石材料断裂韧度,以及围压效应对岩石压剪断裂的影响．     

Experimental and theoretical study of static-dynamic mixed mode brittle fracture of rock

Ｖａｒｉｏｕｓｍｏｄｅ－Ⅰｉｎｖｅｓｔｉｇａｔｉｏｎｓｉｎｔｈｅｔｈｅｏｒｙｏｆｌｉｎｅａｒｅｌａｓｔｉｃｆｒａｃｔｕｒｅｍｅｃｈａｎｉｃｓａｒｅｉｍｐｏｒｔａｎｔｉｎｄｅｔｅｒｍｉｎｉｎｇｔｈｅｆｒａｃｔｕｒｅｃｏｎｓｔａｎｔｓ．Ｔｏａｎａｌｙｓｅ...     

基于动态断裂力学的超声振动切削分析与仿真

为了解释超声振动切削所具有的切削力小等优点的产生原因,进行了超声振动切削的切削机理研究.文中采用动态断裂力学的方法,分析切削过程中由于引入振动所产生的冲击作用,引起了工件内部的动态应力强度因子的变化.利用理论分析与数值仿真相结合的方法,从力学的角度给出切削区产生断裂,从而形成切屑的机理.仿真结果说明了超声振动切削机理:由于振动加入所带来的动态效应使得切削区材料更易发生断裂,导致振动切削力下降.在上述分析基础上,给出了振动切削中正确选择振动参数的方法.     

三角形截面管裂纹的应力强度因子

将守恒律给出的裂纹非自发扩展，即最垂直于裂纹面扩展的能量释放率，应用于求解三角形截面管裂纹的应力强度因子．给出了三角形截面管裂纹张开能量释放率的G-．积分表征，以及和应力强度因子的关系，进而得到三角形截面管横向裂纹的应力强度因子的封闭解．所给出的方法不仅适用于一般箱形结构件的裂纹问题，也适用其他有限边界多边管状结构的三维裂纹问题．