Tensile and tear-type fracture toughness of gypsum material:Direct and indirect testing methods

In this context,four specimens,i.e.(i)circumferentially notched cylindrical torsion(CNCT),(ii)circum-ferentially notched cylindrical direct tension(CNCDT),(iii)edge notch disc bend(ENDB)and(iv)three-point bend beam(3PBB),were utilized to measure the modesⅠandⅢfracture toughness values of gypsum.While the CNCT specimen provides pure modeⅢloading in a direct manner,this pure mode condition is indirectly produced by the ENDB specimen.The ENDB specimen provided lower KⅢc and a non-coplanar(i.e.twisted)fracture surface compared with the CNCT specimen,which showed a planar modeⅢfracture surface.The ENDB specimen is also employed for conducting pure modeⅠ(with different crack depths)and mixed modeⅠ/Ⅲtests.KIc value was independent of the notch depth,and it was consistent with the RILEM and ASTM standard methods.But the modeⅢfracture results were highly sensitive to the notch depth.While the fracture resistance against modeⅢwas significantly lower than that of modeⅠ,the greater work of fracture under modeⅢwas noticeable.

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 ⅡC 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.

Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming

Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(UCS), Brazilian tensile strength(BTS), and elastic modulus(E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets.Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of KIC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination(R2),root mean square error(RMSE), and mean absolute error(MAE) were utilized herein. In the case of testing datasets, the values of R2, RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156,respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R2value and lower errors.

Mode I rock fracture toughness with different types of brazilian disc

According to the results evaluated by researchers for mode I rock fracture toughness measurement, a series of comparison tests with different types Brazilian discs were conducted in order to search for the simplest geometry specimens by which accurate, comparable and consistent mode I rock fracture toughness could obtain.

Fracture Toughness of Glass-Carbon (0/90)_sFiber Reinforced Polymer Composite – An Experimental and Numerical Study

Mode-I fracture behavior of glass-carbon fiber reinforced hybrid polymer composite was investigated based on experimental and finite element analysis. The compact tension (CT) specimen was employed to conduct mode-I fracture test using special loading fixtures as per ASTM standards. Fracture toughness was determined experimentally for along and across the fiber orientation of the specimen. Results indicated that the cracked specimens are tougher along the fiber orientations as compared with across the fiber orientations. A similar fracture test was simulated using finite element analysis software ANSYS. Critical stress intensity factor (K) was calculated at fracture/failure using displacement extrapolation method, for both along and across the fiber orientations. The fractured surfaces of the glasscarbon epoxy composite under mode-I loading condition was examined by electron microscope.

Dynamic ModeⅡfracture behavior of rocks under hydrostatic pressure using the short core in compression(SCC)method

The shear failure of rocks under both a static triaxial stress and a dynamic disturbance is common in deep underground engineering and it is therefore essential for the design of underground engineering to quantitively estimate the dynamic ModeⅡfracture toughness KⅡCof rocks under a triaxial stress state.However,the method for determining the dynamic KⅡCof rocks under a triaxial stress has not been developed yet.With an optimal sample preparation,the short core in compression(SCC)method was designed and verified in this study to measure the dynamic KⅡCof Fangshan marble(FM)subjected to different hydrostatic pressures through a triaxial dynamic testing system.The formula for calculating the dynamic KⅡCof the rock SCC specimen under hydrostatic pressures was obtained by using the finite element method in combination with secondary cracks.The experimental results indicate that the failure mode of the rock SCC specimen under a hydrostatic pressure is the shear fracture and the KⅡCof FM increases as the loading rate.In addition,at a given loading rate the dynamic rock KⅡCis barely affected by hydrostatic pressures.Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.

A MIXED MODE FRACTURE CRITERION BASED ON THE MAXIMUM TANGENTIAL STRESS IN BRITTLE INCLUSION

A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.

MODE II AND MIXED MODE I-II ROCK FRACTURE RESEARCH

of PhD thesis For the mode I rock fracture toughness measurement,three standard methods have been recommended by the ISRM,but there has not been a standard method for the determination of mode II and mixed mode I-II rock fracture toughness. However mode II and mixed mode I-II fracturing of rock structures is more commonly observed than mode I in various geological and structural engineering settings. So it is of great important to thoroughly research these rock fracture problems and establish a standard method for determining the mode II or mixed mode I-II fracture toughness for rock materials. Based on the progress made for mode I rock fracture research,the cracked chevron notched Brazilian disk (CCNBD) specimen was also introduced for mode II and mixed mode I-II rock fracture toughness measurement. When the crack is orientated at an angle with respect to the diametrical loading,the crack of the CCNBD specimen is exposed to the mode II or mixed mode I-II stress distribution conditions. The solutions for stress intensity factors in the vicinity of the crack tip have been evaluated by the stepwise superimposition technique. In order to make sure that the theoretical analysis is correct,numerical calculation method has been employed to calibrate the theoretical results. It has been proved that the theoretical results yielded by the dislocation method are correct and reliable. According to the characteristic that the propagation of the crack in the CCNBD specimen is in its own plane and application of the energy superposition principle,the stress intensity factor of the mixed mode I-II has been defined in dimensionless terms as 212II2Imix])()[(***+=YYY. It was found that the curve of *mixY was concave. There exists a lowest point which corresponds to the maximum external load and indicates the crack has reached its critical state. Since the values of ***IIImix and YYY, are only dependent on the specimen geometry (qaaa and 10B,,),the critical values of ***IIImix and YYY, can be to known as long as the CCNBD specimen is prepared ready. It is only necessary to record the maximum load during the fracture tests. The fracture locus is very useful to know whether the crack in a rock structure has reached its critical condition. According to the amount of practical fracture testing data obtained,the rock fracturing locus was found to be 123IICII23ICI=+KKKK and the S-critical criterion was found to be more suitable for rock mixed mode I-II fracturing assessment.

Is crack branching under shear loading caused by shear fracture? ——A critical review on maximum circumferential stress theory

When a crack is subjected to shear force, crack branching usually occurs. Theoretical study shows that the crack branching under shear loading is caused by tensile stress, but not caused by shear fracture. The co plane shear fracture could be obtained if compressive stress with given direction is applied to the specimen, subsequently, calculated shear fracture toughness, K ⅡC , is larger than K ⅠC . A prerequisite of possible occurrence of mode Ⅱ fracture was proposed. The study of shear fracture shows that the maximum circumferential stress theory considered its criterion as a parametric equation of a curve in K Ⅰ, K Ⅱ plane is incorrect; the predicted ratio K ⅡC / K ⅠC =0.866 is incorrect too. [

Tests and Simulation Analysis on Fracture Performance of Concrete

To obtain the fracture parameters of concrete, fracture tests were conducted with three-point bending beam method aiming at 30 concrete beams with different sizes and different intensity. The concrete specimen with prefabricated crack to determine the fracture parameters of concrete were conducted and the fracture performance of the specimen was analyzed. The test results show that, initial fracture toughness is unrelated to the size of specimens; while unstable fracture toughness is related to the size of specimens. As for specimens of bastard size, when concrete intensity is relatively low, unstable fracture toughness increases along with the increase of intensity; when concrete intensity is relatively high, unstable fracture toughness will decrease; when concrete intensity increases continuously, unstable fracture toughness will further increase somewhat. As for specimens of standard size, unstable fracture toughness will increase along with the increase of intensity. Aiming at concrete beam specimens, we conducted two-dimensional non-linear finite element analysis, obtained the stress intensity factor, and carried out contrastive analysis with the experimental results.

Anisotropy in shear-sliding fracture behavior of layered shale under different normal stress conditions

Shear-sliding mode(mode Ⅱ)fracture of rocks is a vital failure form in deep underground engineering.To gain deep insight into the anisotropic shear fracture behaviors of a typical shale under high normal stress conditions,a series of direct shear tests were conducted on double-notched specimens in three typical bedding orientations(i.e.,the arrester,divider,short-transverse orientations)and under five normal stresses.The modeⅡfracture toughness(K_(Ⅱc))is found to exhibit a significant 3D anisotropy.The maximum K_(Ⅱc)is obtained in the divider orientation,followed by those in the arrester and short-transverse orientations.In contrast,the 3D anisotropy in the critical modeⅡenergy release rate(G_(Ⅱc))is not as significant as that in K_(Ⅱc),and G_(Ⅱc)in the arrester orientation is quite close to that in the divider orientation.The anisotropy in the prepeak input energy accumulated during shearing is found to be exactly consistent with that in G_(Ⅱc),which has not been noted before.Furthermore,the anisotropies in the modeⅡfracture resistances will,unexpectedly,not be weakened by the high normal stress.Owing to the layered structures,tensile cracks are involved during the modeⅡfracture process,resulting in the formation of rough fracture surfaces.

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dy- namic fracture toughness （DFT） of high strength steel, using the split Hopkinson tension bar （SHTB） apparatus, com- bined with a hybrid experimental-numerical method. The center-cracked tension specimen is connected between the bars with a specially designed fixture device. The fracture initiation time is measured by the strain gage method, and dynamic stress intensity factors （DSIF） are obtained with the aid of 3D finite element analysis （FEA）. In this approach, the dimensions of the specimen are not restricted by the connec- tion strength or the stress-state equilibrium conditions, and hence plane strain state can be attained conveniently at the crack tip. Through comparison between the obtained results and those in open publication, it is concluded that the ex- perimental data are valid, and the method proposed here is reliable. The validity of the obtained DFT is checked with the ASTM criteria, and fracture surfaces are examined at the end of paper.

高韧性炭/炭复合材料的制备及研究

C/C复合材料是一种高性能新型复合材料,但是脆性大、韧性差的缺点限制了其广泛应用。因此,本研究利用化学气相渗透(CVI)法,设计并制备了三种C/C复合材料,基体炭分别为粗糙层、光滑层以及粗糙层/各向同性层带状结构热解炭,研究了C/C复合材料的微观结构、沉积机理、断裂行为和增韧机制。结果表明,三种C/C复合材料的抗弯强度分别为189.1、191.5、233.5 MPa。粗糙层和带状结构炭基体的C/C复合材料为假塑性断裂,而光滑层炭基体的C/C复合材料则是明显的脆性断裂。与粗糙层炭基体的C/C复合材料相比,带状结构炭基体的C/C复合材料通过不同结构热解炭之间的界面滑动,使得应变量增加了约70%,韧性得到了提升。因此,通过控制CVI工艺参数,实现带状结构热解炭制备,可以有效优化C/C复合材料的韧性。

3D打印CFRP-Ⅰ型层间断裂韧性的断层替换测试法及参数化分析

为实现3D打印碳纤维增强树脂基复合材料(carbon fiber reinforced polymer,CFRP)Ⅰ型层间断裂韧性的测试分析,并量化评价打印参数对该型断裂韧性的影响规律,推进3D打印CFRP技术在桥梁工程中的应用,分别从试验及仿真角度开展了相关探索。首先,提出了一种新型的3D打印CFRP层间预制裂纹制备方法-断层替换法,利用该方法开展了系统性的试验研究,分析了两类关键打印参数对Ⅰ型层间断裂韧性的影响规律。其次,基于内聚区理论及surface-based cohesive关系,构建了各类打印工况下的预制裂纹试件双悬臂梁(double cantilever beam,DCB)试验的仿真模型,并完成了仿真计算与试验测试的对比分析。结果表明:3D打印CFRP的Ⅰ型层间断裂韧性随着打印温度及速度的提高而增大,且打印温度对断裂韧性的影响更显著,当温度由245℃升至285℃时,断裂韧性提高了294.6%;当速度由20 mm/s增至60 mm/s时,断裂韧性提高了27.6%;当打印温度与速度提高时,试件在打印过程中热量散失更小,Ⅰ型层间力学性能得到提高;但当打印速度过大时,印材在打印过程中无法完全沉积并实现较好的黏结,反而对Ⅰ型层间力学性能造成负面影响。同时,仿真结果与试验数据的相对误差均控制在15%以内,表明提出的断层替换法在I型层间断裂韧性试验数据获取方面是合理且稳定的。因此,该方法可为后续量化评价3D打印CFRP桥梁工程构件的层间力学性能提供试验技术支撑。

The Effects of Cooling Mode on the Properties of Ti–Nb Microalloyed High-strength Hot-rolled Steels

The industrial trials of two cooling modes, i e, water cooling in forepart + air cooling in later part (WAC) and air cooling in forepart + water cooling in later part (AWC), were carried out for a Ti- Nb microalloyed steel. The average cooling rates and coiling temperature were the same for two modes. The continuous cooling transformation (CCT) curve of the tested steel was drawn. The effects of the cooling mode on the microstructure, precipitates, and properties of the steels were investigated. Results show that the strength of the steel in the WAC mode is significantly larger than that in the AWC mode, mainly because the smaller the grain size, the more and finer the grain precipitates. Therefore, when the average cooling rate is constant, the fast cooling in the forepart is an effective method to increase the strength of steels. However, the increase in the strength is accompanied by the decrease in toughness, so that the toughness of the steel should be considered when changing the cooling mode.

Irregular-Mode Cracking in Fe-3 wt pct Si Alloy

Due to the non-uniform nature of crack advance, when a cleavage front encounters a high-angle grain boundary, instead of simultaneous break-through along the whole boundary, the front transmission mode can be irregular, which results in a higher fracture resistance and a tortuous percolation behavior. In this paper, this phenomenon is studied quantitatively through the analysis on the work of separation and the change in strain energy for an Fe-3 wt pct Si alloy. The influences of the crystallographic misorientations, the break-through mode, the cleavage front profile, and the grain boundary properties are discussed in detail.

化学溶液和干湿循环作用下砂岩Ⅰ/Ⅱ复合型断裂韧性劣化特性研究

为研究化学溶液和干湿循环作用下砂岩Ⅰ/Ⅱ复合型断裂韧性的劣化规律,先采用pH为7,9,4的保水溶液,对试件进行干湿循环试验(N=1,3,6,10),随后通过半圆弯曲法测试试件的Ⅰ/Ⅱ复合型断裂韧性。试验结果显示:随着干湿循环次数N的增加,砂岩断裂韧性逐渐劣化,且劣化速度逐渐减缓;化学溶液对断裂韧性的影响为:酸性>碱性>中性;Ⅱ型断裂韧度总劣化度小于Ⅰ型断裂韧度。随后,基于试验结果,发现最大切应力准则(MTS准则)在判别以Ⅱ型断裂为主的复合型裂纹时存在较大误差,而广义最大切应力准则(GMTS准则)则能较好的吻合试验结果。最后,基于GMTS判据,分析裂纹尖端参数的劣化特征:T应力的绝对值与临界极半径r_(c)随着断裂韧性总劣化度的增大而减小;试件的干湿状态对r_(c)影响微弱,印证了r_(c)是反映结构性质的参数。

燃爆载荷冲击下五峰—龙马溪组页岩断裂韧性及破坏模式

燃爆压裂是页岩气储层改造增产的一种无水压裂技术,弄清燃爆载荷冲击下页岩断裂韧性及破坏模式是甲烷燃爆压裂推广应用的关键。断裂韧性是页岩储层压裂效果评价的重要指标,实现燃爆载荷冲击下试样裂纹复杂程度的定量表征以确定页岩的破坏模式。选取四川省宜宾市长宁五峰—龙马溪组一段页岩样品,基于自主搭建的甲烷燃爆冲击和SHPB试验系统开展研究,结合动态断裂理论确定了一种计算各向异性页岩动态断裂韧度的方法,并探究燃爆载荷冲击作用下页岩的断裂韧性及损伤破坏特征。结果表明:在不同燃爆加载速率下,试样动态断裂韧度随层理角度的增加呈线性增加趋势,相比静态断裂韧性显著增大,90°层理页岩试样的断裂韧度最大达到4.98 MPa·m^(1/2);随着加载速率的增大页岩动态断裂韧度显著增大,如0°层理试样在157.57 GPa·m^(1/2)/s的加载速率下的断裂韧度值为4.93 MPa·m^(1/2),而加载速率为35.43 GPa·m^(1/2)/s时的断裂韧度为1.72 MPa·m^(1/2),降低了2.9倍;同时,受页岩层理角度的影响,高加载速率下页岩试样裂纹扩展方向发生偏移转向、顺层延申和切层现象,使得裂缝网络整体结构更加复杂;在燃爆载荷冲击试验中,页岩初始起裂角为0°~70.51°,依据岩石断裂理论可知属于I-II型复合断裂类型;随着燃爆载荷由20~25 MPa增长到66~71 MPa,裂纹的尺寸和数量显著增长,且起裂角分布范围明显增加;燃爆压力达到50 MPa以上时,试样裂纹数量和偏转模式增多,伴随着岩体的剪切滑移现象,能够形成复杂树状裂纹,对页岩储层复杂裂缝网络有着正向作用。

热冲击对花岗岩动态断裂行为的影响研究

为了研究热冲击对加热花岗岩的影响,使用3种冷却方法来提供不同的冷却速率,对花岗岩试样施加不同程度的热冲击作用。通过分离式霍普金森压杆(SHPB)系统对热冲击处理后的花岗岩半圆盘中心直裂纹三点弯曲(NSCB)试样进行冲击断裂试验,并利用高速摄像机记录了试样的断裂模式。试验结果表明:随着试样温度和冷却速率的提升,试样的干密度和纵波波速显著下降,试样的孔隙率加大。试样的断裂韧度变化及破坏模式表明热冲击作用使花岗岩试样受到冲击力时抗裂纹扩展的能力下降,尤其在冲击载荷的加载率高于130 GPa·m^(0.5)/s时下降尤为明显。

基于NSCB方法的冻结红砂岩动态断裂特性试验

采用红砂岩制作中心直裂纹半圆盘弯曲试样(Notched semi-circular bend, NSCB),设置不同的负温温度对岩石试样预处理,随后利用改进后的分离式霍普金森杆(SHPB)实验系统开展动态试验.结果表明:岩石的断裂韧度存在明显的加载率效应,断裂韧度试验值随加载率的增加近似呈指数型增大;当加载率一定时,岩石断裂韧度由常温进入负温后先缓慢后快速增加,在–20℃时达到最大值,随着温度进一步降低,岩石断裂韧度快速减小.进一步对岩石破裂过程分析发现,不同温度下岩石的断裂过程基本一致,且裂纹扩展速度受温度影响较小.基于岩石断面的扫描电子显微镜结果分析岩石断裂模式为:负温下红砂岩的断裂以沿晶破裂和胶结物的撕裂为主,伴有少量的穿晶破裂现象,同时当温度降低至–25℃时,岩石内部微裂隙数量明显增多,说明负温对岩石具有劣化作用.最后探讨了温度对岩石内部结构的影响机制,对分析岩石断裂特性的低温效应具有一定参考意义.