Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

A Review of Experimental Research on the Mode I Fracture Behavior of Bamboo

Bamboo is an eco-friendly material with light weight,high strength,short growth cycle and high sustainability,which is widely used in building structures.Engineered bamboo has further promoted the development of modern bamboo structures due to its unrestricted size and shape.However,as a fiber-reinforced material,fracture damage,especially Mode I fracture damage,becomes the most likely damage mode of its structure,so Mode I fracture characteristics are an important subject in the research of mechanical properties of bamboo.This paper summarizes the current status of experimental research on the Mode I fracture properties of bamboo based on the three-point bending(TPB)method,the single-edge notched beam(SENB)method,the compact tension(CT)method and the double cantilever beam(DCB)method,compares the fracture toughness of different species of bamboo,analyzes the toughening mechanisms and fracture damage modes,discusses the applicability of different theoretical calculation methods,and makes suggestions for future research priorities,aiming to provide a reference for future research and engineering applications in related fields.

MECHANISM ANALYSIS OF THICKNESS EFFECT ON MIXED MODE Ⅰ/Ⅱ FRACTURE OF LC4-CS ALUMINUM ALLOY

Mixed mode Ⅰ/Ⅱ fracture erperiments of LC4-CS aluminum alloy were conductedby using tension--shear specimens with thicknesses of 2, 4, 8 and 14mm. Fracturemechanisms of thickness effect on mixed mode Ⅰ/Ⅱ fracture were first examined fromfracture surface morphology to correlate with the macroscopic fracture behavior andstress state. It is found that specimen thickness has a strong influence on mixed modefracture. As thickness varies from thin to thick the macroscopic fracture surfacesappear the characteristics of plane stress state (2mm, 4mm--thick specimen), three--dimensional stress state (8mm--thick specimens), and plane strain state (14mm--thickspecimens), respectively. The specimens of all kinds of thicknesses are typical of ten-sile type failure under mode Ⅰ loading condition and shear type failure under mode Ⅱloading condition. Two distinct features coexist on the fracture surfaces under mixedmode loading conditions, and the corresponding proportion varies with loading mix-ity. Void--growth processes are the failure mechanism in both predominately tensile-and shears--type fractures. The size and depth of dimples on the fracture surface varygreatly with thickness. Therefore, it is extraordinary necessary to take into accountthe thickness effect when a mixed mode fracture criterion is being established.

基于ABAQUS平台考虑T应力的Ⅰ型裂纹扩展模拟开发

工程结构在制造工艺过程中或使用期间会产生裂纹,对结构断裂路径的预测和研究是防治工程安全问题发生的重要手段。在考虑裂纹尖端应力场常数项T应力的基础上对传统的最大周向应力准则(Maximum tangential stress criterion,MTS)和最小应变能密度因子准则(Minimum strain energy density criterion,SED)进行修正,采用Python语言对ABAQUS的前、后处理和有限元计算模块进行二次开发,通过计算最优解的粒子群算法(Particle swarm optimization,PSO)将修正后的准则编入裂纹自动扩展程序脚本中。利用上述二次开发程序对初始纯Ⅰ型裂纹的扩展路径进行模拟,结果表明:采用ABAQUS脚本程序模拟结果与相关文献实验结果吻合,表明了程序的有效性,进而实现考虑T应力的多种断裂准则对裂纹扩展路径的预测;当T应力值处于一定范围内时,修正的MTS准则无法预测裂纹发生的偏转现象,扩展路径呈直线,此时可采用修正的SED准则进行预测。

浅析OBE理念下的《汽车构造Ⅰ》一流课程建设

为体现以学生为中心、产出导向和持续改进教育理念以及课程的高阶性、创新性以及挑战度,文章以《汽车构造Ⅰ》课程为例,按照线上线下混合式一流课程的建设标准,遵循OBE理念,加强课程总体设计,融入课程思政元素,整合优化教学内容,设计“AEEA”的三阶线上线下混合式教学模式,开展多种教学方法的应用,建立过程化、多元化、混合式的课程考核评价体系,以期为高校专任教师开展一流课程建设与实施应用提供思路。

2D-SiC_(f)/SiC复合材料层间Ⅰ型断裂试验及表征

二维编织碳化硅纤维增强碳化硅复合材料(2D-SiC_(f)/SiC)在航空领域中得到广泛使用,然而该材料层间强度低,使其易萌生层间裂纹,引起分层破坏。为此,本工作采用楔形双悬臂梁法(W-DCB)和悬臂梁法(DCB)开展了层间Ⅰ型断裂试验,获得了2D-SiC_(f)/SiC的层间裂纹驱动的加载数据,得到了其裂纹端口张开力及张开位移变形曲线。在试验加载过程,通过光学显微镜监测了视觉裂纹扩展过程,探究了2D-SiC_(f)/SiC的层间I型裂纹扩展规律。结合理论分析和裂纹视觉特征解释了加载曲线拐点及其他特征点的断裂力学含义。利用扫描电子显微镜分析了2D-SiC_(f)/SiC的层间断面特征,揭示了断面分层裂纹扩展机制。结果表明:W-DCB方法测量的2D-SiC_(f)/SiC层间Ⅰ型初始能量释放率与DCB方法等效;2D-SiC_(f)/SiC层间Ⅰ型断裂过程中,裂纹端口变形曲线的多峰性不符合经典线弹性断裂力学预测的加载峰后特征,反映了2D-SiC_(f)/SiC层间约束关系的复杂性;层间断面为结构性非完全损伤,发生了局部纤维桥连现象。

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.

ATOMISTIC/CONTINUUM SIMULATION OF INTERFACIAL FRACTURE——PART Ⅰ: ATOMISTIC SIMULATION

The phenomenon of interfacial fracture, as manifested by atom- istic cleavage, debonding and dislocation emission, provides a challenge for combined atomistic-continuum analysis. As a precursor for fully coupled atomistic-continuum simulation of interfacial fracture, we focus here on the atomistic behavior within a nanoscopic core surrounding the crack tip. The inter-atomic potential under Em- bedded Atom Method is recapitulated to form an essential framework of atomistic simulation. The calculations are performed for a side-cracked disc configuration un- der a remote K field loading. It is revealed that a critical loading rate defines the brittle-to-ductile transition of homogeneous materials. We further observe that the near tip mode mixity dictates the nanoscopic profile near an interfacial crack tip. A zigzag interface structure is simulated which plays a significant role in the dislocation emission from an interfacial crack tip, as will be explored in the second part of this investigation.

EXPERIMENTAL AND THEORETICAL STUDY OF STATIC-DYNAMIC MIXED MODE BRITTLE FRACTURE OF ROCK

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Visualization of hydraulic fracture interacting with pre-existing fracture

Hydraulic fracturing is considered the main stimulation method to develop shale gas reservoirs. Due to its strong heterogeneity, the shale gas formation is typically embedded with geological discontinuities such as bedding planes and natural fractures. Many researchers realized that the interaction between natural fractures and hydraulic fractures plays a crucial role in generating a complex fracture network. In this paper, true tri-axial hydraulic fracturing tests were performed on polymethyl methacrylate (PMMA), on which pre-existing fracture was pre-manufactured to simulate natural fracture. A cohesive model has been developed to verify the results of the experimental tests. The key findings demonstrate that the experimental results agreed well with the numerical simulation outcomes where three main interaction modes were observed: crossing;being arrested by opening the pre-existing fracture;being arrested without dilating the pre-existing fracture. Crossing behavior is more likely to occur with the approaching angle, horizontal stress difference, and injection rate increase. Furthermore, the higher flow rate might assist in reactivating the natural fractures where both sides of the pre-existing fractures were reactivated as the injection rate increased from 5 to 20 mL/min. Additionally, hydraulic fractures show a tendency to extend vertically rather than along the direction of maximum horizontal stress when they are first terminated at the interface. This research may contribute to the field application of hydraulic fracturing in shale gas formation.

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.

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.

Meso-mechanical anisotropy and fracture evolution of reef limestones from the Maldives Islands and the South China Sea

Reef limestone is a biogenic sedimentary rock widely distributed in coral reef areas, acting as an important foundation for coast construction. Due to its special biogenic origin, reef limestone is different from conventional rocks both in terms of rock structure and mechanical properties. In this study, mesoscale uniaxial compression experiments with five different loading directions were conducted on two kinds of reef limestones from the Maldives Islands and the South China Sea, respectively. The real-time high-resolution videos and images of failure processes were recorded simultaneously to investigate the fracture evolution and fracture surface roughness of reef limestones. It demonstrated that the reef limestones belonged to extremely soft to soft rocks, and their uniaxial compressive strength (UCS) values fluctuated with high discreteness. The mesoscale mechanical properties of reef limestones were highly anisotropic and mainly controlled by pore structure. The occurrence of dissolution pores in reef limestone tended to intensify mechanical anisotropy. With the integration of the fracture initiation and propagation features of reef limestones, it is supposed that the intrinsic mechanism of anisotropy was probably attributed to the differences in coral growth direction and dissolution. Furthermore, the quantified fracture surface roughness was revealed to have a good consistency with density and UCS for the reef limestones from the South China Sea. The findings are helpful for providing theoretical and experimental references for engineering construction in coral reef areas.

Rock fracture under anti-plane shear (Mode Ⅲ) loading

Anti-plane punch-through shear test and anti-planefour-point bending test are used to study the crack initiation and propagation under anti-plane shear (Mode Ⅲ) loading. The tensile and shear stresses at the crack tip are calculated by finite element method. The results show that under Mode Ⅲ loading the maximum principal stress σ1 at crack tip is smaller or a little larger than the maximum shear stress τmax. Since the tensile strength of brittle rock is much lower than its shear strength, σ1 is easy to reach its critical value before τmax reaches its critical value and thus results in Mode I fracture. The fracture trajectory is helicoid and the normal direction of tangential plane with the fractured helicoid is along the predicted direction of the maximum principal stress at the notch tip. It is further proved that Mode Ⅰ instead of Mode Ⅲ fracture occurs in brittle rock under Mode Ⅲ loading. The fracture mode depending on the fracture mechanism must be distinguished from the loading form.

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.

Microscopic characteristics of different fracture modes of brittle rock

Three types of rock specimens, three-point bending specim en , anti-symmetric four-point bending specimen and direct shearing specimen, wer e used to achieve Mode Ⅰ, Mode Ⅱ and mixed mode Ⅰ-Ⅱ fracture, respectively . Microscopic characteristics of the three fracture modes of brittle rock were s tudied by SEM technique in order to analyze fracture behaviors and better understand fr acture mechanisms of different fracture modes of brittle rock. Test results show that the microscopic characteristics of different fracture modes correspond to different fracture mechanisms. The surface of Mode Ⅰ fracture has a great numbe r of sparse and steep slip-steps with few tearing ridges and shows strong britt leness. In the surface of Mode Ⅱ fracture there exist many tearing ridges and d ensely distributed parallel slip-steps and it is attributed to the action of sh ear stress. The co-action of tensile and shear stresses results in brittle clea v age planes mixed with streamline patterns and tearing ridges in the surface of m ixed mode Ⅰ-Ⅱ fracture. The measured Mode Ⅱ fracture toughness K ⅡC and mixed mode Ⅰ-Ⅱ fracture toughness K mC are larger than Mode Ⅰ fracture t oughness K ⅠC . K ⅡC is about 3.5 times K ⅠC , a nd K mC is about 1.2 times K ⅠC .

Experimental study on time-dependent stress and strain of in-plane shear(ModeⅡ) fracture process of rock

Shear-box test with strain measurement was used to study time-dependent stress and strain of in-plane shear(Mode Ⅱ) fracture process of rock and to reveal the mechanism of Mode Ⅱ fracture.Numerical results show that the maximum shear stress τmax at the crack tip is much larger than the maximum tensile stress σ1 and the ratio of τmax/σ1 is about 5,which favors Mode Ⅱ fracture of rock.Test results indicate that the strain-time curve comprises three stages:the linear deformation stage,the micro-cracking stage and the macroscopic crack propagation.The strain in the direction of the original notch plane is negative,due to restraining effect of compressive loading applied to the original notch plane.Both σ1 and τmax are increased as the load increases,but the slope of τmax is larger than that of σ1 and the value of τmax is always larger than that of σ1.Therefore,τmax reaches its limited value at peak load before σ1 and results in Mode Ⅱ fracture of rock.Shear-box(i.e.compression-shear) test becomes a potential standard method for achieving the true Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock.

INFLUENCES OF HEAT-TREATING PROCESS ON DUCTILE FRACTURE MECHANISM UNDER MIXED MODE LOADINGS

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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, f _Ⅱ, 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.

Two Modes and Criterion of Brittle Fracture

The plastic zone at the tip of the flaw (including acute cark and common notch) was investigated. Forthe notch specimen, a formula of toughness K was proposed, and its physical meaning was emphasized.Twomodes of brittle fracture was identified and the evaluating criterion was established.