A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed.This study investigated the fragmentation performance of a new high-carbon silicon-manganese(HCSiMn)steel cylindrical shell through fragment recovery experiments.Compared with the conventional 45Cr steel shell,the number of small mass fragments produced by the HCSi Mn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model.The fragmentation process of the HCSi Mn shell exhibited more brittle tensile fracture characteristics,with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation.On the one hand,the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite,so that microscopic intergranular fracture reduces the characteristic mass of the fragments;on the other hand,the distribution of alloy carbides can exert a"pinning"effect on the substrate grains,causing more initial cracks to form and propagate along the brittle carbides,further improving the shell fragmentation.Although the killing power radius for light armored vehicles was slightly reduced by about 6%,the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26%based on theoretical assessment.These results provided an experimental basis for high fragmentation warhead design,and to some extent,revealed the correlation mechanism between metallographic structure and shell fragmentation.

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.

Experiment on Mode Ⅰ/Ⅱ Mixed Interfacial Fracture Characterization of Foam Core Sandwich Materials at Elevated Temperatures

Foam-cored sandwich materials have been widely used in the civil engineering due to their advantages such as lightweight,high strength,and excellent anti-corrosion ability. However,the interfacial bonding strength of foamcored sandwich materials is weakened at elevated temperatures. In practice,the effect of high temperature cannot be ignored,because the composites and foams are sensitive to the change of temperature in the environment. In this study,a series of single-leg bending beams were tested at different temperatures to evaluate the influences of high temperatures on Mode Ⅰ/Ⅱ mixed interfacial fracture of foam core sandwich materials. The temperature was from29 ℃ to 90 ℃,covered the glass transition temperature of composites and foam core,respectively. The Mode Ⅰ/Ⅱ mixed interfacial crack prorogation and its corresponding interfacial strain energy release rate were summarized.

Dynamic behavior and fracture mode of TiAl intermetallics with different microstructures at elevated temperatures

Experimental studies were conducted on the tensile behaviors and fracture modes of TiAl（Ti-46.5Al-2Nb-2Cr） alloys with near gamma（NG） equiaxed and near lamellar（NL） microstructures over a temperature range from room temperature to 840 ℃ and a strain rate range of 0.001-1 350 s-1.The results indicate that the alloys are both temperature and strain rate dependent and they have a similar dependence.The dynamic strength is higher than the quasi-static strength but almost insensitive to high strain rate range of 320-1 350 s-1.The brittle-to-ductile transition temperature（BDTT） increases with increasing strain rates.NG TiAl yields obviously,while NL TiAl does not.Below BDTT,as the temperature increases,the fracture modes of the two alloys change from planar cleavage fracture to a mixture of transgranular and intergranular fractures,and finally to totally intergranular fracture.

Transition of plasticity and fracture mode of Zr-Al-Ni-Cu bulk metallic glasses with network structures

Effect of network structure on plasticity and fracture mode of Zr？Al？Ni？Cu bulk metallic glasses （BMGs） was investigated. The microstructures of transversal and longitudinal sections were exposed by chemical etching and observed by scanning electron microscopy （SEM）. The mechanical properties were examined by room-temperature uniaxial compression test. The results show that both plasticity and fracture mode are significantly affected by the network structure and the alteration occurs when the size of the network structure reaches up to a critical value. When the cell size （dc） of the network structure is ~3μm, Zr-based BMGs characterize in plasticity that decreases with increasingdc. The fracture mode gradually transforms from single 45° shear fracture to double 45° shear fracture and then cleavage fracture with increasingdc. In addition, the mechanisms of the transition of the plasticity and the fracture mode for these Zr-based BMGs are also discussed.

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。

应力场常数项对Ⅰ型裂纹起裂扩展行为影响

对含裂纹材料与结构断裂力学评估中的最大环向应力准则(MTS)、最小应变能密度因子准则(SED)和平均应变能密度准则(ASED)以及在此基础上考虑应力场常数项影响修正的断裂准则进行介绍;基于考虑裂尖应力场奇异项和常数项的修正MTS准则、修正SED准则和修正ASED准则,对比分析了裂尖应力场常数项对Ⅰ型裂纹的起裂扩展行为,探究了裂纹尖端应力场常数项以及材料泊松比对Ⅰ型裂纹偏折、断裂极限的影响规律,掌握了应力场常数项对Ⅰ型裂纹偏折、起裂扩展影响阀值。研究结果表明,裂纹尖端应力场常数项T应力对Ⅰ型裂纹起裂扩展偏折角及断裂判据的影响不可忽略,研究结果可为含裂纹材料与结构断裂力学评估提供一定参考。

基于辛几何方法测定Ⅰ型应力强度因子

为得到高精度的Ⅰ型应力强度因子,提出了一种基于辛几何方法测定裂纹尖端Ⅰ型应力强度因子的方法。通过在裂纹尖端构建扇形区域,分离辛几何方法下裂纹尖端的全状态向量,结合裂纹尖端的位移场,计算出裂纹的应力强度因子。利用Ⅰ型裂纹尖端位移场的理论解,研究了扇形区域的特征点个数、圆心角大小以及半径长度对应力强度因子精确度的影响。研究结果表明:特征点个数对该方法求解Ⅰ型应力强度因子的精度的影响较大,特征点个数大于37时,相对误差稳定趋向于0;扇形圆心角对应力强度因子的精度影响较小,但是相同精度要求下,不同的扇形圆心角需要的特征点个数不同;扇形半径过小时,由于断裂过程中裂纹尖端塑性区域的影响,应力强度因子的解不稳定且相对误差较大。对比相对误差可以发现该方法计算得到的Ⅰ型应力强度因子的精度较高,且该方法只需得到裂纹尖端的位移场就可以精确得到应力强度因子,解决了以往求解体系在复杂应力等情况下求解步骤复杂,导致无法精确得到Ⅰ型应力强度因子的难题。

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.

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。

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.

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。

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

A new criterion of static dynamic state mixed mode brittle fracture initiation in rock is suggested, i.e. the distortion strain energy criterion.When t →∞, the static state distortion strain energy criteria and the formula for determiming static state fracture angle are obtained. The new static state criterion, suggested by authors, is in good agreement with the author′s experimental results. In addition, the relative accuracy of three current fracture theories and the new criterion in predicting static state mixed mode initiation fracture loading and fracture angle in rock have been evaluated experimentally.

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.

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.

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.