Use of double edge-cracked Brazilian disk geometry for compression-shear fracture investigation of rock

A new specimen geometry-the double edge-cracked Brazilian disk and a relevant fracture analysis by weight function method are proposed for the investigation of rock fracture caused by compression-shear loading. Not only can the mixed mode fracture with any ratio of KI /KII be achieved, but also the pure mode n crack extension can be obtained. The combined mode fracture analysis for this geometry shows that diametral compression in the far-field can induce a compression-shear stress state in the singular stress field ahead of crack tips. Experimental investigations conducted on marble specimens show that the pure mode [I crack extension can be obtained when the dimen-sionless crack length a>0. 7 and the inclined crack angle 5°≤ψ≤40°. Normalized mode I and mode II stress intensity factors decrease from -0. 45 and 2. 47 at ψ= 5° to - 1. 65 and 1. 52 at ψ=40°, respectively. The strains at three points of specimen are also measured in order to investigate the influence of stress singularity on initi     

Microscopic characteristics of different fracture modes of brittle rock

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

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.     

A simple method of determining stress intensity factor KI from isochromatic fringe loops

A new photoelastic method of obtaining mode I stress intensity factor (SIF) is presented. The method considers the influence of far field stress, σ _ox , on the value of SIF. The only information needed for K _I calculation is the area between isochromatic fringe loops. The method is examined by two kinds of specimen in different load cases. Experimental results show that it is quite simple and of high precision. Project supported by the National Natural Science Foundation of China Synopsis of the first author Chen Feng, associate professor, born in October 1949, worked on experimental fracture mechanics in Sweden from 1990 to 1995 as a visiting scholar. Major research fields include perturbation and weight function method and its application, experimental mechanics, rock fracture mechanmics.     

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

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

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.     

Mechanism of action of cracks water on rock landslide in rainfall

In worldwide, the most common triggering factor of rock landslides is extended and intense rainfall. However, different from the soil slope failure caused by softening action of infiltration rainwater, the mechanism of rock landslide in rainfall is not clear. From the view of fracture mechanics, the propagation of cracks on rock slope and the development of sliding surface were researched. Then based on hydraulics formulas and using Sweden arc method, the influence of crack water on stability of rock slope was quantitatively studied. Finally, an example was given to check the theoretical approach. The result shows that the development of sliding surface of rock slope is mainly caused by crack propagation under hydrostatic pressure when the stress intensity factor K _I at crack tip is bigger than the toughness index of rock fractures K _IC, and the failure of slope is the result of hydraulic action of crack water and the softening of materials on sliding surface when the depth of crack water is bigger than a minimum value h _min.     

含界面裂纹的GFRP沥青混合料巴西盘断裂力学分析

为研究GFRP沥青混合料界面裂尖力学特性,对混合料进行强度分析,设计了含预制界面裂纹的双材料巴西盘试件,实测了加载角度在25°90°之间27个巴西盘试件断裂荷载、裂纹扩展路径和断口形式等试验数据,结合试验数据建立了考虑GFRP正交异性双材料巴西盘有限元模型,采用数值外插法反算了界面应力强度因子,进行了GFRP沥青混合料巴西盘断裂力学性能的理论分析和试验研究.结果表明,含预制界面裂纹的双材料巴西盘试件能全面地反映GFRP沥青混合料的断裂形态,是一种有效的试验方法;以界面应力强度因子作为力学评价指标,能够很好地解释试验现象;含预制界面裂纹的GFRP沥青混合料巴西盘符合椭圆强度准则.     

沥青路面多裂纹断裂分析

沥青路面通常在表面裂纹和基础裂纹共存状况下服务。基于断裂力学理论,采用无网格伽辽金/有限元耦合法,对同时含有面层表面裂纹和基层底面裂纹的沥青路面进行了断裂分析,研究了行车荷载行驶过程中裂纹尖端应力强度因子的变化规律。结果显示,在车轮荷载行驶通过基层底面裂纹上方的过程中,基层底面裂纹的复合型应力强度因子K＊存在一个最大极值,且这个最大值不是出现在车轮荷载位于基层正上方的时候;表面裂纹的应力强度因子K1和K2随着交通荷载驶近表面裂纹而逐渐增大,而且增大的速率也逐渐上升;相对于基层底面裂纹,表面裂纹受荷载位置影响更显著。     

基于扩展有限元的混凝土三点弯曲梁断裂性能数值模拟研究

基于扩展有限元法,模拟了不同宽度混凝土三点弯曲梁的断裂破坏过程,得到了荷载-裂缝口位移曲线;对不同宽度、缝高比、跨高比的三点弯曲梁断裂过程进行模拟并利用双K断裂准则得出了不同宽度、缝高比、跨高比等条件下的应力强度因子,研究了这三种参数的变化对应力强度因子的影响。研究结果表明:当跨高比、缝高比等于0.4,梁宽在100~250 mm范围内变化时,其起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un基本保持不变;当梁宽不变,跨高比等于4,缝高比从0.2增大到0.5时,起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un呈现先增大后减小的趋势;当梁宽不变,缝高比等于0.4,跨高比从2.5增大到3.5时,起裂断裂韧度K_Icⁱⁿⁱ保持不变,失稳断裂韧度K_Ic^un将逐渐增大但幅度很小;当跨高比不变,缝高比等于0.4,梁宽在100~250 mm的范围内变化时,起裂断裂韧度K_Icⁱⁿⁱ、失稳断裂韧度K_Ic^un均呈现先增大后减小的趋势,表明小跨高比的K_Icⁱⁿⁱ、K_Ic^un在梁宽度方向存在一定的尺寸效应。     

A MIXED METHOD OF DETERMINING THETHERMAL STRESS FOR COLD ROLLER

Coldrollerisanimportantcomponentofthemill.Thecoldrolleroftherollingprocessisusedathightemperature,whichwouldcracktherollerandshortentheservicelifeoftheroller.UPtonow,ageneralcalculationmethodofthethermalstressofthecoldrolleristoincreasethesafetycoefficient.Thiscalculationmethodlackstheoreticalanalysis.Inordertosolvethisproblem,thispaperappliesforthefirsttimethenewlydevelopedfiniteanalyticalmethodandtheboundaryfittingcoordinatetransformationmethodtomillpracticeandprovidesaanalyticalbasisoftemp…     

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

Anti-plane punch-through shear test and anti-plane four-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 calcualted 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 τ_max. Since the tensile strength of brittle rock is much lower than its shear strength, σ₁ is easy to reach its critical value before τ_max 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. Foundation item: Project (50374073) supported by the National Natural Science Foundation of China; project (2002032256) supported by the Postdoctor Science Foundation of China     

On the calculation of stress intensity factor K for frame components

The stress intensity factorK in the tip of crack which is in the corner of the frame component has been calculated indirectly by means of numeric calculation ofJ Integral. Some laws and relationships among the stress intensity factorK, the applied loads and the crack length for this kind of components have been discovered for the first time. The calculating formula forK has been deduced, the criticalK has been calculated with the formula, that is 5 811.56–6 122.58 MPa · mm^1/2. The conclusions reached in this paper are of great referential and practical value for simplifying the calculation of stress intensity factorK for this type of components. Project supported by Technological Development Foundation of the Nonferrous Metal Industry Corporation of China Synopsis of the first author Liu Yilun, Doctor, associate professor, born in Oct. 30, 1955. Research areas are fatigue strength of component and the technology of continuous casting for non-ferrous metal.     

复合型加载条件下扁平巴西圆盘应力强度因子计算方法

复合型裂纹的研究具有重要的工程实用价值。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扁平巴西圆盘试件的应力强度因子进行了系统的分析。计算结果表明:在一定载荷分布角范围内,可使用分布载荷作用下巴西圆盘应力强度因子的公式去计算扁平巴西圆盘试件的应力强度因子;在断裂力学中圣维南原理依然成立。根据计算结果,推荐在扁平巴西圆盘断裂实验中使用载荷分布角为7.25°的扁平巴西圆盘试件。     

Wing crack model subjected to high hydraulic pressure and far field stresses and its numerical simulation

By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far field stresses was proposed. By introducing the equivalent crack length l _eq of wing crack, two terms make up the stress intensity factor K _I at wing crack tip: one is the component K _I⁽¹⁾ for a single isolated straight wing crack of length 2l subjected to hydraulic pressure in wing crack and far field stresses, and the other is the component K _I⁽²⁾ due to the effective shear stress induced by the presence of the equivalent main crack. The FEM model of wing crack propagation subjected to hydraulic pressure and far field stresses was also established according to different side pressure coefficients and hydraulic pressures in crack. The result shows that a good agreement is found between theoretical model of wing crack proposed and finite element method (FEM). In theory, an unstable crack propagation is shown if there is high hydraulic pressure and lateral tension. The wing crack model proposed can provide references for studying on hydraulic fracturing in rock masses.     

硬岩脆性指标与弹性应变能关系初探

为探讨硬岩脆性指标与弹性应变能之间的关系,采用侧向应变差法确定起裂应力,以岩石起裂应力和峰值强度为桥梁,基于断裂力学理论和能量理论解释了脆性指标与弹性应变能内在的联系,并从两种岩石单轴压缩试验中构建了脆性指标与弹性应变能之间的函数关系.结果表明:脆性指标B_(13)、B_(14)与起裂弹性应变能(单变量)符合幂函数关系,脆性指标B_(15)、B_(16)与起裂弹性应变能(单变量)符合幂函数或线性函数关系,脆性指标B_(13)、B_(14)、B_(15)和B_(16)与峰值弹性应变能(单变量)之间无明显函数关系;新定义的脆性指标可由起裂和峰值弹性应变能(双变量)获得,或由起裂弹性应变能(单变量)获得,脆性指标与峰值弹性应变能关系式的构建,对于研究岩爆倾向性具有重要意义;根据新定义的脆性指标,利用两种岩石算例验证表明,采用起裂弹性应变能的岩石脆性指标计算方法具有一定的可靠性.通过这一研究,为岩石脆性指标与起裂弹性应变能关系的确定提供了一种新方法.     

DZ125合金超高周疲劳微观裂纹萌生机制

DZ125合金具有优良的综合性能表现,已被广泛应用于燃气涡轮高温部件的铸造。关于DZ125合金的疲劳问题研究已有较多文献报道,但从微观断口分析的角度系统阐述该合金超高周疲劳裂纹萌生及失效机制的研究则相对较少。通过研究发现,随着疲劳强度的降低,疲劳数据离散性有增大的趋势;较小的疲劳应力（小于220 MPa）所对应的疲劳寿命并未有明显增加,上述特征与疲劳微观裂纹萌生机制的改变直接相关。在高应力作用下,疲劳裂纹倾向于从材料的表面或次表面萌生,巨型二次裂纹成为其断口形貌的主要特征;在低应力状态下,材料内部的孔洞缺陷是疲劳裂纹萌生的主要区域,并严重影响材料的疲劳寿命。驻留滑移带（PSB）可导致表面粗糙区的形成,成为裂纹尖端的主要特征。主裂纹与其他二次裂纹存在竞争关系,并最终引起疲劳断裂的发生。基于Murakami公式,DZ125合金在裂纹萌生阶段的平均应力强度因子为3.15 MPa·m^1/2,裂纹快速扩展阶段的平均应力强度因子和材料的断裂韧性（K_IC）分别为7.72和15.70 MPa·m^1/2。     

Seismic ultimate bearing capacity of strip footings on slope

The influence of earthquake forces on ultimate bearing capacity of foundations on sloping ground was studied. A solution to seismic ultimate bearing capacity of strip footings on slope was obtained by utilizing pseudo-static analysis method and taking the effect of intermediate principal stress into consideration. Based on limit equilibrium theory, the formulae for computing static bearing capacity factors, Nq, Nc, Nγ, and dynamic bearing capacity factors, Nqd, Ncd, Nγd, which are associated with surcharge, cohesion and self-weight of soils respectively, were presented. A great number of analysis calculations were carried out to obtain the relationship curves of the static and dynamic bearing capacity factors versus various calculation parameters. The curves can serve as the practical engineering design. The calculation results also show that when the values of horizontal and vertical seismic coefficients are 0.2, the dynamic bearing capacity factors Nqd, Ncd and Nγd, in which the effects of intermediate principal stress are taken into consideration, increase by 4%?42%, 3%?27% and 34%?57%, respectively.     

Asymptotic analysis of weakly nonlinear and forced oscillations

The restriction ofK-B averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillationu″+ω ₀ ² u=εkcosωt−εu ³ is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show thatK-B method will break down whena andθ in the zeroth solution of above eqation are not slowly varying functions of timet. The stationary solution of weakly nonlinear oscillation,u″+ω ₀ ² u=εkcosω(ε)t-εu ³ is also analysed. Synopsis of the author Chen Feng, associated professor, born in October 1948, worked on experimental fracture mechanics in Sweden from 1990 to 1995 as a visiting scholar. Major research fields include perturbation and weight function method and its application, experimental mechanics. currently interested in rock fracture mechanics.     

Effects of microstructures on the deformation and fracture behaviors of TiAl-based alloys

The fracture toughnessK _Ic, the tensile deformation and fracture behaviors of different microstructures ofγ-TiAl based alloy, Ti-33Al-3Cr-0.5Mo] were studied at room temperature. It is found that theK _Ic value is lower in the duplex microstructure, and increases with the increase of vol pct of the lamellar microstructure, and that the full lamellar has the highestK _Ic value. Cleavage was the dominant fracture mechanism in the duplex microstructure material. In contrast, for the full lamellar microstructure the high anisotropy of deformation and the large strain discontinuity at grain boundaries resulting in decohesion of grain boundaries are the main fracture processes. Project supported by the National Natural Science Foundation of China and National Advanced Materials Committee of China Synopsis of the first author Chen Xiaoqun, associated professor, born in Jan. 1965, current research fields: physical metallurgy of high-temperature structural intermetallic compounds.