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.     

Microscopic characteristics of different fracture modes of brittle rock

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

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     

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.     

Dynamic Mode Ⅱ fracture 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 Mode Ⅱ fracture toughness K_(ⅡC)of rocks under a triaxial stress state.However, the method for determining the dynamic K_(ⅡC)of 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 K_(ⅡC)of Fangshan marble(FM) subjected to different hydrostatic pressures through a triaxial dynamic testing system. The formula for calculating the dynamic K_(ⅡC)of 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 K_(ⅡC)of FM increases as the loading rate. In addition, at a given loading rate the dynamic rock K_(ⅡC)is barely affected by hydrostatic pressures. Another important observation is that the dynamic fracture energy of FM enhances with loading rates and hydrostatic pressures.     

Influence of interfacial strength on the fracture toughness of glass-ceramic matrix composites

Nine kinds of glass-ceramic matrix composites with different compositions and interfacial strength (τ _s) were prepared. The influence of τ _s on the fracture toughness(K _1c) of composites was studied. It was discoved that, for the system no chemical reaction taking place at the interface, K _1c increased proportionally with τ _s increasing at the first stage, then decreased when τ _s reached a certain value. According to this result, a model of relationship between τ _s, thermal mismatch (Δα _r) and K _1c was built up. If a chemical reaction took place and a new phase was formed in the interface, the K _1c of composite was effected by the combination of τ _s, chemical bonding, radial interfacial stress and other factors. Project supported by the National Natural Science Foundation of China Synopsis of the first author Wang Lingsen, professor, born in 1938, current research field: special ceramic and ceramic matrix composite, etc.     

Viscoelastic properties of monodisperse spherical silica suspension

The viscoelastic properties of the suspension of monodisperse spherical silica produced by hydrolysis of tetraethoxysilane in alcohol solvent with ammonia as a catalyst in polyethylene glycol (PEG) were studied. The results show that the SiO2/PEG suspension possesses the reversible shear thinning and shear thickening behaviors. In the shear thinning region, the loss modulus (G″) almost remains unchanged, whereas the storage modulus (G′) decreases. In the shear thickening region, G″ and G′ increase for the formation of the "clusters". The larger G″ over G′ in all the stress studied shows that the system mainly possesses the viscous property, and that the energy dissipated(Ed) is larger than that stored. Ed of this suspension is proportional to the maximum strain (γmax) rising with the exponent of 1.92 under low shear stress; however, in the shear thickening region, Ed is proportional to γmax rising with the exponent of 5.00.     

A MIXED METHOD OF DETERMINING THETHERMAL STRESS FOR COLD ROLLER

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

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

Ｄｅｔｅｒｍｉｎａｔｉｏｎｏｆｆｒａｃｔｕｒｅｔｏｕｇｈｎｅｓｏｆｂｒｉｔｌｅｍａｔｅｒｉａｌｓｉｓｏｆｇｒｅａｔｉｍｐｏｒｔａｎｃｅｉｎｍｉｎｉｎｇａｎｄｇｅｏｌｏｇｉｃａｌｅｎｇｉｎｅｒｉｎｇ．Ａｖａｒｉｅｔｙｏｆｓｐｅｃｉｍｅｎｇｅｏｍｅｔ...     

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…     

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

Ｖａｒｉｏｕｓｍｏｄｅ－Ⅰｉｎｖｅｓｔｉｇａｔｉｏｎｓｉｎｔｈｅｔｈｅｏｒｙｏｆｌｉｎｅａｒｅｌａｓｔｉｃｆｒａｃｔｕｒｅｍｅｃｈａｎｉｃｓａｒｅｉｍｐｏｒｔａｎｔｉｎｄｅｔｅｒｍｉｎｉｎｇｔｈｅｆｒａｃｔｕｒｅｃｏｎｓｔａｎｔｓ．Ｔｏａｎａｌｙｓｅ...     

确定现代陶瓷材料断裂韧度的人字形裂纹法

人字形裂纹法是测量脆性材料平面应变断裂韧度K_1值最有效的方法。试验期间,裂纹在人字形切口的端部形成,随着载荷的增加而稳定地扩展。人字形切口法的优点是在加载试验的早期阶段就自然形成了一个锐型裂纹,而不再需要制作预裂纹。对于特定的试样和裂口几何形状,最大荷载与裂纹长度有关,而与材料无关。用此最大荷载可以确定断裂韧度,而不再需要测量裂纹的长度。     

A composite material model for investigation of micro-fracture mechanism of brittle rock subjected to uniaxial compression

Ｓｔｕｄｙｏｎｔｈｅｒｏｃｋｆａｉｌｕｒｅｐｒｏｃｅｓｓｆｒｏｍｃｒａｃｋｉｎｉｔｉａｔｉｏｎ ,ｐｒｏｐａｇａｔｉｏｎｔｏｃｏａｌｅｓｃｅｎｃｅｉｓｖｅｒｙｉｍ ｐｏｒｔａｎｔｔｏｕｎｄｅｒｓｔａｎｄｔｈｅｆｒａｃｔｕｒｅｍｅｃｈａｎｉｓｍｏｆｂｒｉｔｔｌｅｒｏｃｋｕｎｄｅｒｕｎｉａｘｉａｌｃｏｍｐｒｅｓｓｉｏｎ .Ｍａｎｙｒｅ ｓｅａｒｃｈｅｒｓｔａｃｋｌｅｄｔｈｉｓｐｒｏｂｌｅｍａｔｔｈｅｍａｃｒｏｓｔｒｕ ｃｔｕｒｅｌｅｖｅｌ.ＨｏｒｉｉａｎｄＮｅｍａｔ Ｎａｓｓｅｒ[1,2 ] ｉｎｖｅｓｔｉｇａ ｔ…     

Finite element and experimental analysis of Vickers indentation testing on Al2O3 with diamond-like carbon coating

Numerical simulation and experimental study of the Vickers indentation testing of the Al₂O₃ ceramic coated by diamond-like carbon (DLC) layer were conducted. The numerical analysis was implemented by a two-dimensional finite element (FE) axis symmetry model. FE analysis results gave insight into the fracture mechanism of DLC films coated on brittle ceramic (Al₂O₃) substrates. The maximum principal stress field was used to locate the most expected area for crack formation and propagation during the Vickers indentation testing. The results show that the median crack initiates in the interface under indenter, before ring crack occurs as the indenter presses down. Finally, the plastic deformation appears when the indenter penetrates into the substrate. The thicker DLC coating increases the Vickers hardness and fracture toughness.     

土石坝有限元分析中土体卸载时计算方法分析

对糯扎渡心墙堆石坝进行了三维有限元计算,对比分析两种常用于邓肯E-B模型的加卸载准则以及回弹模量取值对土石坝应力变形的影响。结果表明:大坝施工过程中,基于加载函数的加卸载准则(简称准则1)判断的卸载回弹区域一直较大;准则1下数值计算所得的坝体位移较小,仅为采用基于应力水平s与偏应力(σ_1-σ_3)的加卸载准则(简称准则2)时计算位移的一半左右,加卸载准则的选取对坝体应力影响较小;监测数据表明糯扎渡大坝采用准则2时计算位移更为准确,在准则2下回弹模量取值对大坝应力变形的影响主要表现为满蓄期坝体水流向位移随回弹模量的增大而减小。     

正交各向异性弹塑性幂硬化材料Ⅲ型静止裂纹的尖端场

本文采用Hill弹塑性理论.合出正交各向异性材料Ⅲ型静止裂纹的尖端场,其结果表明:在裂纹尖端附近各向异性材料的应力应变奇异性与各向同性材料的结果相同.但它们的幅度受各向异性的影响.通过数值计算可以清楚地看出这种影响的结果并根据这些理论结果给出了合理的断裂准则.     

Maximum twin shear stress factor criterion for sliding mode fracture initiation

1　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｐｒｅｓｅｎｔｍｉｘｅｄｍｏｄｅｆｒａｃｔｕｒｅｃｒｉｔｅｒｉａ ,ｆｏｒｅｘａｍｐｌｅ,ｔｈｅｍａｘｉｍｕｍｃｉｒｃｕｍｆｅｒｅｎｔｉａｌｔｅｎｓｉｌｅｓｔｒｅｓｓｃｒｉｔｅｒｉｏｎ[1] ,ｔｈｅｍａｘｉｍｕｍｅｎｅｒｇｙｒｅ     

TC4/ZQSn10-10扩散连接接头残余应力的数值模拟

对TC4/ZQSn10-10异种材料扩散连接接头处的残余应力分布进行了有限元模拟,并结合组织和应力分布讨论了接头的断裂原因。结果表明,TC4/ZQSn10-10接头的最大残余应力出现在金属间化合物Cu3Ti2上,导致裂纹在Cu3Ti2上萌生;最大剪应力也出现在Cu3Ti2上,最大剪应力的存在使裂纹得到扩展,最终导致接头断裂。通过填加中间层Cu可以缓解接头处的应力分布,使接头强度达到192 MPa,相当于铜合金母材强度的80%以上。     

分域边界元法双映射奇异元计算应力强度因子

边界单元法是一种很有效的数值计算方法,目前在很多工程领域的数值分析中都有了广泛的应用,并取得了很好的效果.用它来求解裂纹尖端的应力强度因子就是这种方法在断裂力学中非常成功而有效的应用.文中简单介绍线性单元的分域边界单元法的相关公式,并引入双映射奇异单元,分析了带单边斜裂纹的单向拉伸板的应力强度因子.计算的结果与其他解比较表明:这种方法效果很好,有较高的计算精度.