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.     

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.     

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

Ｖａｒｉｏｕｓｍｏｄｅ－Ⅰｉｎｖｅｓｔｉｇａｔｉｏｎｓｉｎｔｈｅｔｈｅｏｒｙｏｆｌｉｎｅａｒｅｌａｓｔｉｃｆｒａｃｔｕｒｅｍｅｃｈａｎｉｃｓａｒｅｉｍｐｏｒｔａｎｔｉｎｄｅｔｅｒｍｉｎｉｎｇｔｈｅｆｒａｃｔｕｒｅｃｏｎｓｔａｎｔｓ．Ｔｏａｎａｌｙｓｅ...     

Failure mode and strength anisotropic characteristic of stratified rock mass under uniaxial compressive situation

A stratified rock mass model was founded by FLAC^3D. The failure mode and anisotropic characteristic of strength for stratified rock mass were analyzed. The analysis results show that the numerical simulation can visually reflect the failure modes of rock samples under different inclination angles β of structural plane. The stiffness of rock sample before peak strength changes in the compressive procedure. With the increase of β, the compressive strength σ _c of rock sample decreases firstly and then increases; when β is in the range of 20°–30° and 80°–90°, σ _c has the largest sensitivity to β; while β falls in the range of 30°–70°, σ _c varies little. When ϕ _j <β<90° (β _j is friction angle of structure plane), the results obtained from numerical simulation and theoretical analysis are in almost the same values; while β⩽ ϕ _j or β=90°, they are in great different values. The results obtained from theoretical analysis are obvious larger than those from numerical simulation; and the results from numerical simulation can reflect the difference of compressive strength of rock samples for the two situations of β⩾ ϕ _j and β=90°, which is in more accordance with the real situation. Foundation item: Project (50099620) supported by the National Natural Science Foundation of China     

A MIXED METHOD OF DETERMINING THETHERMAL STRESS FOR COLD ROLLER

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

A simple method for determining independent fracture toughness and tensile strength of rock

This paper develops a model that only requires two sets of small-size rock specimens with the ratio of the structural geometry parameter maximum to minimum a_e,max:a_e,min ≥ 3:1 to determine the rock fracture and strength parameters without size effect and predict the actual structural performance of rock. Regardless of three-point-bending, four-point-bending, or a combination of the above two specimen types, fracture toughness K_IC and tensile strength f_t of rock were determined using only two sets of specimens with a_e,max:a_e,min ≥ 3:1. The values K_IC and f_t were consistent with those determined using multiple sets of specimens. The full structural failure curve constructed by two sets of small-size specimens with a_e,max:a_e,min ≥ 3:1 can accurately predict large-size specimens fracture failure, and ±10% upper and lower limits of the curve can encompass the test results of large-size specimens. The peak load prediction curve was constructed by two sets of specimens with a_e,max:a_e,min ≥ 3:1, and ±15% upper and lower limits of the peak load prediction curve can cover the small-size specimen tests data. The model and method proposed in this paper require only two sets of small-size specimens, and their selection is unaffected by the specimen type, geometry, and initial crack length.     

Ascertainment of the hybridization states of Fe atoms in austenite and martensite

Based on Yu Ruihuang's theory of electron structure calculation, applying the boundary condition that "the electron density of the contacting surface between atoms must be continuous" advanced by Cheng Kaijia, the hybridization states of Fec and Fef atoms in C-containing structure unit of austenite and FeⅠ, FeⅡ and FeⅢ atoms in C-containing unit of martensite are ascertained. The hybrid levels of Fec and Fef atoms in austenite are 13 and 14, respectively; and those of FeⅠ , FeⅡ and FeⅢ atoms are 12, 10 and 9, respectively. When the C content is low, the 11th, 10th and 9th levels are also the probable atom, state in martensite.     

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     

Microscopic characteristics of different fracture modes of brittle rock

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

Relationship between attachment probability and surface energy in adhesion process of gold particles to oil-carbon agglomerates

1　INTRODUCTIONInflotationfield ,someattentionshavebeenpaidtomodelingtheprocessofflotationinordertoobtainadeepunderstandingofhowamineralparticleisat tachedtoabubble .Schulze[1] analyzedtheelementaryprocessesofflotationintermsofphysico chemistry .Anfrunsetal[2 ] studiedthebubble particleattachmentexperimentallyinthecaseofpotentialflow .Solarietal[3] investigatedtheeffectofbubblesizesonadhesionprobability .Polatetal[4 ] estimatedthetruedistribu tionofflotationrateconstantsforafirst orderkin…     

High temperature plastic deformation behavior of non-oriented electrical steel

High temperature plastic deformation behavior of non-orientated electrical steel was investigated by Gleeble 1500 thermo-mechanical simulator at strain rate of 0.01−10 s⁻¹ and high temperature of 500–1 200 °C. The stress level factor (a), stress exponent (n), structural factor (A) and activation energy (Q) of high temperature plastic deformation process of non-orientated electrical steel in different temperature ranges were calculated by the Arrhenius model. The results show that, with dynamic elevation of deformation temperature, phase transformation from α-Fe to γ-Fe takes place simultaneously during plastic deformation, dynamic recovery and dynamic recrystallization process, leading to an irregular change of the steady flow stress. For high temperature plastic deformation between 500 and 800°C, the calculated values of a, n, A, and Q are 0.039 0 MPa⁻¹, 7.93, 1.9×10¹⁸ s⁻¹, and 334.8 kJ/mol, respectively, and for high temperature plastic deformation between 1 050 and 1 200 °C, the calculated values of a, n, A, and Q are 0.125 8 MPa⁻¹, 5.29, 1.0×10²⁸ s⁻¹, and 769.9 kJ/mol, respectively. Foundation item: Project(2005038560) supported by the Postdoctoral Foundation of China; Project(05GK1002-2) supported by Key Program of Hunan Province     

Flow stress behavior of Cu13Zn alloy deformed at elevated temperature

Ｃｏｎｓｔｉｔｕｔｉｖｅｍｏｄｅｌｉｓａｍａｔｈｅｍａｔｉｃａｌｒｅｐｒｅｓｅｎｔａｔｉｏｎｏｆｔｈｅｄｅｆｏｒｍａｔｉｏｎｒｅｓｐｏｎｓｅｏｆａｍａｔｅｒｉａｌｔｏｅｘｔｅｒｎａｌｌｙａｐ ｐｌｉｅｄｌｏａｄｉｎｇ ,ｉｎｃｌｕｄｉｎｇｅｎｖｉｒｏｎｍｅｎｔａｌｆａｃｔｏｒｓ .Ｔｈｅｐｒｅ ｃｉｓｅｋｎｏｗｌｅｄｇｅｏｆｔｈｅｃｏｎｓｔｉｔｕｔｉｖｅｂｅｈａｖｉｏｒｏｆｔｈｅｍａｔｅｒｉａｌｉｓｔｈｅｆｏｕｎｄａｔｉｏｎｏｆｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｔｅｃｈｎｏｌｏｇｙｏｆｍａｔｅｒｉ…     

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.     

The Effect of Bi2O3 on the Structure and Microwave Dielectric Properties of Ba6-3xNd8＋2xTi18O54 System（x=2/3）

The structures and dielectric properties of Ba6-3xNd8＋2xTi18O54 system（x=2/3） doped with different contents of Bi2O3, whose final molecular formula is Ba6-3x（Nd1-yBiy）8＋2xTi18O54 were investigated. It is indicated that the dielectric constant increases greatly whereas Q value（f0=4 GHz） decreases with the increase of Bi2O3 content. However, the temperature coefficient could be controlled below 0±30×10^-6/℃ in the experiment. These phenomena are related to the appearance of a new phase, Bi4Ti3O12, which has high dielectric constant. Also, that Bi^3＋（0.13 nm） substitutes for Nd^3＋（0.099 5 nm） will increase the unit cell volume, which will lead to the enlargement of the octahedron B site occupied by Ti^4＋. So the spontaneous polarization of Ti^4＋ ions will be strengthened. Besides, Bi^3＋ will fill up some vacancies which Ba^2＋ or Nd^3＋ ions leave in two A1 sites and four A2 sites. More positive ions polarize, which also contributes to higher dielectric constant. The samples got with the optimium properties are sintered at 1 200 ℃ for 4 h, when y=0.25, ε≈110, Q≈5 400（f0=4 GHz）, TCC=-4.7×10^-6/℃; When y=0.3, ε≈120, Q≈5 000（f0=4 GHz）, TCC=-24×10^-6/℃.     

HYDROPHOBICITY－HYDROPHILICITY BALANCE RELATIONSHIPSFORCOLLECTORLESSFLOTATIONOFSULPHIDEMINERALS

ＨＹＤＲＯＰＨＯＢＩＣＩＴＹ－ＨＹＤＲＯＰＨＩＬＩＣＩＴＹＢＡＬＡＮＣＥＲＥＬＡＴＩＯＮＳＨＩＰＳＦＯＲＣＯＬＬＥＣＴＯＲＬＥＳＳＦＬＯＴＡＴＩＯＮＯＦＳＵＬＰＨＩＤＥＭＩＮＥＲＡＬＳＨＹＤＲＯＰＨＯＢＩＣＩＴＹ－ＨＹＤＲＯＰＨＩＬＩＣＩＴＹＢＡＬＡ...     

Low-temperature sintering and microwave dielectric properties of Li2MgTi3O8 ceramics doped with BaCu（B2O5）

The influences of BaCu(B₂O₅) (BCB) addition on sintering, microstructure and microwave dielectric properties of Li₂MgTi₃O₈ ceramics were investigated using X-ray diffractometry, scanning electron microscopy and microwave dielectric measurements. The experimental results show that a small amount of BaCu(B₂O₅) addition can effectively reduce the sintering temperature to 900 °C, and induce only a limited degradation of the microwave dielectric properties. Typically, the best microwave dielectric properties of ɛ _r=24.5, Q×f =24 622 GHz, τ _f=4.2×10⁻⁶ °C⁻¹ are obtained for 1.0% BCB-doped Li₂MgTi₃O₈ ceramics sintered at 900 °C for 3 h. The BCB-doped Li₂MgTi₃O₈ ceramics can be compatible with Ag electrode, which may be a strong candidate for low temperature co-fired ceramics applications.     

Phase structure and electrical properties of La<Subscript>2</Subscript>O<Subscript>3</Subscript>-doped BiInO<Subscript>3</Subscript>-PbTiO<Subscript>3</Subscript> ceramics with high curie temperature

The phase structure and electrical properties of pure and La2O3-doped Bi-InO3-PbTiO3 （BI-PT） ceramics were studied respectively. In （1 -x）BI-xPT （x=0.72-0.80） ceramics, the stability of tetragonal phase increased with increasing x, and pure perovskite structure was obtained for x=-0.80 ceramics. The phase transition temperature range was between 575 ℃ and 600 ℃ for x=0.72-0.80 ceramics, higher than that of PT （-490 ℃）. The c/a ratio almost linearly decreased with increasing La2O3 content in x-0.80 ceramics. It is believed that Pb^2＋ vacancies were formed by La^3＋ substituting Pb^2＋ in La2O3-doped BI-PT ceramics. Tc shifted to lower temperature by 30 ℃/mol% La2O3. The maximum dielectric constant 8557 around 559 ℃ was exhibited in 0.5mol%-doped BI-0.80PT ceramics. La2O3-doped ceramics could be poled resulting from decreasing of c/a ratio and improving of dielectric loss and resistivity. The maximum piezoelectric coefficient d33 was 12 pC/N for 2mol%-doped BI-0.80PT ceramics.     

Alteration of diaspore by thermal treatment

Diaspore (α-AlOOH) was heated at various temperatures from 300 to 1000 ℃ for 2 h. The alteration of diaspore by thermal treatment was investigated by differential thermal analysis, thermogravimetric analysis and X-ray diffraction. The mechanism of thermal decomposition of diaspore was discussed according to the Coats-Redfern equation. It is found that after thermal treatment at 500 ℃, diaspore is transformed entirely to corundum (α-Al2O3). Combined with the mass loss ratio obtained from the thermogravimetric analysis data, the activation energies for the thermal treatment of diaspore are calculated as Ea=10.4 kJ/mol below 400 ℃ and Eb=47.5 kJ/mol above 400 ℃, respectively, which is directly related to the structural alteration of diaspore during the thermal treatment. The results indicate that the thermal decomposition of diaspore is conducted primarily by means of an interfacial reaction.