Two-parameter fracture criterion (Kρ,c-Tef,c) based on notch fracture mechanics

A two-parameter fracture criterion has been proposed to predict fracture conditions of notched components. This criterion includes the critical notch stress intensity factor K _ρ,c , which represents fracture toughness of a material with a notch of radius ρ, and the effective T-stress. The effective T-stress T _ef has been estimated as the average value of the T-stress distribution in the region ahead of the notch tip at the effective distance X _ef . These parameters were derived from the volumetric method of notch fracture mechanics. The results of numerical T _ef,c -stress estimation are compared to the T _ef,c -stress results obtained from experimental analysis. The material failure curve or master curve K _ρ,c = f(T _ef,c ) has been established as a result of the notched specimen tests. A large T _ef,c range was covered from −0.80 σ _Y to +0.19 σ _Y using SENT, CT, RT (roman tile) and DCB specimens. It was shown that the notch fracture toughness is a linear decreasing function of the T _ef,c -stress. The use of the material failure curve to predict fracture conditions was demonstrated on gas pipes with the surface notch.     

T-Stress solutions for a semi-elliptical axial surface crack in a cylinder subjected to mode-I non-uniform stress distributions

This paper presents the T-stress solutions (T₁₁ and T₃₃) for semi-elliptical axial surface cracks in a cylinder subjected to mode-I non-uniform stress on the crack surface. Two cylindrical geometries with inner radius (R_i) to wall thickness (t) ratios R_i/t = 5 and 10 were considered. The T-stresses were applied along the crack front for normalized crack depth values a/t of 0.2, 0.4 and 0.5 and aspect ratios a/c of 0.2, 0.4, 0.6 and 1.0. Three stress distribution; uniform, linear and parabolic were applied to the crack face. In addition to these solutions, concrete formulation of the superposition principle is given for the T₃₃-stress, which is known as an elastic parameter that describes the out-of-plane crack tip constraint effect. Then, the validity of the formulation was shown through application of our T-stress solutions to the problem of an axial semi-elliptical surface crack in a cylinder subjected to internal pressure, and checking that the principle of superposition holds for the problem.     

Three-dimensional stress state around quarter-elliptical corner cracks in elastic plates subjected to uniform tension loading

Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor T_z around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of T_z are studied in the forward section (0° ? θ ? 90°) of the corner cracks with aspect ratios a/c of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. In the normal plane of the crack front line, T_z drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones (T_z > 0) exist within a radial distance r/a of about 4.6-0.7 for a/c = 0.2-1.0 along the crack front, despite the stress-free boundary conditions far away. At the same radial distance along the crack front in the 3D zones, T_z increases from zero on one free surface to a peak value in the interior, and then decreases to zero on another free surface. The distributions of T_z near the corner points are also discussed. Empirical formulae describing the 3D distributions of T_z are obtained by fitting the numerical results, which prevail with a sufficient accuracy in the valid range of 0.2 ? a/c ? 1.0 and 0° ? θ ? 90° except very near the free surfaces where T_z is extremely low. Combined with the K-T solution, the transition of approximate plane-stress state near the surfaces to plane-strain state in the interior can be characterized more accurately.     

Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates

Three-dimensional finite element analyses have been conducted to calculate the elastic T-stress for semi-elliptical surface cracks in finite thickness plates. Far-field tension and bending loads were considered. The analysis procedures and results were verified using both exact solutions and approximate solutions. The T-stress solutions are presented along the crack front for cracks with a/t values of 0.2, 0.4, 0.6 or 0.8 and a/c values of 0.2, 0.4, 0.6 or 1.0. Based on the present finite element calculations for T-stress, empirical equations for the T-stress at three locations: the deepest, the surface and the middle points of the crack front under tension or bending are presented. The numerical results are approximated by empirical formulae fitted with an accuracy of 1% or better. They are valid for 0.2?a/c?1 and 0?a/t?0.8. These T-stress results together with the corresponding K or J values for surface cracks are suitable for the analysis of constraint effects for surface cracked components.     

Substitution Effect of Ba for Sr on Superconductivity in?the?(Pb0.75P0.25)(Sr2?xBax)(Y0.4Ca0.6)Cu2Oz System

The Pb-based 1212 compounds containing phosphorus were already discovered by us in the (Pb,P)Sr₂(Y,Ca)Cu₂O _z system. Among the almost-single phase samples, a sample with the nominal composition of (Pb_0.75P_0.25)Sr₂(Y_0.4Ca_0.6)Cu₂O _z was a superconductor with the highest T _c of 38 K in the system. Recently, we have been investigating on substitution effect of Ba for Sr on superconductivity in the (Pb_0.75P_0.25)(Sr_2−x Ba _x )(Y_0.4Ca_0.6)Cu₂O _z system. As a result, it is found that the almost–single 1212 phase samples are obtained in the composition area of 0.0≤x≤0.4. In this area, with increase of x, the lattice parameters a,c and the cell volume V are found to be gradually increasing. This finding can be considered to show that larger Ba²⁺ ions certainly occupied the Sr-sites in the sample. However, we obtain such interesting results as that the T _c value is not so enhanced by the substitution in comparison with that of the sample of x=0.0, and that the maximum value of T _c was 40 K for x=0.2 and 0.3 at the best.     

Superconducting transition temperatures in the Ru-1232 system, RuSr2(Gd1? x Ln x Ce1.8Sr0.2)Cu2O z (Ln = Sm, Dy, and Ho)

We have investigated effects of the lanthanide element Ln and the composition changes on the superconducting transition temperatureT _c in the Ru-1232 system, RuSr₂(Gd_1−x Ln _x Ce_1.8Sr_0.2)Cu₂O _z (Ln = Sm, Dy, and Ho). At first, in the case of the samples with Ln = Sm among almost the single 1232 phase samples, the values of the superconducting onset temperatureT _co are almost the same forx=0.00−0.15, and each of the lattice parametersa andc is almost constant. While, in each of the cases of the samples with Ln = Dy and Ho, the sample withx=0.05 shows the maximum values for both the superconducting onset temperatureT _co and the zero resistivity temperatureT _cz. Especially for the sample with Ln = Dy, the values ofT _co andT _cz are 18.5 and 6.5 K, respectively. These are higher than those of the mother sample of RuSr₂(GdCe_1.8Sr_0.2)Cu₂O _z . Moreover, from variations ofT _co, lattice parameters ofa andc in the RuSr₂(Gd_1−x Dy _x Ce_1.8Sr_0.2)Cu₂O _z system as a function of Dy contentx, the relationship between the superconducting transition temperature and the lattice parameters in the present system are investigated.     

Kondo effect and impurity interactions in the resistivity of diluteZnMn alloys

The electrical resistivity of diluteZnMn alloys (c=1.7–2400 ppm Mn) has been investigated in the temperature range from 0.05 to 14 K. For the most dilute sample, single-impurity Kondo behavior is found, well described by the Hamann formula withT _K=0.9 K,S=3/2. ForT<50 mK, aT ² law with _R =0.3 K is expected. In the dilute limit the Kondo slope is –(1/c)d()/d(logT)=3.7±0.2 µ-cm/at % dec. In the more highly concentrated alloys, the slope decreases with increasing c and the lnT-like variation of the Kondo resistivity roughly terminates near a temperatureT _W(c),T _W being related to the average Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction strength between the Mn impurities. For 20 ppm c 1000 ppm, the resistivity slightly decreases at low temperatures and a broad resistivity maximum is observed atT _m (c), withT _m c ^0.7. ForT 2 _m, the resistivity dependence is linear inT, and for the most concentrated alloy aT ^3/2 orT ² dependence is measured at the lowest temperatures attainable. The investigation of the transition temperatureT _c (c) to superconductivity ofZnMn results in a critical concentrationc _cr=18 ppm Mn. The concentration dependence ofT _c below 0.3 K suggests the presence of the Kondo effect, although impurity interactions may also influenceT _c in this temperature range.Supported by Deutsche Forschungsgemeinschaft.     

Superconductivity of Ba1 ? xKxBiO3 (0.35 < x < 1) Synthesized by the High Pressure and High Temperature Technique

Ba_{1 – x} K _x BiO₃ (BKBO) samples with 0.35 < x < 1 were synthesized by the high pressure and high temperature technique. XRD analysis showed that the BKBO samples were single phase for the whole range of the potassium doping concentration. The change of superconducting transition temperature, T _c, as well as lattice parameters have been investigated upon doping concentration. As the K doping concentration (x) increases from x = 0.37, T _c decreases from 30.4 K to almost zero at x = 0.74. However, in some BKBO samples without including any barium in the starting composition (x = 1), which is denoted as KBO samples, superconductivity is observed with T _c as high as 9 K with partial substitutions of Bi at the K site. Depending on the synthesis condition of the KBO samples, T _c and lattice parameters were different from sample to sample. Compared with other superconducting bismuthates, the evolution of T _c by potassium doping in the cubic BKBO system is discussed in terms of its electronic band structure.     

Superconductivity and Ferromagnetism of the Ru-1232 Compounds in the (Ru1?xNbx)Sr2(GdCe1.8Sr0.2)Cu2Oz System

The Ru-1232 compounds have been synthesized in the (Ru_1–xNb _x )Sr₂(GdCe_1.8Sr_0.2)Cu₂O _z system, and effects of Nb substitution for Ru on superconductivity and ferromagnetism of the Ru-1232 compounds have been investigated. First, X-ray powder diffraction study shows that nearly the single 1232 phase samples can be obtained in the x composition range from 0.0 to 0.3. Then, from the electrical resistivity study, it is found that each of the samples shows resistivity dropping phenomenon at two temperatures of T _c ^l and T _c ^h, which originates from superconductivity of the Ru-1232 phase and the Ru-1222 one, respectively. Both of the starting temperatures are lowering with increasing Nb content x. Lastly, from the magnetic susceptibility study, it is found that superconducting transition temperature T _c is 20 K for the Ru-1232 sample with x = 0.0 and the ferromagnetic transition temperature T _m is about 90 K. This study also shows that both of the values of T _c and T _m become low with increasing x from 0.0 to 0.3.     

Stress intensity factor K and the elastic T-stress for corner cracks

The stress intensity factor K and the elastic T-stress for corner cracks have been determined using domain integral and interaction integral techniques. Both quarter-circular and tunnelled corner cracks have been considered. The results show that the stress intensity factor K maintains a minimum value at the mid-plane where the T-stress reaches its maximum, though negative, value in all cases. For quarter-circular corner cracks, the K solution agrees very well with Pickard's (1986) solution. Rapid loss of crack-front constraint near the free surfaces seems to be more evident as the crack grows deeper, although variation of the T-stress at the mid-plane remains small. Both K and T solutions are very sensitive to the crack front shape and crack tunnelling can substantially modify the K and T solutions. Values of the stress intensity factor K are raised along the crack front due to crack tunnelling, particularly for deep cracks. On the other hand, the difference in the T-stress near the free surfaces and at the mid-plane increases significantly with the increase of crack tunnelling. These results seem to be able to explain the well-observed experimental phenomena, such as the discrepancies of fatigue crack growth rate between CN (corner notch) and CT (compact tension) test pieces, and crack tunnelling in CN specimens under predominantly sustained load.     

Formation of the high-Tc phase in lead-doped Bi-Sr-Ca-Cu-O superconductors

The characteristics of Bi-Sr-Ca-Cu-O superconductors have been investigated as a function of the amount of Pb addition. The volume fraction of the high-T _c phase increases with increasing Pb addition up to x=0.3 in (Bi_1–xPb_x)₂Sr₂Ca₂Cu₃O_y and above that it decreases. The grain size is increased and density is decreased with increasing Pb addition, due to two-dimensional grain growth which results from formation of the high-T _c phase. The specimen with x=0.3 has a transition temperature of 104 K and high magnetic susceptibility due to the fact that most of the volume fraction is of the high-T _c phase. Pb addition cause formation of Ca₂PbO₄ as a secondary phase and it produces a partially melted liquid phase below the sintering temperature, which acts as a flux and promotes formation of the high-T _c phase.     

Effects of Mill Speed on Kinetic Breakage Parameters of Four Different Particulate Pumices

In this study, the effect of mill speed was investigated on different particulate pumice samples at batch grinding conditions based on a kinetic model. For this purpose, S _i and B _i,j equations were determined from the size distributions at different grinding times, and the model parameters (S _i , a _T , α, γ, and φ _j ) were compared for three different mill speed (fraction of mill critical speed; 65%, 75%, and 85%).

The effect of fraction of mill critical speed (φ_c) on the grinding for model parameter a _T found to be different for four different pumices. Additionally, in this study it was found that optimum grinding occurs at φ_c = 85% for all pumice samples, in contrast to the 75% of critical speed of the ball mill.     

Influence of sintering time and quenching on the formation of highT c phase

Influence of sintering time and quenching in Bi_{2 −x} Pb _x Ca₂Sr₂Cu₃O _y (x=0.0, 0.1, 0.2, 0.25, 0.3 and 0.4) samples have been studied by resistance and XRD measurements. In samples sintered at 850°C for 4 days,T _c(0) increases with Pb concentration.T _c(0) increased from 81 K forx=0.0 to 109 K inx=0.30 sample and then decreased. Increasing the sintering time to 10 days decreased theT _c Quenching further decreased theT _c(0). From X-ray diffraction patterns, the intensity peaks of low and highT _c phases have been measured. The addition of Pb promotes highT _c-phase. Sintering time, slow cooling and rapid quenching studies show that there is an optimum sintering time and cooling rate to produce a highT _c-phase.     

Temperature effects on quasi-static fracture of PMMA

The effect of temperature on the quasi-static fracture behaviour of PMMA is examined. It is found that the critical stress intensity factor, K ₁₀, at crack growth initiation decreases with temperature up to a certain critical temperature, T _c. Above T _c, K ₁₀ increases rapidly. The speeds with which slow crack growth could be maintained without transition to brittle fracture were found to be significantly higher at high temperatures.     

Effect of uniaxial stress on the superconducting transition temperature of NbSe2

The superconducting transition temperature T _c of 2H NbSe₂ was measured under uniaxial stress applied parallel to the crystal c axis. It was found that T _c decreases as the increasing applied compression, while it increases under hydrostatic pressure. It is concluded that T _c is strongly enhanced by the contractive strain within layers and is insensitive to the interlayer spacing.     

Isovalent Substitution and Heat Treatments Control of T c, Chain Oxygen Disorder and Structural Phase Transition in High T c Superconductors (Y1−x Nd x )SrBaCu3O6+z

We report here on the preparation, X-ray diffraction with Rietveld refinement, AC magnetic susceptibility measurements and effect of heat treatments in (Y_1?x Nd _x )SrBaCu₃O_6+z . Each sample was subject to two types of heat treatment: oxygen annealing [O] and argon annealing followed by oxygen annealing [AO]. For each x, the [AO] heat treatment increases the orthorhombicity ε=(b?a)/(b+a) (for 0≤x<1), T _c (for x>0.2) and the distance d[Cu(1)–(Sr/Ba)] (decrease T _c) for x<0.25 and decrease it (increase T _c) for x>0.25. When x increase from 0 to 1, ε decreases to 0 with transition from orthorhombic to tetragonal structure. ε[O] decreases with T _c[O]. However, T _c[AO] decreases with ε[AO] until x=0.2, increases for x=0.4 and after it decreases by 9.8 K to 77.2 K for x=1 [AO]. Remarkable correlations were observed between T _c(x) and the volume of the unit cell V(x); and between δT _c(x)=T _c[AO]?T _c[O] and δε(x). A combination of several factors such as decrease in d[Cu(1)–(Sr/Ba)]; increase in cationic and chain oxygen ordering; the number p _sh(x) of holes by Cu(2)–O₂ superconducting plans and in-phase purity for the [AO] samples may account for the observed data.     

T-stress solution for DCDC specimens

A finite element study is performed in order to determine the T-stress term for DCDC specimens with holes set off from the specimen centre line. In addition, mixed-mode stress intensity factors K_I and K_II are given and the biaxiality ratio β is computed from T and K_I. The T-stress results are fitted and presented in a simple relation.     

Effect of stress on the superconducting transition temperature of SrTiO3

The superconducting transition temperatures of several specimens of reduced SrTiO₃ and of Nb-doped SrTiO₃ have been investigated as functions of hydrostatic and uniaxial compressive stresses up to 1.8 kbars. Decreases inT _c as large as 0.12 K have been observed in specimens under hydrostatic pressure. Because of the lowT _c and small compressibility of SrTiO₃, (lnT _c)/P and (lnT _c)/(lnV) are orders of magnitude greater than the corresponding effects in elemental superconductors. The effect of uniaxial stress onT _c varied with the direction of stress. Compression along a [111] direction caused large decreases inT _c, while both small increases and small decreases inT _c have been observed for [100] compression. It is believed that the present results reveal the presence of a sensitive volume dependence in one or more of the parameters important to superconductivity in SrTiO₃, and that no significant electron-transfer effects occurred in the range of stresses of this experiment.     

Superconducting Transition Temperatures in the Ru-1232 System, RuSr2(Gd1?xLnxCe1.8Sr0.2)Cu2Oz (Ln = Sm, Dy, and Ho)

We have investigated effects of the lanthanide element Ln and the composition changes on the superconducting transition temperature T _c in the Ru-1232 system, RuSr₂(Gd_{1− x} Ln _x Ce_1.8Sr_0.2)Cu₂O _z (Ln = Sm, Dy, and Ho). At first, in the case of the samples with Ln = Sm among almost the single 1232 phase samples, the values of the superconducting onset temperature T _co are almost the same for x = 0.00–0.15, and each of the lattice parameters a and c is almost constant. While, in each of the cases of the samples with Ln = Dy and Ho, the sample with x = 0.05 shows the maximum values for both the superconducting onset temperature T _co and the zero resistivity temperature T _cz. Especially for the sample with Ln = Dy, the values of T _co and T _cz are 18.5 and 6.5 K, respectively. These are higher than those of the mother sample of RuSr₂(GdCe_1.8Sr_0.2)Cu₂O _z . Moreover, from variations of T _co, lattice parameters of a and c in the RuSr₂(Gd_{1− x} Dy _x Ce_1.8Sr_0.2)Cu₂O _z system as a function of Dy content x, the relationship between the superconducting transition temperature and the lattice parameters in the present system are investigated.