A curvilinear integral method for multiaxial fatigue life computing under non-proportional, arbitrary or random stressing

Some popular concepts for reducing three variable stress components σ_x(t), σ_y(t), τ_xy(t) to one equivalent amplitude spectrum, and the use of the linear damage accumulation hypothesis, have been evaluated as not fully correct when these components vary non-proportionally and arbitrarily. A different approach is suggested: computing damage accumulation by means of an integral directly on the non-radial arbitrary path, called the ‘trajectory’, described in the σ_x−σ_y plane when τ_xy(t) = 0, in the σ_x−τ_xy plane when σ_y(t) = 0, or in a special coordinate space where this trajectory is invariant of stress directions x, y. If the trajectory is random, it may be replaced by a statistical two-dimensional density of distribution. The integrand, called the R-function, is derived from various S−N fatigue curves under different determined loadings. Thus the traditional S−N function is replaced by the R-function for direct damage summation with differential analysis, which allows the loading to be arbitrary (non-cyclic, multiaxial and non-proportional). The method works by means of computer programs and is applicable to real structures.     

Optical transitions near the band edge in bulk CuInxGa1−xSe2 from ellipsometric measurements

From the analysis of the variation of optical absorption coefficient with incident photon energy between 0.8 and 2.6 eV, obtained from ellipsometric data, the energy E_G of the fundamental absorption edge and E_G′ of the forbidden direct transition for CuIn_xGa_1−xSe₂ alloys are estimated. The change in E_G and the spin-orbit splitting Δ_SO=E_G′−E_G with the composition x can be represented by parabolic expression of the form E_G(x)=E_G(0)+ax+bx² and Δ_SO(x)=Δ_SO(0)+a′x+b′x², respectively. b and b′ are called “bowing parameters”. Theoretical fit gives a=0.875 eV, b=0.198 eV, a′=0.341 eV and b′=−0.431 eV. The positive sign of b and negative sign of b′ are in agreement with the theoretical prediction of Wei and Zunger [Phys. Rev. B 39 (1989) 6279].     

Stress relaxation in the interface between creep particle and elastic matrix-strengthening mechanism

The effect of a power law creep particle on interface behavior between the particle and elastic matrix is investigated by stress analysis. Using the results obtained through the stress analysis, the forces due to interaction of an applied stress and stress concentration with an edge dislocation are determined. The direct interaction between the edge dislocation and the creeping particle is studied under fully relaxed stress conditions. Through the investigation the following results are derived. Stress relaxation in the interface can be caused by power law creep along or by diffusion, or a combination of both mechanisms. The degree of stress relaxation caused by diffusion can be defined in terms of the relaxation time for both boundary diffusion and volume diffusion. The amount of stress relaxation caused by the power law creep particle is characterized by the quantity ₂ which is a function of Γ₀ = 2(1/√3)^{1 + m} × (σ_∞/2μ)^m(σ₀/σ_∞t^m), where m is strain rate hardening exponent, σ_∞ is applied stress, μ is the shear modulus, σ₀ is the material constant of the power law creep particle, and t is elapsed time. The value ₂ = 1.0 corresponds to the fully relaxed condition and ₂ = −0.6 corresponds to the initial state. The time to reach a fully relaxed condition is very sensitive to the strain rate exponent, with the smaller m values leading to longer times. The stress state of complete relaxation in the elastic matrix is equivalent to the solution of a void in an elastic matrix superposed on the solution of positive surface traction on the void. This result is identical to that obtained by Srolovitz et al. [Acta. Metall.32, 1979 (1984)]. When the stress is completely relaxed in the particle, all stress components (σ_r, σ_θand σ_rθ) are relaxed, while in the matrix relaxations are observed only for σ_rand σ_θ. The critical resolved shear stress and critical stress to climb the dislocation in the neighborhood of the particle exceed the Orowan stress. Also, the particle attracts the dislocation. Therefore the strengthening of a power law creep particle in an elastic matrix is caused by the Orowan mechanism and by attraction of the dislocation.     

Chemical vapour deposition of molybdenum carbides: aspects of phase stability

Thin films of different molybdenum carbides (δ-MoC_1−x, γ′-MoC_1−x and Mo₂C) have been deposited from a gas mixture of MoCl₅/H₂/C₂H₄ at 800°C by CVD. The H₂ content in the vapour has a strong influence on the phase composition and microstructure. Typically, high H₂ contents lead to the formation of nanocrystalline δ-MoC_1−x films while coarse-grained γ′-MoC_1−x is formed with an H₂-free gas mixture. This phase has previously only been synthesized by carburization of Mo in a CO atmosphere and it has therefore been considered as an oxycarbide phase stabilized by the presence of oxygen in the lattice. Our results, however, show that γ′-MoC_1−x films containing only trace amounts of oxygen can be deposited by CVD. Stability calculations using a FP-LMTO method confirmed that the γ′-MoC_1−x phase is stabilized by oxygen but that the difference in energy between e.g. δ-MoC_0.75 and oxygen-free γ′-MoC_0.75 is small enough to allow the synthesis of the latter phase in the absence of kinetic constraints. Annealing experiments of metastable δ-MoC_1−x and γ′-MoC_1−x films showed two different reaction products suggesting that kinetic effects play an important role in the decomposition of these phases.     

Fractal properties of percolating film structures

We simulate nucleation and growth processes of thin films on the basis of the so-called rate equation approach allowing “atoms” to diffuse and rearrange whereby enhancing their co-ordination number. The resulting percolating structures are different from those obtained by the “pure” percolation model where “atomic diffusion” is not taken into account. However, the fractal properties for p = p_c are the same as for the percolation model with the fractal dimension of d_f = 1.896 and for random walks of d_w = 2.87. Moreover, d_f and d_w are independent on the diffusion time we choose for our simulations.     

Fracture-resistant ultralloys for space-power applications: Normal-spectral-emissivity and electron-emission studies of tungsten, rhenium, hafnium-carbide alloys at elevated temperatures

A series in this journal on high-temperature properties of “fracture-resistant ultralloys for space-power systems” preceded the present paper: the antecedent publications covered tungsten(W), rhenium(Re) alloys with and without thoria(ThO₂) (W, 23Re; W, 27Re; W, 30Re and W, 30Re, 1ThO₂). This paper reports radiative and thermionic effects of hafnium carbide(HfC) and Re variation in W alloys: normal spectral emissivity(ε_λ) is used in pyrometry to determine the true temperature of a surface. Effective work function (φ_e) is an important consideration in the selection of the electrode materials for high-temperature thermionic energy converters in space-power applications. The _0.535μ, ε_0.65μ and φ_e trends of W, Re, 0.35HfC with 5–20% Re were measured in the range of 1700–2500K. The results indicate that ε_λ decreases with increasing temperatures and Re contents. The presence of HfC produced higher ε_λ values than those of sintered materials with comparable W,Re alloy contents. The results also indicate that φ_e increases with rhenium contents. This can be explained as growth of the potential barrier at the metal, vacuum boundary associated with a volume effect—the decrease in the lattice constant of W.     

Computer simulation of martensitic textures

We consider a Ginzburg-Landau model free energy F(ε, e₁, e₂) for a (2D) martensitic transition, that provides a unified understanding of varied twin/tweed textures. Here F is a triple well potential in the rectangular strain (ε) order parameter and quadratic e₁², e₂² in the compressional and shear strains, respectively. Random compositional fluctuations η(r) (e.g. in an alloy) are gradient-coupled to ε, ˜ − ∑_rε(r)[(Δ_x² − Δ_y²)η(r)] in a “local-stress” model. We find that the compatibility condition (linking tensor components ε(r) and e₁(r), e₂(r)), together with local variations such as interfaces or η(r) fluctuations, can drive the formation of global elastic textures, through long-range and anisotropic effective ε-ε interactions. We have carried out extensive relaxational computer simulations using the time-dependent Ginzburg-Landau (TDGL) equation that supports our analytic work and shows the spontaneous formation of parallel twins, and chequer-board tweed. The observed microstructure in NiAl and Fe_xPd_{1 − x} alloys can be explained on the basis of our analysis and simulations.     

A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors K_I and K_II from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, σ_ox. A non-linear equation is developed which relates the stress field in terms of K_I, K_II, and σ_ox to the co-ordinates, r and θ, defining the location of a point on an isochromatic fringe of order N.

Four different approaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line θ = π and the K---N relation can be linearized and simplified, the classical approach in which two data points at (r_m, θ_m) are selected where r_m/θ = 0; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m (>3) arbitrarily located points are selected from the fringe field.

Except for the selected line approach, the method of solution involves an iteractive numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.

All four methods provide solutions to 0.1% providing that the input parameters r, θ, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3–5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and θ are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of K_I, K_II, and σ_ox determinations.     

Doping and electrical characteristics of in-situ heavily B-doped Si1−x−yGexCy films epitaxially grown using ultraclean LPCVD

Doping and electrical characteristics of in-situ heavily B-doped Si_1−x−yGe_xC_y (0.22<x<0.6, 0<y<0.02) films epitaxially grown on Si(100) were investigated. The epitaxial growth was carried out at 550°C in a SiH₄–GeH₄–CH₃SiH₃–B₂H₆–H₂ gas mixture using an ultraclean hot-wall low-pressure chemical vapor deposition (LPCVD) system. It was found that the deposition rate increased with increasing GeH₄ partial pressure, and only at high GeH₄ partial pressure did it decrease with increasing B₂H₆ as well as CH₃SiH₃ partial pressures. With the B₂H₆ addition, the Ge and C fractions scarcely changed and the B concentration (C_B) increased proportionally. The C fraction increased proportionally with increasing CH₃SiH₃ partial pressures. These results can be explained by the modified Langmuir-type adsorption and reaction scheme. In B-doped Si_1−x−yGe_xC_y with y=0.0054 or below, the carrier concentration was nearly equal to C_B up to approximately 2×10²⁰ cm⁻³ and was saturated at approximately 5×10²⁰ cm⁻³, regardless of the Ge fraction. The B-doped Si_1−x−yGe_xC_y with high Ge and C fractions contained some electrically inactive B even at the lower C_B region. Resistivity measurements show that the existence of C in the film enhances alloy scattering. The discrepancy between the observed lattice constant and the calculated value at the higher Ge and C fraction suggests that the B and C atoms exist at the interstitial site more preferentially.     

The neutron EDM experiment at the ILL

The latest-generation neutron electric dipole moment (EDM) experiment has been collecting data at the ILL since 1996. It uses a “cohabiting” atomic-mercury magnetometer to measure and compensate for the magnetic field fluctuations that were the principal source of systematic errors in previous experiments. The first results, which are soon to be published, essentially verify the existing limit on the dipole moment d_n; however, this new measurement is clearly limited by statistical rather than systematic uncertainties.     

Inference of critical cod from Charpy V test result

Correlation between the Charpy absorbed energy and critical COD is investigated to obtain a useful method for estimating critical COD from Charpy V data. The round bar tension test, Charpy V-notch test and static 3-point bend test with fatigue notched specimen are carried out using mild steel, 785 MPa grade high strength steel and A5083 aluminum alloy. Correlation is found between W'_c/σ_Y and δ_c as well as between EW'_c/σ_Y² and Eδ_c/σ_Y, where W'_c is the Charpy absorbed energy obtained by considering temperature difference between the Charpy transition temperature and COD transition temperature. The symbols σ_Y, δ_c and E are yield strength, critical COD and Young's modulus, respectively. The correlations are established for various kinds of metals and over a wide temperature range including not only upper shelf range but also the transition range.     

Some problems in the J-integral

For a blunt crack the j-integral is path dependent on contours which are very close to the crack tip even for elastic material. Using the incremental J-integral theory we introduce a new parameter J_t, characterizing the behavior of a crack tip and prove that the J-integral is almost path independent on contours whose radii are greater than several COD if σ_ij,1Δε_ij — ε_ijΔσ_ij = 0 in plastic regions for elasto-plastic material.     

Dielectric and piezoelectric properties of sol–gel derived Ca doped PbTiO3

Synthesis of Ca doped PbTiO₃ powder by a chemically derived sol–gel process is described. Crystallization characteristics of different compositions Pb_1−xCa_xTiO₃ (PCT) with varying calcium (Ca) content in the range x = 0–0.45 has been investigated by DTA/TGA, X-ray diffraction and scanning electron microscopy. The crystallization temperature is found to decrease with increasing calcium content. X-ray diffraction reveals a tetragonal structure for PCT compositions with x ≤ 0.35, and a cubic structure for x = 0.45. Dielectric properties on sintered ceramics prepared with fine sol–gel derived powders have been measured. The dielectric constant is found to increase with increasing Ca content, and the dielectric loss decreases continuously. Sol–gel derived Pb_1−xCa_xTiO₃ ceramics with x = 0.45 after poling exhibit infinite electromechanical anisotropy (k_t/k_p) with a high d₃₃ = 80 pC/N, ′ = 298 and low dielectric loss (tan δ = 0.0041).     

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement.

We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σ_r (b) = 0 (σ_r = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σ_r (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σ_r (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σ_r (a) = const., R =−σ_r (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σ_r (a) over a range o ≤ a ≤ a_r, (where a_r, the upper bound of the range, is calibrated from computer simulations).

We ran 14 computer simulations with the CTH wavecode and used the results to calibrate a_r for the different cases and to establish the overall validity of our approach.

We show that generally for D_t/D_p > 30, the degree of confinement is higher than 95% (D_t = target diameter; D_p = projectile diameter; and degree of CONFINEMENT = R/R_∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength P_min) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.     

晶粒尺寸对细晶钛酸钡陶瓷介电、压电和铁电性能的影响

以采用水热法制备的BaTiO₃粉体作为原料, 利用普通烧结法和两步烧结法制备出晶粒尺寸为0.25~10.15 μm的BaTiO₃陶瓷, 研究了晶粒尺寸效应对BaTiO₃陶瓷的介电、压电以及铁电性能的影响。结果表明: BaTiO₃陶瓷的四方相含量随着陶瓷晶粒尺寸的增大而增加; 当晶粒尺寸在1 μm以上时, 室温相对介电常数(ε° )和压电系数(d₃₃)随着晶粒尺寸的减小而增大, 并在晶粒尺寸为1.12 μm时分别达到最大值5628和279 pC/N, 然后两者随着晶粒尺寸的进一步减小而迅速下降。BaTiO₃陶瓷的剩余极化强度P_r随晶粒尺寸的增大而提高, 而矫顽场E_c却呈现出相反的趋势。晶粒尺寸对介电性能和压电性能的影响是由于90°电畴尺寸和晶界数量的变化。晶粒的晶体场和晶粒表面钉扎作用的变化影响了电畴, 进而改变电滞回线。     

Fatigue crack initiation from notch root (local-strain damage accumulation process on crack initiation)

Local deformation (i.e. local-strain behavior) at the notch root in a crack initiation process in annealed 0.48% carbon steel was investigated by the real-time fine-grid method. The fatigue crack initiation cycle was controlled by local-strain damage accumulation. For a quantitative expression of cumulative fatigue damage, we propose a new parameter, the “average local-strain accumulation value,” , which is defined by the integration of local-strain histories until crack initiation. The relationship between average local-strain accumulation range, , and crack initiation cycles, N_c, showed a line whose slope was nearly −0.5 on a log-log coordinate graph. This line we term the “local-strain damage accumulation curve.” The mean stress effect in cases of R = −1, 0 on this line ( vs N_c) was very small or negligible. From the results of variable-loading tests, the linear cumulative damage law based on the local-strain value was also confirmed.     

Epitaxial grown K1−xRbxTiOPO4 films with extremely flat surfaces for waveguiding

We report on epitaxial {1 0 0} K_1−xRb_xTiOPO₄ waveguide films for the visible spectral range grown on KTiOPO₄ substrates by liquid phase epitaxy. Using the m-line technique a refractive index increase of Δn_x≈0.007 and Δn_z≈0.004 for TM and TE polarisation has been determined for a K_0.78Rb_0.22TiOPO₄ film. Optical transmission and nearfield distribution are comparable to conventional ion-exchanged waveguides. Typical attenuation of about 1 dB/cm for both TM and TE polarisation was obtained at λ=532 and 1064 nm. Energy-dispersive X-ray spectrometry reveals solid-solution films with graded rubidium composition profiles. X-ray rocking curve analyses confirm the epitaxial growth process and indicate perfect and relaxed K_1−xRb_xTiOPO₄ films. Atomic force microscopy investigations reveal regular step structures with step heights Δh<1.3 nm resulting in rms-roughness values of ≈0.4 nm.     

Parallel time scales and two-dimensional manufacturer and individual customer warranties

We deal with a system whose failures depend on several parallel effects, such as the time in use L and the mileage H. Manufacturer warranties are typically described by a two-dimensional region in the (L, H)-plane. A proper determination of the warranty limits must be based on a two-dimensional distribution of time to failure on this plane. The aim of this paper is to demonstrate the possibility of designing individual warranties for a “nontypical” customer who has a very low or very high usage rate b = H/L, and to show a simple way to calculate warranty limits by minimizing the lifetime coefficient of variation. The latter is carried out by introducing the “best” combined time scale in the form K = (1-ε)L+εH which provides the minimal lifetime coefficient of variation.     

A theoretical study on the second-order nonlinear optical susceptibilities of lithium formate monohydrate crystal, HCOOLi·H2O

Ab initio calculations of the first hyperpolarizabilities of (HCOOLi·H₂O)_2n supermolecules, as the building-blocks of lithium formate monohydrate (LFM) crystal with extended system, were performed for the first time. The dependence of the static β_ijk⁰ values on chain length was explored, and the frequency dependence of β_ijk(−2ω;ω,ω) was measured, and the influences of electron correlation and basis set on β_ijk⁰ were evaluated. Finally, we predicted the second-order nonlinear optical coefficients of LFM crystal. The β_ijk⁰ value of (HCOOLi·H₂O)_2n is linearly dependent on the chain length of supermolecule, which is quite unusual for an extended system connected by the O–Li bonds with ionic characters. Although the static component of β_zzz⁰ tensor is the static largest in these three components under study, the absolute value of frequency-dependent β_zyy(−2ω;ω,ω) element, transforming the smallest into the largest, is the most sensitive to frequency. After the fundamental wavelength is smaller than 500 nm, it is found that the β_ijk(−2ω;ω,ω) value is resonantly enhanced to a great extent due to the double frequency lies in the region of resonance. In addition, the β_zxx⁰ value goes from negative to positive with changes of electron correlation and basis set. Obviously, it is very necessary to take into account the effect of electron correlation, if the hyperpolarizability tensor components must be accurately calculated. Moreover, it is also very important whether it is adopted a complete basis set with diffuse and polarization functions. The calculated nonlinear coefficients at high level suggest that the scaled set reported by Robert seem more reasonable.