Affect of shock-induced phase transformations on dynamic strength of titanium alloys

A series of complex alloyed (+β) VT-16 Titanium alloy targets were subjected to shock loading under uniaxial strain conditions within impact velocity range of 276–600 m/s. The tests reveal a presence of forward (→ω) and (β→ω) phase transitions at the load front and reverse (ω→β ) transition at the release front of compressive pulse. Duration of (β→ω) and (ω → β ) transitions is approximately 0.5 μs. When spallation happens after reverse (ω →β) phase transition, the spall-strength of alloy increases by 25%. Oscillating regime of that transformation proves to widen the impact velocity range where the spall-strength is maximum.     

Analysis of the temperature dependence of the fracture stress of sharp notched bending specimens of a structural steel with respect to intermediate transitions

The flow and fracture stresses, σ_y^g and σ_f^g (δ = crack tip displacement), of sharply notched bending specimens of a structural steel U St 37-1 are measured in the temperature range from full scale to small scale yielding. The best adaption of the experimental results for σ_f^g is obtained by a curve which exhibits an intermediate transition, i.e. which follows in a temperature range between an upper, T_tM¹ and a lower, T_tl¹, transition temperature to the curve σ_y^g(T) for the flow stress with a constant δ = δ₁. This transition corresponds to that of the slip to the twin nucleated fracture. Two analyses [3,5] according to the local fracture stress, σ_f^*, concept show that the amount and the temperature dependence of σ_f^* are somewhat different for both methods, but that both exhibit an increase of σ_f^* in the transition range. It is concluded that each transition in the nucleation mode of the fracture is connected with such a transition in the fracture stress. It may, however, become indistinct or even be covered by the scatter of the experimental points.     

Strain energy density fracture criterion in elastodynamic mixed mode crack propagation

Sih's fracture criterion based on strain energy density, S, for mixed mode crack extension under static loading is extended to dynamic mixed mode, K_I and K_II, crack propagation. Influence of the second order term, σ_ox, which represents the non-singular constant stress acting parallel to the direction of crack propagation, on the S distribution surrounding the crack tip, is demonstrated. Numerical studies show that positive σ_ox enhances the fracture angle and negative σ_oxreduces the fracture angle irrespective of the sign of K_II/K_I, when S is measured at a critical distance r_c from the crack tip. This fracture criterion is verified by the crack curving results of dynamic photoelastic fracture specimens. Omission of σ_ox term leads to predicted fracture angles which are at variance with experimental data.     

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.     

Performance of an electromagnetic liquid krypton calorimeter based on a ribbon electrode tower structure

The NA48 collaboration is preparing a new experiment at CERN aiming to study CP violation in the K⁰- system with an accuracy of 2 × 10⁻⁴ in the parameter e(ε′/ε). Decays in two π⁰'s will be recorded by a quasi-homogeneous liquid krypton calorimeter. A liquid krypton calorimeter has been chosen to combine good energy, position and time resolution with precise charge calibration and long-term stability. The prototype calorimeter incorporating the final design of the electrode read-out structure is presented in this paper. An energy resolution of 3.5%/√E with a constant term smaller than 0.5% has been obtained. The time resolution was found to be better than 300 ps above 15 GeV.     

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.     

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.     

Influence of stress ratio at baseline loading on delayed retardation phenomena of fatigue crack growth in A553 steel and A5083 aluminium alloy

The delayed retardation phenomena of fatigue crack growth following a single application of tensile overload were investigated under the baseline loading with the stress ratio, R = σ_min/σ_max, ranging from −1 to 0.5 for A553 steel and A5083 aluminium alloy. Two different overload cycles were applied; the one is the case that the ratio of peak stress range to baseline stress range, r = Δσ₂/Δσ₁, is equal to two and the other is the case that the ratio of maximum peak stress to maximum baseline stress, σ_2max/σ_1max, is equal to two. The retardation took place stronger in aluminium than in steel. Under the condition of r = 2 the normalized number of cycles, N_D/N_C, (N_D: the number of cycles during retardation, N_C: the number of cycles required for propagation through the overload-affected-zone size) decreased slightly as the R ratio increased from −1 to 0.5, while under the condition of σ_2max/σ_1max = 2 the N_D/N_C-values increased drastically as the R ratio increased from −1 to 0 (or the overload ratio, r, increased from 1.5 to 2) in both the materials. These retardation behaviors were expressed theoretically according to the model proposed by Matsuoka and Tanaka [1, 3] by using four parameters: the overload ratio, r, the exponent in Paris equation, m, the overload-affected-zone size, ω_D, and the distance at the inflection point, ω_B.     

Magneto-transport in porous silicon

Magnetoresistance (MR) measurements have been performed in the temperature range 100–300 K on macroporous porous silicon (P.S.) samples. P.S. layers have been prepared by the anodic dissolution of Si in HF acid. The MR has been found to be positive in P.S. for the temperature range 100–300 K and for the entire range of magnetic field (0–5 kG). However the magnitude of the positive MR is found to be much less than expected on the basis of free electron conduction. Also the value of n in the relation Δρ/ρ_o∞Bⁿ for the temperature range 100–300 K is found to be < 2, implying that there is a contribution of some phenomenon other than the free electron conduction to MR. The measured data suggest that it is the contribution of localized state conduction near the Fermi level and in the localized states near the band edges.     

Computer simulations of martensitic transformations in NiAl alloys

Ni_{1 − x}Al_x alloys in the concentration range 34% < x < 40% exhibit a martensitic transformation from an austenitic phase with bcc structure to a close-packed structured martensitic phase. Above the transformation temperature electron microscopy shows the occurrence of tweed like structures which are accompanied by a considerable softening of the phonon energies at . We have done molecular dynamics simulations employing a semi-empirical model which allows us to study the transformation on an atomistic length scale. Our results show that local distortions of the crystal lattice, which come from the atomic disorder of the alloys, are responsible for the occurrence of tweed phenomena.     

Étude électrique de couches minces de polymère obtenues dans une décharge luminescente II: Caractérisation électrique sous champ alternatif

The aim of this study was to investigate the electrical characteristics under alternating stress of a metal-polymer-metal structure, the dielectric of which was a thin layer created by a glow discharge in styrene.

The study, carried out in the 250 Hz–100 kHz range between −90° and 150°C, indicates two different domains for the variations of ε_r and ε_r'. Using bi-logarithmic coordinates the variation of the a.c. conductivity σ_ac(Ω) obeys the law σ_ac(Ω)∝Ω for temperatures lower than 50°C.

In order to explain this result, two hypotheses are proposed: that dipolar fluctuations occur and that a hopping process takes place.     

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.     

A simple procedure for the accurate determination of stress intensity factors by finite element method

A simple procedure for the accurate determination of stress intensity factors K_I, K_II by the conventional finite element method is proposed. The first step of the method is to calculate the stress σ₂ of the plate without a crack. The second step is to calculate the stress σ_tip, of the plate with the crack. The value of (σ_tip−σ_g) at the crack tip element is regarded to have the intimate relation with K_I, K_II K_I, and K_II are determined from the value of (σ_tip−σ_g) and a standard solution. It is shown that the results obtained for many problems by the proposed method are in excellent coincidence with the analytical solutions. The error is below 1–3% for the most cases.     

Linear Optical Susceptibility of Single-Walled Boron Nitride Nanotubes

A simple model based on an effective-mass approximation is developed to describe the dispersion behavior of the linear optical susceptibility χ1 of an array of aligned, identical single-walled boron nitride nanotubes (BNNTs) in the spectral range where interband π-electron transitions dominate. An analytic closed-form expression for χ⁽¹⁾ valid in the low-frequency part of the spectrum is obtained in terms of the band gap Δ_g of BNNTs and the π-electron transfer integral V_ppπ. To the best of our knowledge, the present analytic calculation is the first for such nanotubes.     

The influence of parent population distribution on d2 values

The two measures of dispersion which are used in statistical quality control are ρ, the expected value of the range of samples of a uniform size n, and σ, the standard deviation of the population from which the samples are taken. Conversion of one into the other is facilitated by use of the quantity called d₂ which is taken to be the ratio of ρ to σ. Tables of d₂ versus n are reproduced in all texts on statistical quality control. These tables are predicated upon the parent population being normally distributed, an assumption which may be unjustified in many instances. To understand the consequences of this assumption of normality, a short table of d₂ values based upon five distributions is presented. The five distributions are: normal, uniform, triangular, Erlang ν = 1 (negative exponential), and Erlang ν = 2. The sample size varies from two through 12, plus 15, 20, and 50. It was observed that for many values of n the normal distribution produced the largest value of d₂, while the negative exponential distribution produced the smallest value. Depending upon the intended use, and whether Type I or Type II error is of more concern, one may wish to use d₂ values based upon other than the normal distribution. Some recommendations are made. A derivation of the formula for computing ρ as a function of n which is dependent upon the parent population distribution is given in an appendix.     

On the effect of substrate properties on the indentation behaviour of coated systems

The indentation behaviour of an elastoplastic coating–substrate system is investigated using a combination of dimensional and finite element analyses. Scaling functions relating the indentation load–depth curves to coating and substrate mechanical properties are given. Based on these scaling functions, the indentation behaviour of various coated systems is examined. The critical indentation depth to coating thickness ratio below which the substrate material has a negligible effect on the indentation response of the coated system is identified for various generic coating–substrate systems. Such ratio is given in terms of the yield strength and Young’s modulus of the coating and substrate, i.e. σ_yc/σ_ys and E_c/E_s. The results of parametric studies revealed that the commonly used rule that the maximum indentation depth should be less than 10% of the coating thickness, is applicable only when σ_yc/σ_ys<10. However, indentation experiments should be carried out up to a maximum depth of 5% of the film thickness to avoid any influence from the substrate when σ_yc/σ_ys≥10 and E_c/E_s>0.1.     

Microwave and far-infrared propagation in conductive microstructured composites

In a recent publication [T.E. Huber, L. Luo, Appl. Phys. Lett. 70 (1997) 2502.] we discussed a structural enhancement of the electromagnetic transmission in composites. We showed that densely packed arrays (76% volume fraction) of 10 μm diameter parallel indium wires exhibit an enhanced transmission, of 10³, relative to an indium foil of equal thickness for far-infrared (10 cm⁻¹ < k < 80 cm⁻¹) propagating along the wire length. The absorption increases as k^{0.45 ± 0.07} and is explained by the dynamic Maxwell-Gannett model, which includes eddy current dissipation. It is of considerable practical interest to extend the range of application of these composite properties to the microwave domain. Here we will discuss recent measurements of the transmission of microwaves in wire array composites in the 8–12 GHz frequency range.     

Simple formulas for the energy loss of ultrarelativistic muons by direct pair production

Simple formulas for direct pair production are derived from the general equation for deeply inelastic lepton scattering. Applications to energy loss by ultrarelativistic muons are discussed. For muons above the critical energy, E_c^μ 200 GeV, where the radiative effects of direct pair production and bremsstrahlung are dominant, the expressions for energy losses are considerably simplified when quoted in terms of the fractional energy loss per radiation length. The differential probability for direct pair production in a thickness x of material of radiation length X₀ for an incident lepton of energy E, mass M, can be expressed as

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where ν is the energy of the produced pair, υ is the fractional energy loss, υ = ν/E, m_e is the electron mass and the variable z is defined by

For indicent muons, this simple expression agrees very well with the exact calculation to within 30% over the entire range of υ, for E 1 TeV. At higher energies complete screening occurs, and the agreement is further improved, to better than 15% (except for the range 0.005 ≤ υ ≤ 0.01 where it is 25%). The integral of this expression gives the energy loss due to direct pair production by muons (complete screening) which is accurate to 10%:

.     

Physics of very thin ITO conducting films with high transparency prepared by DC magnetron sputtering

The preparation of very thin indium tin oxide (ITO) films with extremely high transparency and suitable resistivity, as well as resistivity stability for long term use, is described. In order to obtain these properties, amorphous suboxide films were first prepared and then annealed. Suboxide films with a thickness of 20 to 30 nm were prepared on PET film and glass substrates at a temperature of 60 °C using In₂O₃---SnO₂ targets with a SnO₂ content of 0 to 10 wt% by DC magnetron sputtering in a pure argon gas atmosphere. The films were annealed at a temperature of 150 °C for 1 to 100 h in air. The resistivity of films on PET films was, depending on the SnO₂ content, on the order of 10⁻³ ω cm. An average transmittance above 97% in the visible wavelength range and a resistivity of about 4 × 10⁻³ ω cm, as well as resistivity stability, were attained in ITO films with a SnO₂ content of about 1 wt% prepared on PET films by the low-temperature process. It is thought that these properties result from crystallization which occurred during the annealing, duration up to about 25 h.     

AC Conductivity and Dielectric Response of Polycrystalline and Amorphous C70

The AC conductivity and dielectric constant of polycrystalline and amorphous C₇₀ samples were measured in the 75-300 K temperature range and in the 100 Hz to 1 MHz frequency range. For polycrystalline samples, we observe effects caused by O₂ intercalation due to prolonged exposure to ambient air. The conductivity σ of these samples around 300 K depends on the measuring frequency ν as a σ ∼ νⁿ with n ≈ 0.88, implying a strong reduction of DC conductivity to less than 10^-12 S/cm. The dielectric constant of polycrystalline samples shows an anomaly at 285 K which is interpreted as due to the transition from its intermediate rhombohedral phase into its monoclinic low-temperature phase. In contrast with the polycrystalline samples, the amorphous C₇₀ samples prepared by sublimation do not contain interstitial 0₂, their conductivity at 300 K is of about 10^-6 S/cm, is independent of frequency, and is well described by the hopping mechanism (Davis-Mott T^1/4 law) in the 200-300 K range. All evidence of phase transitions disappears in the amorphous samples.