Grain growth behaviour of the Al-Cu eutectic alloy during superplastic deformation

Grain growth behaviour of the Al-Cu eutectic alloy was investigated as a function of strain (ε), strain rate and deformation temperature (T) over = 10⁻² s⁻¹ and T=400 to 540°C. The grain size increases with increase in strain and temperature. Upon deformation to a fixed strain, the grain growth is generally seen to be more at lower strain rates. The rates of overall grain growth and due to deformation alone , however, increase with increasing strain rate according to and , respectively. The increase in the grain growth rate with strain rate is attributed primarily to the shorter time involved at higher strain rate for reaching a fixed strain. The activation energy for grain growth under superplastic conditions is estimated to be 79 kJ mol⁻¹.     

Crack-tip fields in elastic-plastic material under plane stress mode I loading

New results on the crack-tip fields in an elastic power-law hardening material under plane stress mode I loading are presented. Using a generalized asymptotic expansion of the stress function, higher-order terms are found which have newly-discovered characteristics. A series solution is obtained for the elastic-plastic crack-tip fields. The expansion of stress fields contains both the and terms where t_i is real and t_k is complex; the terms σ⁽ⁱ⁾ _pq(θt_i) and σ^(k) _rsθt_k) are real and complex functions of θ respectively. Comparing the results with that for the plane strain mode I loading shows that: (1) the effect of higher-order solutions on the crack-tip fields is much smaller; and (2) the path-independent integral J also controls the second-order or third-order term in the asymptotic solutions of the crack-tip fields for most of the engineering materials (1 < n < 11) in plane stress, while the J-integral does not control the second and the third-order terms for the plane strain mode I case for n > 3. These theoretical results imply that the crack-tip fields can be well characterized by the J-integral, and can be used as a criterion for fracture initiation under plane stress mode I loading. This is in agreement with existing full-field solutions and experimental data that J at crack growth initiation is essentially independent of in-plane specimen geometry. The comparison confirms the theoretical asymptotic solutions developed in this study. This revised version was published online in August 2006 with corrections to the Cover Date.     

Role of recovery in high temperature constant strain rate deformation

A model based on the three-dimensional distribution of dislocations is used to delineate the role of recovery during high temperature constant strain rate deformation. The model provides a good semi-quantitative explanation for classical work-hardening as well as for high temperature work-softening resulting from rapid recovery. It predicts linear work-hardening, whereby the ratio of the work-hardening rate,H, to the shear modulus,G, is constant when a crystal is tested in the absence of recovery. The slope of the stress-strain curve, θ, for high temperature deformation is related to the low temperature work-hardening rateH; the dislocation annihilation rate , the flow stress a, the free dislocation density ρ, the strain rate , and a parameter which is sensitive to the dislocation distribution. A modified version of the Bailey-Orowan equation for simultaneous work-hardening and recovery during constant strain rate deformation which is derived from the model takes the form

Static recrystallization kinetics of 304 stainless steels

Static restoration mechanism during hot interrupted deformation of 304 stainless steel was studied in the temperature range from 900 to 1100°C, various strain rate from 0.05 to 5/sec and pass strain of 0.25–3 times peak strain. It was clarified that the static recrystallization was happened after 3–10 seconds at first deformation. The static restoration was depended on the pass strain, deformation temperature and strain rate and fractional softening (FS) values increased with increasing strain rate, deformation temperature and pass strain. Recystallization kinetics was explained with Avrami equation and Avrami constant was 1.113. This value was independent of deformation variables significantly. The time of 5, 50, 95% recrystallization was evaluated using such equations: t _0.05 = 2.9 × 10^{–12 –1.17 –0.94} D exp(222000 J/mol/RT), t _0.5 = 2.0 × 10^{–10 –1.56 –0.81} D exp(197000 J/mol/RT), t _0.95 = 1.9 × 10^{–8–1.63 –0.76} D exp(173000J/mol/RT). The predicted values by use of upper equations had a good agreement with a measurement.     

Effects of back pressure on the superplastic forming of domes

The stress state during “simple” superplastic bulge forming (without a back pressure) is different from that when a back pressure is applied. In the former procedure, specimens or components are deformed under a biaxial tensile stress state, while in the latter, the deformation is achieved under the combination of a biaxial tensile stress and a uniaxial compressive stress state. Both theoretical and experimental studies have shown that when a back pressure is present, the deformation cannot be treated as simply governed by the difference between the forming pressure and the back pressure. The analytical expressions for the forming relationships and the influence of back pressure on experimental m-log (where m is the strain-rate sensitivity and is the equivalent tensile strain rate for bulge forming) relationships for Zn-22 wt% Al and Zn-4 wt% Al-1% Cu are given. Results show that with increasing back pressure, the m-log curve shifted towards higher strain rates, but the maximum m values were not affected.     

Creep Behavior of Dispersion-Hardened Aluminum Materials

Dispersion-hardened aluminum materials of pure aluminum with extremely fine oxide and carbide dispersions and very fine grain sizes were creep-deformed under compressive loadings between 573 and 773 K. The creep behavior of the investigated materials is influenced by time, temperature, stress level and microstructure. An increasing content of dispersions causes increasing threshold stresses _thand resistances against creep. The Norton plots of the minimum creep rate versus stress are characterized by extremely high stress exponents n. On the basis of the threshold concept it is demonstrated that the same diffusion process dominates in the dispersion-hardened aluminum materials as in pure aluminum. Their true stress exponents n^*as the slopes of the best fit lines of the are close to 5. The threshold stress decreases considerably with increasing temperature due to the thermally activated recovery of long-range internal back stresses of quasi-planar dislocation structures on the grain boundaries.     

Comparative analysis of the theories of sliding with regular and singular loaded surfaces

We study the possibility of application of the versions of the theory of sliding [1] with regular and singular loading surfaces (Σ) under complex loads in the form of two-link paths and establish the relationships between the stress and strain rates in a small neighborhood of an angular point in the loading path. The advantages of the theory of sliding with singular surfaces are discussed and the impossibility of application of the theories of plastic flow with regular surfaces to the solution of the problems of stability of structural elements is demonstrated. However, their application to the solution of boundary-value problems of determination of the total strains can be reasonable. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 10–16, March–April, 2007.     

Spin-orbit interaction in the field of an optical vortex of a few-mode fiber

A quantum-mechanical analog of the spin-orbit interaction operator is constructed for the fields of optical CV vortices and TE and TM modes in an optical fiber. It is shown that the polarization correction δβ to the propagation constant, which is the mean value of this operator, is a measure of the “level splitting” of the propagation constant in the scalar case. The difference in the operation of the individual parts of the operator on the fields of CV vortices and on the fields of TM and TE modes is indicative of the presence of two different physical processes — circular and linear birefringence in the locally isotropic optical fiber. The conversion of the “scalar” field to a vector field e ₁ as a consequence of the spin-orbit interaction operator can be regarded as resulting from a re-radiation of the additional field e ₁ by the vortex field , which rotates around the optical axis of the fiber. In this picture the additional field e ₁ can be regarded as being a “relativistic” correction to the vortex field for the distortions of the main field and arising as a result of the rotation of the field of the optical vortex in the medium of the few-mode fiber. Zh. Tekh. Fiz. 24, 87–93 (October 26, 1998)     

Vacancy concentration in strain ageing of substitutional f c c alloys

The relation between vacancy concentration, C _v and tensile plastic strain, ɛ, has been constantly expressed as C _v ∞ ɛ ^m . To take into account the grain-size effect, we have recently proposed that C∞ ɛβ_v ∞ϱ_m, where ϱ_m is the mobile dislocation density. With the conventional expression that ϱ_m d ⁻ⁿ , where d is the average grain size, the strain and grain-size dependence of vacancy concentration appears to be C _v ∞ ɛ^βγ d ^-nγ. This equation has proved effective in rationalizing the onset strain, ɛ_c, and stress amplitude, Δσ, of flow instability associated with the Portevin-LeChatelier effect of substitutional f c c alloys, where ɛ_c and Δσ are described by

On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function

Summary Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ^-r of unknown parameter λ of gamma distribution with density ,x> 0, whereb-known parameter, for loss function . Goodmann in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ² of the normal distribution. In particular for quadratic loss function he took weight of the formK(σ²)=C andK(σ²)=(σ²)^-2 only. In this work we obtained the class of all unbiased Lehmanns-estimators of the variance λ² of the exponential distribution, among estimators of the form functions of the sufficient statistics-with quadratic loss function with weight of the form ,C>0.

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Resumen Lehmann en su trabajo [4] generalizó la idea del estimador sin vías en relación a la aceptación de la función de pérdidas. En el trabajo [5] Singh considera de estimadores admisibles para la función λ^-r parámetro desconocido λ de la distribución de gamma, de densidad ,x>0,b>0 parámetro conocido, de la función de pérdidas resulta . Goodman en su trabajo [1] acumulando 3 formas diferentes de funciones de pérdidas encontró estimadores sin biases en el sentido de Lehmann de la variancia de σ² de una distribución normal, en particular para la función de pérdidas con los pesos, solo de la formaK(σ²)=C,K(σ²)=(σ²)^-2. En su trabajo distinguida la clase de todos los estimadores sin biases obtenidos en el sentido de Lehmann de la variancia λ² en la distribución exponencial, entre los estimadores de forma así pues de la función estadística suficiente— por una función de pérdidas al cuadrado con los pesos de la forma ,C>0. Palabras y frases. Estimador sin vías en el sentido de Lehmann, función de pérdidas, riesgo mínimo, suficiente estadística.

     

Transition to chaotization and loss of self-averaging in two-dimensional two-phase media at the flow threshold

Giant fluctuations of the electric field recently identified experimentally in two-dimensional two-phase media at the percolation threshold are discussed. An example of a hierarchical realization of these media is used to show that for Re σ _i=0 (where σ₁ and σ₂ are the phase conductivities) and Im σ ₂/Im σ₁>0, the hierarchy construction procedure yields the Dykhne expression , whereas for Im σ ₂/Im σ₁<0, the procedure becomes randomized and the medium loses its property of self-averaging. Pis’ma Zh. Tekh. Fiz. 23, 89–95 (July 12, 1997)     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Structural features of Σ = 19, [110] GaAs tilt grain boundaries

= 19, [110] tilt grain boundaries have been observed to facet parallel to particular planes; the facets lie along _A/ _B, ( )_A/ )_B and ( )_A/( )_B. The structural unit of the = 19 ( )_A/( )_B [110] boundaries consists of 5- and 7-member rings, which are similar to the core structure of a/2[110] edge dislocations. The polarities in each grain on either side of the boundaries has been confirmed by CBED methods; a lower number of anti-site type cross-boundary bonds occur along the boundaries compared to when the polarity of one grain is reversed. The presence of 7-member rings and anti-site cross-boundary bonds results in a more open atomic structure at the boundary, shortening the distance between the first and the second {331} atomic planes from the boundary plane by 40%.     

A broad-spectrum constitutive modeling technique applied to saline ice

The constitutive behavior of lab-grown saline ice subjected to isothermal, uniaxial tensile loadings is discussed. A rectangular plate specimen of S2 columnar saline ice was subjected to a uniform tensile stress perpendicular to the long axis of the column structure. This loading was selected to represent the stress field which occurs in the plane of natural ice covers under tension. The uniaxial stress state was applied with a recently developed, modified Reversed Direct Stress device. Two successive load histories were applied – creep-recovery cycles and monotonic stress ramps. A broad-spectrum, nonlinear viscoelastic modeling approach is used to develop a constitutive model of the strain response. Each parameter of the model is evaluated from the measured ice response to the creep-recovery loadings. The model provides an accurate representation of the experimental data with a delayed elastic compliance function in time power law form (t _n ,n= ) and a nonlinear stress exponent (σ _q ,q = ). Finally, the model is used to predict the strain response of the ice to the monotonic ramp loadings with good results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Metadynamic recrystallization of austenitic stainless steel

Interrupted torsion tests were performed in the temperature range of 900–1100°C, strain rate range of 5.0 × 10^–2–5.0 × 10⁰/sec and interpass time range of 0.5–100 seconds to study the characteristics of metadynamic recrystallization (MDRX) for austenitic stainless steel. To compare the MDRX with static recrystallization (SRX), the pass strain was applied above the critical strain (_c) (_c = 2.2 × 10^–3 D^1/2 ₀ Z ^0.089, where Z is Zener-Hollomon parameter, Z = exp((380000 J/mol)/RT) and D ₀ is as-received grain size) to obtain the MDRX during interpass time. It was found that the kinetics of MDRX were dependent of the strain rate and deformation temperature but were nearly independent of the change in pass strain after the peak strain. The time for 50% metadynamic softening, t ₅₀, was determined as follows: t ₅₀ = 1.33 × 10^{–11 –0.41} D ₀ exp((230000 J/mol)/RT) and this calculated value was consistent with the measured value. The Zener-Hollomon parameter was impossible to evaluate the MDRX fraction, because the fractional softening values were different at the same Z values. The new parameter (MDRX parameter) considering deformation temperature, strain rate and interpass time was proposed to evaluate the MDRX fraction. The MDRX-parameter was determined as 3.25 × 10^{–19 0.3} t _i ^0.6 T ¹².     

Computer-aided design of small patch antenna using (Al, Mg)TaO2 ceramics

The microwave dielectric properties of (AMT) ceramics and the design of small coplanar waveguide fed antenna (CPWFA) have been investigated. ( and ( have orthorhombic and tetragonal structure, respectively. As ( concentration increased, AMT ceramics transformed into the tetragonal structure. Specimens having tetragonal single phase could be obtained above x=0.6. As ( concentration increased, the grain size, dielectric constant and quality factor (Q) significantly increased and the temperature coefficient of resonant frequency changed from negative to positive. The of was realized at x=0.65 and the Q · f _O value and for this composition were 112 470 GHz and 26.1, respectively. Newly developed dielectric materials were used for 1.5 GHz band CPWFA design and fabrication. The size of the CPWFA can be reduced by using high dielectric constant AMT ceramics, insetting slits into the patch, and fabricating CPW feed line in the ground plane. The slits play a role in not only lowering a center frequency but also fine tuning for the proposed antenna together with the open stub of CPW feed line. The CPWFA with slits has a lower center frequency than the conventional CPWFA, which suggests that the antenna size can be reduced by as much as 16.3%. The structure simulations of the CPWFAs have been performed to obtain impedance matching and to investigate the effects of slits. Experimental results of the fabricated device were in good agreement with the simulation.     

Failure crack orientation at ductile shear fracture of Fe80−x Ni x B20 metallic glass ribbons

Orientation of failure cracks of oblique mode at ductile shear fracture are measured for Fe_80–x Ni _x B₂₀ (x=10, 20, 30, 40, 50, 60) metallic glass ribbons (MGR) uniaxially extended with strain rate from 3.3×10^–6 to 1.25×10^–3 s^–1 at temperatures 300, 77 and 4.2 K. An angle between the failure crack and tension axis is found to depend non-monotonously on nickel concentrationx and strain rate . These dependences are probably due to the presence of dilatancy in shear bands and its variation as a function of concentration, strain rate and temperature.Mean values of quenching stresses in ribbons are estimated by comparing experimentally measured values and those predicted by T. Thomas in 1953.     

Extended region of “anomalous” acceleration in the cathode jet of a vacuum discharge

It is observed that “anomalous” acceleration of ions in a pulsed vacuum discharge is initiated at a certain distance from the surface of the cathode and takes place in the bulk of the cathode jet. It is established that the average ion energy increases as the length l of the discharge gap increases. Pis’ma Zh. Tekh. Fiz. 24, 66–70 (February 26, 1998)     

Dynamic crack propagation and unloading behavior of brittle polymers

The method of caustics in combination with a Cranz–Schardin high-speed camera was utilized to study dynamic crack propagation and unloading behavior of epoxy, PMMA and Homalite-100 specimens. Dynamic stress intensity factor K _ID and crack velocity were evaluated in the course of crack propagation. Caustic patterns at the loading points were also recorded to estimate load P applied to the specimen. Unloading rate , the time derivative of P, was determined as a function of time t, and its time correlation with K _ID or was examined. The findings showed that the change in was qualitatively in accord with the change in K _ID or . However, there existed slight differences among the values of t giving the maximum , and K _ID, so that their order was , and K _ID. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modified four-point bending specimen for determining the interface fracture energy for thin, brittle layers

A well-known four-point bending test has been modified such that the critical energy release rate for delaminating cracks propagating at the interface of a thin, brittle layer bonded to a substrate can be measured. The energy release rate required for crack delaminating at those interfaces is obtained by attaching a stiffening layer to the layer system. Another advantage of this modification is that segmentation of the layer and plastic deformation of the substrate during bending are avoided. The interface fracture energy of a plasma sprayed ZrO₂-ceramic layer on a flame sprayed high alloyed steel substrate has been measured. This revised version was published online in August 2006 with corrections to the Cover Date.