Kinetics of the failure of loaded materials at variable temperature

The possibility of predicting the lifetime of loaded materials at variable (increasing) temperature is demonstrated on the basis of a kinetic approach to the problem of the failure of such materials. Zh. Tekh. Fiz. 68, 76–81 (November 1998)     

A mesoscopic model of the intermixing during nanoenergetic materials processing

A general mesoscopic model for the simulation of thin-film vapor deposition applied to energetic materials, specifically bimetallic multilayers, is presented. We describe the setup of this mesoscopic simulator developed in the frame of a multiscale study by implementing ab initio data into a set of differential equations. We present numerical results relative to the formation of barrier layers as a result of interdiffusion between successive bimetallic AlNi multilayers. The key role of the vacancies species created during deposition is highlighted.     

Spontaneous thermal runaway as an ultimate failure mechanism of materials

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [Z. Phys. 37, 572 (1926)10.1007/BF01397292]. By assuming that two rigid atomic rows in the crystal would move over each other along a slip plane, he derived the ultimate shear strength to be about one-tenth of the shear modulus. Here we present a theoretical study showing that catastrophic failure of viscoelastic materials may occur below Frenkel's ultimate limit as a result of thermal runaway. The thermal runaway failure mechanism exhibits progressive localization of the strain and temperature profiles in space, thereby producing a narrow region of highly deformed material, i.e., a shear band. We calculate the maximum shear strength sigma_{c} of materials and then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.     

Fatigue strength of structural materials at sonic and ultrasonic loading frequencies

Experimental data on the influence of sonic and ultrasonic frequency loading on the fatigue strength of steels, and titanium, aluminium, and nickel-based alloys tested with longitudinal and transverse vibrations at room temperatures are discussed. Results of fatigue tests in liquid nitrogen at low (16 Hz) and high (3 kHz) loading frequencies are also given for a number of materials. The influence of the loading-cycle asymmetry on fatigue strength is studied for structural materials tested at 10 kHz frequency loading with a mean tensile and compressive stress. Limiting amplitude curves are plotted. Measurements of the energy dissipation in materials were carried out during fatigue tests with symmetrical and asymmetrical loading cycles at high-frequency with large amplitude longitudinal vibrations of the specimen. Measurements of the amplitude dependency of the energy dissipation and dependency of the energy dissipation obtained during continuous loading by fatigue tests were also made.     

Modeling DNA beacons at the mesoscopic scale

We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer models; alternative calculations performed using the freely rotating chain and the discrete Kratky-Porod models are reported. Stem formation is modeled according to the Peyrard-Bishop-Dauxois Hamiltonian. The kinetics of opening and closing is described in terms of a diffusion-controlled motion in an effective free-energy landscape. Melting profiles, dependence of melting temperature on loop length, and kinetic time scales are in semiquantitative agreement with experimental data obtained from fluorescent DNA beacons forming poly(T) loops. Variation in strand rigidity is not sufficient to account for the large activation enthalpy of closing and the strong loop length dependence observed in hairpins forming poly(A) loops. Implications for modeling single strands of DNA or RNA are discussed.     

Double scattering of ions from polycrystalline materials

In this paper double scattering of ions from polycrystalline materials has been theoretically investigated. It is shown that double collision events contribute to the yield at low energy as well as to the high energy flanks of the peaks depending on whether or not the azimuthal angle ø₁ is greater than or less than a critical angle ø_1c at a given first scattering angle θ₁. There are various combinations of first scattering angle θ₁ and second scattering angle θ₂ which give the required retained energy in two successive collisions. Scattering cross sections derived from the Bohr potential and a double interpolation sub-routine are used to calculate the scattering yield at various angles. Two systems, Ne⁺ scattered from copper and Ar⁺ scattered from gold, each at 30 keV primary energy, have been compared with experimental results.     

Magnetic texture analysis of polycrystalline ferromagnetic materials

A theory allowing the full determination of the texture function of a polycrystalline ferromagnet with cubic symmetry of the polycrystallites is developed. Standard group theoretical methods are used, which allow to make maximum use of the full symmetry of the system, without imposing any restriction on the generality of the problem. The magnetocrystalline anisotropy energy of the textured sample is expanded in spherical harmonics and the corresponding energy of the crystallites is expanded in a series of symmetry-adapted spherical harmonics. The texture function is expanded in a series of symmetry-adapted generalized spherical harmonics. A relation between the coefficients of these expansions is determined. It is shown that the texture function can be experimentally calculated using torque curves.     

Structural heterogeneity and jumplike deformation of polymers on the mesoscopic level

This paper reports on the results of research into the jumplike deformation of two polymers based on poly(oxymethylene) (POM) with structural aggregates (spherulites) of different micrometer-scale sizes at a temperature of 290 K, as well as of polyimide (PI) and a PI + graphite composite at temperatures of 290 and 690 K. The creep rate under compression is measured with a laser interferometer in 0.3-μm deformation increments. It is found that, in the course of deformation on the micrometer scale, the creep rate varies nonmonotonically. Periodic variations of the creep rate correspond to a jumplike (stepwise) behavior of the creep. It is shown that the mean jumps in the microdeformation correspond to the mean sizes of poly(oxymethylene) grains and graphite particles in polyimide. The results obtained are in agreement with previously drawn conclusions: the deformation jumps are determined by the scale of ordered microaggregates typical of the structure under investigation.     

Temperature dependence of the thermal-expansion coefficient of certain polycrystalline materials

A capacitive dilatometer has been used to study the temperature dependence of the thermal-expansion coefficient of polycrystalline samples of certain refractory metals. The results are compared with calculated results. The reasons for the discrepancies which exist between experiment and theory are analyzed briefly.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 1, pp. 65–68, January, 1969.     

Group-theoretical principles of texture analysis of polycrystalline materials

A unified group-theoretical approach to the problem of reduction of the orientation space of a crystallographic texture has been developed. The concept of a function of invariant internal distance in a group space is introduced. Left and right group translations, internal automorphisms, motions of the general form, and inversion transformations of the space SO(3) have been studied. It is shown that the Dirichlet-Voronoi partition, being dual to the intrinsic point group of the crystallographic lattice of grain with the initial orientation, is regular with respect to the group of motions (right translations) generated by the elements of the intrinsic point group. Invariant derivation of reduced (true) orientation spaces of crystallographic textures, which does not require a particular specific parameterization of the group space SO(3), is reported.     

Anisotropic ac dissipation at the surface of mesoscopic superconductors

In this work we study the ac dissipation of mesoscopic superconductors at microwave frequencies using the time dependent Ginzburg-Landau equations. Our numerical simulations show that the ac dissipation is strongly dependent on the orientation of the ac magnetic field (h_ac) relative to the dc magnetic field (H_dc). When h_ac is parallel to H_dc we observe that each vortex penetration event produces a significant suppression of the ac losses because the imaginary part of the ac susceptibility as a function of H_dc increases before the penetration of vortices, and then it decreases abruptly after vortices have entered into the sample. In the second case, when h_ac is perpendicular to H_dc, we observe that the jumps in dissipation occur at the same values of H_dc but are much smaller than in the parallel configuration. The behavior of the dissipation in the perpendicular configuration is similar to previous results obtained in recent microwave experiments using mesoscopic lithographed squares of Pb [A.D. Hernández, O. Arés, C. Hart, D. Domínguez, H. Pastoriza, A. Butera, J. Low Temp. Phys. 135 (2004) 119].     

Crystalline electric field effects on the paramagnetic susceptibility of polycrystalline materials

The paramagnetic susceptibility of polycrystalline materials having large magnetic anisotropies is considered. It is shown that polycrystalline data in many case may not reflect strong crystalline electric field phenomena, even though these are clearly seen in single crystal data.     

Interface stress in polycrystalline materials: the case of nanocrystalline Pd

Based on a generalization of a capillary equation for solids, we develop a method for measuring the absolute value of grain-boundary stress in polycrystalline samples having a large interface-to-volume ratio. The grain-boundary stress in nanocrystalline Pd is calculated from x-ray diffraction measurements of the average grain size and the residual-strain-free lattice spacings, yielding a value of 1.2+/-0.1 N/m. The random distribution of crystallite orientations in the sample suggests that this value is characteristic of high-angle grain boundaries in Pd.     

Homogenization of random anisotropy properties in polycrystalline magnetic materials

This paper is devoted to the determination of the equivalent anisotropy properties of polycrystalline magnetic materials, modelled by an assembly of monocrystalline grains with a stochastic spatial distribution of easy axes. The mathematical theory of $\Gamma \text{-}\mathrm{convergence}$ is applied to homogenize the anisotropic term in the Gibbs free energy. The procedure is validated focusing on the micromagnetic computation of reversal processes in polycrystalline magnetic thin films.     

Micromechanical model of deformation-induced surface roughening in polycrystalline materials

A micromechanical model has been developed to describe deformation-induced surface roughening in polycrystalline materials. The three-dimensional polycrystalline structure is taken into account in an explicit form with regard to the crystallographic orientation of grains to simulate the micro- and mesoscale deformation processes. Constitutive relations for describing the grain response are derived on the basis of crystal plasticity theory that accounts for the anisotropy of elastic-plastic properties governed by the crystal lattice structure. The micromechanical model is used to numerically study surface roughening in microvolumes of polycrystalline aluminum and titanium under uniaxial tensile deformation. Two characteristic roughness scales are distinguished in the both cases. At the microscale, normal displacements relative to the free surface are caused by the formation of dislocation steps in grains emerging on the surface and by the displacement of neighboring grains relative to each other. Microscale roughness is more pronounced in titanium, which is due to the high level of elastic-plastic anisotropy typical of hcp crystals. The mesoscale roughness includes undulations and cluster structures formed with the involvement of groups of grains. The roughness is quantitatively evaluated using a dimensionless parameter, called the degree of roughness, which reflects the degree of surface shape deviation from a plane. An exponential dependence of the roughness degree on the strain degree is obtained.     

Atomistic calculation of internal stress in nanoscale polycrystalline materials

Internal stress in polycrystalline materials is an intrinsic attribute of the microstructure that affects a broad range of material properties. It is usually acquired through experiment in conjunction with continuum mechanics modelling, but its determination at nanometre and submicron scales is extremely difficult. Here, we report a bottom-up approach using atomistic calculation. We obtain the internal stress in polycrystalline copper with nanosized grains by first computing the stress associated with each atom and then sorting the stress into those associated with different self-equilibrating length scales, i.e. sample scale and grain cell, which gives type I, II and III residual stresses, respectively. The result shows highly non-uniform internal stress distribution; the internal stress depends sensitively on grain size and the grain shape anisotropy. Statistical distributions of the internal stresses, along with the means and variance, are calculated as a function of the mean grain size and temperature. The implementation of this work in assisting the interpretation of experimental results and predicting material properties is discussed.     

Monte Carlo simulation of grain growth in polycrystalline materials

Understanding the kinetics of grain growth, under the influence of second phase (such as impurities, voids and bubbles) is fundamental to advances in the control of microstructural evolution. As a precursor to this objective, we have investigated the grain growth kinetics in a polycrystalline material using a standard Q-state Potts’ model under Monte Carlo settings. Based on physical reasoning, new modifications are suggested to circumvent some of the disadvantages in the basic Potts model. The efficacy of these modifications vis-à-vis the basic model is verified. The influence of second phase particles on the impurity loaded grain boundaries is investigated for the study of grain growth kinetics.     

Geometrically necessary dislocations in FCC polycrystalline metallic materials on the mesoscale

The dislocation structure of deformed copper alloys doped with Mn and Al was determined by selected area diffraction (SAD), performed using a transmission electron microscope. The scalar dislocation density, the density of geometrically necessary dislocations, and the density of statistically stored dislocations were measured. Special attention was given to the size of grains. The effect of size on the accumulation of geometrically necessary dislocations was studied.