An analytical study on the geometrical size effect on phase transitions in a slender compressible hyperelastic cylinder

In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain-energy function in a loading process. We aim to construct the asymptotic solutions based on an axisymmetrical three-dimensional setting and use the results to describe the key features observed in the experiments by others. By using a methodology involving coupled series-asymptotic expansions, we derive the normal form equation of the original complicated system of non-linear PDEs. Based on a phase-plane analysis, we manage to deduce the global bifurcation properties and to solve the boundary-value problem analytically. The explicit solutions (including post-bifurcation solutions) in terms of integrals are obtained. The engineering stress-strain curve plotted from the asymptotic solutions can capture the key features of the curve measured in some experiments. Our results can also describe the geometrical size effect as observed in experiments. It appears that the asymptotic solutions obtained shed certain light on the instability phenomena associated with phase transitions in a cylinder.     

Analysis of phase transformation from austenite to martensite in NiTi alloy strips under uniaxial tension

Phase transformation from austenite to martensite in NiTi alloy strips under the uniaxial tension has been observed in experiments and numerically simulated as a localized deformation.This work presents an analysis using the theory of phase transfor- mation.The jump of deformation gradient across the interface between two phases and the Maxwell relation are considered.Governing equations for the phase transformation are derived.The analysis is reduced to finding the minimum value of the loading at which the governing equations have a unique,real and physically acceptable solution.The equa- tions are solved numerically and it is verified that the unique solution exists definitely. The Maxwell stress,the stresses and strains inside both anstenite and martensite phases, and the transformation-front orientation angle are determined to be in reasonably good agreement with experimental observations.     

Atomistic simulation study on the crack growth stability of graphene under uniaxial tension and indentation

Meccanica - Combining a series of atomistic simulations with fracture mechanics theory, we systematically investigate the crack growth stability of graphene under tension and indentation, with a...     

Possible instability of a rectilinear crack path in an orthotropic plane at uniaxial normal tension

We study the stability of the rectilinear path of a mode I crack whose direction coincides with a symmetry axis of an orthotropic plane. A class of orthotropic materials for which the rectilinear crack path proves to be unstable even in the case of uniaxial normal tension applied at infinity is found.     

Self-similar shapes of the free boundary of a nonlinear-viscous band under uniaxial tension

An equation of evolution of small perturbations of the free boundary of a nonlinear-viscous band under quasi-static uniaxial tension is derived for studying the necking problem in metals under superplasticity conditions. It is shown that the group of symmetry of this linear parabolic equation is equivalent to the group of symmetry of the linear equation of heat conduction with an arbitrary material parameter of the model. Self-similar solutions are obtained in the form of simple and complicated steady localized structures transferred together with the material of the stretched band.     

Asymmetric bifurcations in a pressurised circular thin plate under initial tension

It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl–von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.     

Flow of fluids with substantially different mobilities through a porous medium in the presence of phase transitions: Boundary layer phenomena, spatial phase structures, and instability of the flow

A model of flow through a porous medium with phase transitions which permits an efficient qualitative investigation is proposed for two fluids with sharply different (high-contrast) mobilities. It is shown that the model problem of flow toward a unit sink is singularly perturbed and can be solved using analytic asymptotic matching methods. The nature of the singularity is associated with violation of the condition of the flow contrast in certain zones. The solution can be unstable depending on the direction of interphase mass transfer and the zone in which the process takes place. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 124–135, March–April, 2000. The work was carried out with support from the European Foundation INTAS (grant No. 94-4367) and the Russian Foundation for Basic Research (project No. 95-01-01179a).     

An experimental study on the ratcheting behavior of pure aluminium under uniaxial cyclic stressing

An experimental study was carried out for the cyclic properties of pure aluminium subjected to uniaxial cyclic straining and stressing. For a material of pure aluminium the effects of the cyclic strain amplitude history and mean strain on the cyclic deformation behavior were investigated, and the influences of stress amplitude, mean stress and their histories on cyclic creep (i. e., ratcheting) were analyzed. It is shown that either uniaxial cyclic property under cyclic straining or ratcheting behavior under asymmetric uniaxial loading depends not only on the current loading, but also on the previous loading history. Some significant results were obtained.Financial support from NFSC is acknowledged.     

Elastic-plastic strain concentrations produced by various skew holes in a flat plate under uniaxial tension

The elastic and elastic-plastic surface strain fields around circular holes drilled at various skew angles to a flat plate have been experimentally evaluated in uniaxial tension. A photoelastic coating and moiré technique were used in the low- and high-strain regions, respectively. The maximum strain-concentration factor is shown to increase markedly with horizontal skew angle and decrease slightly with increasing vertical skew angle. Plastic deformation accentuates the differences between normal and skew holes, so that the angular dependence of the strain-concentration factor increases with nominal strain.     

Modeling the effect of diffusion of the ambient medium on the long-term strength of a hollow cylinder under uniaxial tension

The problem of the long-term strength of an extended thick-walled tube containing a corrosive medium in the internal cavity is solved. The diffusion of this medium into the tube material is analyzed. The diffusion equation is solved approximately by introducing the diffusion front, and the error of the solution is estimated. The dependence of the time of fracture of the tube on the variable tensile stress and the concentration of the medium filling the cavity is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 88–93, July–August, 2007.     

An analytical study on the Rayleigh wave generation in a stratified structure

In this paper, an analytical method is used to investigate the Rayleigh wave generation in a stratified structure and the wave generation in a dry sandy layer constrained between the couple stress and inhomogeneous orthotropic half-spaces. This study is devoted to analyzing the impact of various effective parameters associated with the media on the phase velocities of the wave. The displacement components for each medium are derived by implementing the separable variable method. The frequency eq...     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.     

Local solution of the stress and strain fields in the necking section of cylindrical bars under uniaxial tension

The problem of finding the stress and strain fields over the minimum cross section of necked cylindrical bars under uniaxial tensile load has been solved locally using a new fast numerical method. The scheme delivers both the accuracy of the finite element analysis and the applicability of simple closed-form analytical solutions. The required inputs are the distributions of curvature radii for both isostatic and material lines. It is numerically observed that the mathematical formulas available in the literature fail to adequately predict these distributions. Introducing the stress normalized strain-hardening rate as the most decisive parameter affecting the curvature radii, a database and interpolation technique have been developed in order to estimate the necessary information based on the results of the previously FE analyzed samples. Finally, a practical case has been solved and compared with the FE results.     

An analytical study of frost nucleation and growth during the crystal growth period

An analytical study was made to clarify the fundamental nature of the early stage of crystal growth period of frost formation phenomena. A suitable model was developed by using the principles of crystallization and nucleation theory. The effect of four dominant parameters of frost formation; plate temperature, air temperature, air humidity ratio and Reynolds number, was studied. Ice crystal density variation with temperature reported by cloud physicists is used in the model to predict the density variation of frost during the crystal growth period. The temperature variation in the frost layer is formulated and vapor diffusion through the frost layer is taken in the consideration.     

An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression

Strength and deformability characteristics of rock with pre-existing fissures are governed by cracking behavior. To further research the effects of pre-existing fissures on the mechanical properties and crack coalescence process, a series of uniaxial compression tests were carried out for rock-like material with two unparallel fissures.In the present study, cement, quartz sand, and water were used to fabricate a kind of brittle rock-like material cylindrical model specimen. The mechanical properties of rock-like material specimen used in this research were all in good agreement with the brittle rock materials. Two unparallel fissures(a horizontal fissure and an inclined fissure) were created by inserting steel during molding the model specimen.Then all the pre-fissured rock-like specimens were tested under uniaxial compression by a rock mechanics servocontrolled testing system. The peak strength and Young's modulus of pre-fissured specimen all first decreased and then increased when the fissure angle increased from 0?to 75?.In order to investigate the crack initiation, propagation and coalescence process, photographic monitoring was adopted to capture images during the entire deformation process.Moreover, acoustic emission(AE) monitoring technique was also used to obtain the AE evolution characteristic of prefissured specimen. The relationship between axial stress, AE events, and the crack coalescence process was set up: when a new crack was initiated or a crack coalescence occurred, thecorresponding axial stress dropped in the axial stress–time curve and a big AE event could be observed simultaneously.Finally, the mechanism of crack propagation under microscopic observation was discussed. These experimental results are expected to increase the understanding of the strength failure behavior and the cracking mechanism of rock containing unparallel fissures.     

On the wrinkling of a pre-stressed annular thin film in tension

Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ(?1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ(μ,n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ→∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.     

A micro mechanical study on failure initiation of dual phase steels under tension using single crystal plasticity model

Both experimental and numerical methods were employed to investigate the mechanism of failure in dual phase steels. The tensile test was interrupted in different steps to capture the mechanism of void initiation and void growth during material failure. The results can be considered as a first report for the commercial DP800 steel. Numerical simulations, which were carried out using the real micro-structure, are able to predict the void initiation in the material. In addition, through the numerical simulation a new understanding of the deformation localization was gained. Deformation localization, which causes severely deformed regions in the material, is most probably the main source of rupture in the final stages of the failure. In the SEM micrographs of the material after failure some voids are observable which can validate the results obtained by the simulation.     

An arbitrarily oriented crack in a semi-infinite medium with a surface layer under tension

The title problem is analyzed by the use of the continuous distribution of dislocations in the framework of plane elastostatics. A set of singular integral equations for the dislocation density is readily set up, whose solution is obtained in the form of the product of the series of Chebyshev polynomials of the first kind and their weight function. The variation of the stress intensity factor due to the geometrical configuration and the material combination is shown in graphs. The probable angle of crack growth due to Erdogan-Sih criterion for brittle materials is also shown.