Power-law creep and residual stresses in a carbopol gel

We report on the interplay between creep and residual stresses in a carbopol microgel. When a constant shear stress σ is applied below the yield stress σ _y, the strain is shown to increase as a power law of time, γ(t) = γ ₀ + (t/τ) ^α , with an exponent α = 0.39 ± 0.04 that is strongly reminiscent of Andrade creep in hard solids. For applied shear stresses lower than some typical value σ _c ? 0.2σ _y, the microgel experiences a more complex, anomalous creep behavior, characterized by an initial decrease of the strain, that we attribute to the existence of residual stresses of the order of σ _c that persist after a rest time under a zero shear rate following preshear. The influence of gel concentration on creep and residual stresses are investigated as well as possible aging effects. We discuss our results in light of previous works on colloidal glasses and other soft glassy systems.     

Slow gas motions and the negative drag of a strongly heated spherical particle

In the slow flows of a strongly and nonuniformly heated gas, in the continuum regime (Kn → 0) thermal stresses may be present. The theory of slow nonisothermal continuum gas flows with account for thermal stresses was developed in 1969–1974. The action of the thermal stresses on the gas results in certain paradoxical effects, including the reversal of the direction of the force exerted on a spherical particle in Stokes flow. The propulsion force effect is manifested at large but finite temperature differences between the particle and the gas. This study is devoted to the thermal-stress effect on the drag of a strongly heated spherical particle traveling slowly in a gas for small Knudsen numbers (M ～ Kn → 0), small but finite Reynolds numbers (Re ≤ 1), a linear temperature dependence of the transport coefficients µ ∝ T, and large but finite temperature differences ((T _w ? T _∞ )/T _M8 ～ 1). Two different systems of equations are solved numerically: the simplified Navier-Stokes equations and the modified Navier-Stokes equations with account for the thermal stresses.     

Effect of thermal exposure on the residual stress relaxation in a hardened cylindrical sample under creep conditions

This paper describes the effect of thermal exposure (high-temperature exposure) (T = 675?C) on the residual creep stress relaxation in a surface hardened solid cylindrical sample made of ZhS6UVI alloy. The analysis is carried out with the use of experimental data for residual stresses after micro-shot peening and exposures to temperatures equal to T = 675?C during 50, 150, and 300 h. The paper presents the technique for solving the boundary-value creep problem for the hardened cylindrical sample with the initial stress–strain state under the condition of thermal exposure. The uniaxial experimental creep curves obtained under constant stresses of 500, 530, 570, and 600 MPa are used to construct the models describing the primary and secondary stages of creep. The calculated and experimental data for the longitudinal (axial) tensor components of residual stresses are compared, and their satisfactory agreement is determined.     

Dual yielding in capillary suspensions

Rheological measurements were performed to examine the yielding behavior of capillary suspensions prepared by mixing cocoa powder as dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid. Here, we investigated the yielding behavior of solid-fluid-fluid systems with varying particle volume fraction, ?, spanning the regime from a low volume fraction (? = 0.25) to a highly filled regime (? = 0.65) using dynamic oscillatory measurements. While for ? ≤ 0.4 with a fixed water volume fraction (? _w ) of 0.06 as the secondary fluid, capillary suspensions exhibited a single yield point due to rupturing of aqueous capillary bridges between the particles, while capillary suspensions with ? ≥ 0.45 showed a two-step yielding behavior. On plotting elastic stress (G^′ γ) as a function of applied strain (γ), two distinct peaks, indicating two yield stresses, were observed. Both the yield stresses and storage modulus at low strains were found to increase with ? following a power law dependence. With increasing ? _w (0 – 0.08) at a fixed ? = 0.65, the system shifted to a frustrated, jammed state with particles strongly held together shown by rapidly increasing first and second yield stresses. In particular, the first yield stress was found to increase with ? _w following a power law dependence, while the second yield stress was found to increase exponentially with ? _w . Transient steady shear tests were also performed. The single stress overshoot for ? ≤ 0.4 with ? _w = 0.06 reflected one-step yielding behavior. In contrast, for high ? (≥ 0.45) values with ? _w = 0.06, two stress overshoots were observed in agreement with the two-step yielding behavior shown in the dynamic oscillatory measurements. Experiments on the effect of resting time on microstructure recovery demonstrated that aggregates could reform after resting under quiescent conditions.     

Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.     

Direct Numerical Simulation and Theory of a Wall-Bounded Flow with Zero Skin Friction

We study turbulent plane Couette-Poiseuille (CP) flows in which the conditions (relative wall velocity ΔU _w ≡ 2U _w , pressure gradient dP/dx and viscosity ν) are adjusted to produce zero mean skin friction on one of the walls, denoted by APG for adverse pressure gradient. The other wall, FPG for favorable pressure gradient, provides the friction velocity u _τ , and h is the half-height of the channel. This leads to a one-parameter family of one-dimensional flows of varying Reynolds number Re ≡ U _w h/ν. We apply three codes, and cover three Reynolds numbers stepping by a factor of two each time. The agreement between codes is very good, and the Reynolds-number range is sizable. The theoretical questions revolve around Reynolds-number independence in both the core region (free of local viscous effects) and the two wall regions. The core region follows Townsend’s hypothesis of universal behavior for the velocity and shear stress, when they are normalized with u _τ and h; on the other hand universality is not observed for all the Reynolds stresses, any more than it is in Poiseuille flow or boundary layers. The FPG wall region obeys the classical law of the wall, again for velocity and shear stress. For the APG wall region, Stratford conjectured universal behavior when normalized with the pressure gradient, leading to a square-root law for the velocity. The literature, also covering other flows with zero skin friction, is ambiguous. Our results are very consistent with both of Stratford’s conjectures, suggesting that at least in this idealized flow turbulence theory is successful like it was for the classical logarithmic law of the wall. We appear to know the constants of the law within a 10% bracket. On the other hand, that again does not extend to Reynolds stresses other than the shear stress, but these stresses are passive in the momentum equation.     

Operator method for solving the plane elasticity problem for a strip with periodic cuts

In the present paper, we use the conformal mapping z/c = ζ?2a sin ζ (a, c?const, ζ = u + iv) of the strip {|v| ≤ v ₀, |u| < ∞} onto the domain D, which is a strip with symmetric periodic cuts. For the domain D, in the orthogonal system of isometric coordinates u, v, we solve the plane elasticity problem. We seek the biharmonic function in the form F = C ψ ₀ + S ψ*₀ + x(C ψ ₁ ? S ψ ₂) + y(C ψ ₂ + S ψ ₁), where C(v) and S(v) are the operator functions described in [1] and ψ ₀(u), …, ψ ₂(u) are the desired functions. The boundary conditions for the function F posed for v = ±v ₀ are equivalent to two operator equations for ψ ₁(u) and ψ ₂(u) and to two ordinary differential equations of first order for ψ ₀(u) and ψ*₀(u) [2]. By finding the functions ψ _j (u) in the form of trigonometric series with indeterminate coefficients and by solving the operator equations, we obtain infinite systems of linear equations for the unknown coefficients. We present an efficient method for solving these systems, which is based on studying stable recursive relations. In the present paper, we give an example of analysis of a specific strip (a = 1/4, v ₀ = 1) loaded on the boundary v = v ₀ by a normal load of intensity p. We find the particular solutions corresponding to the extension of the strip by the longitudinal force X ^∞ and to the transverse and pure bending of the strip due to the transverse force Y ^∞ and the constant moment M ^∞, respectively. We also present the graphs of normal and tangential stresses in the transverse cross-section x = 0 and study the stress concentration effect near the cut bottom.     

Stress-concentration factors for semielliptical notches in beams under pure bending

Elliptical notches in rectangular beams under pure bending are examined photoelastically. Stress-concentration factors due to a single elliptical notch are obtained for wide ranges of 2a/h andd/h, where 2a, d, andh are the width of notch, depth of notch, and depth of beam, respectively. In particular, the geometries of the optimum elliptical notches producing the least stress concentrations are obtained. Almost the whole elliptical boundary of these notches are stressed to the same peak, which indicates that these notches will probably produce the least stress concentrations among all notches, elliptical or nonelliptical. The graphs herein will enable the designers to find the stress-concentration factors of elliptical notches and to pick out the geometry of the optimum notch which will give the least stress concentration for any given values of 2a/h andd/h. Stresses and the stress-concentration factors at the bottom of the beam opposite the notch are also obtained. These stresses, though smaller in magnitude, are of an opposite sign to the peak stress at the notch. For brittle materials, a smaller tensile stress may be more critical than a large compressive stress; therefore, these stress-concentration factors are also given.     

Wall slip and multi-tier yielding in capillary suspensions

Impact of wall slip on the yield stress measurement is examined for capillary suspensions consisting of cocoa powder as the dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid using smooth and serrated parallel plates. Using dynamic oscillatory measurements, we investigated the yielding behavior of this ternary solid-fluid-fluid system with varying particle volume fraction, ?, from 0.45 to 0.65 and varying water volume fraction, ?_w, from 0.02 to 0.08. Yield stress is defined as the maximum in the elastic stress (G^′γ), which is obtained by plotting the product of elastic modulus (G^′) and strain amplitude (γ) as a function of applied strain amplitude. With serrated plates, which offer minimal slippage, capillary suspensions with ? ≥?0.45 and a fixed ?_w =?0.06 showed a two-step yielding behavior as indicated by two peaks in the plots of elastic stress as a function of strain amplitude. On the other hand with smooth plates, the capillary suspensions showed strong evidence of wall slip as evident by the presence of three distinct peaks and lowered first yield stresses for all ? and ?_w. These results can be interpreted based on the fact that a particle-depleted layer, which is known to be responsible for slip, is present in the vicinity of the smooth surfaces. The slip layer presents itself as an additional “pseudo-microstructure” (characteristic length scale) besides the two microstructures, aqueous bridges and solid particle agglomerates, that may occur in the system. With serrated plates, both the yield stresses (σ₁σ₂) and storage moduli plateau at lower strain (before the first yield point) and at higher strain (before the second yield point) (G\(^{\prime }_{p1}\), G\(^{\prime }_{p2}\)) were found to increase with ? (at a fixed ?_w =?0.06) following power-law dependences. Similarly with increasing ?_w (0.02 – 0.08) at a fixed ? =?0.62, the system behaved as a solid-like material in a jammed state with particles strongly held together as manifested by rapidly increasing σ₁ and σ₂. The usage of smooth surfaces primarily affected σ₁ which was reflected by an approximately 70–90% decrement in the measured σ₁ for all values of ?. By contrast, σ₂ and G\(^{\prime }_{p2}\) were found to be unaffected as shown by close agreement of values obtained using serrated geometry due to vanishing slip layers at higher strain amplitudes.     

Inverse problem of fracture mechanics for a compound cylinder

We consider the plane problem of fracture mechanics for a compound cylinder. We assume that the sleeve (internal cylinder) is reinforced with negative allowance by the external cylinder and that near the sleeve surface there are N arbitrarily located rectilinear cracks of length 2l _k (k = 1, 2, ..., N). A minimax criterion is used to determine the negative allowance in the junction theoretically minimizing the fracture parameters (the stress intensity coefficients) of the compound cylinder. A simplified method for minimizing the fracture parameters of the compound cylinder is considered separately.     

Mechanical Properties of Hard W-C Coating on Steel Substrate Deduced from Nanoindentation and Finite Element Modeling

Mechanical properties of a hard and stiff W-C coating on steel substrate have been investigated using nanoindentation combined with finite element modeling (FEM) and extended FEM (XFEM). The significant pile-up observed around the indents in steel substrate caused an overestimation of hardness and indentation modulus. A simple geometrical model, considering the additional contact surfaces due to pile-up, has been proposed to reduce this overestimation. The presence of W-C coating suppressed the pile-up in the steel substrate and a transition to sink-in behavior occurred. The FEM simulations adequately reproduced the surface topography of the indents in the substrate and coating/substrate systems as well. The maximum principal stresses of the indented W-C/steel coated system were tensile; they were always located in the coating and evolved in 3 stages. Cohesive cracking occurred during loading in the sink-in zone (stage III) when the ultimate tensile strength (σ _max ) of the coating was reached. The obtained hardness (H _c ), indentation modulus (E _c ), yield stress (Y) and strength (σ _max ) of the W-C coating were H _c ? =?20 GPa, E _c ? =?250 GPa, Y?=?9.0 GPa and σ _max ? =?9.35 GPa, respectively. XFEM resulted in fracture energy of the W-C coating of G?=?38.1 J?·?m^-2 and fracture toughness of K _IC ? =?3.5 MPa?·?m^0.5.     

Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 1: Linear Stability Analysis

The development of the thermo-viscous fingering instability of miscible displacements in homogeneous porous media is examined. In this first part of the study dealing with stability analysis, the basic equations and the parameters governing the problem in a rectilinear geometry are developed. An exponential dependence of viscosity on temperature and concentration is represented by two parameters, thermal mobility ratio β _T and a solutal mobility ratio β _C , respectively. Other parameters involved are the Lewis number Le and a thermal-lag coefficient λ. The governing equations are linearized and solved to obtain instability characteristics using either a quasi-steady-state approximation (QSSA) or initial value calculations (IVC). Exact analytical solutions are also obtained for very weakly diffusing systems. Using the QSSA approach, it was found that an increase in thermal mobility ratio β _T is seen to enhance the instability for fixed β _C , Le and λ. For fixed β _C and β _T , a decrease in the thermal-lag coefficient and/or an increase in the Lewis number always decrease the instability. Moreover, strong thermal diffusion at large Le as well as enhanced redistribution of heat between the solid and fluid phases at small λ is seen to alleviate the destabilizing effects of positive β _T . Consequently, the instability gets strictly dominated by the solutal front. The linear stability analysis using IVC approach leads to conclusions similar to the QSSA approach except for the case of large Le and unity λ flow where the instability is seen to get even less pronounced than in the case of a reference isothermal flow of the same β _C , but β _T  = 0. At practically, small value of λ, however, the instability ultimately approaches that due to β _C only.     

Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics(MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations(PDEs)subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations(ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles,Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x-and z-directions are boosted with maximizing the values of nanoparticle solid volume fraction ? and rotation λ. Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.     

The string-net analog of flexure of prismatic beams

Plots of the stress function (obtained graphically from enlarged photos of the string net), and of the shear-stress distribution over the normal section of beams in cantilever loading, for beams of rectangular, and of circular section, compare well with the exact mathematical solutions. Regions of increasing stress, leading to points of stress concentration are clearly shown. String nets were built for rectangular sections of ratio of half widthb to half deptha, R=b/a=1/4, 1/2, 1, 2, 4, 8. The form of the net forR≦|1| suggested the assumption of a plane for part of φ(x, y). ForR?|1| another simple approximation was assumed for φ(x, y). The simple approximate mathematical analyses obtained from the values of φ(x, y) helped to show where the concentrations of stress are and how they vary withR.     

Effect of vibration on the creep of tensile-test specimens of the aluminum alloy Al−Mg−Si (PA-4)

In this work are presented the results of research on vibrational creep at normal temperature of an aluminum alloy containing magnesium and silicon (designated PA-4). A uni-directional positive load is applied to a tensile-test specimen, such that the stress intensity in the specimen is of the type\(\sigma (t) = \sigma _m (1 + Asin\omega t)\) whereσ _m is the mean (static) stress intensity andA =σ _a /σ _m is the ratio of the vibratory-stress intensity to the mean intensity. The results are given in the form of families of curves of plastic (i.e., permanent) deformation for various values ofA, namely,A=0.0000, 0.0065, 0.05500, 0.1000 and 0.2000. Taking the creep limit for plastic strain as ε _p = 1.8 percent, equations for this creep limit were deduced from experimental data. The following conclusions are drawn from these investigations:

1. 1.
   Vibrations of small-stress-amplitude ratioA encourage creep, particularly with more lengthy tests.     
   
   

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

The stationary and time-dependent aerodynamic coefficients of a slender blunt cone with a flap located near the base section of the model are experimentally investigated. The freestream parameters (M_∞ = 6, Re _L = 0.88 × 10⁷, and γ = 1.4) ensured a turbulent regime of flow over the conical surface and the flap. At high angles of attack (α ～ 10°) laminar-turbulent transition is observable in the separation zone on the leeward side of the body. Emphasis is placed on the determination of the trimming angles of attack for different positions of the center of rotation and the static and dynamic stability coefficients (the model oscillation damping coefficient).     

Kinetic Fokker-Planck equation for free-molecular,thermally nonequilibrium Brownian particles in an inhomogeneous gas

A kinetic equation for the translational and angular velocity distribution function of spherical rigid Brownian particles in an inhomogeneous monatomic gas is derived. The particle diameters are much smaller than the average free path of the gas molecules and the interaction between the particles and their effect on the carrier (gas) phase are neglected. The particle temperatures T _p are the same and differ from the local gas temperature T. The molecular velocity distribution function is specified by the first approximation of the Chapman-Enskog method. The difference between the characteristic phase velocities is small as compared with the mean thermal molecular velocity. The dependences of the diffusion coefficients in velocity space on the ratio T _p/T, which characterize the effect of thermal nonequilibrium, i.e., violation of the thermodynamic equilibrium between the phases of the disperse system, are found using a specular-diffuse law of reflection of the molecules from the particle surface.     

The mathematical model of reflection and refraction of longitudinal waves in thermo-piezoelectric materials

In this paper, the basic equations of motion, of Gauss and of heat conduction, together with constitutive relations for pyro- and piezoelectric media, are presented. Three thermoelastic theories are considered: classical dynamical coupled theory, the Lord–Shulman theory with one relaxation time and Green and Lindsay theory with two relaxation times. For incident elastic longitudinal, potential electric and thermal waves, referred to as qP, φ-mode and T-mode waves, which impinge upon the interface between two different transversal isotropic media, reflection and refraction coefficients are obtained by solving a set of linear algebraic equations. A case study is investigated: a system formed by two semi-infinite, hexagonal symmetric, pyroelectric–piezoelectric media, namely Cadmium Selenide (CdSe) and Barium Titanate (BaTiO₃). Numerical results for the reflection and refraction coefficients are obtained, and their behavior versus the incidence angle is analyzed. The interaction with the interface give rises to different kinds of reflected and refracted waves: (i) two reflected elastic waves in the first medium, one longitudinal (qP-wave) and the other transversal (qSV-wave), and a similar situation for the refracted waves in the second medium; (ii) two reflected potential electric waves and a similar situation for the refracted waves; (iii) two reflected thermal waves and a similar situation for the refracted waves. The amplitudes of the reflected and refracted waves are functions of the incident angle, of the thermal relaxation times and of the media elastic, electric, thermal constants. This study is relevant to signal processing, sound systems, wireless communications, surface acoustic wave devices and military defense equipment.     

The stress state of a plate subjected to a piecewise homogeneous load

We consider the stress-strain state of a plate having a doubly connected domain S bounded from the outside by a circle of radius R and from the inside by an ellipse with two rectilinear cuts. The cuts lie symmetrically on the x-axis. The plate is subjected to various forces: the hole contour (the ellipse) is under the action of uniformly distributed forces of intensity q, and the cut shores are free of loads; at the points ±ib of the imaginary axis, the plate is under the action of a lumped force P.The solution of the problem is reduced to determining two analytic functions φ(z) and ψ(z) satisfying certain boundary conditions (depending on the type of the acting loads).We use the Kolosov-Muskhelishvili method to reduce the problem to a system of linear algebraic equations for the coefficients in the expansions of the functions φ(z) and ψ(z). The solution thus obtained is illustrated by numerical examples.     

Stress distributions in a semi-infinite plate due to a pin determined by interferometric method

The stress distributions in a semi-infinite plate due to a loaded pin of the same material as the plate are systematically investigated by an interferometric method which has been developed by the authors. For the experiments, a finite plate of diallylphthalate with a circular hole is used. It is supported at one side and loaded in the direction normal to the opposing straight edge by a pin which just fits the hole. The ratio of the distancee between the hole center and the straight edge to the diameterd of the hole is varied in steps from 4.0 to 1.0. At each step, the distributions of principal stresses σ₁ and σ₂ along the hole edge, line of symmetry and straight edge, which have not been fully investigated especially whene/d is small, are obtained separately from the isopachic and isochromatic fringes of the interfero-stress patterns. The relations between the maximum values of these stresses and the shape factore/d are determined.