Comparative Analysis of the Profile Evolutions of an Elastic Harmonic Wave Caused by the Second and Third Harmonics

Cattani, Carlo; Rushchitsky, J. J.; Sinchilo, S. V.

doi:10.1023/b:inam.0000028597.32722.be

Cited by 12 publications

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“…Analytic approaches to the investigation of elastic wave effects in composite and granular composite materials can be found in [3][4][5][6][7]. Several studies [8,13] evidenced that finite-element analysis can be used as a very useful tool for process…”

Section: Introductionmentioning

confidence: 99%

“…Nowadays, the powder metallurgy industry is based on expensive trial and error procedures for product and die design, as well as for process parameter setup. Experimental investigations of the stress distribution into processing powders are not feasible, even using ultrasonic nondestructive stress analysis [1,2].Analytic approaches to the investigation of elastic wave effects in composite and granular composite materials can be found in [3][4][5][6][7]. Several studies [8,13] evidenced that finite-element analysis can be used as a very useful tool for process…”

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Computational modeling of the cold compaction of ceramic powders

Carlone

Palazzo

2006

Int Appl Mech

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A finite-element model of the cold compaction of ceramic powders by uniaxial pressing is developed and validated by comparison with experimental data. The mechanical behavior of processing powders is assumed according to the modified Drucker-Prager cap model. The frictional effects and the mechanical behavior of tools involved in the process are taken into account. The proposed model allows evaluation of the density distribution into the processed part, as well as stress and strain fields. Variations of the density distribution due to the unloading and the ejection of the part are evaluated Keywords: cold compaction, powder metallurgy, finite-element method, numerical modeling, DruckerPrager cap model Introduction.Manufacturing processes that allow obtaining near net-shape products using powders as raw material are referred to as powder metallurgy. The most relevant steps of powder metallurgy are the production of (pure or pre-alloyed) powders, the powder cold compaction process, and the sintering process. Sometimes, after these processes, the part is subjected to finishing processes, such as recompaction, resintering, heat treatment, and machining operations, to improve its geometrical and mechanical properties. The physical and chemical properties of processing powders are very important to achieve the desired mechanical properties of the final product.Metallic or ceramic powders can be obtained by several processes: mechanical processes, such as machining, sledging, grinding, granulating, shot blasting, and atomization; physical or physical-chemical processes, such as condensation and thermal decomposition; chemical processes, such as oxide reduction, solution precipitation, and corrosion; and electrolytic methods. The obtained powders are then subjected to mechanical and thermal treatments to improve density, to mix different kinds of powders, and to remove hardening effects and impurities.Cold compaction processes are used to shape powders into porous parts, called greens, whose mechanical resistance allows manipulating them during the sintering process. Typical processes of powder compaction are uniaxial pressing, isostatic pressing, high speed forming, extrusion forming, vibration forming, centrifugal forming, rolling forming, continuous forming, gravity forming, and mixture forming. The sintering process is heat treatment used to achieve stable cohesion of compacted powders. The sintering temperature is lower than the melting temperature of the main component of the powder mixture or of all different powders.The powder compaction process is very important to obtain a final product characterized by the desired mechanical and geometrical features. Indeed, plasticity phenomena, internal friction of a porous medium, and frictional effects between the die wall and the processing material may induce inhomogeneous density and residual stress distributions. As a consequence, during the sintering process, nonuniform shrinkage, local distortions, or cracks may occur. Nowadays, the powder metallurgy industry is base...

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Computational modeling of the cold compaction of ceramic powders

Carlone

Palazzo

2006

Int Appl Mech

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“…We additionally assume that these functions are quadratically nonlinear, thus neglecting higher nonlinearities. Such an assumption was earlier adopted in nonlinear acoustics to analyze nonlinear elastic waves in Cartesian coordinates [2,3,5,[11][12][13][14][15].…”

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“…The classical linear solution for a cylindrical wave (when the right-hand side of Eq. (63) is equal to zero) has the form u r z t u J r e u [5,10,13]. Therefore, in view of the form of the nonlinear right-hand side, it is easy to solve the nonlinear wave equation (63) by the method of successive approximations and to predict that the second harmonic will appear and the form of amplitude will become more complex.…”

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Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Axisymmetric and Other States

Rushchitsky

2005

Int Appl Mech

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A rigorous approach of nonlinear continuum mechanics is used to derive nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. Nonlinearity is introduced by means of metric coefficients, the Cauchy-Green strain tensor, and the Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. Quadratically nonlinear wave equations are derived for three states (configurations): (i) axisymmetric configuration dependent on the radial and axial coordinates and independent of the angular coordinate, (ii) configuration dependent on the angular coordinate, and (iii) axisymmetric configuration dependent on the radial coordinate. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. Six different systems of wave equations are written Keywords: nonlinear continuum mechanics, rigorous approach, nonlinear hyperelastic cylindrical waves, quadratically nonlinear wave equations, geometrical and physical nonlinearities, axisymmetric stateThe nonlinear wave equations describing the propagation of hyperelastic waves have been derived in [6]. This paper demonstrated a rigorous approach, passed over even in the textbooks [7,9,10,16], to deriving nonlinear wave equations in cylindrical (orthogonal) coordinates. The approach is based on the concepts of modern nonlinear continuum mechanics. Nonlinearity was introduced by means of metric coefficients, the Cauchy-Green strain tensor, and the Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. A configuration (state) of an elastic medium dependent on the coordinates r, ϑ and independent of the coordinate z was analyzed. This configuration is often called plane-strain state. For this case, the corresponding equations of motion and analytical expressions for the stress tensor in terms of the deformation gradient were derived. Four ways of introducing physical and geometrical nonlinearities to the wave equations were analyzed. For one of the ways, the nonlinear wave equations were written explicitly.The present paper extends the analysis performed in [6] to several partial configurations (states) omitted there. State I. It is an axisymmetric configuration dependent on the coordinates r and z and independent of the coordinate ϑ. The Oz-axis is the axis of symmetry. This state is typical of, for example, a longitudinal torsional wave propagating along a cylinder.State II. It is a configuration that depends only on the angular coordinate ϑ. Its axis of symmetry is Oz. This state is typical of, for example, a transverse torsional wave propagating along a cylinder.State III. It is an axisymmetric configuration that depends only on the coordinate r. Its axis of symmetry is Oz. This state is typical of, for example, a classical cylindrical wave or Volterra translational distortions in a hollow cylinder.As in [6], we introduce a cylindrical (orthogonal) coordinate system: θ θ θ 1 2 3 = = = r z , , ϑ . In this system, the length of a vec...

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Nonlinear Plane Longitudinal Waves in Elastic Materials (Murnaghan Model, Five-Constant Model)

Rushchitsky

2014

Foundations of Engineering Mechanics

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Comparative Analysis of the Profile Evolutions of an Elastic Harmonic Wave Caused by the Second and Third Harmonics

Cited by 12 publications

References 7 publications

Computational modeling of the cold compaction of ceramic powders

Computational modeling of the cold compaction of ceramic powders

Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Axisymmetric and Other States

Nonlinear Plane Longitudinal Waves in Elastic Materials (Murnaghan Model, Five-Constant Model)

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