Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion

Belhadj, Asma; Bessrour, Jamel; Bouhafs, M.; Barrallier, Laurent

doi:10.1007/s10973-009-0094-4

Cited by 52 publications

(36 citation statements)

References 28 publications

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“…where B 4k are the 4k-order Boubaker polynomials [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], r k are B 4k minimal positive roots, N 0 is a prefixed integer, and ξ k | k=1,...,N0 are unknown pondering real coefficients. This expression refers to the Boubaker polynomials expansion scheme (BPES) [29][30][31].…”

Section: Governing Equationsmentioning

confidence: 99%

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

Boubaker

2012

ISRN Metallurgy

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Shape memory alloys (SMA) are metals which can restore their initial shape after having been subjected to a deformation. They exhibit in general both nonlinear shape memory and pseudoelastic effects. In this paper, shape memory alloy (SMA) and its constitutive model with an empirical kinetics equation are investigated. A new formulation to the martensite fractiondependent Young modulus has been adopted and the plastic deformation was taken into account. To simulate the variations, a one-dimensional constitutive model was constructed based on the uniaxial tension features.

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Section: Governing Equationsmentioning

confidence: 99%

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

Boubaker

2012

ISRN Metallurgy

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“…Optothermal investigation has been based on variation of the Amlouk-Boubaker Optothermal expansivity ψ AB , which is a synthetic physical parameter defined and used in precedent studies [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. This parameter has been defined by…”

Section: Indium and Ytterbiummentioning

confidence: 99%

Quantum Effects of Indium/Ytterbium Doping on ZnO-Like Nano-Condensed Matter in terms of Urbach-Martienssen and Wemple-DiDomenico Single-Oscillator Models Parameters

Boukhachem

Ouni

Bouzidi

et al. 2012

ISRN Condensed Matter Physics

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Conducting and transparent optical ZnO thin films were deposited on glass substrates by a simple mini spray technique. Alternatively, some of the obtained films were doped with indium and ytterbium at the molar rates of: 1, 2, and 3% (In) and 100, 200, and 300 ppm (Yb). In addition to the classical structural investigations including XRD, microhardness vickers (Hv), and optothermal techniques, thorough optical measurements have been carried out for comparison purposes. The refractive indices and the extinction coefficients of the differently doped layers have been deduced from their transmission-reflection spectra over an extended wavelength range. Analysis of the refractive index data through Wemple-DiDomenico single oscillator model yielded quantum characteristics along with the values of long-wavelength dielectric constant, average oscillator wavelength, average oscillator strength, average oscillator energy and dispersion energy. Real and imaginary parts of dielectric constant have also been used to calculate free carrier plasma resonance frequency, optical relaxation time, and free carriers concentration-to-effective mass ratio. Finally, analysis of Urbach-Martienssen model parameters allowed proposing nanoscale explanations to the divergence about doping-related evolution of Urbach tails, this intriguing item having been intensively discussed in the literature in the last decades.

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“…The Boubaker Polynomials Expansion Scheme (BPES) [26][27][28][29][30][31][32][33][34][35] is a resolution protocol which has been successfully applied to several applied physics and mathematics problems. The BPES protocol ensures the validity of the related boundary conditions regardless main equation features.…”

Section: The Boubaker Polynomials Expansion Scheme (Bpes)mentioning

confidence: 99%

“…Several solution have been proposed through the BPES in many fields such as numerical analysis [26], material characterization [27], theoretical physics [28], mathematical algorithms [29], heat transfer [31,32], and homodynamics [33][34][35].…”

Section: The Boubaker Polynomials Expansion Scheme (Bpes)mentioning

confidence: 99%

A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning

Boubaker

2012

ISRN Polymer Science

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A model to core-shell structured polymer nanofibers deposited via coaxial electrospinning is presented. Investigations are based on a modified Jacobi-Gauss collocation spectral method, proposed along with the Boubaker Polynomials Expansion Scheme (BPES), for providing solution to a nonlinear Lane-Emden-type equation. The spatial approximation has been based on shifted Jacobi polynomials P (α,β) T,N (x) with α, β(−1, ∞), T > 0 was n the polynomial degree. The Boubaker Polynomials Expansion Scheme (BPES) main features, concerning the embedded boundary conditions, have been outlined. The modified Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique, and a comparison is made with existing results. It has been revealed that both methods are easy to implement and yield very accurate results.

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Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and Boubaker polynomials expansion

Cited by 52 publications

References 28 publications

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

Quantum Effects of Indium/Ytterbium Doping on ZnO-Like Nano-Condensed Matter in terms of Urbach-Martienssen and Wemple-DiDomenico Single-Oscillator Models Parameters

A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning

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