Transition Theory of Elastic-Plastic Deformation, Creep and Relaxation

Seth, B. R.

doi:10.1038/195896a0

Cited by 54 publications

(51 citation statements)

References 3 publications

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“…For finding thermal creep stresses and strain rates, the transition function is taken through the principal stress difference (see Seth, 1962Seth, , 1966Thakur, 2011Thakur, , 2014Thakur et al, 2016Thakur et al, , 2017 at the transition point P → −1. We define the transition function ψ as…”

Section: Analytical Solutionmentioning

confidence: 99%

“…Seth's transition theory does not acquire any assumptions like the yield condition, incompressibility condition, and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out. This theory utilizes the concept of a generalized strain measure and asymptotic solution at critical points or turning points of differential equations defining the deformed field and has been successfully applied to a large number of problems (Seth, 1962(Seth, , 1966Thakur, 2011Thakur, , 2014Thakur et al, 2016Thakur et al, , 2017. Seth (1962) defined the concept of generalized strain measures as…”

Section: Introductionmentioning

confidence: 99%

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Thermal creep stress and strain analysis in non-homogeneous spherical shell

Thakur

Singh

Pathania³

et al. 2017

jtam

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The purpose of this paper is to present study of thermal creep stress and strain rates in a non-homogeneous spherical shell by using Seth's transition theory. Seth's transition theory is applied to the problem of creep stresses and strain rates in the non-homogeneous spherical shell under steady-state temperature. Neither the yield criterion nor the associated flow rule is assumed here. With the introduction of thermal effect, values of circumferential stress decrease at the external surface as well as internal surface of the spherical shell. It means that the temperature dependent materials minimize the possibility of fracture at the internal surface of the spherical shell. The model proposed in this paper is used commonly as a design of chemical and oil plants, industrial gases and stream turbines, high speed structures involving aerodynamic heating.

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Section: Analytical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal creep stress and strain analysis in non-homogeneous spherical shell

Thakur

Singh

Pathania³

et al. 2017

jtam

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“…For finding the plastic stress, the transition function is taken through the principal stress (see SETH [5,6], HULSURKAR [7], GUPTA etl. [4,[10][11][12], SHUKLA [8,9 ] , THAKUR [14 -42]) at the transition point P → ±∞ .…”

Section: Solution Through the Principal Stressesmentioning

confidence: 99%

“…Gupta et al [4] solved the problems effect of non-homogeneity on elastic-plastic transition in a thin rotating disc by using Seth's transition theory and plane stress condition. This theory [5] does not required any assumptions like an yield condition, incompressibility condition and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out. It utilizes the concept of generalized strain measure and asymptotic solution at critical points or turning points of the differential equations defining the deformed field and has been successfully applied to a large number of problems [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical model in a thin non-homogeneous rotating disc for isotropic material with rigid shaft by using Seth's transition theory

Thakur¹,

Kaur²,

Satya³

2015

Kragujevac J Sci

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ABSTRACT. In this paper we investigate stresses and displacement in thin nonhomogeneous rotating disc has been derived by using Seth's Transition theory and results have been discussed and depicted graphically. Non-homogeneity is assumed due to the variation of modulus of rigidity. As a numerical example, it has been seen that in the presence of non-homogeneity having values k > 0 at the bore, reduces stresses, displacement and the angular speed as compare to lesser value i.e. k <0 of nonhomogeneity. Radial stresses maximum at the internal surface.

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Torsion of a Transversely Isotropic Cylinder in the Theory of Creep

Gupta

Rana

1980

Z Angew Math Mech

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Transitional stresses for a transversely isotropic circular cylinder subjected to torsion have been derived. It has beeii shown that thr asymptotic solution through the stress and stress-dijJerence gives the plastic and creep stresses respectively. The effect of transverse isotropy i s presented graphically. The results indicate that the value of maximum shenr stresn for a cylinder of transversely isotropic material i s greater than thnt of a n isotropic incompressible material and it increase3 with the increase in measure 'n'. For a n isotropic incompressible material, as a particular case, the results are the same a.9 given by M a r i n . E3 wurden die ~bergangaspannungen eines transversal isotropen Kreiszylinders bei Torsion bestinimt. Es wurde gezeigt, daJ die asymptotische Losung infolge der Spannung und Spannungsdafferenz entsprechend die plastischen und Kriech-spannung~n liefert. Der Efjekt der transversalen Isotropie wird graphisch veranschaulicht. Die Ergebnisse Zeigen, daJ der maximale Wert der Schubspannungen bei eineni Zylinder rnit transversal isotropem Material gr@er ist als bei einem mit isotrop inkompressiblem Material. Er wachet mit der VergroJerung des MaJes W . Fur den Spezinlfnll des isotrop inkompressiblen Materials stirnmen die Ergebnisse mit denen von M a r in iiberein. Oupenene~m IiepexonHbre HanpfimeHWrr TpaHceepcanbHo uaoTpoiiHoro Kpyrotloro ~~a n~n r r [ p a npki ~paueiriirr. Tponm npenmaanee rpa@usecKu. P~~~J I L T~T L I I I O K~~~J I H , YTO MaHcWManbHoe 3~a~e~u e HanpnxeHmi cnusra rTOKaaaH0, lITO aCEiMIITOTEiYeCKOe peUeHI4e 11OCI)enCTBOM HaIIpRmeHWR Ei E)a3HOCTki HalIPRWeHUfI ItaeT lIJIaCTUWCKOf2 HanpFIX(eHWe ki HanpRWeHWe IlOJI3yYeCTEi COOTReTCTBeIlHO. 3@@eKT TpaHCBejlCaJIbHOii 1130y IltfJtklHnpa 113 TpaHCRepCaJIbHO I130TPOnHOI'O MaTepMaJltl60JIblIIe, 9 e M y 4lIJlLiHJI~~a 113 W3OTpOnHOrO HeCWEi-MaeMOL' O MaTepMaJIa li YTO 3 T 0 3HaYeHkle BO3paCTaeT C BO3paCTaHlleM hlepb1 , t l ' . PC3yJlLTaTL1, IlOJIY' IeHIIbIe B 'IBCTIIOM CJIyqae A30TPOIIHOrO HeCXiMMaehlOTO MLiTePMaJla, CORIIaIKiIOT C E)C3J' Jll>TaTaMki hi a p W H a.

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Transition Theory of Elastic-Plastic Deformation, Creep and Relaxation

Cited by 54 publications

References 3 publications

Thermal creep stress and strain analysis in non-homogeneous spherical shell

Thermal creep stress and strain analysis in non-homogeneous spherical shell

Mathematical model in a thin non-homogeneous rotating disc for isotropic material with rigid shaft by using Seth's transition theory

Torsion of a Transversely Isotropic Cylinder in the Theory of Creep

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