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• W2103686987 abstract "The response of an isotropic, nonlinear viscoelastic, thin-walled tube to combinations of axial force F , axial couple G and pressure difference p is considered theoretically and experimentally. Theory is based on the membrane theory of thin shells, applied to a thin-walled circular cylindrical tube. The components of two dimensional stress and strain in the wall of the tube are derived, allowing for arbitrarily large deformations; but restriction to small deformations is shown to be necessary if the history of stress is to be controlled at will through F , G and p . For arbitrary choice of F , G and p as functions of time the strain is shown to depend on three stress tensors P , Q , R independent of time, and three scalar functions of time. An expression for the linear strain tensor in terms of P , Q , R is obtained which involves four scalar functions ϕ 0 , ϕ 1 , ϕ 2 , ϕ 3 . These functions depend on the invariants of P , Q , R and on the three scalar functions of time. If any one of P , G , p is always zero then R = 0 and only ϕ 0 , ϕ 1 , ϕ 2 are required. In the case of proportional loading ( Q = R = 0 ) only ϕ 0 and ϕ 1 are required and any one of the three strain components can be calculated from the remaining two. Creep and recovery experiments under simultaneous axial force and couple were conducted on a thin-walled tube of polypropylene at 65.5 °C. Theory was used to calculate the circumferential tensile strain from the measured shear strain and longitudinal tensile strain. For this particular tube <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi mathvariant=italic>ϕ</mml:mi> <mml:mrow> <mml:mn mathvariant=normal>0</mml:mn> </mml:mrow> </mml:msub> </mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi mathvariant=italic>ϕ</mml:mi> <mml:mrow> <mml:mn mathvariant=normal>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> were found to be related in a special manner, implying that nonlinearity can be adcquatcly described by allowing the shear creep compliance to change with stress history. By varying separately combinations of the invariants of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mi mathvariant=italic>P</mml:mi> <mml:mo mathvariant=normal>,</mml:mo> </mml:math> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi mathvariant=italic>ϕ</mml:mi> <mml:mrow> <mml:mn mathvariant=normal>1</mml:mn> </mml:mrow> </mml:msub> </mml:math> was found to depend on both hydrostatic and deviatoric components ofthe applied stress." @default.
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• W2103686987 date "1976-05-20" @default.
• W2103686987 modified "2023-09-27" @default.
• W2103686987 title "Small deformations of a nonlinear viscoelastic tube: theory and application to polypropylene" @default.
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• W2103686987 doi "https://doi.org/10.1098/rsta.1976.0049" @default.
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