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Longitudinal vertical crack analysis in beam with relaxation stresses

Longitudinal vertical crack analysis in beam with relaxation stresses This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.Design/methodology/approachTime-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.FindingsThe variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.Originality/valueThe time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png World Journal of Engineering Emerald Publishing

Longitudinal vertical crack analysis in beam with relaxation stresses

World Journal of Engineering , Volume 18 (3): 6 – May 28, 2021

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Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
1708-5284
DOI
10.1108/wje-05-2020-0181
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.Design/methodology/approachTime-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.FindingsThe variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.Originality/valueThe time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Journal

World Journal of EngineeringEmerald Publishing

Published: May 28, 2021

Keywords: Inhomogeneous beam; Relaxation stresses; Strain energy release rate; Viscoelastic model

References