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1
Content available Lengthwise crack study of a beam with non-linear creep
Rizov Victor Iliev
Engineering Transactions
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2024
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Vol. 72, iss. 1
15--38
EN
An analytical study of the strain energy release rate for an inhomogeneous beam structure with a lengthwise crack subjected to non-linear creep is developed. The beam is inhomogeneous along its length. Two cases are analysed (material with identical creep behaviour in tension and compression, and material with asymmetrical creep behaviour). Since the stress cannot be determined explicitly from the non-linear stress-strain-time relationship, an approach for obtaining of time-dependent solutions of the strain energy release rate is developed by expressing the z-coordinate as a function of the stress. The analysis indicates that the asymmetrical creep behaviour leads to an increase in the strain energy release rate.
2
Content available Multi-layered non-linear viscoelastic beams subjected to torsion at a constant speed: a delamination analysis
Rizov Victor Iliev, Altenbach Holm
Engineering Transactions
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2022
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Vol. 70, iss. 1
53--66
EN
A non-linear mechanical model with a linear spring, a linear dashpot and a non-linear dashpot is used for studying the non-linear viscoelastic behaviour of a multi-layered inhomogeneous beam with a delamination crack. The beam with a circular cross-section is under a torsion moment that increases at a constant speed. The non-linear stress-strain-time constitutive law of the model is obtained by adding the non-linear shear strain to the strain in the linear spring and linear dashpot. Solutions of the time-dependent strain energy release rate are derived, which take into account the non-linear viscoelastic behaviour of the beam and the torsion moment rate.
3
Content available remote Lengthwise fracture study of transversely inhomogeneous rods
Rizov Victor Iliev
Engineering Transactions
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2020
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Vol. 68, iss. 3
253--268
EN
A lengthwise crack in a rod that exhibits smooth (continuous) material inhomogeneity in the transverse direction is studied. The rod has a circular cross-section. The lengthwise crack is located arbitrarily along the thickness of the rod. A solution to the strain energy release rate is derived assuming that the moduli of elasticity in tension and compression are distributed continuously in the transverse direction. The strain energy release rate is also analyzed by applying the compliance method for verification. The influences of various factors such as the crack location, material inhomogeneity and the different mechanical behavior of the material in tension and compression on the fracture are investigated and discussed in detail.
4
Content available remote Analysis of two lengthwise cracks in a viscoelastic inhomogeneous beam structure
Rizov Victor Iliev
Engineering Transactions
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2020
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Vol. 68, iss. 4
397--415
EN
The present paper considers the time-dependent fracture in a continuously inhomogeneous viscoelastic cantilever beam with two lengthwise cracks. Time-dependent analytical solutions to the strain energy release rate, which take into account the viscoelastic behaviour of the material, are derived. A rheological model with two springs and two dashpots is used for studying the viscoelastic behaviour of the beam. A stress-strain-time relationship is obtained for the case when the rheological model is loaded by stress that increases linearly with time up to a certain level and then it remains constant. The variation of the strain energy release rate with time is analysed.
5
Content available remote Effects of three-axial material inhomogeneity on lengthwise cracks in non-linear elastic beams
Rizov Victor Iliev
Engineering Transactions
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2019
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Vol. 67, iss. 1
35--54
EN
The present paper investigates lengthwise crack behaviour in three-axial inhomogeneous non-linear elastic cantilever beams, i.e., beams which exhibit inhomogeneous material properties along the width, height and length. The non-linear mechanical behaviour of the inhomogeneous material is described by the Ramberg-Osgood equation assuming that the modulus of elasticity varies linearly along the width, height and length of beams. A solution to the strain energy release rate is derived by considering the balance of the energy. The results obtained in the present paper indicate that the three-axial inhomogeneous material properties have a significant influence on the strain energy release rate in non-linear elastic beams.
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