Elastodynamic stress field and bifurcation of a running penny-shaped crack

1976 ◽  
Vol 27 (6) ◽  
pp. 791-800
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Field ◽  
Penny Shaped Crack ◽  
Shaped Crack

Local Stress Field for Torsion of a Penny-Shaped Crack in a Functionally Graded Strip

2004 ◽  
Vol 261-263 ◽  
pp. 123-128
Author(s):  
Wen Jie Feng ◽  
R.J. Hao ◽  
Li Bin Wang ◽  
Juan Liu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Local Stress ◽  
Hankel Transform ◽  
Functionally Graded ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Functionally Graded Strip

The torsion of a penny-shaped crack in a functionally graded strip is considered. Hankel transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. Numerical results show that increasing the gradient of shear modulus can suppress crack initiation and growth, and that the stress intensity factor varies little with the increasing of the strip's highness.

Fractional thermoelasticity problem for an infinite solid with a penny-shaped crack under prescribed heat flux across its surfaces

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190289 ◽  
Author(s):  
Y. Povstenko ◽  
T. Kyrylych
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Stress Field ◽  
Fractional Calculus ◽  
Heat Conduction Equation ◽  
Thermoelasticity Problem ◽  
Conduction Equation ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Fractional Heat Conduction

The time-nonlocal generalization of the Fourier law with the ‘long-tail’ power kernel can be interpreted in terms of fractional calculus and leads to the time-fractional heat conduction equation with the Caputo derivative. The theory of thermal stresses based on this equation was proposed by the first author ( J. Therm. Stresses 28 , 83–102, 2005 ( doi:10.1080/014957390523741 )). In the present paper, the fractional heat conduction equation is solved for an infinite solid with a penny-shaped crack in the case of axial symmetry under the prescribed heat flux loading at its surfaces. The Laplace, Hankel and cos-Fourier integral transforms are used. The solution for temperature is obtained in the form of integral with integrands being the generalized Mittag-Leffler function in two parameters. The associated thermoelasticity problem is solved using the displacement potential and Love’s biharmonic function. To calculate the additional stress field which allows satisfying the boundary conditions at the crack surfaces, the dual integral equation is solved. The thermal stress field is calculated, and the stress intensity factor is presented for different values of the order of the Caputo time-fractional derivative. A graphical representation of numerical results is given. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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