Torsion of a cylinder with a shallow external crack

Abstract

a b s t r a c tThe torsional problem of a finite elastic cylinder with a circumferential edge crack is studied in this paper. An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations. Unlike the Srivastav approach, this regularization transforms dual equations into a Fredholm integral equation of the second kind given on the crack surface. Hence, exact asymptotic expansions of the Fredholm equation solution, the stress intensity factor and the torque are derived for the case of a shallow crack. The asymptotic expansions are certain power-logarithmic series of the normalized crack depth. Coefficients of these series are found from recurrent relations. Calculations for a shallow crack manifest that the stress intensity factor exhibits the rather weak dependence upon the cylinder length when the torque is fixed and the triple length is larger than the diameter.

Torsion analysis of finite solid circular cylinders with multiple concentric planar cracks

“…As it can be seen there is a good agreement between the results. Also the stress intensity factor of the crack tip is increased by crack growth. Example We consider an infinite cylinder with base radius R weakened by a circular edge crack with the crack depth Table gives a comparative analysis of the dimensionless stress intensity factor obtained by use of the present method and those attained by references . The crack surface was under the constant moment The stress intensity factor has been normalized with aid of a divisor .…”

“…Also torsion problem of a finite cylinder was treated by Chang , Zhang , Zhang and Zhang , Zhang , Liang and Zhang , Zlatin and Uflyand , and also Malits . At the above‐mentioned studies the materials of cylinders were made of isotropic [, ], orthotropic or FGM . In FG cylinders the shear modulus of the cylinder was varied as a power form in the radial direction ) except for reference in which a power‐form variation of the shear modulus of the cylinder was considered in the axial direction.…”

“…Axial torsion problem of an infinite cylinder was studied by Qizhi [14], Kassir [15], Xue-Li and Duo [16], Shibuya et al [17], Kazuyoshi et al [18], Noda and Takase [19], Akiyama et al [20], Zlatin and Uflyand [21]. Also torsion problem of a finite cylinder was treated by Chang [22], Zhang [23], Zhang and Zhang [24], Zhang [25], Liang and Zhang [26], Zlatin and Uflyand [27], and also Malits [28]. At the above-mentioned studies the materials of cylinders were made of isotropic [14, 17-22, 24, 27, 28], orthotropic [23,25] or FGM [15,16,25,29].…”

“…The crack type plays an important rule in solution of crack problems. In this regards, the concentric penny-shaped crack was the subject of the references [14][15][16] and [22][23][24][25][26] while the circumferential edge crack was considered at the works done by the references [17][18][19][20][21] and [27][28][29].…”

The stress state of the finite cylinder with the circular cracks

“…For example in [1][2][3] are considered the circular cracks. The problems with the boundary cracks were solved in [4,5]. The stress state of the multilayered cylinders under the torsion loading was investigated significantly less [6].…”