Cracks Of Equal Length Research Articles

Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Saint-Venant torsion of a circular bar with radial cracks incorporating arbitrarily varied surface elasticity

ABSTRACTWe analytically investigate the contribution of arbitrarily varied surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack. The varied surface elasticity is incorporated by using a modified version of the continuum-based surface/interface model of Gurtin and Murdoch. In our discussion, the surface shear modulus is assumed to be arbitrarily varied along the crack surfaces. Both internal and edge cracks are studied. By using Green's function method, the boundary value problem is reduced to the Cauchy singular integro-differential equation of first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials, and the collocation method. The torsion problem of a cylinder containing two symmetric collinear radial cracks of equal length with symmetrically varied surface elasticity is also solved by using a similar method. Our numerical results indicate that the variation of the surface elasticity exerts a significant influence on the strengths of the logarithmic stress singularity at the crack tips, the torsional rigidity, and the jump in warping function.

Effect of Couple Stresses on the Stress Intensity Factors for Two Parallel Cracks in an Infinite Elastic Medium under Tension

Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple‐stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the rotation at the upper crack are expanded through a series of functions that are zero valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors can be determined using the characteristics of the integrands for an infinite value of the variable of integration. Numerical calculations are carried out for selected crack configurations, and the effect of the couple stresses on the stress intensity factors is revealed.

Stress intensity factors for cracks at the vertex of a rounded V-notch

The method of singular integral equations was applied to determine the stress intensity factors for a system of cracks emanating from the vertex of an infinite rounded V-notch subjected to symmetric loading. The numerical values were obtained for two cases—the case of a single crack and the case of a system of two cracks of equal length. The influence of the rounding radius of the vertex of the notch and its opening angle on the stress intensity factors at the crack tips was analyzed. The solution obtained as a result has a general nature—the stress intensity factors at the crack tip are expressed as a function of the V-notch stress intensity factor and, hence, this solution could be treated as an asymptotic relation for finite bodies with deep V-notches subjected to symmetric loads.

Stress intensity factors for cracks at a double row of holes

The presence of cracks at more than one fastener hole in a row of fastener holes limits the safe use of a component more than if cracks exist at the edge of one hole only, since the stress intensity factor is greater, the crack growth-rate is faster, and the fatigue lifetime is less. The limitations can be made less severe if the component is made with alternate fastener holes in the row displaced to form another parallel row. The compounding method of evaluating stress intensity factors is used to calculate the stress intensity factor as a function of crack length, hole spacing, and row separation. Fatigue growth-rates are calculated for the particular case of a periodic array of holes with two cracks of equal length at each hole.

On the interaction between two inclined cracks under biaxial load

An analysis of the in-plane biaxial loading of an infinite homogeneous and isotropic elastic plate with two inclined collinear cracks of equal length is performed. The boundary value problem is solved by using the complex potentials method. The influence of the lateral load on the local stress distributions as well as on the crack tips behaviour is analyzed and the features of the interaction are described.

One case of the equilibrium of a system of radial cracks

The plane-elasticity problem of the equilibrium of a system of uniformly distributed cracks of equal length intersecting in a single point is considered. The system is located with concentrated forces applied to the tips of the wedges cut out by the cracks and acting along the bisectrices of the wedges. An analytical expression is found for the singularity coefficient of the stress field at the tip of the cracks.

Longitudinal and Bending Stresses in a Beam with Saw Cut Edge Cracks∗

Abstract The Griffith-Irwin theory of brittle fracture of elastic solids predicts the propagation of cracks on the basis of the energy release rate. This depends upon the stress intensity factors for a given crack configuration. The present paper provides these informations for the problem of an infinite number of periodic, non-coplanar, parallel edge cracks in a strip. Two types of crack configurations, namely, periodic cracks of equal length starting from one edge and a set of two coplanar symmetrical edge cracks of equal length are solved for constant and linearly varying pressure distributions. These problems arise naturally in structural mechanics while investigating stresses in extension and bending of cracked strips. Final results are obtained from the numerical solution of certain Fredholm integral equations of the second kind derived from a dual series of Papkovich-Fadle eigenfunctions