Rigid Line Inclusion Research Articles

Stress analysis of a kinked crack initiating from a rigid line inclusion. Part 1: Formulation

The problem of a kinked crack which has initiated from the tip of a rigid line inclusion is analyzed as a mixed boudary value problem. The stress distribution, stress intensity factors, singularity at the inclusion tip, and the resultant moment on the rigid line inclusion are investigated for various angles of the kinked crack and crack lengths. The rotation of the rigid line inclusion, when loaded by a uniform farfield stress, is calculated. The cases in which the inclusion is free to rotate or is fixed are separately considered.

Stress analysis of a kinked crack initiating from a rigid line inclusion. Part II: Direction of propagation

The propagation direction of a kinked crack initiating from a rigid line inclusion is investigated. The criteria of maximum energy release rate, maximum Mode I stress intensity factor, and zero Mode II stress intensity factor are used as predictors for the kinked crack direction. Uniform farfield tension and pure shear loading conditions are used for illustration.

Dynamic response of an embedded rectangular foundation to antiplane shear waves

The steady state response of a deep, narrow, rectangular foundation to antiplane shear waves is studied. Consideration is given first to the dynamic response of a single rigid line inclusion. This result is used to model a rectangular foundation in a manner similar to Haritos and Keer who studied the problem of a rigid block partially embedded in an elastic half-space. Because the problem is antiplane, the results arrived at for the deep, narrow, rectangular foundation also apply to a shallow, wide, rectangular foundation.

The second fundamental crack problem and the rigid line inclusion problem in plane elasticity

The second fundamental problem of plane isotropic elasticity for a cracked infinite medium, that is the problem in which the displacement derivatives are given along the crack edges, as well as the closely related rigid line inclusion problem in plane elasticity are treated by using the method of complex potentials. Without restrictive assumptions on geometry and boundary conditions, these problems are reduced to a complex Cauchy type singular integral equation along the crack or the inclusion, the numerical solution of which can easily be obtained by using the Lobatto-Chebyshev method.

On the Changing Order of Singularity at a Crack Tip

The nature of the transition in the crack tip stress singularity from an inverse square root to an inverse fractional power as a crack tip reaches a phase boundary or a geometrical discontinuity for interface cracks is examined. This is done by analyzing the simple closed-form solution to the problem of a rigid line inclusion with one side partially debonded for the case of antiplane deformation. For this example, the crack tip stress singularity changes from an inverse square root to an inverse three-quarters power as the crack tips approach the inclusion tips (i.e., when one face of the rigid line inclusion is completely debonded). A detailed analysis, based on series expansions of the closed-form solution, is used to show how the singularity transition occurs. Moreover, the expansions indicate difficulties that may be encountered when solving such problems by approximate methods.

A Westergaard-type stress function for line inclusion problems

A direct correspondence is shown to exist between the Westergaard stress function for crack problems and a newly-introduced stress function for rigid line inclusion problems. A correspondence is also shown to exist between stress intensities in the crack and the inclusion problems, as well as between the opening displacement of the crack and the axial force in the inclusion. A scheme is presented to modify these rigid-inclusion solutions to account approximately for non-zero compliance of real fibers in a composite material.

Interfacial Slip Around Rigid Fiber Inclusions

Interface slip in a composite material is modeled by considering a finite length, rigid line inclusion (fiber) embedded in a two-dimensional elastic matrix with sliding fiber-matrix interface cracks extending from the fiber tips. The crack faces are assumed to remain in contact; the resulting fric tion forces between the crack faces are taken to be constant. A closed form solution for this problem is presented which is used to study the stable size of interface cracks based on the concept of a critical stress intensity factor. The relaxation of axial fiber force as a result of constant load debonding is examined. In addition, the change in fiber force due to stable unbonding under monotonic increasing loads is considered. Finally, the loading conditions leading to closed sliding cracks are identified.