On the Contact Stresses at the Indenting Edge of a Shaft-Hub Interference Fit Subject to Bending and Shear Forces

The contact stress field is addressed that is developed at the indenting edge of a keyless shaft-hub interference fit, in the case that both bending and shear forces are applied, and in the absence of friction. The combined effect of a set of elementary load cases is assessed for the sharp notch case in terms of a generalized stress intensity factor, with the aid of Finite Elements and for a class of shaft-hub geometries. In fact, linearity is preserved in the case of a sharp edged bore up to the incipient detachment condition; such event, which may occur as a result of e.g. excessive bending loads, may be forecast based on the proposed framework. Contact stresses in the case of rounded edge may be subsequently predicted by scaling an appropriate local solution; fatigue analysis may then be performed in the case of rotating or fluctuating loads. An exhaustive design table is finally compiled to assist the designer in dimensioning an interference fit in the presence of an arbitrary combination of time varying bending and shear forces.

Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters ( α and β ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

Adhesion and pull-off force of an elastic indenter from an elastic half-space

The adhesion between an elastic punch and an elastic half-space is investigated for plane and axisymmetric geometries. The pull-off force is determined for a range of material combinations. This configuration is characterized by a generalized stress intensity factor which has an order less than one-half. The critical value of this generalized stress intensity factor is related to the work of adhesion, under tensile loading, by using a cohesive zone model in an asymptotic analysis of the separation near the elastic punch corner. These results are used in conjunction with existing results in the literature for the frictionless contact between an elastic semi-infinite strip and half-space in both plane and axisymmetric configurations. It is found that the value of the pull-off force includes a dependence on the maximum stress of the cohesive zone model. As expected, this dependence vanishes as the punch becomes rigid in that case the order of the singularity approaches one-half. At the other limit, when the half-space becomes rigid, the stresses become bounded and uniform and the pull-off force depends linearly on the cohesive stress and is independent of the work of adhesion. Thus, the transition from fracture-dominated adhesion to strength-dominated adhesion is demonstrated.

Influence of the V-Notch Opening Angle on Critical Applied Force Values for the Crack Initiation from the Sharp V-Notch

The aim of this paper is to estimate a value of the critical applied force for a crack initiation from the sharp V-notch tip. The classical approach of the linear elastic fracture mechanics (LELM) was generalized, because the stress singularity exponent differs from 0.5 in studied case. The value of the stress singularity exponent depends on the V-notch opening angle. The finite element method was used for a determination of stress distribution in the vicinity of the sharp V-notch tip and for the estimation of the generalized stress intensity factor depending on the V-notch opening angle. Critical value of generalized stress intensity factor was obtained by using stability criterion based on the tangential stress component averaged over a critical distancedfrom the V-notch tip. Calculated values of the critical applied force were compared with experimental data taken from the literature.

A Comparison of Two Direct Methods of Generalized Stress Intensity Factor Calculations of Bi-Material Notches

The study of bi-material notches is becoming a topical problem as they can model geometrical or material discontinuities efficiently. Assessing the conditions for crack initiation in bimaterial notches makes it necessary to calculate the generalized stress intensity factors H. In contrast to the determination of the K factor for a crack in an isotropic homogeneous medium, for the ascertainment of a generalized stress intensity factor (GSIF) there is no procedure incorporated in the calculation systems. The calculation of these fracture mechanics parameters is not trivial and requires certain experience. Nevertheless, the accuracy of the H-factor calculation directly influences the reliability of the assessment of the singular stress concentrators. Direct methods of the estimation of H factors usually require choosing the length parameter entering into the calculation. Two types of direct methods of calculating the GSIFs are presented, tested and mutually compared. Recommendations for reliable estimation of H factors are suggested.

When does a notch behave like a crack?

The characteristic asymptotic fields at the tip of sharp, semi-infinite cracks and notches are first compared with corresponding features present in selected finite bodies (edge cracks and notches). This gives an explicit view of the gradual divergence of the semi-infinite and finite problem solutions as the observation point becomes remote from the tip. Hence, upper bounds for the local plastic zone to be characterized by the singular field are known. Asymptotic solutions for semi-infinite rounded features are introduced, whose remote fields may be matched to the sharp singular fields through the medium of the corresponding generalized stress intensity factor. Thus the semi-infinite sharp and rounded problems converge remotely but diverge as the apex of the feature is approached. This comparison sets a lower bound for loads at which the outer boundary of the plastic zone is characterized by the singular field. Thus, the range of loads for the plastic zones to be controlled by the singular solutions are derived. We then proceed to compare critically the nature of the semi-infinite sharp notch and semi-infinite crack states of stress, defining the circumstances in which these are alike. All these elements considered together enable the closeness of various notch plastic zones to that of the classical semi-infinite crack to be gauged.