Published elastic stress concentration factors are shown to underestimate stresses in the root of a shoulder filleted shaft in bending by as much as 21 percent, and in tension by as much as forty percent. For this geometry, published charts represent only approximated stress concentration factor values, based on known solutions for similar geometries. In this study, detailed finite element analyses were performed over a wide range of filleted shaft geometries to define three useful relations for bending and tension loading: (1) revised elastic stress concentration factors, (2) revised elastic von Mises equivalent stress concentration factors and (3) the maximum stress location in the fillet. Updated results are presented in the familiar graphical form and empirical relations are fit through the curves which are suitable for use in numerical design algorithms. It is demonstrated that the first two relations reveal the full multiaxial elastic state of stress and strain at the maximum stress location. Understanding the influence of geometry on the maximum stress location can be helpful for experimental strain determination or monitoring fatigue crack nucleation. The finite element results are validated against values published in the literature for several geometries and with limited experimental data.

In a previous paper, popular stress concentration factor charts for shoulder filleted shafts in bending and tension were shown to be in error, and more accurate solutions were published. In this paper, improved stress concentration factor information is presented for torsional loading, based on detailed finite element analyses. The new solutions agree with previous design charts, but cover a wider range of geometries. A concise engineering equation is presented for the stress concentration factor and maximum equivalent stress under each of three loading modes, along with another equation that reveals the location of each maximum stress component in the fillet. It is shown that the maximum stress locations for bending and tension loading are approximately the same, but can differ significantly from the maximum torsional stress location. In those cases, sharp surface gradients can cause the maximum equivalent notch stress under combined bending/axial and torsional loading to be overestimated when computed based on the maximum stress concentration factors for each load component. An example is used to demonstrate how the surface strain gradient causes the placement and size of a strain gage to have a strong influence on strain measurements.

A multiaxial fatigue damage criterion has been formulated based on observations that fatigue crack development is governed by stresses and strains acting on critical planes in materials. The damage parameter incorporates both Mode I and Mode II loading. Failure is defined as the development of an engineering size crack (approximately 1 mm in surface length). The proposed method can be applied to both proportional and nonproportional multiaxial loading as well as to uniaxial loading. Predictions based on the proposed method were compared to uniaxial and multiaxial in-phase and out-of-phase test data for three materials. The approach demonstrated improved life predictions relative to other methodologies.

Coiled tubing is a long, continuous string of steel tubing that is used in the oil well drilling and servicing industry. Bending strains imposed on coiled tubing as it is deployed and retrieved from a well are considerably into the plastic regime and can be as high as 3 percent. Progressive growth of tubing diameter occurs when tubing is cyclically bent-straightened under constant internal pressure, regardless of the fact that the hoop stress imposed by typical pressure levels is well below the material’s yield strength. A new incremental plasticity model is proposed in this study that can predict multiaxial cyclic ratcheting in coiled tubing more accurately than the conventional plasticity models. A new hardening rule is presented based on published experimental observations. The model also implements a new plastic modulus function. The predictions based on the new theory correlate well with experimental results presented in Part II of this paper. Some previously unexpected trends in coiled tubing deformation behavior were observed and correctly predicted using the proposed model. [S0094-4289(00)00402-3]

An experimental program was conducted to evaluate the plasticity model proposed in a separate paper (Part I). Constant pressure, cyclic bend-straighten tests were performed to identify material parameters required by the analytical model. Block pressure, bend-straighten tests were conducted to evaluate the proposed model. Experiments were performed on full-size coiled tubing samples using a specialized test machine. Two commonly used coiled tubing materials and four specimen sizes were subjected to load histories consisting of bending-straightening cycles with varying levels of internal pressure. It was observed that cyclic ratcheting rates can be reversed without reversing the mean stress, i.e., diametral growth of coiled tubing can be followed by diametral shrinkage even when the internal pressure is kept positive, depending on the loading history. This material behavior is explained in the context of the new theory. The correlation between the predictions and the test data is very good. [S0094-4289(00)00502-8]