James R. Sorem

Updated Stress Concentration Factors for Filleted Shafts in Bending and Tension

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: (I) 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.

Design Curves for Maximum Stresses in Blocks Containing Pressurized Bore Intersections

Intersecting bore geometries are used in a number of industrial applications such as in fluid ends of reciprocating pumps. Maximum tensile stresses at stress concentration points in the block can be many times the fluid pressure in the bores. Obtaining good estimates of the maximum stresses in the structure is necessary for making sound design decisions on the block dimensions. Finite element models of the bore intersection geometry were analyzed for ranges of bore sizes and block dimensions. Results of the finite element model were compared with predictions provided by a popular approximation method based on mechanics of materials principles. The approximation method was found to underpredict the maximum stresses in the block in almost every case analyzed. For some conditions, the maximum stresses computed from the finite element model were more than two times the predictions provided by the approximation method. Design curves, based on the ratio of the sizes of the intersecting bores, are presented for selecting block dimensions to meet desired maximum stress criteria.

Residual stress estimation in crossbores with Bauschinger effect inclusion using FEM and strain energy density

Crossbore intersections in liquid ends of positive displacement pumps (PDPs) have regions with high stress concentration. Due to the cyclic loading that occurs in most PDPs, these stress concentration points are susceptible to fatigue cracking. In order to prolong their life, the liquid ends are often overpressurized (autofrettaged), thus inducing beneficial compressive hoop stresses in these critical regions upon removal of the autofrettage pressure. This autofrettage process drives the region of high stress concentration beyond the elastic limit and well into the elastic-plastic region. Elastic-plastic stresses and strains due to loading and unloading were analyzed in crossbore geometries, with Bauschinger effect included, using 3-D finite element analysis of the liquid end. For comparison, an analytical approach was developed, based on the strain energy density criterion first proposed by Glinka. The approach was modified to include the Bauschinger effect for precise estimation of such stresses and strains. Good correlation was observed between elastic-plastic crossbore stresses and strains predicted by the analytical approach and the finite element analysis.

Evaluation of the Autofrettage Effect on Fatigue Lives of Steel Blocks with Crossbores Using a Statistical and a Strain-Based Method

A problem of fundamental and industrial interest is the effect of autofrettage on fatigue lives and the structural integrity of engineering components. The component considered is a steel block containing crossbores, a situation found in many industrial applications such as the fluid ends of positive displacement pumps. Twenty-one steel blocks containing intersecting perpendicular crossbores were autofrettaged with pressures ranging from 79 to 172 MPa. The specimens were subsequently fatigue tested on a specially designed test facility under 53 and 69-MPa pressures. Statistical procedures based on analysis of variance were used to analyze the effect of the different autofrettage pressure levels on fatigue lives of specimens. The reverse plasticity criterion was also used to investigate the fatigue enhancement limit of the autofrettage process. Results of the statistical methodology correlated with results of the reverse plasticity criterion showed the existence of an “optimal” autofrettage pressure.

An analytical procedure for estimating residual stresses in blocks containing crossbores

Intersecting bore geometries are used in a number of industrial applications such as the fluid ends of reciprocating pumps and have regions with high stress concentration. To increase the fatigue life of a fluid end, a reduction in the operating mean stress is helpful. This can be achieved with the introduction of compressive residual stresses in these critical regions by means of proof loading or autofrettage. Accurate estimation of fluid end fatigue lives necessitates accurate evaluation of the residual stresses induced by autofrettage. In this paper, finite element models were used to obtain hoop stress to pressure ratios, at the most highly stressed plane, in blocks of different sizes and bore ratios. The hoop stress to pressure ratios were used along with Neubers rule and kinematic hardening to select an autofrettage pressure and to estimate the elastoplastic residual stresses on this plane. The suggested method estimates residual stress magnitudes close to finite element solutions, and eliminates the need for a lengthy and costly elastoplastic finite element analysis.

The effect of proof loading on the fatigue behaviour of stud link chain

Abstract Although stud link chain is routinely proof loaded during its manufacture, the effect of residual stresses imposed by this operation on the fatigue strength of the chain has not been quantitatively investigated. This paper discusses the results of constant amplitude fatigue tests on stud link chain segments which have received proof loading at various levels. The chain was heat treated before fatigue testing to relieve manufacturing residual stresses and then proof loaded at various levels from zero to 86% of its break strength. Tests were performed at two mean load levels and three load amplitudes. Failure site trends are reported and correlated with results of a finite element stress analysis. Residual stress estimates are used with standard fatigue damage parameters to estimate the fatigue life of the chain and predictions are compared to the experimental data. Low cycle fatigue parameters were derived from a previous test programme for open link chain. Proof loading was shown to increase substantially the fatigue life of the stud link chain. Residual stresses can explain the increase in fatigue life. Neubers rule demonstrated the ability to model the data trends.