Much modern engineering design work uses S -N curves and empirical applications thereof. In industry, currently popular methods for predicting fatigue life under complex loading use ad hoc cycle counting algorithms along with Miner's rule, in spite of its known weaknesses. Many ad hoc alternatives to Miner's rule have been proposed, each with limited experimental justification. Of these, Manson's double linear damage rule (DLDR) is widely considered to be good. In this paper, we bring a new perspective to empirical, as opposed to mechanistic, fatigue damage evolution models. It is first assumed, with reasonable justification, that there is a scalar, abstract, damage variable f, whose evolution under cyclic loading satisfies _ fZ af m , where a and m are unknown functions of load parameters. One main contribution of the paper lies in deducing what the functions a and m must be in order to obtain consistency with fatigue data in handbooks. A small correction to this basic power law model is then developed. The final explicit model initially has 10 unknown fitted parameters, but these are brought down to three unknowns; the accompanying discussion is the other main contribution of the paper. Finally, comparison with Manson's and other data suggests that, with two fitted parameters, our model works as well as the DLDR and much better than Miner's rule. For other parameter choices, our model reduces to Miner's rule. We conclude with speculation about ways in which the model might be extended beyond the scope of the DLDR.

We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. Prior computational treatments of this problem were based on adding elementlevel gyroscopic terms to the governing equations. Here, we begin with a direct continuum formulation wherein gyroscopic terms need not be added on separately and explicitly: all gyroscopic effects are captured implicitly within the continuum elastodynamics. We present two new methods for obtaining the whirl speed, where we project the dynamic equilibrium equations of the rotor on to a few of its non-spinning vibration mode shapes. The first modal projection method is direct and more accurate, but requires numerical evaluation of more demanding integrals. The second method is iterative and involves a small approximation, but is simpler. Both the methods are based on one new insight: the gyroscopic terms used in other treatments are essentially the result of a prestress in the rotor caused by the non-zero spin rate, and may be incorporated as such in the continuum formulation. The accuracy of the results obtained, for several examples, is verified against detailed calculations with a commercial finiteelement package, against our own nonlinear finite-element code or against analytical estimates. For further verification and illustration, a closed-form analytical solution for a simple problem, obtained using our method, matches the results obtained with explicit gyroscopic terms.

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Automotive turbocharger components frequently experience complex Thermo-Mechanical Fatigue (TMF) loadings which require estimation of nonlinear plastic stresses for fatigue life calculations. These field duty cycles often contain rapid fluctuations in temperatures and consequently transient effects become important. Although current FE software are capable of performing these nonlinear finite element analyses, the turnaround time to compute nonlinear stresses for complex field duty cycles is still quite significant and detailed design optimizations for different duty cycles become very cumbersome. In recent years, a large number of studies have been made to develop analytical methods for estimating nonlinear stress from linear stresses. However, a majority of these consider isothermal cases which cannot be directly applied for thermo-mechanical loading. In this paper a detailed study is conducted with two different existing analytical approaches (Neuber’s rule and Hoffman-Seeger) to estimate the multi-axial nonlinear stresses from linear elastic stresses. For the Neuber’s approach, the multi-axial version proposed by Chu was used to correct elastic stresses from linear FE analyses. In the second approach, Hoffman and Seeger’s method is used to estimate the multiaxial stress state from plastic equivalent stress estimated using Neuber’s method for uniaxial stress. The novelty in the present work is the estimation of nonlinear stress for bilinear kinematic hardening material model under varying temperature conditions. The material properties including the modulus of elasticity, tangent modulus and the yield stress are assumed to vary with temperature. The application of two analytical approaches were examined for proportional and non-proportional TMF loadings and suggestions have been proposed to incorporate temperature dependent material behavior while correcting the plasticity effect into linear stress. This approach can be effectively used for complex geometries to calculate nonlinear stresses without carrying out a detailed nonlinear finite element analysis.