The non-proportionality of local stress paths in engineering applications

Abstract

A scalar measure, which describes the non-proportionality of local stress paths in engineering applications, is introduced. For this purpose the moment of inertia approach by Meggiolaro is modified in a way that the stress time history is evaluated in a tresca-stress-space. This modification makes the non-proportionality factor invariant with respect to the coordinate system. An optimization procedure is implemented to derive a test setup for new component tests with 2 load channels. The aim of the planned tests is to get a high non-proportionality at the potential crack initiation site. It is not possible to obtain a high non-proportionality factor at the failure location without selective weakening of the component (housing of a rear axle steering). Therefore specific areas of the structure are cut out and the optimization procedure is repeated. As a result of the optimization a test setup with high local non-proportionality at the potential crack initiation site is achieved for the weakened structure. Another setup with slightly less non-proportionality but with a very localized damage is derived. This setup is preferred, because of the robustness in the physical test.

On Scaled Normal Stresses in Multiaxial Fatigue and Their Exemplary Application to Ductile Cast Iron

“…Damage parameter values according to Smith, Watson, and Topper (SWT [47]) are then calculated for each hysteresis loop, and Miner's rule can be applied against an SWT-Wöhler curve. Riess et al account for nonproportional hardening by implementing the proposal of Socie and Marquis [13] of modifying the cyclic strength coefficient of the material by using a nonproportionality factor [48] (see Section 2.4).…”

“…F is a measure for the nonproportionality of an applied load. Multiple definitions for F have been suggested (see, e.g., compilations in [40,48]), which shall not be discussed here. However, for most definitions of F, proportional loading results in F = 0 and maximum nonproportionality (e.g., 90 • phase shift) results in F = 1.…”

The contrast of simplicity and accuracy in modeling multiaxial notch fatigue

“…[15]). Within this contribution, a non-proportionality factor (NPF) from the latter group, which was previously presented in [16], is chosen. It is an improved version of the inertia based NPF proposed by Meggiolaro and Castro [17].…”

“…xy σ xx − σ yy dp 3with the length of the stress path L and the infinitesimal segment dp [16]. Thereupon, the non-proportionality factor f np is defined as the root of the ratio of both principal moments of inertia:…”