Abstract
This paper presents a system of plastic flow equations which uses and generalizes to the multiaxial case a number of concepts commonly employed in the so-called Local Strain Approach to low cycle fatigue. Everything is built upon the idea of distance between stress points. It is believed that this will ease the generalization to the multiaxial case of the intuitive methods used in low cycle fatigue calculations, based on hysteresis loops, Ramberg?Osgood equations, Neuber or ESED rule, etc. It is proposed that the stress space is endowed with a quadratic metric whose structure is embedded in the yield criterion. Considerations of initial isotropy of the material and of the null influence of the hydrostatic stress upon yielding leads to the realization of the simplest metric, which is associated with the von Mises yield criterion. The use of the strain?hardening hypothesis leads in natural way to a normal flow rule and this establishes a linear relationship between the plastic strain increment and the stress increment.
Highlights
W e are trying to develop a theory of cyclic plasticity which allows fatigue designers to make calculations for multiaxial loads in a way as similar as possible to which they do when using the well-known Local Strain methodology for uniaxial low cycle fatigue problems
We would like to define concepts that translate to multiaxial loadings in a simple manner the tools of that trade, namely, the use of the Cyclic Stress-Strain Curve and hysteresis loops, the invocation of the memory rule when hysteresis loops are “closed”, the extension of the Neuber or ESED rules to multiaxial loading, etc
We have found it useful to base our theory in the idea of distance between stress points and to calculate these distances by using the expression for the yield criterion [1,2,3,4,5,6]
Summary
W e are trying to develop a theory of cyclic plasticity which allows fatigue designers to make calculations for multiaxial loads in a way as similar as possible to which they do when using the well-known Local Strain methodology for uniaxial low cycle fatigue problems. We would like to define concepts that translate to multiaxial loadings in a simple manner the tools of that trade, namely, the use of the Cyclic Stress-Strain Curve and hysteresis loops, the invocation of the memory rule when hysteresis loops are “closed”, the extension of the Neuber or ESED rules to multiaxial loading, etc. We have found it useful to base our theory in the idea of distance between stress points and to calculate these distances by using the expression for the yield criterion [1,2,3,4,5,6]. To keep the discussion at the simplest possible level we will restrict the treatment given here to the case of combined tension and torsion loading
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