PSI - Issue 18

Matthias Hell et al. / Procedia Structural Integrity 18 (2019) 823–836 Author name / Structural Integrity Procedia 00 (2019) 000–000

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due to growing global demand require rapid decisions on possible material substitutions. Local strain-based fatigue design approaches allow an accelerated evaluation of the impact of changes in geometry or the material on the structural durability of components on basis of a reduced number of simple strain-controlled fatigue tests on un notched specimens. In order to improve the quality of the fatigue life estimation and reduce the numerical effort simultaneously, different transfer concepts can be employed, which implement the consideration of particularities in the cyclic material behaviour, size effects and load sequence effects on fatigue life. The majority of safety relevant components, for example chassis parts in passenger and commercial vehicles, are exposed to variable amplitude loading with purely elastic loading in the high cycle fatigue regime as well as elasto plastic loading in the low cycle fatigue regime. In presence of stress-concentrations, the elasto-plastic half cycles lead to a shift of the mean stresses and strains, which affects the following elastic load-cycles. In addition, during elasto plastic deformation, also the stress-strain relation may be altered by transient effects, such as, for example, cyclic softening or hardening. As local fatigue phenomena as well as the local damage accumulation are governed by the stress-strain state, the quality of the fatigue life estimation depends on the quality of the assessment of the local stress strain state to a large extent. The application of state of the art strain-based fatigue design methods in order to evaluate the local damage accumulation will entail the usage of a highly complex numerical representation of the elasto-plastic material behaviour in a continuous analytical formulation. In addition, the effect of arbitrary load time functions on fatigue life has to be evaluated by a piecewise calculation in order to account for load sequence effects. In order to reduce the experimental effort for the derivation of material parameters and the allocation of numerical resources for the fatigue life estimation, the presented work employs a simplified practical approach. In order to reduce the analytical effort, the material behaviour is discretised into a cycle dependent elasto-plastic stress-strain relation. The influence of the component geometry, e.g. size effects and the extension of local plasticity throughout the component cross section and the load range in which the Neuber rule is valid, is then estimated with elasto-plastic simulations. While storing the position in the original load-time function, loads, which caus a stable shift in the mean stress for subsequent loads, are extracted from the load time function. Using a discretized elasto-plastic material behaviour, the local stress strain response is then calculated for the elasto-plastic loading by finite element simulations. From the results of the finite element simulations, a shift vector, which contains the magnitude of the mean stress and the position in the original load time function, is derived. The shift vector is then used to modify the original load time function with respect to the mean stress shift resulting from the load sequence. Afterwards, a simple linear damage accumulation hypotheses, for example according to Palmgren-Miner, may be employed in order to evaluate the local damage accumulation. A comparison of the numerical with experimental results shows, that the consideration of load sequence effects and peculiarities in the stress-strain behaviour may improve the accuracy of the fatigue life estimation. 2. Fatigue design approaches with elasto-plastic material behaviour Many components are subjected to load-time functions, which are composed of cyclic loads with variable amplitudes. The load-time function usually consists of loads from the proper use and overloads from misuse. While overloads due to misuse are in most cases accompanied by large plastic strains, also the load cycles during proper use of the component cause locally limited plastic deformations within the highly loaded regions of the component. An appropriate fatigue design approach therefore has to allow the estimation of the damage contribution of elasto-plastic as well as purely elastic load cycles by considering the evolution of the local stress-strain state with respect to the load sequence and a stress-strain behaviour, which may be modified continuously during cyclic loading [1]. The elasto plastic notch base approach estimates the fatigue strength of components on the basis of material parameters, which are derived by strain-controlled testing on un-notched specimen, Fig. 1.