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In this paper, the effect of the polycrystalline microstructure on crack-tip opening displacement and crack closure is investigated for microstructural short plane strain fatigue cracks using the finite-element method. To this end, cracks are introduced in synthetically generated microstructures and the grain properties are described using a single crystal plasticity model with kinematic hardening. Additionally, finite-element calculations without resolved microstructure and von Mises plasticity with kinematic hardening are performed. Fully-reversed strain-controlled cyclic loadings are considered under large-scale yielding conditions as typical for low-cycle fatigue problems. The crack opening stress and the cyclic crack-tip opening displacement are significantly influenced by the local grain structure. While the stabilized crack opening stresses obtained with the microstructure-based finite-element model are in good accordance with the von Mises plasticity results, the differences in the cyclic crack opening displacement are addressed to the asymmetric plastic strain fields in the plastic wake behind the crack-tip of the microstructure-based model. The asymmetric plastic strain fields result in discontinuous and premature contact of the crack flanks.
Ein tiefgreifendes Verständnis des zyklischen Plastizitätsverhaltens metallischer Werkstoffe ist sowohl für die Optimierung der Materialeigenschaften als auch für die industrielle Auslegung und Fertigung von Bauteilen von hoher Relevanz. Insbesondere moderne Legierungen wie Duplex-Stähle zeigen unter Lastumkehr aufgrund des komplexen mehrphasigen Gefüges sowie der Neigung zu verschiedenen Ausscheidungsreaktionen einen ausgeprägten Bauschinger-Effekt, welcher bei technischen Umformvorgängen berücksichtigt werden muss. Der Bauschinger-Effekt begründet sich maßgeblich in der Entstehung von Rückspannungen, welche aus dem unterschiedlichen Plastizitätsverhalten der austenitischen und ferritischen Phase resultieren. Instrumentierte Mikroindenter-Versuche in ausgewählten Ferrit- und Austenitkörnern haben gezeigt, dass austenitische Gefügebestandteile durch einen deutlich früheren Fließbeginn sowie eine stärkere Rückplastifizierung während der Entlastung charakterisiert sind. Zudem wurde nachgewiesen, dass Ausscheidungen im Rahmen einer 475°C-Versprödung diesen Phasenunterschied verstärken und somit in einem höheren Bauschinger-Effekt resultieren.
Cyclic micro-bending tests on fcc single crystal Ni-base Alloy 718 cantilevers with different crystal orientations were performed to analyze the influence of activated slip systems on dislocation plasticity, latent hardening and the Bauschinger effect. The investigations indicate that plasticity in single crystal micro-cantilevers is significantly influenced by two phenomena - dislocation interaction and dislocation pile-up at the neutral plane. Both phenomena occur at the same time. Their ratio seems to be determined by the activated slip systems. Slip trace analysis indicates that the activation of only one slip system leads to a strong localization of plasticity to a limited number of parallel slip bands. This results in low dislocation interaction and consequently pronounced pile-ups at the neutral plane. In multi slip orientation, the second slip system leads to activation of significantly more dislocation sources, causing a much earlier and more homogeneous elastic-plastic transition zone. In stress-strain hysteresis loops during bending, pronounced dislocation interaction in multi slip orientation leads to a more pronounced latent hardening. The results suggest that on a microstructural length scale, plasticity behavior is strongly affected by activated slip systems, which determine local dislocation phenomena. Based on the results presented in this paper, a finite element analysis of latent hardening and the Bauschinger effect using a single crystal plasticity model with latent kinematic hardening is presented in Part II.
In this paper, the Bauschinger effect and latent hardening of single crystals are assessed in finite element calculations using a single crystal plasticity model with kinematic hardening. To this end, results of cyclic micro-bending experiments on single crystal Alloy 718 in different crystal orientations (single slip and multi slip) with respect to the loading direction are used to determine the slip system related material properties of the single crystal plasticity model. Two kinematic hardening laws are considered: a kinematic hardening law describing latent hardening and a kinematic hardening law without latent hardening. For the determination of material properties for both hardening laws, a gradient-based optimization method is used. The results show that the different strength levels observed for micro-bending tests on different crystal orientations can only be described with latent kinematic hardening well, whereas the pronounced Bauschinger effect is described well by both kinematic hardening laws. It is concluded that cyclic micro-bending experiments on single crystals using different crystal orientations give an appropriate data base for the determination of the slip system related material properties of the single crystal plasticity model with latent kinematic hardening.