Propagation mechanisms of microstructurally short cracks—Factors governing the transition from short- to long-crack behavior
Introduction
Particularly in the case of high-cycle-fatigue-loaded smooth components, the major part of the service life is determined by crack initiation and early crack growth. The propagation behavior of such microstructurally short fatigue cracks deviates considerably from that of long fatigue cracks. For the latter, the size of the plastic zone in the vicinity of the crack tip is negligibly small as compared to the crack length a, and the corresponding crack growth rate da/dN follows a characteristic relationship with the applied stress intensity factor ΔK, being described by the well-known Paris law [1], or more generally by the Klesnil–Lukáš relationship [2]:accounting for the stress ratio R and the threshold value ΔKth for initiation of “technical” cracks. The factor C and the exponent m are material constants. Microstructurally short cracks may initiate and grow well below the threshold for long cracks ΔKth. They are of the same order of magnitude than the characteristic microstructure features [3] and exhibit an oscillating growth behavior [4]. Once a microstructural crack has been initiated, e.g., by accumulated irreversible slip or elastic anisotropy of the microstructure constituents, it usually grows along crystallographic slip bands driven by the cyclic shear displacement at the crack tip [5]. Depending on the crystallographic relationship between neighboring grains of the same or different phases and on the geometry and particular strength of the grain or phase boundaries, various propagation scenarios of microstructurally short cracks have been observed: (i) slip bands may cause slip steps in the boundary planes followed by intercrystalline cracking [6], (ii) the grain and phase boundaries may act as barriers against slip transmission and reduce the crack propagation rate [7], and (iii) depending on the orientation of the slip planes with respect to the local stress state and the lattice structure of the respective grains, the microcrack propagation mechanism can change from single slip to alternating multiple slip operating at the crack tip [8]. The latter mechanism is often referred to as stage II crack propagation driven by the nominal normal stress perpendicular to the direction of crack advance. However, even under these conditions the crack can still be very short, and the plastic zone is not necessary small compared to the crack length. Additionally, the microstructure may have an influence on the crack propagation, so the crack growth rate cannot directly be described by continuum mechanics, certainly not by linear elastic fracture mechanics. Hence, one should define a transition stage between stage I microcrack propagation along crystallographic slip bands and stage II crack propagation resulting in fatigue striations. This is shown schematically in Fig. 1, being valid for both, crack propagation along the specimen surface as well as into the bulk.
Prediction of the crack propagation rate during the early stage of fatigue damage requires a model that accounts for alterations in the local resistance to crack advance. Navarro and de los Rios [9] and Taira et al. [10] developed analytical models where such alterations are attributed to a dislocation pile up between the crack tip and the grain boundary. Once the pile-up stress acting on a dislocation source in the adjacent grain exceeds a critical stress, plastic slip sets in giving rise to an intermittent increase in the crack propagation rate.
While the analytic model of Navarro and de los Rios considers the relationship between local crystallographic orientation and the variation in crack propagation only in one dimension by an average orientation factor, Section 4 of the present paper introduces a numerical two-dimensional short crack model that is capable to treat single- and two-phase microstructures with measured variation in the grain size and crystallographic orientation distribution.
Section snippets
Experimental details
Microcrack propagation was studied on electro-polished, shallow-notched specimens (Fig. 2) of an austenitic–ferritic (γ–α) duplex steel 1.4462 (ASTM A182 F51) with an average grain size of d(α) = 46 μm and d(γ) = 33 μm, respectively, and an α/γ-volume ratio of approximately 0.5. The barrier strength of γγ and αα grain boundaries as well as of the αγ phase boundaries was quantified by means of a cyclic Hall–Petch analysis, applying incremental step tests on ferritic steel 1.4511 and austenitic steel
Results and discussion
In most cases, cracks in the γα duplex steel are initiated in the vicinity of grain or phase boundaries. This might be attributed to the interdependence between the elastic constants and the crystallographic orientation of the two-phase microstructure constituents (elastic anisotropy). As an example, Fig. 3 shows a surface microcrack initiated at a γ-austenite twin-boundary, and further growing from (1) by alternate operating (1 1 1) 〈1 1 0〉-slip systems in a similar way as it was recently observed
Numerical modeling of short cracks
Analogously to the model of Navarro and de los Rios [9], a numerical short crack model has been developed by Schick [13], which accounts for microstructural features, and which is briefly introduced in the following (for more details see Ref. [8]). The model describes a propagating microcrack and its adjacent plastic zones as yield strips, consisting of an array of mathematical dislocation dipole elements (boundary elements) according to Fig. 4a. By means of the algebraic expression of the
Summary
Crack initiation and propagation during high-cycle fatigue of an austenitic-ferritic duplex steel were shown to be determined by the local microstructural features, crystallographic orientation, morphology and size of grains and phase patches, as well as the structure of the grain and phase boundaries. In the two-phase alloy microcracks grow either in a crystalline manner governed by single-slip (mainly bcc ferrite grains) or perpendicular to the applied normal stress axis governed by multiple
Acknowledgement
The financial support of Deutsche Forschungsgemeinschaft (DFG) in the framework of the priority program SPP1036 “Mechanism-Based Life Prediction for Cyclically Loaded Metallic Materials” is gratefully acknowledged.
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