Digital Repository, Giornata IGF Forni di Sopra (UD) 2011

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Dislocation-based model of crack-tip shielding effects
J. Pokluda

Last modified: 2011-02-25


Along with external forces and the macro-geometry of cracked bodies, the local stress intensity
factors k (or Δk) at fronts of brittle and fatigue cracks are also determined by internal residual stress fields and
the crack front microgeometry (extrinsic shielding). Consequently, the values of k (Δk) that represent a real
crack driving force can be significantly different from those of the remote K (ΔK). This means that, even in the
frame of linear-elastic fracture mechanics, a characterization of the crack-tip stress field by a single K (ΔK)
parameter is not sufficient.
The paper presents a discrete dislocation model of extrinsic crack-tip shielding effects that appear in fatigue due
to small-scale yielding. The main advantages of this multi-scale model with respect to LEFM models based on
continuum mechanics are its simplicity and physical transparency. This enables us to directly asses the
magnitude of both plasticity and roughness-induced components of crack closure which is not possible by
means of multi-parameter continuum LEFM models of the crack-tip stress field. Also beyond the frame of
continuum models, the dislocation model includes a physically justified parameter expressing an influence of
microstructure on the roughness-induced shielding term. Based on the analytical formula and standard materials
data on mechanical properties and microstructure, the closure components can be simply extracted from
experimentally measured values of ΔK which is not possible by experimental crack-closure measurements. In
this way, the effective threshold ΔKth,eff can be obtained as nearly independent of microstructure coarseness and
applied cyclic ratio. The practical importance of the dislocation-based model is documented by the fact that the
threshold ΔKth is a basic material characteristic used in predictions of fatigue strength and life of cracked

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