Growth of a short fatigue crack – A long term simulation using a dislocation technique

Abstract

a b s t r a c tIn this study, the growth of a short edge crack during more than 14 000 cycles of fatigue loading is investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, is modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles are fully reversed ðR ¼ À1Þ, and the load range is well below the threshold for long fatigue cracks. The developing local plasticity consists of discrete edge dislocations that are emitted from the crack tip. The movements of discrete dislocations are restricted to slip along preferred slip planes. The present model is restricted to a 2D plane strain problem with a through-thickness crack, assuming no 3D irregularities. A remote load is applied perpendicular to the crack extension line, and the material parameters are those of a BCC crystal structure. The competition between influence of the global loading on and local shielding of the crack tip governs the crack growth. The growth rate increases in discrete steps with short periods of retardation, from approximately the size of Burgers vector, b, up to 25 b per cycle as the length of the crack is tripled. The plastic zone changes from having an elongated, slender form to include a low angle grain boundary, which, eventually, divides into two parts. The crack growth is found to change from constant acceleration to constant growth rate as the event of the low-angle grain boundary split is approached. The results are compared to long crack characteristics, for which linear elastic fracture mechanics and Paris law can be used to predict fatigue crack growth. The exponent in Paris law varies between 1 and 0 in the present study, i.e. smaller than typical values for ductile BCC materials. The ratio between static and cyclic plastic zone sizes is found to increase during crack growth, and the angle of the general plastic zone direction increases, showing a tendency towards long crack values. The characteristics of the simulated crack growth, found in the present study, are typical for below-threshold growth, with slow acceleration, constant growth rate, and, eventually, either arrest or transition to long crack growth behaviour, as reported in the literature.

An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

“…Several studies have been carried out so far using dislocation dynamics (DD) modelling with a view to simulate fatigue crack propagation under mode-I and mode-II [9][10][11][12][13][14][15][16][17][18][19]. Navarro and de los Rios [9] have developed a 2D micromechanical model based on the continuous distribution of dislocations.…”

“…Subsequently, many authors have conducted complementary discrete dislocation studies [10][11][12][13][14][15][16][17][18][19][20], for example, to identify threshold conditions for stage-I crack propagation [10], to study the influence of the normal stress on the threshold stress intensity factor for stage-I FCP [13] and to examine the growth of mode-I short cracks in a FCC material, in combination with a cohesive surface in front of the crack tip [14,15]. In another approach based on the boundary element method (BEM), the crack is represented by sets of dislocation dipoles and crystal plasticity results from the discrete dislocations (or dipole elements) movements along certain slip planes [16][17][18][19]. BEM has been used to simulate short crack propagation through simulated microstructures taken as a statistical distribution of grain geometries and crystallographic orientations in 2D space [16].…”

“…BEM has been used to simulate short crack propagation through simulated microstructures taken as a statistical distribution of grain geometries and crystallographic orientations in 2D space [16]. Zig-zag paths of a stage-I crack propagating in a grain [17] and crack morphologies in mode-I and mode-II were investigated [17][18][19]. Previous studies, though mainly 2D, were able to capture important aspects of cyclic plasticity and crack growth of the order of a few Burgers vectors.…”

On the transition of short cracks into long fatigue cracks in reactor pressure vessel steels

“…After initiation short cracks propagate at higher rate as compared to the long cracks for the same value of applied stress intensity factor range. Linear elastic fracture mechanics (LEFM) is not applicable in short cracks regime and the propagation behaviour of short fatigue cracks cannot be predicted by the famous ParisErdogan law [3]. Unlike long cracks, the short cracks during propagation highly interact with the inherent microstructural features of the material such as grain boundaries, phase boundaries and inclusions [4][5][6].…”

Role of plasticity-induced crack closure in fatigue crack growth

“…[1][2][3]6,7]. Conclusions about the PICC mechanisms based on both dislocation and continuum plasticity analyses are contradictory, cf., e.g., Deshpande et al [8] or Pippan and Riemelmoser [9] vs. Louat et al [3] or Bjerkén and Melin [10], Budianski and Hutchinson [11] vs. Noroozi et al [12], and McClung et al [13] vs. Toribio and Kharin [14]. PICC is used to be accepted as the factor directly responsible for the dependence of FCG, apart from the load range, on the load maximum or ratio, as well as on over-or under-loads along the loading routes, forming thus the framework to interpret FCG trends.…”