Cyclic softening of martensitic steels at high temperature—Experiments and physically based modelling

A dislocation-based model for high temperature cyclic viscoplasticity of 9–12Cr steels

“…6 for the P91 steel of the present study [36]. The work of Sauzay and coworkers [14,15,33], concluded that the physical mechanisms behind cyclic softening in 9-12Cr steels are: (i) a loss in overall dislocation density, (ii) a loss of the LAB dislocations eventually resulting in a disappearance of the LAB and a decrease in the angle of misorientation between LABs, (iii) a subsequent coarsening of the martensitic lath microstructure and (iv) precipitate coarsening at higher temperatures. Due to the presence of M 23 C 6 precipitates along boundaries, it is assumed that HABs (PAGs, packets and blocks) do not coarsen due to cyclic deformation.…”

“…Following the work of Cheong and Busso [28,29], the probability of a mobile dislocation consumption event occurring is P=0.5Aρ m , where A is the critical area for consumption of mobile dislocations. The present study extends the approach of [28,29] to the macro-scale and includes consumption of mobile dislocations via the mechanisms discussed in [17]; namely (i) mutual annihilation of two mobile dislocations, (ii) the formation of immobile locked configurations and (iii) dipole dislocation formation, as well as incorporating LAB annihilation as described in [14,15]. The critical areas for consumption for each event are illustrated schematically in Fig.…”

“…Coarsening of LABs is attributed here to the mechanism of LAB annihilation in which the angle of misorientation reduces to zero. As Sauzay and co-workers [15] have illustrated for lath coarsening, the M 23 C 6 precipitates, which were originally present on LABs, remain behind after the LAB has disappeared and form part of the coarsened lath interior. …”

“…This matrix structure is further strengthened by various precipitates and solutes, which are described in more detail below. Typical dimensions for the PAGs are approximately 100 μm, blocks are approximately 4 μm [15] and the width of the martensitic laths are of the order of 0.37-0.7 μm [6,15]. This complex microstructure forms due to the heat treatment of 9-12Cr steels, as illustrated schematically in Fig.…”

“…Strain gradient crystal plasticity (CP) material models [28][29][30][31][32] have been employed to obtain a back-stress for the Bauschinger effect through the inclusion of geometrically necessary dislocations (GNDs) within a crystal plasticity UEL user subroutine, as well as the presence of carbides geometrically in the finite element (FE) model. Sauzay et al [14,15,33] have presented a physically-based model for cyclic softening of 9-12Cr steels. However, to date, no corresponding model based on the physical mechanisms of the Bauschinger effect and kinematic hardening has been developed.…”