Creep Strain Modeling of 9 to 12 Pct Cr Steels Based on Microstructure Evolution

Abstract

Creep deformation is simulated for 9 pct Cr steels by using the Norton equation with the addition of back stresses from dislocations and precipitates. The composite model is used to represent the heterogeneous dislocation structure found in 9 to 12 pct Cr steels. Dislocation evolution is modeled by taking capturing and annihilation of free dislocations into account. Recovery of immobile dislocations is derived from the ability of dislocation climb. In spite of the fact that the initial dislocation density is high and is reduced during creep, primary creep is successfully modeled for a P92 steel. Subgrain growth is evaluated using a model by Sandstro¨m (1977). The long time subgrain size corresponds well to a frequently used empirical relation, with subgrain size inversely proportional to the applied stress.

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

“…The evolution of lath interior immobile dislocations accounts for the loss of mobile dislocations due to the formation of immobile locked configurations and the loss of immobile dislocations via climb processes. Thus, the evolution equation is defined as [21,22]: (18) where m cl is the climb mobility rate of dislocations. From the Taylor , and equation (11), the density of immobile dislocations at lath walls is: (19) with a subsequent rate evolution given by: …”

“…The overall dislocation density of the 'as-received' material is approximately 10% greater than that at the lath walls [55], such that the initial lath boundary immobile dislocation density, ρ w,0 , is 0.9ρ 0 . The initial lath interior immobile dislocation density is assigned a low value of 1 10 11 m -2 [21]. The critical distance for a dipole dislocation to form is assigned a value of 7b.…”

“…where t w is the cell wall thickness and is assigned a constant value of 100b [21]. To account for the effect of the Mo interstitial atoms reducing the climb mobility rate, m cl is defined as [21]:…”

“…To account for the effect of the Mo interstitial atoms reducing the climb mobility rate, m cl is defined as [21]:…”

“…Due to the complex nature of the evolution of the microstructure of 9-12Cr steels [5,6], a multi-scale modelling approach is required. One of the key requirements for A number of material models based on the physical mechanisms of creep have been developed [16][17][18][19] and applied to 9-12Cr steels [20][21][22][23][24][25][26]. Material models, e.g.…”