A Determination Of Carbon Solubility Limit In Bcc-Iron From Low-Temperature Age Hardening By Bayesian Inference

The carbon solubility limit in bcc-iron in equilibrium with cementite at 973 K was estimated by exploiting the age-hardening behavior of a quenched specimen at 323 K and Bayesian inference. The cold-rolled steel containing 0.045 wt% carbon was subjected to decarburization annealing at 973 K in a salt bath for different times up to 10 hours; subsequently, they were water-quenched. These specimens showed carbon contents of 0.005 to 0.045 wt% depending on the annealing time. The quenched specimens were kept at 323 K in a silicone oil bath and the Vickers hardness was sequentially measured to evaluate an age-hardening curve. The maximum hardness of each aging curve showed the following changes with carbon content: when the carbon content decreased from 0.045 wt%, the hardness showed a constant value up to certain carbon content (Region I), decreased with further decreases in the carbon content (Region II), and finally showed a constant value again. Bayesian inference for the above relation was performed by a Markov chain Monte Carlo method. The boundary between Region I and Region II was rigorously estimated. The 95% confidence interval at the boundary between Region I and Region II was determined to be 0.023 +/- 0.003 wt%. Based on the strengthening mechanism for each region, the above value was inferred to be the solubility limit of carbon in ferrite equilibrated with cementite at 973 K.