Consider the carburizing of a steel bar to create a hard surface. To obtain the desired hardness, we need to control the diffusion of carbon into the surface and the phases obtained during heat treatment and cooling. The base steel has a composition of 0.2 wt%C. For mathematical simplicity we consider an infinitely thick bar and a diffusivity that does not vary with concentration. All concentrations are in weight percent.
a) Use the diffusion data in Callister (Table 5.2 in the later editions) and the simple formula for the "diffusion distance" (i.e. Dt2) to create a graph in Excel. (Graphs are helpful for visualizing phenomena.) This graph should provide estimates of the depth of carbon expected for diffusion treatments at 950°C, 1050°C and 1150°C and for times up to 10000s. Plot time on the horizontal x-axis (in seconds) and diffusion distance on the vertical y-axis (in microns).
b) Use the graph you have created to estimate the times required for a diffusion depth of 600 microns (i.e. 0.6 mm) for each of the three temperatures.
c) Now create a graph of the carbon concentration as a function of depth for a diffusion treatment at 1050°C for 2700s. Assume the furnace atmosphere is controlled to maintain a surface carbon concentration in the steel of 1.5 wt%. Plot distance from the surface on the x-axis (up to 1500 microns) and carbon concentration (in wt%) on the y-axis.
d) Imagine the sample is cooled to 800°C and held there for a time long enough to achieve phase equilibrium but not long enough for any significant change in the carbon concentration. From your graph in c) establish over what range of depths from the surface the material is likely to be present entirely as single phase austenite?
e) From your graph in c), establish the depth at which the material has the eutectoid composition. For the material at this depth what phase(s) will be present if the material is cooled rapidly to 400°C, held there for 1000s and then air cooled to room temperature.
f) Repeat the treatment in e) but this time hold only for 50s at 400°C, then rapidly heat to 600°C, hold for 5s and then quench in water. What phases will you have now?