$\quad - 17.7N_i - 12.1C_r - 7.5M_o$ (°C)
Martensite fraction (Koistinen-Marburger):
$f_M = 1 - \exp(-0.011(M_s - T_q))$
Adjust carbon content, alloy type and cooling rate to see the CCT diagram and cooling curve in real time. Instantly check Ms temperature, estimated hardness and microstructure fractions.
The starting temperature for martensite formation is critical. It's predicted empirically using the Andrews equation, which accounts for the chemical composition of the steel.
$$M_s = 539 - 423C - 30.4Mn - 17.7Ni - 12.1Cr - 7.5Mo \quad (\text{°C})$$Variables: $M_s$ is the martensite start temperature (°C). $C, Mn, Ni, Cr, Mo$ are the weight percentages (wt%) of carbon, manganese, nickel, chromium, and molybdenum in the steel. Notice the massive coefficient for carbon ($-423$), showing its dominant effect on lowering $M_s$.
Once cooling passes below $M_s$, martensite forms progressively. The volume fraction of martensite at a given quenching temperature $T_q$ is modeled by the Koistinen-Marburger relationship.
$$f_M = 1 - \exp(-0.011(M_s - T_q))$$Variables: $f_M$ is the fraction of martensite (0 to 1). $T_q$ is the temperature during quenching (°C). The equation shows that the amount of martensite increases as you quench further below $M_s$, but the transformation is never 100% complete until very low temperatures.
Automotive Component Manufacturing: Critical parts like gears, shafts, and springs require precise strength and toughness. Engineers use CCT diagrams to design the quenching process (oil, water, or air cooling) to achieve the exact mix of martensite and bainite needed for performance, avoiding cracks from overly fast cooling.
Welding and Joining: The heat-affected zone (HAZ) next to a weld undergoes a complex thermal cycle. Metallurgists refer to CCT diagrams for the specific steel grade to predict the HAZ microstructure and hardness, which helps prevent cold cracking and ensures joint integrity.
Tool and Die Steel Heat Treatment: Tools like drills and molds must be extremely hard and wear-resistant. The heat treatment process is meticulously planned using CCT data to ensure the steel transforms fully to martensite upon quenching, followed by proper tempering to relieve stresses.
Pipeline Steel Production: For large-diameter pipelines, controlled rolling followed by accelerated cooling is used. The target is often a fine bainitic microstructure for an optimal combination of strength and weldability. CCT diagrams guide the cooling rate on the production line to hit this target consistently.
When you start using this simulator, there are several pitfalls that engineers, especially those with less field experience, often fall into. The first is not understanding the practical meaning of the "cooling rate" value. Even if you set it to "100°C/s" in the simulator, whether that cooling rate can be achieved in an actual part is a different matter. For example, when water quenching a round bar with a 50mm diameter, the cooling rate can differ by more than 10 times between the surface and the core. Even if you obtain the ideal microstructure with the tool, a heat treatment design that ignores the part size (mass effect) will fail.
The second is the misconception of simply adding up the effects of alloying elements. While the Andrews formula is indeed linear, interactions exist between elements. For instance, it is known that adding Cr and Mo simultaneously results in a greater improvement in hardenability than the sum of their individual effects (a synergistic effect). Since the simulator is based on standard models, you must be aware that predictions may deviate from actual measurements for special high-alloy steels.
The third is judging the microstructure based solely on hardness. A martensite fraction of 90% and 10% will have vastly different hardness values. However, even with the same 90% martensite fraction, toughness will be worlds apart depending on whether the remaining 10% is fine bainite or coarse ferrite. While the simulator's phase fraction is an important indicator, the key to preventing cracking and brittle fracture is to not just think "if the hardness passes, it's OK," but to also imagine the expected morphology of the microstructure.
For a 1045 steel (0.45 wt% C, 0.8 wt% Mn) cooled at 50°C/s in oil: the simulator plots a cooling curve intersecting the bainite region, predicting Ms = 310°C, estimated hardness 52 HRC. Adding 1.0 wt% Cr shifts curves leftward; same cooling rate now avoids pearlite nose entirely, yielding full martensite at 48 HRC. Furnace cooling (1°C/s) the Cr-containing alloy produces mixed pearlite–bainite, ~35 HRC, demonstrating hardenability's critical role in part design.