Andrews Equation (Ms)
$M_s = 539 - 423C - 30.4M_n$$\quad - 17.7N_i - 12.1C_r - 7.5M_o$ (°C)
Martensite fraction (Koistinen-Marburger):
$f_M = 1 - \exp(-0.011(M_s - T_q))$
Adjust carbon content, alloy type and cooling rate to see the CCT diagram and cooling curve in real time. Instantly check Ms temperature, estimated hardness and microstructure fractions.
The starting temperature for martensite formation is critical. It's predicted empirically using the Andrews equation, which accounts for the chemical composition of the steel.
$$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.
The concepts behind CCT diagram simulation are, in fact, deeply connected to various engineering fields. One is welding engineering. The heat-affected zone (HAZ) in welding undergoes an extremely complex heating and cooling cycle from the weld thermal cycle. Understanding continuous cooling transformation behavior is essential for predicting microstructural changes in this area, and it is applied in evaluating weldability and determining preheat temperatures to prevent cold cracking.
Another is materials design and informatics. Tweaking the effects of Ni or Cr in this tool is essentially a "virtual experiment." Building on this, research is progressing to use machine learning to predict the Ms point and hardness with high accuracy when combining numerous elements. Furthermore, in the field of phase transformation kinetics, there are approaches that describe the nucleation and growth rates of transformations using mathematical models (e.g., the Johnson-Mehl-Avrami-Kolmogorov equation) to calculate phase fractions on a more physics-based level. $$ f = 1 - \exp(-k t^n) $$ Here, $f$ is the transformed fraction, $t$ is time, and $k$ and $n$ are material constants. Such fundamental equations may lie in the background of the simulator.
Finally, there is the linkage with manufacturing process simulation (CAE). To predict heat treatment distortion, it is necessary to solve for the temperature field, microstructural changes, and deformation in a coupled manner. The "cooling rate → microstructure → hardness" relationship obtained from this tool becomes important material property data input into such large-scale CAE analyses.
Once you are comfortable with this simulator and think "I want to know more," try moving to the next step. For practical learning, we recommend trying to replicate actual material standard steels (JIS or AISI) in the simulator. For example, compare S45C (a carbon steel with 0.45% C) and SCM440 (a Cr-Mo steel) by setting them up and seeing how the hardness and Ms point change under the same cooling rate. The difference between catalog values and simulation results will give you a tangible feel for the model's limitations and the effective impact of alloying elements.
If you want to learn the mathematical background, touching on the basics of thermodynamics and diffusion equations will deepen your understanding. Pearlite transformation is dominated by carbon diffusion, while martensite transformation is a diffusionless shear transformation. This "presence or absence of diffusion" is the fundamental reason for microstructure selection based on cooling rate. Also, the aforementioned Koistinen-Marburger equation is actually a simplification of a transformation kinetics model under certain assumptions. Learning more detailed models will reduce the "black box" feeling of the simulation.
The next recommended topic is "TTT diagrams (isothermal transformation diagrams)". While CCT diagrams are for "continuous cooling," TTT diagrams represent microstructural changes when "held at a constant temperature." The ability to interpret both CCT and TTT diagrams becomes essential when designing more advanced heat treatment processes like tempering or austempering. If this tool has a function to "hold during cooling," it should be your first step into the world of TTT diagrams.