Phase Diagrams & Heat Treatment Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Phase Diagrams & Heat Treatment: theory, method, and sources

This materials science workspace publishes 9 governing equations, 6 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Eleven modules cover the lever rule, eutectic phase fractions, carbon steel equilibrium phases, Avrami transformation kinetics, Arrhenius time–temperature equivalence, grain growth, the Hollomon–Jaffe tempering parameter, cooling rate, carburizing case depth, Jominy hardenability, and sigmoidal phase fraction.

Equilibrium phase fractions and time-dependent transformation kinetics sit side by side, which makes the gap between what a phase diagram predicts and what a real cooling rate produces explicit.

Calculators and topics covered

phase diagrams
heat treatment
steel
grain growth
kinetics
lever rule
Avrami
Hollomon Jaffe
Jominy
eutectic

Core equations

\text{lever rule:}\quad \mathrm{W}_{\alpha } = \frac{C_{\beta } - C_{0}}{C_{\beta } - C_{\alpha }}

carbon steel: proeutectoid and pearlite fractions from the 0.76 wt% eutectoid composition

\text{Avrami equation:}\quad X = 1 - \exp \left(- kt^{n}\right)

\text{Arrhenius time equivalence:}\quad t_{2} = t_{1} \exp \left[\left(\frac{Q}{k}\right) \left(\frac{1}{T_{2}} \frac{- 1}{T_{1}}\right)\right]

\text{grain growth:}\quad d^{n} - d_{0}^{n} = kt

\text{Hollomon–Jaffe parameter:}\quad P = \frac{T \left(C + log_{10}\; t\right)}{1000}

\text{cooling rate:}\quad R = \frac{T_{\mathrm{start}} - T_{\mathrm{end}}}{t}

\text{case depth:}\quad x = \text{factor} \cdot \sqrt{Dt}

\text{Jominy hardness decay:}\quad HRC = \operatorname{floor} + \left(H_{0} - \text{floor}\right) \exp \left(\frac{- \text{distance}}{\text{decay}}\right)

Method and assumptions

Assumptions

The lever rule assumes equilibrium at the stated temperature, which real cooling rates rarely achieve.
Carbon steel fractions use the simplified Fe–Fe₃C diagram with a 0.76 wt% eutectoid and 6.7 wt% cementite.
Avrami kinetics assume isothermal transformation with constant n and k.
Grain growth and case depth use single-mechanism power law and parabolic forms respectively.
The Jominy model is an exponential fit for teaching the shape of a hardenability curve, not a substitute for measured Jominy data.
Alloying element effects on transformation temperatures and hardenability are not modelled.

Limitations and design boundaries

Educational screening models only. Material certification, process qualification, applicable standards, statistical variability, environmental conditioning, and professional engineering judgment are required for real selection or design.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Callister and Rethwisch, Materials Science and Engineering: An Introduction
Askeland and Wright, The Science and Engineering of Materials