Dilatometric Data Analyzer

Composition wt-%

Carbon (C)0.150 Silicon (Si)0.30 Manganese (Mn)1.5 Nickel (Ni)0 Molybdenum (Mo)0.000 Chromium (Cr)0.000 Vanadium (V)0.000 C trapped in α 0.020

▸ EXTENDED COMPOSITION Σ = 0.000 wt%

Optional. These elements affect the mole-fraction normalisation in the lattice equations even though most have zero coefficient in the Yang & Bhadeshia formula. Click to expand.

Lattice & expansivities

Linear expansivity α 1/°C Linear expansivity γ 1/°C Pure austenite lattice parameter m

Overwrite the calculated lattice parameter

Ferrite lattice parameter m

Dilatometer data CSV / DAT / TXT

⤓

Drop a file here, or click to browse

Accepts CSV (Temperature, ΔL/L, ΔD/D, Time) or LENGTH.DAT format

no data loaded

Cycle detection

Smoothing window (points)5 Hold tolerance |dT/dt| 0.5 °C/s Min segment duration (s)5 Segments are classified by the smoothed dT/dt sign and magnitude. Heating (red), Holding (purple), Cooling (blue).

Detected segments

— no segments yet —

Click a segment to highlight it on the chart and use it for downstream analysis.

Temperature vs Time Thermal cycle map

Heating Holding Cooling Selected segment endpoints

Strain vs Temperature of selected segment

Detection method

Offset method (Yang & Bhadeshia 2007)

Offsets the parent thermal-contraction line by a strain corresponding to a chosen volume fraction of product (default 1 vol-%). Recommended.

Lever-rule method

Linear extrapolations of parent (above) and product (below) phases bracket the curve. T_s, T_f are the points where the lever-rule fraction reaches 1% and 99%.

First-deviation (Expansion) method

Detects the first temperature where strain leaves the 95% confidence band of the parent thermal-contraction line. Sensitive to noise.

Derivative (dε/dT) inflection

Strain channel:

ΔL/L (length)

ΔD/D (diameter)

Offset volume fraction 1.00 % For Offset method. Offset strain ε₀ recomputes from the lattice-parameter equations (eqns 2–4 of Yang & Bhadeshia, MST 23 (2007) 556). Derivative threshold 0.50 × slope_parent For Derivative method. The threshold is the fractional change of the parent slope that counts as "departure". Lower → more sensitive (catches Ts earlier); higher → only large excursions register.

Fit ranges (parent / product): sliders

Click a button, then click two points on the chart below to set that range. Or use the sliders.

Parent T_hi 650 °C Parent T_lo 450 °C Product T_hi 200 °C Product T_lo 25 °C

Offset strain — · V=1.0%

a_α at 25 °C (ferrite/ martensite)

— nm

a_γ at 25 °C (austenite)

— nm

Offset strain ε₀

—

Result Offset · 1.0%

T_s · transformation start

— °C

T_f · transformation finish

— °C

Parent fit slope m_p

— /K

Product fit slope m_q

— /K

RMS noise σ_ε

—

Strain vs Temperature ΔL/L

Data (transformation segment) Parent linear fit Parent + ε₀ (1% transformed → T_s) Product linear fit Product - ε₀,T_f (99% transformed → T_f) T_s T_f

Volume fraction — lever rule from fitted parent & product

V_p (lever) = (ε − ε_parent) / (ε_product − ε_parent) 0% & 100% reference T_s position T_f position

Phase fraction — Bhadeshia per-point V_α(T) inversion

Direct mass-balance inversion of the dilatometer trace, after Bhadeshia's dilat-b.f / dilat2-b.f (Cambridge MAP_STEEL; Bhadeshia, David, Vitek & Reed, MST 7 (1991) 686–698). At every measured (T, ΔL/L) the lattice equation A₁ = 1 − 3·ΔL/L − a_γ(T)³ / [a_{γ_enr}(T)³ + (2·a_α(T)³ − a_{γ_enr}(T)³)·A₂] = 0 with A₂ = 1 / [1 + (2·(1−V_α)/V_α)·(a_α(T)/a_{γ_enr}(T))³] is solved for V_α by Newton iteration with bisection fallback. Inside the loop, a_{γ_enr} (carbon-enriched residual γ) is sub-iterated against the carbon mass-balance: X_γ = (V_α·ρ_α·(X̄ − X_α) + X̄·ρ_γ·(1−V_α)) / ((1−V_α)·ρ_γ); a_{γ_enr} = a_γ(T) + 0.033·(X_γ − X̄)·(1+(T−25)·β_γ) Å. No kinetic model — V_α is determined point-by-point from lattice physics alone. Same algorithm applies to isothermal data and continuous cooling.
Lattice room-T parameters: a_α from Roberts 1953 (carbon) + Leslie/Wever/Hume-Rothery (substitutional, mole-fraction weighted); a_γ from Dyson & Holmes 1970 (J. Iron Steel Inst. 277, 469). Thermal expansion uses the parent slope detected on tab 03 for β_γ (and product slope for β_α when physical). ΔL/L for the inversion is referenced to the parent (un-transformed γ) line, not to ε at start of cooling.
Cooling segments only — the algorithm assumes γ → α/p/b/m. Heating segments are skipped. Phase fraction inversion using the mass-balance of carbon and unit-cell volumes (Bhadeshia 1991). For each point, V_α is solved by Newton iteration to satisfy the measured strain ΔL/L. Cooling segments only — the algorithm assumes γ → α/p/b/m. Heating segments are skipped.

x_α (wt% C trapped in α) Strain channel β source

V_α at end of cool

—

V_γ retained

—

peak X_γ

—

a_α(298 K)

—

a_γ(298 K)

—

V_α(T) — Bhadeshia mass-balance inversion V_γ(T) = 1 − V_α(T) (dashed) X_γ(T) (residual γ carbon, wt%) — right axis (red)

Measured ΔL/L Parent (γ) extrapolation ΔL/L Model Reconstruction

Koistinen–Marburger — 1 − V_α' = exp{β·(M_S − T)}

M_S source f range for fit [0.02, 0.98] T range auto (transformation window)

Fit β by linear regression on ln(1 − V_α') = β·(M_S − T), using V_α'(T) from the lever rule above. Restrict the temperature range with the inputs above to confine the fit to martensite.

β (K⁻¹)

—

M_S (°C)

—

R²

—

N points fitted

—

                      Linearisation

                      Vα'(T) overlay

data points linear fit (slope = β) M_S marker on overlay

Analysis mode

JMAK isothermal kinetics

For hold segments. Plots ln(ln(1/(1−f))) vs ln(t) and fits the Avrami equation f = 1 − exp(−k·tⁿ) by linear regression.

DILAT2 (Bhadeshia–Lalam)

Newton iteration on the density-balance residual to compute V_p(T,t) and X_γ(T,t) for any segment direction.

Strain channel:

ΔL/L (length)

ΔD/D (diameter)

DILAT2 controls

Newton sensitivity SENS 0.10 Convergence |F| 1e-6 Max iterations10000

DILAT2 implements the Bhadeshia–Lalam Newton iteration on the density-balance residual.

Summary statistics

Points fitted

—

V_p max (product)

—

X_γ max wt%

—

Mean iter

—

Volume fraction of product vs Temperature

Volume fraction from DILAT2

Carbon enrichment vs Temperature

Per-point output table

Export options

All exports use the values currently shown in tabs 1–4. Re-run any computation before exporting if you have changed the inputs.

Run summary

Composition	—
Cooling rate (selected)	—
Detection method	—
T_s	—
T_f	—
Offset strain ε₀	—
Max V_α (DILAT2)	—
Max X_γ	—

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