Materials Engineering

Hardenability Through-Thickness Estimator — Core and Surface Hardness Calculator

Calculate core hardness and surface hardness using section thickness, hardenability index, carbon content, alloy factor, and quench severity.

Unit-aware inputs Deterministic calculation Engineering interpretation
Calculation workspace

Enter the known values and review the calculated result

Deterministic calculation
01
Parameters

Input parameters

Use consistent values and select the intended engineering units.

Material properties

Geometry

Heat treatment conditions

02
Output

Results

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Engineering reference

Method, application and limitations

Review the calculation method, intended application and engineering assumptions before using the result in a design decision.

01
Method

Formula and calculation method

Core hardness formula:

Jeff = J · A · Q

ratio = t / Jeff

decay = e−ratio

Hsurface,base = 150000000 + 900000000 · C

Hsurface = Hsurface,base · (0.7 + 0.3 · A)

Hcore = Hsurface · decay

Surface hardness formula:

Hsurface,base = 150000000 + 900000000 · C

Hsurface = Hsurface,base · (0.7 + 0.3 · A)

where:

  • Hcore — Core hardness (Pa)
  • Hsurface — Surface hardness (Pa)
  • J — Hardenability index / Jominy proxy (m)
  • Jeff — Effective hardening depth (m)
  • A — Alloy factor (-)
  • Q — Quench severity (-)
  • t — Section thickness (m)
  • C — Carbon content (wt%)
  • ratio — Section thickness divided by effective hardening depth (-)
  • decay — Exponential hardness reduction through thickness (-)
02
Application

When to use this calculator

When to use this calculator:

  • Estimate core hardness for a steel section using hardenability index, section thickness, carbon content, alloy factor, and quench severity.
  • Compare surface hardness and core hardness for a selected material and quenching condition.
  • Check whether section thickness is too large relative to effective hardening depth.
  • Evaluate hardness drop from surface to core before selecting a heat treatment route.
  • Estimate soft-core risk from the calculated through-hardening ratio.
03
Decision support

How to interpret the result

Core hardness is defined as the estimated hardness at the core after the surface hardness is reduced by exponential decay through the section thickness.

Surface hardness is defined as the carbon-content-based hardness level corrected by alloy factor.

Core hardness depends on surface hardness, section thickness, hardenability index, alloy factor, and quench severity. Increasing section thickness decreases core hardness. Increasing hardenability index, alloy factor, or quench severity increases effective hardening depth and increases core hardness.

Surface hardness depends on carbon content and alloy factor. Increasing carbon content increases surface hardness. Increasing alloy factor increases surface hardness.

  • Safe — through-hardening ratio ≥ 0.9
  • Limit — through-hardening ratio ≥ 0.75 and < 0.9
  • Warning — through-hardening ratio ≥ 0.5 and < 0.75
  • Unsafe — through-hardening ratio < 0.5
  • Invalid — input or model condition is outside the allowed JS validation range.

The result is used to compare surface hardness against core hardness and evaluate whether the selected section thickness, material hardenability, and quenching condition produce sufficient through-thickness hardening.

04
Worked case

Calculation example

Example:

A user wants to estimate whether a 60 mm steel section can achieve acceptable through-hardening after quenching.

  • J — Hardenability index (Jominy proxy): 0.08 m
  • t — Section thickness: 0.06 m
  • Q — Quench severity: 2
  • C — Carbon content: 0.40 wt%
  • A — Alloy factor: 1.5

Jeff = 0.08 · 1.5 · 2 = 0.24 m

ratio = 0.06 / 0.24 = 0.25

Hsurface = (150000000 + 900000000 · 0.40) · (0.7 + 0.3 · 1.5) = 586500000 Pa

Hcore = 586500000 · e−0.25 = 456741850 Pa

05
Model boundaries

Assumptions and limitations

  • Effective hardening depth is calculated as hardenability index multiplied by alloy factor and quench severity.
  • Core hardness decreases exponentially with section thickness divided by effective hardening depth.
  • Surface hardness is calculated from carbon content and alloy factor only.
  • The model is limited to hardenability index values within 0 < J ≤ 1 m.
  • The model is limited to section thickness values within 0 < t ≤ 2 m.
  • The model is limited to quench severity values within 0 < Q ≤ 5.
  • The model is limited to carbon content values within 0 < C ≤ 1.2 wt%.
  • The model is limited to alloy factor values within 0 < A ≤ 4.
  • The model rejects cases where section thickness divided by effective hardening depth is greater than 20.
  • The model rejects cases where calculated surface hardness exceeds 3500000000 Pa.
06
Questions

Frequently asked questions

How to calculate core hardness?
Core hardness is calculated from surface hardness multiplied by an exponential decay factor through the section thickness. The core hardness formula uses effective hardening depth, section thickness, carbon content, alloy factor, and quench severity.
How to calculate surface hardness?
Surface hardness is calculated from a carbon-content-based hardness level multiplied by the alloy factor correction. Increasing carbon content increases surface hardness, and increasing alloy factor also increases surface hardness.
What affects core hardness the most?
Core hardness depends on surface hardness and the thickness-to-effective-depth ratio. Increasing section thickness decreases core hardness. Increasing hardenability index, alloy factor, or quench severity increases effective hardening depth and increases core hardness.
When is the core hardness formula not valid?
The formula is not valid when the hardenability index is outside 0 < J ≤ 1 m, section thickness is outside 0 < t ≤ 2 m, quench severity is outside 0 < Q ≤ 5, carbon content is outside 0 < C ≤ 1.2 wt%, or alloy factor is outside 0 < A ≤ 4.
Can this calculator be used to evaluate soft-core risk?
It can be used when soft-core risk is interpreted from the calculated through-hardening ratio. The model marks the result as unsafe when the through-hardening ratio is below 0.5 and invalid when the section is too thick for meaningful core hardening.
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Engineering notice. Verify input data, assumptions, applicable standards and required safety factors before using results for design release or safety-critical decisions.