What are the axes of a deformation-mechanism map?

The standard Ashby–Frost map plots normalised shear stress (σ/G, stress over shear modulus) on the vertical axis against homologous temperature (T/Tm, temperature over melting point) on the horizontal. Using normalised axes lets one map style compare different materials.

What do the fields represent?

Each field is the range of stress and temperature where one mechanism dominates the strain rate: elastic behaviour at low stress, dislocation glide (plasticity) at high stress, power-law (dislocation) creep at intermediate conditions, and diffusional creep — Coble at lower temperature, Nabarro–Herring at higher — at low stress and high temperature.

Why do the contours matter?

Overlaid on the fields are constant strain-rate contours. They let you read off the strain rate at a given stress and temperature, or conversely find the stress that keeps creep strain rate below a design limit — which is exactly what high-temperature design needs.

Mechanical · guide

Reading deformation-mechanism maps

At high temperature a material can deform by several competing mechanisms, and which one wins changes the whole stress–strain-rate relationship. Ashby and Frost compressed that picture into a single map — a field diagram of which mechanism dominates, with strain-rate contours on top.

Normalised axes

The map plots normalised shear stress against homologous temperature:

vertical: σ_s / G horizontal: T / T_m

Normalising stress by the shear modulus G and temperature by the melting point T_m makes the map roughly transferable between materials of the same crystal class — a stainless steel and a nickel alloy look similar on these axes.

The fields

Each region marks where one mechanism sets the strain rate:

Elastic — low stress, no permanent flow.
Dislocation glide (plasticity) — high stress, near or above the yield surface.
Power-law creep — intermediate stress and temperature; strain rate ∝ σⁿ with n ≈ 3–8 (dislocation climb-glide).
Diffusional creep — low stress, high temperature; linear in stress. Coble creep (grain-boundary diffusion) dominates at lower temperature, Nabarro–Herring (lattice diffusion) at higher.

Power law vs diffusional

The key practical split at high temperature is between power-law and diffusional creep. Their stress dependence differs sharply:

power-law: ε̇ ∝ σⁿ (n ≈ 3–8) diffusional: ε̇ ∝ σ¹

So at low stress diffusional creep — strongly grain-size dependent — takes over, which is why fine-grained alloys creep faster in that regime and why turbine blades are grown as coarse or single crystals.

Open the calculatorDeformation-mechanism map tool →Generate the Ashby–Frost map for a material, with the mechanism fields, strain-rate contours, and your operating point located on it.

Using the map in design

Locate your operating point (stress, temperature) on the map: the field tells you the dominant mechanism and therefore which mitigation works — raise stress out of diffusional creep, coarsen grains, change alloy, or drop temperature. The strain-rate contours then give the actual creep rate to compare against the design life and the Larson–Miller allowable.

Frequently asked

What are the axes of a deformation-mechanism map?: The standard Ashby–Frost map plots normalised shear stress (σ/G, stress over shear modulus) on the vertical axis against homologous temperature (T/Tm, temperature over melting point) on the horizontal. Using normalised axes lets one map style compare different materials.
What do the fields represent?: Each field is the range of stress and temperature where one mechanism dominates the strain rate: elastic behaviour at low stress, dislocation glide (plasticity) at high stress, power-law (dislocation) creep at intermediate conditions, and diffusional creep — Coble at lower temperature, Nabarro–Herring at higher — at low stress and high temperature.
Why do the contours matter?: Overlaid on the fields are constant strain-rate contours. They let you read off the strain rate at a given stress and temperature, or conversely find the stress that keeps creep strain rate below a design limit — which is exactly what high-temperature design needs.

References

H.J. Frost, M.F. Ashby, "Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics," Pergamon, 1982.
M.F. Ashby, "A first report on deformation-mechanism maps," Acta Metallurgica, 1972.
F.R.N. Nabarro, "Deformation of crystals by the motion of single ions," 1948; C. Herring, J. Applied Physics, 1950.
R.L. Coble, "A model for boundary diffusion controlled creep in polycrystalline materials," J. Applied Physics, 1963.

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