Step 1: Recall what a deformation mechanism map shows.
A deformation mechanism map, also called an Ashby map, is a two dimensional plot with normalized shear stress \(\sigma/G\) on one axis (where \(G\) is the shear modulus) and homologous temperature \(T/T_m\) on the other (where \(T_m\) is the melting point). The map is divided into fields, each labelled with the mechanism that dominates plastic deformation in that region of stress and temperature, such as dislocation glide, power law creep, and diffusional creep (Nabarro-Herring and Coble creep).
Step 2: Identify what extra information the map carries.
Superimposed on the mechanism fields are contour lines of constant strain rate, \(\dot{\varepsilon}\). Given a stress and a temperature for a component in service, the map is read like a graph to find which mechanism controls deformation there, and the contour lines directly give the steady state strain rate produced by that mechanism. This steady state, time dependent plastic strain rate under a fixed stress and temperature is exactly what is called the creep rate.
Step 3: Rule out the other options.
(A) Fatigue strength: Fatigue strength comes from S-N curves built from cyclic loading tests, not from a static stress-temperature-mechanism map. Incorrect.
(C) Tensile strength: Tensile strength is read from a stress-strain curve obtained in a uniaxial tensile test at a fixed strain rate, unrelated to the mechanism fields of this map. Incorrect.
(D) Impact toughness: Impact toughness is measured using notched-bar impact tests, such as Charpy or Izod, which capture energy absorbed under sudden dynamic loading. It has no connection to the mechanism map. Incorrect.
Step 4: Final Answer.
A deformation mechanism map is used to find the dominant deformation mechanism and read off the corresponding strain rate, which is the creep rate, for a given stress and temperature.
\[
\boxed{\text{Creep rate}}
\]