A map with normalized stress and homologous temperature as axes, showing the fields of the mechanism that deforms fastest, such as dislocation glide, power-law creep and diffusion creep.
Japanese name: 変形機構図
Deformation mechanism map appears in 1 practice question across 1 topic, including High-temperature materials and creep.
The deformation mechanism map was proposed by Ashby in 1972, and maps for many metals and ceramics were collected in his 1982 book with Frost. Values such as diffusion coefficients, shear modulus, atomic volume and grain size are inserted into the rate equation of each mechanism, such as dislocation glide, power-law creep and diffusion creep, and the rate is calculated for each combination of stress and temperature. Rates of mechanisms that act independently are added, while for mechanisms that act as alternatives the faster one is chosen, and the field of the mechanism with the largest contribution is shaded. A boundary line is the condition at which the rates of two neighboring mechanisms are equal.
Using the homologous temperature T/Tm, the absolute temperature divided by the melting point Tm, on the horizontal axis lets the high-temperature behavior of materials with different melting points be compared on the same scale. As a guide, creep becomes noticeable once T/Tm exceeds about 0.4. Room temperature, 20 °C, is only T/Tm ≈ 0.08 for tungsten (Tm ≈ 3695 K) but as much as about 0.49 for lead (Tm ≈ 601 K). Old lead pipes and roofing sag slowly under their own weight because they are in the creep regime even at room temperature. Conversely, T/Tm = 0.6 for pure Ni corresponds to about 1040 K, or around 760 °C.
A deformation mechanism map is calculated from model rate equations and literature constants for a fixed grain size and purity. Just as refining the grains enlarges the diffusion creep field, the boundaries move considerably when the microstructure changes, and maps for pure metals cannot be applied directly to alloys containing precipitates. The constants in the rate equations carry errors, so the positions of the boundaries need to be checked by experiment. The map also shows the rate of steady-state deformation and does not tell when fracture occurs. For fracture, separate fracture mechanism maps have been made, showing fields such as cleavage, intergranular fracture and ductile fracture in the same way.
Placing the service stress and temperature on the map shows which mechanism dominates, and the contours of constant strain rate drawn on the map give a rough idea of the deformation rate. If the point lies in the diffusion creep field, coarser grains help; if it lies in the power-law creep field, precipitates or solute elements that hinder dislocation motion help, so the effective remedy differs. If the point is near a boundary, a slight change in conditions can switch the mechanism, and extrapolation from short tests is likely to fail. In the Earth sciences, maps for rocks and ice are also used to consider the mechanisms of flow in the mantle and in glaciers.
Answer: A. For a fixed grain size, it shows the field of the fastest mechanism at each stress and temperature; diffusion creep lies at low stress and high temperature, and power-law creep at higher stresses
A deformation mechanism map uses the rate equation of each mechanism to find which one deforms the material fastest at a given stress and temperature, and shades its field. Because several mechanisms act in parallel, the fastest one is taken to be dominant. Dislocation glide dominates at high stresses close to the ideal strength, power-law creep involving dislocation climb at intermediate stresses and high temperatures, and diffusion creep at low stresses and high temperatures. Since the rate of diffusion creep is inversely proportional to the square or cube of the grain size, refining the grains enlarges the diffusion creep field, so the boundaries do move. Contours of constant strain rate are also drawn, so the mechanism and the deformation rate under service conditions can be read off. Placing dislocation glide on the low-stress side gets the layout wrong.
It is the absolute temperature T divided by the melting point Tm (also absolute), T/Tm. The ease of atomic diffusion becomes similar across materials when referred to the melting point, so it is used as a guide to high-temperature deformation. Dividing Celsius temperatures gives a meaningless value, so it must always be calculated with absolute temperatures.
Because the rates of dislocation motion and creep depend not on the stress itself but on how large the stress is relative to the strength of interatomic bonding. Using σ/G, divided by the shear modulus G, lets materials of different strength be compared on the same scale. Maps often also carry a scale of actual stress (MPa) alongside.
It is the combination of stress and temperature at which two neighboring mechanisms produce deformation at the same rate. On the line their contributions are equal, and farther from it one of them dominates. A boundary is not a line where the mechanism switches abruptly; near it, both mechanisms are at work.
A deformation mechanism map uses the rate equation of each mechanism to find which one deforms the material fastest at a given stress and temperature, and shades its field.
Which statement about the deformation mechanism map of Ashb…Dislocation Power-law creep Diffusion creep Larson–Miller parameter Nickel-based superalloy Parabolic rate law Pilling–Bedworth ratio Thermal barrier coating