Deformation Mechanism Maps

These pages provide information and code for constructing materials' deformation mechanism maps, as documented in the book by Harold Frost and Mike Ashby in 1981; and extended somewhat by Philip Sargent and Mike Ashby during the 1980s.

This software was ported from IBM mainframe Fortran to an Acorn BBC personal computer with a 32-bit coprocessor. Then a simpler variant was ported to Turbo Pascal which was then used by several other people (Ho Sung Kong, Mike Ashby) to produce Densification Maps as HIP diagrams (Hot Isostatic Pressing) using techniques derived from Brian Derby's Diffusion Bonding Maps and David Wilkinson's Sintering Maps. The code here is a much-worked-upon improvement in the code body, unifying many special purpose extensions and branches.

While the basic principles are simple and easily understood, it is surprisingly difficult to construct software to robustly produce mechanism maps for a variety of materials showing all the main plasticity mechanisms: high-temperature power-law creep, low-temperature power-law creep, volume diffusion creep, grain-boundary diffusion creep, Harper-Dorn creep, dynamic recrystallization, phonon-drag-controlled glide, obstacle-controlled-glide, electron-drag controlled glide, lattice-resistance-controlled glide, adiabatic shear.

This difficulty is partly because the transitions between the dominant mechanisms are of several different types: the overall strain rate can be additive or substitutive for the two major mechanisms at any point, but also the common algebraic expressions for some mechanisms omit important terms because "everyone knows" e.g. that phonon-drag-controlled glide does not happen at low stresses and high temperatures. Unfortunately, such omissions must be correctly formulated and inserted in the software before a good map can be created. These formulations are sometimes a significant research project in their own right. The file DFMMODLS.PAS contains the most recent code that manages this.

Finally there are ordinary computational issues with large and small numbers, e.g. the factor dornLT is bothersome because it gets very small at low temperatures, but is multiplied by a huge stress term (later). So we split dornLT into two small numbers and defer multiplying them until we have the stress term as well; in procedure STRAIN_RATES.

Some "rare" materials have entirely different mechanisms, e.g. ice, with its hydrogen-bonds causing unusual strength near the melting point. The software uses the same code for many different isomechanical classes of solid, but there are three major classes for which different code is required: ice, ceramics and metals.

Download the software archive (1,335 kB). This includes all the original Fortran, the reworked Fortran and the latest Pascal code and data. You can browse some of the deformation mechanisms coding: Fortran and Pascal.

The executable program dfm290.exe in directory DefmMaps-pascal\Distribution will create a stress/temperature or a strain-rate/temperature map for any of the following materials:

ALUMINA CAMPHENE CO-EPSLON COPPER FE-ALPHA FE-DELTA GERMANIUM INSB LEAD MAGNESIA MAR-M200 MO-TEST MOLYBDM NICKEL POTASSIUM ROCKSALT SI3N4 SIC SILICON SILVER SS-316 T-STEEL TI-ALPHA TI-BETA TIN TUNGSTEN URANIA Y-BA-CUO ZIRCONIA ZR-ALPHA ZR-BETA AL-FINE NI-FINE ALUMINIUM

You can also edit these data files and create your own. Every set of data is checked against the isomechanical class of the material to help you decide if you have made a mistake in entering data. References to the data supplied are given. Many of the data sets provided do contain items which are outside the norms for each group, e.g. SIC, which is atypical even for a sphalerite ceramic.

The source archive contains a variety of documentation, including an operating manual in Word, a quick HTML-port of which is online here (without Contents and Index).

The Presentation of High Strain Rates on Deformation Mechanism Maps
P.M.Sargent and M.F.Ashby
Cambridge University Engineering Dept. Technical Report
CUED/C-MATS/TR.98 March 1983.

A Deformation Mechanism Map for IN 738 LC
J.G.Carey, P.M.Sargent and D.R.H.Jones
J.Materials Science Letters 9 (1990) 572-575.

Comments on: A Rational Method for Calculating Mechanism Maps
P.M.Sargent and B.Derby
Scripta Metallurgica 19 (1985) 1013-1014.

A Deformation Map for a III-V Compound, Indium Antimonide
P.M.Sargent and M.F.Ashby
Scripta Metallurgica 18 (1984) 219-224.

Deformation Mechanism Maps for Alkali Metals
P.M.Sargent and M.F.Ashby
Scripta Metallurgica 18 (1984) 145-150.

A Deformation Map for Silicon Carbide
P.M.Sargent and M.F.Ashby
Scripta Metallurgica 17 (1983) 951-957.

A Deformation Map for Cobalt
P.M.Sargent and M.F.Ashby
Scripta Metallurgica 17 (1983) 625-629.

Deformation Maps of Titanium and Zirconium
P.M.Sargent and M.F.Ashby
Scripta Metallurgica 16 (1982) 1415-1422.

See my full list of publications for technical and unpublished reports on these and similar subjects: http://purl.oclc.org/NET/sargents/Philip/publications/

Sometime I suppose I should create a PURL for these webpages