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Program MAP_STEEL_PM2000

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of program's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary routines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

C. Capdevila and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge CB2 3QZ, U.K.

E-mail: cc226@cus.cam.ac.uk

Added to MAP: November 1999.

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A crystalline solid can deform plastically by a number of alternative, often competing, mechanisms. The aim of the present program is to produce a deformation-mechanism map which shows the field of stress, temperature and strain-rate over which each mechanism is dominant in PM2000 ODS alloy.

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Language: FORTRAN
Product form: Source code.

Complete program.

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All the maps are divided into fields, within each of which a given mechanism is dominant. The field boundaries are the loci of points at which two mechanism contribute equally to the overall strain-rate, and are computed by equating pairs (or groups) of rate equations, and solving for stress as a function of temperature. Superimposed on this are the contours of constant strain-rate, obtained by summing the rate-equations in an appropiated way to give a total shear strain-rate, and plotting the loci of points for which the total shear strain-rate has constant values.

Rate equation for discrete-obstacle controlled plasticity

Equation 1.

where Delta_F is the activation energy required to overcome the obstacle without aid from external stress, tau is the shear stress, k is the Boltzmann constant, T is the absolute temperature, and tau^ is the athermal flow strength, i.e. the shear strength in the absence of thermal energy. When Delta_F is large (as here), the stress dependence of the exponential is so large that the pre-exponential can be treated as a constant.

Rate equation for lattice resistance plasticity

Equation 2

Rate equation for power-law creep

Equation 3

where A2 is a dimensionless material constant and Deff is an effective diffusion coefficient expressed by the equation:

Equation 3.1

where aC is the area of the dislocation core in which fast diffusion is taken place, Dv is the lattice diffusion coefficient (Dv = Dov exp[-[(Qv)/RT] ]), and Dc is the core diffusion coefficient (Dc = Doc exp[-[(Qc)/RT] ]). In a high temperature regime, Dv >> Dc and the lattice diffusion (Figure 6.3) is predominant. This represents high temperature creep (HT Creep). By contrast, at lower temperatures, Dc > or = Dv so core diffusion is dominant mechanism. This is a Low Temperature Creep regime (LT Creep).

Rate equation for diffusional flow

Equation 4


Equation 4.1

and delta is the thickness of the grain boundary (normally 5 Å). At high temperatures, lattice diffusion controls the rate creep; the resulting flow is known as Nabarro-Herring creep and its rate scales as [(Dv)/(d2)]. At lower temperatures, grain boundary diffusion takes over, the flow is then Coble creep and scales as [(Db)/(d3)].

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  1. H. J. Frost and M. F. Ashby, 1982, Deformation mechanism maps, Pergamon Press, Oxford.

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Input parameters

PRAD - double precision
Particle radius (m).

GSIZE - double precision
Grain size of unrecrystallised alloy (m).

DDENS - double precision
Dislocation density (m-2).

DDIF - double precision
Fe diffusivity coefficient (m2s-1).

QES - double precision
Self-diffusion activation energy for Fe (J/mol).

SMOD - double precision
Shear modulus at 0 K (Pa).

BUGV - double precision
Burgers vector (m).

MATRD - double precision
Matrix density (Kgm-3).

PARTD - double precision
Particle density (Kgm-3).

PWT - double precision
Volume fraction of particles.

SRATE - double precision
Strain rate (s-1).

GSREC - double precision
Recrystallised grain size (m).

GAR - double precision
Grain aspect ratio.

IT - integer
Type of grain structure: Set IT=1 if the aspect ratio is approximately = 1. Set IT=2 if the aspect ratio is >1 and <10. Set IT=3 if the aspect ratio is > 10.

Output parameters

TEMPERATURE, Homologous Temperature, T/Tm - double precision
Ratio of temperature at which calculations were performed (kelvin) to the melting temperature (kelvin).

THRESHOLD - double precision
Ratio of threshold stress and shear modulus (dimensionless) for each temperature value.

BORDER-FIELD - double precision
Ratio of shear stress and shear modulus (dimensionless) for each temperature value. These values define the border between power law creep and diffusional flow.

PLASTICITY-FIELD - double precision
Ratio of shear stress and shear modulus (dimensionless) for each temperature value. These values define the border between power law creep and dislocation glide mechanism.

Normalized Stress - double precision
Ratio between the shear stress and shear modulus. Calculated for each input temperature at the specified input value for the strain rate.

CreepMecahnism - character
The dominating creep mechanism (power law or diffusional flow).

Sub-mecahnism - character
The dominating mechanism for movement of dislocations during creep (core diffusion or lattice diffusion).

GlideMechanism - character
The dominating glide mechanism (discrete obstacles or lattice resistance).

Diffusional - character
The mechanism for movement of dislocations during diffusional flow (lattice diffusion (Nabarro-Herring creep) or grain-boundary diffusion (Coble creep)).

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Error Indicators


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No information supplied.

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Further Comments


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1. Program text

Complete program.

2. Program data

PRAD = 5.695D-09
GSIZE = 1D-06
DDENS = 10D+14
DDIF = 5.0D-05
QES = 240000.0
SMOD = 8.4D+10
BUGV = 2.485D-10
MATRD = 7180.0
PARTD = 5020.0
PWT = 0.005
SRATE = 1.0E-04
GSREC = 90.0E-6
GAR = 10.00
IT = 2

3. Program results

File 'DMAP_borders'

0.4000000E-01     0.1964252E-03     0.1368226E-02     0.3408159E-01
0.7000000E-01     0.1964252E-03     0.1435070E-02     0.1981294E-01
0.1000000E+00     0.1964252E-03     0.1460493E-02     0.1412213E-01
0.1300000E+00     0.1964252E-03     0.1479092E-02     0.1133390E-01
0.1600000E+00     0.1964252E-03     0.1483756E-02     0.9700164E-02
0.1900000E+00     0.1964252E-03     0.1488455E-02     0.8626389E-02
0.2200000E+00     0.1964252E-03     0.1493188E-02     0.7877795E-02
0.2500000E+00     0.1964252E-03     0.1490843E-02     0.7322838E-02
0.2800000E+00     0.1964252E-03     0.1495620E-02     0.6892277E-02
0.3100000E+00     0.1964252E-03     0.1493267E-02     0.6544504E-02
0.3400000E+00     0.1964252E-03     0.1490897E-02     0.6266061E-02
0.3700000E+00     0.1964252E-03     0.1495728E-02     0.6036068E-02
0.4000000E+00     0.1964252E-03     0.1493349E-02     0.5811598E-02
0.4300000E+00     0.1964252E-03     0.1490952E-02     0.5599985E-02
0.4600000E+00     0.1964252E-03     0.1488538E-02     0.5408675E-02
0.4900000E+00     0.1964252E-03     0.1478777E-02     0.5245227E-02
0.5200000E+00     0.1964252E-03     0.1468942E-02     0.5095246E-02
0.5500000E+00     0.1964252E-03     0.1459032E-02     0.4966272E-02
0.5800000E+00     0.1964252E-03     0.1441634E-02     0.4843721E-02
0.6100000E+00     0.1964252E-03     0.1066960E-02     0.4697907E-02
0.6400000E+00     0.1964252E-03     0.7192688E-03     0.4543497E-02
0.6700000E+00     0.1964252E-03     0.4363820E-03     0.4365675E-02
0.7000000E+00     0.1964252E-03     0.2886748E-03     0.4109346E-02
0.7300000E+00     0.1964252E-03     0.2200833E-03     0.3808230E-02
0.7600000E+00     0.1964252E-03     0.1964252E-03     0.3458765E-02
0.7900000E+00     0.1964252E-03     0.1964252E-03     0.3048685E-02
0.8200000E+00     0.1964252E-03     0.1964252E-03     0.3017418E-02
0.8500000E+00     0.1964252E-03     0.1964252E-03     0.2843635E-02
0.8800000E+00     0.1964252E-03     0.1964252E-03     0.2686709E-02
0.9100000E+00     0.1964252E-03     0.1964252E-03     0.2538854E-02
0.9400000E+00     0.1964252E-03     0.1964252E-03     0.2400928E-02
0.9700000E+00     0.1964252E-03     0.1964252E-03     0.2273901E-02
0.1000000E+01     0.1964252E-03     0.1964252E-03     0.2148599E-02

File 'DMAP_isocurves'

 Strain Rate= 0.1000000E-03

Normalized Stress     Homologous Temperature
0.3480657E-01         0.0000000E+00
0.3185586E-01         0.4000000E-01
0.1832378E-01         0.7000000E-01
0.1294885E-01         0.1000000E+00
0.1007927E-01         0.1300000E+00
0.8300280E-02         0.1600000E+00
0.7087250E-02         0.1900000E+00
0.6212554E-02         0.2200000E+00
0.5559015E-02         0.2500000E+00
0.5043422E-02         0.2800000E+00
0.4631483E-02         0.3100000E+00
0.4288395E-02         0.3400000E+00
0.4007713E-02         0.3700000E+00
0.3768400E-02         0.4000000E+00
0.3570923E-02         0.4300000E+00
0.3393856E-02         0.4600000E+00
0.3237430E-02         0.4900000E+00
0.3101882E-02         0.5200000E+00
0.2980066E-02         0.5500000E+00
0.2864729E-02         0.5800000E+00
0.2532731E-02         0.6100000E+00
0.2190700E-02         0.6400000E+00
0.1793638E-02         0.6700000E+00
0.1334170E-02         0.7000000E+00
0.8509662E-03         0.7300000E+00
0.4635646E-03         0.7600000E+00
0.2629502E-03         0.7900000E+00
0.3246521E-03         0.8200000E+00
0.3019618E-03         0.8500000E+00
0.2869809E-03         0.8800000E+00
0.2710842E-03         0.9100000E+00
0.2638117E-03         0.9400000E+00
0.2560656E-03         0.9700000E+00
0.2477982E-03         0.1000000E+01

File 'DMAP_mechanisms'

T/Tm           CreepMecahnism    Sub-mecahnism    GlideMechanism    Diffusional
0.4000000E-01  Power-Law         Core             Discrete-Obstacl  Boundary
0.7000000E-01  Power-Law         Core             Discrete-Obstacl  Boundary
0.1000000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.1300000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.1600000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.1900000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.2200000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.2500000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.2800000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.3100000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.3400000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.3700000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.4000000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.4300000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.4600000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.4900000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.5200000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.5500000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.5800000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.6100000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.6400000E+00  Power-Law         Core             Discrete-Obstacl  Boundary
0.6700000E+00  Power-Law         Lattice          Discrete-Obstacl  Boundary
0.7000000E+00  Power-Law         Lattice          Discrete-Obstacl  Boundary
0.7300000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.7600000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.7900000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.8200000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.8500000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.8800000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.9100000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.9400000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.9700000E+00  Power-Law         Lattice          Discrete-Obstacl  Lattice
0.1000000E+01  Power-Law         Lattice          Discrete-Obstacl  Lattice

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Auxiliary Routines


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ODS, creep, ferritic steel, steel

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Download source code

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