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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.

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.

Language: | FORTRAN |

Product form: | Source code. |

Complete program.

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

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,

Rate equation for lattice resistance plasticity

Rate equation for power-law creep

where A_{2} is a dimensionless material constant and D_{eff} is an effective diffusion coefficient expressed by the equation:

where a_{C} is the area of the dislocation core in which fast diffusion is taken place, D_{v} is the lattice diffusion coefficient (D_{v} = D_{ov} exp[-[(Q_{v})/RT] ]), and D_{c} is the core diffusion coefficient (D_{c} = D_{oc} exp[-[(Q_{c})/RT] ]). In a high temperature regime, D_{v} >> D_{c} and the lattice diffusion (Figure 6.3) is predominant. This represents high temperature creep (HT Creep). By contrast, at lower temperatures, D_{c} > or = D_{v} so core diffusion is dominant mechanism. This is a Low Temperature Creep regime (LT Creep).

Rate equation for diffusional flow

where

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 [(D_{v})/(d^{2})]. At lower temperatures, grain boundary diffusion takes over, the flow is then Coble creep and scales as [(D_{b})/(d^{3})].

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

**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 (m
^{2}s^{-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.

**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)).

None.

No information supplied.

None.

Complete program.

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

File 'DMAP_borders' T/Tm THRESHOLD BORDER-FIELD PLASTICITY-FIELD 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

None.

ODS, creep, ferritic steel, steel

**
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
**