Materials Algorithms Project
Program Library

Program MAP_STEEL_FLOW

Provenance of code.
Purpose of code.
Specification.
Description of program's operation.
References.
Parameter descriptions.
Error indicators.
Accuracy estimate.
Any additional information.
Example of code
Auxiliary routines required.
Keywords.
Download source code.
Links.

Provenance of Source Code

C. N. Hulme-Smith
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
27 Charles Babbage Road,
Cambridge, CB3 0FS, U.K.

E-mail: C. N. Hulme-Smith

Added to MAP: July 2019.

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This code simulates the contribution to room temperature, static yield strength of the Peierls stress, substitutional and interstitial solid solution strengthening, precipitate-related strengthening, grain size strengthening and work hardening. It then predicts the evolution of yield stress for a given strain rate (i.e. the flow stress) at a specified temperature.

STEELFLOW was originally written under the name CaNDYFloSS (Calculator for novel design: yield and flow stress in steels) for the InnovateUK project Series production of Lightweight parts by Isostatic pressing of Metal powders to give Material and Energy Reduction (SLIMMER).

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Specification

Language:	FORTRAN 2008
Product form:	Source code and executables compatible with Mac, Windows and Linux-based systems.
Platform:	Linux - tested on Debian 8.0 (Jessie) and Debian 9.0 (Stretch); Mac running OSX 10.11.6 (El Capitan), MacOS 10.12 (Sierra) and OSX 10.14 (Mojave). Theoretically, any system with a modern FORTRAN compiler will be capable of executing the script by recompiling the source code using a compiler in the same operating system. During testing, executables compiled on Linux did not run on Mac and vice-versa. If your computer fails to read the input files, please check what kind of line encoding should be used. For most situations, "Unix (LF)" or "Linefeed" is appropriate.

Complete program.

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Description

CaNDYFloSS stands for Calculator for Novel Design: Yield and Flow Stress in Steels. It uses multiple sub-models to calculate the expected static, room temperature yield stress in steels and then converts this to a stress-strain curve for a specified temperature and strain rate.

CaNDYFloSS works by calculating the contribution to strength from the following sources:

the intrinsic strength of the lattice, also known as the Peierls stress, σ₀;
solid solution strengthening, calculated separately for carbon (σ_C) and substitutional elements (σ_ss);
precipitation strengthening, σ_p from an arbitrary number of precipitate populations. Coherency strengthening, σ_co. is always considered but is almost always very low. Whichever of cutting, σ_cut and bowing σ_bow stresses is lower is also considered to contribute to the strengthening;
grain refinement, σ_gr with Hall-Petch strengthening used for grain sizes above 1 μm and the model of Langford & Cohen below this limit;
strengthening due to dislocation interactions, σ_d;

It is assumed that each of these contributions is independent of all others and that the total strength, σ, may, therefore, be found by summing the individual contributions: σ = σ₀ + σ_C + σ_ss + σ_p + σ_gr + σ_d

In order to run the program, the user must specify the properties of the material being considered. This is done in a series on input files. The default name of the main input file, which contains the names of the other input files is "config_mechmod.dat". This may be changed by editing the source code (line 36) and recompiling the program. All other settings may be changed by editing the relevant configuration file and there is no need to recompile the program.

      ./steelflow

Files included in the download:

atomic_masses.csv	A list of atomic masses, used to convert between wt% and at.%.
steelflow.f08	FORTRAN 77 source code.
composition001.csv	Contains the composition of the matrix of the material, used to calculate solution strengthening.
config_mechmod.dat	Input data file, containing the names of other input files, information about the system being simulated and parameters for the calculations.
config_ppts.dat	Contains descriptions of the precipitate population(s), if any, present in the system.
gfortran_final_compile.sh	Script containing the recommended flags for compiling the source code in the most robust manner possible and to produce the most efficient executable.
steelflow-linux	Linux-compatible executable compiled using the source code steelflow.f08. This version contains all necessary libraries inside the executable and is, therefore, designated as "static". It should work on all Linux systems but has only been teste don Debian 8.0 (Jessie) and 9.0 (Stretch).
steelflow-mac	Mac-compatible executable compiled using the source code steelflow.f08. This version contains all necessary libraries inside the executable and is, therefore, designated as "static". It should work on all Mac systems, but has only been tested on MacOS 10.12 Sierra.
output_example.txt	A results file containing the output obtained when the contents of input_example.dat is used as input data.

Follow the steps listed below to use the module:

Download the file.

Unzip and untar it using the following command:

          gunzip -c MAP_STEEL_STEELFLOW.tar.gz | tar xvf -

Edit the input files to meet your needs.

If required, compile the source code (steelflow.f08) using the following command:

          ./gfortran_final_compile.sh steelflow [output_executable_file_name]

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References

Steels, microstructure and properties, (2017) 4th edition, Bhadeshia and Honeycombe
Bainite in steels, 3rd edition, Bhadeshia
G. R. Speich & P. R. Swann, Yield strength and transformation substructure of quenched iron-nickel alloys, Journal of the Iron and Steel Institute 203 (1965) p.480-485.
W. C. Leslie, Iron and its dilute substitutional solid solutions, Metallurgical Transactions 3 (1972), p.5-26
C. E. Lacy & M. Gensamer, The tensile properties of alloyed ferrites, Transactions of the American Society of Metals 32 (1944), p.88-109.
C. H. Young & H. K. D. H. Bhadeshia, Strength of mixtures of bainite and martensite, Materials Science and Technology 10 (1994), p. 209-214.
S. Takeuchi, Solid-solution strengthening in single crystals of iron alloys, Journal of the Physical Society of Japan 27 (1969), p.929-940.
S. Takeuchi, H. Yoshida & T. Taoka, Soli-solution strengthening in iron alloys, Transactions of the Japanese Institute of Metals 9S (1968), p.715-719.
T. Narita, S. Ukai, S. Ohtsuka & M. Inoue, Effect of tungsten addition on microstructure and high temperature strength of 9CrODS ferritic steel, Journal of Nuclear Materials 417 (2011) p. 158-161.
ISSS: Speich and Warlimont, Winchell and Cohen
G. R. Speich & H. Warlimont, Yield strength and transformation substructure of low carbon martensite, Journal of the Iron and Steel Institute 206 (1968), p.385-392.
P. G. Winchell & M. Cohen, The strength of martensite, Transactions of the American Society of Metals 55 (1962), p.347-361.
N. F. Mott & F. R. N. Nabarro, An attempt to estimate the degree of precipitation hardening, with a siple model, Proceedings of the Physical Society 52 (1940), p.86–89.
Cutting: E. A. Wilson, Quantification of early stages of age hardening in Fe-12Ni-6Mn maraging type alloy, Materials Science and Technology 14 (1998), p.277-282.
E. O. Hall, The Deformation and Ageing of Mild Steel: III Discussion of Results Proceedings of the Royal Physical Society B 64 (1951), p.747–753.
N. J. Petch, The cleavage strength of polycrystals, Journal Of The Iron And Steel Institute 174 (1953), p.25–28.
G. Langford, & M. Cohen, Calculation of Cell-Size Strengthening of Wire-Drawn Iron, Metallurgical Transactions 1 (1970), p.1478–1480.
C. Zener & J. H. Hollomon, Effect of strain rate upon plastic flow of steel, Journal of Applied Physics 15 (1944), p.22–32.
O. Bouaziz & N. Guelton, Modelling of TWIP effect on work-hardening, Materials Science and Engineering A 319-321 (2001), p.246-249.
W. Roberts and B. Ahlblom, A nucleation criterion for dynamic recrystallization during hot working, Acta Metallurgica 26 (1977), p.801-813.
R. Sandström & R. Lagneborg, A model for how working occurring by recrystallization, Acta Metallurgica 23 (1975(, p.387-398.

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Parameters

Input parameters

In the file config_mechmod.dat:

COMPFILE — CHARACTER: Name of the file that contains the composition of the matrix of the material being considered.
PPTFILE — CHARACTER: Name of the file containing information about the precipitate population(s) if any.
ELENUM — INTEGER: The number of solute elements in the material.
WHATUNIT(2) — TWO INTEGERS: An integer flag that indicates the units of composition for (1) the bulk (overall) composition and (2) the matrix of the material once any precipitates have formed. This is a 2×1 matrix of integers. 1 = wt.%, 2 = at.%.
MASSFILE — CHARACTER: The name of the file that contains the list of atomic masses.
COEFILE — CHARACTER: The name of the file containing the coefficients of solid solution strengthening.
FERTYPE — CHARACTER: Character flag that designates what type of ferrite is present - M = martensite, B = bainite, F = pearlite or diffusionally-formed ferrite.
GRAINSIZE — DOUBLE PRECISION: The effective grain size of the matrix in metres.
BULKMOD — DOUBLE PRECISION: The bulk modulus of the modelled material in Pa.
YOUNGMOD — DOUBLE PRECISION: The Young's modulus of the materials being modelled.
POISSON — DOUBLE PRECISION: Poisson's ratio of the material being modelled.
SHEARMOD — DOUBLE PRECISION: The shear modulus of the material being modelled.
TAYLOR — DOUBLE PRECISION: The Taylor factor that is to be used for Orowan bowing calculations. A default value of 0.33 is appropriate for non-textured polycrystalline samples. Different values may be chosen to represent texture, to suit the user's requirements.
PPTPOPS — INTEGER: The number of precipitate populations that are to be modelled.
MATRIXSPACING — DOUBLE PRECISION: The effective interatomic spacing in the matrix. This is related to the lattice parameter.
MATRIXATOMVOL — DOUBLE PRECISION: The atomic volume of the matrix.
FLOW_TEMP_AIM — DOUBLE PRECISION: The temperature at which the flow stress is to be calculated in °C.
STR_RATE_AIM — DOUBLE PRECISION: The strain rate at which the flow stress is to be calculated.
ACTIVATION — DOUBLE PRECISION: The activation energy for dislocation motion. A value of 0 will lead to no temperature or strain rate effects. A negative value will cause a default value of 400 J mol^-1 to be used, according to Zener & Holloman, J. App. Phys. 15 (1944) p.23-33.
EXPONENT — DOUBLE PRECISION: The strain rate exponent of yield strength, according to the treatment of Zener and Holloman. A negative value will result in a default value of 0.0125 to be used. This is appropriate for many pearlitic/ferritic steels.
STR_RATE_STATIC — DOUBLE PRECISION: The effective strain rate at which the "static" yield stress was measured. This allows the appropriate conversions to be made to different strain rates. A negative value will result in a default value of 0.01 s^-1 to be assumed.
STR_RATE_TARGET — DOUBLE PRECISION: The target strain rate at which the yield tress should be calculated. A negative value will cause this variable to be set equal to the yield stress at which the "static" yield strength was measured. This will result in no strain rate effects being accounted for.
AMBIENT — DOUBLE PRECISION: The temperature at which the yield stress was measured. A value below 0 K (-272.15 °C) will result in the ambient temperature being set to 20 °C (293.15 K).
STRAINSTEP — DOUBLE PRECISION: The step to be used in simulating the evolution of properties during plastic straining.
PATHCONST — DOUBLE PRECISION: A variable that sets the effective mean free path of dislocations. This is equivalent to the constant k in Bouaziz & Guelton, Mater. Sci. Eng A 319-321 (2001) p. 246-249.
ENDSTRAIN — DOUBLE PRECISION: The maximum strain for which the evolution of properties is to be calculated.
HARDCONST — DOUBLE PRECISION: A variable that determines how sensitive the flow stres sis to dislocation density.
RECOVERYCONST — DOUBLE PRECISION: A variable that affects the rate of recovery. This is variable f in Bouaziz & Guelton, Mater. Sci. Eng A 319-321 (2001) p. 246-249.
GB_ENERGY — DOUBLE PRECISION: The grain boundary energy in J m^-2.
MOBILITY(1) — DOUBLE PRECISION: The pre-exponential factor for grain boundary mobility in m⁴ s^-1 J^-1.
MOBILITY(2) — DOUBLE PRECISION: The activation energy for grain boundary mobility for grain boundary mobility in J mol^-1.
RESULTSFILE — DOUBLE PRECISION: The path to the results file, taken from the directory containing the executable. Both relative and absolute paths are allowed. Just providing a file name will cause the program to assume that the file is in the same directory as the executable.
SHEARTEMP — DOUBLE PRECISION: The temperatuer at which shear is to be modelled. If "FERTYPE" is set to "F", this variable is not required for the calculation, but a value must be set to allow the program to execute.
PEIERLS — DOUBLE PRECISION: The Peierls stress (intrinsic or lattice strength) of the material. In the published program, the matrix is assumed to be ferrite. An austenitic matrix will have a very small Peierls stress and it is commonly assumed to be zero.
DEFACT — DOUBLE PRECISION: The effective activation energy (in J mol^-1) for deformation.
REXACT — DOUBLE PRECISION: The effective activation energy for recrystallisation in J mol^-1
REXCONST — DOUBLE PRECISION: The exponent to which the time step must be raised to calculate the fraction of material that recrystallises in a given step.
REXRHO — DOUBLE PRECISION: The dislocation density assumed (or measured) in any newly-recrystallised material, expressed in m^-2 (or, equivalently m m^-3).
GROWTHACT — DOUBLE PRECISION: The activation energy for grain growth, in J.

On each line of the file named in the variable COMPFILE, containing the composition information with ELENUM solute elements (iron is assumed to be the residue of the material and is designated as the zeroth element in the matrices):

ELEMENTS(i), BULKCOMP(i), MATRIXCOMP(i)

ELEMENTS — CHARACTER (LENGTH = 2): The name of the element, using its atomic symbol. There is no need to add a trailing space to elements with single letter symbols, e.g. C, N, O. Each value forms the ith element of an array of size 1 + ELENUM.
BULKCOMP — DOUBLE PRECISION: The bulk composition of the alloy, in the units denoted by the value of WHATUNIT(1). Each value forms the ith element of an array of size 1 + ELENUM.
GROWTHACT — DOUBLE PRECISION: The composition of the solid solution in the matrix (i.e. after al precipitates have formed). This is expressed in the units denoted by WHATUNIT(2). Each value forms the ith element of an array of size 1 + ELENUM.

On each line of the file named in the variable PPTFILE:

PPTNAME(j), PPTSIZE(j), PPTDENSITY(j), PPTFRAC(j), PPTSPACING(j), PPTSHAPE(j), RELEQM(j), PPTFACTOR(j), PPTBETA(j), PTDELTA(j), PPTEPSILON(j), PPTKAPPA(j), PPTBULK(j), PPTATOMVOL(j)

Each variable is written to the jth element of an array of size PPTPOPS, i.e. the number of precipitate populations in the material. It is assumed that all precipitate populations independently and additively strengthen the steel. Any precipitate populations that do not contribute significantly to the strength should not be included in this program.

PPTNAME — CHARACTER: A name chosen by the user to identify each precipitate class.
PPTSIZE — DOUBLE PRECISION: The average size of the precipitate in metres. This is either the radius or half the side length, depending on whether the precipitate is spherical or cubic.
PPTDENSITY — DOUBLE PRECISION: The number density (number per unit volume) of precipitates in each class, expressed in m^-3.
PPTFRAC — DOUBLE PRECISION: The total volume fraction of precipitates in each class.
PPTSPACING — DOUBLE PRECISION: The atomic spacing in precipitates for precipitates in each class.
PPTSHAPE — INTEGER: A flag to set the shape of the precipitates: 1 = cubic, 2 = spherical, 3 = any other.
PPTFACTOR — DOUBLE PRECISION: The constant of proportionality between the cube of the radius/half-side-length and the precipitate volume. For a cube, this is equal to 8.0 and for a sphere it is ^4π⁄₃. For any other shape (as defined by the variable PPTSHAPE), the user must specify a value.
RELEQM — INTEGER: A flag to determine whether the lattice mismatch between the precipitate and matrix, equivalent to the absolute value of the difference between the two divided by the lattice spacing in the matrix, si to be calculated. A value of 1 causes the calculation to proceed and thus considers coherency strengthening. Any other value causes no coherency strengthening to be included in the overall calculation of yield strength.
PPTBETA — DOUBLE PRECISION: A variable that, relates the precipitate size and volume fraction to cutting stress. The derivation of PPTBETA is explained in the appendix to E. A. Wilson, Mater. Sci. Technol. 14 (1998) p277-282. This variable may be calculated by the program and relies on the given Taylor factor, matrix shear modulus, matrix interatomic spacing and PPTKAPPA. If the user knows a value of this variable in advance, it may be entered here. If not enter a negative value and the program will calculate it.
PPTDELTA — DOUBLE PRECISION: A variable that describes the linear strain of precipitation from a matrix, equal to two-thirds of the difference of the atomic volumes between the matrix and precipitate. The derivation of PPTBETA is explained in Appendix 1 of E. A. Wilson, Mater. Sci. Technol. 14 (1998) p277-282. A user may specify a value of PPTDELTA, or enter a negative value to force the program to calculate it based on atomic volumes or interatomic spacings.
PPTEPSILON — DOUBLE PRECISION: A variable that describes the strain energy of precipitation from a matrix, equal to two-thirds of the difference of the atomic volumes between the matrix and precipitate. The value of PPTKAPPA depends on PPTDELTA and the shear modulus, Poisson ratio and Young's modulus of the matrix, the Poisson ratio of the matrix. The derivation of PPTBETA is explained in Appendix 1 of E. A. Wilson, Mater. Sci. Technol. 14 (1998) p277-282. A user may specify a value of PPTEPSILON, or enter a negative value to force the program to calculate it.
PPTKAPPA — DOUBLE PRECISION: A variable that relates precipitate size and volume fraction to the strengthening due to bowing or cutting. It is taken to be equal to approximately 6.598, as described in E. A. Wilson, Mater. Sci. Technol. 14 (1998) p277-282.
PPTBULK — DOUBLE PRECISION: The bulk modulus of the precipitate in Pa.
PPTATOMVOL — DOUBLE PRECISION: The average atomic volume in the precipitate in metres.

Output parameters

STEELFLOW writes to the terminal by default, but the output may be redirected into a file using the standard Unix instruction ./[path_to_executable] > [path_to_results], for example ./[PATH TO EXECUTABLE] > results_01.txt. The program also writes a summary of the flow stress results to a named results file, with the name given by the variable RESULTSFILE and specified in config_mechmod.dat. However, there are no commands to write the output to a file.

Using the input files available from this page, the following output is obtained:

                           _____ _            _ ______ _                                
                          / ____| |          | |  ____| |                               
                         | (___ | |_ ___  ___| | |__  | | _____      __                 
                          \___ \| __/ _ \/ _ \ |  __| | |/ _ \ \ /\ / /                 
                          ____) | ||  __/  __/ | |    | | (_) \ V  V /                  
                         |_____/ \__\___|\___|_|_|    |_|\___/ \_/\_/                   
                                                                                        
 
                  Calculator for Novel Design: Yield and Flow Stress in Steels          
        --------------------------------------------------------------------------------
                                Copyright Dr Chris Hulme-Smith                          
                                    University of Cambridge                             
                                         September 2017                                 
        --------------------------------------------------------------------------------
 
        The Peierls (intrinsic) strength is set to   2.0 MPa.
        The contribution to yield strength due to grain refinement is  189.7 MPa.
 
        The defined composition is:
        -------------------------------------------------------
        Element |   wt%    |   at.%   | mass frac. | mol. frac.
        --------|----------|----------|------------|-----------
           Fe   |  69.0879 |  68.0000 |  0.690879  |  0.680000
           C    |   0.0437 |   0.2000 |  0.000437  |  0.002000
           Ni   |   8.5426 |   8.0000 |  0.085426  |  0.080000
           Cr   |  17.0276 |  18.0000 |  0.170276  |  0.180000
           Si   |   1.0219 |   2.0000 |  0.010219  |  0.020000
           Mo   |   0.5237 |   0.3000 |  0.005237  |  0.003000
           Co   |   3.7526 |   3.5000 |  0.037526  |  0.035000
        -------------------------------------------------------
 
        Strength contribution due to coherency strains is   0.0 MPa due to ppt1      
        Strength contribution due to coherency strains is 808.4 MPa due to ppt2      
 
                   1  0.27000000000000002        3.0000000000000000        74000000000.000000        1.6679649276888289E-010   100000000000000.00        1.0000000000000000E-008
        The Orowan bowing stress is    0.1E+01 MPa. for ppt1      
                   2  0.27000000000000002        3.0000000000000000        74000000000.000000        1.6679649276888289E-010   1000000000000.0000        1.0000000000000001E-005
        The Orowan bowing stress is    0.8E+00 MPa. for ppt2      
 
        The strengthening due to cutting of precipitates is    NaN MPa for ppt1      
        The strengthening due to cutting of precipitates is    NaN MPa for ppt2      
 
        ------------------------------------------------------------------------------------------------------------------------------------------
                  Substitutional solid solution strengthening according to model by Young, Bhadeshia, Narita et al. and Takeuchi et al.
        ------------------------------------------------------------------------------------------------------------------------------------------
         Element |  amount  |   Strengthening coefficient / MPa/%  | Strengthening contribution / MPa | Cumulative strengthening / MPa | Unit (%)
        ---------|----------|--------------------------------------|----------------------------------|--------------------------------|----------
           C     |  0.04370 |             1725.50000               |              360.72317           |             360.72317          |   mass
           Ni    |  8.54256 |               37.00000               |              316.07488           |             676.79805          |   mass
           Cr    | 17.02755 |              -30.00000               |             -510.82663           |             165.97142          |   mass
           Si    |  1.02191 |               84.00000               |               85.84059           |             251.81202          |   mass
           Mo    |  0.52369 |               13.00000               |                6.80798           |             258.62000          |   mass
           Co    |  3.75264 |                0.00000               |                0.00000           |             258.62000          |   none
        ------------------------------------------------------------------------------------------------------------------------------------------
                                                                           Total substitutional solid solution stregnthening =    258.62000 MPa
        ------------------------------------------------------------------------------------------------------------------------------------------
 
        -------------------------------------------------------------------------------------------------------------------------------
                                    Substitutional solid solution strengthening according to model by Lacy
        -------------------------------------------------------------------------------------------------------------------------------
         Element |   at.%   | Strengthening coefficient / MPa/at.% | Strengthening contribution / MPa | Cumulative strengthening / MPa
        ---------|----------|--------------------------------------|----------------------------------|--------------------------------
           Fe    | 68.00000 |                0.00000               |                0.00000           |               0.00000
           C     |  0.04370 |             1725.50000               |              360.72317           |             360.72317
           Ni    |  8.00000 |               20.00000               |              160.00000           |             520.72317
           Cr    | 18.00000 |                3.00000               |               54.00000           |             574.72317
           Si    |  2.00000 |               26.00000               |               52.00000           |             626.72317
           Mo    |  0.30000 |               13.00000               |                3.90000           |             630.62317
           Co    |  3.50000 |                2.30000               |                8.05000           |             638.67317
        -------------------------------------------------------------------------------------------------------------------------------
                                                                   Total substitutional solid solution stregnthening =    638.67317 MPa
        -------------------------------------------------------------------------------------------------------------------------------
 
        -------------------------------------------------------------------------------------------------------------------------------
                                   Substitutional solid solution strengthening according to model by Leslie
        -------------------------------------------------------------------------------------------------------------------------------
         Element |   at.%   | Strengthening coefficient / MPa/at.% | Strengthening contribution / MPa | Cumulative strengthening / MPa
        ---------|----------|--------------------------------------|----------------------------------|--------------------------------
           Fe    | 68.00000 |                0.00000               |                0.00000           |               0.00000
           C     |  0.20000 |             1725.50000               |              360.72317           |             360.72317
           Ni    |  8.00000 |                0.00000               |                0.00000           |             360.72317
           Cr    | 18.00000 |                3.60000               |               64.80000           |             425.52317
           Si    |  2.00000 |                0.00000               |                0.00000           |             425.52317
           Mo    |  0.30000 |               40.00000               |               12.00000           |             437.52317
           Co    |  3.50000 |               18.00000               |               63.00000           |             500.52317
        -------------------------------------------------------------------------------------------------------------------------------
                                                                   Total substitutional solid solution stregnthening =    500.52317 MPa
        -------------------------------------------------------------------------------------------------------------------------------
 
        For ppt1       both cutting and bowing occur simultaneously.  That stress is therefore taken as the precipitate strengthening mechanism.
        For ppt2       both cutting and bowing occur simultaneously.  That stress is therefore taken as the precipitate strengthening mechanism.
 
        Total yield strength including the substitutional solid solution strengthening according to the model by Young  is   1259.6 MPa.  Estiated hardness is 378 HV.
        Total yield strength including the substitutional solid solution strengthening according to the model by Lacy   is   1639.7 MPa.  Estiated hardness is 492 HV.
        Total yield strength including the substitutional solid solution strengthening according to the model by Leslie is   1501.5 MPa.  Estiated hardness is 450 HV.
 
        Activation energy for dislocation motion set to 41,840J in accordance with the value for pearlite (and used for diffusional ferrite) in Zener and Holloman, J. App. Phys. 15 (1944), p.22-32.
 
        Flow stress at 900.0 C and 0.1E-01 / s with static ambient yield stress of 1259.6 MPa is 1090.0 MPa.
        Flow stress at 900.0 C and 0.1E-01 / s with static ambient yield stress of 1639.7 MPa is 1418.8 MPa.
        Flow stress at 900.0 C and 0.1E-01 / s with static ambient yield stress of 1501.5 MPa is 1299.3 MPa.
 
        -------------------------------------------------------------------------------------------------------------------------------------
          Strain   | Disln density / m^(-2) |  RT Strengthening / MPa | Strengthening / MPa |               Yield stress / MPa
                   |                        |                         |                     |    Lacy    |   Leslie   | Young/Takeuchi et al.
        -------------------------------------------------------------------------------------------------------------------------------------
         0.000E+00 |        0.100E+15       |         222.2           |        192.2        |   1451.9   |   1831.9   |      1693.8
         0.100E-01 |        0.104E+15       |         226.8           |        196.2        |   1455.9   |   1835.9   |      1697.8
         0.200E-01 |        0.108E+15       |         231.2           |        200.0        |   1459.7   |   1839.7   |      1701.6
         0.300E-01 |        0.112E+15       |         235.4           |        203.7        |   1463.3   |   1843.4   |      1705.2
         0.400E-01 |        0.116E+15       |         239.4           |        207.2        |   1466.8   |   1846.9   |      1708.7
         0.500E-01 |        0.120E+15       |         243.3           |        210.5        |   1470.1   |   1850.2   |      1712.0
         0.600E-01 |        0.124E+15       |         246.9           |        213.7        |   1473.3   |   1853.4   |      1715.2
         0.700E-01 |        0.127E+15       |         250.5           |        216.7        |   1476.4   |   1856.4   |      1718.3
         0.800E-01 |        0.131E+15       |         253.8           |        219.6        |   1479.3   |   1859.3   |      1721.2
         0.900E-01 |        0.134E+15       |         257.0           |        222.4        |   1482.0   |   1862.1   |      1723.9
         0.100E+00 |        0.137E+15       |         260.1           |        225.1        |   1484.7   |   1864.7   |      1726.6
        -------------------------------------------------------------------------------------------------------------------------------------
        ************** The calculated dislocation density exceeded that required for recrystallisation during the deformation.***************
 
        All contributions to yield stress successfully modelled.  SteelFlow will save all data and close all files.  Goodbye!
        SteelFlow completed and terminated at 24/09/2017 at 23:47:16
 
                           _____ _            _ ______ _                                
                          / ____| |          | |  ____| |                               
                         | (___ | |_ ___  ___| | |__  | | _____      __                 
                          \___ \| __/ _ \/ _ \ |  __| | |/ _ \ \ /\ / /                 
                          ____) | ||  __/  __/ | |    | | (_) \ V  V /                  
                         |_____/ \__\___|\___|_|_|    |_|\___/ \_/\_/                   
                                                                                        
        --------------------------------------------------------------------------------
                                Copyright Dr Chris Hulme-Smith                          
                                    University of Cambridge                             
                                         September 2017                                 
        --------------------------------------------------------------------------------

In the file with the name given by the variable RESULTSFILE, the flow stress is summarised. A statement is also made as to whether recrystallisation is predicted to occur, but the recrystallisation behaviour is beyond the capabilities of this model:

        Strain,Dislocation density / m^(-2),RT Strengthening / MPa,Strengthening / MPa,Yield stress / MPa,,
        ,,,,Lacy,Leslie et al.,"Young & Bhadeshia, Takeuchi et al., etc."
         0.000E+00, 0.100E+15, 222.2, 192.2,1451.9,1831.9,1693.8
         0.100E-01, 0.104E+15, 226.8, 196.2,1455.9,1835.9,1697.8
         0.200E-01, 0.108E+15, 231.2, 200.0,1459.7,1839.7,1701.6
         0.300E-01, 0.112E+15, 235.4, 203.7,1463.3,1843.4,1705.2
         0.400E-01, 0.116E+15, 239.4, 207.2,1466.8,1846.9,1708.7
         0.500E-01, 0.120E+15, 243.3, 210.5,1470.1,1850.2,1712.0
         0.600E-01, 0.124E+15, 246.9, 213.7,1473.3,1853.4,1715.2
         0.700E-01, 0.127E+15, 250.5, 216.7,1476.4,1856.4,1718.3
         0.800E-01, 0.131E+15, 253.8, 219.6,1479.3,1859.3,1721.2
         0.900E-01, 0.134E+15, 257.0, 222.4,1482.0,1862.1,1723.9
         0.100E+00, 0.137E+15, 260.1, 225.1,1484.7,1864.7,1726.6

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Error Indicators

The program will print out descriptive error indicators should the program execute abnormally. Each error message is unique and will provide a quick way to find the affected part of the source code.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Input data

In the file config_mechmod.dat:

composition01.dat ! name of composition file.
config_ppts.dat ! name of file containing precipitate information (required even if there are no precipitates).
6 ! number of elements in composition file.
2 ! specify units of bulk composition (1=wt%, 2=at.%, 3=mass fraction, 4=molar fraction).
2 ! specify units of matrix composition (1=wt%, 2=at.%, 3=mass fraction, 4=molar fraction).
atomic_masses.csv ! specify the name of the file containing the atomic masses.
sol_sol_coeffs.csv ! specify the name of the file containing the coefficients contained in the expressions solid solution strengthening
F ! identify the type of ferrite ("M" = martensite, "B" - bainite, "F" = other - allotriomorphic, idiomorphic, Widmsnastaetten, etc.)
1.0D-05 ! specify the effective grain size in metres.
1.4D+11 ! bulk modulus of modelled material in Pa.
1.93D+11 ! Young's modulus of modelled material in Pa.
2.7D-01 ! Poisson ratio of modelled material.
7.4D+10 ! Shear modulus of modelled material, in Pa.
3.0D+00 ! Taylor factor to be used in Orowan bowing stress calculation.
2 ! number of precipitate populations - need the correct number of lines in the file containing precipitate information: one for each population.
2.889 ! specify the effective interatomic spacing of the matrix in Angstrom.
1.2D-29 ! specify the (substitutional) atomic volume of the matrix.
9.00D+02 ! specify the temperature in Celsius to be used in the flow stress calculations.
1.0D-02 ! specify the strain rate in reciprocal seconds to be used in flow stress calculations.
-4.203D+04 ! specify the activation energy for flow - a negative value leads to the use of default values from Zener and Holloman J. App. Phys. 15 (1944) p.23-33.
-6.092D+01 ! specify the exponent (r in Zener and Holloman J. App. Phys. 15 (1944) p.23-33) for flow stress calculations. A negative value is reset to 0.0125, as specified in Zener and Holloman J. App. Phys. 15 (1944) p.23-33.
-4.24792D+00 ! specify the strain rate used in the static yield stress measurements. A negative value leads to a default of 0.01 being used.
-4.00D+02 ! specify the temperature at which the static yield stress experiments were performed. A value below absolute zero will lead to 20C being used instead.
1.0D-02 ! specify the step in strain to be used during work hardening calculations.
1.1D-02 ! specify the constant k from Bouaziz & Gueltonm Mater. Sci. Eng. A 319-321 (2001) p. 246-249, which affects the mean free path of dislocation glide.
1.0D-01 ! specify the maximum strain to be included in work hardening calculations.
4.0D-01 ! specify the factor governing how sensitive the flow stress is to dislocation density.
3.0D+00 ! specify how rapid recovery is (variable f in Bouaziz & Guelton, Mater. Sci. Eng. A 319-321 (2001) p. 246-249).
8.0D-01 ! specify the grain boundary energy (J m^(-2)) for use in recrystallisation calculation
3.5D+04 ! specify the pre-exponential factor for grain-boundary mobility (m^(4) s^(-1) J^(-1)).
3.6D+05 ! specify the activation energy for grain boundary mobility (J mol^(-1)).
2.0D+00 ! the temperature in Celsius at which shear transformations are expected in the alloy. A value mus be provided, but will not be used if the FERTYPE is set to 'F', i.e. if the ferrite that forms is from a reconstructive transformation.
4.0D+01 ! specify the Peierls stress to be used when calculating the total yield (and flow) stress.
4.6D+04 ! Effective activation energy for deformation, the original value of 46,000J (11,000 cal/gm) taken from Zener and Holloman's original paper as an average for a few steels.
3.0D+05 ! effective activation energy or recrystallisation in Joules.
1.0D+00 ! Exponent to raise the time fraction by to calculate the fraction of material that recrystallise in each timestep; n in Bombac et al.
1.0D+09 ! dislocation density of recrystallised material.
4.0D+05 ! activation energy for grain growth in Joules.

In the file composition01.dat:

        Element,"Bulk composition","Matrix composition"
        C,0.2,0.2
        Ni,8,8
        Cr,18,18
        Si,2,2
        Mo,0.3,0.3
        Co,3.5,3.5

In the file config_ppts.dat:

        "Name [PPTNAME]" "Average size / m [PPTSIZE]" "Number density / m-3 [PPTDENSITY]" "Volume fraction of precipitates [PPTFRAC] - negative value causes the program to calculate the actual value based on other variables" "Effective interatomic spacing / m [PPTSPACING]" "Shape indicator (1=spherical; 2=cubic; 3=other) [PPTSHAPE]" "Calculate lattice mismatch? 1 = yes; any oher value = no [RELEQM]" "Shape factor - specifying spherical or cubic precipitates causes this value to be ignored otherwise it is the constant of proportionality between the cube of the radius/half-edge length and precipitate volume.  For cubic precipitates  the value is taken to be 8.0 and for spherical precipitates it is 4pi/3" "Cutting constant [PPTBETA]" "Linear strain of precipitation [PPTDELTA]" "Strain energy of precipitation [PPTEPSILON]" "Bowing factor [PPTKAPPA]" "Bulk modulus of precipitate / Pa [PPTBULK]" "Average atomic volume in the precipitate / m3"
        ppt1 0.00000001 1.00E+14 -0.36425 0 1 1 -96.3 -9.33 -63.5 0 -7.11 10000000000 0
        ppt2 0.00001 1.00E+12 -5.29 0 1 1 46.6 -47200 -3.95 -98300 -4.34 20000000000 0

3. Program results

In the file output-example.txt:

        Strain,Dislocation density / m^(-2),RT Strengthening / MPa,Strengthening / MPa,Yield stress / MPa,,
        ,,,,Lacy,Leslie et al.,"Young & Bhadeshia, Takeuchi et al., etc."
         0.000E+00, 0.100E+15, 222.2, 192.2,1451.9,1831.9,1693.8
         0.100E-01, 0.104E+15, 226.8, 196.2,1455.9,1835.9,1697.8
         0.200E-01, 0.108E+15, 231.2, 200.0,1459.7,1839.7,1701.6
         0.300E-01, 0.112E+15, 235.4, 203.7,1463.3,1843.4,1705.2
         0.400E-01, 0.116E+15, 239.4, 207.2,1466.8,1846.9,1708.7
         0.500E-01, 0.120E+15, 243.3, 210.5,1470.1,1850.2,1712.0
         0.600E-01, 0.124E+15, 246.9, 213.7,1473.3,1853.4,1715.2
         0.700E-01, 0.127E+15, 250.5, 216.7,1476.4,1856.4,1718.3
         0.800E-01, 0.131E+15, 253.8, 219.6,1479.3,1859.3,1721.2
         0.900E-01, 0.134E+15, 257.0, 222.4,1482.0,1862.1,1723.9
         0.100E+00, 0.137E+15, 260.1, 225.1,1484.7,1864.7,1726.6

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

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Materials Algorithms ProjectProgram Library

Program MAP_STEEL_FLOW

Input parameters

Output parameters

1. Input data

3. Program results

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