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Program MAP_COMP_ESHCON

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

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Provenance of Source Code

T.W. Clyne,
Composites and Coatings Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

E-mail
T.W. Clyne: twc10@cus.cam.ac.uk

Released: January 1998.
Added to MAP: October 1999.

 

Purpose

This program calculates either the electrical or the thermal conductivity of
a composite material, using the Eshelby equivalent homogeneous inclusion
method.

 

Specification

 Language:    N/A
 Product form:Executable files for use on almost any Apple Macintosh or PC.

Complete Program.

 

Description

This program calculates either the electrical or the thermal conductivity of
a composite material, using the Eshelby equivalent homogeneous inclusion
method [1]. The composite is modelled in terms of ellipsoidal
reinforcements, all with their major axis parallel to one another (the axial
direction), embedded in a homogeneous matrix material. The reinforcements
are assumed to be transversely isotropic and so, consequently, is the
composite. The program uses the mean field adaptation of the Eshelby model
and assumes that the inclusions are non-contacting. This model is not
applicable to insulating matrices.

The input data required by the program are the thermal conductivities of the
matrix and reinforcement, the volume fraction of the reinforcement and its
aspect ratio. These are screen input in response to a series of prompts. The
aspect ratio can be greater than 1 (prolate spheroids), equal to 1 (spheres)
or less than 1 (oblate spheroids). This program can also be used to
calculate the electrical conductivity of a composite. In this case the
electrical resistivities of the matrix and reinforcement materials are
requested as input instead of the thermal conductivities. The electrical
resistivity of the composite is then given as output by the program. (The
resistivity is the reciprocal of the conductivity.)

The results, as a function of reinforcement volume fraction, are written to
2 different files:

     <filename>.cax - axial conductivity (resistivity)
     <filename>.ctr - transverse conductivity (resistivity)

(<filename> refers to a user-supplied name for the output files.)

Downloading and running the program
Compiled versions of the programs have been produced as stand-alone
applications. They are run simply by double-clicking on the icon concerned.
They should run on virtually any Apple Macintosh or PC. Data input is via
the screen. Data output is to files which are named by the user. These are
produced as files for the plotting application "Kaleidagraph", but they can
be read as text files from many other plotting or spreadsheet applications.
These output files are normally created within the currently-active folder.
The program quits after each complete set of computations. For further use,
it is necessary to double-click on the icon again.

The executable files for downloading have been compressed using STUFFIT
EXPANDER on the Macintosh and WINZIP or PKUNZIP on the PC. These decoders
can be downloaded from the following websites:

STUFFIT EXPANDER at http://www.aladdinsys.com/expander/
WINZIP at http://www.winzip.com/

The run time depends on the number of values requested (and on machine
speed), but even on a relatively slow machine and with the maximum number of
values (100), the program only takes a few seconds to run.

 

References

  1. T.W. Clyne and P.J. Withers, 1993, An Introduction to Metal Matrix
     Composites, (Cambridge: Cambridge University Press), 280-282.

 

Parameters

Input parameters

   * For calculations of the thermal conductivity:
        o Thermal conductivity of the unreinforced matrix (W/m/K).
        o Thermal conductivity of the reinforcement in the axial direction
          (W/m/K).
        o Thermal conductivity of the reinforcement in the transverse
          direction (W/m/K).
   * For calculations of the electrical conductivity:
        o Electrical resistivity of the unreinforced matrix (micro-ohm cm).
        o Electrical resistivity of the reinforcement in the axial direction
          (micro-ohm cm).
        o Electrical resistivity of the reinforcement in the transverse
          direction (micro-ohm cm).
   * Reinforcement aspect ratio.
   * Maximum reinforcement volume fraction (between 0 and 1).
   * Number of reinforcement volume fractions (maximum 100). Calculations
     are made at equi-spaced values between 0 and the maximum value
     specified for the volume fraction.

Output parameters

 f          -  The volume fraction of the reinforcement (between 0 and 1).
               Thermal conductivity of the composite in the axial direction
 AxTherCon  -  (W/m/K).

               Thermal conductivity of the composite in the transverse
 TranTherCon-  direction (W/m/K).

 AxElecRho  -  Electrical resistivity of the composite in the axial
               direction (micro-ohm cm).

 TranElecRho-  Electrical resistivity of the composite in the transverse
               direction (micro-ohm cm).

The following files are produced which contain the output:

                 reinforcement volume fraction and axial thermal
 <filename>.cax- conductivity
                 (or electrical resistivity)
                 reinforcement volume fraction and transverse thermal
 <filename>.ctr- conductivity
                 (or electrical resistivity)

 

Error Indicators

None.

 

Accuracy

No information supplied.

 

Further Comments

Further information about this program can be obtained from the Composites
and Coating Group website at http://www.msm.cam.ac.uk /mmc/mmc.html and is
one of a series of programs produced by Bill Clyne and co-workers in the
Materials Science Department at Cambridge.

It should be noted:
Nothing is expected of anyone downloading a program and there is no
obligation to use results obtained from it in any particular manner.
Equally, there is no liability on the part of the supplier and no guarantee
that the programs do not incorporate errors or invalid data. In general,
however, the offer is aimed at researchers and is designed to stimulate
collaborative work. Anyone downloading a program is therefore invited to
give their address to the supplier and is also welcome to enter into contact
if they wish to explore any details. In the event that results obtained
using any of the programs are published in any form, it would be appreciated
if their source could be acknowledged.

 

Example

1. Program text

Complete program.

2. Program data

Eshelby model for the (thermal or electrical) conductivity of composites
 @ TW Clyne, Cambridge University, 1991
 ref: An Introduction to Metal Matrix Composites, T.W.Clyne & P.J.Withers, CUP (1993), p.280-282
(Unlimited distribution version  -  please acknowledge when publishing)

Particulate or unidirectionally aligned fibre composites
Mean field adaptation of the Eshelby model
Inclusions are non-contacting:  not applicable to insulating matrices

Electrical (E) or thermal (T) conduction?  T
Enter conductivity of unreinforced matrix (in W/m K)  201
Enter reinforcement axial conductivity (in W/m K)  23
Enter reinforcement transverse conductivity (in W/m K))  23
Enter reinforcement aspect ratio (>0) 2
Enter max. reinforcement volume fraction (>0 and <1) 0.12
Enter number of reinforcement volume fraction values (max. 100) 6

Calculating......
Computation complete.  Output is stored in 2 files.
Enter prefix for these data files eshconth

Eshelby model for the (thermal or electrical) conductivity of composites
 @ TW Clyne, Cambridge University, 1991
 ref: An Introduction to Metal Matrix Composites, T.W.Clyne & P.J.Withers, CUP (1993), p.280-282
(Unlimited distribution version  -  please acknowledge when publishing)

Particulate or unidirectionally aligned fibre composites
Mean field adaptation of the Eshelby model
Inclusions are non-contacting:  not applicable to insulating matrices

Electrical (E) or thermal (T) conduction?  E
Enter resistivity of unreinforced matrix (in micro-ohm cm)  2.65
Enter reinforcement axial resistivity (in micro-ohm cm)  53
Enter reinforcement transverse resistivity (in micro-ohm cm)  53
Enter reinforcement aspect ratio (>0) 2
Enter max. reinforcement volume fraction (>0 and <1) 0.12
Enter number of reinforcement volume fraction values (max. 100) 6

Calculating......
Computation complete.  Output is stored in 2 files.
Enter prefix for these data files eshconel

3. Program results

Below are the output files for the calculation of the thermal conductivity:

           eshconth.cax                         eshconth.ctr

              f     AxTherCon(W/mK)                  f   TranTherCon(W/mK)
 0.000000E+0000 2.010000E+0002            0.000000E+0000 2.010000E+0002
 2.000000E-0002 1.968087E+0002            2.000000E-0002 1.954495E+0002
 4.000000E-0002 1.926476E+0002            4.000000E-0002 1.900243E+0002
 6.000000E-0002 1.885163E+0002            6.000000E-0002 1.847201E+0002
 8.000000E-0002 1.844147E+0002            8.000000E-0002 1.795329E+0002
 1.000000E-0001 1.803424E+0002            1.000000E-0001 1.744589E+0002
 1.200000E-0001 1.762990E+0002            1.200000E-0001 1.694945E+0002

Below are the output files for the calculation of the electrical
resistivity:

           eshconel.cax                         eshconel.ctr

              fAxElecRho(microohm cm)                  fTranElecRho(microohm cm)
 0.000000E+0000 2.650000E+0000            0.000000E+0000 2.650000E+0000
 2.000000E-0002 2.711447E+0000            2.000000E-0002 2.734438E+0000
 4.000000E-0002 2.775294E+0000            4.000000E-0002 2.822094E+0000
 6.000000E-0002 2.841686E+0000            6.000000E-0002 2.913155E+0000
 8.000000E-0002 2.910778E+0000            8.000000E-0002 3.007823E+0000
 1.000000E-0001 2.982737E+0000            1.000000E-0001 3.106318E+0000
 1.200000E-0001 3.057747E+0000            1.200000E-0001 3.208875E+0000

 

Auxiliary Routines

None.

 

Keywords

composite, laminate, coating, conductivity, thermal, electrical,
resistivity, reinforcement, matrix, Eshelby

 

Download

Download MAP files
Download executable file for the PC
Download executable file for the Macintosh

 

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                        the University of Cambridge.

               MAP Website administration / map@msm.cam.ac.uk
 

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