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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.

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

Language: | N/A |

Product form: | Executable files for use on almost any Apple Macintosh or PC. |

Complete Program.

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:

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

(<*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.

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

- For calculations of the
*thermal*conductivity:

- Thermal conductivity of the unreinforced matrix (Wm
^{-1}K^{-1}). - Thermal conductivity of the reinforcement in the axial direction (Wm
^{-1}K^{-1}). - Thermal conductivity of the reinforcement in the transverse direction (Wm
^{-1}K^{-1}).

- Thermal conductivity of the unreinforced matrix (Wm
- For calculations of the
*electrical*conductivity:

- Electrical resistivity of the unreinforced matrix (micro-ohm cm).
- Electrical resistivity of the reinforcement in the axial direction (micro-ohm cm).
- 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.

f | - | The volume fraction of the reinforcement (between 0 and 1). |

AxTherCon | - | Thermal conductivity of the composite in the axial direction (Wm^{-1}K^{-1}). |

TranTherCon | - | Thermal conductivity of the composite in the transverse direction (Wm^{-1}K^{-1}). |

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:

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

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

None.

No information supplied.

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.

Complete program.

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

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

eshconth.caxeshconth.ctrf 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.caxeshconel.ctrfAxElecRho(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

None.

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

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