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  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.

Provenance of Source Code

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

T.W. Clyne: twc10@cus.cam.ac.uk

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

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This program calculates the through-thickness stress distribution resulting from progressive deposition of a coating onto a hollow, cylindrical substrate, for a specified deposition stress and subsequent temperature change.

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

Complete Program.

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An analytical model has been developed [1] to predict the residual stress distribution in progressively deposited coatings, (such as those produced by thermal spraying). This is based on the concept of a misfit strain, caused by either the deposition stress (e.g. due to quenching of splats in thermal spraying) or by differential thermal contraction between substrates and coating during cooling. The deposition stress is introduced as the coating is formed layer-by-layer, with a specified layer thickness, such that the misfit strain is accommodated after each layer addition (rather than for the coating as a whole).

The program calculates the through-thickness stress distribution resulting from progressive deposition of a coating onto a hollow, cylindrical substrate for a specified deposition stress and subsequent temperature change. The analytical solutions used to carry out the calculations are given in detail in reference 1.

Input data are required in the form of the elastic constants, thermal expansivities and thicknesses of substrate and deposit, deposition ("quenching") stress, the post-deposition temperature change, and the number and thickness of the layers used to model the deposition. These are screen input in response to a series of prompts. The option to use a default set is given at the beginning.

The results are written to 6 different files:

<filename>.axq - radial position (mm) and axial stress due to deposition (MPa)
<filename>.axt - radial position (mm) and axial stress due to temperature change (MPa)
<filename>.raq - radial position (mm) and radial stress due to deposition (MPa)
<filename>.rat - radial position (mm) and radial stress due to temperature change (MPa)
<filename>.hoq - radial position (mm) and hoop stress due to deposition (MPa)
<filename>.hot - radial position (mm) and hoop stress due to temperature change (MPa)
(<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 or by selection of default cases which are offered. 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 layers specified (and on machine speed), but even on a relatively slow machine and with the maximum number of layers (100) specified, the program only takes a few seconds to run.

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  1. Y.C. Tsui and T.W. Clyne, 1997, Thin Solid Films, 306, 34-51.

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Input parameters

Output parameters

The following output files are produced:

r - Radial position (mm).
sigaxialQ - Axial stress due to deposition (MPa)

r - Radial position (mm).
sigaxialT - Axial stress due to temperature change (MPa).

r - Radial position (mm).
sigradialQ - Radial stress due to deposition (MPa).

r - Radial position (mm).
sigradialT - Radial stress due to temperature change (MPa).

r - Radial position (mm).
sighoopQ - Hoop stress due to deposition (MPa).

r - Radial position (mm).
sighoopT - Hoop stress due to temperature change (MPa).

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Error Indicators


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No information supplied.

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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.

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1. Program text

Complete program.

2. Program data

Residual Stresses in Thermal Spray Coatings - Cylindrical Analytical Model
 @ YC Tsui & TW Clyne, Cambridge University, 1997
ref: Thin Solid Films, vol.306 (1997) p.34-51
(Unlimited distribution version - please acknowledge when publishing)

Stresses arise from quenching of splats & from differential thermal contraction

Default case (NiCrAlY (1.04mm) on PK33 (6 & 8 mm inner & outer radii))? (Y/N)  n
Enter substrate Young modulus (GPa) 167
Enter substrate Poisson ratio 0.31
Substrate biaxial modulus (GPa) =    242.029
Enter substrate inner radius (mm) 6
Enter substrate outer radius (mm) 8
Enter deposit Young modulus (GPa) 34.1
Enter deposit Poisson ratio 0.31
Deposit biaxial modulus (GPa) =     49.420
Enter deposit thickness (mm) 1.0
Enter number of incremental layers in deposit (max. = 100) 50
Enter quenching stress (MPa) = 65
Enter post-deposition temperature drop (K) = 480
Enter substrate expansivity at deposition temperature (microstrain/K) = 12.87
Enter substrate expansivity at ambient temperature (microstrain/K) = 12.1
Enter deposit expansivity at deposition temperature (microstrain/K) = 12.41
Enter deposit expansivity at ambient temperature (microstrain/K) = 12.0
Computation complete.
Output (principal stresses from deposition & from cooling) stored in 6 files.
(Sum these to obtain net stress distribution.)

Enter prefix for these 6 files costcy

3. Program results

Below are extracts from the output files.

                   costcy.axq                               costcy.axt

               r(mm)      sigaxialQ(MPa)               r(mm)      sigaxialT(MPa)
          6.04000000        -78.48244363          6.04000000          5.00650996
          6.08000000        -78.48244363          6.08000000          5.00650996
          6.12000000        -78.48244363          6.12000000          5.00650996
          6.16000000        -78.48244363          6.16000000          5.00650996
          ...                 ...                 ...                 ...
          8.93000000        135.39023467          8.93000000         -8.24601640
          8.95000000        135.70881959          8.95000000         -8.24601640
          8.97000000        136.02737644          8.97000000         -8.24601640
          8.99000000        136.34590351          8.99000000         -8.24601640

                   costcy.raq                               costcy.rat

               r(mm)     sigradialQ(MPa)               r(mm)     sigradialT(MPa)
          6.04000000         -2.55136516          6.04000000          0.03020552
          6.08000000         -5.05254025          6.08000000          0.05981684
          6.12000000         -7.50483314          6.12000000          0.08884945
          6.16000000         -9.90950936          6.16000000          0.11731832
          ...                 ...                 ...                 ...
          8.93000000         -0.92951307          8.93000000          0.05931414
          8.95000000         -0.61883549          8.95000000          0.04222515
          8.97000000         -0.30900103          8.97000000          0.02525034
          8.99000000          0.00000000          8.99000000          0.00838870

                   costcy.hoq                               costcy.hot

               r(mm)       sighoopQ(MPa)               r(mm)       sighoopT(MPa)
          6.04000000       -383.98469411          6.04000000          4.54598090
          6.08000000       -381.48351901          6.08000000          4.51636958
          6.12000000       -379.03122612          6.12000000          4.48733697
          6.16000000       -376.62654990          6.16000000          4.45886809
          ...                 ...                 ...                 ...
          8.93000000        137.99220338          8.93000000         -7.59656236
          8.95000000        138.23909703          8.95000000         -7.57947337
          8.97000000        138.48791825          8.97000000         -7.56249856
          8.99000000        138.73850319          8.99000000         -7.54563692

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Auxiliary Routines


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composite, laminate, coating, cylinder, deposition, temperature change, substrate, strain, stress, temperature, cylindrical

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

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