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Program MAP_COMP_COSTPL

  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.

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

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

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Purpose

This program calculates the through-thickness distribution of (in-plane) stresses resulting from progressive deposition of a coating onto a planar substrate for a specified deposition stress and subsequent temperature change. Also given are the specimen curvature and the strain energy release rate for interfacial debonding.

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Specification

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

Complete Program.

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Description

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 distribution of (in-plane) stresses resulting from progressive deposition of a coating onto a planar substrate for a specified deposition stress and subsequent temperature change. Also given are the specimen curvature and the strain energy release rate for interfacial debonding. 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>.kap - deposit thickness (mm) and curvature (m-1)
<filename>.stq - distance from interface (mm) and stress from deposition (MPa)
<filename>.stt - distance from interface (mm) and stress due to temperature change (MPa)
<filename>.stn - distance from interface (mm) and net stress (MPa)
<filename>.std - distance from interface (mm) and net stress after interfacial debonding (MPa)
<filename>.ssb - thickness of deposit removed (mm) and strain registered at the underside of the substrate (millistrain)
(<filename> refers to a user-supplied name for the output files.)

In addition, the strain energy release rate for interfacial debonding after deposition and after the subsequent temperature change are given as screen outputs.

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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References

  1. Y.C. Tsui and T.W. Clyne, 1997, Thin Solid Films, 306, 23-33.

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Parameters

Input parameters

Output parameters

Gr - The strain energy release rate for interfacial debonding after deposition (a) before and (b) after the subsequent temperature change.


The following output files are produced:

<filename>.kap
hd - Thickness of the deposited layer (mm).
kappa - Curvature of the specimen (m-1).

<filename>.stq
z - Distance from the interface between the substrate and the deposited layer (mm).
sigQ - Stress due to deposition (MPa).

<filename>.stt
z - Distance from the interface between the substrate and the deposited layer (mm).
sigT - Stress due to the post-deposition temperature change (MPa).

<filename>.stn
z - Distance from the interface between the substrate and the deposited layer (mm).
sigNet - Net stress (MPa).

<filename>.std
z - Distance from the interface between the substrate and the deposited layer (mm).
sigNet Debond - Net stress after interfacial debonding (MPa).

<filename>.ssb
z - Thickness of deposit removed (mm).
epsBot - Strain registered at the underside of the substrate (millistrain).

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Error Indicators

None.

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Accuracy

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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Example

1. Program text

Complete program.

2. Program data

Residual Stresses in Thermal Spray Coatings - Planar Analytical Model
  YC Tsui & TW Clyne, Cambridge University, 1997
ref: Thin Solid Films, vol.306 (1997) p.23-33
(Unlimited distribution version - please acknowledge when publishing)

Stresses arise from quenching of splats & from differential thermal contraction
Substrate is free to bend

Default case (NiCrAlY (1.04mm) on PK33 (1.65mm))? (Y/N)  n
Enter substrate Young modulus (GPa) 167
Enter substrate Poisson ratio 0.31
Substrate biaxial modulus (GPa) =    242.029
Enter substrate thickness (mm) 1.62
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) = 400
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
Calculating......
Gr before cooling =     84.064 J/m2
Gr after cooling =     74.772 J/m2
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 costpl

3. Program results

Below are extracts from the output files.

                   costpl.kap                               costpl.stn

              hd(mm)          kappa(m-1)               z(mm)         sigNet(MPa)
          0.01000000          0.01230517         -1.62000000        102.16314733
          0.03000000          0.02477967                   0       -151.72803220
          0.05000000          0.03741594          0.01000000         28.16332021
          0.07000000          0.05020636          0.03000000         28.19630675
          ...                 ...                 ...                 ...
          0.95000000          0.66040999          0.93000000         58.41684603
          0.97000000          0.67350847          0.95000000         59.61493324
          0.99000000          0.68652041          0.97000000         60.82978772
          0.99000000          0.64753794          0.99000000         62.06102778


                   costpl.stq                               costpl.std

               z(mm)           sigQ(MPa)               z(mm)   sigNetDebond(MPa)
         -1.62000000        108.15463538         -1.62000000          0.00000000
                   0       -161.02106422                   0         -0.00000000
          0.01000000         31.78156818          0.01000000          5.26998214
          0.03000000         31.77602422          0.03000000          4.59871486
          ...                 ...                 ...                 ...
          0.93000000         60.26269080          0.93000000          3.12783208
          0.95000000         61.42224751          0.95000000          3.62166546
          0.97000000         62.59857148          0.97000000          4.13226612
          0.99000000         63.79128104          0.99000000          4.65925235


                   costpl.stt                               costpl.ssb

               z(mm)           sigT(MPa)               z(mm) epsBot(millistrain)
         -1.62000000         -5.99148805          1.00000000         -0.42211106
                   0          9.29303202          0.98000000         -0.41599504
          0.01000000         -3.61824798          0.96000000         -0.40971560
          0.03000000         -3.57971747          0.94000000         -0.40327681
          ...                 ...                 ...                 ...
          0.93000000         -1.84584477          0.06000000         -0.02778311
          0.95000000         -1.80731427          0.04000000         -0.01850718
          0.97000000         -1.76878376          0.02000000         -0.00924547
          0.99000000         -1.73025326          0.00000000          0.00000000

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Auxiliary Routines

None.

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Keywords

composite, laminate, coating, plane, deposition, temperature change, substrate, strain, stress, temperature, planar

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Download

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

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