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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.

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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.



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.

 

Specification

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

Complete Program.

  

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 (1/m)
     <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.

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.

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/

  

References

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

  

Parameters

Input parameters

   * Young's modulus of the substrate (GPa).
   * Poisson ratio of the substrate.
   * Thickness of the substrate (mm).
   * Young's modulus of the material being deposited (GPa).
   * Poisson ratio of the material being deposited.
   * Thickness of the material being deposited (mm).
   * Number of incremental layers in the deposited layer (maximum 100).
   * Quenching stress (MPa).
   * Post-deposition temperature drop of the composite (K).
   * Expansivity of the substrate at the deposition temperature
     (microstrain/K).
   * Expansivity of the substrate at the ambient temperature
     (microstrain/K).
   * Expansivity of the deposit at the deposition temperature
     (microstrain/K).
   * Expansivity of the deposit at the ambient temperature (microstrain/K).

Output parameters

      The strain energy release rate for interfacial debonding after
 Gr -  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 (1/m).

<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).

  

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

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

  

Auxiliary Routines

None.

  

Keywords

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

 

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