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This is a working document under consideration by an ASM International Thermal Spray Society
Committee. It is available solely to obtain comments from interested parties, and may not be relied upon orutilized for any other purpose. Working documents may change substantially in future versions.
1
ASM International TSS
Accepted Practice for Mechanical Properties #1 Published in 2002
AP MP001-02
Modified Layer Removal Method for
Evaluating Residual Stresses in Thermal Spray Coatings
January 1, 2002
ASM International, Thermal Spray Society
9639 Kinsman Road
Metals Park, OH 44073-0002
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Keywords- ASM International TSS Accepted Practice,
Residual Stress Evaluation Procedure,
Thermal Spray Coatings,Residual Stresses, Layer Removal Method
Prepared and Approved by
ASM International Thermal Spray Society
Accepted Practice Committee on
Evaluation of Mechanical Properties of Thermal Spray Coatings
Date: __ July 31, 2001 _
Approved byASM International Thermal Spray Society Board of Directors
Date: __December 31, 2001__
Abstract This Accepted Practice contains the procedure for evaluating residual stresses in
thermal spray coatings using a modified layer removal method. It cites the dimensions ofthe test specimen, the equipment needed, the procedure for applying gages, the procedure
for removing layers, and the method for interpreting the data to evaluate residual stresses.
ASM International World Headquarters
ASM International Thermal Spray Society
9639 Kinsman Road
Metals Park, OH 44073-0002 USA
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3
Statement of the Use of
ASM International Thermal Spray Society Accepted Practices
ASM International is not a standards writing organization. Yet, the increased use of
thermal spray coatings and the need for documentation on methods to evaluate mechanicalproperties have generated a need for Accepted Practices. In response to this need, the ASM
International Thermal Spray Society formed three Committees on Accepted Practices. This
document is prepared by the Committee on Evaluating Mechanical Properties of Thermal Spray
Coatings. The purpose of this document is to present a written description of a method for
evaluating residual stresses in thermal spray coatings. The method is the Modified Layer
Removal Method (MLRM). The MLRM is an extension of the well-known Layer Removal
Method to include the Young's modulus and Poisson's ratio properties of the thermal spray
coating material and the substrate.
DISCLAIMER: This document is a collective effort involving a number of volunteer
specialists. Great care is taken in the compilation and production of this document, but it should
be made clear that NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING, WITHOUT
LIMITATION, WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
PARTICULAR PURPOSE, ARE GIVEN IN CONNECTION WITH THIS DOCUMENT.
Although this information is believed to be accurate by ASM, ASM cannot guarantee that
favorable results will be obtained from the use of this document alone. This document is intended
for use by persons having technical skill, at their sole discretion and risk. It is suggested that you
consult your own network or professionals. Since the conditions of product or material use are
outside of ASM's control, ASM assumes no liability or obligation in connection with any use ofthis information. No claim of any kind, whether as to products or information in this document,
and whether or not based on negligence, shall be greater in amount than the purchase price of thisproduct or document in respect of which damages are claimed. THE REMEDY HEREBY
PROVIDED SHALL BE THE EXCLUSIVE AND SOLE REMEDY OF BUYER, AND IN NO
EVENT SHALL EITHER PARTY BE LIABLE FOR SPECIAL, INDIRECT OR
CONSEQUENTIAL DAMAGES WHETHER OR NOT CAUSED BY OR RESULTING FROM
THE NEGLIGENCE OF SUCH PARTY. As with any material, evaluation of the material under
end use conditions prior to specification is essential. Therefore, specific testing under actual
conditions is recommended.
Nothing contained in this document shall be construed as a grant of any right of manufacture,
sale, use, or reproduction, in connection with any method, process, apparatus, product,
composition, or system, whether or not covered by letters patent, copyright, or trademark, andnothing contained in this document shall be construed as a defense against any alleged
infringement of letters patent, copyright, or trademark, or as a defense against liability for such
infringement.
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Comments, criticisms, and suggestions are invited, and should be forwarded to ASM
International.
Attn: Committee on Evaluating Mechanical Properties of Thermal Spray Coatings
ASM International World HeadquartersASM International Thermal Spray Society
9639 Kinsman Road
Metals Park, OH 44073-0002 USA
E-mail: Bob Uhl
Phone: 440 338-5151
Fax: 440 338-4634
Photocopy Rights
No part of this document may be reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the
written permission of the copyright owner.
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5
Personnel
ASM International Thermal Spray Society
Accepted Practice Committee onEvaluation of Mechanical Properties of Thermal Spray Coatings
Edmund F. Rybicki, Chair University of Tulsa
Oludele Popoola Consultant
Christopher Berndt SUNY at Stony Brook
Joseph DeFalco Sulzer Metco
Humin Gassot Institut de Physique Nucleaire de ORSAY
Warren D. Grossklaus, Jr. GE Aircraft Engines
Ian D. Harris Edison Welding Institute
Robert Hilgenberg PRAXAIR Surface Technologies
Xin-qing Ma Aoyama Gakuin University
Roy T. R. McGrann SUNY at Binghamton
Manuel Maligas FMC Corporation
Sanjay Sampath SUNY at Stony Brook
Elliot Sampson PRAXAIR TAFA
John Sauer Belcan EngineeringAnnie Savarimuthu Hanover Corporation
Mark F. Smith Sandia National Laboratories
David A. Somerville Engelhard
Robert A. Sulit Sulit Engineering
Jan Wigren Volvo Aero Corporation
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Table of Contents
Page No.
Key Words 2
Abstract .. 2Statement of the Use of ASM International Thermal Spray
Society Accepted Practices . 3
Personnel .. 5
Table of Contents .. 6
List of Figures .. 6List of Tables . 6
Scope .. 7
Referenced Documents 7
Terminology 7
I. Introduction and Background 8
II. Equipment and Supplies 10
III. Description of the Residual Stress Specimen 12IV. Procedure for Applying Strain Gages 13
V. Initial Strain Gage and Dimensional Data 13
VI. Layer Removal Procedure .. 14
VII. Data Analysis . 17VIII. References . 21Appendix A. Analysis for the Modified Layer Removal Method ... 22Appendix B. Dimensioned Drawing of the Residual Stress Specimen Fixture .. 25
Appendix C. Acknowledgements 25
List of Figures
Figure 1. Fixture for Holding Four Residual Stress Specimens . 11
Figure 2. Dimensions of the Thermal Spray Coating Residual
Stress Specimen with Strain Gages . 12
Figure 3. Half Bridge Configuration with Temperature
Compensating Strain Gage . 14
Figure 4. Modified Layer Removal Method Program Input .. 18
Figure 5. Longitudinal Residual Stress Distribution .. 19Figure 6. Transverse Residual Stress Distribution 20
Figure A-1. Free-Body Diagram for Modified Layer Removal Method
Applied to a Thermal Spray Coated Specimen 22
Figure B-1. Dimensions of the Residual Stress Specimen Fixture . 25
List of Tables
Table 1. Data Sheet for Strain Gage Readings and Thickness Measurements 16
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Residual stresses: Stresses that exist in a solid material without any external mechanical loadings
applied to the solid. Residual stresses can be generated at room temperature or at higher or lower
temperatures.
Strain gage: A device used to monitor the change in strain of a specimen subjected to changes in
stresses.
Strain rosette: A combination of strain gages used to measure the strains in more than one
direction .e.g. rectangular rosette, delta rosette.
Substrate: A material, which serves as a foundation for a thermal spray coating.
Thermal spray coating: A coating of material sprayed on another material called a substrate.
Thermal spray coatings are used to enhance resistance to wear or corrosion and for dimensional
restoration.
I. Introduction and Background
Thermal spray coatings are used extensively by many industries in applications including
wear and corrosion protection, dimensional restorations, and thermal insulation. The materialsused in thermal spray coatings include metals, carbides, and ceramics. There are several different
commercially available processes to apply thermal spray coatings and newer processes are being
developed. The following four questions and answers were selected to provide an introduction to
residual stresses in thermal spray coatings.
What Causes Residual Stresses in Thermal Spray Coatings?
In most combinations of coating material and application process, there is a temperature
difference between the coating and the substrate caused by heating the coating and having the
substrate at a different temperature than the applied coating. As the two materials cool to room
temperature, they shrink by different amounts causing residual stresses in the coating and the
substrate. Other factors, such as particle impact velocity and splat cooling rate, influence coating
residual stresses. The result is that there are residual stresses in the coating and substrate,and
these stresses can be tensile or compressive. [1]
Why are the Residual Stresses in Thermal Spray Coatings of Interest?
Residual stresses have been shown to affect the performance of tungsten carbide (WC)
thermal spray coated components in gas turbine engines [2] and the fatigue life of HVOF sprayed
WC on aluminum [3] and steel [4]. The bond strength of coatings has also been shown to be
affected by residual stress [5].
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How can Residual Stresses be Evaluated in TSC's using Laboratory Procedures?
There are several methods used to determine the residual stresses in thermal spray
coatings. The X-ray method, the hole drilling method, bending deflection method, the neutrondiffraction method, the Modified Layer Removal Method (MLRM) and other methods have been
used.
What is the difference Between the Layer Removal Method and the Modified Layer Removal
Method?
The Modified Layer Removal Method is an extension of the Layer Removal Method.
The Layer Removal Method was developed in 1945 By Rosenthal and Norton [6]. In 1965, it
was written as a Society of Automotive Engineers Information Report [7]. The Layer Removal
Method was developed for a single uncoated material, such as steel, aluminum, or titanium. The
Layer Removal Method does not recognize the Young's modulus and Poisson's ratio associated
with thermal spray coated materials. Thus, there is a need for a layer removal procedure toevaluate residual stresses in coated materials. The Modified Layer Removal Method was
developed specifically to meet this need for evaluating residual stresses in thermal spray coatings
[1] [8].
The Modified Layer Removal Method has been used to determine the residual stress
distributions through the thickness of the coating and the substrate for a variety of coatings
including tungsten carbide, aluminum, thermal barrier yttria stabilized zirconia, copper, and steel.
[3], [4], [5], [8] [9], [10], [11]
Both the Layer Removal Method and the Modified Layer Removal Method were
developed for isotropic material behavior.
The following sections describe equipment and the laboratory procedure for the MLRM .
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10
II. Equipment and Supplies
The following is a list of equipment and materials needed for the Modified Layer Removal
Method.
.
ITEM DESCRIPTION
Surface cleaning supplies Silicon carbide paper 220-00 grit, gauze sponges,
degreasers, water-based acidic surface cleaners, and
neutralizers as recommended by strain gage supplier.
Strain gages 90biaxial (2 gages) rosette. One rosette per specimen.
Gage adhesive Follow recommendation of strain gage supplier
Strain gage wires 2-wire, twisted, multi-strand, copper.
Soldering iron Small tip iron
Protective coating Non-conductive, waterproof, mechanical protection,following recommendation of strain gage supplier.
Strain Indicator At least 0 to 2999 microstrain range with 1 microstrainresolution.
Metallographic polishing
machine
Vertical shaft for horizontal wheel, fitted with polishing
head to hold the sample to the polishing wheel for semi-
automatic grinding /polishing.
Polishing wheel 8-inch diameter diamond polishing disc with 125 micron
diamond chips.
Fixture to hold specimens Four-specimen holder to match to polishing head (see
Figure 1).Micrometer 0.0001 inch (0.0025 mm) resolution.
Computer to run MLRM
program
Windows 95 or NT or later to run Excel 97 or later.
Modified Layer Removal
Excel Program based on
References [1], [8] on
MLRM
Contact
Bob Uhl
at ASM, International to download program
.
It should be noted that the fixture shown in Figure 1 is provided as an example of a
fixture that works with polishing equipment of one type. Since there are several types ofpolishing equipment, details of the fixture may have to be different to interface with
different polishing equipment.
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Figure 1a. Specimen fixture showing coating side of four specimens installed in fixture.
Figure 1b. Specimen fixture showing gage wires tucked into cavities above specimens.
Fixture
SpecimensSet screws to
secure specimens
Strain gage wires
Roll pin to match with
polishing head
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III. Description of the Residual Stress Specimen
The residual stress specimen is shown in Figure 2. The specimen is 25.4 mm by 25.4 mm
by 6.35 mm. The coating is sprayed on one of the 25.4 mm by 25.4 surfaces as shown in the
Figure 2. The gages are applied after the coating is applied. Based on experience, the coating
thickness is recommended to be between 0.13 mm and 1.5 mm (5 mils to 60 mils).
a. Isometric view
b. Bottom view
Figure 2. Dimensions of the Thermal Spray Coating Residual Stress Specimen with Strain Gages
Coating
Substrate
25.4mm
25.4mm
6.35mm
h
900Biaxial
Strain Rosette
25.4mm
25.4mm
900Biaxial
Strain Rosette
Substrate
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IV. Procedure for Applying Gages
Procedures for applying or installing bonded resistance strain gages are available from
strain gage suppliers. Also ASTM E 1237-93 (Reapproved 1998) "Standard Guide for Installing
Bonded Resistance Strain Gages" provides good guidelines. Some aspects of applying strain
gages specific to the MLRM are reviewed below.Mount the strain rosette at the center of the substrate 25.4 x 25.4 mm surface. Align the
sensitive axes of the 90rosette parallel to the 25.4 mm edges of the specimen as shown in Figure2. Solder one lead to each solder tab of the two gages on the rosette. Make all leads from all
gages the same length and wire diameter. Follow ASTM E 1237 to check the gage installation.
Label each gage with specimen and gage identification using a masking tape label on the gage
wires or other method. Designate one of the two gages on each specimen as Longitudinal and
the other as Transverse. Apply a non-conductive protective coating to the gage that will keep
the gage, wires, and solder joints absolutely dry and reduce the chance of mechanical damage to
the gage or wires during handling and grinding. Apply a rosette to an uncoated specimen that is
made of the same material as the substrate material and approximately the same size as the coated
specimens to use as a Reference gage and for Temperature Compensation. Wire the
Reference/Compensating gages the same way as specimen gages: make all lead wire the samelength as specimen gage lead wires. Label one of the gages as Reference and the other as
Compensating, and apply protective coatings.
V. Initial Strain and Dimensional Data
Two types of measurements are taken: 1) strain; and 2) specimen thickness. Initial
measurements of these quantities are required before any polishing is done on the specimens.
It is important that strain measurements are made before thickness measurements becausehandling the specimen to make thickness measurements might increase the temperature of the
specimen relative to the temperature of the Compensating gage. Allow time for the substratespecimen on which the Reference gage and Temperature Compensating gage are mounted to
reach room temperature at the location where all strain measurements will be made. Connect the
Reference and Compensating gages to the strain indicator in a half-bridge as shown in Figure 3
and balance the bridge (set output indication to zero). Solid lines in Figure 3 indicate Reference
gage or Specimen gage, Compensating gage, and lead wires. (Dashed lines in this figure indicate
internal components of the strain bridge and are provided here to show the entire bridge
configuration.) Disconnect the Reference gage lead wires from the strain indicator,but leave the
Compensating gage attached. Connect in turn each of the two gages on a coated specimen to the
strain indicator as shown in Figure 3 and record the indicated strains in the first line of the sample
data sheet shown in Table 1. Repeat for each coated specimen. To minimize measurement error
when balancing the strain bridge and when making specimen strain measurements, always insert
the gage wires into the strain indicator terminal post to the same point on the wire.Use the micrometer to measure the thickness of each coated specimen at the four corners
of the specimen outside the area covered by protective coating and enter the data on the first lineof the data sheet in Table 1.
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Figure 3. Half Bridge configuration with temperature compensating gage. (Dashed lines
represent internal strain bridge elements.) Leads, labeled L, should be the same length.
VI. Layer Removal Procedure
After taking initial strain and specimen thickness measurements, insert the specimens into
the four-specimen fixture (Figure 1) and mount the fixture to the polishing head. The specimens
should be secured in the fixture with the coating side down and flat on the polishing wheel of the
metallographic polishing machine referred to in the Table in Section II. The strain gage wires
should be tucked into the specimen holder cavities above the specimens, and the cavities then
covered with duct tape to reduce exposure of the gages to the water used in the polishing process.
Begin the polishing process by pressurizing the polishing head and turning on the
polishing wheel and water. A wheel rotation speed of about 120 rpm works well for most
coatings. Make a brief initial run with a polishing head pressure of zero to provide an idea of the
rate of material removal. Increase the pressure if necessary to increase the material removal rate.
Thickness of layers removed should be between about 0.7 thousandths of an inch (0.017 mm) and
2 or 3 thousandths (0.05 0.08 mm). If the coating layer removed is too thin, the strain change
may be below the noise floor of the measuring system. If this happens, simply polish more
material for that layer before recording the new strain readings. The time required to remove a
layer of sufficient thickness is not fixed, but rather depends on the type of coating and the
condition of the polishing wheel. For a polishing wheel that is in good condition, the time
Temperaturecompensating
R1
R2
L
L
L
L
Strainreadout
Powersupply
Reference orSpecimen
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required can vary from a few minutes (for thermal barrier coatings, to an hour or more for
tungsten carbide wear resistance coatings).
After a layer of sufficient thickness has been removed by polishing, the specimens are
removed from the fixture, dried, and allowed to reach room temperature. No strain measurements
should be made within one half-hour after removing the specimens from the fixture in order to
allow time for the specimen to reach thermal equilibrium with the substrate specimen on whichthe temperature-compensating gage is mounted. Also for this reason, it is important to measure
the strain before handling the specimen to measure thickness. Before measuring the specimen
strains, connect the Reference gage and the Temperature Compensating gage to the strain
indicator in the half-bridge configuration as shown in Figure 3 and balance the bridge (set output
to read zero). To make strain measurements for the specimens, the reference gage is replaced by
specimen strain gages connected in turn into the half-bridge configuration with the Temperature
Compensating gage as shown in Figure 3. To minimize measurement error when balancing the
strain bridge and when making specimen strain measurements, always insert the gage wires into
the strain indicator terminal post to the same point on the wire.
Thickness measurements are made by micrometer at the four corners of the specimen.
Strain and thickness data can be recorded in the data sheet shown in Table 1,starting with the row
immediately below the initial thickness and strain data. The average thickness is calculated incolumn six. The last column in the table is for comments. Usually, the point in the layer removal
process at which the last coating layer is removed from the specimen is recorded in this column.
Continue the layer removal process until the coating has been completely removed from
the specimen. Additional layers can be removed if information on the residual stress levels in the
substrate near the coating/substrate interface is desired. As successive layers of the substrate are
removed, usually the strain measurements stop changing. This indicates that the residual stresses
in the remaining substrate are negligible, and the process can be terminated.
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Table 1. Data Sheet for Strain Gage Readings and Thickness Measurements
Material ThicknessTo CoatSubstrate
* Thickness (in.) * Strain (Date/Initials1 2 3 4 Average Long. Trans.
Thickness of
layer removed(in.)
Comments
* Measure the strain first and then the thickness.
SpecimenNumber
Gage Resistance Gage Factor
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VII. Data Analysis
An Excel spreadsheet program with macros for the analysis shown in Appendix A has
been written. After the data are recorded on the Data Form values for the average thickness
column on the data sheet can be calculated and written on the data sheet. The data are then
entered into the spreadsheet program.
An example of the spreadsheet is shown in Figure 4. The modulus of elasticity and the
Poisson's ratio for the substrate and the coating are inputs. One method for evaluating the
modulus of elasticity and Poisson's ratio is described in Reference [12] The thickness of the
coating is an input. The other inputs are the thickness of the specimen (the average of 4 thickness
measurements) and the strain gage readings. The program will calculate the through-thickness
residual stress distribution for the depth that layers were removed.
- The Program, "MLRM for Residual Stresses" can be downloaded from the ASM,International website: www.ASM-international.org/
- An Example Case is shown in Figures 4, 5 and 6.
A few notes about the program are helpful. The purpose for the program is to make the
computational part of the Modified Layer Removal Method easier for the user. Thus, while the
graphics are perhaps neat looking for the transverse and longitudinal stress distributions for the
example case, any new case may require some changes in the fonts, axis scales, units, ranges,
location of the inset, or other aspects of the graphs. This will have to be done by the user. The
inset is left ungrouped, so the user can modify it. The user can remove the line connecting the
data points. The procedures of Excel apply. The text boxes are not grouped so the user can add
the specific type of coating or substrate. The dashed vertical line denoting the interface between
the coating and the substrate is moveable for different coating thicknesses.
The program calculates a table of through-thickness residual stress values, in the
longitudinal and transverse directions, in the main page, Figure 4. The values are plotted inFigures 5 and 6. Notice the thermal spray coating is plasma sprayed Ni-5Al. The substrate is
steel. Some of the characteristics of the stress distributions in Figures 5 and 6 are mentioned to
help the user. The vertical axis of Figure 3 shows the residual stress in psi. Positive numbers are
tensile residual stresses and negative numbers are compressive residual stresses. The horizontal
axis of Figure 4 shows the distance from the coating surface. There is tension in the coating.
Notice there are some peaks in the tensile residual stress distribution. This could be because
measurements are not exact or because the residual stresses are changing in that region. Recallthat 4 specimens are recommended to examine reproducibility of the residual stresses. There can
be some specimen-to-specimen variation in the residual stress distributions. When this happens,
data from the 4 residual specimens can indicate a range of reproducibility on the results. The user
can select statistics parameters to examine for example confidence intervals of the data.
The compression residual stress in the substrate, near the interface, is due to "gritblasting" the substrate before the coating was sprayed. The Modified Layer Removal Method
analysis assumes that the last remaining piece is stress free and calculates residual stresses up to
and on the gaged surface.
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Insert data in the Blue Bold cells only Substrate Modulus,E 29000000
Thick ELong ETran Substrate Poisson's Ratio,V 0.3
0.2115 364 735 Coating Modulus,Ecoating 12000000
0.2085 355 725 Coating Poisson's Ratio,Vcoating 0.25
0.2059 342 714 Press Long Coating Thickness,Tcoating 0.023
0.2033 331 705 Button for
0.1973 301 673 graph Z LONG TRAN0.1902 270 645 1.5000E-03 1.05E+04 1.12E+04
0.1861 264 638 4.3000E-03 1.65E+04 1.50E+04
0.1834 270 646 6.9000E-03 1.35E+04 1.21E+04
0.1778 264 636 Do Not insert Rows 1.1200E-02 1.69E+04 1.76E+04
0.1705 242 617 or Columns 1.7750E-02 1.37E+04 1.29E+04
anywhere. 2.3350E-02 -1.39E+03 -7.32E+02
2.6750E-02 -1.63E+04 -1.76E+04
3.0900E-02 -2.24E+03 -6.88E+02
3.7350E-02 2.93E+03 2.21E+031.2625E-01 -1.61E+03 -1.58E+03
2.1150E-01 5.02E+03 4.93E+03
If more rows are needed for data points, the References can be moved to make
room for the data points.
REFERENCES
Greving, D. J., Rybicki, E. F., and Shadley, J. R., "Through-Thickness Residual Stress
Evaluations for Several Industrial Thermal Spray Coatings Using a Modified Layer Removal
Method", The Journal of Thermal Spray Technology, Vol. 3, No. 4, December 1994, pp. 379-388.
McGrann, R.T.R., Rybicki, E.F., and Shadley, J.R., Applications and Theory of the
Modified Layer Removal Method for the Evaluation of Through-Thickness Residual Stresses
in Thermal Spray Coated Materials, Proceedings of the Fifth International Conference on
Residual Stresses, held in Linkping, Sweden, June 16-18, 1997.
The Macros for the Excel Program were written by Mr. Sulaiman Al-Musallami
Figure 4. Input and Output Screen for MLRM Program
RunRun
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19
Figure 5. Through-Thickness Longitudinal Residual Stress Distribution
-20,000
-15,000
-10,000
-5,000
0
5,000
10,000
15,000
20,000
0.00 0.05 0.10 0.15 0.20 0.25
Distance From Coating Surface, Z (inch)
ResidualStress
(psi)
Coating
Substrate
Z
Coating Substrate
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20
Figure 6. Through Thickness Transverse Residual Stress Distribution
-20,000
-15,000
-10,000
-5,000
0
5,000
10,000
15,000
20,000
0.00 0.05 0.10 0.15 0.20 0.25
Distance From Coating Surface, Z (inch)
ResidualStre
ss(psi)
Coating
Substrate
Coating Substrate
Z
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21
VIII. References
[1]. Greving, D. J., Rybicki, E. F., and Shadley, J. R., "Through-Thickness Residual Stress
Evaluations for Several Industrial Thermal Spray Coatings Using a Modified Layer RemovalMethod", The Journal of Thermal Spray Technology, Vol. 3, No. 4, December 1994, pp. 379-388.
[2]. Pejryd, L., Wigren, J., Greving, D.J., Shadley, J.R., and Rybicki, E.F., Residual Stresses as aFactor in the Selection of Tungsten Carbide Coatings for a Jet Engine Application, The Journal of
Thermal Spray Technology, Vol. 4, No. 3, September, 1995, pp. 268-274.
[3]. McGrann, R.T.R., Greving, D.J., Shadley, J.R., Rybicki, E.F., and Bodger, B.E., The Effect
of Residual Stress in HVOF Tungsten Carbide Coatings on the Fatigue Life in Bending of
Thermal Spray Coated Aluminum,Jl. Thermal Spray Technology, Vol. 7, No. 4, Dec. 1998, pp.546-552.
[4]. McGrann, R.T.R., Shadley, J.R., Rybicki, E.F., Kruecke, T.L., and Bodger, B.E. The Effect
of Coating Residual Stress on the Fatigue Life of Thermal Spray Coated Steel and Aluminum,
The Journal of Surface & Coatings Technology, Volumes 108-109 (1998), pp. 59-64.
[5]. Greving, D. J., Shadley, J. R., and Rybicki, E. F., "Effects of Coating Thickness and Residual
Stresses on the Bond Strength of ASTM C633-79 Thermal Spray Coating Test Specimens," The
Journal of Thermal Spray Technology, Vol. 3, No. 4, December 1994, pp. 371-378.
[6]. Rosenthal, D. and Norton, J. T., "A Method of Measuring Triaxial Residual Stress in Plates,"
Welding Journal, Vol. 24 Research Supplement, PP. 295S- 307S , May 1945.
[7]. SAE Information Report, Methods of Residual Stress Measurement, SAE J936, (Dec 1965).
[8]. McGrann, R.T.R., Rybicki, E.F., and Shadley, J.R., Applications and Theory of the
Modified Layer Removal Method for the Evaluation of Through-Thickness Residual Stresses in
Thermal Spray Coated Materials, Proceedings of the Fifth International Conference on Residual
Stresses, held in Linkping, Sweden, June 16-18, 1997.
[9]. McGrann, R.T.R., E.F. Rybicki, J.R. Shadley, and W.J. Brindley, Factors Influencing
Residual Stresses in Yttria Stabilized Zirconia Thermal Barrier Coatings, Proceedings of the
NASA Materials and Structures Base R&T Conference, held at NASA Lewis Research Center,
Cleveland, Ohio, May 1, 1997.
[10]. R.T.R. McGrann, E.F. Rybicki, J.R. Shadley, D.J. Greving, J. Wigren, L. Pejryd, and W.J.
Brindley, Residual Stress Development in Thermal Barrier Coatings, poster presentation at the
Thermal Barrier Coating Workshop, sponsored by the TBC Interagency Coordination Committee,
Cincinnati, Ohio, May 19-21, 1997.
[11]. McCune, R.C., Donlon, W.R., Cartwright, E.L., Papyrin, A.N., Rybicki, E.F., and Shadley,
J.R., Characterization of Copper and Steel Coatings Made by the Cold Gas-Dynamic Spray
Method, Thermal Spray: Practical Solutions for Engineering Problems, Proceedings of the 1996
National Thermal Spray Conference, Cincinnati, Ohio, 7-11 October 1996, Ed. C.C. Berndt
(Metals Park, Ohio: ASM International, 1996), pp. 397-404.
[12]. Rybicki, E.F., Shadley, J.R., Xiong, Y., and Greving, D.J., A Cantilever BeamMethod for Evaluating Youngs Modulus and Poissons Ration of Thermal Spray
Coatings, The Journal of Thermal Spray Technology, Vol. 4, No. 4, December, 1995,pp. 377-383.
[13]. Jones, R.M., Mechanics of Composite Materials (NY: Hemisphere Publishing Corp.,
1975), pp. 170-1.
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22
Appendix A. Description of the MLRM Analysis for one Layer Removed.
The layer removal method [6] [7] which was developed for a single material, has been
modified to handle thermal spray coated materials. The MLRM uses the mechanics of compositematerials analysis for a two-material non-symmetric layered plate [13].
The analysis is based on the free-body diagram shown in Figure A-1. The force acting on
the layer removed in the x-direction is denoted by Fx. The force and moment acting on the
remaining piece are related to Fxby the force and moment equilibrium equations. Figure A-1
shows a layer of coating with thickness h removed. The remaining coating thickness is h. The
thickness of the substrate is H. A biaxial strain gage is attached to the bottom of the substrate as
shown. Note that this figure shows a quarter section of the specimen with the z-axis through the
center of the entire specimen. The dimensions bx and by are half of the actual specimen
length and width. The z = 0 plane is located at the center of the remaining piece after layer
removal, that is, at (H+h)/2.
Figure A-1. Free-Body Diagram for Modified Layer Removal Method
Applied to a Thermal Spray Coated Specimen
The changes in strain in the remaining piece due to replacing a layer (this is the negative
of the change in strain measured at the strain gage) are given by:
x x0 x z y y0 y z (1)
Mx
z
x
Fx
Fx
Mx
Strain
Gage
bx
by
h
Hz = 0
y
hFx
Fx
Layer Removed
Mx
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23
where:xand
yare the curvatures.
For plane stress, the stress-strain equations are:
x
y
x
y
E
1
1 (2)
where: E is the following function of the material properties:
E
Eb
b
b1 -
for the substrate, and
EE
c
c
c1-
for the coating.
The resultant forces and resultant moments, defined as the force per unit length, Fx
and Fy
, and
the moment per unit length, Mx
and My
, are related to the stresses by:
F
F z
x
y
x
yH + h
H + h
2
2
d and
M
Mz z
x
y
x
yH + h
H + h
2
2
d (3)
Substituting Eqn. (1) and Eqn. (2) into Eqn. (3) gives:
(4)
where: A11 = A22= Eb H + Ec h ; A12= b bE H + c cE h ;
B11= B22= E Ec b Hh
2; B12=
c c b b Hh2
E E;
D11 = D22=
E E
b 2 c 2H
12H h
h
12h H3 3
2 2
D12=
b b 2 c c 2H
12 H h
h
12 h H
E E
3 32 2
Using Eqn. (1) and the strain readings at the strain gage to derive an equation for x0
and y0
gives: x0 xG xH + h
2
F
F
M
M
A A B B
A A B B
B B D D
B B D D
x
y
x
y
11 12 11 12
12 22 12 22
11 12 11 12
12 22 12 22
x0
y0
x
y
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Appendix B. Dimensioned Drawing of the Residual Stress Specimen Fixture.
Using the Modified Layer Removal Method requires a fixture to hold the 4 specimens during
polishing to remove each layer. Below is a drawing of the fixture with dimensions.
Figure I Dimensions of the Residual Stress Specimen Fixture in Inches.
Appendix C. Acknowledgements .
Acknowledgements for Contributions to the MLRM Program.
The MLRM program is based on the analyses described in References [1] and [8]. The
main computational program was written by Dr. Daniel Greving, currently at Honeywell. The
macros for the Excel program were written by Mr. Sulaiman Al-Musallami. The Graphics were
done by Ms. Annie Savarimuthu, currently at Hanover Corp. All contributors named above were
Mechanical Engineering graduate students at The University of Tulsa.