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This article, prepared under the auspices of the ASM Thermal Spray Society Committees on Accepted Practices, describes a procedure for evaluating residual stresses in thermal spray coatings, which 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. It presents questions and answers that were selected to introduce residual stresses in thermal spray coatings. The article describes equipment and the laboratory procedure for the modified layer removal method and provides the description of the residual stress specimen. It also describes the procedures for applying or installing bonded resistance strain gages, the dimensions of the test specimen, the procedure for removing layers, and the method for interpreting the data to evaluate residual stresses.

The spreadsheet program, “MLRM for Residual Stresses,” is available as a supplement to this document.

The increased use of thermal spray coatings and the need for information on methods to evaluate their mechanical properties have generated a need for Accepted Practice documentation. This document, prepared under the auspices of the ASM Thermal Spray Society Committees on Accepted Practices, describes a procedure for evaluating residual stresses in thermal spray coatings. The test provides information on through-thickness residual stresses in the coating and in the substrate. The modified layer removal method 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. The method is destructive and requires a sample specimen to be sprayed and evaluated. The modified layer removal method is useful for selecting thermal spray processes to control residual stresses.

This document specifically references ASTM E1237-93(1998), “Standard Guide for Installing Bonded Resistance Strain Gages.” Additional published papers are cited throughout this document and listed in the “References” section of this document.

isotropic material. A material that has a Young's modulus and Poisson's ratio that are the same in all directions.

layer removal method. A test method based on the concept that removing a layer from the surface of a plate having residual stresses changes the force and moment acting in the remaining piece. This method is used to determine the through-thickness residual stress distribution in the material.

modified layer removal method (MLRM). A test method used to determine the residual stress distributions through the thickness of the coating and the substrate by including the properties of the coating material and the substrate.

modulus of elasticity. The slope of the stress-strain curve within the elastic limits.

Poisson’s ratio. The negative value of the ratio of the lateral strain to the longitudinal strain for uniaxial uniform stress loading.

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. Mechanical deformation in a body or structure as a result of stress. It is also defined as the ratio of the change in length after deformation to the original length before deformation.

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. Examples include rectangular rosette, delta rosette.

substrate. A material that 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.

Thermal spray coatings are used extensively for industrial applications including wear and corrosion protection, dimensional restorations, and thermal insulation. The materials used 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 introduce 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]

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]

Several methods are used to determine the residual stresses in thermal spray coatings. The X-ray method, the hole drilling method, bending deflection method, the neutron diffraction method, the modified layer removal method (MLRM), and other methods have been used.

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 published 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, and it 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 to evaluate residual stresses in coated materials. A modified layer removal method was developed specifically to meet the 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.[3-5, 8-11]

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 modified layer removal method.

Following is a list of equipment and materials needed for the modified layer removal method.

ItemDescription
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 90° biaxial (2 gages) rosette. One rosette per specimen 
Gage adhesive Follow recommendation of strain gage supplier 
Strain gage wires Two-wire, twisted, multi-strand, copper 
Soldering iron Small tip iron 
Protective coating Nonconductive, waterproof, mechanical protection, following recommendation of strain gage supplier 
Strain indicator At least 0 to ±2999 microstrain range with ±1 microstrain resolution 
Metallographic polishing machine Vertical shaft for horizontal wheel, fitted with polishing head to hold the sample to the polishing wheel for semiautomatic grinding/polishing 
Polishing wheel 8-in. diameter diamond polishing disc with 125 micron diamond chips 
Fixture to hold specimens Four-specimen holder to match to polishing head (see Fig. 1). 
Micrometer 0.0001 in. (0.0025 mm) resolution 
Computer to run MLRM program Windows 95 or NT or later to run Microsoft Excel 97 or later 
Modified layer removal Excel program based on References [1, 8] Available to be downloaded as a supplementary file with this document 
ItemDescription
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 90° biaxial (2 gages) rosette. One rosette per specimen 
Gage adhesive Follow recommendation of strain gage supplier 
Strain gage wires Two-wire, twisted, multi-strand, copper 
Soldering iron Small tip iron 
Protective coating Nonconductive, waterproof, mechanical protection, following recommendation of strain gage supplier 
Strain indicator At least 0 to ±2999 microstrain range with ±1 microstrain resolution 
Metallographic polishing machine Vertical shaft for horizontal wheel, fitted with polishing head to hold the sample to the polishing wheel for semiautomatic grinding/polishing 
Polishing wheel 8-in. diameter diamond polishing disc with 125 micron diamond chips 
Fixture to hold specimens Four-specimen holder to match to polishing head (see Fig. 1). 
Micrometer 0.0001 in. (0.0025 mm) resolution 
Computer to run MLRM program Windows 95 or NT or later to run Microsoft Excel 97 or later 
Modified layer removal Excel program based on References [1, 8] Available to be downloaded as a supplementary file with this document 

It should be noted that the fixture shown in Fig. 1 is provided as an example of a fixture that works with polishing equipment of one type. Details of the fixture may have to be adjusted to work with different polishing equipment.

Figure 1(a)

Specimen fixture showing coating side of four specimens installed in fixture.

Figure 1(a)

Specimen fixture showing coating side of four specimens installed in fixture.

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Figure 1(b)

Specimen fixture showing gage wires tucked into cavities above specimens.

Figure 1(b)

Specimen fixture showing gage wires tucked into cavities above specimens.

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The residual stress specimen is shown in Fig. 2. The specimen is 25.4 by 25.4 by 6.35 mm. The coating is sprayed on one of the 25.4 by 25.4 mm surfaces as shown in Fig. 2. The gages are applied after the coating is applied. Based on experience, the coating thickness is recommended to be between 0.13 and 1.5 mm (5 to 60 mils).

Figure 2

Dimensions of the thermal spray coating residual stress specimen with strain gages

Figure 2

Dimensions of the thermal spray coating residual stress specimen with strain gages

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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. Important aspects of applying strain gages specific to the MLRM are reviewed below.

Mount the strain rosette at the center of the substrate 25.4 × 25.4 mm surface. Align the sensitive axes of the 90° rosette parallel to the 25.4 mm edges of the specimen as shown in Fig. 2. 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 E1237 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 that is 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 same length as specimen gage lead wires. Label one of the gages as “Reference” and the other as “Compensating,” and apply protective coatings.

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 because handling 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 substrate specimen 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 Fig. 3 and balance the bridge (set output indication to zero). Solid lines in Fig. 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 Fig. 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.

Figure 3

Half bridge configuration with temperature compensating gage. (Dashed lines represent internal strain bridge elements.) Leads (L) should be the same length.

Figure 3

Half bridge configuration with temperature compensating gage. (Dashed lines represent internal strain bridge elements.) Leads (L) should be the same length.

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Table 1
Data sheet for strain gage readings and thickness measurements
graphic
graphic

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 line of the data sheet in Table 1.

After taking initial strain and specimen thickness measurements, insert the specimens into the four-specimen fixture (Fig. 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 section “Equipment and Supplies” in this document. 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 depends on the type of coating and the condition of the polishing wheel. For a polishing wheel that is in good condition, the time 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 30 minutes after removing the specimens from the fixture in order to allow time for the specimen to reach thermal equilibrium with the substrate specimen on which the 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 Fig. 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 Fig. 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 in column 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.

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 Fig. 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 four thickness measurements) and the strain gage readings. The program will calculate the through-thickness residual stress distribution for the depth that layers were removed.

Figure 4

Input and output screen for the modified layer removal Excel spreadsheet program

Figure 4

Input and output screen for the modified layer removal Excel spreadsheet program

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The spreadsheet program, “MLRM for Residual Stresses,” is available as a supplement to this document.

An example case is shown in Fig. 4, 5, and 6.

Figure 5

Through-thickness longitudinal residual stress distribution

Figure 5

Through-thickness longitudinal residual stress distribution

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Figure 6

Through thickness transverse residual stress distribution

Figure 6

Through thickness transverse residual stress distribution

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A few notes about the program are helpful. Its purpose is to make the computational part of the modified layer removal method easier for the user. Thus, while the graphics are neat looking for the transverse and longitudinal stress distributions for the example case, any new case may require 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 general procedures for using 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, Fig. 4. The values are plotted in Fig. 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 Fig. 5 and 6 are mentioned to help the user. The vertical axis of Fig. 3 shows the residual stress in psi. Positive numbers are tensile residual stresses and negative numbers are compressive residual stresses. The horizontal axis of Fig. 4 shows the distance from the coating surface. There is tension in the coating.

Notice there are 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. Recall that four specimens are recommended to examine reproducibility of the residual stresses. There can be specimen-to-specimen variation in the residual stress distributions. When this happens, data from the four 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 “grit blasting” 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.

This Accepted Practice is intended to be used as a baseline, but it does not replace local test or laboratory instructions. Additional requirements may apply based on the available equipment, testing materials, customer requirements, and other criteria.

This Accepted Practice document was approved for distribution by the ASM Thermal Spray Society Board of Directors on December 31, 2001. The document was created by the Thermal Spray Society Accepted Practice Committee on Evaluation of Mechanical Properties of Thermal Spray Coatings, with the following membership: 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 Engineering; Annie Savarimuthu, Hanover Corporation; Mark F. Smith, Sandia National Laboratories; David A. Somerville, Engelhard; Robert A. Sulit, Sulit Engineering; Jan Wigren, Volvo Aero Corporation.

The MLRM program is based on the analyses described in References [1] and [8]. Daniel Greving wrote the main computational program. The macros for the Excel program were written by Sulaiman Al-Musallami. Annie Savarimuthu created the graphics. All contributors named above were Mechanical Engineering graduate students at The University of Tulsa at the time the program was developed.

[1]
D.J.
 
Greving
,
E.F.
 
Rybicki
and
J.R.
 
Shadley
,
“Through-Thickness Residual Stress Evaluations for Several Industrial Thermal Spray Coatings Using a Modified Layer Removal Method”
,
Journal of Thermal Spray Technology
, Vol
3
, No.
4
,
December
1994
, p
379
-
388
[2]
L.
 
Pejryd
,
J.
 
Wigren
,
D.J.
 
Greving
,
J.R.
 
Shadley
and
E.F.
 
Rybicki
,
“Residual Stresses as a Factor in the Selection of Tungsten Carbide Coatings for a Jet Engine Application,”
Journal of Thermal Spray Technology
, Vol
4
, No.
3
,
September
1995
, p
268
-
274
.
[3]
R.T.R.
 
McGrann
,
D.J.
 
Greving
,
J.R.
 
Shadley
,
E.F.
 
Rybicki
and
B.E.
 
Bodger
“The Effect of Residual Stress in HVOF Tungsten Carbide Coatings on the Fatigue Life in Bending of Thermal Spray Coated Aluminum,”
Journal of Thermal Spray Technology
, Vol
7
, No.
4
,
December
1998
, p
546
-
552
[4]
R.T.R.
 
McGrann
,
J.R.
 
Shadley
,
E.F.
 
Rybicki
,
T.L.
 
Kruecke
and
B.E.
 
Bodger
“The Effect of Coating Residual Stress on the Fatigue Life of Thermal Spray Coated Steel and Aluminum,”
Journal of Surface and Coatings Technology
, Vol
108-109
(
1998
), p
59
-
64
[5]
D.J.
 
Greving
,
J.R.
 
Shadley
and
E.F.
 
Rybicki
“Effects of Coating Thickness and Residual Stresses on the Bond Strength of ASTM C633-79 Thermal Spray Coating Test Specimens,”
Journal of Thermal Spray Technology
, Vol
3
, No.
4
,
December
1994
, p
371
-
378
[6]
D.
 
Rosenthal
and
J.T.
 
Norton
“A Method of Measuring Triaxial Residual Stress in Plates,”
Welding Journal
, Vol
24
Research Supplement, p
295S
-
307S
,
May
1945
[7]
SAE Information Report
,
“Methods of Residual Stress Measurement,”
SAE J936,
December
1965
[8]
R.T.R.
 
McGrann
,
E.F.
 
Rybicki
and
J.R.
 
Shadley
“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 Linköping
,
Sweden
,
June
16
-
18
,
1997
[9]
R.T.R.
 
McGrann
,
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]
R.C.
 
McCune
,
W.R.
 
Donlon
,
E.L.
 
Cartwright
,
A.N.
 
Papyrin
,
E.F.
 
Rybicki
and
J.R.
 
Shadley
“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
), p
397
-
404
[12]
E.F.
 
Rybicki
,
J.R.
 
Shadley
,
Y.
 
Xiong
and
D.J.
 
Greving
“A Cantilever Beam Method for Evaluating Young’s Modulus and Poisson’s Ratio of Thermal Spray Coatings,”
Journal of Thermal Spray Technology
, Vol
4
, No.
4
,
December
1995
, p
377
-
383
[13]
R.M.
 
Jones
Mechanics of Composite Materials
(
NY
:
Hemisphere Publishing Corp
.,
1975
), p
170
-
1

The layer removal method, [6, 7] which was developed for a single material, has been modified to work with thermal spray coated materials. The modified layer removal method uses the mechanics of composite materials analysis for a two-material non-symmetric layered plate. [13]

The analysis is based on the free-body diagram shown in Fig. A1. 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 Fx by the force and moment equilibrium equations. The figure 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 A1

Free-body diagram for modified layer removal method applied to a thermal spray coated specimen

Figure A1

Free-body diagram for modified layer removal method applied to a thermal spray coated specimen

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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:
εx=εx0+Kxzεy=εy0+Kyz
(Eq A1)

where Kx and Ky are the curvatures.

For plane stress, the stress-strain equations are:
{σxσy}=E[1vv1]{εxεy}
(Eq A2)
where: E is the following function of the material properties:
Eb=Eb(1vb)forthesubstrate,andEc=Ec(1vc)forthecoating.
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:
{FxFy}=(H+h)2(H+h)2{σxσy}dzand{MxMy}=(H+h)2(H+h)2{σxσy}zdz
(Eq A3)
Substituting Eq A1 and Eq A2 into Eq A3 gives:
{FxFyMxMy}=[A11A12B11B12A12A22B12B22B11B12D11D12B12B22D12D22]{εx0εy0KxKy}
(Eq A4)
where:
A11=A22=EbH+Ech;A12=vbEbH+vcEch;B11=B22=(EcEb)Hh2;B12=(vcEcvbEb)Hh2;D11=D22=EbH12(H2+3(h)2)+Ech12((h)2+3H2)D12=vbEbH12(H2+3(h)2)+vcEch12((h)2+3H2)
Using Eq A1 and the strain readings at the strain gage to derive an equation for εx0 and εy0 gives:
εx0=ΔεxG+Kx(H+h2)εy0=ΔεyG+Ky(H+h2)
(Eq A5)

Eq A5 can be substituted into Eq A4 to eliminate εx0 and εy0.

The force and moment equilibrium equations are then used. These equations are:
{FxFyMxMy}={σx Lhσy Lhσy Lh(H+h+h2)σy Lh(H+h+h2)}
(Eq A6)

where σxL and σyL are the stresses in the layer removed.

Equation A6 and Eq A4, with the substitution of Eq A5, give four equations with four unknowns: two stresses and two curvatures, in terms of the change in strain at the gage and other specimen properties.

Equation A7 shows the four equations to be solved for the stresses in the layer removed.

[h0A11T+B11A12T+B120hA12T+B12A22T+B22Th0B11T+D11B12T+D120ThB12T+D12B22T+D22]{σxLσyLKxKy}=[A11A12A12A22B11B12B12B22]{ΔεxGΔεyG}where:  T= (H+h)2,andT=(H+h+h)2
(Eq A7)

Equation A7 is solved for the stress in the layer removed, σxL and σyL, and the change in Kx and Ky. Equation A5 can be used to find εx0 and εy0. Then the change in residual stresses in the remaining piece can be evaluated from Eq A2 and A1.

Using the modified layer removal method requires a fixture to hold the four specimens during polishing to remove each layer. Figure B1 is a drawing of the fixture with dimensions.

Figure B1

Dimensions of the residual stress specimen fixture in inches.

Figure B1

Dimensions of the residual stress specimen fixture in inches.

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