SIST-TS CEN/TS 1071-11:2006

Advanced technical ceramics - Methods of test for ceramic coatings - Part 11: Determination of internal stress by the Stoney formula

This Technical Specification specifies a method for the determination of the internal stress in thin ceramic coatings by application of the Stoney formula to the results obtained from measurement of the radius of curvature of coated strips or discs.

Hochleistungskeramik - Verfahren zur Prüfung keramischer Schichten - Teil 11: Bestimmung der inneren Spannung nach der Stoney-Gleichung

Diese Technische Spezifikation legt ein Verfahren zur Bestimmung der inneren Spannung in dünnen keramischen Schichten fest, indem die Stoney Gleichung auf die Ergebnisse aus der Messung des Krümmungsradius angewendet wird, der durch die Beschichtung von streifen  oder scheibenförmigen Proben entsteht.

Céramiques techniques avancées - Méthodes d'essais pour revetements céramiques - Partie 11 :Détermination de la contrainte interne par la formule de Stoney

Sodobna tehnična keramika – Preskusne metode za keramične prevleke – 11. del: Določanje notranjih napetosti po formuli Stoney

General Information

• Status: Published
• Publication Date: 30-Jun-2006
• ICS: 25.220.99 - Other treatments and coatings
• ICS: 81.060.30 - Advanced ceramics
• Technical Committee: I13 - Imaginarni 13
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 01-Jul-2006
• Due Date: 01-Jul-2006
• Completion Date: 01-Jul-2006
• Ref Project: CEN/TS 1071-11:2005 - Advanced technical ceramics - Methods of test for ceramic coatings - Part 11: Determination of internal stress by the Stoney formula

Overview

CEN/TS 1071-11:2005 specifies a test method to determine internal stress in thin ceramic coatings using the Stoney formula. The method calculates coating stress from measurements of the radius of curvature of coated strips or discs. It is intended for advanced technical ceramics and thin-film ceramic coatings where the coating is significantly thinner than the substrate.

Key topics

• Principle: Stress in the coating is deduced from substrate curvature after single-sided coating, using the Stoney equation: σ ≈ −(E_s · h_s^2) / [6 · (1 − ν_s) · h_f · R_exp] where σ = mean film stress, E_s = substrate Young’s modulus, ν_s = substrate Poisson’s ratio, h_f = coating thickness, h_s = substrate thickness, R_exp = measured radius of curvature.
• Assumptions & limits:
  • Coating thickness < 2% of substrate thickness (h_f << h_s).
  • Curvature should be approximately spherical.
  • Deformation must remain elastic (no plastic substrate deformation).
  • If measurement temperature differs from deposition temperature, results include thermal mismatch stress.
• Specimen preparation:
  • Use well-characterised, stress-free substrates (anneal if necessary).
  • Preferred geometry: strip samples; discs are also allowed.
  • Surface finish should support accurate curvature measurement (minimum 1 200 grit for general tests).
• Measurement apparatus:
  • Optical profilometer, high-magnification optical microscope with precise focusing position sensor, contact probe profilometer (with minimal load), or optical bench / Newton’s rings for polished discs.
  • For in-situ or inaccessible samples, laser-deflection optical lever techniques on clamped strips are possible (with caveats).
• Data requirements:
  • Accurate coating thickness (EN 1071-1, -2, -10 referenced), substrate thickness, E and ν for substrate, and measured curvature profile over a defined measuring range.

Applications

• Quantifying residual/internal stress in thin ceramic films used in cutting tools, wear-resistant components, thermal barrier coatings, MEMS, and optical coatings.
• Supporting coating development, process optimization (deposition temperature, thickness), failure analysis, and stress-driven performance modelling.
• Useful in laboratories performing thin film characterization, quality control for coated components, and research on ceramic coating mechanics.

Who should use this standard

• Materials scientists, coating engineers, failure analysts, and test laboratories involved with advanced technical ceramics and thin-film coatings.
• Laboratories aiming for traceable, comparable stress measurements (complements EN ISO/IEC 17025 competence requirements).

Related standards

• EN 1071 series (Parts 1–10: coating thickness, adhesion, porosity, hardness, etc.)
• CEN/TS 1071-10 (cross section thickness measurement)
• EN ISO/IEC 17025 (laboratory competence)

Keywords: advanced technical ceramics, ceramic coatings, internal stress, Stoney formula, radius of curvature, thin films, coating stress measurement, profilometer, substrate Young’s modulus.

Standards Content (Sample)

SLOVENSKI STANDARD
01-julij-2006
6RGREQDWHKQLþQDNHUDPLND±3UHVNXVQHPHWRGH]DNHUDPLþQHSUHYOHNH±GHO
'RORþDQMHQRWUDQMLKQDSHWRVWLSRIRUPXOL6WRQH\
Advanced technical ceramics - Methods of test for ceramic coatings - Part 11:
Determination of internal stress by the Stoney formula
Hochleistungskeramik - Verfahren zur Prüfung keramischer Schichten - Teil 11:
Bestimmung der inneren Spannung nach der Stoney-Gleichung
Céramiques techniques avancées - Méthodes d'essais pour revetements céramiques -
Partie 11 :Détermination de la contrainte interne par la formule de Stoney
Ta slovenski standard je istoveten z: CEN/TS 1071-11:2005
ICS:
25.220.99 Druge obdelave in prevleke Other treatments and
coatings
81.060.30 Sodobna keramika Advanced ceramics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

TECHNICAL SPECIFICATION
CEN/TS 1071-11
SPÉCIFICATION TECHNIQUE
TECHNISCHE SPEZIFIKATION
October 2005
ICS 81.060.30
English Version
Advanced technical ceramics - Methods of test for ceramic
coatings - Part 11: Determination of internal stress by the
Stoney formula
Céramiques techniques avancées - Méthodes d'essais Hochleistungskeramik - Verfahren zur Prüfung keramischer
pour revêtements céramiques - Partie 11 :Détermination de Schichten - Teil 11: Bestimmung der inneren Spannung
la contrainte interne par la formule de Stoney nach der Stoney-Gleichung
This Technical Specification (CEN/TS) was approved by CEN on 8 August 2005 for provisional application.
The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to submit their
comments, particularly on the question whether the CEN/TS can be converted into a European Standard.
CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS available
promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the CEN/TS)
until the final decision about the possible conversion of the CEN/TS into an EN is reached.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TS 1071-11:2005: E
worldwide for CEN national Members.

Contents Page
Foreword .3
1 Scope .4
2 Normative references .4
3 Principle.4
4 Apparatus .5
5 Preparation of test specimens .6
6 Procedure .6
7 Limits to method .9
8 Test report .10
Annex A (informative) Determination of suitable dimensions for the test sample.11
Bibliography.13

Foreword
This CEN Technical Specification (CEN/TS 1071-11:2005) has been prepared by Technical Committee
CEN/TC 184 “Advanced technical ceramics”, the secretariat of which is held by BSI.
EN 1071 Advanced technical ceramics — Methods of test for ceramic coatings consists of 11 parts:
Part 1: Determination of coating thickness by contact probe filometer
Part 2: Determination of coating thickness by the crater grinding method
Part 3: Determination of adhesion and other mechanical failure modes by a scratch test
Part 4: Determination of chemical composition by electron probe microanalysis (EPMA)
Part 5: Determination of porosity
Part 6: Determination of the abrasion resistance of coatings by a micro-abrasion wear test
Part 7: Determination of hardness and Young's modulus by instrumented indentation testing
Part 8: Rockwell indentation test for evaluation of adhesion
Part 9: Determination of fracture strain
Part 10: Determination of coating thickness by cross sectioning
Part 11: Measurement of internal stress by the Stoney formula
Parts 5 to 6 are European prestandards.
Parts 7 to 11 are Technical Specifications.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to announce this CEN Technical Specification: Austria, Belgium, Cyprus, Czech Republic,
Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland
and United Kingdom.
1 Scope
This Technical Specification specifies a method for the determination of the internal stress in thin ceramic
coatings by application of the Stoney formula to the results obtained from measurement of the radius of
curvature of coated strips or discs.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
EN ISO/IEC 17025, General requirements for the competence of testing and calibration laboratories (ISO/IEC
17025:2005)
3 Principle
Coating stress often plays a major role in the performance of coated tools and machine parts. Different
techniques have been developed for the determination of coating stress. The technique considered in this
document calculates the stress from measurement of the bowing of thin discs or strips of well characterised
materials of known thickness that have been coated on one side only. It is assumed that the deformation is
elastic, i.e. if the coating were to be removed, the substrate would return to its initial shape.
Provided that the coating is thin compared to the thickness of the substrate (coating thickness < 2 % of substrate
thickness); that the curvature has a spherical form; and that the substrate was initially flat or of known curvature,
then the stress in the coating can be calculated using the Stoney formula (see 6.6) without the need to know the
elastic properties of the coating material.
The technique requires an accurate knowledge of the thickness of the coating, the thickness of the substrate,
and the Young’s modulus and Poisson’s ratio of the substrate material.
NOTE 1 Coating thickness can be determined by techniques such as step height measurement (see EN 1071-1 [1]),
crater grinding (see EN 1071-2 [2]) and cross sectioning (see CEN/TS 1071-10 [3]).
As ceramic coatings are normally deposited at elevated temperatures, the stress determined at any other
temperature will be a combination of the intrinsic growth stress and stress introduced by virtue of the difference
in thermal expansion between the coating and the substrate.
The internal stress σ in the coating is deduced from the measured radius of curvature R , through the
o exp
application of the Stoney formula [4]:
1 E h 1
s s
σ = −
o
6 1−ν h R
s f exp
where and h denote the thickness of the coating and substrate respectively, and where E and ν
h
s
f s s
denote Young's modulus and Poisson's ratio of the substrate respectively.
NOTE 2 σ is the mean value of the local stress through the thickness of the coating (h < o f s
h
1 f
σ = σ (z)dz
o f
∫
h
f
where σ (z) is the film stress as a function of position perpendicular to the plane of the substrate.
f
The radius of curvature R is obtained from the profile of the sample.
exp
4 Apparatus
The profile can be measured by means of an optical profilometer, a high magnification optical microscope
(resolution in the order of 1 µm), equipped with an accurate (better than 5 µm resolution) position sensor
along the focusing direction and a micrometer equipped translation stage, or other suitable technique. For a
disc shaped sample with a polished surface, e.g. a circle cut from a polished silicon wafer, the radius of
curvature can be obtained by treating it as a convex or concave mirror and measured using an optical bench
or other suitable technique, e.g. by the use of Newton’s rings. However, in all cases it is essential to ensure
that the measurement technique used does not alter the profile of the sample.
Where a microscope with a translation stage is used for the measurement, care shall be taken to ensure that
the stage is level with respect to the perpendicular to the optical axis. The simplest way to check this is to
ensure that the surface of the translation stage remains in focus over a distance equivalent to the overall
length of the sample, with the microscope at its highest magnification. For all measurement methods, care
shall be taken to ensure that they are calibrated and traceable to national standards.
If a contact probe profilometer is to be used, care shall be taken to use the lowest load possible,
commensurate with obtaining an accurate result, in order to avoid the contact force changing the profile of the
sample.
EXAMPLE The deflection of a beam, supported at its extremities, by the application of a load in the central zone is:
FL
δ =
48EI
bt
where L is the length of the beam, F the applied load, E is Young's modulus and I = (b = width and t = thickness).
Thus, for an Al substrate for which E = 70 GPa, L = 100 mm, b = 10 mm and t = 0,5 mm, replacing these values in the
formulae gives:
-3
δ = 4,8 x 10 F (m)
For a 0,75 mN force (see EN ISO 3274 [5]), the deflection will be 3,6 microns, i.e. an error of ~ 0,5 % for a
total deflection of 1 mm. It should be noted that, with this beam geometry, a total deflection of 1 mm
corresponds to a curvature radius of 1,7 m and for this substrate thickness such a deflection can be reached
by a 1 micron film with a 2,45 GPa residual stress.
NOTE If measurements are to be made during the deposition process or in other cases where the sample is not
accessible, e.g. whilst it is held in a furnace in order to investigate thermal stress relief, it is possible to use a strip sample
that is clamped at one end. The change in bowing can then be determined by treating the sample as an optical lever and
measuring the deflection of a known point by use of a laser and suitable scale. However, it should be appreciated that the
use of a sample that is free to bend during the coating deposition will result in the calculated stress being different from
that determined using a fully clamped sample as the deposition conditions, particularly temperature, will be different in the
two cases. In addition, as the sample begins to bend it may be possible for some coating to be deposited on the back
surface thus reducing the curvature that would otherwise be measured.
5 Preparation of test specimens
As the test method depends upon the determination of the curvature introduced into a substrate by the
intrinsic stresses in a coating deposited thereon, the use of a test specimen manufactured from a well-
characterised material is a prerequisite for the method.
Test specimens with a strip-shaped geometry are to be preferred, but specimens in the form of a disc can be
used. The test specimen shall be manufactured from a material of known mechanical properties that will not
be affected by any elevated temperature experienced during the coating process. It shall have a uniform
thickness and shall be in a stress free state prior to the deposition of the coating.
NOTE 1 If necessary, test specimens should be annealed at a temperature above the coating temperature prior to
coating deposition in order to remove stresses induced by the manufacturing process, e.g. from rolling, grinding or
polishing.
Test specimens shall have a surface finish on the side to be coated that is commensurate with accurate
measurement of the radius of curvature produced by the coating. Where the value of internal stress obtained
in the test will be used for modelling with real components, care shall be taken to ensure that the surface
texture of the test specimen is close to that of these real components. For all other test specimens the surface
finish produced by careful grinding on 1 200 grit emery paper is a minimum requirement.
The dimensions of the sample shall be chosen such that the radius of curvature after coating, R , is as low
exp
as possible to improve the accuracy of the measurement. However, care should be taken in order not to have
plastic deformation of the substrate. This may require that initial testing be done to obtain an approximate
value for the stress in order that the test specimen dimensions can be selected more accurately.
NOTE 2 The elastic/plastic characteristics of the substrate materials depend on the temperature. Thus, to avoid plastic
deformation, if depositions are performed with substrate heating and/or coated samples are submitted to annealing at high
temperatures, the estimations for the admissible radius values should be done with the σ /E (σ = yield stress, E =
y y
Young's modulus) ratio of the substrate material determined at those temperatures (see Annex A).
Where measurement of the curvature is made at a temperature different from that at which the deposition is
made, the measured stress will be a combination of intrinsic growth stresses and those resulting from
differential thermal expansion between substrate and coating. In such cases computation of the coating
intrinsic stress requires knowledge of the valu
...