ISO 19674:2025

International
Standard
ISO 19674
Second edition
Fine ceramics (advanced ceramics,
2025-06
advanced technical ceramics) —
Methods of test for ceramic coatings
— Determination of internal stress
in ceramic coatings by application
of the Stoney formula
Céramiques fines (céramiques avancées, céramiques techniques
avancées) — Méthodes d'essai des revêtements céramiques
— Détermination de la contrainte interne des revêtements
céramiques par application de la formule de Stoney
Reference number
© ISO 2025
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle . 1
5 Apparatus . 2
6 Preparation of test specimens . 3
6.1 Material .3
6.2 Sample geometry .3
6.3 Sample surface finish . .3
6.4 Sample dimensions .3
7 Procedure . 4
7.1 Measuring range and initial profile .4
7.2 Deposition of the coating .4
7.3 Coating thickness .5
7.4 Adjusting the sample geometry after deposition of the coating .5
7.5 Measuring the final profile .5
7.6 Calculation of stress .6
7.6.1 h / h < 0,02 .6
f s
7.6.2 0,02 ≤ h / h < 0,1 .7
f s
7.7 Number of repeat measurements .7
8 Limits to method . 7
9 Test report . 7
Annex A (informative) Determination of suitable dimensions for the test sample . 9
Annex B (informative) Internal stress calculation in ceramic coating of real components .11
Bibliography .13

iii
Foreword
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This document was prepared by Technical Committee ISO/TC 206, Fine ceramics.
This second edition cancels and replaces the first edition (ISO 19674:2017), which has been technically
revised.
The main changes are as follows:
— in the Scope, the substrate is limited to isotropic ones;
— in Clause 5, the contents of EXAMPLE are all deleted due to an incorrect Formula (2) and its weak
correlation;
— in 7.5, the calculation for R has been revised;
exp
— at the end of 7.5, a schematic diagram (Figure 1) and an approximate calculation of R from deflection
exp
has been added and the formula renumbered to Formula (3);
— Annex B has been added.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
There is an increasing use of coatings to improve the functional performance of materials and components.
This can be to protect against damage due to exposure to demanding environments including high stresses
and aggressive chemical environments, but can also be to modify many other properties, e.g. thermal
conductivity through thermal barrier coatings, friction through low friction coatings, such as diamond like
carbon (DLC), and optical reflectivity through coatings with controlled optical properties.
Appropriate choice of coatings for particular applications depends on the mechanical and other functional
requirements that arise. One factor that can be crucial in determining coating performance and lifetime
is the residual stress that is generated by the deposition process and/or by thermal expansion mismatch
between the coating and the substrate as the component is cooled from the processing temperature.
This document describes the application of a simple experimental technique using the Stoney formula to
analyse the coating induced bending of coupons, of known mechanical properties, to determine the residual
stress in the coating.
v
International Standard ISO 19674:2025(en)
Fine ceramics (advanced ceramics, advanced technical
ceramics) — Methods of test for ceramic coatings —
Determination of internal stress in ceramic coatings by
application of the Stoney formula
1 Scope
This document specifies a method for determination of the internal stress in thin ceramic coatings. The
internal stress is determined by application of the Stoney formula to the results obtained from measurement
of the radius of curvature of isotropic strips or discs with single-face coating.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 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-characterized
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 7.6) without
the need to know the elastic properties of the coating material.
The technique does require accurate knowledge of the thickness of the coating, the thickness of the
substrate, and 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 ISO 18452),
[4]
crater grinding (see ISO 26423), and cross-sectioning (see EN 1071-10 ).
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
0 exp
[6]
application of the Stoney formula as shown in Formula (1):
Eh
1 1
s s
σ =− (1)
61−ν hR
s fexp
where
h is the thickness of the coating;
f
h is the thickness of the substrate;
s
E is Young’s modulus of the substrate;
s
R is the radius of curvature;
exp
ν is Poisson’s ratio of the substrate.
s
NOTE 2 σ is the mean value of the local stress through the thickness of the coating (h << h ):
0 f s
h
f
σσ= z dz (2)
()
0 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
5 Apparatus
The profile can be measured by means of an optical profilometer, a high magnification optical microscope
(resolution in the order of 1 μm), laser measurement system (resolution in the order of 5 μm), equipped with
an accurate (better than 5 μm resolution) position sensor along the focusing direction and a micrometer
(1 μm resolution) equipped with a translation stage (10 μm resolution), 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, care should be taken 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 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 should 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.
NOTE If measurements are to be made during the deposition process or in other cases where the sample is not
accessible, e.g. while 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, please note 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 can be possible for some coating to be deposited
on the back surface, thus reducing the curvature that would otherwise be measured.

6 Preparation of test specimens
6.1 Material
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-
characterized material is a prerequisite for the method.
6.2 Sample geometry
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 such
as elastic modulus and Poisson's ratio 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.
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.
6.3 Sample surface finish
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 before
coating, the surface finish produced by careful grinding on 1 200 grit emery paper or diamond paste with
the same fineness is a minimum requirement.
6.4 Sample dimensions
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.
The elastic/plastic characteristics of the substrate material 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
σ
y
done with the (σ = yield stress, E = Young’s modulus) ratio of the substrate material determine at those
y
E
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 values for the coefficient of thermal expansion of both substrate
and coating.
Where coating materials with anisotropic properties, e.g. those with HCP crystallography, are the subject
of test, it is necessary to determine any crystallographic preferred orientation in the coating resulting from
the deposition process.
7 Procedure
7.1 Measuring range and initial profile
Before depositing the coating, it is necessary to determ
...