SIST-TP CEN/TR 13233:2007
(Main)Advanced technical ceramics - Notations and symbols
Advanced technical ceramics - Notations and symbols
This Technical Report defines the symbols to be used to represent physical, mechanical and thermal characteristics, as determined by methods described in relevant CEN publications, for advanced technical ceramics, including ceramic matrix composites. It is a guide for writing the symbols of quantities of these materials to avoid confusion in reporting measurements and characteristics of products.
Where possible, the definitions are in accordance with the relevant parts of ISO 31 and ISO 80000. In addition the symbols used in undertaking measurements of these characteristics are also defined.
Hochleistungskeramik - Benennungen und Formelzeichen
In dieser Europäischen Norm werden die Bezeichnungen und Formelzeichen zur Beschreibung der Prüfungen
und Prüfergebnisse der Klasse von Werkstoffen festgelegt, die unter die Bezeichnung Hochleistungskeramik
fallen und keramische Pulver, monolithische Keramik, keramische Schichten und Verbundwerkstoffe mit
keramischer Matrix einschließen. Außerdem wird die Schreibweise für Formelzeichen und Größen zur
Kennzeichnung der mechanischen und thermischen Eigenschaften dieser Werkstoffe angegeben. Besonders
für endlosfaserverstärkte Verbundwerkstoffe mit keramischer Matrix werden die Bezeichnungen definiert, die
für die zueinander rechtwinkligen Verstärkungsrichtungen 1, 2, 3 anzuwenden sind.
Céramiques techniques avancées - Notations et symboles
Le présent rapport technique définit les symboles a utiliser pour représenter les caractéristiques physiques, mécaniques et thermiques, telles que déterminées par les méthodes décrites dans les publications CEN applicables, pour les céramiques techniques avancées, y compris les composites a matrice céramique. Il s’agit d’un guide relatif aux regles d’écriture des symboles des grandeurs qui caractérisent les matériaux concernés et qui permettent d’éviter toute confusion en termes de notation des mesures et des caractéristiques des produits.
Dans toute la mesure du possible, les définitions sont conformes aux parties applicables de l’ISO 31 et de l’ISO 80000. Par ailleurs, les symboles utilisés pour la réalisation des mesures de ces caractéristiques sont également définis.
Sodobna tehnična keramika - Sistem simbolov in simboli
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST-TP CEN/TR 13233:2007
01-maj-2007
1DGRPHãþD
SIST ENV 13233:2000
6RGREQDWHKQLþQDNHUDPLND6LVWHPVLPERORYLQVLPEROL
Advanced technical ceramics - Notations and symbols
Hochleistungskeramik - Benennungen und Formelzeichen
Céramiques techniques avancées - Notations et symboles
Ta slovenski standard je istoveten z: CEN/TR 13233:2007
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
01.075 Simboli za znake Character symbols
81.060.30 Sodobna keramika Advanced ceramics
SIST-TP CEN/TR 13233:2007 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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TECHNICAL REPORT
CEN/TR 13233
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
February 2007
ICS 01.060; 01.075; 81.060.30 Supersedes ENV 13233:1998
English Version
Advanced technical ceramics - Notations and symbols
Céramiques techniques avancées - Notations et symboles Hochleistungskeramik - Benennungen und Formelzeichen
This Technical Report was approved by CEN on 25 December 2006. It has been drawn up by the Technical Committee CEN/TC 184.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, 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
© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 13233:2007: E
worldwide for CEN national Members.
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CEN/TR 13233:2007 (E)
Contents Page
Foreword. 3
1 Scope. 4
2 Normative references. 4
3 Symbols, units and notations. 4
3.1 General symbols. 4
3.2 Symbols and notations specific to ceramic matrix composites. 4
3.3 Symbols, definitions and units. 7
Bibliography . 17
2
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Foreword
This document (CEN/TR 13233:2007) has been prepared by Technical Committee CEN/TC 184
“Advanced technical ceramics”, the secretariat of which is held by BSI.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such
patent rights.
This document supersedes ENV 13233:1998.
3
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CEN/TR 13233:2007 (E)
1 Scope
This Technical Report defines the symbols to be used to represent physical, mechanical and thermal
characteristics, as determined by methods described in relevant CEN publications, for advanced
technical ceramics, including ceramic matrix composites. It is a guide for writing the symbols of
quantities of these materials to avoid confusion in reporting measurements and characteristics of
products.
Where possible, the definitions are in accordance with the relevant parts of ISO 31 and ISO 80000. In
addition the symbols used in undertaking measurements of these characteristics are also defined.
2 Normative references
Not applicable.
3 Symbols, units and notations
3.1 General symbols
Contrary to monolithic materials, continuous fibre reinforced ceramic matrix composites show a
directional dependence in their thermal and mechanical properties, because of their anisotropic
nature. A specific set of standards different from those for monolithic materials is required in order to
characterize these properties, both at room temperature and at the anticipated high application
temperatures. To allow adequate representation of the directional dependence, a notation convention
is needed to identify the reinforcement directions in a right-hand orthogonal coordinate system for
purposes of sampling test pieces and for the presentation of results.
3.2 Symbols and notations specific to ceramic matrix composites
The use of the subscripts 1, 2, 3 attached to the symbols used for mechanical properties makes it
possible to define the mechanical characteristics of a material along one of its principal directions. The
use of the subscripts (12, 13, 23) attached to the symbols used for mechanical properties makes it
possible to give a material characteristics in one of the principal planes, for example:
σ : tensile strength in the 1 direction;
1,t,m
G : shear modulus in the 12 plane.
12
Figures 1 to 4 give examples of denotation on long fibre ceramic matrix composite materials.
4
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3
2
1
Figure 1 — Schematic diagram of a 1D material (see 3.2 for reference to axes 1, 2 and 3)
3
2
1
Figure 2 — Schematic diagram of a 2D material (see 3.2 for reference to axes 1, 2 and 3)
5
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CEN/TR 13233:2007 (E)
Figure 3 — Schematic diagram of an xD (2 < x ≤ 3) material
1
2
3
Figure 4 — Schematic diagram of a 3D material (see 3.2 for reference to axes 1, 2 and 3)
6
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3.3 Symbols, definitions and units
Tables 1 to 4 give symbols, definitions and units generally used for quantities referred to in standards
for advanced technical ceramics.
NOTE The quantities listed are referred to in the standards given in the final column of each table, although
it is possible that the corresponding symbols have not been used. In this case, it is anticipated that they will be
incorporated in the next revision of the standard.
7
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CEN/TR 13233:2007 (E)
Table 1 — Symbols related to physical quantities
Physical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
3
Density Ratio of the mass of a body to its volume kg/m Applies to true density 623-2, 725-7,
ρ
of powders 1159-2
3
Apparent density Ratio of the mass of the body to its total kg/m Applies to compacted 725-10
ρ
a
volume powders
3
Bulk density ρ Ratio of the mass of the dry material of a kg/m Applies also to tapped 623-2, 725-8,
b
porous body to its volume bulk density of 1389
powders
Linear density t Ratio of the mass of a multifilament tow to its Tex Tex is the mass in 1007-2
length grams per 1 000 m
P
Porosity Ratio of the total volume of pores in a - 623-2, 1389
porous body to its total volume
Apparent porosity P Ratio of the volume of open pores to total - 623-2, 1389
a
volume
Grain size g Mean linear intercept grain size determined µm 623-2
mli
either by the line or circle method applied to
micrographs of polished cross-sections
Phase volume fraction V Fractional volume of phase of type j - 623-5
f,j
determined from micrographs of polished
cross-sections
8
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CEN/TR 13233:2007 (E)
Table 2 — Symbols related to geometrical quantities of test pieces
Geometrical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
Length
Total length l, l Total length of the test piece mm 843-1, 843-2
t
l
Initial length Initial length of test piece in thermal mm 821-1
0
expansion measurement
Gauge length L Initial distance between reference points on mm 658-1, 658-2,
0
the test piece in the calibrated length 1892, 1893
Distance between outer rollers L Outer support span in three or four-point mm In flexural strength and 658-3
a
bending configuration modulus testing
Distance between inner rollers L Inner loading span in four-point bending mm In flexural strength and 821-1, 843-1,
i
configuration modulus testing 843-2, 843-3,
658-3
2
Cross-section A Cross-section area mm
2
Initial cross-section area A Initial cross-section area of the test piece mm 1892
0
within the calibrated length at test
temperature
NOTE 1 When the material is protected by a surface treatment, two initial cross-section areas can be defined:
2
Apparent cross-section area A Geometrical area of the cross-section mm 1893
0,a
2
Effective cross-section area A Geometrical area corrected by a factor, to mm 1893
0,e
account for the presence of a surface
treatment
Distance between notches L In inter-laminar shear testing, the spacing mm 658-4, 1894
between opposed notches
Width and thickness
Width b Width of a test piece (normal to loading mm 658-3, 843-1,
direction in flexure) 843-2, 1892
9
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CEN/TR 13233:2007 (E)
Geometrical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
NOTE 2 When the material is protected by a surface treatment, two widths can be defined :
Apparent width b Geometrical width mm 1893
a
Effective width b Geometrical width corrected by a factor to mm 1893
e
account for the presence of a surface
treatment
NOTE 3 When width changes along the length, a numerical subscript is added to symbol b, b is the width in the calibrated length, b , b , . are the other widths. These
1 2 3
subscripts are defined in individual documents.
Thickness h Thickness or width of a test piece (parallel to mm 843-1, 843-2
the direction of loading in flexure)
Thickness of test piece mm 821-2
NOTE 4 When the material is protected by a surface treatment, two thicknesses can be defined:
h
Apparent thickness Geometrical thickness mm 1893
a
Effective thickness h Geometrical thickness corrected by a factor mm 1893
e
to account for the presence of a surface
treatment
NOTE 5 When thickness changes along the length, a numerical subscript is added to symbol h, h is the thickness in the calibrated length
1
h , h , . are the other thicknesses. These subscripts are defined in individual documents.
2 3
Indentation diagonal length (in hardness In hardness testing, the lengths of the mm 843-4
δ
testing) diagonals of a Vickers indentation or long
axis of a Knoop indentation
Initial crack or notch depth a In fracture toughness testing, the length of mm 14425-3
0
the initial crack or notch
Deflection
Flexural deflection d Displacement of the loading points relative mm Used with various 843-2
to the support points (or any other reference subscripts
points) in flexure
Mass
10
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CEN/TR 13233:2007 (E)
Geometrical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
Mass m Quantity of matter in a body g 623-2, 843-2
Diameter
Diameter d Diameter of the test piece in the calibrated mm 1892
length
NOTE 6 When the material is protected by a surface treatment, two diameters can be defined:
Apparent diameter d Geometrical diameter mm 1893
a
Effective diameter d Geometrical diameter corrected by a factor mm 1893
e
to account for the presence of a surface
treatment
NOTE 7 When diameter changes along the length, a numerical subscript is added to symbol d, d is the diameter in the calibrated length, d , d . are the other diameters.
1 2 3
These subscripts are defined in individual documents.
Blend radius r Transition radius between parts of the mm The type of radius can 1892
specimen with different cross-section be defined in each
document by use of a
subscript
11
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CEN/TR 13233:2007 (E)
Table 3 — Symbols related to mechanical quantities
Mechanical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
Deformation
Flexural deformation Flexural deflection, as defined in each case mm 820-4, 820-5
δ
843-2
Longitudinal deformation ∆L Variation in the gauge length caused by an mm Tensile/compressive 658-1
applied load. Variation is positive in tensile test 658-2
and negative in compressive test 1892
Longitudinal tensile deformation at ∆L Value of longitudinal tensile deformation mm 658-1
t,m
maximum force corresponding to the maximum force 1892
Longitudinal compressive deformation at ∆L Value of longitudinal compressive mm 658-2
c,m
maximum force deformation corresponding to the maximum
force
Strain
ε
Strain Relative change in the gauge length defined - Tensile/compressive 658-1
test 1892
as the ratio ∆L/L
0
Tensile strain at maximum force ε Value of strain corresponding to the - 658-1
t,m
maximum tensile force 658-2
Compressive strain at maximum force ε Value of strain corresponding to the - 658-1
c,m
maximum compressive force 658-2
Shear strain γ The change in angle of an originally -
orthogonal set of lines as a consequence of
a shear load
Force
Force F Force applied to the test piece during the N 658-1, 820-4,
test 820-5, 843-1,
843-2, 1892,
1893
12
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CEN/TR 13233:2007 (E)
Mechanical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
Peak force at fracture F Maximum force during a test or at fracture N 843-3
m
Stress and strain
Stress (tensile/compressive/shear) Ratio of the force carried by the test piece at MPa Sign convention – 658-1
σ
any time in the test by the initial cross- tensile is positive, 843-1
section area compression is 843-2
negative 843-5
Strain (tensile/compressive) ε Fractional increase in dimension of a body -
1892
subjected to stress
Shear strain The change in angle of an originally -
γ
orthogonal set of lines as a consequence of
a shear load
Flexural stress The nominal stress on the outer surface of MPa 658-3
σ
the test piece, calculated at mid span
In plane shear stress Ratio of the force carried by the test piece by MPa 12289
τ
the initial cross-section subjected to shear
Stressing rate Rate of change of stress with time MPa/s 843-3
σ&
Strength
Strengths correspond to stresses at maximum force during a test carried out to rupture
Tensile strength Ratio of the maximum tensile force to the MPa 658-1
σ
t,m
initial cross-section area
Compressive strength σ Ratio of the maximum compressive force to MPa 658-2
c,m
the initial cross-section area
Flexural strength Maximum flexural stress applied to a test MPa 658-3
σ
f,m
piece that fractures during a flexural test
Interlaminar shear strength Ratio of the maximum force applied to the MPa 12289
σ
ILSS
initial cross-section area
13
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CEN/TR 13233:2007 (E)
Mechanical quantities
Quantity Symbol Definition Unit Remark Relevant EN,
ENV or
CEN/TS
In plane shear strength τ Ratio of the maximum force applied to the MPa 658-4, 658-5,
m
initial cross-section area 658-6, 12289
NOTE 1 The symbols listed here for mechanical quantities at rupture (strength and strain) have a first subscript indicating the type of test (t for tensile, c for compressive, f for
flexure).
A second subscript, m is added to indicate the maximum value. Other subscripts may be added to refer to test conditions (for example temperature). These additional subscripts
are set between brackets.
EXAMPLE 1 σ = tensile strength at 1 500 °C under vacuum
t, m (1500)(vacuum)
Elastic properties
Elastic modulus tensile/compressive E Slope of the linear part of the stress strain GPa
658-1, 658-2,
(Young Modulus) curve when the linear part starts at the origin
1892, 12289
G
Elastic modulus in shear Slope of the linear part of the shear stress GPa
843-2
strain curve when the linear part starts at the
origin
NOTE 2 When the material is protected by a surface treatment, two types of mechanical quantities can be considered to determine whether the apparent or effective cross-
section area is used:
The subscript 'a' for apparent is added when the apparent cross-section area is used.
The subscript 'e' for effective is added when the effective cross-section area is used.
EXAMPLE 2 σ = effective tensile strength
t,m,e
Proportionality Coefficient Or Pseudo Modulus
Proportionality coefficient in Slope of a linear portion of the stress strain GPa The quantity is used for 658-1, 658-2,
E (σ ,σ )
p 1 2
tensile/compressive materials which do not 1892, 12289
curve between 2 values (σ , σ )
1 2
have a linear behaviour
Proportionality coefficient in shear G (τ ,τ ) Slope of a linear portion of the shear stress GPa
p 1 2
at the origin
shear strain curve between 2 values (σ , σ )
1 2
Poisson ratio Ratio of lateral strain to axial strain in axially - 843-2
ν
stressed body
Mode of vibration n Modal analysis is used to characterize -
resonant vibration in machinery and
structures. A mode of vibration is def
...
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