Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BRITISH STANDARD BS EN 15305:2008 Incorporating corrigendum January 2009 Non-destructive Testing — Test Method for Residual Stress analysis by X-ray Diffraction ICS 19.100 NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAW Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 National foreword This British Standard is the UK implementation of EN 15305:2008, incorporating corrigendum January 2009 The UK participation in its preparation was entrusted to Technical Committee WEE/46, Non-destructive testing A list of organizations represented on this committee can be obtained on request to its secretary This publication does not purport to include all the necessary provisions of a contract Users are responsible for its correct application Compliance with a British Standard cannot confer immunity from legal obligations This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 September 2008 © BSI 2009 ISBN 978 580 66870 Amendments/corrigenda issued since publication Date Comments 30 June 2009 Implementation of CEN corrigendum January 2009 Modification of the fourth paragraph of the CEN Foreword Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI EUROPEAN STANDARD EN 15305 NORME EUROPÉENNE EUROPÄISCHE NORM August 2008 Incorporating corrigendum January 2009 ICS 19.100 English Version Non-destructive Testing - Test Method for Residual Stress analysis by X-ray Diffraction Essais non-destructifs - Méthode d'essai pour l'analyse des contraintes résiduelles par diffraction des rayons X Zerstörungsfreie Prüfung - Röntgendiffraktometrisches Prüfverfahren zur Ermittlung der Eigenspannungen This European Standard was approved by CEN on July 2008 CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN Management Centre or to any CEN member This European Standard exists in three official versions (English, French, German) A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the official versions 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 © 2008 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members B-1050 Brussels Ref No EN 15305:2008: E Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Contents Page Foreword Introduction Scope Normative references 3.1 3.2 Terms, definitions and symbols Terms and definitions Symbols and abbreviations 4.1 4.2 4.3 Principles 10 General principles of the measurement 10 Biaxial stress analysis 12 Triaxial stress analysis .13 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.2 5.2.1 5.2.2 5.2.3 Specimen 14 Material characteristics .14 General 14 Shape, dimensions and weight 15 Specimen composition/homogeneity 15 Grain size and diffracting domains 16 Specimen X-ray transparency 16 Coatings and thin layers .16 Preparation of specimen 17 Surface preparation .17 Stress depth profiling 17 Large specimen or complex geometry 17 6.1 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.3 6.4 6.5 6.5.1 6.5.2 6.6 6.6.1 6.6.2 6.6.3 Equipment 17 General 17 Choice of equipment 18 General 18 The ω-method .19 The χ-method .20 The modified χ-method .21 Other geometries 21 Choice of radiation 21 Choice of the detector 23 Performance of the equipment 24 Alignment .24 Performance of the goniometer 24 Qualification and verification of the equipment .24 General 24 Qualification 24 Verification of the performance of the qualified equipment 26 7.1 7.2 7.3 7.4 Experimental Method 27 General 27 Specimen positioning 27 Diffraction conditions 28 Data collection .29 8.1 8.2 8.2.1 Treatment of the data 30 General 30 Treatment of the diffraction data 30 General 30 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) 8.2.2 8.2.3 8.2.4 8.3 8.3.1 8.3.2 8.4 8.4.1 8.4.2 8.4.3 Intensity corrections 30 Determination of the diffraction line position 31 Correction on the diffraction line position 32 Stress calculation 32 Calculation of strains and stresses 32 Errors and uncertainties [16], [17] .33 Critical assessment of the results .34 General 34 Visual inspection 34 Quantitative inspection .34 Report 35 10 10.1 10.2 10.3 10.4 10.5 10.6 Experimental determination of XECs 36 Introduction 36 Loading device 37 Specimen 37 Loading device calibration and specimen accommodation 38 Diffractometer measurements 38 Calculation of XECs 38 11 11.1 11.2 11.2.1 11.2.2 11.2.3 11.3 11.3.1 11.3.2 Reference specimens 39 Introduction 39 Stress-free reference specimen 39 General 39 Preparation of the stress-free specimen 39 Method of measurement .40 Stress-reference specimen 40 Laboratory qualified (LQ) stress-reference specimen 40 Inter-laboratory qualified (ILQ) stress-reference specimen 41 12 12.1 12.2 12.3 12.4 12.5 12.6 12.6.1 12.6.2 12.7 Limiting cases 41 Introduction 41 Presence of a subsurface stress gradient 42 Surface stress gradient .42 Surface roughness 42 Non-flat surfaces 42 Effects of specimen microstructure 43 Textured materials .43 Multiphase materials 43 Broad diffraction lines 44 Annex A (informative) Schematic representation of the European XRPD Standardisation Project 46 Annex B (informative) Sources of Residual Stress .47 B.1 General 47 B.2 Mechanical processes 47 B.3 Thermal processes 47 B.4 Chemical processes 47 Annex C (normative) Determination of the stress state - General Procedure 48 C.1 General 48 C.2 Using the exact definition of the deformation 49 C.2.1 General 49 C.2.2 Determination of the stress tensor components .49 C.2.3 Determination of θ and d0 50 C.3 Using an approximation of the definition of the deformation .50 C.3.1 General 50 C.3.2 Determination of the stress tensor components .51 C.3.3 Determination of θ0 and d0 51 Annex D (informative) Recent developments .52 D.1 Stress measurement using two-dimensional diffraction data 52 D.2 Depth resolved evaluation of near surface residual stress - The Scattering Vector Method 54 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) D.3 Accuracy improvement through the use of equilibrium conditions for determination of stress profile 55 Annex E (informative) Details of treatment of the measured data .56 E.1 Intensity correction on the scan 56 E.1.1 General 56 E.1.2 Divergence slit conversion 56 E.1.3 Absorption correction 57 E.1.4 Background correction .58 E.1.5 Lorentz-polarisation correction 58 E.1.6 K-Alpha2 stripping .59 E.2 Diffraction line position determination 59 E.2.1 Centre of Gravity methods 59 E.2.2 Parabola Fit 60 E.2.3 Profile Function Fit 60 E.2.4 Middle of width at x% height method 61 E.2.5 Cross-correlation method 61 E.3 Correction on the diffraction line position 61 E.3.1 General 61 E.3.2 Remaining misalignments 61 E.3.3 Transparency correction 62 Annex F (informative) General description of acquisition methods 64 F.1 Introduction 64 F.2 Definitions 64 F.3 Description of the various acquisition methods 67 F.3.1 General method 67 F.3.2 Omega (ω ω) method .68 F.3.3 Chi (χ χ) method 69 F.3.4 Combined tilt method (also called scattering vector method) 71 F.3.5 Modified chi method 73 F.3.6 Low incidence method 76 F.3.7 Modified omega method .77 F.3.8 Use of a 2D (area) detector 78 F.4 Choice of Φ and Ψ angles 79 F.5 The stereographic projection .80 Annex G (informative) Normal Stress Measurement Procedure" and "Dedicated Stress Measurement Procedure 82 G.1 Introduction 82 G.2 General 82 G.2.1 Introduction 82 G.2.2 Normal stress measurement procedure for a single specimen 82 G.2.3 Dedicated Stress Measurement Procedure for very similar specimens 82 Bibliography 84 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Foreword This document (EN 15305:2008) has been prepared by Technical Committee CEN/TC 138 “Non-destructive testing”, the secretariat of which is held by AFNOR This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by February 2009, and conflicting national standards shall be withdrawn at the latest by February 2009 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 The topic "Non destructive testing – X-ray diffraction from polycrystalline and amorphous material" is considered in the present document and several other European Standards, namely: ⎯ EN 13925-1, General principles; ⎯ EN 13925-2, Procedures; ⎯ EN 13925-3, Instruments; ⎯ EN 1330-11, Non-destructive testing – Terminology – Terms used in X-ray diffraction from polycrystalline and amorphous materials In order to explain the relationship between the topics described in the different standards, a diagram illustrating typical operation involved in XRPD is given in Annex A According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: 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 the United Kingdom Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Introduction Residual strains in crystalline materials may be determined by X-ray diffraction analysis Assuming linear elastic distortions, the related residual stresses are calculated In this document the principles of the measure procedure and the analysis technique are described Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Scope This European Standard describes the test method for the determination of macroscopic residual or applied stresses non-destructively by X-ray diffraction analysis in the near-surface region of a polycrystalline specimen or component All materials with a sufficient degree of crystallinity can be analysed, but limitations may arise in the following cases (brief indications are given in Clause 12): Stress gradients; Lattice constants gradient ; Surface roughness; Non-flat surfaces (see 5.1.2); Highly textured materials; Coarse grained material (see 5.1.4); Multiphase materials; Overlapping diffraction lines; Broad diffraction lines The specific procedures developed for the determination of residual stresses in the cases listed above are not included in this document The method described is based on the angular dispersive technique with reflection geometry as defined by EN 13925-1 The recommendations in this document are meant for stress analysis where only the diffraction line shift is determined This European Standard does not cover methods for residual stress analyses based on synchrotron X-ray radiation and it does not exhaustively consider all possible areas of application Radiation Protection Exposure of any part of the human body to X-rays can be injurious to health It is therefore essential that whenever X-ray equipment is used, adequate precautions should be taken to protect the operator and any other person in the vicinity Recommended practice for radiation protection as well as limits for the levels of X-radiation exposure are those established by national legislation in each country If there are no official regulations or recommendations in a country, the latest recommendations of the International Commission on Radiological Protection should be applied 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 13925-1:2003, Non-destructive testing – X-ray diffraction from polycrystalline and amorphous material – Part 1: General principles Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) EN 13925-2:2003, Non-destructive testing – X-ray diffraction from polycrystalline and amorphous materials – Part 2: Procedures EN 13925-3:2005, Non-destructive testing – X-ray diffraction from polycrystalline and amorphous materials – Part 3: Instruments ISO 5725-1, Accuracy (trueness and precision) of measurement methods and results – Part 1: General principles and definitions ISO 5725-2, Accuracy (trueness and precision) of measurement methods and results – Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method Terms, definitions and symbols For the purposes of this document, the following term, definition and symbols apply 3.1 Terms and definitions 3.1.1 Residual stress self-equilibrating internal stresses existing in a free body which has no external forces or constraints acting on its boundary 3.2 Symbols and abbreviations 2θ The diffraction angle; this is the angle between the incident and diffracted X-ray beams θ The Bragg angle; this is the angle between the diffracting lattice planes and the incident beam ω The angle between the incident X-ray beam and the specimen surface at χ = φ The angle between a fixed direction in the plane of the specimen and the projection in that plane of the normal to the diffracting lattice planes ψ The angle between the normal of the specimen and the normal of the diffracting lattice planes χ The angle χ rotates in the plane perpendicular to that containing ω and 2θ; the rotation axis of χ is orientated perpendicular to both the ω and the ϕ axis {hkl Family of crystal lattice planes defined by the indices h, k and l εφψ Strain measured in the direction defined by the angles φ and ψ d0 Interplanar distance (d spacing) of a strain free specimen dφψ Interplanar distance (d spacing) of strained material in the direction of measurement defined by the angles φ and ψ (S1, S2, S3) Specimen coordinate system (L1, L2, L3) Laboratory coordinate system Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Ψ = sign( ω − θ) ArcCos(cos χ cos(ω − θ) ) sin χ Φ = ϕ + ∆ϕ with ∆ϕ = ArcTan tan( ω − θ) (F.9) For given values of Φ and Ψ there is an infinite set of (χ, ϕ, ω) values which can be obtained by rotating the r incident and diffracted beams around the measurement direction n by an angle η The penetration depth is given from formulae (E.3) and (E.4) with γ = : z= cos Ψ sin θ − sin Ψ cos θ sin η 2µ sin θ cos θ (F.10) z= cos χ sin( 2θ − ω) sin ω 2µ sin θ cos(θ − ω) (F.11) By varying η from zero (χ method) to 90° (ω method), the penetration depth can be varied without changing Φ and Ψ 72 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) X X X X X S2 ỗ ỗ ỗ ỗ ç S1 Key (S , S , S ) and (G , G , G ) superposed reference systems L3 is normal to the diffracting {hkl} lattice planes 2θ the diffraction angle; this is the angle between the incident and diffracted X-ray beams ω the angle between the incident X-ray beam and the specimen surface at χ = ψ the angle between the normal of the specimen and the normal of the diffracting lattice planes χ The angle χ rotates in the plane perpendicular to that containing ω and 2θ X the incident beam direction ° (open circle) the diffracted beam • (black dot) the bisector of the incident and diffracted beams r r r r r r Figure F.5 - Perspective drawing of the combined method for Φ = 70°, Ψ = 60° and η = 22.5° (left) Stereographic representation for Φ = 70°, Ψ = 60° and values of η : 0, 22.5°, 45°, 67.5° and 90° F.3.5 Modified chi method This mode is used on some portable goniometers with two detectors placed symmetrically on each side of the incident beam Angle ω is set equal to π/2 so that at χ = the incident beam is normal to the specimen surface The χ and ϕ rotations are used to vary the measurement direction The use of two detectors allows to compensate for the ∆ϕ so that Ψ ≈ χ with minor systematic errors on the sin Ψ slope (which can be easily corrected) For detector 1, angle γ is equal to zero and for detector 2, angle γ is equal to π Ψ = ArcCos(cos χ sin θ) Detector : π −1 Φ = ϕ + + ∆ϕ with ∆ϕ = ArcTan sin χ tan θ (F.12) 73 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Ψ = ArcCos(cos χ sin θ) Detector : π Φ = ϕ + + ∆ϕ with ∆ϕ = ArcTan sin χ tan θ (F.13) As can be seen, the two ∆ϕ compensate each other Thus, when the strains measured by the two detectors are averaged they disappear The measured strain (equation (5) of main text) can thus be written: ε φψ = 21 S{2hkl} sin θ sin χ (σ φ − σ 33 ) + 21 S{2hkl} sin θ sin 2χ τ φ + K (F.14) where: K = S1{hkl}Tr (σ) + 21 S{2hkl} (sin θ σ 33 + cos θ σ φ+ π / ) (F.14bis) This equation can be used exactly like equation (5) by replacing Ψ by χ, and, in the end divide the obtained normal stress and shear stress values by sin θ The penetration depth is identical for the two detectors: z= cos ψ ( sin θ −1 ) cos χ (1 − cot an θ) = 2µ µ sin θ (F.15) It should be noted that the diffracting crystallites sampled by the two detectors are not the same This can cause some problems in the case of textured specimens or large crystallite size specimens 74 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) ỗ ỗ ỗ ỗ ỗ ç X X X X X ç ç ç ç ç ç ç X XS2 ç S1 Key (S , S , S ) and (G , G , G ) superposed reference systems r r r r r r L3 is normal to the diffracting {hkl} lattice planes 2θ the diffraction angle; this is the angle between the incident and diffracted X-ray beams χ The angle χ rotates in the plane perpendicular to that containing ω and 2θ Ψ the angle between the normal of the specimen and the normal of the diffracting lattice planes X the incident beam direction ° (open circle) the diffracted beam • (black dot) the bisector of the incident and diffracted beams D1 detector D2 detector Figure F.6 - Perspective drawing of the modified chi method (left) Starting position (up) with ω = 90°, ϕ = χ = Position for χ = 60° et ϕ = (down), which corresponds to a measurement in direction r S i.e., after averaging the strains obtained from the two detectors, to the direction Φ = 90° Stereographic representation for 2θ = 140°, ω = 90°, ϕ = and values of χ : 0, 15°, 30°, 45°, 60°, 75° and 90° (right) 75 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) It can be noticed in Figure F.6 that the values of Ψ are always greater than the corresponding values of χ For detector 1, Ψ varies from 20° to 90° while Φ varies from to 50° Fir detector, Ψ varies from 20° to 90° while Φ varies from 180° to 130° F.3.6 Low incidence method This mode is used to achieve shallow penetration depth and wide irradiated surfaces The idea is to set ω at a fixed value α typically to 5° The χ and ϕ rotations are used to vary the measurement direction A 0D detector with long Soller slits is used to reduce optical aberrations so γ = : Ψ = ArcCos(cos χ cos(α − θ) ) sin χ Φ = ϕ + ∆ ϕ ∆ ϕ = with ArcTan α − θ tan( ) (F.16) The penetration depth is given directly from equation (E.11) by setting ω = α : z= cos χ sin( 2θ − α) sin α 2µ sin θ cos(θ − α) (F.17) Another way to define this mode is to keep constant at a given value α the angle between the surface of the specimen and the incident beam, i.e to keep constant the value of sinα = cosχ sinω 76 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) XXXXXX ỗ ỗ ỗ ç ç ç ç S2 S1 Key (S , S , S ) and (G , G , G ) superposed reference systems r r r r r r L3 is normal to the diffracting {hkl} lattice planes 2θ the diffraction angle; this is the angle between the incident and diffracted X-ray beams χ The angle χ rotates in the plane perpendicular to that containing ω and 2θ α is a fixed value of ω typically comprised between and degrees X the incident beam direction ° (open circle) the diffracted beam • (black dot) the bisector of the incident and diffracted beams Figure F.7 - Perspective representation of the low incidence mode (left) On top, starting position with ω = α, χ = ϕ = Down, position for χ = 60° and ϕ = Stereographic representation for ω = α = 5°, 2θ = 120°, ϕ = and values of χ : -75°, -60°, -30°, 0, 30°, 60°, 75° It can be noticed in Figure F.7 that, in this configuration, Ψ varies from 55° to 82° while Φ varies simultaneously from 146° to 214° F.3.7 Modified omega method This mode is used on some portable goniometers It is very similar to an omega mode but the Ψ0 angle that is set on the goniometer is taken between the normal to the specimen surface and the incident beam 77 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) π Ψ = Ψ0 + − θ Φ = ϕ (F.18) with a penetration depth given by (F.6) Key (S1, S2, S3) specimen coordinate system (G , G , G ) goniometer reference system (L1, L2, L3) laboratory coordinate system 2θ the diffraction angle; this is the angle between the incident and diffracted X-ray beams r r r Figure F.8 - Perspective drawing of the modified omega method By comparing with Figure F.3, it is clear that the two methods only differ through the origin in Ψ F.3.8 Use of a 2D (area) detector The use of a 2D detector allows to acquire a whole section of the diffraction cone (of the Debye ring), i.e a whole range of γ values According to equations (F.1) and (F.2), it corresponds to a whole range of Ψ and Φ values Theoretically, one acquisition is sufficient to obtain enough information for calculating some stress components however in practice the acquisition range in Ψ is too small to give reasonable accuracies At least a second acquisition for another value of χ, ω or ϕ is advised The relevant equations for this method are (F.1) to (F.4), i.e the general equations 78 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Key (S , S , S ) and (G , G , G ) superposed reference systems r r r r r r L3 is normal to the diffracting {hkl} lattice planes 2θ diffraction angle; this is the angle between the incident and diffracted X-ray beams ω angle between the incident X-ray beam and the specimen surface at χ =0 X incident beam direction ° (open circle) diffracted beam • (black dot) bisector of the incident and diffracted beams A for y = B for y ≠ Figure F.9 - Perspective representation of a possible set-up to work with a 2D detector for ω = θ = 70° and χ = ϕ = (left) In Figure F.9 a plane detector is shown, but cylindrical detectors also exist The detector acquires a section of the diffraction cone for γ varying from - 45° to + 45° On the right, stereographic representation for ω = θ = 70° and ϕ = and values of γ : -60°, -45°, -30°, -15°, 0, 15°, 30°, 45°, 60° On top, representation for χ = : it can be seen that Ψ varies from to 20° while Φ varies simultaneously from - 90° to + 90° Down, representation for χ = 40°, Ψ varies from 22° to 58° while Φ varies from 90° to 115° F.4 Choice of Φ and Ψ angles When measurements are performed in only one direction Φ, the minimum number of tilt angle Ψ is for a biaxial stress state and for a triaxial stress state However, due to sampling effects linked to the microstructure of the material, it is generally acknowledged that this minimum is actually not sufficient That is why the present standard recommends four or five tilts for the biaxial case and seven for the triaxial case The same question arises for tensor analysis The minimum number of (Φ, Ψ) couples is six, taken in, at least, three independent Φ directions Several ways are possible to choose the Φ directions One of the most common is to take: Φ = 0, 45° and 90° with positive and negative Ψ values (F.19) However, as it can be seen on a stereographic representation, this is not the best sampling possible, i.e the directions are not spread as uniformly as possible in the whole available solid angle If three Φ directions are 79 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) chosen, a better choice is: Φ = 0, 60° and 120° with positive and negative Ψ values (F.20) Whether (F.19) or (F.20) is chosen is the same problem as for rosette strain gauges: if the principal stresses are known before the measurement, (F.19) is easier to use, but if they are not known, (F.20) will be more accurate More than three directions can be chosen It is necessary to check the consistency of the results, to calculate the uncertainty on the stress components and it will increase the overall accuracy of the measurement It is thus advised to use at least four Φ directions If n is the number of directions, the Φ values can be separated by: ∆Φ = 180°/n (F.21) For instance, for five Φ directions, the Φ values can be : 0, 36°, 72°, 108° and 144° Figure F.10 - Stereographic representations of different choices for the Φ directions In Figure F.10 on the left, three directions are chosen according to (F.19) On the middle, three directions are chosen according to (F.20) or (F.21) On the right, five directions are chosen according to (F.21) F.5 The stereographic projection The stereographic projection is a useful tool to represent accurately directions (crystallographic directions, measurement directions, diffracted and incident beams…) emanating from a specimen which is assumed (S , S , S ) The direction ofrinterest intersects a r sphere of radius R centred on O The intersection point is then projected on to the (S , S ) plane of the punctual and located at the origin O of the reference system r r r specimen surface The projection issues from a centre H which is the south pole of the sphere 80 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Key S1, S2, S3 specimen coordinate system H the south pole of the sphere Φ the angle between a fixed direction in the plane of the specimen and the projection in that plane of the normal to the diffracting lattice planes Ψ the angle between the normal of the specimen and the normal of the diffracting lattice planes Figure F.11 - Example of a stereographic representation of a direction and Ψ=45° (right) r n described by angles Φ = 60° In Figure F.11 the angle Φ can be read directly on the projection and angle Ψ can be read along a radius of the projection circle On the perspective drawing on the left, only one eighth of the sphere is represented r r r r intersects the sphere at point N The line (HN) intersects the plane S1 , S at point N’ which is the r stereographic projection of n (black dot on Figure F.10) The coordinates of N’ in the reference system r r S1 , S are : For instance, let’s take a direction n described by the two angles Φ and Ψ The straight line directed by n ( ( ) ) Ψ x = R cos Φ tan y = R sin Φ tan Ψ 2 (F 22) To make the use of a stereographic projection easier, it is graduated every 10° in Φ and every 10° in Ψ The r S3 direction (corresponding to Ψ=0) is at the centre of the projection circle while the direction for which Ψ = 90° are located on the external edge of the circle Thus, on Figure F.10, the values of Φ (60°) and Ψ (45°) can be read directly and unambiguously The incident beam (X mark) and the diffracted beam (white dot) can also be represented clearly as compared with a perspective drawing that would be confusing 81 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Annex G (informative) Normal Stress Measurement Procedure" and "Dedicated Stress Measurement Procedure G.1 Introduction This annex introduces concepts for a Dedicated Stress Measurement Procedure It is to be verified and it shall become normative in the future i G.2 General G.2.1 Introduction Two stress measurement procedures are defined and described that conform to this standard and that yield results (stress values) of which it is allowed to be denoted as "stress measurements according to this standard": a) the Normal Stress Measurement Procedure that shall be applied to specimens with an unknown stress state and to specimens where the stress state is not assessed or proven; b) the Dedicated Stress Measurement Procedure that can be applied to series of very similar specimens (routine analyses) e.g with the purpose of reducing the measurement effort The Dedicated Stress Measurement Procedure is introduced to enable qualified and standardized stress measurements for e.g quality control and stress mapping, and it shall guarantee a proven and tractable one to one relationship between the results obtained with the Normal Procedure and the Dedicated Stress Measurement Procedure G.2.2 Normal stress measurement procedure for a single specimen The normal stress measurement procedure is described in Clauses 7.1 to 7.4 G.2.3 Dedicated Stress Measurement Procedure for very similar specimens Specimens are regarded here as "very similar" if the differences between their stress states (not the stress values), their chemical and phase compositions, their texture, their microstructure are expected to be insignificant for the stress values to be determined For a series of such specimens a laboratory can define and describe a Dedicated Stress Measurement Procedure In order to conform to this standard such a Dedicated Stress Measurement Procedure shall be validated through the execution of the Normal Procedure as well as the Dedicated Stress Measurement Procedure The validation procedure requires that: 82 1) the validation measurements shall be performed on several specimens of the series to establish the allowable range of stress values; 2) the equipment shall be aligned and validated/qualified according to Clauses 6.5 and 6.6 before starting the validation of the Dedicated Stress Measurement Procedure as well as before starting the measurement on the series of specimens; Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) 3) it proves that the value obtained by the Dedicated Stress Measurement Procedure is appropriate and sufficient for the purpose, i.e that the reduction of measurement effort is justified The procedure shall define (i) quantitatively the acceptable deviations from the expectations of the intermediate results (e.g the linearity of εφψ versus sin ψ plots, the shear stress value, the peak width) that are relevant to the stress determination and (ii) the procedure to be followed if unacceptable deviations are observed If the Dedicated Stress Measurement Procedure obeys the above, then the stress results obtained using that procedure are accepted as conforming to this standard 83 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) Bibliography [1] CEN ISO TS 21432, Non-destructive testing - Test method for measurement of residual stress by neutron diffraction [2] MOORE, M.G., EVANS, W.P., Mathematical correction for stress in removed layers in X-ray diffraction residual stress analysis, SAE Transactions, vol 66, 1958, pp 340-345; Handbook on Techniques of Residual Stresses Measurement”, SEM (American Society for Experimental Mechanics), J Lu and M.R James editors, 1996) [3] E1237-93(2003), Standard Guide for Installing Bonded Resistance Strain Gages, ASTM International [4] PFEIFFER, W., A new intensity and background correction procedure for Ω-diffractometers Materialprűfung 37, 7-8, s292-295 (1995) [5] FRANÇOIS, M et al., Reference specimens for x-ray stress analysis: the French experience, Metrologia 41 (2004) pp 33-40 [6] FRANÇOIS, M., LEBRUN, J.L., X-ray stress determination on materials with large size crystallitestheoretical approach, Proc of the 3rd European Conf on Residual Stresses (ECRS 3), 4-6 Nov 1992, Frankfurt, Germany [7] HENNION, V., SPRAUEL, J.M., and MICHAUD., H., Contribution to residual–stress evaluation in highstress-gradient zones by X-ray diffraction, J.Appl.Cryst (2000) 33, 26-34 [8] FRANÇOIS, M., DIONNET, B., SPRAUEL,J.M., NARDOU, F., The influence of cylindrical geometry on X-ray stress tensor analysis, part I, general formulation, J of Applied Crystallography, vol 28, 1995, pp 761-767 [9] DIONNET, B., FRANÇOIS, M., SPRAUEL, J.M., NARDOU, F., The influence of cylindrical geometry on X-ray stress tensor analysis, part II: applications, J Appl Cryst (1999) 32, pp 883-891 [10] HAUK, V., BEHNKEN, H., REIMERS, W., PFEIFFER, W., GENZEL, Ch., et al., Structural and Residual Stress Analysis by Non destructive Methods, Elsevier, 1997, ISBN 444 824 766 [11] HE, B B., The 20 ASM Heat Treating Society Conference Proceedings, Vol.1, pp 408-417, St Louis, Missouri, 2000 [12] GENZEL, Ch., A Self-Consistent Method for X-Ray Diffraction Analysis of Multiaxial Residual Stress Fields in the Near Surface Region of Polycrystalline Materials I Theoretical Concept J Appl Cryst., 32 (1999), pp 770 - 778 [13] GENZEL, Ch., BRODA, M., DANTZ, D., REIMERS, W., A Self-Consistent Method for X-Ray Diffraction Analysis of Multiaxial Residual Stress Fields in the Near Surface Region of Polycrystalline Materials II Examples, J Appl Cryst., 32 (1999), pp 779 - 787 [14] SPRAUEL, J.M and MICHAUD, H., Global X-ray method for determination of stress profiles, Materials Sciences forum Vols 404-407 (2002), pp 19-24 [15] PFEIFFER, W (1994), The role of the peak location method in X-ray stress measurement Proc of the Fourth Int Conf on Resid Stresses, SEM, Bethel, CT, USA, pp 148-155 [16] ISO 1993, Guide to the Expression of Uncertainty in Measurement (Geneva, Switzerland: International Organisation for Standardisation) [17] KIRKUP, L., A guide to GUM, Eur J Phys 23 (2002), pp 483–487 84 th Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 EN 15305:2008 (E) [18] HAUK, V., BEHNKEN, H., REIMERS, W., PFEIFFER, W., GENZEL, Ch., et al., Structural and Residual Stress Analysis by Non-destructive Methods, Elsevier, 1997, ISBN 444 824 766 [19] NOYAN, I.C., and COHEN, J.B., Residual Stress: Measurement by Diffraction and Interpretation, Springer-Verlag, 1987 [20] Handbook of Residual Stress and Deformation in Steel, ASM International, 2002 [21] ASTM E915-96, Standard test method for verifying the alignment of x-ray diffraction instrumentation for residual stress measurement, ASTM International, 2002 [22] ASTM E1426-98, Standard test method for determining the effective elastic parameter for x-ray diffraction measurements of residual stress, ASTM International, 2003 [23] LODINI, A., PERRIN, M., ed., Analyse des contraintes résiduelles par diffraction des rayons X et des neutrons, INSTN/CEA, 1996 [24] LU, J., RETRAINT, D., Review of recent developments and applications in the field of X-ray diffraction for residual stress studies, Journal of Strain Analysis for Engineering Design, v 33, n 2, 1998, pp 127136 [25] FITZPATRICK, M.E., FRY, A.T., HOLDWAY, P., KANDIL, F.A., SHACKLETON, J and SUOMINEN, L., NPL Good Practice Guide No 52: Determination of Residual Stresses by X-ray Diffraction, March 2002, ISSN 1368-6550 [26] SCHOLTES, B., Verfahrensbeschreibung - Röntgenographische Ermittlung von Spannungen Ermittlung und Bewertung homogener Spannungszustände in kristallinen, makroskopisch isotropen Werkstoffen, Arbeitsgemeinschaft Wärmebehandlung und Werkstofftechik e.V (AWT), 2000 [27] EN 1330-11, Non-destructive testing – Terminology – Terms used in X-ray diffraction from polycrystalline and amorphous materials [28] CEN ISO/TR 25107, Non-destructive testing – Guidelines for NDT training syllabuses (ISO/TR 25107:2006) 85 Licensed Copy: Wang Bin, ISO/EXCHANGE CHINA STANDARDS, 02/11/2009 06:18, Uncontrolled Copy, (c) BSI BS EN 15305:2008 BSI - British Standards Institution BSI is the independent national body responsible for preparing British Standards It presents the UK view on standards in Europe and at the international level It is incorporated by Royal Charter Revisions British Standards are updated by amendment or revision Users of British Standards should make sure that they possess the latest amendments or editions It is the constant aim of BSI to improve the quality of our products and services We would be grateful if anyone finding an inaccuracy or ambiguity while using this British Standard would inform the Secretary of the technical committee responsible, the identity of which can be found on the inside front cover Tel: +44 (0)20 8996 9000 Fax: +44 (0)20 8996 7400 BSI offers members an individual updating service called PLUS which ensures that subscribers automatically receive the latest editions of standards Buying standards Orders for all BSI, international and foreign standards publications should be addressed to Customer Services Tel: +44 (0)20 8996 9001 Fax: +44 (0)20 8996 7001 Email: orders@bsigroup.com You may also buy directly using a debit/credit card from the BSI Shop on the Website http://www.bsigroup.com/shop In response to orders for international standards, it is BSI policy to supply the BSI implementation of those that have been published as British Standards, unless otherwise requested Information on standards BSI provides a wide range of information on national, European and international standards through its Library and its Technical Help to Exporters Service Various BSI electronic information services are also available which give details on all its products and services Contact Information Centre Tel: +44 (0)20 8996 7111 Fax: +44 (0)20 8996 7048 Email: info@bsigroup.com Subscribing members of BSI are kept up to date with standards developments and receive substantial discounts on the purchase price of standards For details of these and other benefits contact Membership Administration Tel: +44 (0)20 8996 7002 Fax: +44 (0)20 8996 7001 Email: membership@bsigroup.com Information regarding online access to British Standards via British Standards Online can be found at http://www.bsigroup.com/BSOL Further information about BSI is available on the BSI website at http:// www.bsigroup.com Copyright BSI Group Headquarters 389 Chiswick High Road, London, W4 4AL, UK Tel +44 (0)20 8996 9001 Fax +44 (0)20 8996 7001 www.bsigroup.com/ standards Copyright subsists in all BSI publications BSI also holds the copyright, in the UK, of the publications of the international standardization bodies Except as permitted under the Copyright, Designs and Patents Act 1988 no extract may be reproduced, stored in a retrieval system or transmitted in any form or by any means – electronic, photocopying, recording or otherwise – without prior written permission from BSI This does not preclude the free use, in the course of implementing the standard, of necessary details such as symbols, and size, type or grade designations If these details are to be used for any other purpose than implementation then the prior written permission of BSI must be obtained Details and advice can be obtained from the Copyright and Licensing Manager Tel: +44 (0)20 8996 7070 Email: copyright@bsigroup.com