A NATIONAL MEASUREMENT A NATIONAL MEASUREMENT GOOD PRACTICE GUIDE GOOD PRACTICE GUIDE No. 7 No. 9 Flexural strength Palmqvist Toughness testing of ceramics for Hard and and hardmetals Brittle Materials Measurement Good Practice Guide No. 7 Flexural Strength Testing of Ceramics and Hardmetals Roger Morrell Centre for Materials Measurement and Technology National Physical Laboratory Abstract: This guide is intended to aid the establishment of good practice in flexural testing of beam test-pieces of non-ductile materials, especially ceramics and hardmetals, whether or not it is performed in accordance with standardised procedures. There is discussion of the different purposes behind undertaking flexural testing and the influence this may have on the choice of procedure. Background information is provided to explain why the practices and test-piece geometries and tolerances have been adopted in standards. There is guidance on what the important factors are in interpreting the results of flexural testing, including fractographic investigation. The mathematical basis for analysing the stress errors in non-standard tests when assuming simple thin-beam bending equations is presented. A summary of Weibull statistical analysis is given, together with some of the pitfalls in using the derived information for design purposes. This guide will have value to those considering commissioning, setting up to perform, or undertaking flexural testing, as well as to those using the results from series of tests. © Crown Copyright 1997 Reproduced with the permission of the Controller of HMSO and Queen’s Printer for Scotland ISSN 1386–6550 September 1997 Updated with new standards references, November 2007 National Physical Laboratory Teddington, Middlesex, UK, TW11 0LW Acknowledgements This guide has been produced in a Characterisation of Advanced Materials project, part of the Materials Measurement programme sponsored by the EAM Division of the Department of Trade and Industry. The advice and steer from the Ceramics and Hardmetals Industrial Advisory Group in reviewing earlier versions of this Guide are gratefully acknowledged. This document reflects the discussions held in CEN Technical Committee 184, Working Group 3 during its development of EN 843-1 for advanced technical ceramics, and also the ongoing debate on test methods in the British Hardmetal Association Research Group which has prompted the VAMAS initiative in flexural strength testing as well as recent proposals to ISO for changes to the current standard. The author would also like to acknowledge the long-standing collaboration and philosophical argument with George D. Quinn of the Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, USA, and formerly of US Army Materials Laboratory, Watertown, Mass., USA, without whose inspiration and attention to detail the compilation of this Guide would never have been accomplished. Several NPL colleagues are also thanked: John Cox and Liam Byrne for test-jig design and operation experience, and Lewis Lay and Bryan Roebuck for reviewing the manuscript and offering helpful suggestions. For further information on Materials Measurement contact the Materials Enquiry Point at the National Physical Laboratory: Tel: 0208-943 6701 Fax: 0208-943 7160 E-mail: [email protected] Flexural Strength Testing of Ceramics and Hardmetals Contents Executive summary List of symbols 1 Introduction........................................................................................................................... 1 2 Objectives of strength testing .............................................................................................. 2 2.1 What is ’strength’ of a brittle material?...................................................................... 2 2.2 Determining strength using flexural testing............................................................... 2 2.3 Choosing between three and four-point bending....................................................... 5 2.4 Uses of strength testing............................................................................................... 5 2.5 Standardised versus non-standardised test arrangements.......................................... 6 3 Standardised testing geometries and requirements ......................................................... 7 3.1 Definitions................................................................................................................... 7 3.2 Standards..................................................................................................................... 8 3.3 Demonstrating that standardised geometries are effective........................................ 9 3.4 Non-standard geometries ........................................................................................... 11 4 Test-jig design....................................................................................................................... 12 4.1 Reducing friction effects............................................................................................ 13 4.2 Achieving articulation................................................................................................ 15 4.3 Achieving alignment.................................................................................................. 17 4.4 Test-jig materials........................................................................................................ 18 4.5 Unacceptable design features .................................................................................... 18 5 Test-piece preparation......................................................................................................... 19 5.1 Sampling..................................................................................................................... 19 5.2 As-moulded or as-fired test-pieces............................................................................ 19 5.3 Machined test-pieces.................................................................................................. 21 5.4 Machining test-pieces from components .................................................................. 23 5.5 Test-piece dimensions and tolerances....................................................................... 23 5.6 Machining chamfers................................................................................................... 24 5.7 Annealing test-pieces................................................................................................. 26 5.8 Handling precautions ................................................................................................. 26 5.9 Good practice for surface finish ................................................................................ 27 6 Test procedure...................................................................................................................... 27 6.1 Equipment .................................................................................................................. 27 6.2 Measuring test-piece dimensions .............................................................................. 28 6.3 Undertaking the test ................................................................................................... 29 7 Test method accuracy and error budget........................................................................... 36 7.1 Error budget for standard tests................................................................................... 36 7.2 Systematic errors........................................................................................................ 36 7.3 Discrimination between data sets .............................................................................. 37 8 Statistical analysis ................................................................................................................ 37 8.1 Mean and standard deviation..................................................................................... 37 8.2 Weibull analysis......................................................................................................... 38 8.3 Value of Weibull analysis.......................................................................................... 39 9 Bibliography ......................................................................................................................... 41 Annex A - Stresses in beams and derivation of bending equations ........................................ 42 A.1 Bending moments and curvature............................................................................... 42 A.2 Stresses in thin beams ................................................................................................ 43 A.3 Assumptions behind the thin-beam analysis............................................................. 44 A.4 Finite element analysis (FEA) of non-thin beams .................................................... 47 A.5 Shearing effects.......................................................................................................... 47 A.6 Curved beams............................................................................................................. 48 A.7 Large deflections........................................................................................................ 49 A.8 Bibliography..............................................................................................................