《BS-903-5-2004.pdf》由会员分享，可在线阅读，更多相关《BS-903-5-2004.pdf（48页珍藏版）》请在三一文库上搜索。
1、BRITISH STANDARD BS 903-5:2004 Physical testing of rubber Part 5: Guide to the application of rubber testing to finite element analysis ICS 83.060 ? Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004
2、 This British Standard was published under the authority of the Standards Policy and Strategy Committee on 2 August 2004 BSI 2 August 2004 The following BSI references relate to the work on this British Standard: Committee reference PRI/22 Draft for comment 03/100129 DC ISBN 0 580 43926 7 Committees
3、 responsible for this British Standard The preparation of this British Standard was entrusted to Technical Committee PRI/22, Physical testing of rubber, upon which the following bodies were represented: British Rubber Manufacturers Association Ltd. CIA Chemical Industries Association Materials Engin
4、eering Research Laboratory Ltd. RAPRA Technology Ltd. Royal Society of Chemistry SATRA Technology Centre Tun Abdul Razak Research Centre Amendments issued since publication Amd. No.DateComments Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:00 2
5、006, Uncontrolled Copy, (c) BSI BS 903-5:2004 BSI 2 August 2004 i Contents Page Committees responsibleInside front cover Forewordii 1Scope1 2Normative references1 3Terms and definitions1 4Symbols3 5Introduction to FEA3 6Stressstrain behaviour4 7Mechanical failure19 8Friction32 9Thermal properties33
6、10Heat build-up36 Annex A (informative) Stress-extension relationships in simple deformations and parameter optimization37 Annex B (informative) Relationship between stress in simple shear and pure shear38 Annex C (informative) An example of fitting models to experimental data38 Bibliography42 Figur
7、e 1 Values of I1 and I2 for different deformation modes.10 Figure 2 Schematic diagram of apparatus for equibiaxial straining of a flat sheet13 Figure 3 Schematic diagram of apparatus for inflation of a sheet14 Figure 4 Schematic diagram of pure shear apparatus15 Figure 5 Schematic diagram of apparat
8、us for constrained compression17 Figure C.1 Fits to experimental data in uniaxial tension39 Figure C.2 Prediction of behaviour in pure shear based on fits to experimental data in uniaxial tension40 Figure C.3 Prediction of behaviour in equibiaxial extension based on fits to experimental data in unia
9、xial tension41 Table 1 Fracture test pieces for rubber22 Table C.1 Constants derived from fits to uniaxial tension data38 Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004 ii BSI 2 August 2004 Forew
10、ord This British Standard has been prepared by Technical Committee PRI/22. 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 does not of itself confer immunity from legal obli
11、gations. Summary of pages This document comprises a front cover, an inside front cover, pages i and ii, pages 1 to 43 and a back cover. The BSI copyright notice displayed in this document indicates when the document was last issued. Licensed Copy: London South Bank University, London South Bank Univ
12、ersity, Fri Dec 08 05:32:59 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004 BSI 2 August 2004 1 1 Scope This part of BS 903 gives recommendations for test procedures and guidance on appropriate methods for determining model parameters from test data for use in finite element analysis (FEA)
13、of rubber. It covers stressstrain characterization, mechanical failure, friction, thermal properties and heat build-up. It is applicable to solid vulcanized rubbers of hardness 20 to 80 IRHD for which the deformation is predominantly elastic, and to cellular materials formed using such rubbers. It m
14、ight prove useful for other materials which can be deformed elastically to large strain. 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
15、of the referenced document (including any amendments) applies. BS 903-A1, Physical testing of rubber Part A1: Determination of density. BS 903-A2, Physical testing of rubber Part A2: Method for determination of tensile stress-strain properties. BS 903-A4, Physical testing of rubber Part A4: Determin
16、ation of compression stressstrain properties. BS 903-A10 (BS ISO 132), Rubber, vulcanized or thermoplastic Part A10: Determination of flex cracking and crack growth (De Mattia). BS 903-A14, Physical testing of rubber Part A14: Method for determination of modulus in shear or adhesion to rigid plates
17、Quadruple shear method. BS 903-A21, Physical testing of rubber Part A21: Determination of rubber to metal bond strength. BS 903-A42 (BS ISO 3384), Physical testing of rubber Part A42: Determination of stress relaxation in compression at ambient and at elevated temperatures. BS 903-A51, Physical test
18、ing of rubber Part A51: Determination of resistance to tension fatigue. BS 903-A61 (BS ISO 15113), Physical testing of rubber Part A61: Determination of the frictional properties. BS 7608, Code of practice for fatigue design and assessment of steel structures. BS EN 12667, Thermal performance of bui
19、lding materials and products Determination of thermal resistance by means of guarded hot plate and heat flow meter methods Products of high and medium thermal resistance. BS ISO 34-1, Physical testing of rubber Determination of tear strength Part 1: Trouser, angle and crescent test pieces. BS ISO 46
20、64, Rubber Guide to the determination of dynamic properties. BS ISO 23529, Rubber Physical test methods Preparation and conditioning of test pieces and preferred test conditions. 3 Terms and definitions For the purposes of this British Standard, the following terms and definitions apply. 3.1 finite
21、element analysis FEA numerical method of analysing a product in which the numerical calculations are carried out for discrete, linked elements of the product NOTEFEA is usually carried out using a commercial software package which allows visual simulation of the product to aid creation of the finite
22、 element model and viewing of the results of the analysis. Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004 2 BSI 2 August 2004 3.2 deformation mode deformation arising through a particular relatio
23、nship of the principal extension ratios NOTEExamples are uniaxial tension, uniaxial compression, pure shear, simple shear or equibiaxial extension. 3.3 deviatoric deformation deformation involving change of shape with no associated change of volume 3.4 volumetric deformation deformation involving ch
24、ange of volume with no associated change of shape 3.5 extension ratio ratio of deformed to undeformed length of a line element of material in a specified direction NOTE 1This is also known as a stretch ratio. NOTE 2The term extension is used to cover all types of deformation; thus a compression is d
25、efined with an extension ratio less than one. 3.6 hyperelastic deforming to high strains under the application of stresses, and returning to the original shape when the stresses are reduced, such that there is no loss of energy 3.7 incompressible deforming without a change in volume NOTEFor infinite
26、simal strains, incompressibility is equivalent to a Poissons ratio of 0.5. For large deformations, the condition is that 123 = 1. 3.8 model computer simulation of a product or structure, containing all the information necessary to carry out a finite element analysis 3.9 model description, expressed
27、mathematically, of some aspect of the behaviour of the material, which is implemented in the FEA package 3.10 principal strain axis one of three orthogonal directions within the material along which the deformation results only in changes in length of a line element of the material without any rotat
28、ion of the element, other than that associated with any rigid body rotation 3.11 principal stress stress acting on a surface element of material normal to a principal stress axis 3.12 principal extension ratio i ratio of deformed to undeformed length of an element of material in the direction of one
29、 of the principal strain axes 3.13 principal stress axis one of three orthogonal directions in the material with the property that the stress acting on a surface normal to it has the same direction Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:
30、00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004 BSI 2 August 2004 3 3.14 stable showing an increase in stress for an increase in extension NOTEThis guide applies only to elastic materials for which unstable models are not physically possible. 3.15 stiffness ratio of force to deflection of a test p
31、iece or product NOTEDynamic stiffness is the ratio of the amplitude of the periodic force to that of an applied sinusoidal deformation. 3.16 strain energy function mathematical expression for the strain energy per unit unstrained volume (strain energy density) of the hyperelastic material in terms o
32、f its deformation 3.17 strain invariant I1, I2, I3 function of the principal extension ratios which is independent of the choice of co-ordinate axes NOTEThe most commonly used are defined in Clause 4. 4 Symbols The following symbols are used with the following definitions throughout this part of BS
33、903. Other symbols are defined in the clauses in which they appear. 5 Introduction to FEA FEA has become a popular tool for design engineers and others. It provides a means of obtaining a computer simulation of the behaviour of a product from which useful quantitative predictions may be made. Some o
34、f the uses of FEA for products containing rubber are: to simulate the response of the product under a system of applied forces or deflections; to optimize the design (shape) of a component; to identify regions where failure can occur; to estimate the sealing pressure of a seal; to optimize the cure
35、time and temperature of a bulky product. The widespread use of FEA among engineers has been aided by the development of a number of commercial FEA software packages, which enable those without a specialist knowledge of mathematics or numerical analysis methods to carry out FEA. As well as the progra
36、m which performs the analysis (the solver), many such software packages also contain programs which allow a visual simulation of the product on the computer screen (the pre- and post-processor). These are very useful for generating the correct input for the analysis (the FEA model) and for viewing t
37、he results, such as the deformed shape of the product, or the temperature distribution following a thermal analysis. Relatively simple, so-called “linear”, FEA packages are available and are suitable for carrying out analyses where the strains are small, such as stress analysis of metals. Two diffic
38、ulties make such packages unsuitable for analysing rubber products: they assume that the strains are very small, and that the material is compressible (Poissons ratio significantly less than 0.5). Instead, for mechanical analyses of rubber products, so called “non-linear” FEA packages are required.
39、Non-linear packages are also required for most transient thermal analyses, such as simulating heat flow during vulcanization. I1 is the first strain invariant, defined such that I1 = 12 + 22 + 32; I2 is the second strain invariant, defined such that I2 = 1222 + 2232 + 3212; I3 is the third strain in
40、variant, defined such that I3 = 122232; Wis the strain energy density, as defined in 3.16; 1, 2, 3are the three principal extension ratios. Licensed Copy: London South Bank University, London South Bank University, Fri Dec 08 05:32:59 GMT+00:00 2006, Uncontrolled Copy, (c) BSI BS 903-5:2004 4 BSI 2
41、August 2004 As with any computer simulation, the accuracy of the analysis is heavily dependent on the quality of the information supplied to the computer. The skill of the FEA practitioner lies in selecting the best analysis method, and also in using sensible models for describing the behaviour of t
42、he materials, with accurately measured values of the model parameters. Adequate models for some features of rubber behaviour are not yet provided with any existing commercial FEA package, notably for: a) dynamic properties of rubber (see 6.3); b) the Mullins effect (see 6.3); c) heat build-up (see C
43、lause 10). The purpose of this guide is to give some background information on the material models available in FEA packages for modelling rubber, and to recommend suitable test methods for measuring the model parameters. 6 Stressstrain behaviour 6.1 Solid (incompressible) rubbers 6.1.1 Introduction
44、 Traditionally, rubber is modelled as a perfect hyperelastic material. This means that features such as set, hysteresis and strain softening are ignored. Commercial FEA packages are gradually introducing models which do take account of these features, but such models do not always provide a realisti
45、c description of the material behaviour, so should be used with caution. Further details are given in 6.3. 6.1.2 Hyperelastic models Commercial FEA packages normally provide a choice of hyperelastic models expressed as strain energy functions, and the user is required to input one or more parameters
46、 of the function. The strain energy function is a mathematical expression for the amount of energy stored in the material, arising from work done in deforming it. In its most general form, it may be written as: or where the symbols have the meanings given in Clause 4. Stressstrain equations may be o
47、btained directly from equation (1) by differentiation and, conversely, experimental stressstrain curves may be used to fit the parameters of the strain energy function. The necessary equations are given in Annex A. Many FEA packages also provide a curve-fitting procedure in which the user may enter
48、tables of experimental stressstrain data and the program provides the best-fit values of the parameters for the chosen function (see 6.7). Alternatively, the function need not have an explicit form, but values required to fit a particular experimental data set may be obtained numerically (see 6.1.4.
49、7). 6.1.3 Choosing a hyperelastic model 6.1.3.1 If a model has a large number of parameters which are fitted from a limited amount of test data it is possible that the model will be unstable and unrepresentative of any real material for strains or deformation modes outside those covered by the test data. Therefore the model with the fewest number of fitted parameters which is able to give a satisfactory