MTS ADHESIVES PROGRAMME PERFORMANCE OF ADHESIVE JOINTS

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1 MTS ADHESIVES PROGRAMME PERFORMANCE OF ADHESIVE JOINTS Project: PAJ1; Failure Criteria and their Application to Visco-Elastic/Visco-Plastic Materials Report 6 MEASUREMENT OF CREEP AND STRESS RELAXATION IN RUBBER AND RUBBER TYPE MATERIALS F HU A OLUSANYA This report represents deliverables in Task2 and Task 5, Milestones M5 and M19 December 1997

2 Crown copyright 1997 Reproduced by permission of the Controller of HMSO ISSN National Physical Laboratory Teddington, Middlesex, UK, TW11 0LW No extracts from this report may be reproduced without the prior written consent of the Managing Director National Physical Laboratory; the source must be acknowledged. Approved on behalf of Managing Director, NPL, by Dr C Lea, Head of Centre of Materials Measurement & Technology 2

3 CONTENTS 1. Introduction 4 2. Creep And Stress Relaxation In Rubber Materials 4 3. Test Methods Creep Tests Stress Relaxation Tests Creep Rupture Tests Compressive Creep Tests 7 4.Presentation Of Creep Data 7 5.The Creep Power Law 8 6. Concluding Remarks 9 7.References 10 8.List Of Figures 10 3

4 MEASUREMENT OF CREEP AND STRESS RELAXATION IN RUBBER AND RUBBER TYPE MATERIALS 1. Introduction Failure criteria under creep and stress relaxation are important in many applications and especially for rubber and rubber-like components. In structural joints that employ flexible adhesives, creep or stress relaxation of the adhesive will result in stress redistribution in the bond line leading to deformation that increases with service time. The creep and stress relaxation properties of adhesives are essential data requirements for design engineers so that the adhesively bonded components can be designed and utilised effectively and safely. The objective of this report is to review test methods for the measurement of creep and stress relaxation of rubber materials. 2. Creep and Stress Relaxation in Rubber Materials The concepts of creep and stress relaxation and other related time dependent responses of rubbers are depicted in Figure 1 for a simple tension stress system of stress, σ and strain, ε. The behaviour of linear elastic materials is also shown in Figure 1 (dashed lines) for comparison. Creep is defined as the continuing time dependent deformation under constant stress, while stress relaxation is defined as the time dependent decay in stress that results from the application of a constant deformation. Unlike metallic materials that only show creep and stress relaxation under relatively large stresses or at high temperature, all rubbers exhibit these characteristics whenever they are subjected to force or deformation. In general for structural uses these characteristics are undesirable, however these properties can be used to advantage in compression loading for, seals and flanges and vibration damping components for automotive, aerospace and assorted diverse engineering applications The typical creep performance of a rubber under high and low stresses is illustrated in Figure 2. A linear relationship is often obtained when the deformation is plotted against the logarithm of time. However, under a very high stress and extended time periods, the linear relationship may be succeeded by an upward curve leading to creep rupture. The initial elastic deformation due to the applied load and a typical recovery curve obtained when the applied load is removed are also shown in Figure Test Methods 3.1 Creep tests Creep tests can be carried out by applying a constant load to the test specimen, and measuring its deformation as a function of time. Creep tests may involve stressing specimens in almost any mode, tension, compression, flexure, shear, etc., depending on the proposed use of the material. 4

5 It may be necessary to devise tests to apply combinations of the above stress modes, however, the uniaxial tension creep test is the most widely used because it is simple and easy to carry out. If the material is isotropic and displays a linear creep response, its behaviour under complex stresses can be fully characterised by the time dependent tensile creep modulus and the time dependent creep lateral contraction ratio, Poisson s ratio. The stress can be applied by hanging weights on the specimen and the elongation can be determined by an extensometer, periodically measuring the distance between two fiducial marks on the specimen. If there is no slippage in the grips holding the specimen, the device for measuring the elongation may be attached to the specimen grips and changes in length may be determined from the separation of the grips. ASTM 2990 gives general guidance for the creep testing of rubbers. It is found that the specimen alignment is critical and the load eccentricity should be within 1% of the axis of specimen loading. The sensitivity of the extensometer for the measurement of change in length should be in/in or better. The tests are all performed at a constant temperature. The main standards relating to measurement of creep of plastics and rubbers are listed in Table 1. Physical testing of rubber, BS903 covers visco-elastic properties in the following sections: Part A5: Determination of tension set; Part A6: Determination of compression set after constant strain; Part A15: Measurement for determination of creep in compression or shear; Part A34: Determination of stress relaxation of rubber rings in compression; Part A42: Determination of stress relaxation. Figure 3 shows the uniaxial creep test arrangements using single-lever or two-lever loading systems. The stresses are generally achieved by the application of simple dead loads. Creep tests have been conducted at NPL for the study of the behaviour of metallic and polymeric materials. The existing facilities include three types of measurement instrument: i) constant-load single-lever machines without strain measurement, ii) constant-stress cam-lever machines with strain measurement, iii) constant strain rate screw-driven machines with strain measurement operated under constant load. Temperature and humidity are also controlled. The measurements in this project will be performed using constant-load single-lever machines without strain measurement. Operational procedures for carrying out uniaxial creep testing are listed in Table 2. 5

6 3.2 Stress relaxation tests In a stress-relaxation test, the specimen is deformed a fixed amount, and the stress required to maintain this deformation is measured for the requisite period of time. The maximum stress occurs when the deformation takes place, and the stress decreases gradually with time from this maximum value. Many types of instruments have been used to measure stress relaxation. Relatively simple instruments can be used for rubber materials. The apparatus must be rigid compared to the specimens and the transducer used to measure the stress must be capable of operating with very little deformation. Figure 4 shows an apparatus for measuring stress relaxation. The stress is measured by a strain gauge attached to a cantilever beam spring. When a stress is applied to the specimen, the beam is displaced a slight amount. This displacement is transmitted to the strain gauge, changing its resistance and the electrical output; the electrical input is fed into the recorder to give a trace proportional to stress (or force) versus time. The elongation is applied to the specimen by quickly pulling down on the lower rod. The elongation stop allows one to impose any fixed elongation to the specimen. The elongation is held constant by tightening the lower set screw. 3.3 Creep rupture tests A creep rupture test measures the time to break under constant stresses. Specimens are under high stresses, usually expressed as a fraction of the ultimate, short term failure strength. Creep rupture test data are usually presented by as a creep-rupture envelope, a graphical representation of applied stress against the logarithm of rupture time. These envelopes indicate the limits of a material s load-bearing capability. For adhesive joints, the creep rupture data of adhesive materials is possibly the most important time-dependent property as a short-term safe joint could potentially fail as the service time increases. Therefore, the degradation of joint strength against the service time should be determined by using the creep rupture data of adhesives. A creep rupture curve requires a minimum of seven stress levels and rupture should occur at approximately the following times: 1, 10, 30, 100, 300, 1000 and 3000 hours. The selection of temperatures for creep rupture testing depends on the work condition of the material. Measurements should be carried out at a minimum of two test temperatures. Examples of this type of test are rarely seen in practice as rubber components such as seals are generally operating at stress levels far below their working limits. Similar stress rupture tests are described in ASTM2992, UK Oil and Offshore Association standards, UKOOA, describing tests relevant to plastic pipes under internal pressure. 6

7 3.4 Compressive creep tests Compressive creep tests can be used to determine the creep modulus and the creep lateral contraction, Poisson s ratio for rubber materials. A uniaxial compression test is performed by loading a sample of material between lubricated surfaces. The loading surfaces are lubricated to prevent the sticking of the test sample to the loading faces and also to minimise the barrelling effect that lead to deviations from homogeneous compression stress-strain situation. Satisfactory lubrication of the end faces is difficult to achieve and in any event the resultant stress-strain curve is dependent on the shape of the test sample, in particular the ratio of the axial to the lateral dimension. Thus data from the stress strain curve requires modification to model different shapes of the same material. It is found that the superposition of a tensile or compressive stress on a loaded incompressible body realises different stresses but does not result in a change of deformation. Thus apparently different loading conditions are actually equivalent in their deformation and are therefore equivalent test. As a result, a uniaxial compression test can be realised by a equibiaxial tension test. It is found under superposition of stresses that these tests are equivalent; Uniaxial tension Equibiaxial compression Uniaxial compression Equibiaxial tension Planar tension Planar compression. It is also found that uniaxial tension and uniaxial compression are independent from each other, as is the case for equibiaxial tension and equibiaxial compression. 4. Presentation of Creep Data The primary data of creep tests are normally displayed as creep curves, Figure 5. This shows the total deformation (or strain) against logarithmic time at different stress levels. For uniaxial tension creep tests, the stress levels can be selected from the following range, 0.01σ ult, 0.02σ ult, 0.05σ ult, 0.1σ ult, 0.2σ ult, 0.3σ ult, 0.5σ ult, 0.7σ ult, 0.8σ ult and 0.9σ ult, where σ ult is the short-term ultimate failure strength of the material. Each group of these curves is measured from the specimens cut from the same batch and tested at the same temperature and moisture conditions. The result of stress relaxation tests can be presented as shown in Figure 6. The measured stress is plotted against logarithmic time for each specimen tested under a different constant strain. A stress-log time curve can also be obtained by interpolating the data from creep curves if the data represents a wide range of stress levels. For a specific strain level (dotted line in Figure 5), 5 to 8 pairs of stress - log time values can generate a curve in Figure 6, this is not the same curve though, for a particular strain. 7

8 Creep rupture tests will generate a curve as shown in Figure 7, in which time to failure is recorded for each constant stress applied. The stress levels can be selected as 0.95σ ult, (σ ult is the short-term ultimate strength), 0.90σ ult, 0.85σ ult, 0.80σ ult, 0.75σ ult, to 0.30σ ult. Under higher stresses, the creep rate is higher and the material fails in a shorter time. Tests are normally started from high stress level. A test is usually terminated in 2000 to 3000 hours if it does not fail under a lower stress level. The highest stress at which specimens do not break is called creep limit strength. From a set of creep curves at various stresses, Figure 5, it is possible to construct isochronous stress-strain curves, Figure 8, by drawing lines at fixed time period, for example 0, 1, 10, 100 hours. Creep curves can also be presented in a 3-dimensional stress-straintime co-ordinate system. 5. The Creep Power Law This section describes an experimental procedure which enables the determination of the material constants that appear in the creep power law. The terminology of the finite element modelling software program ABAQUS 5 will be used. As:. cr n k ε = Aq t (1.1). cr where ε is the equivalent creep strain rate, q is the von Mises equivalent stress, t is time and A, n and k are material constants to be determined. Integrating equation (1) leads to: = A k + 1 q t (1.2) ε cr n k+1 where ε cr form: is the equivalent creep strain. Equation (1.2) can be converted to a logarithmic log ( ε cr ) = A log ( ) ( ) where B=A/(k+1). + nlogq + k + 1 logt = logb + nlogq + k +1 logt (1.3) k +1 Equation (1.3) can be used in conjunction with uniaxial creep experimental data to determine the material constants, A, n and k. 8

9 The experimental procedure is as follows: i) A uniaxial creep test is carried out where the applied load is constant. The creep strain as a function of time is measured, i.e. q, the von Mises equivalent stress, is constant and the time t is varied. For a uniaxial tensile test, ε cr,the equivalent creep strain rate, is equal to the creep strain and q is equal to the applied stress. A plot of logε cr vs. logt is produced. The gradient of the regression line that fits the experimental data, will be equal to (k+1), hence k can be evaluated. The intercept of the line will be equal to (logb+nlogq). ii) A number of creep tests with various constant loads are carried out and the resulting creep strain after a constant time period, i.e. keep t constant and vary q is measured. A plot of log ε cr vs. logq, will have a gradient equal to n. The intercept will be equal to {logb+(k+1)logt)}. As k is now known, B and hence A can now be ascertained. A cross check on accuracy can be carried out by calculating B via the intercept obtained in procedure i. Note that in all of the above, it is assumed that a constant applied load gives rise to a constant stress, q, therefore, the above procedure is valid only if the reduction in the specimen s cross section during creep, is negligible. 6. Concluding Remarks Adhesives can be considered as isotropic materials, thus for linear behaviour only the creep modulus and creep lateral contraction ratio, Poisson s ratio, are required to characterise their creep behaviour under multi-axial stresses. These two creep parameters can be measured just by an uniaxial tension creep test. Compressive creep testing can also be used to measure these two parameters, for linear behaviour, but this method of testing is not feasible for rubbers. It is necessary to conduct creep rupture tests to measure the creep strength in fixed amount of time. Creep rupture envelopes at different temperatures can be generated by creep rupture tests under specified stress levels. 9

10 7.References 1. J. G. Williams, Stress analysis of polymers, Longman Group Ltd., G. C. Ives, J. A. Mead and M. M. Riley, Handbook of plastics test methods, ILIFFE Books, P. K. Freakley and A. R. Payne, Theory and practice of engineering with rubber, Applied Science Publishers, S. Osgerby and M. S. Loveday, Creep laboratory manual, NPL Report DMM(A)37, June ABAQUS User s and Theory Manuals, Version 5.5, Hibbit, Karlsson & Sorensen Inc., USA, List Of Figures Figure 1 Time-dependent features of rubbers Figure 2 Creep curves at high and low stresses Figure 3 Typical loading systems for tensile creep tests Figure 3(a) Single lever loading system Figure 3(b) Two lever creep machine Figure 4 Apparatus for measuring stress relaxation Figure 5 Creep curves: Strain Vs time at various constant stresses. Figure 6 Stress relaxation curves: Stress Vs time at various constant strains. Figure 7 Creep rupture curve: Stress Vs time to failure. Figure 8 Stress - strain curves at different loading times. 10

11 Table 1:Standards relating to measurement of creep and stress relaxation in rubber and polymeric materials BS903: Part A15: 1990: Physical testing of rubber: Method for determination of creep in compression or shear. (Identical to ISO 8013). BS903: Part A34: 1978: Physical testing of rubber: Determination of stress relaxation of rubber rings in compression. BS903: Part A42: 1992: Physical testing of rubber: Method for determination of stress relaxation in compression at ambient and at elevated temperature. (Identical to ISO 3384). BS903: Part A52: 1986(1995): Physical testing of rubber: Determination of ageing characteristics by measurement of stress at a given elongation. (Identical to ISO 6914). BS4618: 1970 (1994): Recommendations for the presentation of plastics design data; Part 1: Mechanical properties; Section 1.1 Creep: Creep in uniaxial tension or compression (with particular reference to solid plastics) Creep in flexure at low strains Creep lateral contraction ratio (Poisson s ratio) BS5350: Methods of test for adhesives; Part C7: 1990: Determination of creep and resistance to sustained application force. ISO 899-1: 1993: Plastics - Determination of creep behaviour - Part 1: Tensile creep. ISO 899-2: 1993: Plastics - Determination of creep behaviour - Part 1: Flexural creep by three-point loading. ASTM D , Test method for rubber - viscosity, stress relaxation and prevulcanisation characteristics (Mooney viscometer). ASTM D , Practice for conducting creep tests of metal-to-metal adhesives. ASTM D , Standard test method for tensile, compressive, and flexural creep and creep rupture of plastics. ASTM D , Standard test method for creep properties of adhesives in shear by compression loading (metal-to-metal). ASTM D , Standard test method for creep properties of adhesives in shear by tension loading (metal-to-metal). 11

12 ASTM D , Standard test method for strength properties of adhesives in shear by tension loading at elevated temperatures (metal-to-metal). ASTM D2992(1977), Standard Method for Obtaining Hydrostatic Design Basis for Reinforced Thermosetting Resin Pipes and Fittings. UKOOA GRP Work Group, Specifications and Recommended Practice for the Use of Piping Offshore, Table 2:Operational procedures for NPL creep laboratory. Code Intro TSP1 TSP2 TSP3 TSP4 TSP5 TSP6 TSP7 CSP1 CSP2 CSP3 CSP4 CSP5 CSP6 CSP7 CSP8 Title Creep laboratory manual: Introduction Initiation of test and progress chasing Material identification and registry Measurement of specimens Creep test method Specimen manufacture Repair and maintenance of equipment Laboratory environment and service Machine load calibration Load cell calibration Thermocouple calibration Transducer calibration Extensometer calibration Calibration of specimen measurement apparatus Calibration of weights Verification of laser extensometer calibrator 12

13 Figure 1 Time-dependent features of rubbers 1. 13

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15 15 NPL Report CMMT(B)158

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17 Strain Stress 5 Stress 4 Stress 3 Stress 2 Stress 1 Log time Figure 5 Creep curves: Strain Vs time at various constant stresses. Stress Strain 5 Strain 1 Log time Figure 6 Stress relaxation curves: Stress Vs time at various constant strains. Stress Log time Figure 7 Creep rupture curve: Stress Vs time to failure. 17

18 Stress Increasing time t 1 t 2 t 3 Strain Figure 8 Stress - strain curves at different loading times. 18