Static and dynamic characterization of elastomers by a modified hardness test
Abstract: Today rubber can be found in many different applications, such as vibration dampers, tyres, clothes and gaskets. Two different types of rubbers are used today, namely the natural rubber and synthetic rubber. Natural rubber is made of a milky substance called latex, which is obtained from special trees found in tropical countries. Synthetic rubber is also made from latex, but the latex is obtained in labs by combining different chemicals together. Different fillers can also be added in order to change the properties of both natural and synthetic rubber, resulting in over 1000 different rubber materials with different characteristics and behaviours. A standard hardness test is always done on rubber which classifies the hardness of the rubber and is measured in either a Shore scale or IRHD scale. The static and dynamic material parameters, which are used in finite element simulations, are traditionally characterized using experimental methods which relies on homogenous stress states. Simple shear test is most commonly used when both static and dynamic characterizations are done, but in practice it is hard to obtain homogenous stress state because of several different factors. The static material parameters are obtained by fitting a hyperelastic material model, such as the Yeoh model, with the response (stresses and strains) obtained from experimental tests. The dynamic parameters are obtained by fitting experimental data, such as dynamic shear modulus [G_dyn] and damping [d], with viscoelastic-elastoplastic material models using a minimization approach. An alternative method has been evaluated in this project, where the standard hardness test is modified into doing a displacement-controlled loading with the indentation force being measured for a fixed number of indentation depths. The material parameters are then obtained by using an energy balance equation, which contains: - the response (force and displacement) measured from the experiments, - the state of deformation obtained from finite element method and - the unknown material parameters (hyperelastic constants for static analysis, [G_dyn] and [d] for dynamic analysis). When it comes to the static analysis of the modified hardness test it has shown to be a very good method in a work done by Austrell (1997), where three natural rubbers with different hardness values were evaluated using the finite element method. The dynamic analysis has been evaluated in this thesis, and three synthetic rubbers with different responses were used. The goal is to be able to find the dynamic shear modulus [G_dyn(κ_eq,f)] and damping [d(κ_eq,f)] which are similar to the ones obtained from simple shear test in order to use the same fitting procedure when obtaining the viscoelastic-elastoplastic material parameters. The damping is calculated the same way as for simple shear test and should not be a problem to calculate since it is insensitive to the boundary condition. The problem is to find a connection between the indentation amplitude [u_dyn] and the shear amplitude [κ_dyn], and what was done in this project was that pure compression was assumed for the modified hardness test, and the strain invariants for compression and shear were put equal to each other resulting in the following approximative connection [ u_shear = √3∙u_compression ] The basis of the dynamic analysis is the same energy balance as for the static analysis, but with a slight modification in order to connect the tangential modulus [K_dyn] from the modified hardness test with the dynamic shear modulus [G_dyn] from the simple shear test. Only the most influenced elements were used in the energy balance equation, but the results obtained from this method were not good at all. Dynamic shear modulus did not show any dependence of the frequency nor the amplitude, and it also varied between the different types of materials. Therefore another approach was tested, where [K_dyn] was compared directly with [G_dyn] by assuming a linear connection [ α∙K_dyn = G_dyn ] This method showed to be very good since a single value of alpha was obtained for the different rubber materials, and the frequency and amplitude dependence where almost spot on compared to the simple shear test when the amplitude connection [u_shear = √3∙u_compression] was used. The damping obtained from the modified hardness test showed a similar behaviour as for the simple shear test when it comes to the frequency dependence, but there was a slight difference in amplitude dependence, this when both the same amplitudes were used, and when the amplitude connection [u_shear = √3∙u_compression] was used.
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