Experimental tests and analytical model of high damping rubber dissipating devices

Abstract

High damping rubber (HDR) consists of natural rubber to which black carbon filler is added to increase its damping properties. The use of HDR as a dissipating device in structural systems is very promising in terms of controlling the response under live actions like wind or earthquake. The use of HDR does however entail some problems because its dynamic behaviour is not completely understood and the few HDR models that exist are not completely satisfactory for seismic analysis of structures equipped with HDR-base dissipation devices. Experimental tests were performed to obtain more accurate information about the behaviour of the material under cyclic shear paths with different strain rate and strain amplitude. A nonlinear viscoelastic damage model was proposed to describe the behaviour of rubber under cyclic loads.

Introduction

In the last few years great interest has been generated in high damping rubber (HDR) due to its increasing use in industry, for example in vibration isolators, earthquake bearings, dissipating devices, but also because of its extensive use in vehicle tyres. HDR consists of natural rubber to which black carbon filler is added in order to improve a wide range of desirable material properties such as the strength and damping capacities. The addition of this filler however also has other effects, that are not always desirable, such as the Mullins effect described below.

The use of HDR as a dissipating device in structural systems is very promising in terms of controlling the structural response under live actions like wind or earthquake. This type of dissipating device can in fact be used to realize dissipative steel bracings which may be placed in the interior of reinforced concrete or steel frames. The dampers may be connected directly to the bottom of the beams and to the rigid braces so as to endure shear strain under store drift. The result is an increase of the frame stiffness and energy dissipation capacity so that both the control of lateral displacements in the case of small tremors and the reduction of damage in the case of strong motions are ensured [1], [2].

With respect to other types of damper devices, based on elasto-plastic, viscous or shape memory materials, the HDR-based damper seems to be a promising energy dissipating device for a number of reasons. First, it is preferable with respect to dissipating devices based on elasto-plastic behaviour because the filled rubber is a fading memory material so that no permanent strains exist even after strong seismic events. In addition it permits dissipating energy even for the small lateral displacements produced by wind or minor earthquakes. Similar properties are also common to visco-elastic and viscous devices, but their energy dissipation capacity is very sensitive to the strain rate, contrary to HDR-based devices which show a lower strain-rate sensitivity.

The difficulty in the use of HDR material is that its behaviour is quite complex because it is strain-rate, strain-amplitude and process dependent. The dependence on the process is known as the Mullins effect which consists of a rapid decrease of stiffness in the early load cycles (stress softening) due to a strain-induced evolution of the microstructure of the material [3]. This phenomenon is not completely understood and few models of HDR exist. Additionally, the behaviour of rubber is affected by temperature, but only marginally in the temperature range of interest for seismic applications [4].

It should be noted that the use of rubber with enhanced dissipating properties is not new in the mitigation of seismic effects although, up to now, it has almost exclusively been adopted to produce bearings for seismic isolation of bridges or buildings. In the case of seismic isolation the main aim was to obtain a shift of the natural frequencies by means of very deformable supports. The dissipative properties of the material may be considered as a secondary effect. Very simplified models neglecting strain-rate dependence and the Mullins effect may be acceptable for the design [5], [6], [7]. These models do not furnish an adequate description of the dynamic behaviour of HDR devices analyzed in this paper that are usually used to increase dissipation and stiffness. It should also be noted that the rubber of these devices undergoes strain (homogeneous pure shear strain) which is different from the strain experienced by isolator rubber (simple shear and compression).

A number of experimental works on carbon filled rubber have been published in the scientific literature and a complete overview may be found in [8] and [9]. These works show that the behaviour of HRD materials is mainly influenced by nonlinear elasticity coupled with a number of inelastic effects: nonlinear rate dependence, the Mullins effect and its dependence on strain amplitude. Several analytical papers do in fact propose models for these inelastic behaviours. In particular, in some works the quasi-static behaviour was studied and rate independent models of the Mullins effect based on the elasticity theory [3], [10], the pseudo-elasticity theory [11] and the continuum damage theory were proposed. Only in work [12] is the damage theory applied to viscoelasticity in order to obtain a rate dependent damage model. The Mullins effect has however usually been analyzed as a phenomenon occurring on the virgin material only whereas further investigation is required to evaluate if the initial stiffness may be recovered after a sufficiently long period. This aspect is particularly important in devices used for reducing the effect of seismic events which rarely happen.

In other works, like [9], [13], the dynamic behaviour of rubbers under cyclic loads was studied by experimental tests and uni-axial rheological models, successively extended to the three-dimensional case, were proposed on the bases of experimental data. In these models the nonlinear strain-rate dependence and the small rate independent hysteresis of the stable loops are included in order to match the energy dissipating property, but the Mullins effect related to early cycles was not considered.

In general, these models and the experimental tests did not aim at analyzing rubber based dissipation devices where pure shear strain occurs, but their main aim was to characterize the tension–compression behaviour under loading–unloading paths. There is thus a lack of experimental information in this regard and the proposed relations between stress and strain tensors are not as accurate in describing the pure shear, as required in foreseeing the dynamic behaviour of structures.

In order to define a model for the dynamic analysis of a structure equipped with HDR devices, the authors carried out a test program that aims at overcoming the previously cited limitations of existing tests and focuses on describing the device behaviour in the range of strain and strain rate of interest to mitigate seismic effects.

Lastly, an analytical model is proposed. It is based on a rheological, thermodynamically compatible, approach and permits describing the main phenomena of relevance in the dynamic response of structures equipped with HDR-based dissipation devices.