A BASE ISOLATION DEVICE WITH BARS IN SHAPE MEMORY ALLOYS

Transcription

1 A BASE ISOLATION DEVICE WITH BARS IN SHAPE MEMORY ALLOYS Fabio Casciati*, Lucia Faravelli* and Karim Hamdaoui* *University of Pavia Department of Structural Mechanics, via Ferrata 1, Pavia Italy This contribution is focused on a new concept of base isolator in which the inverse pendulum is realized by a special geometry of metallic bars. They are then made in a Cu-based shape memory alloy (SMA). It ensures energy dissipation by the hysteresis within the super-elastic constitutive law which characterize this kind of alloys. The design pursues the so-called self re-centring property: after loading-unloading cycles, the device moves back to its initial configuration. A mathematical model is built and some results are compared with the ones obtained by testing the material on a shaking table. The device performance is targeted on its ability to recover to the initial configuration. Keywords: Cu-SMA, Base Isolator, Inverse Pendulum, Laboratory Testing, Loading- Unloading Cycles 1 Introduction By using a base isolation approach, the structure is decoupled from the ground. This result is usually obtained by an inverse pendulum designed to give the building a much lower fundamental frequency than the ones predominant in the excitation. Thus the building moves and deflects without absorbing energy. Base isolation solutions are discussed in detail in (Soong-Dargush, 1997). This book makes evident how a dissipative component is also welcome. A new concept of base isolator realized by metallic bars instead of the commonly used rubber-steel layers was presented in (Casciati et al., 2006 a) and is discussed in this paper. More sophisticated solution can be reached in a semi-active framework (Casciati et al., 2006 b). In the concept of the isolator system presented in this paper, the inverse pendulum consists of a number of bars that are made in a Cu-base shape memory alloy (SMA) and assembled in a special geometry. The energy dissipation is guaranteed here by the SMA hysteresis within the super-elastic constitutive law characterizing the selected alloys. (Tahirji et al., 2004) The claimed self-healing aspect is its recovering capability. 2 The realized device The proposed device (Figure 1) is supposed to bear a steel plate that serves as superimposed tray, where the system to be isolated is mounted. 1 Springer 2007

2 The design variables in this inverse pendulum system are the number, diameter and inclination of the bars. They are positioned to contrast their falling under any vertical load acting on the superimposed tray. With the use the of SMA bars, (Auricchio et al., 2001) (Casciati-Faravelli, 2004), the dissipation is ensured by the super-elastic hysteresis and, when the load is removed, the relative displacement disappears, allowing the re-centring of the system. Conversely, if the bars were made by stainless steel, hysteretic cycles would require excursions in the plasticity area, and the associated displacements would have an irreversible nature. Figure 1: Realization of the proposed passive device 3 Shape memory alloys SMA s metals exhibit two very unique properties: The pseudo-elasticity (almost rubber-like flexibility), and the shape memory effect (the ability to return to their original shape, after being severely deformed, when they are heated above certain temperature) (Faravelli, 2002). The SMA s have two stable phases: the austenite (high-temperature phase) with cubic crystal structure and, the martensite one (low-temperature phase) with monoclinic crystal structure. The later phase can be found as twinned or detwinned form. Figure 2 illustrates the different phase of SMA and its microscopic diagram effect when loading, heating and cooling. Figure 2: Microscopic Diagram of the Shape Memory Effect 2 Springer 2007

3 The loading and unloading stress strain curve, for this kind of alloys, shows two distinct plateaus. In both cases a stiff-soft-stiff path is followed. As shown in Figure 3, the material is first loaded (ABC), showing a nonlinear behavior, then the reverse transformation occurs when unloaded (CDA). Thence, the global behavior is hysteretic with no permanent strain. These unusual properties (pseudo-elasticity and shape memory effect) are being applied to a wide variety of applications in a number of different fields (space shuttle, hydraulic fittings for airplanes, thermostats ). In this paper, the free recovery property is illustrated when the device made of SMA bars is deformed. Once the application of axial and/or lateral forces is removed, then, the system returns to its previous position when unloaded: this is the so-called self re-centring property. Several numerical tests were drawn to illustrate this property. Graphs and results gathered from the analysis of the built model are presented in the next section. 4 The device numerical model The code ANSYS (ANSYS, 2003), as most finite-element general purpose codes, offers the user the possibility to build his/her own material constitutive law in the form of user subroutine. Moreover, ANSYS comes with its implemented routine for shape memory alloys depending on the definition of six parameters. These parameters define the stress-strain behavior in both loading and unloading for the uniaxial stress-state (figure 3). They are: AS σ S (C 1 ): Starting stress value for the forward phase transformation. AS σ F (C 2 ): Final stress value for the forward phase transformation. σ (C 3 ): Starting stress value for the reverse phase transformation. SA S SA σ F (C 4 ): Final stress value for the reverse phase transformation. ε (C 5 ): Maximum residual strain. 5 L 6 α (C 6 ): Parameter accounting for material responses in tension and compression. For the adopted Cu-based alloy (Casciati-Faravelli, 2004), the following set of data is adopted for ambient temperature: 1 E = MPa (modulus of elasticity of the SMA in the austenite phase) 2 ν = 0.3 (Poisson's ratio) 3 C 1 = 140 MPa 4 C 2 = 270 Mpa 5 C 3 = 200 Mpa 6 C 4 = 70 MPa 7 C 5 = C 6 = Springer 2007

4 Figure 3: Idealization of a typical super-elastic behavior of SMA The device model shown in Figure 4 is numerically built by adopting the 3-D 8-node structural solid element SOLID 185 (ANSYS, 2003) for each SMA bar. In particular, the device is supposed made by bars available in the laboratory of diameter 5.3 mm. The device is formed by 12 SMA bars of 5 cm length, disposed in a Y shape; the SMA bars are assembled at the top and at the bottom by steel plates. The finite element model consists of 5159 nodes and elements. The system is fixed at the bottom and loaded first by a vertical compression (to simulate the action of the superimposed structure), and then a horizontal load is added. The unloading is done by releasing first the horizontal force and then the vertical one to close the cycle. Let the vertical load be kn, i.e., along the z axis, and let an additional horizontal force of 5.6 kn be applied in the x direction. The achieved vertical displacements are mm and 1.74 mm, respectively. Note that the horizontal force was increased sinusoidally. Consider a node located at the base of the SMA bars, where the axial compression sums with the compression induced by the bending. The von Mises stress varies with time as in Figure 5. The plot shows an evident asymmetry and, with it, the consequent hysteresis of the stress strain diagram. Figure 4: Numerical model for the device: four bars are incorporated in each of the three sets 4 Springer 2007

5 Figure 5: Variability in time of the von Mises stress during axial loading followed by bending and subsequent unloading 4.1 Numerical characterization The global behavior of the device is conveniently described by diagrams plotting the horizontal force (of sinusoidal type) versus the three generalized displacements (along x, along y and the rotation around z) of the top plate. They are summarized in Figure 6 a, b and c for one cycle of loading-unloading, then in Figures 7 a, b and c for two cycles. It is also of interest to see, for both cases, how the force is related with the velocity along x: this is plotted in Figures 6 d and 7 d. The sets of Figures 6 and 7 illustrate that the proposed device is able to re-center itself as soon as the external excitation ends. After releasing the applied forces, the displacements in, x direction (figure 6 (7) a), y direction (figure 6 (7) b) and the rotation around z (figure 6 (7) c) return to the initial position for one cycle or various cycles of loading-unloading. This recentering property is achieved by utilizing the hyper-elastic behavior of shape memory alloys. 4.2 Experimental characterization Figure 8 is the plot of the strain time history recorded by a strain gage in a bar of diameter 3 mm made of the Cu-Al-Be alloy discussed above. The bar is tensioning a system mounted on a shaking table. The following steps can be envisaged: a b 5 Springer 2007

6 c d x Ve locity (m/s) Figure 6: a, b and c: maximum top displacements vs. horizontal force for a sinusoidal variation of the horizontal load (1 cycle only). d: Top horizontal velocity in the x direction vs. horizontal force Horizontal Force a b c d Figure 7: a, b and c: maximum top displacements vs. horizontal force for a sinusoidal variation of the horizontal load (2 cycles). d: Top horizontal velocity in the x direction vs. horizontal force 1. the bar is pre-tensioned, A, to a load value of 1.2 kn; the strain reached at the end of 0.5% correspond to the value 6 mv one reads in Figure 8; 2. the system is shaken by a sequence, B-G, of acceleration white noises of increasing intensity. Step 1 corresponds to the mounting of the device (i.e., under permanent loads) and step 2 represents the vibrations induced by the time-variant loads. Figure 8 emphasizes the recentering of the deformation at the end of the vibration which is lost only for high intensity vibrations. On the other side there is a modest trend to recover the strain which should be justified by viscosity. A correct management of this aspect requires suitable thermal and/or mechanical treatments. 6 Springer 2007

7 Figure 8: Voltage (measured with gain 500) vs. time. A: pre-tensioning the SMA wire, B: acceleration white noise excitation (intensity in term of max span: 6mm), C: acceleration white noise excitation (30mm), D: acceleration white noise excitation (60mm), E: acceleration white noise excitation (75mm), F: acceleration white noise excitation (112.5mm), G: acceleration white noise excitation (150mm) 5 Conclusions This paper is focused on the interpretation of self-healing in metals as in terms of re-centering properties. This re-centering property is achieved by utilizing the hyper-elastic behavior of shape memory alloys. The nonlinear character of their constitutive law makes the numeric analysis cumbersome and very sensitive to the values of the many parameters to be specified. Therefore, experiments on the special stock of alloy one intends to utilize are always necessary in view of a reliable validation. ACKNOWLEDGEMENTS The results summarized in this paper were achieved within the research project WIND-CHIME (Wide-range Non-intrusive Devices toward Conservation of Historical Monuments in the Mediterranean Area) of the 6th Framework Plan of the European Union, for which the first author is serving as coordinator. REFERENCES 1. ANSYS Users Manual ANSYS Inc. 2. Auricchio, F., Faravelli, L., Magonette, G. and Torra, V Shape Memory Alloys: Advances in Modelling and Applications, CIMNE, Barcelona, Spain. 3. Casciati, F., Faravelli, L Experimental Characterisation of a Cu-based Shape Memory Alloy toward Its Exploitation in Passive Control Devices, Journal de Physique IV, vol. 115, pp Casciati F., Faravelli L & Hamdaoui K. 2006a. Reliability Study for a New Concept of Base Isolator. Fifth international conference on computational stochastic mechanics. June Rhodes,: Greece. 5. Casciati, F., Magonette, G. and Marazzi, F. 2006b. Semi-active Devices and Applications in Vibration Mitigation, John Wiley & Sons, Chichester, UK. 6. Faravelli, L Experimental Approach to the Dynamic Behaviour of SMA in Their Martensitic Phase, in F. Casciati (ed.), Proceedings of the 3 rd word conference on structural control, John Wily & Sons, Chichester: UK, Vol 2: Soong, T.T., Dargush, G.F Passive Energy Dissipation Systems in Structural Engineering, John Wiley & Sons, Chichester, UK. 7 Springer 2007

8 8. Tahiri V-L., Patoor E. and Eberhardt A An Analysis of the Thermomechanical Behaviour of a Shape Memory Alloy/elastomer Composite, Journal de Physique IV, vol. 115, pp Springer 2007