3.4 The Novel SMA-Reinforced Laminated Glass Panel Concept
3.4.2 Exploratory Finite-Element (FE) Numerical Study
As a preliminary investigative study, the potentiality of SMA wires embed- ded in traditional LG panels was investigated by means of FE numerical models implemented in ABAQUS/Standard [23].
Exploratory FE simulations were carried out on several geometrical con- figurations of practical interest for structural glass applications in buildings, as partly discussed in the following sections, so that rational assessment of their potentiality could be obtained. It is expected, based on the obtained outcomes, that the current results could be successively extended and vali- dated by means of full-scale experiments, in the prospective of prototyping the so-called “SMA-reinforced LG panels”, as well as in view of a possible implementation of design rules and recommendations of practical use.
3.4.2.1 General FE Model Assembly Approach and Solving Method Nonlinear static incremental simulations (inls) were carried out on several configurations. Various influencing parameters (e.g. glass panel dimen- sions, boundary conditions, loads, LG cross-sectional properties, as well as geometrical properties of the embedded SMA wires) were taken into account. For clarity of presentation, two main case studies and applications of SMA embedded reinforcements are discussed in detail in this chapter, see Table 3.2.
For both the M1 and M2 cases, as well as for further geometrical con- figurations not included in this contribution, the parametric study was carried out by means of FE models with specific features, but typically assembled with almost an identical method.
The typical FE model consisted in fact of 3D solid elements for the interlayer films, 2D monolithic shell elements for the glass panels, and
1D beam elements for the embedded SMA wires (Figure 3.6b). A key role was assigned to several types of FE interactions in order to reproduce the expected mechanical performance of the examined SMA-reinforced LG panels. A rigid “tie” connection was in fact first introduced at both the interfaces between the interlayer and glass elements. In this manner, all the possible relative displacements and rotations among the correspond- ing mesh nodes belonging to the middle solid elements and to the adjacent external shell elements were fully neglected.
At the same time, each FE analysis was carried out in the form of three separate steps so that the effects of temperature variations in the SMA wires (e.g. initial pre-stress) as well as the transmission of these effects to the adjacent LG panels, could be properly take into account. These steps were detected and defined respectively as follows:
t Phase I: application of the temperature variation in the SMA wires. The “initial condition” option available in the ABAQUS/Standard library [23] for predefined conditions was used. At this stage, each SMA wire was assumed to be simply supported at the ends and rigidly connected to the adjacent LG elements, via localized “tie” fully rigid connectors. The initial principal stress in them due to tem- perature variations was calculated, for each simulation, based on the available experimental stress–temperature rela- tionship (see Figure 3.10), by taking into account a specific operating temperature T.
Table 3.2 Reference geometrical configurations for the SMA-reinforced LG panels object of the parametric FE investigations.
Case
study Cross section Boundaries Loads
Typical application
M1 Doubly
symmetric, three-layer LG
section (e.g. Figure 3.4b)
Long edges simply supported;
short edges fully unrestrained
q = 1 kN/m2 (wind pressure,
3 s)
Roof
M2 Doubly
symmetric, three-layer LG
section (e.g. Figure 3.4b)
Point-supported glass panel
q = 1 kN/m2 (wind pressure,
3 s)
Faỗade panel
t Phase II: application of the structural interaction between the SMA wires and the adjacent LG panel, via an “embedded”
constraint able to provide a full coupling between the SMA wires and the surrounding PVB film. At the beginning of Phase II, the end restraints of each SMA wire were fully released, while the desired boundary condition (e.g. contin- uous simply supports, point supports) was assigned to the examined LG panels.
t Phase III: loading phase. Once reproduced the desired effects due to temperature variations T, each SMA-reinforced LG panel was subjected to a linear increasing, uniform pressure q acting on the surface of glass.
3.4.2.2 Mechanical Characterization of Materials
The structural performance of SMA-reinforced glass panels was investi- gated with careful consideration for two major aspects: (i) the pre-cracked response and (ii) the first-glass cracking configuration. The (iii) post-cracked response was neglected, at this current stage of investigation. It is expected, however, that further refined assessment of the SMA-reinforcement tech- nique for LG panels could emphasize additional advantages deriving from this novel design concept. While the performance of structural glass ele- ments in general is strictly related to the limited tensile strength of glass, it is expected in fact that the embedded SMA wires could provide structural efficiency both in the pre-cracked stage (e.g. increased elastic stiffness and resistance of the composite cross section) and in the post-cracked phase (e.g. additional ductility and residual resistance, compared to the tradi- tional LG section, due to the presence of the SMA net). For this purpose, the mechanical properties of the basic materials were properly calibrated.
3.4.2.2.1 Glass and Interlayer
Glass was described in ABAQUS/Standard in the form of a linear elastic material, with Eg = 70 GPa the nominal elastic modulus and g = 0.23 its Poisson’s ratio [8]. The post-cracked mechanical behavior of glass was then described by means of the “concrete-damaged plasticity” material model available in the ABAQUS/Standard library [23]. A crucial phase was rep- resented by the refined calibration of its key input parameters so that the expected tensile brittle behavior of glass could be properly reproduced in accordance with earlier research studies (e.g. [19]). At the same time, a compressive ultimate characteristic strength equal to 1000 MPa was con- ventionally taken into account, e.g. coinciding with the nominal theoreti- cal compressive resistance of glass (Section 3.2).
The thermoplastic PVB film bonding together the glass panes was described in the form of an equivalent, isotropic, elasto-plastic material with int = 0.49 Poisson’s ratio. The yielding stress of PVB was convention- ally set equal to y,int = 11 MPa, in accordance with the FE approach vali- date in [64]. At the same time, hardening effects in its plastic response were fully neglected, with int,u = 400% the elongation at failure. Concerning the elastic modulus Eint, its value was properly calculated by taking into account a specific time loading and temperature condition based on master curves available in the literature (see Figure 3.5).
3.4.2.2.2 SMA Wires
Regarding the SMA wires, their mechanical calibration was based on experimental measurements. SMA NiTi actuator wires, straight, oxide- free, martensitic wire samples, with a 0.51 mm diameter circular cross sec- tion were used, obtained from Dynalloy, Inc. In order to characterize the phase transformation temperatures of the NiTi wire specimens, a differen- tial scanning calorimetry (DSC) test was performed, using a SETARAM- DSC92 thermal analyser (Figure 3.8). The temperature program comprised a thermal cycle where the sample, tested as-received, was heated up to 130 °C, held at this temperature for 6 min, and then cooled to –20 °C, with heating and cooling rates of 7.5 °C/min. Prior to the DSC experiment, the sample was submitted to a chemical etching (10 vol.% HF + 45 vol.%
HNO3 + 45 vol.% H2O) in order to remove the oxide and the layer formed by the cutting operation.
According to the obtained results, the transformation temperatures associated to the start and end of transformation between the martensite and austenite phases, during heating, were found to be around 40 °C and
Figure 3.8 Differential scanning calorimetry (DSC) test.
–0.25–20 –0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2
0 20 40 60 80 100 120
DSC[mW/mg]
T[°C]
80 °C. This range of transition temperatures seem to be particularly suited for the proposed adaptive approach, since the shear stiffness degradation of PVB films due to temperature increase occurs in almost the same range (e.g. Figure 3.5).
In order to characterize the full relation between force and temperature in the NiTi wires, during a thermal cycle, a NiTi wire specimen with a total length of 715 mm was placed within a rigid frame, which was equipped with a miniature load cell (Figure 3.9). The load cell enabled the force readings in the NiTi wire. Heating of the NiTi wire actuator was done via Joule heating, which is resistively heating the actuator using electric current. For this effect, a Sorensen programmable DC power supply (PPS), model XHR 40-25, was used. The temperature of the NiTi wire was monitored with the same T-type thermocouple (Copper-Constantan), with a temperature reading range from –40 °C to 100 °C, connected to a NI SCXI-1112 8 Channel Thermocouple Amplifier. The general platform for the data acquisition and control was a NI PXI-1052. During the experiment, the temperature program comprised a thermal cycle where the NiTi wire was heated up to 110 °C and then cooled to 20 °C, with heating and cooling rates of 20 °C/min.
According to the obtained stress–temperature relationship (see Figure 3.10), it is possible to notice that within the expected temper- ature range for the proposed adaptive LG panel (up to T ≈ 50–60 °C, for faỗade and roof panels exposed to sunshine), the relation between
Figure 3.9 Overview of the experimental prototype.
Clamp
Frame Sma wire Thermocouple
Load cell PPS
Electrical wires
temperature and stress in the NiTi wire is almost linear, with measured stresses up to about 120 MPa. As expected, maximum stress higher than 500 MPa could also be obtained for the same NiTi wire, but for very high temperatures only, typically requiring an activation system (T ≈ 100 °C).
By limiting the stress levels of the SMA wires to ≈120 MPa, moreover, it is rationally expected that the SMA net could guarantee an exceptional per- formance of the system, regarding stability with cycling.
For FE investigation purposes, the SMA wires were described by means of an equivalent, elasto-plastic material with ESMA Young’s modulus and
SMA = 0.3 Poisson’s ratio. Based on test data, ESMA was assumed equal to 40 GPa for temperatures up to 50 °C and equal to 50 GPa for T = 60 °C, respectively. Although the FE study was carried out in a range of tempera- tures within 30 °C and 60 °C, the elasto-plastic constitutive law was used to ensure the attainment of maximum principal stresses in the SMA wires exceeding the value of ≈500 MPa (Figure 3.10). In doing so, for each refer- ence temperature T, the initial pre-stress in the SMA wires was also derived from the experimental data, based on the stress–temperature relationship of Figure 3.10.