Rapid de-stiffening of multilayer transparent structures using controlled thermoplastic softening

Thermoplastic softening is one of the most desirable de-stiffening methods because of its reversibility, scalability, and applicability in many of current multi-layered structures without compromising structural performance. Despite the advantages, long activation times and high activation power requirements are generally considered as the main drawbacks for this method which can potentially limit its application in scenarios where fast de-stiffening is required. The aim of this study is to identify the key design requirements of heating element to minimise the de-stiffening response time using thermoplastic softening while maximising transparency. The focus of this study is on multilayer transparent structures, with low heating element content. A systematic investigation, including experimental and numerical investigation, is performed to study the effect of the fill factor and the heating element’s length scale on the response time of de-stiffening. Melting of the polymer and melting or electrical breakdown of the heating element are observed as practical limitations and are introduced as constraints to the design maps. The fill factor is found to have considerable influence on improving the response time, especially at low fill factors (i.e. below 10%). For the material combinations investigated here, the design maps show that heating elements with wire diameters up to 7 μm, at maximum transparency of 2% fill factor and up to 12 μm at 20% fill factor can achieve sub-second response times for temperature increase of 30 °C. This new understanding will accelerate the technology readiness level of active structural control technology to be used in the future multi-functional and smart structures with a wide range of application in robotics, shape morphing, active damping, and active impact protection.

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Introduction
Development of multi-functional structure (MFS) is a response to the increasing demand for lightweight, efficient, and resilient structures and has gained significant traction over the last decade.MFSs are often hybrid materials/structures that utilise the interaction between their constituent materials to achieve either tunable properties or to deliver multiple functionalities.Employing stimuli responsive materials as a constituent material in MFSs provides the capability to control these functionalities.Physical properties of stimuli responsive materials can be changed using external stimuli such as heat, pressure, electrical current, magnetic or electrical field, or changes in moisture, pH level or light.This allows the properties or functionalities of MFSs to be changed actively on demand or as result of a changing environment.The MFSs often combine load-bearing capacity with other functionalities such as thermal/electrical conductivity or insulation, electromagnetic shielding, energy storage, self-healing, stiffness modulation, or any combination of them.
In this paper, our focus is on stiffness modulation i.e. structures with variable stiffness, which have a wide range of applications in aerospace [1], automotive [2], electronics [3], robotics [4] and medicine [5].Stiffness modulation is common in the natural world which allows a high degree of adaptation to a changing environment, crucial for maximising survival [6][7][8].These changes can be slow or fast in time [9].Slow stiffness modulation can be found in plants where stiffness variation is driven by diffusion (moisture uptake and release) which is inherently a slow process.Much faster stiffness modulation has also been observed in the animal world.A remarkable example of this can be seen in echinoderms, such as sea cucumber, where the mechanical stiffness changes by a factor of 10 in less than 1 s [10].This is achieved by controlling the stress transfer between the adjacent collagen fibrils through transiently established interaction [11].This reversible rigidcompliant transition of the sea cucumber serves as a defending mechanism against predators [12].
Inspired by stiffness tuning in nature, various synthetic materials have been developed for active structural control including flexible fluidic composites, shape memory materials, electroactive polymers, electro/magneto rheological materials and low melting point materials.The magnitude of stiffness modulation, the required time, and the efficiency of the process are dependent on the choice of the material and on the structural configuration.Wang et al [13] compared the performance of various 'tunable rigidity materials' in terms of magnitude of stiffness, stiffness variation potential, response time, and energy consumption.The fastest response time was found for electro-rheostatic (ER) and magneto-rheostatic (MR) materials, with recorded response times of less than 10 ms.On the other hand, the largest stiffness variation was found for low melting point alloys, with a modulus variation ratio of 8600.As the authors mentioned, achieving a combination of large stiffness variation, a fast response time and energy efficient stiffness tuning still remains as an unsolved challenge as there is always a trade-off between these requirements.For example, ER and MR materials are highly effective in achieving fast response times, however, they have a low elastic modulus (up to 35 kPa for MR [14] and 10 kPa for ER [15]), relatively high-power requirements (2 W-150 W) [13], and up to an order of magnitude stiffness variation range [13].Pressurised gas has also been used as a mean for fast actuation.Mosadegh et al [16] designed and fabricated a pneumatic network for their soft robot.The actuation time of 50 ms was achieved by minimising the required volume change.Barret et al [17] used chemical reaction (i.e.combustion) to generate fast moving motions such as jumping in their 3D printed soft robot.Granular materials and fluid-polymer composites, utilising internal pressure variation to modulate their stiffness, can also achieve a reasonable modulus variation ratio of 50-60 [13].Large power requirements and bulky additional components required for activation often limit the applicability of these materials [18].
Amongst various de-stiffening mechanisms, glass transition-based softening has been frequently reported.Polymers such as thermoplastics, when approaching or going beyond their glass transition temperature (T g ) become significantly softer.Haines et al [19] used glass transition-based softening in nylon and polyethylene fibres to produce artificial muscles with load carrying capability 100 times greater than human muscles.The glass transition-based softening has also been employed in carbon fibre reinforced composites.Tridech et al [20] employed a thermoplastic coating (polyacrylamide) on carbon fibres and achieved 88% reduction in flexural stiffness.Thermoplastic interleaving was also employed [21] to produce stiffness-tuning in carbon fibre composites.At elevated temperatures, 98% reduction in stiffness was observed.
Despite many advantages in thermoplastic softening such as ease of application, reversibility, scalability, and applicability in many of current multi-layered structures without compromising structural performance, the long activation time and high activation power requirement are considered as main drawbacks.This is the result of the dependency of this method on the rate of thermal conduction (long activation) and the volume of material to be heated (high power).The method of transferring thermal energy to the thermoplastic can affect both of these parameters.Transferring thermal energy can be done using either internal or external heating.Internal heating can be achieved by embedded heating elements in the structures that introduce a temperature field, usually by Joule heating or hot fluids.Some examples of methods used for delivering thermal energy include embedded thermal blankets in composite beams [22], using a metallic coil for a surgical robot [23], utilising localised heaters [24] and introducing internal micro-fluidic channels [12].
All of these dependencies results in a large variation [13] in the response time reported in the literature, ranging from a few hundreds of seconds to response times of less than 1 s [13], demonstrating that despite limitations, fast de-stiffening can still be achieved using thermal energy.Here, we aim to identify the key design requirements for achieving fast de-stiffening via Joule heating, using embedded metallic wires as heating elements, of a thermoplastic layer.The current design is intended for applications that require high optical transparency, which limits the areal coverage of the heating element.The electro-thermo-mechanical behaviour of the structure is studied using three-point bending test under constant current excitation both experimentally and numerically.The effect of heating element fill factor and its length scale, on de-stiffening response time is further investigated.

Materials
Two types of samples were prepared for the current study.The first type consisted of two layers of polyvinyl butyral (PVB) with embedded round silver wires; this will be referred to as the 'Interlayer' configuration.The second type consisted of the Interlayer sandwiched between two layers of polycarbonate (PC).This will be referred to as the 'Laminated' configuration.A schematic of the samples can be seen in figure 1.The PVB material was supplied by Pilkington, and the PC and silver wires were purchased from Goodfellow.

Manufacturing
The interlayer samples were manufactured using aluminium moulds in a conventional Carbolite oven.The manufacturing process of the samples were divided into four steps: (i) assembly of the layers using a Mylar-PVB-wires-PVB-Mylar layout, (ii) pre-heat at 60 • C for 10 min with a minimum pressure of 5 kPa, (iii) curing at 120 • C for 45 min with a pressure of 14 kPa and (iv) slowly cooling down to ambient temperature while maintaining the pressure.A layer of Mylar polyester was placed between the sample and the mould to prevent PVB from adhering to aluminium.Mylar was chosen as a release film because it is chemically inactive for temperatures up to 200 • C and has low surface energy.
The laminated samples were manufactured using a heated press and aluminium moulds.Shims of appropriate thickness were placed to control the minimum thickness of the samples.The manufacturing process of the samples were divided into four steps: (i) assembly of the layers following a PC-PVBwires-PVB-PC configuration, (ii) placing the sample between the compression plates with the appropriate shims and a layer of Mylar to prevent any scratches on the heat-press plates, (iii) thermally treat the sample with the temperature-force sequence shown in figure 2 and (iv) slowly cooling down to room temperature with no pressure, i.e. zero force.The last part of the process required approximately one hour.For clarity purpose, the graph in figure 2 displays the sequence for the first 30 min, as the system was subsequently left to naturally cool down to room temperature.
For all the manufactured samples, two rectangular pieces of brass with a thickness of 0.1 mm were placed either side of the ends of the silver wires and embedded on the sides of the PVB, as shown in figure 1.The pads improve electrical connection and ensure that the voltage applied across the individual wires was uniform.The reference dimensions for each type of sample can be seen in table 1.

Electro-thermo-optical measurements
To heat up the interlayer and laminated samples, shown in figure 1, Joule heating was employed.For this purpose, the current passed through the silver wires by connecting a power supply (420 W, 60 V/20 A, CPX400S Power Supply Unit, AIM-TTI Instruments) to the brass sides of the sample.A range of currents between 3 A and 12 A were applied.The resulting thermal field was measured using a thermal imaging camera (FLIR-A6750 MWIR), equipped with a 3-5 µm 17 mm f/2.5 FPO Manual Bayonet lens, with ±2 • C accuracy.
The sample was placed approximately 15 cm away from the camera, with a vertical angle φ of 5-10 • , and a black-body plate was placed behind the sample.The black body was calibrated by the manufacturer and serves as the reference point.To further eliminate any external source of thermal radiation, the whole setup was enclosed in an insulated cardboard box.A schematic of the layout can be seen in figure 3.
An FTIR scan over the spectrum of 4000 cm −1 -400 cm −1 was performed using a Perkin Elmer UATR-Two to assess the transmittance characteristics of PVB.Two single-layer and two bi-layer PVB samples were manufactured according to the interlayer sample manufacturing process with PVB thicknesses of 0.38 mm and 0.76 mm.Each sample was scanned in three distinct positions to assess the variation in transmittance across the sample.An example scan can be seen in figure 4. Further analysis of the scan showed that the sample has constant transparency for the operational spectrum of the thermal imaging camera lens, apart from a small region at 2960 cm −1 -2870 cm −1 .All samples had the same transmittance (average deviation of 0.05%), which signifies that the difference in thickness of PVB and the number of layers has a minimum influence on the transparency.The scan on the distinct positions showed the same transmittance (average deviation of 0.12%), proving that the manufacturing process creates samples with uniform transparency.The peaks on the FTIR graph show the characteristic chemical groups that are representative of PVB [25,26].
To understand the potential degree of influence any reflected thermal signals may have (e.g. from camera electronics), the reflectivity of PVB can be determined using Fresnel's equation: where n 1 is the refractive index of PVB (with the value of 1.458 [27]) and n 2 is the refractive index of air (which is approximately 1).This leads to a reflectivity of approximately 4%.The low reflectivity signifies that there is minor influence in the temperature recording from the reflection of any external heat generating source.

Thermo-mechanical measurements
The thermo-mechanical properties of PVB were measured using a dynamic mechanical analysis (DMA) test.The test was performed using TA Instruments DMA Q800.The range The material constants C 1 and C 2 are determined using the least square fitting to the DMA data gathered from TA Rheology Advantage Data Analysis.T 0 is the reference temperature, T is the target temperature, and a T are the shifting factors.The least-square fitting evaluated the material constants as C 1 = 452.9and C 2 = 2416 K at a reference temperature of 288.5 K.The generated master curve can be seen in figure 5.
The thermo-mechanical properties of PC were measured using the three-point bending test in a thermal chamber.The testing was performed using the Instron Universal testing system.The test was performed following the ASTM D790-03-Procedure A. The setup parameters for the test can be seen in table 2.
The samples were left in the thermal chamber for 5 min to reach thermal equilibrium before starting the test.The tested temperatures were 22 • C, 35 • C and 50 • C. The tangent modulus was calculated according to the ASTM D790-03 standard at 3% strain, as the stress-strain graph was linear from 1% to 5% strain.Over the range of temperature studied, the modulus of PC was found to be a linear function of temperature T. Therefore, the modulus was approximated using the following equation: (3)

Electro-thermo-mechanical measurements
The mechanical properties of the laminated samples were evaluated using the three-point bending test.The test was performed following the ASTM D790-03-Procedure A in ambient temperature using the Instron Universal testing system 68FM100.The setup parameters for the test can be seen in table 3. The loading and the support rollers were covered with insulating tape when the test included electrical excitation.Each test was performed at least two times to assess   C. The current range of these experiments was limited to 3 A -9 A, that were supplied via the brass sides of the sample.The current was supplied in parallel with the crosshead motion and removed once the cross-head reached the target displacement.

Numerical modelling
The finite element (FE) method was used to simulate the electro-thermo-mechanical behaviour of the samples.The simulations were performed using Abaqus/Explicit 2020.For the interlayer samples, only the electro-thermal behaviour was simulated using a coupled thermal-electrical analysis with two degrees of freedom (voltage/temperature) [28].In a coupled FE model, different physical phenomena or variables are simulated independently, but their results are interconnected and influence each other.The governing equation is: where I is the introduced current, R (T) is the resistance of the wire at temperature T, m is mass, c p (T) represents the specific heat at temperature T, and dT is the temperature difference with index 1 referring to silver and index 2 to PVB, h is the coefficient of convection at temperature T, A ext is the external surface of the structure and T ∞ is the ambient temperature.
The wire is assumed to make full contact with the PVB, assuming no thermal contact resistance.At the interface, assuming the heat rate continuity throughout the entire contact area, the heating rate for the two materials is calculated using Fourier's law of conduction: where k and ∇T is the coefficient of thermal conduction and temperature gradient with index 1 referring to silver and index 2 to PVB.   , where σ 0 is the resistivity at 20 • C, α is the temperature coefficient of resistance, and T 0 is the reference temperature.b The specific heat equation is linearly fitted in the experimental data presented in the referenced publications.
For the laminated samples, the electro-thermo-mechanical behaviour was simulated using a fully coupled electrothermo-structural analysis with 8 degrees of freedom (3 displacements/3 rotations/voltage/temperature).A fully coupled electro-thermo-structural analysis is the combination of a coupled thermal-displacement analysis and a coupled thermalelectrical analysis [28].In this approach, all relevant physical phenomena are considered simultaneously, and their interactions are accounted for during the analysis.The electrothermal model was discretised using linear coupled thermalelectrical brick elements with eight nodes (DC3D8E).The fully coupled electro-thermo-mechanical model was discretised using an 8-node brick element with reduced integration and hourglass control (Q3D8R).The parts of the model near the wire were partitioned to facilitate the mesh transition and provide structured mesh.The mesh was refined near the mechanical contact areas, as shown in figure 6, with a typical element size of 0.45 mm × 0.4 mm × 0.5 mm.The smallest elements used for wires had a typical size of 5 µm in the radial direction.In both models mentioned above, the silver wires, PC, PVB, and brass pads were modelled as elastic bodies with material properties shown in table 4.
For the interlayer model, as shown in figure 6, due to the model's symmetry, only half of the model was simulated to reduce the computational cost, with a total of 151 818 elements.For the laminated model, as shown in figure 6, due to the model's quarter symmetry, one-fourth of the model was simulated to reduce the computational cost, with a total of 91 709 elements.The respective symmetry boundary conditions were employed on the symmetry planes.The rollers were modelled as rigid shells, having a fixed (encastre) boundary condition for the bottom roller, and fixed perpendicular displacement for the upper roller.The rollers had frictional contact (µ = 0.12) with the structure.The current input and ground voltage were applied on the surface of the brass pads.
The surface film condition interaction was applied to the entire model's outer surface to represent heat convection.The ambient temperature was set to 22 • C. The heat convection coefficient was analytically calculated as a function of temperature [29]: The elastic modulus E (t) for PVB was modelled using the following equation: where E ∞ is the long-term elastic modulus, E i is the elastic modulus associated with the relaxation time, and τ i is the relaxation time.The results of the DMA in figure 5 were used to calibrate the viscoelastic parameters E i and the relaxation time τ i .The values be found in table 5.

Results and discussion
The experimental study was primarily conducted to validate the numerical models, which are later used to conduct the parametric study.This is crucial for confirming the validity of the assumptions, material models and material properties used.The numerical models are validated for a conducting element with a diameter of 50 µm and a fill factor of approximately 2%, and then, used to assess for different scale factors, fill factors and current densities.

Electro-thermal measurement
The temperature field of the PVB interlayer during the mechanical testing is the parameter that determines the stiffness of the structure.Due to the multi-layer nature of the laminated samples, a direct measurement of the temperature can not be attained, as it would not be possible to distinguish the temperature between the layers.An estimation of the induced temperature field under the same amperage was achieved by conducting electro-thermal measurements, using a thermal imaging device, on the interlayer samples.The results of this measurement, provide evidence to determine the range of amperages that could impact the stiffness of the structure, as well as the magnitude and the required time to achieve this. Figure 7 shows the recorded temperature for a sample under a 6 A excitation.All wires demonstrate a uniform and consistent temperature profile along their lengths; hence, the maximum temperature of each wire for every time increment is used to describe the wire's temperature.The increase of the average (minimum, maximum) value of the maximum recorded temperature over a period of 15 s was 22.2 • C (18.8 • C, 24.1 • C).
Figure 8 shows the maximum and average surface temperature measurements for a typical sample under current excitations of 3 A, 6 A, and 8 A, for a 15 s excitation period.The shaded area represents the variation between the samples.The average surface temperature recorded is the average temperature across the full width of the sample, and along its full length, excluding the brass pads.The difference between maximum and average temperatures does not exceed 1.5 • C for the 3 A current.The difference is more pronounced with the 6 A and 8 A current, which approaches 7 • C and 15 • C, respectively.The results of the numerical simulation were compared to those of experiments in figure 9.The experimental repeats were included to account for the experimental variability.In general, a good agreement can be observed between the numerical and experimental results.
The numerical model is used to obtain further temperature information for the heating element and the midpoint of the substrate between each pair of wires.Figure 10 displays the temperature history of the three distinct locations of interest: (i) at the wire (Point 1 in figure 10), (ii) at the midpoint between two central wires (Point 2 in figure 10) and (iii) at the top surface above point 1 (Point 3 in figure 10).Initially, the transient thermal response is dominant where there is a logarithmic increase in temperature.After this transient period, the temperatures gradient between Point 1 and Point 3 (i.e. through thickness or out-of-plane thermal gradient), and between Point 1 and Point 2 (i.e.in-plane thermal gradient) reach an approximately constant difference.The constant difference is demonstrated after about 5 s for the various excitation inputs in figure 10.The values for the maximum surface temperature, the constant temperature difference between Points 1 and 3 and Points 2 and 3, and the temperature increase rate of the midpoint can be seen in table 6.
After the application of 8 A, the samples exhibited damage due to local melting of the PVB close to the wires (figure 11).Despite the damage to the substrate, the samples were functional, without any alteration of their electrical resistance.
In contrast, after the application of 10 A, the samples lost their functionality due to large scale damage as shown in figure 12.At a time period of less than 2 s, the samples, especially close to the brass, started melting and the geometry was permanently deformed.Some areas of the wires pierced through the polymer and were exposed to air and some of the wires snapped.

Electro-thermo-mechanical measurement
To assess the effect of electrical excitation and resulting Joule heating in the sample on the mechanical properties, a series of electro-thermo-mechanical tests were performed.As can be seen from figure 10, the temperature increase of the midpoint when 3 A was applied is negligible, therefore, no mechanical  tests were performed for this current input.Also, due to the loss of functionality observed when 10 A were applied, the maximum current for the mechanical testing experiments was set to 9 A.
Tests were performed with and without applying current and the difference in reaction force was recorded.Figure 13 depicts the results of the reaction force against cross head displacement.All samples displayed similar performance with the relative error being less than 4%.For an 8 mm displacement, the reaction force was recorded as 176.9 N under no current, 144.0 N under 6 A, and 142.4 N under 9 A which indicate a force reduction of 18.6% for 6 A and 19.5% for 9 A. The difference between the experimental data for the 6 A and 9 A is negligible.The numerical simulation results show good agreement with the experimental data.
Damage was also observed in the laminated samples when excited by a current of 9 A, but the samples maintained their functionality.This validates the choice of 9 A as maximum current input for this experimental study.Figure 14 depicts a sample with bubbles and haze that were caused from the induced temperature field.

Parametric study on the effect of scale and fill factor
As observed experimentally (figure 13), increasing the current from zero to 6 A has a considerable effect on the de-stiffening the structure.However, a further increase from 6 A to 9 A has a negligible effect (stiffness decrease by 19.5%).This would seem to be counter to the numerical simulations which predicted a continued increase in temperature which should lead to a further, although less significant, de-stiffening effect (stiffness decrease by 29.3%).This would indicate that either there is a physical limit for heat propagation in the real interlayer or that notable de-stiffening can be accomplished without the need for the heat to fully propagate through the interlayer.In this section, the limits in the response time using thermal softening for de-stiffening and how the system's size contributes to improving the response times will be explored numerically.The scale factor is introduced as a unitless parameter to determine the system's size, ranging from 1 to 10 000, that represents a system with an embedded circular heating element from 1 µm to 10 mm radius, respectively.The wire current density ranges from 100 Amm −2 to 5000 Amm −2 .The maximum current density for silver is bound to 5000 Amm −2 as electromigration and electrical breakdown would occur at higher current densities [37].The fill factor, ff, is defined as the ratio of the actual conductive area to the total geometric area of interest in the through-thickness symmetry plane, as shown in figure 10.In other words, it represents the fraction of the area that is effectively utilized for conducting electricity.Increasing the diameter of wires or reducing spacing between wires both can lead to increase in fill factor.Fill factor here ranges between 2% to 20%.The material properties for silver and PVB are listed in table 4.
A first approach to understand the dependency of the response time on the scale factor and the wire current density was to assume a unit cell, with a circular silver wire embedded to a PVB substrate with an appropriate width, representing a material sample cross-section.The thickness of the unit cell is considered semi-infinite.For this purpose, a relatively large thickness for the unit cell was considered to ensure that the thermal boundary conditions, such as convection, have no influence on the results.the minimum τ r .For a scale factor smaller than this optimum, τ r10 increases as the transient thermal response becomes dominant.Here, the thermal inertia of the system becomes small enough to facilitate the fast propagation of the heat wave.As the distance needed for the heat wave to travel to the mid-point is very small, the thermal gradient rapidly reduces along the symmetry plane between the wires causing heat to preferentially flow towards the out-of-plane volume of the system; thus, reducing the resulting temperature retention of the inplane volume.For a scale factor larger than the optimum, τ r10 increases again but this time the system's significant thermal inertia causes the heat wave propagation to slow.The slow dissipation of heat introduces temperatures, within the PVB, that are high (⩾200 • C) and apply practical limitations.The practical limitations refer to the melt of the PVB at the silver-PVB interface, due to the excessive heating.The melting temperature for PVB is around 140 • C-150 • C [38], and for the current study, the value of 140 • C is considered.
In practical applications, such as the one studied in the previous sections, the unit cell has a finite thickness that introduces a thermal boundary condition, such as convection.To understand the influence of the thermal boundary condition, a new series of simulations were conducted where the unit cell had a width to thickness ratio equal to 3.3, similar to the    ratio used in the experiment.Also, the heat convection boundary condition was applied on the outer side of the unit cell according to equation (6). Figure 16 displays a design map, that correlates the scale factor to the response time τ r for a temperature increase of 10 • C (τ r10 ) and 30 • C (τ r30 ) at the midpoint, for ff equal to 2% and 10%, and various current densities.
The behaviour of τ r10 is similar to that displayed in figure 15 for large scale factors, as all current densities converge asymptotically.The saddle point for each current density is shifted  towards lower scale factors.The shift is more pronounced with increasing fill factor.On the contrary, for the same current density, the saddle point is shifted towards higher scale factors as the target temperature increases, i.e. from 10 • C to 30 • C.
The influence of the thermal boundary condition is more pronounced for scale factors smaller than that for the saddle point, where the system attains a quasi-infinite (>10 6 s) response time, as the in-plane temperature retention, combined with the heat loss in the boundaries, result in a protracted, if not unattainable, target temperature increase.
Although the solid lines in figure 16 show the potential response times of various current densities, some of these values are unable to be achieved because of the practical consideration including the melt of PVB and silver.The new boundaries associated with these are shown as dashed lines in figure 16.As can be seen in figure 16, these boundaries become more important at the higher length scales, limiting the minimum response time that can be achieved.Three experimentally measured data points associated with experiments in figure 10 for 3 A, 6 A and 8 A are also plotted in figure 16 for comparison.The results show a reasonable agreement between the experimental and numerical values.As indicated in the figure, the data points for 6 A and 8 A are close to the physical boundary dictated by melting PVB.This is the reason as why further increase of the current from 6 A does not result in a lowering of the response time any further.Melting can occur at the interface between silver and PVB which causes the loss of contact and consequently loss of heat transfer between the two materials, as seen in figures 11 and 12.According to figure 16, for maximum current density of 5000 Amm −2 and scale factor of one, the minimum response time τ r10 of 5.3 ms and 2.0 ms can be achieved for ff of 2% and 10%, respectively.The minimum τ r30 becomes 152.3 ms and 5.9 ms for ff of 2% and 10%, respectively.To investigate the effect of fill factor on the achievable minimum response time further, a range of fill factors from 2% to 20% was investigated in figure 17.The curves in figure 17 represent the current density of 5000 Amm −2 .As can be seen in figure 17, initially increasing fill factor from 2% to 10% has a considerable effect on lowering the response time.However, a further increase in fill factor has a less significant impact on lowering the response time.
Similar to figure 16, the boundary associated with melting PVB is also shown as a dashed line.The blue-shaded area in figure 17, shows the minimum response times that can be achieved for a combination of silver and PVB with various fill factors under current density of 5000 Amm −2 without exceeding the PVB melting temperature range.When optical properties are required, a further deduction to the blue-shaded area can be applied (by application of further physical constraint and boundaries).The optical transparency, haze, or refractive index are some of the optical properties that are affected by the scale factor and the fill factor [39,40].

Conclusions
A systematic investigation was conducted on the effect of fill factor and length scale of the heating element on response time of de-stiffening in thermoplastic softening using Joule heating.Electro-thermal and electro-thermo-mechanical simulations performed in Abaqus demonstrated a good agreement with experimental results.
Design maps were developed to include the practical limitations of thermoplastic or heating element melting, as well as electrical break down of the heating element caused by excessive current densities.Such design maps can be used to identify the key design parameters to decrease the response time while ensuring the device is able to survive.To achieve fast response times, a high fill factor (constrained by level of transparency required and manufacturing method) and fine scale should be employed within the design, although there are diminished benefits of using increasingly large fill factors.Response time also decreases with increasing wire current density.
The influence of increasing wire current density on improving the response time is more pronounced at the smaller scale factors.At high scale factors, response times were found to converge for a wide range of current densities.For systems with finite thickness where the influence of heat dissipation in boundaries is more considerable, a limit in lowering the scale factor was observed beyond which the target temperature was unattainable.This limit in scale factor increases for lower current densities.For the material combinations used here, the sub-second response time to 30 • C temperature increase can be achieved by using heating elements with diameters up to 7 µm or 12 µm, at maximum current of 5000 Amm −2 , for a fill factor of 2% and 20%, respectively.

Figure 1 .
Figure 1.Schematic and manufactured product of the interlayer and laminated sample.The scalebar is 20 mm.

Figure 2 .
Figure 2. Force and temperature profile for the manufacturing process of laminated samples using the heat press.

Figure 3 .
Figure 3. Schematic of the experimental setup.

Figure 4 .
Figure 4. Representative transmittance curve of sample-1 (single layer with thin PVB) from the FTIR scan.

Figure 5 .
Figure 5. Master curve for the characterisation of the mechanical properties of PVB at the reference temperature of 288.5 K.

Figure 6 .
Figure 6.Numerical model for the thermo-electrical (a), and the electro-thermo-mechanical (b) simulation.

Table 4 .
Properties for the simulated materials.Temperature-dependent materials are expressed as functions of temperature T. Material Density (kg m −3) Electrical conductivity (S m −1 ) Thermal conductivity (W m −1 • C −1 ) Elastic modulus (GPa) Specific heat (J kg −1

Figure 7 .
Figure 7. Average measured value of the wires' maximum recorded temperature using the thermal imaging camera with a current excitation of 6 A. The error bars show the deviation of the wires' temperature.The thermal image is a snapshot of the heating up to visualise the temperature difference between PVB/wires and the localised heating of the surface after 15 s.The plate on the background serves as reference point.The scalebar is 5 mm.

Figure 8 .
Figure 8. Measured average and maximum surface temperature increase under a current excitation of 3 A, 6 A and 8 A.
Figure 15 depicts the results of the dependency of the response time on the scale factor and the current density.The results are for the response time τ r10 , i.e. a temperature increase of 10 • C.The τ r10 for different current densities converges asymptotically for high scale factors.For each current density, a saddle point represents the optimum scale factor to achieve

Figure 9 .
Figure 9.Comparison of maximum temperature increase from experimental and numerical data on the surface of the sample for a current excitation of 3 A (a), 6 A (b), and 8 A (c).

Figure 10 .
Figure 10.The temperature of the wire (Point 1), midpoint (Point 2), and polymer surface above the wire (Point 3) for the simulated sample at 3 A (blue), 6 A (red), and 8 A (green).

Table 6 .
Numerical results for maximum surface temperature after a time period of 15 s, temperature offset between surface-wire and surface-midpoint, and temperature increase rate of the midpoint.• C s −1 8 A 47.4 • C 26.1 • C −18.7 • C 2.08 • C s −1

Figure 11 .
Figure 11.Local melting of the PVB close to the wires due to the current input of 8 A. The scale bar is 2 mm.

Figure 12 .
Figure 12.Damage to the with a current excitation of 10 In areas (a), PVB melt and was permanently deformed.In areas (b), the embedded wires snapped.The scalebar is 2 mm.

Figure 13 .
Figure 13.The effect of 6 A and 9 A on the reaction force under three-point bending at the deformation rate of 24 mm min −1 .

Figure 14 .
Figure 14.Damaged laminated sample after being excited with 9 A. The marked areas (a) displayed bubbles close to the wires and some wires have created a zone of melted polymer.The scale bar is 20 mm.

Figure 15 .
Figure 15.The dependency of τ r10 on the scale factor and the wire current density (a) for a fill factor of 2%, and (b) for a fill factor of 10%.

Figure 16 .
Figure 16.Design map of response time for different scale factors and wire current density J.The plots on the left refer to a system with a 2% fill factor, and on the right, for a 10% fill factor.

Figure 17 .
Figure 17.Design maps showing the combined effect of scale and fill factors on response time a target temperature increase of (a) 10 • C, and (b) 30 • C, at maximum current density of 5000 Amm −2 .

Table 1 .
Dimensions of two sample configurations used for the current study.
Sample thickness (mm) Initial Final Interlayer 0.38 ± 0.05 -0.05 ± 0.005 180 ± 5 24 ± 0.1 0.76 ± 0.01 0.75 ± 0.01 Laminated 0.38 ± 0.05 2.0 ± 0.1 0.05 ± 0.005 175 ± 1 18 ± 0.1 4.8 ± 0.1 4.6 ± 0.1 of temperatures used for the DMA test was from −45 • C to +55 • C, with a 5 • C incremental change.The spectrum of frequencies used at each temperature increment was from 1 Hz to 100 Hz.The time-temperature superposition was employed to widen the spectrum of frequencies and create a master curve for a specific temperature.The equation used to widen this spectrum is based on the equation proposed by William-Landel-Ferry:

Table 2 .
Testing parameters for the three-point bending test.

Table 3 .
Testing parameters for the three-point bending test.
the reproducibility of the results.All of the experiments were conducted at room temperature, with a starting temperature of 22

Table 5 .
Viscoelastic parameters and relaxation times for the characterisation of the mechanical properties of PVB.The instantaneous modulus E 0 = E∞ + ∑ E i and E∞ = 0.5 MPa.