Shape Memory Alloy—Polymer Composites: Static and Fatigue Pullout Strength under Thermo-Mechanical Loading

This work was carried out within the context of an R&D project on morphable polymer matrix composites (PMC), actuated by shape memory alloys (SMA), to be used for active aerodynamic systems in automotives. Critical issues for SMA–polymer integration are analyzed that are mostly related to the limited strength of metal–polymer interfaces. To this aim, materials with suitable thermo-mechanical properties were first selected to avoid premature activation of SMA elements during polymer setting as well as to avoid polymer damage during thermal activation of SMAs. Nonstandard samples were manufactured for both static and fatigue pullout tests under thermo-mechanical loading, which are made of SMA wires embedded in cylindrical resin blocks. Fully coupled thermo-mechanical simulations, including a special constitutive model for SMAs, were also carried out to analyze the stress and temperature distribution in the SMA–polymer samples as obtained from the application of both mechanical loads and thermal activation of the SMA wires. The results highlighted the severe effects of SMA thermal activation on adhesion strength due to the large recovery forces and to the temperature increase at the metal–polymer interface. Samples exhibit a nominal pullout stress of around 940 MPa under static mechanical load, and a marked reduction to 280 MPa was captured under simultaneous application of thermal and mechanical loads. Furthermore, fatigue run-out of 5000 cycles was achieved, under the combination of thermal activation and mechanical loads, at a nominal stress of around 200 MPa. These results represent the main design limitations of SMA/PMC systems in terms of maximum allowable stresses during both static and cyclic actuation.


Introduction
Shape memory alloys (SMAs) are being used in an ever-increasing number of medical and industrial applications [1] due to their unique functional features and exceptional strain and force recovery capabilities, namely shape memory effect (SME) and pseudoelastic effect (PE). These properties are linked to a reversible solid-solid phase transition, the so-called thermoelastic martensite transformation (TMT), between two distinct crystal structures: the parent-bodycentered cubic austenite (B2) and the product monoclinic martensite (B19 ) [2]. Thermoelastic martensite transformation can be triggered by either temperature variations (SME) between the phase transition temperatures (TTs) or by mechanical stress (PE) between characteristic transformation stresses. Among the different types of SMAs, the binary nickel-titanium system (NiTi) exploits the best mechanical and functional performance, coupled with good corrosion resistance and biocompatibility, and its commercial success has seen an exceptional increasing trend in the last decades. Following the first widespread application of NiTi in medicine [3], 1.
Condition #1: The polymer curing temperature (T C ) must be below the SMA activation temperature (Austenite start, A s ) to avoid early activation during polymer setting; 2.
Condition #2: The polymer glass transition temperature (T G ) must be higher than the SMA activation temperature (Austenite finish, A f ) to prevent composite damage during thermal activation; 3.
Condition #3: Mechanical strength of the polymer must be compatible with the stress-strain generated by shape memory recovery in SMA (ε SMA ).
highlight of the phase transition temperatures (TTs) is also shown (namely austenite start (As), austenite finish (Af), martensite start (Ms) and martensite finish (Mf)) together with the shape memory recovery strain (εSME). Significant properties of polymers are also illustrated in the figure in terms of curing temperature (TC) and glass transition temperature (TG). Both manufacturing and operative constraints are identified as described below: 1. Condition #1: The polymer curing temperature (TC) must be below the SMA activation temperature (Austenite start, As) to avoid early activation during polymer setting; 2. Condition #2: The polymer glass transition temperature (TG) must be higher than the SMA activation temperature (Austenite finish, Af) to prevent composite damage during thermal activation; 3. Condition #3: Mechanical strength of the polymer must be compatible with the stress-strain generated by shape memory recovery in SMA (εSMA).
Based on the above conditions/constraints, a set of commercial materials was selected for SMA-polymer samples, as reported in Table 1. Other possible combinations of commercial materials that fit the above constraints could be identified, but it is out of the scope of this investigation. Significant thermomechanical properties of the selected SMA and polymer materials are reported in the following subsections.   Based on the above conditions/constraints, a set of commercial materials was selected for SMA-polymer samples, as reported in Table 1. Other possible combinations of commercial materials that fit the above constraints could be identified, but it is out of the scope of this investigation. Significant thermomechanical properties of the selected SMA and polymer materials are reported in the following subsections.

Polymer Properties
The selected polymer (Epoxy crystal ng) is a two-component epoxy resin, with aminic hardener, having a good chemical stability that is mainly used for cold manufacturing processes. Polymerization occurs at room temperature without significant material shrinkage. This is a fundamental feature to avoid premature activation of the SMA wire during polymer setting (Condition #1 Figure 1). The main physical and thermo-mechanical properties of the resin, which are relevant for this study, are illustrated in Table 2.  The test was carried out after a complete thermal cycle by heating above A f and cooling down below M f to reset the material pre-strain, carried out by the manufacturer, and to obtain a full martensite structure. The main mechanical parameters of the SMA are also shown in the figure, namely Young's modulus of twinned (E − M ) and detwinned/oriented (E + M ) martensite, detwinning/reorientation stress (σ det ) and strain (ε L ) and yield strength (σ y ).

SMA Thermomechanical Properties
Figure 2a illustrates the measured isothermal (T = 25 °C) stress-strain curve of the selected SMA as obtained from a strain-controlled tensile test of an SMA wire (d = 0.3 mm). The test was carried out after a complete thermal cycle by heating above Af and cooling down below Mf to reset the material pre-strain, carried out by the manufacturer, and to obtain a full martensite structure. The main mechanical parameters of the SMA are also shown in the figure, namely Young's modulus of twinned ( − ) and detwinned/oriented ( + ) martensite, detwinning/reorientation stress ( ) and strain ( ) and yield strength ( ). Figure 2b shows the differential scanning calorimetry (DSC) thermogram of the selected SMA, as obtained from a complete heating cooling cycle in the range −50 ÷ 150 °C, together with the values of the transformation temperatures (TTs).  Evidence of intermediate rhombohedral phase (R phase) occurring during cooling from the austenite (B2-R) is shown on the DSC thermogram not directly exploited in this investigation. Thermal constraints (see previous section) are satisfied, as the measured value of the austenite start temperature (As = 58 • C) is higher than the curing temperature (T C = 25 • C) of the polymer (condition #1), and the austenite finish (A f = 78 • C) is lower than the glass transition temperature (T G~1 20 • C). However, actual activation temperature in SMAs can be higher than Af measured from DSC due to marked thermo-mechanical coupling effects, which are linked to both martensite pre-strain (ε M ) and applied mechanical stress.
To this aim, systematic studies were carried out to measure the shape recovery properties and related TTs under different loading conditions for different pre-strain values and applied recovery stress, as shown in Figure 3. Figure 3a reports the strain vs. temperature hysteresis loop of a wire, with a martensite pre-strain ε M = 6%, subjected to the first thermal activation (T > A f ) and subsequent complete thermal cycles in the range of 10 ÷ 130 • C under a constant stress σ = 150 MPa.
from the austenite (B2-R) is shown on the DSC thermogram not directly exploited in this investigation. Thermal constraints (see previous section) are satisfied, as the measured value of the austenite start temperature (As = 58 °C) is higher than the curing temperature (TC = 25 °C) of the polymer (condition #1), and the austenite finish (Af = 78 °C) is lower than the glass transition temperature (TG~120 °C). However, actual activation temperature in SMAs can be higher than Af measured from DSC due to marked thermo-mechanical coupling effects, which are linked to both martensite pre-strain (εM) and applied mechanical stress.
To this aim, systematic studies were carried out to measure the shape recovery properties and related TTs under different loading conditions for different pre-strain values and applied recovery stress, as shown in Figure 3. Figure 3a reports the strain vs. temperature hysteresis loop of a wire, with a martensite pre-strain εM = 6%, subjected to the first thermal activation (T > Af) and subsequent complete thermal cycles in the range of 10 ÷ 130 °C under a constant stress σ = 150 MPa. Figure 3. Shape memory effect in SMA wire: (a) strain vs. temperature thermal hysteresis for a martensite prestrain εM = 6% under an applied recovery stress σ = 150 MPa; (b) evolution of the Figure 3. Shape memory effect in SMA wire: (a) strain vs. temperature thermal hysteresis for a martensite prestrain ε M = 6% under an applied recovery stress σ = 150 MPa; (b) evolution of the shape memory recovery strain (ε SME ) with martensite pre-strain (ε M ); (c) evolution of the transformation temperatures with martensite pre-strain; (d) stress-temperature diagram.
A marked decrease in the strain recovery (ε SME ) between the first and second thermal activation is observed, together with negligible differences under subsequent thermal cycles. Figure 3b shows that strain recovery at the first activation cycle increases with martensite pre-strain, within the range 4-8%, whereas a non-monotonic trend is observed for the stabilized strain recovery, with a maximum value around 3.7% at ε M = 6%.
A shift of the austenite TTs is also observed at the first thermal activation, due to martensite pre-strain, with a reset to the initial TTs at the second activation cycle. A similar behavior was observed for all investigated cases for martensite pre-strain (ε M ) ranging from 4% to 8%, and the main results are summarized in Figure 3c. The shift of the austenite TTs increases almost linearly with martensite pre-strain up to a difference of about 20 • C at ε M = 8%, corresponding to A f around 90 • C.
Finally, Figure 3d reports the stress-temperature phase diagram of the alloy that is used to define the evolution of transformation temperatures with applied stress. This graph was built by a linear fit of TTs, as obtained from thermal hysteresis cycles (see Figure 3a), under different values of the applied stress in the range 50-375 MPa. The slopes of the curves (C As , C Af , C Ms , C Mf ) represent the Clausius-Clapeyron constants for the four TTs of the material. Distinct values for the four TTs were captured, as reported in the figure, ranging between 7.9 and 13.7 MPa/ • C. Furthermore, it is shown that the activation temperature (A f ) rises to around 100 • C under an applied stress of about 200 MPa.

SMA-Polymer Sample Manufacturing
SMA wires with a diameter (d) of 0.3 mm were used for SMA-polymer samples because they combine a good recovery force (F rec around 20 N) with a large surface to volume ratio. The latter parameter is important, as it directedly affects the interfacial adhesion strength in SMA-polymer samples. As illustrated in Figure 4, samples are made of an SMA wire embedded at the center of a cylindrical polymer block (D = 10 mm, L = 20 mm). An ad hoc Teflon mold was used for sample preparation (see Figure 4). Polymer setting was carried out at room temperature (25 • C for 48 h) according to the manufacturer recommendations (see Table 2).
cycles. Figure 3b shows that strain recovery at the first activation cycle increases with martensite pre-strain, within the range 4-8%, whereas a non-monotonic trend is observed for the stabilized strain recovery, with a maximum value around 3.7% at εM = 6%.
A shift of the austenite TTs is also observed at the first thermal activation, due to martensite pre-strain, with a reset to the initial TTs at the second activation cycle. A similar behavior was observed for all investigated cases for martensite pre-strain (εM) ranging from 4% to 8%, and the main results are summarized in Figure 3c. The shift of the austenite TTs increases almost linearly with martensite pre-strain up to a difference of about 20 °C at εM = 8%, corresponding to Af around 90 °C.
Finally, Figure 3d reports the stress-temperature phase diagram of the alloy that is used to define the evolution of transformation temperatures with applied stress. This graph was built by a linear fit of TTs, as obtained from thermal hysteresis cycles (see Figure 3a), under different values of the applied stress in the range 50-375 MPa. The slopes of the curves (CAs, CAf, CMs, CMf) represent the Clausius-Clapeyron constants for the four TTs of the material. Distinct values for the four TTs were captured, as reported in the figure, ranging between 7.9 and 13.7 MPa/°C. Furthermore, it is shown that the activation temperature (Af) rises to around 100 °C under an applied stress of about 200 MPa.

SMA-Polymer Sample Manufacturing
SMA wires with a diameter (d) of 0.3 mm were used for SMA-polymer samples because they combine a good recovery force (Frec around 20 N) with a large surface to volume ratio. The latter parameter is important, as it directedly affects the interfacial adhesion strength in SMA-polymer samples. As illustrated in Figure 4, samples are made of an SMA wire embedded at the center of a cylindrical polymer block (D = 10 mm, L = 20 mm). An ad hoc Teflon mold was used for sample preparation (see Figure 4). Polymer setting was carried out at room temperature (25 °C for 48 h) according to the manufacturer recommendations (see Table 2).

Static Pullout Tests
Static pullout tests were carried out to measure the adhesion strength of SMApolymer samples by using a universal testing machine (E 10000, Instron, Norwood, USA)

Static Pullout Tests
Static pullout tests were carried out to measure the adhesion strength of SMA-polymer samples by using a universal testing machine (E 10000, Instron, Norwood, MA, USA) and a special loading tool, as shown In Figure 5a. Displacement controlled tests were carried out under different thermo-mechanical loading conditions: These load cases were selected to estimate the adhesion strength under both mechanical and thermal stresses, generated by SMA shape recovery, as well as to investigate on damage caused by cyclic SMA activations. Three different samples for each load cases were tested. Figure 5b show a schematic depiction of the mechanical loading condition together with the expected distribution of shear stresses at the interface, whereas Figure 5c is relative to the combined application of mechanical load and thermal recovery of the SMA wire.

Thermo-Mechanical Fatigue Tests
A special testing rig was designed and manufactured for fatigue testing of SMApolymer samples under combined mechanical loading and thermal activation, as shown in Figure 6.
One free extremity of the SMA wire is gripped at the upper crossbeam of the frame that incorporates a load cell for direct measurement of the mechanical load. The resin block is positioned in a loading tool, whose design is similar to the one used for static tests (see Figure 5a). The connection rod of the tool is mounted in the central crossbeam by a low friction prismatic joint. Constant stresses can be applied by deadweights, and a linear variable displacement transducer (LVDT), mounted on the lower crossbeam of the frame, is used for measuring the displacement. Cyclic thermal loads can be applied by the Joule effect by a controlled electric current. The current is provided by a fully controllable electric power supplier (CPX400DP, Thurlby Thandar Instruments Ltd., Huntingdon, UK) whose cables are connected to the SMA wire in the near extremities of the resin block (see Figure 6). This setup allows for thermal activation of a limited length of the wire embedded in the resin block. A data acquisition system (QuantumX, Catman, Hottinger Brüel & Kjae r, Marlboro, USA) and a personal computer are used for real-time current control and data acquisition. Finally, the temperature of the SMA wire is captured by an infrared camera (A615, Teledyne FLIR LLC, Wilsonville, USA) with a resolution of 640 × 480 pixels and a thermal sensitivity of 0.05 °C. These load cases were selected to estimate the adhesion strength under both mechanical and thermal stresses, generated by SMA shape recovery, as well as to investigate on damage caused by cyclic SMA activations. Three different samples for each load cases were tested. Figure 5b show a schematic depiction of the mechanical loading condition together with the expected distribution of shear stresses at the interface, whereas Figure 5c is relative to the combined application of mechanical load and thermal recovery of the SMA wire.

Thermo-Mechanical Fatigue Tests
A special testing rig was designed and manufactured for fatigue testing of SMA-polymer samples under combined mechanical loading and thermal activation, as shown in Figure 6.

Numerical Modeling
Finite element simulations were carried out, by using a commercial software code (COMSOL Multiphysics ® , 5.0, COMSOL Inc., Stockholm, Sweden) to analyze the stress and temperature distribution in the SMA-polymer sample under different thermomechanical loading conditions (see Figure 5). A 2D axisymmetric model was developed that is made of about 36 k four-node quadrilateral elements, with a refined mesh at the metal-polymer interface for an accurate simulation of the local thermo-mechanical interaction between the two materials (see Figure 7). One free extremity of the SMA wire is gripped at the upper crossbeam of the frame that incorporates a load cell for direct measurement of the mechanical load. The resin block is positioned in a loading tool, whose design is similar to the one used for static tests (see Figure 5a). The connection rod of the tool is mounted in the central crossbeam by a low friction prismatic joint. Constant stresses can be applied by deadweights, and a linear variable displacement transducer (LVDT), mounted on the lower crossbeam of the frame, is used for measuring the displacement. Cyclic thermal loads can be applied by the Joule effect by a controlled electric current. The current is provided by a fully controllable electric power supplier (CPX400DP, Thurlby Thandar Instruments Ltd., Huntingdon, UK) whose cables are connected to the SMA wire in the near extremities of the resin block (see Figure 6). This setup allows for thermal activation of a limited length of the wire embedded in the resin block. A data acquisition system (QuantumX, Catman, Hottinger Brüel & Kjaer, Marlborough, MA, USA) and a personal computer are used for real-time current control and data acquisition. Finally, the temperature of the SMA wire is captured by an infrared camera (A615, Teledyne FLIR LLC, Wilsonville, OR, USA) with a resolution of 640 × 480 pixels and a thermal sensitivity of 0.05 • C.

Numerical Modeling
Finite element simulations were carried out, by using a commercial software code (COMSOL Multiphysics ® , 5.0, COMSOL Inc., Stockholm, Sweden) to analyze the stress and temperature distribution in the SMA-polymer sample under different thermo-mechanical loading conditions (see Figure 5). A 2D axisymmetric model was developed that is made of about 36 k four-node quadrilateral elements, with a refined mesh at the metal-polymer interface for an accurate simulation of the local thermo-mechanical interaction between the two materials (see Figure 7).

Numerical Modeling
Finite element simulations were carried out, by using a commercial software code (COMSOL Multiphysics ® , 5.0, COMSOL Inc., Stockholm, Sweden) to analyze the stress and temperature distribution in the SMA-polymer sample under different thermomechanical loading conditions (see Figure 5). A 2D axisymmetric model was developed that is made of about 36 k four-node quadrilateral elements, with a refined mesh at the metal-polymer interface for an accurate simulation of the local thermo-mechanical interaction between the two materials (see Figure 7).  A special non-linear constitutive model for SMAs was adopted, based on the Lagoudas model [44] already implemented in COMSOL. The basic mechanical equation of the model is as follows: where σ is the stress tensor, ε e and ε tr are the elastic and transformation strain tensors, T 0 is the reference temperature, ξ is the martensite volume fraction, E(ξ) and α(ξ) are the elastic matrix the coefficient of thermal expansion (CTE) tensors whose coefficients are expressed as a function of the martensite volume fraction as follows: where subscript A and M denote the austenite and martensite phases, respectively. Furthermore, fully coupled electric-thermal-mechanical models were developed to simulate the thermal activation of the SMA wire by Joule effects. To this aim, heat transfer phenomena were set as conductive at the metal/polymer interface and convection with external environment.
The resin was modeled as an elastic material with Young's modulus (E R ) defined as a linear function of the temperature: where E R0 is the Young's modulus at the reference temperature T 0 , which was set to 6.5 GPa at 25 • C, and k was set to 2.63 × 10 −2 GPa/ • C, corresponding to E R = 4 GPa at T = 120 • C. The CTE of the resin (α R ) was assumed constant within the investigated temperature range. Table 3 summarizes the electric, thermal and mechanical properties of both SMA and resin used in this study. Table 3. Main physical parameters of SMA and polymer used in the FE model.

FE Model Parameter Value Description Symbol
Transformation temperatures Maximum recoverable strain ε SME, max 0.061 Poisson's ratios Heat capacity constant pressure The values of TTs used in the FE model (Table 3) are slightly different than the ones measured from DSC (Figure 2b), and they were obtained from a fine-tuning calibration process based on comparisons with experimentally measured strain-temperature hysteresis. This is to overcome basic model limitations that do not consider different slopes of the curves in the stress-temperature phase diagram (see Figure 3d).
The calibration procedure is beyond the aim of this study, but a significant comparison between numerical and experimental results is shown in Figure 8 for the sake of completeness. The values of TTs used in the FE model (Table 3) are slightly different than the ones measured from DSC (Figure 2b), and they were obtained from a fine-tuning calibration process based on comparisons with experimentally measured strain-temperature hysteresis. This is to overcome basic model limitations that do not consider different slopes of the curves in the stress-temperature phase diagram (see Figure 3d).
The calibration procedure is beyond the aim of this study, but a significant comparison between numerical and experimental results is shown in Figure 8 for the sake of completeness. Figure 8a-c shows the strain-temperature hysteretic response of the material, as obtained from a complete thermal activation cycle of the SMA (25-130 °C) subjected to a martensite pre-strain εM = 4% under different constant stress recovery conditions: 104 MPa, 169 MPa and 222 MPa.
The martensite pre-strain was directly set in the transformation strain tensor, due to the flexibility of the adopted FE package, in which thermal activation can be directly simulated without direct prior application of the mechanical pre-strain. Both stationary and transient simulations were carried out to estimate the thermomechanical interaction between metal and polymer occurring under static and fatigue thermo-mechanical loading, respectively. This is of major concern due to the marked timedependency of both conductive and convective heat transfer phenomena mainly affecting the temperature distribution of the sample under cyclic electric activations. To this aim, transient simulations were carried out in two steps: Step #1: Transient electric-thermal simulations; Step #2: Stationary thermo-mechanical simulations; A simplified mesh was adopted for simulating transient phenomena due to electricthermal coupling, consisting of about 5 k elements, to reduce the computational cost. The simulation time was set to 60 s, and an adaptive time step in the range of 0.001-0.1 s was adopted to improve the convergence of the model. The electrical load increment is based on discrete event step, to better simulate the behavior of the power supply. In particular, small time pulses are applied to the SMA material with a fixed time period.
The resulting maximum temperature distribution within the sample as obtained from transient electric-thermal simulation step, occurring at the end of the electric pulse, The martensite pre-strain was directly set in the transformation strain tensor, due to the flexibility of the adopted FE package, in which thermal activation can be directly simulated without direct prior application of the mechanical pre-strain.
Both stationary and transient simulations were carried out to estimate the thermomechanical interaction between metal and polymer occurring under static and fatigue thermo-mechanical loading, respectively. This is of major concern due to the marked timedependency of both conductive and convective heat transfer phenomena mainly affecting the temperature distribution of the sample under cyclic electric activations. To this aim, transient simulations were carried out in two steps: Step #1: Transient electric-thermal simulations; Step #2: Stationary thermo-mechanical simulations; A simplified mesh was adopted for simulating transient phenomena due to electricthermal coupling, consisting of about 5 k elements, to reduce the computational cost. The simulation time was set to 60 s, and an adaptive time step in the range of 0.001-0.1 s was adopted to improve the convergence of the model. The electrical load increment is based on discrete event step, to better simulate the behavior of the power supply. In particular, small time pulses are applied to the SMA material with a fixed time period.
The resulting maximum temperature distribution within the sample as obtained from transient electric-thermal simulation step, occurring at the end of the electric pulse, is subsequently applied to the full discretized model, and the resulting stress distribution is obtained by stationary thermo-mechanical coupled simulations. Figure 9 shows the effects of electric current on the temperature of the wire as obtained from IR measurements. In particular, Figure 9a shows the time evolution of the temperature for a square current signal with amplitude ranging from 0.32 to 1.6 A, and a pulse duration of 35 s. After a transient time, the temperature reaches a maximum steady state value T SS , corresponding to the thermodynamic equilibrium between heat generated by the Joule effect and heat exchange with the environment. Complete cooling down to room temperature is always obtained around 15 s after the pulse duration.

Electric Activation of SMA Wires
room temperature is always obtained around 15 s after the pulse duration. Figure 9a also shows a highlight of the temperature range for the thermal activation of the wire between the activation temperature of the SMA (TA = 100 °C) and the glass transition temperature of the polymer. A zoomed view of the graph within this temperature region shows the approximate values of the activation time tA defined as the time needed to reach the activation temperature TA. Figure 9b summarizes results of the experiments in terms of steady state temperature (TSS) and actuation time (tA). It is shown that a minimum current of around 1 A is required to reach temperature TA, with an actuation time ranging from between 1.4 s at i = 1.6 A to 6 s at i = 0.96 A. Additional experiments were carried out at higher electric currents, starting from the minimum current i = 1.15 A, with the aim of reducing the actuation time tA and to speed up the fatigue experiments. However, steady-state conditions were not reached in these high current experiments, as the corresponding temperature TSS would be extremely high for both polymer and SMA wire, as also shown in Figure 9a.
Square signals with small pulse duration (0.5 s, 0.75 s and 1 s) and current amplitude between 1.15 and 4 A were analyzed as shown in Figure 10.   Figure 9b summarizes results of the experiments in terms of steady state temperature (T SS ) and actuation time (t A ). It is shown that a minimum current of around 1 A is required to reach temperature T A , with an actuation time ranging from between 1.4 s at i = 1.6 A to 6 s at i = 0.96 A.
Additional experiments were carried out at higher electric currents, starting from the minimum current i = 1.15 A, with the aim of reducing the actuation time t A and to speed up the fatigue experiments. However, steady-state conditions were not reached in these high current experiments, as the corresponding temperature T SS would be extremely high for both polymer and SMA wire, as also shown in Figure 9a.
Square signals with small pulse duration (0.5 s, 0.75 s and 1 s) and current amplitude between 1.15 and 4 A were analyzed as shown in Figure 10. Figure 10a shows the temperature evolution for a current of 3.4 A and a pulse duration of 0.75 s, representing the typical response for all investigated cases. Maximum temperature results as a function of the input current are summarized in Figure 10b together with a highlight of the temperature activation range. It is shown that a minimum current of 2 A can be used for a pulse time of 1.0 s and a maximum current of around 3.  Figure 10a shows the temperature evolution for a current of 3.4 A and a pulse duration of 0.75 s, representing the typical response for all investigated cases. Maximum temperature results as a function of the input current are summarized in Figure 10b together with a highlight of the temperature activation range. It is shown that a minimum current of 2 A can be used for a pulse time of 1.0 s and a maximum current of around 3.4 A can be applied for a pulse time of 0.5 s.
A current amplitude of 3 A and a pulse time of 0.75 s has been selected for the subsequent fatigue experiments according to these results.   Figure 11 shows the results of static pullout tests of as manufactured SMA-polymer samples subjected to mechanical load (load case #1), as obtained from experimental tests ( Figure 11a) and FE simulations (Figure 11b).  Figure 10a shows the temperature evolution for a current of 3.4 A and a pulse duration of 0.75 s, representing the typical response for all investigated cases. Maximum temperature results as a function of the input current are summarized in Figure 10b together with a highlight of the temperature activation range. It is shown that a minimum current of 2 A can be used for a pulse time of 1.0 s and a maximum current of around 3.4 A can be applied for a pulse time of 0.5 s.

Static Mechanical Strength
A current amplitude of 3 A and a pulse time of 0.75 s has been selected for the subsequent fatigue experiments according to these results. Figure 11 shows the results of static pullout tests of as manufactured SMA-polymer samples subjected to mechanical load (load case #1), as obtained from experimental tests ( Figure 11a) and FE simulations (Figure 11b).  The left vertical axis in Figure 11a represents the actual normal stress in the cross section of the SMA wire, whereas the right axis is the average shear stress at the wire-polymer interface. This latter parameter is different than the maximum interface shear stress that occurs in the near extremity regions of the resin block, as clearly shown in Figure 11b.

Static Mechanical Strength
Adhesion strength under axial loading is larger than the yield strength of the SMA wire (900 MPa) a normal stress to failure (σ f ) around 940 MPa and an average shear stress to failure (τ f ) of about 3.5 MPa, corresponding to a pullout force F = 66.5N. A little dispersion among the three samples was also captured with a coefficient of variation (σ/µ) around 5%. All samples exhibit an almost sharp drop beyond the peak load with a negligible residual strength after the first damage, and complete adhesive failure occurred at the metal-polymer interface. Figure 11b illustrates the shear stress distribution at the wire-resin interface along the contact length at the maximum pullout force F max = 66.5 N, as obtained from the FE simulation.
A maximum shear stress τ max of around 30 MPa is observed at the extremity of the bi-material sample where pullout force is applied (force application side) with a rapid drop to around 5 MPa in the first 5 mm (0.75 < x/l < 1), as also shown in the zoomed view with stress distribution contour maps in Figure 11b.

Static Thermo-Mechanical Strength
According to the electric activation results, thermal activation was carried out by a continuous electric current of 1.12 A, which allows for full activation of the SMA wire with a maximum steady state temperature (T SS ) higher than 100 • C (T A ) (see Figure 9). However, the effects of electric actuation of the SMA wire on the SMA-polymer sample were analyzed by fully coupled electric-thermal-mechanical FE simulations. Figure 12a,b shows the FE results of the temperature and Young's modulus distribution in the SMA-polymer sample under steady state conditions, resulting from electric activation of the wire. The temperature in the resin block exhibits a rapid decrease from 120 • C at the SMA-polymer interface to about 40 • C at the external surface of the resin. However, effective temperature distribution under cyclic actuation is mainly affected by transient phenomena as analyzed in the following section. Figure 12b reports the evolution of the Young's modulus of the polymer resulting from material heating, according to Equation (4). A reduction from about 6.0 GPa at the outer surface to 4 GPa at the wire interface is observed. This causes an increase in the deformation in the near interface region considered to play a role on the overall adhesion strength of the SMA-polymer sample.
polymer interface. This latter parameter is different than the maximum interface shear stress that occurs in the near extremity regions of the resin block, as clearly shown in Figure 11b.
Adhesion strength under axial loading is larger than the yield strength of the SMA wire (900 MPa) a normal stress to failure (σf) around 940 MPa and an average shear stress to failure (τf) of about 3.5 MPa, corresponding to a pullout force F = 66.5N. A little dispersion among the three samples was also captured with a coefficient of variation (σ/μ) around 5%. All samples exhibit an almost sharp drop beyond the peak load with a negligible residual strength after the first damage, and complete adhesive failure occurred at the metal-polymer interface. Figure 11b illustrates the shear stress distribution at the wire-resin interface along the contact length at the maximum pullout force Fmax = 66.5 N, as obtained from the FE simulation.
A maximum shear stress τmax of around 30 MPa is observed at the extremity of the bimaterial sample where pullout force is applied (force application side) with a rapid drop to around 5 MPa in the first 5 mm (0.75 < x/l < 1), as also shown in the zoomed view with stress distribution contour maps in Figure 11b.

Static Thermo-Mechanical Strength
According to the electric activation results, thermal activation was carried out by a continuous electric current of 1.12 A, which allows for full activation of the SMA wire with a maximum steady state temperature (TSS) higher than 100 °C (TA) (see Figure 9). However, the effects of electric actuation of the SMA wire on the SMA-polymer sample were analyzed by fully coupled electric-thermal-mechanical FE simulations. Figure 12a,b shows the FE results of the temperature and Young's modulus distribution in the SMApolymer sample under steady state conditions, resulting from electric activation of the wire. The temperature in the resin block exhibits a rapid decrease from 120 °C at the SMApolymer interface to about 40°C at the external surface of the resin. However, effective temperature distribution under cyclic actuation is mainly affected by transient phenomena as analyzed in the following section. Figure 12b reports the evolution of the Young's modulus of the polymer resulting from material heating, according to Equation (4). A reduction from about 6.0 GPa at the outer surface to 4 GPa at the wire interface is observed. This causes an increase in the deformation in the near interface region considered to play a role on the overall adhesion strength of the SMA-polymer sample.  Figure 13 shows FE results of the evolution of the martensite volume fraction (ξ M ) in the SMA wire resulting from thermal activation. It is clearly shown that a fully austenitic structure is observed in the near free extremity of the sample (ξ M = 0). On the contrary, partial transformations occur within the sample, leading to ξ M = 0.6 in the middle section where only 40% of martensite is transformed in austenite, although the temperature is higher than the nominal A f temperature. This is attributed to the normal stresses in the wire, resulting from SMA activation, which causes the actual A f to rise according to the Clausius-Clapeyron relation, as also illustrated in the phase diagram of Figure 3d. (b) Evolution of the Young's modulus in the resin block. Figure 13 shows FE results of the evolution of the martensite volume fraction (ξM) in the SMA wire resulting from thermal activation. It is clearly shown that a fully austenitic structure is observed in the near free extremity of the sample (ξM = 0). On the contrary, partial transformations occur within the sample, leading to ξM = 0.6 in the middle section where only 40% of martensite is transformed in austenite, although the temperature is higher than the nominal Af temperature. This is attributed to the normal stresses in the wire, resulting from SMA activation, which causes the actual Af to rise according to the Clausius-Clapeyron relation, as also illustrated in the phase diagram of Figure 3d.    (b) Evolution of the Young's modulus in the resin block. Figure 13 shows FE results of the evolution of the martensite volume fraction (ξM) in the SMA wire resulting from thermal activation. It is clearly shown that a fully austenitic structure is observed in the near free extremity of the sample (ξM = 0). On the contrary, partial transformations occur within the sample, leading to ξM = 0.6 in the middle section where only 40% of martensite is transformed in austenite, although the temperature is higher than the nominal Af temperature. This is attributed to the normal stresses in the wire, resulting from SMA activation, which causes the actual Af to rise according to the Clausius-Clapeyron relation, as also illustrated in the phase diagram of Figure 3d.    Figure 14a shows a significant reduction in the applied mechanical stress to failure with respect to load case #1 with σ f = 277 MPa and τ f = 1.2 MPa corresponding to a pullout force F = 19.6 N. However, the total internal axial stress in the SMA sample is given by the combination of the applied mechanical stress and the recovery stress generated by SMA thermal activation, as schematically shown in Figure 4. The effects of the two loading conditions on the shear stress at the wire-resin interface are shown in the FE results of Figure 14b. It is shown that the SMA thermal activation generates a self-equilibrated and antisymmetric shear stress distribution with opposite signs at the two sides of the samples, with a maximum value of about 25 MPa. The maximum mechanical shear stress component is around 8 MPa, which is much lower than the load case #1 (30 MPa). Furthermore, the mechanical component at the bottom side of the sample (force application side), has an opposite direction with respect to the thermal one, resulting in a lower total shear stress with respect to the upper side (free end side) where only thermal stresses are present.
Nevertheless, these results demonstrate that the two load cases exhibit similar maximum shear stresses at failure around 30 MPa for load case #1 and 25 MPa for load case #2, although in the second case the external applied mechanical force is more than three times lower (66.5 N vs. 19.6 N).
However, normal stresses in the radial direction are also generated at the SMA-polymer interfaces that are expected to play an important role on pullout forces due to friction mechanisms. These stress components can be attributed to two distinct phenomena: (i) transversal mechanical strain components due to Poisson's effects and (ii) differences in the thermal strains between SMA wire and polymer.
Regarding the Poisson's effects, tensile stress in the wire causes a transversal diameter contraction, and similarly, compressive stress in the near interface zone of the polymer generates a hole contraction. Balance between these transversal strain components, which are due to different stresses and Poisson's ratios in SMA and polymer, could lead to either normal tensile or compressive stresses at the interface. This is an even more complex phenomenon in SMAs due to the distinct Poisson's ratios of the austenite and martensite phases.
Accurate measurements/estimation of the Poisson's ratios of the two phases is extremely difficult due to the combination of thermal and stress-induced transformation phenomena, such that Poisson's effects are intricately coupled with thermal and shape memory strains. However, it was found that martensite phase show values of the Poisson's ratio in the range of 0.31-0.44 [28,44,45] that seem to be significantly lower than the austenite one, which would be in the range of 0.37-1.77 [28,44,45]. This is considered as an important effect when comparing pullout forces from load cases #1 and #2. In the case of combined application of mechanical stresses and thermal activation (case #2), the SMA wire is in austenite phase, and it would experience a larger diameter contraction with respect to the mechanical force only (case #1), resulting in a reduced pullout force. This effect was also observed in previous investigations [28] where pullout force under isothermal conditions in martensitic wires was found to be higher than in austenitic ones.
More intricate thermomechanical coupling effects occur in the present experiments due to the combination of mechanical loading and thermal activation of the SMA wire. Poisson's effects are coupled with different thermal strains in SMA and polymer, which can be attributed to dissimilar coefficients of thermal expansion (CTE) and different temperature distributions in the two materials. From this standpoint, a larger expansion would be expected in the wire mainly due to the much higher temperature, resulting in a compressive normal stress and improving the pullout resistance. However, the total transversal effects in the SMA-polymer samples cannot be easily estimated due to simulation complexities and uncertainties about the evolution of material properties during stress and/or thermally induced phase transformation, such as in terms of CTEs and Poisson's ratios.
However, the maximum normal stress is always higher than the detwinning stress of martensite (150 MPa) that is a critical condition for reversible actuation of the SMA-polymer system. Furthermore, a serrated trend of the curve is observed beyond the peak load that is attributed to stick-slip phenomena at the SMA-polymer interface, probably attributed to the increased polymer ductility at higher temperature.

Thermo-Mechanical Fatigue
Based on the thermal activation measurements described in Section 3.1, the cyclic actuation current was selected for thermo-mechanical fatigue tests with an electric current i = 3 A and a pulse duration of 0.75 s. This condition allows for complete thermal activation of the SMA wire (T A > 100 • C) without excessive overheating that could cause polymer degradation.
The effects of thermal activation of the wire in the SMA-polymer sample were also analyzed by time-dependent FE simulations using a fully coupled electric-thermal-mechanical model. Figure 15 reports the time evolution of the temperature in the SMA wire for two subsequent thermal activation cycles (current 3 A, pulse time 0.75 s, period 30 s).

Thermo-Mechanical Fatigue
Based on the thermal activation measurements described in Section 3.1, the cyclic actuation current was selected for thermo-mechanical fatigue tests with an electric current i = 3 A and a pulse duration of 0.75 s. This condition allows for complete thermal activation of the SMA wire (TA > 100 °C) without excessive overheating that could cause polymer degradation.
The effects of thermal activation of the wire in the SMA-polymer sample were also analyzed by time-dependent FE simulations using a fully coupled electric-thermalmechanical model. Figure 15 reports the time evolution of the temperature in the SMA wire for two subsequent thermal activation cycles (current 3 A, pulse time 0.75 s, period 30 s). Maximum temperature (around 145 °C) is almost the same as the one measured by IR investigations on the SMA wire (Figure 10b). It is attributed to the negligible heat exchange with the resin block in the short pulse time (0.75 s). Similarly, a fast cooling is observed after the pulsed current with a sharp decrease in the first 5 s (to around 50 °C), as the resin block acts as a heat sink, and a subsequent slow decrease to room temperature is obtained after about 30 s. Accordingly, a period of 30 s was set for thermomechanical fatigue tests. Figure 16a,b reports the FE results of the temperature and Young's modulus distribution in the resin block at the maximum current time (t = 0.75 s), respectively. Both figures show that thermal effects in the resin block are confined in a small radial distance from the SMA wire, where a sharp decrease to T < 100 °C is observed within a radial distance of around 100 μm and resin heating vanishes at around 800 μm. This result is significantly different with respect to the continuous current activation as reported in Figure 12, where generalized heating of the resin sample is observed with a temperature at the outer radius higher than 50 °C. Maximum temperature (around 145 • C) is almost the same as the one measured by IR investigations on the SMA wire (Figure 10b). It is attributed to the negligible heat exchange with the resin block in the short pulse time (0.75 s). Similarly, a fast cooling is observed after the pulsed current with a sharp decrease in the first 5 s (to around 50 • C), as the resin block acts as a heat sink, and a subsequent slow decrease to room temperature is obtained after about 30 s. Accordingly, a period of 30 s was set for thermomechanical fatigue tests. Figure 16a,b reports the FE results of the temperature and Young's modulus distribution in the resin block at the maximum current time (t = 0.75 s), respectively. Both figures show that thermal effects in the resin block are confined in a small radial distance from the SMA wire, where a sharp decrease to T < 100 • C is observed within a radial distance of around 100 µm and resin heating vanishes at around 800 µm. This result is significantly different with respect to the continuous current activation as reported in Figure 12, where generalized heating of the resin sample is observed with a temperature at the outer radius higher than 50 • C.
Thermo-mechanical fatigue tests were executed with a run out of 5000 cycles, and mechanical load was selected in the range 200-270 MPa. The lower value (200 MPa) is close to the minimum allowable stress for martensite detwinning (150 MPa), whereas the upper one (270 MPa) corresponds to the average value of the maximum static strength obtained from pullout tests in load case #2 (see Figure 12b). Figure 17a shows the characteristic evolution of displacement versus number of cycles, as directedly measured from the LVDT transducer of the testing rig (see Figure 6), which was obtained under a mechanical stress of 225 MPa. The curve shows an almost constant displacement amplitude associated with an increase in the average displacement, mainly attributed to creep-like phenomena and strain ratcheting of the SMA wire. These effects are more rapid in the first 100 cycles and then evolve almost linearly with further increases in the number of cycles. Fatigue damages are observed around 80-90% of fatigue life, which are attributed to stick-slip phenomena before complete failure. The latter phenomenon is exactly the same as for the static pullout tests, that is, the complete debonding between SMA wire and polymer block. Thermo-mechanical fatigue tests were executed with a run out of 5000 cycles, and mechanical load was selected in the range 200-270 MPa. The lower value (200 MPa) is close to the minimum allowable stress for martensite detwinning (150 MPa), whereas the upper one (270 MPa) corresponds to the average value of the maximum static strength obtained from pullout tests in load case #2 (see Figure 12b). Figure 17a shows the characteristic evolution of displacement versus number of cycles, as directedly measured from the LVDT transducer of the testing rig (see Figure 6), which was obtained under a mechanical stress of 225 MPa. The curve shows an almost constant displacement amplitude associated with an increase in the average displacement, mainly attributed to creep-like phenomena and strain ratcheting of the SMA wire. These effects are more rapid in the first 100 cycles and then evolve almost linearly with further increases in the number of cycles. Fatigue damages are observed around 80-90% of fatigue life, which are attributed to stick-slip phenomena before complete failure. The latter phenomenon is exactly the same as for the static pullout tests, that is, the complete debonding between SMA wire and polymer block. Figure 17b reports fatigue data obtained from all tested samples in the log-log S-N diagram. Data points are well fitted by a straight line (R 2 = 0.95), and the corresponding parameters of the Basquin's equation are also shown in the figure. Samples tested at σ = 200 MPa experienced run-out (5000 cycles), whereas failure always occurred at higher stress values, ranging from about 150 cycles at σ = 270 MPa to around 1500 cycles at σ = 235 MPa. These results make SMA-polymer integration compatible for the realization of smart composites, as 200 MPa is higher than the detwinning stress of SMA, which is required to obtain pre-strain at low temperature and shape recovery reversibility with heating and cooling cycles. However, great attention should be paid to the design task to not exceed this critical stress level given by the combination of the elastic bias of the deformed composite and the applied external load. To better understand the role of cyclic thermal loads of the SMA-polymer samples, pullout tests were repeated after 1000 thermal activation cycles with no external stress applied. Results of pullout tests of such fatigued samples are reported in Figure 18 in terms of experimental stress vs. displacement curve (Figure 18a) and FE results ( Figure  18b). Direct comparison with results obtained from static mechanical tests (see Figure 11) shows a reduction of the adhesion strength, with a decrease in the mean values from 942 to 808 MPa. Accordingly, a slightly lower maximum shear stress at the near extremity of the sample (25 MPa) is observed with respect to load case #1 (30 MPa), as shown in Figure  18b. These results confirm the important role of combined thermal activation and mechanical stress on static and fatigue damage of SMA-polymer samples attributed to both stresses generated by SMA activation and polymer degradation with increasing temperature.  Samples tested at σ = 200 MPa experienced run-out (5000 cycles), whereas failure always occurred at higher stress values, ranging from about 150 cycles at σ = 270 MPa to around 1500 cycles at σ = 235 MPa. These results make SMA-polymer integration compatible for the realization of smart composites, as 200 MPa is higher than the detwinning stress of SMA, which is required to obtain pre-strain at low temperature and shape recovery reversibility with heating and cooling cycles. However, great attention should be paid to the design task to not exceed this critical stress level given by the combination of the elastic bias of the deformed composite and the applied external load.
To better understand the role of cyclic thermal loads of the SMA-polymer samples, pullout tests were repeated after 1000 thermal activation cycles with no external stress applied. Results of pullout tests of such fatigued samples are reported in Figure 18 in terms of experimental stress vs. displacement curve (Figure 18a) and FE results (Figure 18b). Direct comparison with results obtained from static mechanical tests (see Figure 11) shows a reduction of the adhesion strength, with a decrease in the mean values from 942 to 808 MPa. Accordingly, a slightly lower maximum shear stress at the near extremity of the sample (25 MPa) is observed with respect to load case #1 (30 MPa), as shown in Figure 18b. These results confirm the important role of combined thermal activation and mechanical stress on static and fatigue damage of SMA-polymer samples attributed to both stresses generated by SMA activation and polymer degradation with increasing temperature. To better understand the role of cyclic thermal loads of the SMA-polymer samples, pullout tests were repeated after 1000 thermal activation cycles with no external stress applied. Results of pullout tests of such fatigued samples are reported in Figure 18 in terms of experimental stress vs. displacement curve (Figure 18a) and FE results ( Figure  18b). Direct comparison with results obtained from static mechanical tests (see Figure 11) shows a reduction of the adhesion strength, with a decrease in the mean values from 942 to 808 MPa. Accordingly, a slightly lower maximum shear stress at the near extremity of the sample (25 MPa) is observed with respect to load case #1 (30 MPa), as shown in Figure  18b. These results confirm the important role of combined thermal activation and mechanical stress on static and fatigue damage of SMA-polymer samples attributed to both stresses generated by SMA activation and polymer degradation with increasing temperature.

Conclusions
A novel class smart composite with shape morphing capabilities, combining shape memory alloys (SMA) and polymer matrix composites (PMC), are being investigated for possible use in active aerodynamic components in automotives. SMA/PMC systems combine advantageous strength-and stiffness-to-weight ratios of polymer composites with the unique force and shape recovery capabilities of SMAs. The main issues for SMA-polymer integration were analyzed, which are mostly related to the limited strength of metal-polymer interfaces. To this aim, systematic tests of SMA-polymer samples were carried out under both complex static and fatigue thermomechanical loading conditions. Numerical simulations were also carried out, by using coupled electric-thermal-mechanical models for a better understanding of damage phenomena occurring under both mechanical load and SMA thermal activation. The main results can be summarized as follows: • Static pullout strength of samples subjected to mechanical load (around 900 MPa) is remarkably higher than the martensite reorientation stress and is close to the maximum recoverable stress of SMA wires; • Static pullout stress of the SMA-polymer samples are mainly unaffected by cyclic activation cycles (up to 1000). Maximum stress obtained from pullout tests is similar to that of manufactured samples; • A marked reduction in pullout stress is observed under combined application of mechanical load and SMA thermal activation. This is attributed to the large interface stresses, which are due to both mechanical load and shape recovery in SMA, coupled with a reduction in polymer strength with increasing temperature; • Fatigue strength corresponding to runout (5000 cycles) is still higher than the stress for martensite reorientation. This makes the SMA-polymer bi-material system suitable for repeated activations of morphable surfaces.