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Crack-tip thermal and mechanical hysteresis in Shape Memory Alloys under fatigue loading
Materials Science & Engineering A 616 (2014) 281–287
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Crack-tip thermal and mechanical hysteresis in Shape Memory Alloys under fatigue loading C. Maletta a,n, L. Bruno a, P. Corigliano b, V. Crupi b, E. Guglielmino b a b
Department of Mechanical, Energy and Management Engineering, University of Calabria, Ponte P. Bucci 46 C, 87036 Rende, CS, Italy University of Messina, Department of Industrial Chemistry and Materials Engineering, Contrada di Dio, Sant’Agata (ME), 98166 Messina, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 21 May 2014 Received in revised form 31 July 2014 Accepted 1 August 2014 Available online 10 August 2014
Crack tip stress-induced phase transformation mechanisms in nickel–titanium alloys (NiTi), subjected to fatigue mechanical loads, have been analyzed by full field measurement techniques. In particular, Infrared thermography (IR) and Digital Image Correlation (DIC), have been applied to analyze the cyclic temperature and displacement evolutions in the crack tip region of a commercial pseudoelastic alloy, together with the associated thermal and mechanical hysteresis, by using Single Edge Crack (SEC) specimens. IR investigations revealed a global temperature variation of the specimen due to crack formation and propagation mechanisms, which is similar to common engineering metals, i.e. surface temperature rises quickly in an initial phase, then it reaches an almost constant value, and finally it increases rapidly as a consequence of the fatigue crack growth. In addition, cyclic thermal variation in the crack tip region and related hysteresis (temperature vs load) has been measured, which can been directly related to the thermal effects of the reversible stress-induced phase transformations. Furthermore, a proper experimental setup has been made, based on a reflection microscope, for direct measurements of the crack tip displacement field by the DIC technique. Furthermore, a fitting procedure has been developed to calculate the mode I Stress Intensity Factor (SIF), starting from the displacement field, and the related mechanical hysteresis (SIF vs load). & 2014 Elsevier B.V. All rights reserved.
Keywords: Shape Memory Alloy Stress-Induced Transformation Fracture Fatigue Infrared thermography Digital Image Correlation
1. Introduction Shape Memory Alloys (SMAs), and in particular the near equiatomic nickel titanium ones (NiTi), have seen an increasing interest in last years, from both scientific community and industrial sector, thanks to their interesting functional features, coupled with good mechanical properties and biocompatibility [1]. Indeed, NiTi alloys undergo a reversible solid state phase transition between a parent austenitic phase (B2) and a product martensitic one (B190 ) [2], the so-called Thermoelastic Martensitic Transformation (TMT), which can be activated by temperature changes (TIM, Thermally-Induced Martensite) or by mechanical loads (SIM, Stress-Induced Martensite). Due to these reversible microstructural transitions NiTi alloys exhibit unique shape recovery capabilities, the so-called Shape Memory Effect (SME) and Pseudoelastic Effect (PE). In particular, thanks to SME NiTi alloys are able to recover large pseudo-plastic mechanical deformations by temperature changes (TIM), while PE represents a high recovery capability obtained by mechanical unloading (SIM). These functional properties are currently exploited for the implementation
n
Corresponding author. E-mail address: [email protected] (C. Maletta).
http://dx.doi.org/10.1016/j.msea.2014.08.007 0921-5093/& 2014 Elsevier B.V. All rights reserved.
of several active and/or tunable devices in many fields of engineering, such as for actuation systems, for vibration control and damping, for self-healing and/or high impact resistance composite materials. However, the most successful applications of NiTi alloys are currently in the field of bio-engineering and medicine, where PE is mainly exploited for the realization of several high valueadded components (e.g. cardiovascular stents, embolic protection filters, micro surgical devices, orthopedic grips, etc.). Although, the high scientific and technological interest in NiTi alloys, many aspects related to their mechanical behavior are still unknown, especially because the hysteretic stress and/or thermally induced phase transformations significantly affect the damage mechanisms occurring under fatigue loadings, i.e. the crack formation and propagation mechanisms. In fact, as a direct consequence of the marked non linear and hysteretic behavior, classic elastic and/or elastic–plastic theories cannot be directly applied to SMAs. In addition, the constitutive laws implemented in commercial finite element software are based on phenomenological approaches and on theory of plasticity, i.e. they use plasticity-like concepts to describe the effects of phase transformation mechanisms on the macroscopic response of NiTi alloys [3]. Though these numerical methods represent useful design tools to simulate the macroscopic response of simple or complex SMA based systems, special care should be taken when they are used to study the local effects in
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the proximity of high stress concentration regions. In particular, it has been demonstrated that the high values of local stresses arising in the crack tip region of NiTi alloys cause stress-induced phase transition mechanisms [4–21], which significantly affect the crack tip stress distribution and, consequently, the crack evolution under both static and fatigue loading conditions. In addition, repeated stress-induced phase transitions, occurring during fatigue loading, cause an unusual temperature evolution, which can be directly related to the exothermic and endothermic effects of direct (B2-B190 ) and reverse (B190 -B2) phase transformations, respectively. Despite the increasing number of research activities on fracture and fatigue of NiTi alloys in recent years, much effort should be devoted for an effective understanding of the role of the hysteretic stress and/or thermally-induced phase transformations in the crack formation and propagation mechanisms. Within this context, the development and application of full field techniques to analyze the local transformation mechanisms near geometrical discontinuities and, in particular, in the crack tip region, represent a highly challenging scientific goal. For this purpose, synchrotron X-ray micro-diffraction (XRD) [4–6], infrared thermographic (IR) [7] and Digital Image Correlation (DIC) [8,9] techniques have been recently applied, to better understand the mechanisms of phase transformation in the notch and/or crack tip proximity. In particular, a pseudoelastic NiTi alloy for medical applications has been analyzed in [4] by using miniature compact-tension (CT) specimens, which were directly obtained from thin-walled tubes, similar to those used for manufacturing self-expanding stents. XRD microdiffraction investigations of fatigue pre-cracked specimens revealed that the crack tip local strain are due to both B2 to B190 transformation and to the subsequent loading of the martensitic phase. Strain and texture evolution near the crack tip of a martensitic NiTi alloy have been analyzed in [5], by synchrotron X-ray experiments, after fatigue crack propagation in a compacttension (CT) specimen; it has been found that texture evolution is mainly due to detwinning, the main deformation mechanism in martensitic NiTi alloys. Both martensitic and austenitic alloys have been analyzed in [6], by using miniaturized CT specimens [10] after fatigue crack propagation, which revealed the presence of detwinned martensite at the crack tip of both martensitic and austenitic specimens. Miniature CT specimens were also analyzed in [7] by using IR thermography which highlighted the reversibility of crack tip phase transformation, i.e. the direct B2 to B190 transformation during loading and the reverse B190 to B2 transformation during unloading. An austenitic NiTi alloy has been analyzed in [8] by DIC analysis of thin edge cracked specimen, which allowed direct measurement of the crack tip strain field related to stress-induced transformation. These experimental investigations, together with other several recent numerical [11– 13] and analytical [14–21] studies, provide very useful information about the occurrence of crack tip transition mechanisms in NiTi alloys subjected to static and/or monotonic loads. However, the role of these mechanisms on the fracture properties on NiTi alloys is not yet completely defined, i.e. no reliable methodologies have been developed for an effective design against fracture. In addition, the evolution of microstructural changes at the crack tip occurring during fatigue loading, i.e. the thermal and mechanical hysteretic behavior, has been not yet investigated. This topic is of major concern as the hysteretic nature of phase transitions is expected to play a significant role on the crack growth mechanisms. Within this context, the main goal of this research activity consists in the development and application of full field experimental techniques to analyze the mechanisms of phase transformation in NiTi alloys under cyclic mechanical loads. In particular, IR and DIC techniques have been applied to analyze the evolution of temperature and displacement field in the crack tip region of a
Single Edge Crack (SEC) specimen, obtained by electro discharge machining (EDM) from a commercial NiTi sheets with pseudoelastic behavior. IR investigations were applied to analyze the global temperature evolution of the specimen, as well as to track the cyclic temperature changes at the crack tip during mechanical loading, together with the associated thermal hysteresis, in terms of temperature vs load. DIC method has been used to analyze the displacement field in the crack tip region and to estimate the mode I stress-intensity factor (SIF) by a data fitting procedure, based on the William's series expansion [22], as well as to measure the mechanical hysteretic response in terms of SIF vs load.
2. Materials and methods 2.1. Materials A commercial nickel–titanium sheet (thickness t ¼0.5 mm) with pseudoelastic properties at room temperature (50.8 at% Ni– 49.2 at% Ti, Type S, Memry, Germany) was used in this investigation. Fig. 1 shows the isothermal (T¼ 298 K) stress strain (σ ε) response of the material obtained from a complete loading– unloading cycle up to a maximum deformation of about 6.2%, corresponding to a complete stress-induced martensite transformation. The figure also reports the values of the main thermomechanical parameters of the alloy: transformation stresses (σAM s , MA σAM and σMA f , σs f ), tranformation strain (εL), Young's moduli of austenite and martensite (EA and EM) and Clausius–Clapeyron constants (CA and CM). Fig. 2 shows the DSC thermogram of the alloy, which was measured in the temperature range between 173 K and 373 K at a heating/cooling rate of 10 K/min. The figure clearly shows a two stage phase transformation during cooling (B2-R-B190 ), while there is no evidence of the R-phase transformation during heating (B190 -B2). The figure reports also the values of all transformation temperatures (Ms, Mf, As, Af, Rs and Rf) as well as the latent heat of transformation. 2.2. Methods Sigle Edge Crack (SEC) specimens were used for the fatigue tests, as illustrated in Fig. 3. In particular, specimens were directly obtained from commercial NiTi sheets and a pre-crack with a notch radius of about 100 μm and with a length ratio, a/W, equal to 0.3 were made by wire electro discharge machining (EDM). Subsequently, fatigue cracks were produced by fatigue mechanical
Fig. 1. Isothermal (T ¼298 K) stress strain (σ ε) response of the SMA under a complete loading–unloading cycle.
C. Maletta et al. / Materials Science & Engineering A 616 (2014) 281–287
loads, carried out by using a servo hydraulic testing machine (Instron 8500) and with the following parameters: frequency f ¼5 Hz, load ratio R ¼0 and maximum load Pmax ¼100 N (σmax ¼ Pmax/Wt¼20 MPa). No surface treatments were performed on the specimens, which were tested in the as-supplied conditions, thus outer surface is characterized by a titanium oxide layer with a roughness Ra¼ 0.24 70.03 μm, measured by a contact measuring system (MahrSurf III, Mahr). Load frequency f was chosen by preliminary tests with the aim of satisfying two opposite needs: low enough to obtain a significant number of infrared images per cycle, according to the maximum frame rate of the IR camera (100 Hz), and sufficiently high to keep low heat exchange during stress-induced transformations. This issue has also been discussed in a previous study [7], where only single loading cycles under high deformation rate have been analyzed by IR investigations, in order to reduce the thermal exchange and, consequently, to get the maximum temperature variation of the specimen.
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It is worth noting that the loading rate in SMAs has a much more important role, if compared with common engineering alloys, even under monotonic loading conditions [26], because it significantly affects the specimen temperature and, consequently, the stress–strain response, according to the Clausius–Clapeyron relation. The effects of both surface roughness and load frequency were not investigated in the present paper. Specimens for IR instigations were black painted, in order to have a good emissivity value (ε ¼ 0.95), and infrared images were recorded during fatigue tests (R¼0, Pmax ¼350 N, f ¼5 Hz), in order to capture the temperature pattern during loading cycles. An IR camera (FLIR, SC7200) was used, with a resolution of 320 256 pixels, and results were analyzed by a commercial IR imaging software (Flir, Altair). Thermal analyses were carried out by two different methods, namely the global and the local analyses. In the global analysis the temperature pattern and evolution in a surrounding area of the notch, with a dimension of 1 mm 1 mm (see Fig. 3), were studied during crack grow, while in the local analysis the temperature change at a point near the crack tip, was monitored. Digital Image Correlation analyses were carried to measure the crack tip displacement field, by using a non commercial ad-hoc configuration, based on a reflection microscope. In particular, the lighting was achieved through a Köhler optical scheme, using as a light source a square CREELED of side 3.3 mm. The camera (Sony XCD- X910 model) has a CCD sensor with 1280 960 squares pixels of 4.65 μm. The focus of the images was performed using a Linos Photonics microscope objective with a 4 magnification and a numerical aperture of 0.1, which ensures, in conditions of correct illumination, a resolution of approximately 2.5 μm, and therefore lower than the pixel size of the camera. 3. Results and Discussions 3.1. Thermographic analysis
Fig. 2. Differential scanning calorimetric curve of the SMA.
Thermographic analyses presented in this section were carried out by considering the evolution of a relative temperature (Tr),
Fig. 3. Single Edge crack specimen with a focus of the notch region.
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Fig. 4. Evolution of the maximum temperature within the investigated area (T*area), as a function of the number of loading cycles (N).
which represents the difference between the current temperature (T) and initial temperature (T0) of the specimen (Tr ¼T T0). Fig. 4 illustrates the results of the global analysis, i.e. the temperature evolution in the surrounding area (Tr,area) of the notch (see Fig. 3) during fatigue loading (f¼5 Hz, R¼0, Pmax ¼300 N, σmax ¼ 60 MPa). In particular, the evolution of the maximum temperature within the investigated area (Tr,area), as a function of the number of loading cycles (N), is analyzed. The figure clearly shows that the obtained Tr,area–N curve is characterized by three subsequent phases (namely, Phase I, II and III) similar to high cycle [23] and low-cycle [24] fatigue behavior of common engineering metals. In particular, when a specimen is cyclically loaded above its fatigue limit, the temperature of the specimen surface usually rises quickly in the initial phase (Phase I), then reaches an almost asymptotic value (Phase II), and finally there is a very high temperature increment (Phase III) as soon as the crack size becomes significant, leading to fracture after a few cycles. This temperature evolution is closely related to the internal microstructural changes, as demonstrated in [25]. The large scatter of the data in Fig. 4, is mainly attributed to the cyclic temperature variations, i.e. to the repeated stress-induced exothermic and endothermic transformations (see Fig. 2) in the notch/crack tip region. For a better understanding of this effect a local thermal analysis at the crack tip has been carried out, i.e. by measuring and analyzing the local relative temperature at the crack tip (Tr,tip) during fatigue loading. Fig. 5 illustrates the evolution of the temperature Tr,tip and of the applied load P, as a function of the time, for two subsequent loading cycles in Phase I (see Fig. 4). In addition, the figure illustrates a schematic depiction of the stress strain curve of the alloy with some characteristic points (1–6) and their corresponding positions on the load and temperature curves. In particular, five loading regions are identified: (1–2) athermal elastic deformation of austenite, (2–3) direct exothermic A-M transformation, (3–4) athermal elastic unloading of stress-induced martensite, (4–5) reverse endothermic M-A transformation and (5–6) athermal elastic unloading of austenite. The figure clearly shows a direct correlation between the thermal effects of the loading cycle, e.g. of the five aforementioned regions, and the evolution of the crack tip temperature (Tr,tip). In the region (1–2) the local temperature is almost constant, since no phase transformations occur. The local temperature suddenly increases in the second region (2–3), as a result of the exothermic phase transformation from austenite to martensite (A-M), up to the maximum
Fig. 5. Evolution of the crack tip temperature, Tr,tip, and of the applied load, P, as a function of the time, for two subsequent loading cycles in Phase I.
temperature Tmax r,tip . A temperature decrease is observed in region (3–4), due to spontaneous cooling, as well as in the subsequent region (4–5), due to the endothermic M-A transformation, down to a minimum temperature Tmin r,tip, which could be even negative, i.e. current temperature is below the initial specimen temperature. As a consequence of this overcooling a spontaneous temperature increase is observed during the elastic recovery (5–6). A similar trend of the crack tip temperature was observed in the three different phases, as shown in Fig. 6, although they exhibit different values for the maximum and minimum temperamax ture (Tmin r,tip and Tr,tip ). In particular, the figure reports the temperature evolution in 1 s, corresponding to five subsequent thermal cycles, taken at given number of cycles for each of the three aforementioned phases (Phase I – N E1000, Phase II – N E5000, Phase III – N E10,000). Fig. 6 also illustrates IR images of the temperature patterns corresponding to the maximum and minimum temperature. A comparison among the three temperature curves shows an max increase of both Tmin r,tip and Tr,tip with increasing the number of cycles together with an increase of the mean temperature Tmean r,tip , as it is also evident from Fig. 4. Furthermore, a marked increase of the temperature range, ΔTr,tip, is observed only in the third phase. This effect can be directly attributed to the crack growth and, consequently, to the higher values of crack tip stresses which, in turn, increase the fraction of material undergoing phase transformation. In addition, the temperature plateau (1–2) is less evident in phase III as the phase transition mechanisms at the crack tip become predominant with respect to the athermal elastic deformations. Finally, Fig. 7 illustrates the relation between applied load and crack-tip temperature for the three subsequent phases. The figure clearly shows a marked thermal hysteretic behavior, which is directly related to the hysteresis in the stress-induced phase transition mechanism. As discussed above Phase III shows a more evident hysteresis, i.e. a higher value of the temperature range, due to the larger amount of material subjected to phase transformation. 3.2. DIC analysis Fig. 8 illustrates the fringe plots of the near crack tip displacement field (500 μm 500 μm), in a specimen with a crack length/ width ratio (a/W) equal to 0.48 and for an applied load (P) equal to 300 N. This corresponds to a nominal remote stress (σ0 ¼ P/tW) of pffiffiffiffiffiffi 60 MPa and a remote stress intensity factor (K 0 ¼ σ 0 πa) equal to 1/2 7.40 MPa m . In particular, Fig. 8a and b illustrates the contour
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Fig. 6. Evolution of the crack tip temperature, Tr,tip, in the three phases and temperature patterns corresponding to the maximum and minimum temperatures.
Fig. 7. Thermal hysteresis, Temperature vs Load, obtained in the three loading phases.
plots of the horizontal (ux) and vertical (uy) displacement components, respectively, which were obtained from fitting of the DIC data by the William's series expansion [22]. Furthermore, for a given value of the Young's modulus, which was assumed to be constant and equal to that of austenitic untransformed structure (EA ¼ 68 GPa), the fitting procedure allows a direct estimation of the mode I stress-intensity factor (KI). Fig. 9, shows the evolution of KI as a function of K0 during a complete loading–unloading cycle with σ0 varying between 0 and 60 MPa. As expected, the KI–K0 curve shows a marked non-linear hysteretic behavior, which can be directly attributed to the complex stress–strain hysteretic behavior of SMAs (see Fig. 1) and, as well known, this result is in contrast with the Linear Elastic Fracture Mechanics (LEFM) theory, according to which a linear relationship between KI and K0 is expected. In fact, it has been demonstrated that the high values of local stresses, occurring in the crack tip region, cause stress-induced microstructural transitions which significantly affects the stress and strain distribution [16]; in addition, these mechanisms are
expected to be path dependent according to hysteresis associated with the austenite to martensite transformation kinetics. Furthermore, the mismatch between the Young's moduli of the two phases (see Fig. 1) represents an uncertainty factor in estimating the values of the stress intensity factor from displacement fitting methods, as discussed above. To better understand the effect of phase transition mechanisms on the estimation of stress intensity factor, by the William's series expansion, different systematic calculations have been carried out by varying the dimension of the fitting area around the crack tip. In particular, the curves reported in Fig. 10 were obtained by decreasing the edge of the square region, by step of 50 μm, hence the lowest curve was that of Fig. 9, evaluated on an area of 500 μm 500 μm, while the highest one was evaluated on a region of 200 μm 200 μm. The results show that for an area greater than or equal to 500 μm x 500 μm the calculation of KI is independent by the dimension of the area itself, while for smaller regions the value of KI increases, at the beginning slowly and then more rapidly. Furthermore, it can be noticed that when the calculation of KI is performed on a small area a kind of regime value for KI occurs, i. e. KI reaches a stable maximum value over a wide range of K0 and it can be directly attributed to the crack tip stress-induced transformation, which occurs on a stress–strain transformation plateau (see Fig. 1). However, it is worth noting that, similarly to plasticity in common metals, the transformation mechanisms significantly affect the crack tip stress and strain fields with respect to the LEFM theory, i.e. the application of William's series expansion, to obtain KI from displacement field, could give inaccurate results. As a consequence, KI becomes more and more different from the LEFM predictions and the range of applicability of this parameter to SMAs should be proven by specific studies, by identifying the K-dominant region [17]. In addition, a more accurate evaluation of KI should take into account the variation of Young's modulus due the stress-induced transition, which decreases to EM ¼ 48 GPa in the region where the transformation is complete.
4. Conclusions Two full field techniques were applied to study the phase transition mechanisms at the crack tip in NiTi alloys: Infrared
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Fig. 8. Fringe plots of the crack tip displacement obtained from fitting of the DIC data (dimensions and displacement values expressed in μm): (a) horizontal displacement component ux (orthogonal to the loading direction) and (b) vertical displacement component uy (parallel to the loading direction).
Fig. 9. Mode I stress intensity factor KI as a function of the applied remote stress intensity factor K0.
Fig. 10. Mode I stress intensity factor KI as a function of the applied remote stress intensity factor K0 calculated by varying the dimension of the data fitting area around the crack tip.
technique (IR) and Digital Image Correlation (DIC). To this aim Single Edge Crack (SEC) specimens, obtained from a commercial NiTi sheets with pseudoelastic behavior by Electro Discharge Machining (EDM), were analyzed. IR investigations were applied to analyze the global temperature evolution of the specimen, which clearly identifies the crack propagation mechanisms similarly to common engineering alloys, as well as to track the cyclic temperature changes at the crack tip during mechanical loading. This temperature evolution has been directly related to the direct and reverse crack tip stress-induced phase transformation mechanism occurring during loading and unloading; a marked thermal hysteresis, in terms of temperature vs load, has been noticed, which is expected to significantly affect the crack propagation mechanisms in SMAs. DIC method has been used to analyze the displacement field in the crack tip region and data fitting procedures, based on the William's series expansion, have been applied to estimate the mode I Stress-Intensity Factor (SIF). As expected, the SIF vs load curves show a marked non-linear hysteretic behavior, which can be directly attributed to the
complex stress–strain hysteretic behavior of SMAs. Future studies will be addressed to better understand the role of both thermal and mechanical hysteretic behavior on the crack propagation mechanisms in NiTi alloys.
Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.msea.2014.08.007.
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Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Crack-tip thermal and mechanical hysteresis in Shape Memory Alloys under fatigue loading C. Maletta a,n, L. Bruno a, P. Corigliano b, V. Crupi b, E. Guglielmino b a b
Department of Mechanical, Energy and Management Engineering, University of Calabria, Ponte P. Bucci 46 C, 87036 Rende, CS, Italy University of Messina, Department of Industrial Chemistry and Materials Engineering, Contrada di Dio, Sant’Agata (ME), 98166 Messina, Italy
art ic l e i nf o
a b s t r a c t
Article history: Received 21 May 2014 Received in revised form 31 July 2014 Accepted 1 August 2014 Available online 10 August 2014
Crack tip stress-induced phase transformation mechanisms in nickel–titanium alloys (NiTi), subjected to fatigue mechanical loads, have been analyzed by full field measurement techniques. In particular, Infrared thermography (IR) and Digital Image Correlation (DIC), have been applied to analyze the cyclic temperature and displacement evolutions in the crack tip region of a commercial pseudoelastic alloy, together with the associated thermal and mechanical hysteresis, by using Single Edge Crack (SEC) specimens. IR investigations revealed a global temperature variation of the specimen due to crack formation and propagation mechanisms, which is similar to common engineering metals, i.e. surface temperature rises quickly in an initial phase, then it reaches an almost constant value, and finally it increases rapidly as a consequence of the fatigue crack growth. In addition, cyclic thermal variation in the crack tip region and related hysteresis (temperature vs load) has been measured, which can been directly related to the thermal effects of the reversible stress-induced phase transformations. Furthermore, a proper experimental setup has been made, based on a reflection microscope, for direct measurements of the crack tip displacement field by the DIC technique. Furthermore, a fitting procedure has been developed to calculate the mode I Stress Intensity Factor (SIF), starting from the displacement field, and the related mechanical hysteresis (SIF vs load). & 2014 Elsevier B.V. All rights reserved.
Keywords: Shape Memory Alloy Stress-Induced Transformation Fracture Fatigue Infrared thermography Digital Image Correlation
1. Introduction Shape Memory Alloys (SMAs), and in particular the near equiatomic nickel titanium ones (NiTi), have seen an increasing interest in last years, from both scientific community and industrial sector, thanks to their interesting functional features, coupled with good mechanical properties and biocompatibility [1]. Indeed, NiTi alloys undergo a reversible solid state phase transition between a parent austenitic phase (B2) and a product martensitic one (B190 ) [2], the so-called Thermoelastic Martensitic Transformation (TMT), which can be activated by temperature changes (TIM, Thermally-Induced Martensite) or by mechanical loads (SIM, Stress-Induced Martensite). Due to these reversible microstructural transitions NiTi alloys exhibit unique shape recovery capabilities, the so-called Shape Memory Effect (SME) and Pseudoelastic Effect (PE). In particular, thanks to SME NiTi alloys are able to recover large pseudo-plastic mechanical deformations by temperature changes (TIM), while PE represents a high recovery capability obtained by mechanical unloading (SIM). These functional properties are currently exploited for the implementation
n
Corresponding author. E-mail address: [email protected] (C. Maletta).
http://dx.doi.org/10.1016/j.msea.2014.08.007 0921-5093/& 2014 Elsevier B.V. All rights reserved.
of several active and/or tunable devices in many fields of engineering, such as for actuation systems, for vibration control and damping, for self-healing and/or high impact resistance composite materials. However, the most successful applications of NiTi alloys are currently in the field of bio-engineering and medicine, where PE is mainly exploited for the realization of several high valueadded components (e.g. cardiovascular stents, embolic protection filters, micro surgical devices, orthopedic grips, etc.). Although, the high scientific and technological interest in NiTi alloys, many aspects related to their mechanical behavior are still unknown, especially because the hysteretic stress and/or thermally induced phase transformations significantly affect the damage mechanisms occurring under fatigue loadings, i.e. the crack formation and propagation mechanisms. In fact, as a direct consequence of the marked non linear and hysteretic behavior, classic elastic and/or elastic–plastic theories cannot be directly applied to SMAs. In addition, the constitutive laws implemented in commercial finite element software are based on phenomenological approaches and on theory of plasticity, i.e. they use plasticity-like concepts to describe the effects of phase transformation mechanisms on the macroscopic response of NiTi alloys [3]. Though these numerical methods represent useful design tools to simulate the macroscopic response of simple or complex SMA based systems, special care should be taken when they are used to study the local effects in
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the proximity of high stress concentration regions. In particular, it has been demonstrated that the high values of local stresses arising in the crack tip region of NiTi alloys cause stress-induced phase transition mechanisms [4–21], which significantly affect the crack tip stress distribution and, consequently, the crack evolution under both static and fatigue loading conditions. In addition, repeated stress-induced phase transitions, occurring during fatigue loading, cause an unusual temperature evolution, which can be directly related to the exothermic and endothermic effects of direct (B2-B190 ) and reverse (B190 -B2) phase transformations, respectively. Despite the increasing number of research activities on fracture and fatigue of NiTi alloys in recent years, much effort should be devoted for an effective understanding of the role of the hysteretic stress and/or thermally-induced phase transformations in the crack formation and propagation mechanisms. Within this context, the development and application of full field techniques to analyze the local transformation mechanisms near geometrical discontinuities and, in particular, in the crack tip region, represent a highly challenging scientific goal. For this purpose, synchrotron X-ray micro-diffraction (XRD) [4–6], infrared thermographic (IR) [7] and Digital Image Correlation (DIC) [8,9] techniques have been recently applied, to better understand the mechanisms of phase transformation in the notch and/or crack tip proximity. In particular, a pseudoelastic NiTi alloy for medical applications has been analyzed in [4] by using miniature compact-tension (CT) specimens, which were directly obtained from thin-walled tubes, similar to those used for manufacturing self-expanding stents. XRD microdiffraction investigations of fatigue pre-cracked specimens revealed that the crack tip local strain are due to both B2 to B190 transformation and to the subsequent loading of the martensitic phase. Strain and texture evolution near the crack tip of a martensitic NiTi alloy have been analyzed in [5], by synchrotron X-ray experiments, after fatigue crack propagation in a compacttension (CT) specimen; it has been found that texture evolution is mainly due to detwinning, the main deformation mechanism in martensitic NiTi alloys. Both martensitic and austenitic alloys have been analyzed in [6], by using miniaturized CT specimens [10] after fatigue crack propagation, which revealed the presence of detwinned martensite at the crack tip of both martensitic and austenitic specimens. Miniature CT specimens were also analyzed in [7] by using IR thermography which highlighted the reversibility of crack tip phase transformation, i.e. the direct B2 to B190 transformation during loading and the reverse B190 to B2 transformation during unloading. An austenitic NiTi alloy has been analyzed in [8] by DIC analysis of thin edge cracked specimen, which allowed direct measurement of the crack tip strain field related to stress-induced transformation. These experimental investigations, together with other several recent numerical [11– 13] and analytical [14–21] studies, provide very useful information about the occurrence of crack tip transition mechanisms in NiTi alloys subjected to static and/or monotonic loads. However, the role of these mechanisms on the fracture properties on NiTi alloys is not yet completely defined, i.e. no reliable methodologies have been developed for an effective design against fracture. In addition, the evolution of microstructural changes at the crack tip occurring during fatigue loading, i.e. the thermal and mechanical hysteretic behavior, has been not yet investigated. This topic is of major concern as the hysteretic nature of phase transitions is expected to play a significant role on the crack growth mechanisms. Within this context, the main goal of this research activity consists in the development and application of full field experimental techniques to analyze the mechanisms of phase transformation in NiTi alloys under cyclic mechanical loads. In particular, IR and DIC techniques have been applied to analyze the evolution of temperature and displacement field in the crack tip region of a
Single Edge Crack (SEC) specimen, obtained by electro discharge machining (EDM) from a commercial NiTi sheets with pseudoelastic behavior. IR investigations were applied to analyze the global temperature evolution of the specimen, as well as to track the cyclic temperature changes at the crack tip during mechanical loading, together with the associated thermal hysteresis, in terms of temperature vs load. DIC method has been used to analyze the displacement field in the crack tip region and to estimate the mode I stress-intensity factor (SIF) by a data fitting procedure, based on the William's series expansion [22], as well as to measure the mechanical hysteretic response in terms of SIF vs load.
2. Materials and methods 2.1. Materials A commercial nickel–titanium sheet (thickness t ¼0.5 mm) with pseudoelastic properties at room temperature (50.8 at% Ni– 49.2 at% Ti, Type S, Memry, Germany) was used in this investigation. Fig. 1 shows the isothermal (T¼ 298 K) stress strain (σ ε) response of the material obtained from a complete loading– unloading cycle up to a maximum deformation of about 6.2%, corresponding to a complete stress-induced martensite transformation. The figure also reports the values of the main thermomechanical parameters of the alloy: transformation stresses (σAM s , MA σAM and σMA f , σs f ), tranformation strain (εL), Young's moduli of austenite and martensite (EA and EM) and Clausius–Clapeyron constants (CA and CM). Fig. 2 shows the DSC thermogram of the alloy, which was measured in the temperature range between 173 K and 373 K at a heating/cooling rate of 10 K/min. The figure clearly shows a two stage phase transformation during cooling (B2-R-B190 ), while there is no evidence of the R-phase transformation during heating (B190 -B2). The figure reports also the values of all transformation temperatures (Ms, Mf, As, Af, Rs and Rf) as well as the latent heat of transformation. 2.2. Methods Sigle Edge Crack (SEC) specimens were used for the fatigue tests, as illustrated in Fig. 3. In particular, specimens were directly obtained from commercial NiTi sheets and a pre-crack with a notch radius of about 100 μm and with a length ratio, a/W, equal to 0.3 were made by wire electro discharge machining (EDM). Subsequently, fatigue cracks were produced by fatigue mechanical
Fig. 1. Isothermal (T ¼298 K) stress strain (σ ε) response of the SMA under a complete loading–unloading cycle.
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loads, carried out by using a servo hydraulic testing machine (Instron 8500) and with the following parameters: frequency f ¼5 Hz, load ratio R ¼0 and maximum load Pmax ¼100 N (σmax ¼ Pmax/Wt¼20 MPa). No surface treatments were performed on the specimens, which were tested in the as-supplied conditions, thus outer surface is characterized by a titanium oxide layer with a roughness Ra¼ 0.24 70.03 μm, measured by a contact measuring system (MahrSurf III, Mahr). Load frequency f was chosen by preliminary tests with the aim of satisfying two opposite needs: low enough to obtain a significant number of infrared images per cycle, according to the maximum frame rate of the IR camera (100 Hz), and sufficiently high to keep low heat exchange during stress-induced transformations. This issue has also been discussed in a previous study [7], where only single loading cycles under high deformation rate have been analyzed by IR investigations, in order to reduce the thermal exchange and, consequently, to get the maximum temperature variation of the specimen.
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It is worth noting that the loading rate in SMAs has a much more important role, if compared with common engineering alloys, even under monotonic loading conditions [26], because it significantly affects the specimen temperature and, consequently, the stress–strain response, according to the Clausius–Clapeyron relation. The effects of both surface roughness and load frequency were not investigated in the present paper. Specimens for IR instigations were black painted, in order to have a good emissivity value (ε ¼ 0.95), and infrared images were recorded during fatigue tests (R¼0, Pmax ¼350 N, f ¼5 Hz), in order to capture the temperature pattern during loading cycles. An IR camera (FLIR, SC7200) was used, with a resolution of 320 256 pixels, and results were analyzed by a commercial IR imaging software (Flir, Altair). Thermal analyses were carried out by two different methods, namely the global and the local analyses. In the global analysis the temperature pattern and evolution in a surrounding area of the notch, with a dimension of 1 mm 1 mm (see Fig. 3), were studied during crack grow, while in the local analysis the temperature change at a point near the crack tip, was monitored. Digital Image Correlation analyses were carried to measure the crack tip displacement field, by using a non commercial ad-hoc configuration, based on a reflection microscope. In particular, the lighting was achieved through a Köhler optical scheme, using as a light source a square CREELED of side 3.3 mm. The camera (Sony XCD- X910 model) has a CCD sensor with 1280 960 squares pixels of 4.65 μm. The focus of the images was performed using a Linos Photonics microscope objective with a 4 magnification and a numerical aperture of 0.1, which ensures, in conditions of correct illumination, a resolution of approximately 2.5 μm, and therefore lower than the pixel size of the camera. 3. Results and Discussions 3.1. Thermographic analysis
Fig. 2. Differential scanning calorimetric curve of the SMA.
Thermographic analyses presented in this section were carried out by considering the evolution of a relative temperature (Tr),
Fig. 3. Single Edge crack specimen with a focus of the notch region.
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Fig. 4. Evolution of the maximum temperature within the investigated area (T*area), as a function of the number of loading cycles (N).
which represents the difference between the current temperature (T) and initial temperature (T0) of the specimen (Tr ¼T T0). Fig. 4 illustrates the results of the global analysis, i.e. the temperature evolution in the surrounding area (Tr,area) of the notch (see Fig. 3) during fatigue loading (f¼5 Hz, R¼0, Pmax ¼300 N, σmax ¼ 60 MPa). In particular, the evolution of the maximum temperature within the investigated area (Tr,area), as a function of the number of loading cycles (N), is analyzed. The figure clearly shows that the obtained Tr,area–N curve is characterized by three subsequent phases (namely, Phase I, II and III) similar to high cycle [23] and low-cycle [24] fatigue behavior of common engineering metals. In particular, when a specimen is cyclically loaded above its fatigue limit, the temperature of the specimen surface usually rises quickly in the initial phase (Phase I), then reaches an almost asymptotic value (Phase II), and finally there is a very high temperature increment (Phase III) as soon as the crack size becomes significant, leading to fracture after a few cycles. This temperature evolution is closely related to the internal microstructural changes, as demonstrated in [25]. The large scatter of the data in Fig. 4, is mainly attributed to the cyclic temperature variations, i.e. to the repeated stress-induced exothermic and endothermic transformations (see Fig. 2) in the notch/crack tip region. For a better understanding of this effect a local thermal analysis at the crack tip has been carried out, i.e. by measuring and analyzing the local relative temperature at the crack tip (Tr,tip) during fatigue loading. Fig. 5 illustrates the evolution of the temperature Tr,tip and of the applied load P, as a function of the time, for two subsequent loading cycles in Phase I (see Fig. 4). In addition, the figure illustrates a schematic depiction of the stress strain curve of the alloy with some characteristic points (1–6) and their corresponding positions on the load and temperature curves. In particular, five loading regions are identified: (1–2) athermal elastic deformation of austenite, (2–3) direct exothermic A-M transformation, (3–4) athermal elastic unloading of stress-induced martensite, (4–5) reverse endothermic M-A transformation and (5–6) athermal elastic unloading of austenite. The figure clearly shows a direct correlation between the thermal effects of the loading cycle, e.g. of the five aforementioned regions, and the evolution of the crack tip temperature (Tr,tip). In the region (1–2) the local temperature is almost constant, since no phase transformations occur. The local temperature suddenly increases in the second region (2–3), as a result of the exothermic phase transformation from austenite to martensite (A-M), up to the maximum
Fig. 5. Evolution of the crack tip temperature, Tr,tip, and of the applied load, P, as a function of the time, for two subsequent loading cycles in Phase I.
temperature Tmax r,tip . A temperature decrease is observed in region (3–4), due to spontaneous cooling, as well as in the subsequent region (4–5), due to the endothermic M-A transformation, down to a minimum temperature Tmin r,tip, which could be even negative, i.e. current temperature is below the initial specimen temperature. As a consequence of this overcooling a spontaneous temperature increase is observed during the elastic recovery (5–6). A similar trend of the crack tip temperature was observed in the three different phases, as shown in Fig. 6, although they exhibit different values for the maximum and minimum temperamax ture (Tmin r,tip and Tr,tip ). In particular, the figure reports the temperature evolution in 1 s, corresponding to five subsequent thermal cycles, taken at given number of cycles for each of the three aforementioned phases (Phase I – N E1000, Phase II – N E5000, Phase III – N E10,000). Fig. 6 also illustrates IR images of the temperature patterns corresponding to the maximum and minimum temperature. A comparison among the three temperature curves shows an max increase of both Tmin r,tip and Tr,tip with increasing the number of cycles together with an increase of the mean temperature Tmean r,tip , as it is also evident from Fig. 4. Furthermore, a marked increase of the temperature range, ΔTr,tip, is observed only in the third phase. This effect can be directly attributed to the crack growth and, consequently, to the higher values of crack tip stresses which, in turn, increase the fraction of material undergoing phase transformation. In addition, the temperature plateau (1–2) is less evident in phase III as the phase transition mechanisms at the crack tip become predominant with respect to the athermal elastic deformations. Finally, Fig. 7 illustrates the relation between applied load and crack-tip temperature for the three subsequent phases. The figure clearly shows a marked thermal hysteretic behavior, which is directly related to the hysteresis in the stress-induced phase transition mechanism. As discussed above Phase III shows a more evident hysteresis, i.e. a higher value of the temperature range, due to the larger amount of material subjected to phase transformation. 3.2. DIC analysis Fig. 8 illustrates the fringe plots of the near crack tip displacement field (500 μm 500 μm), in a specimen with a crack length/ width ratio (a/W) equal to 0.48 and for an applied load (P) equal to 300 N. This corresponds to a nominal remote stress (σ0 ¼ P/tW) of pffiffiffiffiffiffi 60 MPa and a remote stress intensity factor (K 0 ¼ σ 0 πa) equal to 1/2 7.40 MPa m . In particular, Fig. 8a and b illustrates the contour
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Fig. 6. Evolution of the crack tip temperature, Tr,tip, in the three phases and temperature patterns corresponding to the maximum and minimum temperatures.
Fig. 7. Thermal hysteresis, Temperature vs Load, obtained in the three loading phases.
plots of the horizontal (ux) and vertical (uy) displacement components, respectively, which were obtained from fitting of the DIC data by the William's series expansion [22]. Furthermore, for a given value of the Young's modulus, which was assumed to be constant and equal to that of austenitic untransformed structure (EA ¼ 68 GPa), the fitting procedure allows a direct estimation of the mode I stress-intensity factor (KI). Fig. 9, shows the evolution of KI as a function of K0 during a complete loading–unloading cycle with σ0 varying between 0 and 60 MPa. As expected, the KI–K0 curve shows a marked non-linear hysteretic behavior, which can be directly attributed to the complex stress–strain hysteretic behavior of SMAs (see Fig. 1) and, as well known, this result is in contrast with the Linear Elastic Fracture Mechanics (LEFM) theory, according to which a linear relationship between KI and K0 is expected. In fact, it has been demonstrated that the high values of local stresses, occurring in the crack tip region, cause stress-induced microstructural transitions which significantly affects the stress and strain distribution [16]; in addition, these mechanisms are
expected to be path dependent according to hysteresis associated with the austenite to martensite transformation kinetics. Furthermore, the mismatch between the Young's moduli of the two phases (see Fig. 1) represents an uncertainty factor in estimating the values of the stress intensity factor from displacement fitting methods, as discussed above. To better understand the effect of phase transition mechanisms on the estimation of stress intensity factor, by the William's series expansion, different systematic calculations have been carried out by varying the dimension of the fitting area around the crack tip. In particular, the curves reported in Fig. 10 were obtained by decreasing the edge of the square region, by step of 50 μm, hence the lowest curve was that of Fig. 9, evaluated on an area of 500 μm 500 μm, while the highest one was evaluated on a region of 200 μm 200 μm. The results show that for an area greater than or equal to 500 μm x 500 μm the calculation of KI is independent by the dimension of the area itself, while for smaller regions the value of KI increases, at the beginning slowly and then more rapidly. Furthermore, it can be noticed that when the calculation of KI is performed on a small area a kind of regime value for KI occurs, i. e. KI reaches a stable maximum value over a wide range of K0 and it can be directly attributed to the crack tip stress-induced transformation, which occurs on a stress–strain transformation plateau (see Fig. 1). However, it is worth noting that, similarly to plasticity in common metals, the transformation mechanisms significantly affect the crack tip stress and strain fields with respect to the LEFM theory, i.e. the application of William's series expansion, to obtain KI from displacement field, could give inaccurate results. As a consequence, KI becomes more and more different from the LEFM predictions and the range of applicability of this parameter to SMAs should be proven by specific studies, by identifying the K-dominant region [17]. In addition, a more accurate evaluation of KI should take into account the variation of Young's modulus due the stress-induced transition, which decreases to EM ¼ 48 GPa in the region where the transformation is complete.
4. Conclusions Two full field techniques were applied to study the phase transition mechanisms at the crack tip in NiTi alloys: Infrared
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Fig. 8. Fringe plots of the crack tip displacement obtained from fitting of the DIC data (dimensions and displacement values expressed in μm): (a) horizontal displacement component ux (orthogonal to the loading direction) and (b) vertical displacement component uy (parallel to the loading direction).
Fig. 9. Mode I stress intensity factor KI as a function of the applied remote stress intensity factor K0.
Fig. 10. Mode I stress intensity factor KI as a function of the applied remote stress intensity factor K0 calculated by varying the dimension of the data fitting area around the crack tip.
technique (IR) and Digital Image Correlation (DIC). To this aim Single Edge Crack (SEC) specimens, obtained from a commercial NiTi sheets with pseudoelastic behavior by Electro Discharge Machining (EDM), were analyzed. IR investigations were applied to analyze the global temperature evolution of the specimen, which clearly identifies the crack propagation mechanisms similarly to common engineering alloys, as well as to track the cyclic temperature changes at the crack tip during mechanical loading. This temperature evolution has been directly related to the direct and reverse crack tip stress-induced phase transformation mechanism occurring during loading and unloading; a marked thermal hysteresis, in terms of temperature vs load, has been noticed, which is expected to significantly affect the crack propagation mechanisms in SMAs. DIC method has been used to analyze the displacement field in the crack tip region and data fitting procedures, based on the William's series expansion, have been applied to estimate the mode I Stress-Intensity Factor (SIF). As expected, the SIF vs load curves show a marked non-linear hysteretic behavior, which can be directly attributed to the
complex stress–strain hysteretic behavior of SMAs. Future studies will be addressed to better understand the role of both thermal and mechanical hysteretic behavior on the crack propagation mechanisms in NiTi alloys.
Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.msea.2014.08.007.
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