Shape memory response of porous NiTi shape memory alloys fabricated by selective laser melting

  • Soheil Saedi
  • Sayed E. Saghaian
  • Ahmadreza Jahadakbar
  • Narges Shayesteh Moghaddam
  • Mohsen Taheri Andani
  • Sayed M. Saghaian
  • Y. Charles Lu
  • Mohammad Elahinia
  • Haluk E. Karaca
Biomaterials Synthesis and Characterization Original Research
Part of the following topical collections:
  1. Biomaterials Synthesis and Characterization


Porous NiTi scaffolds display unique bone-like properties including low stiffness and superelastic behavior which makes them promising for biomedical applications. The present article focuses on the techniques to enhance superelasticity of porous NiTi structures. Selective Laser Melting (SLM) method was employed to fabricate the dense and porous (32–58%) NiTi parts. The fabricated samples were subsequently heat-treated (solution annealing + aging at 350 °C for 15 min) and their thermo-mechanical properties were determined as functions of temperature and stress. Additionally, the mechanical behaviors of the samples were simulated and compared to the experimental results. It is shown that SLM NiTi with up to 58% porosity can display shape memory effect with full recovery under 100 MPa nominal stress. Dense SLM NiTi could show almost perfect superelasticity with strain recovery of 5.65 after 6% deformation at body temperatures. The strain recoveries were 3.5, 3.6, and 2.7% for samples with porosity levels of 32%, 45%, and 58%, respectively. Furthermore, it was shown that Young’s modulus (i.e., stiffness) of NiTi parts can be tuned by adjusting the porosity levels to match the properties of the bones.

1 Introduction

Due to their outstanding shape memory effect, superelasticity, high damping ratio (0.038 ± 0.004 in austenite; 0.002 ± 0.004 in martensite) [1], high ductility (up to 8%) [2], low corrosion rate (< 0.89 mpy) [3], adequate fatigue life (2Nf = 1271 at εmax = 3.0%) [4], and biocompatibility [5] NiTi alloys have been employed in various cardiovascular and orthodontic devices [6, 7, 8]. The mechanical hysteresis that NiTi alloys offer is uniquely similar to natural bones, make them ideal candidates for metallic scaffolds and orthopedic implants [9, 10]. Another general requirement for these implants is a low stiffness at the level of bone in order to avoid stress shielding effect, which is the major reason for implant loosening and failure [11, 12, 13]. Titanium, cobalt-based, and stainless steel are other commonly available alloys being used in this application. These alloys present stiffness of about 110 GPa, 190 GPa, and 210 GPa, respectively [14, 15], which are much higher than the human cancellous ( < 3 GPa) or cortical (12–20 GPa) bones [16]. High stiffness implants carry the major portion of loading as they shield the surrounding bone from carrying any load. While referencing Wolf’s law, damage from stress-shielded bones can be explained due to a lack of required level of stress, thus, the bones begin to resorb and continue to do so until the failure of the implant [14, 15]. NiTi presents much lower stiffness (40–60 GPa), however it is still imperative to decrease further.

One promising solution is to adjust this stiffness by introducing porosity into the metallic implants [16, 17, 18]. It is possible to engineer and optimize the equivalent stiffness of implants by controlling the porosity level, pore size, pore shape, and pore distribution to better match the stiffness of natural bones [19, 20]. It has been shown that porosity level in the range of 35–80% and regular porosity type results in a bone-level stiffness [21]. The porosity of metallic implant offers other advantages such as bone ingrowth, body fluid circulation, and heightened strength of implant/bone interconnections [5]. The optimum range of pore size has been reported to be 100 to 600 µm to ensure bone ingrowth in the highly porous structures [8, 22, 23]. However, pore size, geometry, and connectivity can all be tailored to reduce the density and increase the permeability in order to allow blood vessels to migrate [8, 15].

In addition to bone-matched stiffness, it is desirable to maintain and enhance the superelastic behavior of porous NiTi structures. Superelasticity of NiTi occurs as a result of stress-induced martensitic transformation during loading and subsequent reverse transformation upon unloading. This phenomena happens only at a specific temperature range which is higher than the austenite finishing temperature, Af. Binary NiTi alloys have their transfromation temperatures (TTs) typically between −40 and 100 °C and show a temperature hysteresis of 20–40 °C [24, 25, 26]. It is possible to dramatically decrease the TTs of the alloys (about 93 °C/at% with Ni content), when introducing a slightly higher Ni content in NiTi alloys [27]. Moreover, it is more likely for Ni-rich NiTi alloys to show superelasticity since they have the higher intrinsic strength and can be precipitation hardened with heat treatments. However, the heat treatment may result in an increase in TTs and strength of Ni-rich NiTi alloys by the formations of Ni-rich Ni4Ti3, Ni3Ti2 and Ni3Ti precipitates [28, 29]. Consequently, proper aging is extremely important for precipitation characteristics and the corresponding shape memory properties.

Powder metallurgical (PM) processing routes have great potentials for manufacturing open cell porous NiTi parts [30]. Several conventional powder metallurgy methods such as conventional sintering (CS), spark plasma sintering (SPS), self-propagating high-temperature synthesis (SHS), and metal injection molding (MIM) have been investigated in previous studies to produce porous NiTi alloys. However, most of these methods, except MIM, lack the ability to control the geometric flexibility, porosity characteristics (e.g., amount of porosity, pore size, the arrangement of pores, and interconnection of pores), and freeform of design. Further, NiTi components produced by most of the PM techniques usually contain high levels of contamination (e.g., impurity content and intermetallic phases) [31], which may considerably degrade the structural and functional properties of NiTi. The formation of these secondary phases is mostly unavoidable since their formation is much more thermodynamically favorable compared to the formation of NiTi [23]. Typically these inclusions are carbides TiC, intermetallic oxides Ti4Ni2Ox or intermetallic phases like NiTi2, Ni3Ti, Ni4Ti3. Although the presence of Ni4Ti3 precipitates is highly desired, carbides and oxides are not. These phases are detrimental to corrosion resistance, biocompatibility, fatigue life, and transformation temperatures of NiTi. Their formation is usually as a result of available impurities like Oxygen, Carbon, and Nitrogen in the environment that can be picked up during the fabrication and heat treatment processes. Additive Manufacturing (AM) techniques have recently attracted significant attention since they overcome the problems associated with traditional processes. SLM, the most common powder-bed based AM technique, uses a high power laser to melt successive powder layers according to a given CAD information selectively. For medical applications, SLM makes manufacturing patient-specific implants feasible, with an acceptable level of impurity contents [32, 33]. Successful fabrication and the effects of porosity on the density of SLM NiTi scaffold have been recently reported [30, 34, 35]. The compression fatigue, shape memory effect and cyclic stability of near equiatomic SLM NiTi have also been investigated [36, 37]. It has also been shown that the thermo-mechanical behavior of the SLM parts can be tailored by adjusting the processing parameters (laser power, scanning speed, etc) [38]. The shape memory response of dense Ni-rich SLM fabricated Ni50.8Ti49.2 with various heat treatments (i.e., solution annealing and aging) have been previously studied [39]. It has been shown that the SLM fabricated NiTi shows very similar functional properties to the conventional NiTi and with proper aging, strain recovery of up to 5.5% (with a recovery ratio of 95%) can be achieved at 65 °C [40, 41]. However, for biomedical applications, it is essential to have the superelastic response at body temperatures. Up to now, no work has been conducted to investigate the superelasticity behavior of porous SLM NiTi structures exclusively at body temperatures for orthopedic implant applications.

In this experimental work, we examined dense and porous SLM fabricated Ni50.8Ti49.2 (at.%) structures with porosity levels ranging from 32 to 58% to cover the stiffness range of cortical bones, and therefore, minimize the risk of stress shielding for biomedical implants. After an appropriate heat treatment, the shape memory effect, superelastic and cyclic response of dense and porous SLM NiTi parts were investigated at target temperatures. Finally, the superelastic responses of dense and porous SLM samples were simulated numerically with an existing constitutive SMA model, and the results were compared to experimental findings.

2 Experimental procedure

The Ni50.8Ti49.2 (at %) ingot was purchased from Nitinol Devices & Components, Inc. (Fremont, CA). The ingot was atomized into powder by TLS Technik GmbH (Bitterfeld Germany) using an electrode induction melting gas atomization (EIGA) technique. Using scanning electron microscopy (SEM) micrograph, the average size of powders was determined to be about 50 μm. SLM fabrication was conducted by PXM Phenix/3D Systems was equipped with a 300 W Ytterbium fiber laser. Energy input of 55.5 J/mm3 (laser power = 250 W, scanning speed = 1.25 mm/s, powder thickness = 30 μm, hatching space = 120 μm) employed and dense and porous samples were successfully fabricated [42]. The dimension of dense and porous samples were 10 mm × 6 mm × 6 mm and 8 mm × 8 mm × 8 mm, respectively. For porous samples, two plates were also attached to the bottom and top of each to facilitate the compression test. The porosity of samples was determined to be 32, 45, and 58 % (Note: Porosity is defined as the pore volume divided by the bulk volume). Optical images of the same were obtained using Keyence VHZ250R optical microscopy. Perkin-Elmer Pyris 1 Differential Scanning Calorimetry (DSC) with a heating/cooling rate of 10 °C/min, in a nitrogen atmosphere, was used to determine the TTs. Lindberg/Blue M BF514541 Box furnace was used to carry out solution annealing of the alloys. Samples were placed in argon-filled quartz ampoules, separated from each other using ceramics and pure titanium to avoid oxidation. They were kept in the furnace at 950 °C for 5.5 h and then water quenched. Subsequent thermal treatments were conducted using a Whip Mix Pro Press 200 furnace in a vacuum in which samples were aged for 15 min at 350 °C and then quenched in water. Compression tests were conducted using a 100 kN MTS Landmark servo-hydraulic test platform. A strain rate of 10−4 s−1 was employed during loading while unloading was performed under force control at a rate of 100 N/s. The strain was measured by an MTS high-temperature extensometer which was attached to the grips and the stress level was measured with the load over initial cross-section area (F/A) equation regardless of the porosity level of the samples. Therefore, all of the given stress and strain values throughout the article are nominal. Heating of the specimens occurred by means of mica band heaters retrofitted to the compression grips and cooling was achieved through internal liquid nitrogen flow in the compression grips.

3 Experimental results

Figure 1a–d show the cross-section images of the fabricated parts. Porous parts were generated by repeating identical unit cells in x, y, and z directions. The unit cell consisted of four struts that intersect at the midpoint. This pattern is called Simple Cubic (SC). It is visible that pore size gets larger as the porosity level increases. The pore distribution is uniform with a pore diameter of 0.35 mm, 0.60 mm, and 0.75 mm for 32%, 45%, and 58% respectively. Three important porosity parameters are strut-diameter (D), midpoint cell length (L), and the number of repeating unit cells along each direction [43]. The horizontal D is 1.4 mm, 1.2 mm and 1.0 mm for 32%, 45% and 58% porosities, respectively. The L was constant at 2 mm and 4 × 4 × 4 number of each cell was repeated for all the porous samples in order to fabricate the whole part.
Fig. 1

Optical micrographs of a dense, b 32%, c 45%, and d 58% porous SLM fabricated Ni50.8Ti49.2

Figure 2 illustrates the typical DSC curves of SLM fabricated Ni50.8Ti49.2 in as-fabricated, solutionized and 350 °C-15 min aged conditions. The time and temperature have been selected based on a previous aging study [40]. The as-fabricated condition has broad transformation peaks with Af of 32 °C, meaning that the sample can be a mixed phase at room temperature. Solution annealed sample has sharper peaks and its TTs shift to lower temperatures where Ms and Af, are −11 °C and 12 °C, respectively. After aging the TTs were decreased once again and the Ms and Af temperatures were found to be −17 °C and 7 °C, respectively. The reason for the TTs change after solution annealing and aging has been discussed thoroughly in our previous studies [39, 40]. The forward transformation shows a wavy and broad peak while the backward transformation happens with a sharp peak. The broad peak for the martensitic transformation of the aged sample can be attributed to the formed precipitates. The Af of the aged sample is 6 °C, thus it is austenite at room and body temperature.
Fig. 2

DSC curves of SLM Ni50.8Ti49.2 in as-fabricated, solutionized and aged conditions

Figure 3a–d shows the thermal cycling under constant compressive stress responses of 350C-15 min aged dense, 32%, 45%, and 58% porous SLM NiTi, respectively. In each cycle, compressive stress was applied at a temperature above Af, and the sample was cooled to below Mf to fully transform to martensite and then heated up again to above Af. The applied stress was kept constant during each cycle and successively increased for the next thermal cycles until the maximum transformation strain was obtained. All the samples showed shape memory effect and their TTs were increased with increasing the compressive stress. Figure 3a shows that dense sample had a full recovery after 300 MPa and irrecoverable strain of 0.6% was observed after 400 MPa. Figure 3b, c indicate that irrecoverable strain was firstly observed at 200 MPa for 32% porous and at 100 MPa for 45% porous sample. The 58% porous sample showed the highest irrecoverable strain of 0.37% under 100 MPa. The irrecoverable strains were 0.8%, 1.75% and 2.5 % for the 32%, 45% and 58% porous samples, respectively, under 200 MPa.
Fig. 3

Thermal cycling under nominal stress for a dense, b 32% porous, c 45% porous, and d 58% porous SLM Ni50.8Ti49.2

Figure 4 illustrates the stress-strain responses of the dense and aged sample from10 to 50 °C. The specimen was loaded up to 3% strain and then unloaded, followed by heating to a temperature beyond Af. The same procedure was repeated as the testing temperature was increased by 10 °C before each loading. The dense sample showed full strain recovery of 3% in the target temperature range of 20–40 °C. Superelastic testing at 50 °C resulted in a small remnant strain of 0.3% in which further strain of 0.18% is recovered with subsequent heating indicating the formation of retained martensite.
Fig. 4

Temperature-dependent stress-strain curves of dense SLM Ni50.8Ti49.2

To examine the maximum recoverable strain, the incremental superelasticity experiments were conducted at exact 24 °C (i.e., room temperature) and 37 °C (i.e., body temperature) as it is shown in Figure 5a, b. The samples were loaded from 2% up to 6% strain and then unloaded. Fig. 5a shows that dense sample could fully recover the total strain of 4% at room temperature. Even after loading up to 6%, the total recoverable strain was 5.65%. Likewise, the sample was recovered almost fully up to 4% at 37 °C (Fig. 5b). After loading till 6%, the irrecoverable strain of only 0.375% was observed.
Fig. 5

Superelastic response of aged (S + 350C-15 min) dense sample a 24 °C and b 37 °C

To investigate the stability of superelastic responses, cycling tests were conducted at 24 and 37 °C. The same samples were loaded till 800 MPa then unloaded for 10 cycles. After 10 cycles, they were heated up to a temperature above Af to observe the recoverable strain after cycling. Figure 6a, b display the cycling results for dense at 24 and 37 °C. As the number of cycles was increased, the stress hysteresis and irrecoverable strain were decreased and the response was stabilized. After 10 cycles, the stabilized superelastic responses of 3.55 and 3.0% were obtained while total irrecoverable strains were 2.17% and 3.6% at 24 °C and 37 °C, respectively. More than 1% of the unrecovered strain was regained through heating indicating remained martensite in the sample and the residual strain due to plastic deformation was not recovered.
Fig. 6

Superelastic cyclic response of SLM Ni50.8Ti49.2 at a room, b body temperatures

Figure 7a–c is superelastic cyclic responses of porous samples at body temperature. The experiments were carried out with 4% constant strain limit for all test samples. Similar experiments were conducted with considering stress limit for loading. Since for dense sample cyclic tests provided in Fig. 7a, 800 MPa had been selected, therefore 544, 440, and 336 MPa stress were applied for 32%, 45% and 58% porous samples, respectively. Figure 7d shows the experimental result for 58% porous sample with 340 MPa stress limit. Other samples were not presented to avoid repetition. All samples displayed their highest irrecoverable strain in the first cycle where their response stabilizes with further cycling along with degradation. From Fig. 7a, b, both 32 and 45% porous samples with similar behaviors have recovered about 3.5% of the deformation at first cycle after 4% deformation. The last cycle of both experiments showed a full strain recovery of 2.75%. The 58% porous sample demonstrated a poorer response in the first cycle and recovers 2.7%. At 10th cycle, the sample still could show 1.75% superelasticity.
Fig. 7

Superelastic cyclic response of 32, 45, and 58% porous SLM Ni50.8Ti49.2 at body temperature a–c with 4% strain limit and d with 400 MPa stress limit

4 Modeling of superelastic response of porous NiTi alloys

The superelastic responses of porous NiTi samples were further simulated numerically by the finite element method (FEM) using 3D constitutive model [44] implemented into commercial program Abaqus 6.14. As illustrated in Fig. 8a, a porous structure was consisted of repeating the unit cell in all x, y, and z directions. The geometry of unit cell model of the porous structures was consisted of three orthogonal struts, intersecting at the mid-point. To minimize the simulation cost a proper unit cell as shown in Fig. 8b had been constructed for each porous structures and utilized in FEM analysis. The porosity level was formulated by the ratio of the diameter to the length of a strut. Symmetric periodic boundary conditions were defined and the nominal stress was calculated by dividing the axial force with the projected area of the unit cell on the plane normal to the loading direction.
Fig. 8

a The geometry and unit cell model for a 45% porous NiTi alloy and b the unit cell FE models for all dense and porous NiTi alloys (20, 32, 45, 58, and 71%)

Fig. 9

Comparisons of 10th cycle of experimental loading (solid line) and simulation (dashed line) for SLM Ni50.8Ti49.2 at body temperature) with different porosities

The material parameters of the dense and porous parts including the modulus of martensite and austenite, TTs, and critical transformation stresses were extracted from the tenth cycle of the experimental results at body temperature (from Fig. 7) and used for the simulations. Table 1 summarizes the material parameters used in the FE analysis. The actual strain values of each sample from experimental results were used as an input for displacement to control the loading and unloading in the simulation. For 71 and 20%, the strain values were assumed to be equal with the strains of dense and 58% samples.
Table 1

Summary of material properties of SLM NiTi in 10th cycle, used for FE simulation

Austenite modulus EA (GPa)

Martensite modulus EM (GPa)

γA, γM

Critical stress-martensite start σMs (MPa)

Critical stress-martensite finish σMs (MPa)

Critical stress-austenite start σAs (MPa)

Critical stress-austenite finish σAf (MPa)








Figure 9 depicts the comparisons of experimental and simulated superelastic responses of dense and porous samples. The predictions for NiTi alloys with 20 and 71% porosities have been included as well. Simulations and experiments showed similar trends in stiffness reduction as the percentage porosity increased.
Fig. 10

a Recoverable and irrecoverable strain as a function of porosity, b recovery ratio of dense and porous SLM Ni50.8Ti49.2 as a function of applied stress

5 Discussion

Figure 3 suggests a clear connection between the strength and strain recovery with the level of porosity since the irrecoverable strain has increased with porosity level at the same nominal stress level. While the total strain always increased with stress for all samples the recoverable part of this strain was initially increased with stress and then dropped at higher stress. As the volume fraction of favored martensite variants increases with stress the transformation strain increases, however, if the applied stress was enough to trigger the plastic deformation in the material the full recovery may not be obtained. At this point, the irrecoverable strain starts to appear which increases with stress level and as the porosity level evolves; since their strength decreases drastically such deformation is initiated at lower stress levels. In all cases, thermal hysteresis increases with stress as well. Thermal hysteresis is related to the energy dissipation during the phase transformation, and the absence of plastic deformation can increase or decrease depending on the compatibility of the transforming phases. However, with the presence of plastic deformation, it always increases. This explains the greater thermal hysteresis under the same nominal stress level of different porosities. For instance, the higher dislocation density is established in 58% porous sample under 50 MPa stress than that of the 32%. The TTs are also strongly affected by stress and porosity, since the local stress increases with porosity level and higher than the nominal stress; the TTs also increase more in the samples with higher porosity levels when the same nominal stress is applied. The asymmetry in cooling and heating curves is commonly observed in SMAs, especially when R-phase transformation or precipitates are observed [45]. They affect the nucleation and growth of martensite plates, as well as the elastic energy storage that affects the back transformation. In general, at low-stress levels, the nominal strain increases with porosity as the local stress values are higher with increased porosity.

For better comparison, Fig. 10a depicts the recoverable and irrecoverable strains of all the samples as a function of porosity level - which were extracted from Fig. 3 for two highest stress levels (100 and 200 MPa). Figure 10b presents the ratio of recoverable strain to total strain as a function of applied stress. The recovery ratio for all samples regardless of their porosity decrease with applied stress level. However, the decreasing trend is drastic when the porosity is too high. For instance, the 99% recovery ratio of the dense, drops to only 52% for 58% porous sample when both tested under 100 MPa while the dense part displayed 95% recovery even under 300 MPa. When porous samples are compared, the decreasing trend of recovery ratio for 32 and 45% porous displays a sharp fall in higher than 100 MPa while it happens between 50 to 100 MPa for 58%.

As it was shown in Fig. 5, up to 5.7% superelasticity is achievable for dense SLM Nitinol. However, such strain recovery is not likely for highly porous structures. According to Fig. 7a, b both 32 and 45% porous samples could show 3.5% strain recovery after 4% deformation. The main reason for such favorable superelastic behavior in the higher density sample is the continuous connectivity between adjacent unit cells. However, for porous specimen, such connectivity either is not established, or it does not transpire in a uniform manner. Therefore, the superelastic response is diminished. In similar studies for porous NiTi (fabricated by a different method), usually, much lower levels of porosities have been considered. A 12–13% porous SPS fabricated Ni50.9Ti49.1 aged at 320 °C for 30 min has been reported to show up to 5% superelasticity [46, 47]. A 16% porous HIP fabricated Ni51Ti49 homogenized at 1000C-4 h and aged at 400C-4 h demonstrated 3 and 6% strain recovery after 4 and 8% deformation, respectively [14]. In a different study, 27% porous HIP fabricated Ni50.8Ti49.2 (aged at 450C-30 min) were cyclically loaded at different strain levels [48]. The higher porosities also can be found in literature; for instance MIM produced 51% porous Ni50.6Ti49.4 has shown 3.5% recovery after 4% deformation at body temperature [49] and again MIM produced 61% porous Ni50.8Ti49.2 (aged at 500C-1 h) has shown only partial recovery at body temperature while its Af temperature was 60 °C [50].

One of the main concerns regarding NiTi is the stability of the shape memory response. In general, the significant changes in the shape memory behavior occur in the initial cycles, then the response subsequently stabilizes. Figure 11 shows stabilized superelastic response and accumulated irrecoverable strain with cycling extracted from Fig. 7a–c. It should be kept in mind that in order to deform samples 4% they have been loaded to different stress levels, 335, 265, 175 MPa with respect to their porosities. Regardless of porosity level, samples have exhibited similar characteristics and accumulated strains which increased and then suppressed. The increase is more pronounced and steep in early cycles and not significant in later ones, this can be attributed to the high irrecoverable strain in the first cycles. With further cycling, superelastic response stabilizes as the irrecoverable strain decreases. It is noteworthy that there is a slight difference in irreversible strain between 32 and 45% samples at first cycle. The same trend has been continued for the rest of the cycles. In contrast, the 58% porous sample shows a significantly higher irrecoverable strain at first cycle. It seems that porosity higher than 50% drastically lowers the strength. However, similar accumulation characteristic with cycling is observable.
Fig. 11

Stabilized recovery (solid line) and accumulation of irrecoverable strain (dashed line) during cycling tests for 32, 45, and 58% porous SLM Ni50.8Ti49.2 at body temperature

As mentioned, the mismatch between NiTi and bone’s yield strength and Young modulus have been one of the remaining problems during the previous years preventing in vivo experiments for bone implants. Table 2 displays Young’s modulus of the austenite phase and critical stress for plastic deformation of test samples at 37 °C extracted from the first cycle of experiments in Fig. 7. It should be noted that this information was extracted from loading to higher stress levels of the samples, e.g., Fig. 7d. The table indicates that elastic modulus of dense SLM NiTi drops from 47 to 9 GPa by adding 58% porosity. The decrease is roughly 80%. The stiffness of NiTi structure can be tailored to the stiffness level of the compact bone (<20 GPa) with only 32% porosity. This stiffness matching allows the avoidance of bone resorption and local weakness that usually occurs due to stress shielding between bone and the implant materials. In addition, critical stress for plastic deformation decreases with porosity as expected due to the existence of larger stress concentration for higher porosities. However, the critical stress of the porous SLM NiTi alloys which ranged from 300 to 1224 MPa is still well above the compression strength of human cortical bone (100–230 MPa) [51]. Simulations results presented in Fig. 10, displayed similar trends in stiffness reduction as the percentage porosity increased. The agreement between simulation results and experimental and the predictions clearly indicates that properties of SLM NiTi can be further tailored with introducing porosity to the parts as well as engineering the geometry and level of porosity. The deviations between simulation and experimental results can be correlated to the slight differences between CAD model and the actual SLM fabricated scaffold. Additionally, while the size and shapes of pores are changed with each cycle of loading during the experimental testing, this is not considered in the modeling and it is assumed that the tenth loading cycle is applied to a fresh sample as if it is the first loading. As expected, this deformation effect is even higher as the porosity level is increased.
Table 2

Variation of young modulus and plastic deformation of SLM Ni50.8Ti49.2 with porosity at body temperature

Porosity (%)





Young’s modulus (GPa)





Critical stress for plastic deformation (MPa)





In the end, it can be concluded that the unique combination of inter-connected pore characteristics, low elastic modulus, high strength and large superelastic recovery strain makes SLM NiTi a good candidate for ideal long-term, load-bearing hard tissue implants. In addition, according to the provided results, mechanical properties of porous NiTi alloys are directly related to the pore characteristics, and it can be well designed and controlled by SLM methods which opens a promising window for future works.

6 Conclusion

Dense and porous NiTi parts with 32% up to 58% porosity levels were fabricated using SLM. Samples were solution annealed and aged for 15 min at 350 °C and their superelasticity and cyclic behavior were characterized at body temperatures. The conclusions of this study are reported here:
  • Thermal cycling under constant stress experiments proved that SLM porous sample can show proper shape memory effect under stress. In addition, the alloys displayed a perfect superelastic loop covering both room and body temperatures after adjusted thermal treatment.

  • The superelastic response of samples was examined at body temperature and those with 32 and 45% porosity recovered 3.5 of 4% of the deformation at first cycle. The last cycle of both experiments showed a full strain recovery of 2.75%. The 58% porous sample demonstrated a poorer response with strain recovery of 2.7% at first and 1.75% at the 10th cycle. The good superelastic behavior of the higher density samples was attributed to the higher mechanical strength and continuous connectivity between adjacent unit cells. Furthermore, increasing the porosity and pore size results in lower elastic modulus and compressive strength.

  • Simulation results showed a very good agreement with experimental findings which suggests that modeling can be implemented to predict the behavior of NiTi parts with a variety of porosity levels and geometry.



The authors wish to acknowledge partial support for this research from Third Frontier (State of Ohio) grant 15–791, titled “Additive Manufacture of Stiffness-Matched Skeletal Fixation Hardware”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Soheil Saedi
    • 1
  • Sayed E. Saghaian
    • 1
  • Ahmadreza Jahadakbar
    • 2
  • Narges Shayesteh Moghaddam
    • 2
  • Mohsen Taheri Andani
    • 2
    • 3
  • Sayed M. Saghaian
    • 1
  • Y. Charles Lu
    • 1
  • Mohammad Elahinia
    • 2
  • Haluk E. Karaca
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of KentuckyLexingtonUSA
  2. 2.Dynamic and Smart Systems Laboratory, Mechanical Industrial and Manufacturing Engineering DepartmentThe University of ToledoToledoUSA
  3. 3.Department of Mechanical Engineering, S.M. Wu Manufacturing Research Center, College of EngineeringUniversity of MichiganAnn ArborUSA

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