**3. Modeling**

The bone fixation plates that we prepared were 3 mm thick with five different levels of porosity (bulk (0%), 17%, 20%, 24%, 27%, and 30%) were designed based on the methodology explained in the methods section. The STL file of designed bone fixation plates was re-meshed and proper volume meshes (10-node tetrahedral elements (C3D10)) were created and verified in a mesh convergence study. The final volume meshes were exported as INP files and imported to Abaqus (V2019, Dassault Systems; Providence, RI, the USA for finite element modeling). An Abaqus user-defined material subroutine (UMAT) developed based on the micro-plane theory [37–39] was used for capturing the mechanical behavior of the NiTi bone fixation plates. The UMAT is capable of simulating both superelastic and shape memory effects of shape memory alloys under multiaxial loading conditions [15] and requires the thermomechanical properties of the standard coupons (e.g., Young's modulus for austenite and martensite, transformation temperatures, critical stresses, etc.) as the input. More details on the utilized UMAT can be found elsewhere [40].

Thermomechanical properties of Ni50.1Ti from [41] were used for tuning the UMAT mentioned above. Followed by preparing the FE model, the uniaxial tensile test of the bone fixation plates was simulated. The load-displacement response of the bone fixation plates under tensile loading is summarized in Figure 2. As it is seen in Figure 2, adding different levels of porosity to the bone fixation plates alters the stiffness of the plates and can be used for achieving engineered levels of stiffness. As the next step, the simulated bone fixation plates were fabricated and used for validating the FE simulations.

**Figure 2.** The load–displacement response of simulated plates with different levels of porosity.

#### **4. Mechanical Evaluation**

To validate the simulation results, a series of uniaxial tensile mechanical testing on the first series of bone fixation plates with different levels of porosity was performed. All the parts were fabricated horizontally and on a support structure. As shown in Figure 3, the same trend was observed for the load-displacement response of the fabricated bone fixation plates, so that the stiffness of the plate decreased as the level of porosity goes up. For making a comparison between experimental and simulation data, the results of two extreme conditions (bulk bone fixation plate, 30% porosity) were plotted in Figure 4, and as it can be seen, the simulation results are in good agreemen<sup>t</sup> with experimental data.

**Figure 3.** The experimental result of an SLM NiTi fixation plate with different porosity levels under tension.

**Figure 4.** Comparison of experimental and simulation results of (**a**) bulk plate (0% of porosity) and (**b**) the plate with the porosity of 30%.

As was shown in the previous sections, the stiffness of the bone fixation plates, regardless of their overall geometry, can be modulated and tuned to a specific level based on the stiffness of the bone to which it will be attached. However, based on our reading of the clinical literature, it would be useful to be able to create superelastic bone fixation plates in order to recover a larger level of deformation and insure compression between adjacent bone segments that are healing. The superelasticity of bone fixation plates could also act as a shock absorber to prevent failure of the implant in case of short term high impact forces or extreme, but unusual, loading conditions (i.e., failsafe). In addition, it is sometimes useful to apply constant pressure where the bone fixation plates are used. Contact pressure (compression) created by the bone fixation plate should improve the healing procedure and reduce the micromotions that would rip apart the healing region. However, as it can be seen in the load-displacement response (Figures 3 and 4), the fabricated bone fixation plates did not exhibit superelasticity and a noticeable level of recoverable strain. Therefore, after validation of the design, modeling, and fabrication procedure, we replaced the Ni50.1Ti powder used for the SLM procedure with a more Ni-rich powder (Ni50.8Ti) to reduce the transformation temperatures and create superelastic bone fixation plates. The next section discussed the details of the transition to superelastic bone fixation plates.

#### **5. Superelastic Sti**ff**ness-Modulated Bone Fixation Plates**

In order to investigate the superelastic response of bone fixation plates, only bone fixation plates with the most complex geometry (minimum thickness = 1.5 mm) and an extreme level of porosity (i.e., 46%) was considered. To create a realistic geometry for the bone fixation plate, a 4-hole 1.5 mm thick bone fixation plate as shown in Figure 5a was provided by Stryker (Kalamazoo, MI, USA). The plate was then scanned using a micro computed tomography (micro-CT), and its CAD model was created (Figure 5b). Using the same methodology explained earlier, the porosity (0.6 mm pore cells) and a covering thin-wall structure (0.2 mm) added to the CAD model (Figure 5c,d). After creating the final CAD model for the porous plate, by following the previous procedure, an FE model for simulating the tensile behavior as well as an STL file for the SLM fabrications was created. In order to accurately characterize the tensile behavior of the Ni50.8Ti bone fixation plates, standard tensile samples were also designed and prepared for fabrication in addition to the bone fixation plates. Figure 6 shows the fabricated bone fixation plates immediately after fabrication and before the support removal procedure. Localized and overall thermomechanical behavior of the standard tensile coupon as well as the bone fixation plates, is discussed in the next section.

**Figure 5.** Preparation of a bone fixation plate with an extreme level of porosity and the realistic geometry. (**a**) Conventionally fabricated Ti64 bone fixation plate with standard geometry used as the reference, (**b**) reconstructed CAD through Micro CT, (**c**) porosity cell, and (**d**) porous bone fixation plate.

**Figure 6.** NiTi porous bone fixation plates and tensile samples fabricated via the SLM method.

#### *5.1. Thermomechanical Behavior*

DSC results, as well as the transformation temperatures of Ni-rich porous bone fixation plates, standard dog-bone samples, and powder particles, are shown and reported in Figure 7 and Table 4, respectively. For the porous plate, the DSC samples were cut from three different regions as shown in Figure 6. Based on the location that the DSC samples were cut from, different transformation temperatures were achieved. The transformation temperatures (TTs) variation can be explained by the nature of the SLM process and the complex shape of the porous plates that resulted in different thermal histories. The effect of different thermal histories during the SLM process can be compared to different heat treatment procedures, which are performed on the final parts. As different heat treatment procedures lead to different TTs, for instance, different thermal histories also can lead to non-homogeneous microstructure [42] as a result, different TTs. This non-homogeneity and variation in TTs variation indicate the necessity of the heat treatment as a post-processing procedure for the as-fabricated samples for creating a homogeneous part. In this study, we did not optimize the heat treatment procedure for the bone fixation plates. That will be studied at a later time.

**Table 4.** The transformation temperatures (TTs) of powder, dog-bone, and the porous samples.


**Figure 7.** The differential scanning calorimetry (DSC) results of the as-fabricated porous bone fixation plate from three different locations, the dog bone sample, and Ni50.8Ti powder.

To measure the material properties of the fabricated Ni-rich bone fixation plates and updating the FE model, two standard tensile samples were tested, and the results are shown in Figure 8. The first sample was loaded up to the failure with a low strain rate (0.0001 <sup>S</sup>−1) to maintain the isothermal condition. Based on the stress-strain plot of the first sample, a loading-unloading test on the second sample was designed. The second sample was loaded up to the end of the plateau region (3% strain) and then unloaded to zero loads. The transformation strain of 2.6% (81% of total strain) was achieved for the as-fabricated part under tension. The material showed around 0.6% of irrecoverable strain that could be a result of permanent strain (slip) or the locked-in detwinned martensite and can be recovered by heating [43].

**Figure 8.** Stress–strain response of SLM dog-bone samples.

The mechanical properties of the as-fabricated material were reported in Table 5. The austenite (EA) and martensite (EM) modulus of elasticity were captured from loading and unloading plots, respectively. Followed by obtaining the material properties from the tensile samples, the Ni-rich bone fixation plate was simulated under tensile loading and unloading. The as-fabricated Ni-rich bone

fixation plates were then mechanically tested under the same boundary conditions. Figure 9 shows the simulations as well as mechanical testing of the Ni-rich bone fixation plate.

**Table 5.** The mechanical properties of the standard tensile sample fabricated via SLM.

**Figure 9.** The load–displacement response of as-fabricated porous plate under tensile loading.

After inspection of the fabricated Ni-rich bone fixation plates, we observed a relative geometrical difference between the fabricated part and the CAD model. The size had increased in comparison with the previous case (i.e., the first series of bone fixation plates with larger dimensions). As reported by others [27], as-fabricated SLM fabricated parts could exhibit a geometrical expansion that is related to the laser width, melt pool diameter, and the fact that the part is surrounded by loose powder. The geometrical expansion of SLM-fabricated parts has a more significant effect when the parts include fine details that are close to the laser width. In the case of fabricating Ni-rich bone fixation plates with the extreme geometrical features, the geometrical expansion led to a higher difference with the simulations and the expected behavior. In addition, because of the fine features of the Ni-rich bone fixation plates, a higher amount of un-melted powder was trapped in the pore cells that affect the mechanical response and could affect their biocompatibility. Therefore, we have investigated a chemical polishing method to remove the un-melted powder particles attached to the parts, while not disturbing the fine geometries. This procedure is discussed in the next section. Eventually, the polished bone fixation plate that showed 23% mass loss was mechanically tested, and the load–displacement response is shown in Figure 9.

#### *5.2. Chemical Polishing*

Using the selective laser melting process, the complex geometries required for the bone fixation plates can be accurately fabricated. However, the SLM process often results in un-melted powders and other undesirable features that remain fused to the fabricated product. In order to remove the un-melted powder and to add a smooth finish to the part to improve performance (e.g., mechanical, cleaning, and sterilization reliability), a finishing process is required. Due to the complex geometries and fine porous structure of Ni-rich implants, current mechanical finishing processes are not efficient. They may damage the components and cannot reach fine internal features. Therefore, a chemical

etching process was opted for. The chemical etching and finishing processes of additively manufactured nickel–titanium components is not well researched. Therefore, a series of tests were undertaken in order to better optimize the etching solution used for the bone fixation plates.

The tests consisted of two di fferent etching solutions and three di fferent times for submerging the components within those solutions (Table 3). The samples were cleaned in water using an ultrasonic bath for 5 min both before and after the chemical finishing process. Both solutions were composed of hydrofluoric acid (HF), nitric acid (HNO3), and purified distilled water (H2O). It is known that the HF in the etching solution act as a dissolvent while the HNO3 behaves as a passivator [44]. The distilled water is used to dilute the solution in order to prevent excessively rapid corrosion/material loss. The samples were submerged for 2 min, 4 min, and 6 min.

Figure 10 shows the results of the chemical etching process on the mass loss of the samples etched the two trialed solutions. Three bone-plate was etched within the etching solution 1 while three others were etched within the solution 2. The mass loss increased proportionally with the time for both solutions. The results show that the second solution with reduced HF and increased HNO3, removed material at nearly twice the rate of solution 1.

**Figure 10.** The percentage of mass loss versus time for two di fferent etching solutions.

The e ffect of the etching procedure on the geometry, as well as the surface finish of the samples, is reflected in the SEM images in Figure 11. As it can be seen in the "As-built" sample, excessive un-melted powder is attached to the surface of the as-built sample and almost entirely covered the pores. S1-2, S1-4, and S1-6 show the SEM images of samples etched with solution 1 with the di fferent durations of 2, 4, and 6 min. The un-melted powder was partially removed on S1-2. S1-4 and S1-6 that were submerged for a long time showed the best result of the chemical polishing. In order to make a more accurate comparison on the e ffect of chemical polishing, the distance between the pores was measured and compared with the original distance on the CAD file. Based on this comparison, the size and geometry of S1-2 had the most consistency with the original CAD model, and therefore it was reported as the optimized polishing procedure. The polishing by solution 2 for 2 min (S2-2) was almost good but still more than required. While the polishing with solution 2 for 4 and 6 min (S2-4 and S2-6) was too aggressive and caused excessive degradation of the pore structures.

**Figure 11.** The SEM result of chemically polished porous plates under six different etching conditions.

#### *5.3. Chemical Composition Analysis*

Understanding the chemical composition of bone fixation plates is critical. Since this is a medical implant, strict controls are required to ensure biocompatibility (i.e., lack of toxicity). Analyzing and accounting for any precipitates or ion formation due to the additive manufacturing process is, therefore, a necessity. The results for our chemical analysis of these bone fixation plates is displayed in Table 6. The elements analyzed were carbon (C), hydrogen (H), oxygen (O), nitrogen (N), nickel (Ni), cobalt (Co), copper (Cu), chromium (Cr), iron (Fe), niobium (Nb), and titanium (Ti). The composition analysis is compared with the allowable values of nickel–titanium shape memory alloys for medical devices and surgical implants, as described in ASTM F 2063 [45]. The results show that the AM Nitinol compositions were within expected parameters with respect to total weight percentage. However, the nitrogen plus oxygen level was slightly above the acceptable ASTM requirement at this stage in our work. The cobalt, copper, chromium, nitrogen, carbon, hydrogen, and niobium were not present in a quantity sufficient to alter the predicted mechanical performance. Ratios of iron and oxygen were also low and do not present an obstacle to the performance and safety of these bone fixation plates.


**Table 6.** The results of the chemical composition analysis.
