Stent Material Nitinol Determination of Characteristics

and Component Simulation Using the Finite Element Method

K. KOOP, D. LOOTZ, C. KRANZ, C. MOMMA, B. BECHER*, M. KIECKBUSCH

Institute for Implant Technology, Rostock-Warnemünde, Germany

*Institute for Biomedical Engineering, University of Rostock, Rostock, Germany

Summary

Intravascular scaffolding devices, known as stents, are in clinical use for the treatment of vessel stenoses. A stentis first compressed to a small diameter, then transferred to the stenosed part of the vessel by means of a catheter,and finally expanded to its nominal diameter. The expansion is effected either by a balloon or by a material-inher-ent ability to self-expansion. Self-expanding stents, which are being used increasingly often in the peripheral ves-sels, are preferably made of the shape-memory alloy Nitinol. In the first step, the goal of this investigation is todescribe the properties of this material that are related to device construction, as well as to indicate possible meansof thermo-mechanical treatments for the tailoring of material characteristics. Using these results, parameters aredefined that lead to characteristics fulfilling the requirements to a stent material. In a second step, a material lawis deduced from the material data that is suited for use within a Finite Element program. This method is validatedby direct comparison to experimental results from tension tests. Finally, the enormous potential of this method isexemplified by presenting calculations of selected loading states of vascular stents.Key Words

Stent, self-expanding stent, shape memory alloy, Nitinol, finite element analysis

Introduction

Nitinol (Nickel Titanium Naval Ordinance Laborato-ry), a binary alloy consisting of nickel and titanium, isthe most commonly used shape-memory alloy in med-icine due to its known biocompatibility. The principlebehind these alloys was discovered and described inthe 60's. The essential characteristics are the tempera-ture-dependent shape-memory effect, and the super-elasticity (especially the possible elastic strain of max.8 %). The material characteristics are defined by thecomposition of the two alloy components, and can beadapted to the given requirements by choosing theappropriate heat treatment. This results in a multitudeof interesting possibilities for application. However,because of the difficult requirements and the detailed

knowledge of materials science required of the pro-ducer of the material, the use of the material has so farbeen limited to a few fields such as air or space travel,or medical technology. This is also because research,development, and manufacturing with Nitinol is verycost-intensive.

Many different shape memory alloys are used in indus-try, mainly based on Fe, Cu, or NiTi. In medical tech-nology, the binary nickel-titanium alloy is the mostcommon, since the superelastic and shape-memoryeffects are optimal and are active at temperatures nearbody temperature, and also because the materialexhibits excellent biocompatibility [1]. Comparisonsmade between slotted-tube stents made of stainless

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238steel and those made of Nitinol in rabbit vesselsshowed that the uncoated stainless steel stents weremore thrombogenic and caused more vessel injury thandid Nitinol [2].

Using finite element (FE) analysis, the load history ofa stent can be simulated. Of interest are load cases thatcan occur in vivo, as well as those dependent on pro-duction technologies; here, the dependence betweenthe material characteristics and the surrounding tem-perature must be taken into consideration. The conven-tional calculation procedures and standard characteris-tic values from linear structural mechanics are nolonger applicable. Non-linear FE analysis with consti-tutive equations adapted to the specific case is indis-pensable to the simulation of component behavior [3].The constitutive equations must be experimentallydetermined for the material being used at the time andits processing status. Experimental testing is essentialfor validation of the results of FE analysis.Materials and Methods

Properties of Nitinol

Heat Treatment of Nitinol: To simplify, heat treatmentcan induce three fundamental effects: separation reac-tions, recrystalization heating without significant sepa-ration, or a combination of these two and diffusion-freestructural rearrangements [1]. However, separationreactions require a precipitable alloy.

In a precipitable alloy, nickel-rich compounds (mainlyNi4Ti3) begin to diffuse out of the structural matrix oncea specific temperature (ca. 300 °C) is reached; this takesthe form of grains in the structure. The form and size ofthese grains, as well as the exact temperatures, areextremely dependent on the composition of the alloy,the prehistory of the material (imperfections, displace-ment due to strain-hardening), the duration of heattreatment, and the temperature profile [1]. In principle,however, the concentration of nickel in segregatedareas leads to less Ni in the lattice structure. This is thereason for the increase in the transformation tempera-tures with an increase in time or temperature. The seg-regations that appear are also disruptions in the lattice,comparable to the effects of cold working. The resultsare increased tensile strength, a reduction in the elonga-tion at fracture, and an influence on the thermal hys-teresis. Depending on the alloy, the maximum tempera-ture for this separationprocess is about 400 – 450 °C.At higher temperatures, the growth of grains is increas-

May 2001ingly inhibited, and as the temperature increases furtherthey begin to dissolve. Between 450 °C and 550 °C,both processes are in equilibrium. The alloy remains re-latively uninfluenced, even after longer annealing times.However, even in the range between 450 – 550 °C, therecrystalization begins, in which the disrupted pointscaused by cold work begin to be remedied. Theprocesses that occur in this temperature range can becharacterized as combined reactions. At a temperatureof 600 °C and a duration of 60 min, a complete homog-enization of structure can be expected [1]. At evenhigher temperatures, the structure finally reaches thestarting point as it was solidified from the melt.

The Nitinol is heated using a hollow furnace. A tem-perature range of 270 °C to 650 °C was chosen in atime interval of 5 min to 60 min, where the focus wasplaced in the range above 450 °C. In this range, it ispossible to set a shape in Nitinol, since the stent blankis laser-cut from a tube smaller than its end diameter.This effect is caused by the beginning recrystalizationprocesses, as well as structural rearrangements.Determination of Phase Transformation Temperatures:Since most physical characteristics of Nitinol changeupon reaching phase transformations (e.g., specificelectrical resistance, elastic modulus), each of thesechanges in the material characteristics, in principle,can be used for a measurement procedure to determinethe phase transformation temperature. The procedureused in this study is differential scanning calorimetry(DSC). This procedure determines the latent transfor-mation heat for the phase transformations.

The emphasis here was on the influence of heat treat-ment on the phase transformation temperatures [4], andthe resulting possibility of changing the transformationtemperatures (Martensite ↔Austenite) [5]. WhenNitinol is cooled down from the high-temperatureaustenitic phase, the martensitic transformation startsand ends at certain temperatures (Ms, martensite start,and Mf, martensite finish, respectively). In a subsequentretransformation different temperatures apply (As,austenite start, and Af, austenite finish, respectively).There is a temperature difference between Afand Msthat is called temperature hysteresis. For the use of thematerial as a stent, based on the principle of superelas-ticity [6], an Af-temperature significantly below thebody temperature should be ensured. In turn, Mfand Asexert influence on the crimpability of the stent.

To determine the transformation temperatures, small

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May 2001239Figure 1. Left: Hot plate in nitrogen reservoir; right: test object (Nitinol) and reference test object (air) in hot plate.

circular discs (D = 3.5 mm) are laser-cut from aNitinol tube (5 x 0.2 mm; delivery condition) with atotal mass of 14 ± 1 mg, and are then heated. A hotplate with DSC function manufactured by MettlerToledo is used to determine the phase transformationtemperatures (Figure 1). The temperature intervalbetween -50 °C and +80 °C was scanned twice foreach sample with a heating/cooling rate of 5 K/min.The cooling took place in a nitrogen reservoir con-taining 5 liters of liquid nitrogen so that environmen-tal temperatures in the area of the hot plate down to -60 °C could be reached.

Mechanical Characteristics of Nitinol: The mechanicalcharacteristics were determined via uni-axial tensile test-ing with a testing machine manufactured by the compa-ny Zwick. For the test objects, \"shoulder\" bars are cutfrom the Nitinol tube (5 x 0.24 mm;delivery condition)using a laser (Figure 2).The sample geometry is chosenanalogously to the strut-width of the stent in order tojudge the influence of thin struts. To determine the hys-teresis in the stress-strain diagram, the test objects arecyclically stressed with a deformation speed of 1mm/min. The first cycle includes the strain of the testobject into the superelastic range (8 % strain) with sub-sequent slackening to 1 MPa. In the second cycle, thetest object is then stressed to fracture. The cyclic stresstesting is carried out in a temperature equalizationchamber at 37 °C.

The Finite Element Procedure

Due to Nitinol's nonlinear material relationships, theconventional calculation procedures and characteristicvalues, which are derived from linear elasticity theory,are not applicable. In addition, the structure of a stentis generally so complex that analytical calculationresults only provide very gross approximations of theactual stress- and strain-status in the stent. To make anexact prediction of the function and lifetime of animplant of this type, as well to optimize these qualities,it is absolutely necessary to obtain an exact knowledgeof the mechanical status of the stent in all phases of

Figure 2. Test object geometry for the cyclic stress test.

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240May 2001Cyclic load testing for verification of the materialmodel

Cyclic loading of a tension test bar was simulated withFE in order to validate the constitutive equations thatwere implemented. The calculated results can bedirectly compared with the experimental results fromthe tension tests. The dimensions of the model corre-spond to those of the tension test objects that were usedin the experiment. By exploiting all symmetry condi-tions, the calculation was limited to 1/8 of the geome-try. The meshing was carried out with 8-node, solidelements (ANSYS type 45), and is displayed in Figure 3.The total number of elements is 72.

ANSYS does not offer a predefined material model toconduct calculations for shape memory alloys such asNitinol. Since the program is, however, an open sys-tem, the user has various possibilities for constructingan individual model for the material. For this study, itwas decided to directly program the recorded repre-sentative material behavior (Figure 4) into an ANSYS-input file. The principal procedure is to discretize thematerial behavior into a finite number of materialcurves using the austenite and martensite E-modules,as well as the four individual stress-strain pairs A, B, Cand D. Via the entry of these values, the material modelcan be adapted to the given tension test data.

During the calculation, the stress is computed for eachelement at every iteration step, dependent on the cur-rent equivalent stress. Figure 5 shows the materialbehavior, with a representative curve, that was gener-ated by ANSYS from the input data. The constitutiveequations that were found in this way are only the firststep toward simulation of the complete material char-acteristics of Nitinol. A number of simplifications were

Figure 3. Display of meshed tension test bar with boundaryconditions.

use, from expansion to crimping to implantation in thevessel. At this time, the only tool for performing thesetasks is the method of numerical simulation (finite ele-ment analysis, FEA). The module described in thisstudy is created and calculated using the FEA programANSYS (ANSYS Inc., USA). The starting point was aparasolid geometry file created with the 3-D volume-modeling system Unigraphics (Unigraphics SolutionsInc., USA), which is imported into the FE system andthen meshed. The complete stent geometry is not nec-essary for FE simulation; appropriate border condi-tions can be selected in conjunction with the existingsymmetries so that the size of the model (number ofelement) can be reduced. Special attention is paid tothe material model, since this is decisive for the pre-dictive capacity of the results. The parameters neces-sary for this material model are determined in the ten-sion test.

Figure 4. Stress-strain behavior of Nitinol in the tension test.Figure 5. Constitutive equations for the finite element analysis.

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May 2001241The stent geometry (Figure 6) was created with itsactual dimensions using Unigraphics, and importedinto ANSYS via the parasolid interface. The smallestrepeating element of the structure was determined andmeshed with solid elements of ANSYS type 45 (Figure7). Mesh refinements were undertaken in areas wherethe strain gradients were expected to be higher, such asat branchings in the structure. Due to the consistent uti-lization of the repeating symmetric structure, the num-ber of elements in the model could be kept to 15530,which is an acceptable range.Results and DiscussionFigure 6. 3-D-display of two ring segments with a plane ofsymmetry.Figure 7. 3-D-display of a calculated stent segment with amembrane.used, such as neglecting the influence of temperatureon the transformation stresses, possible lasting defor-mations (permanent sets), or significant differences inthe tension-compression behavior of the material.Finally, the strain-dependent material assignment tothe elements is based on the determination of theequivalent stress or equivalent strain for each element.Whether these assumptions are allowable must beresearched further.Calculation of a Stent Segment: In this study, the FEanalyses were limited to the load cases of expansionwith subsequent low-strain annealing and crimping.Determination of Transformation TemperaturesDSC analyses were performed to determine the trans-formation temperatures. From the graphs, only thecharacteristics Af(austenite finish) and As(austenitestart) could be determined and evaluated with certain-ty. Figure 8 displays examples of the regions of inter-est for determination of the characteristic values AfandAsfor a heat-treated Nitinol test object.The curves displayed in Figure 9 show sample progres-sions of the Af - and As-temperatures as a function of theannealing temperature for two different annealingtimes. In the range where the Af- and As-temperaturesare increasing, the nickel-rich composites diffuse out ofthe matrix, which is accompanied by segregation intonickel grains. The time-dependency becomes smallerand smaller at higher temperatures, which is a furtherindication for diffusion as the cause of this effect, sincediffusion processes are time-dependent. Temperaturesabove the turning point lead to dissolution of the nickelgrains, and the alloy becomes increasingly homoge-nized until the grains reach their transformation tem-perature determined from the melt. In order to examinethe transformation range at the turning point in Figure 9even more closely, additional annealing times wereresearched in the indicated region of interest. As shownin Figure 10, there was a strong temperature depen-dence for very short annealing times. Mechanical Characteristics of NitinolIn Figure 11, the stress-strain behavior of a representa-tive heat-treated Nitinol test object under cyclic stress isdisplayed. In addition, the characteristic points for theupper and lower plateaus are shown, as well as the E-modules Eausteniteand Emartensite. With the characteristicpoints, the characteristic values for UPS (upper plateauProgress in Biomedical Research

242May 2001Figure 8. Phase transformation for a heat-treated test object made of Nitinol; left: detail of annealing curve; right: detail ofcooling curve.

stress) and LPS (lower plateau stress) can be derived asaverages from the stresses at points 1 and 2.

Figure 12 depicts the variation of the upper plateaustress as a function of temperature and heat-treatmentduration. The heat treatment generally causes theplateau to sink by about 100 MPa with reference to thestarting material. Dependence on the annealing tem-perature is not significant. Figure 13 shows the lengthof the plateau for different heat treatments. Comparingthis with Figure 9, it is clear that maximal transforma-tion temperatures correspond to a minimum of super-elasticity. The segregations that are most frequent atthis annealing temperature operate as additionalsources of structural disruption, which inhibits the for-

mation and spread of martensitic structure. At highertemperatures, the length of the plateau increases sig-nificantly, which can be explained by the dissolution ofthe nickel deposits and by the recrystalization effects.Finite Element Modeling

In order to assess the design of the stent, in a firstapproximation the following stress cases were simulat-ed using a 3-D model:

•••

Expansion of the stent to the nominal diameter,Stress-free annealing,

Crimping of the stent at the internal diameter of thedelivery device.

Figure 9. As(austenite start) and Af(austenite end) as afunction of annealing times (20 min and 60 min).

Figure 10. Dependence of As(austenite start) and Af(austenite end) temperatures on the annealing time at a con-stant annealing temperature.

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May 2001243These calculations offer the developer important con-structive information regarding maximum strains andstresses in the individual stress steps. The stent geom-etry can then be modified and optimized both quicklyand efficiently. Calculating a 2-D model of stentdeployment can also be performed for an initial esti-mation. However, for complex stent geometries, itmust be considered that the calculations carry no pre-dictive weight regarding, e.g., counterrotations of indi-vidual segment rings or the protrusion of individualstruts during the expansion and crimping processes.Figure 11. Stress-strain behavior of a representative heat-treated stress test object under cyclic load.Validation of the Constitutive Equations In order to validate the self-formulated constitutiveequations, the force- and displacement data were deter-mined for the nodal point where the load was applied.The data were then converted into a stress-strain dia-gram (Figure 14) in order to make them easier to com-pare. No differences were found between this curveand the formulated material curve.Strain and Stress After ExpansionOne of the possible production steps is to cut the stentstructure into a small tube using a laser, and then toexpand the tube to its significantly larger nominaldiameter. Then, the material is subjected to a specialheat treatment that leaves the material in a stress-freestate, in order to set the stent shape at the nominaldiameter [7]. The maximum stresses and strains aremonitored so that the production process does not leadto component failure. The maximum stress and strainare shown in Figure 15 and Figure 16 for a representa-tive expansion diameter. All calculated values werewithin the superelastic range, and thus far below theelongation at rupture.Figure 12. Upper plateau stress UPS as a function of thetemperature and the annealing time.Figure 13. Length of the upper plateau as a function of theheat-treatment factors.Figure 14. Stress-strain curve for the nodal point where theload was applied.

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244May 2001Figure 15. Depiction of the equivalent stress as per v. Misesafter the expansion of a stent segment.

Figure 17. Display of equivalent stress as per v. Mises afterthe crimping process of a stent segment.

Figure 16. Depiction of equivalent strain as per v. Misesafter the expansion of a stent segment.

Strain and Stress After Crimping

Crimping is the radial compression of the stent to adiameter that is as small as possible in order to load thestent onto the delivery system. This procedure prefer-ably occurs at temperatures below As, since at this tem-perature, pseudoplastic displacements of the marten-site lattice occur that, upon heating above Af, com-pletely degenerate due to transformation into austenite.For the FE-simulation of this load-step, all stressesfrom the previous load-step are set to zero, so that onlythe deformed shape displaying the nominal diameterremains. This is the equivalent of stress-free annealing.

Figure 18. Display of equivalent strain as per v. Mises afterthe crimping process of a stent segment.

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May 2001Then, the stent segment is radially compressed via con-tact formulation. The strains and stresses that result forthis status are displayed in Figure 17 and Figure 18. Aswith the expansion process, no values outside of thesuperelastic range were recorded.Conclusion

From the parameter studies that were carried out, anoptimal heat treatment was able to be found for theapplication of the material Nitinol as an implant mater-ial. The parameters are not very time-critical, and guar-antee secure form setting. The Af-temperature after heattreatment of the material lies significantly below thetemperature at which the material is used (37 °C bodytemperature), ensuring optimal stent mechanical char-acteristics and full functionality in vivo. For Af, a rangeof about 15 – 25 °C is viewed as ideal. If Afis higher,then in some cases the austenite transformation mightnot be complete, and the stent no longer expands entire-ly in the vessel, and does not reach is maximumstrength (collapse pressure). At a lower Af, the \"perma-nent set\" (superelastic window) and the plateau stressesare higher, which is especially disadvantageous for thelower plateau (higher forces upon release, higher pres-sure of stent against vessel wall). It must be attemptedto maximize the plateau length (about 7 %) in order toachieve maximum one-way effects.

Difficulties such as obtaining and inputting a charac-teristic material curve for the microstructure of theindividual struts of a stent, the construction of a mate-rial model with consideration of hysteresis, as well asmodeling the crimping geometry through reliable con-tact calculation were able to be overcome. In addition,it was shown that the constitutive equations that wereobtained experimentally could be implemented in anFEA system. Further research must be conductedregarding the allowability of the assumptions that weremade; these included the neglect of both the tempera-ture and the differences in compression-tension behav-ior.

In addition, failure analyses of stent structures made ofNitinol, conducted with FEA, are also necessary withrespect to product approval as per EN 12006-3. Losscriteria must then be formulated that offer a moreextensive load history of the stent; these can includedeployment, vessel anatomy, and physiology. Thesewill be integrated into the stent design as constructionrequirements. The FE analysis is an extremely impor-

245tant tool in the development of a materials-optimizedstent design. The results should, however, always bevalidated with data that are obtained experimentallywith stent test objects.Acknowledgement

We thank the company CAD-FEM (Berlin, Germany)for their generous support in creating models and con-verting the experimental data into implementable con-stitutive equations for finite element analysis viaANSYS.References

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Treppmann. Thermomechanische Behandlung von NiTi. In:Fortschrittberichte VDI, Reihe 5: Grund- und Werkstoffe No.462. Düsseldorf: VDI-Verlag. 1997.

Sheth S, Litvack F, Fishbein MC, et al. Subacute thrombosisand vascular injury resulting from slotted-tube Nitinol andstainless steel stents in rabbit carotid artery model.Circulation. 1996; 94: 1733-1740.

Duerig TW, Pelton AR, Stöckel D, et al. In: Duerig TW.Engineering Aspects of Shape Memory Alloys. London:Butterworth-Heinemann. 1990.

Bataillard L, Gotthardt R. Influence of Thermal Treatment onthe Appearance of a Three Step Martensitic Transformationin NiTi. Journal de Physique IV. 1995; 5: 647-652.

Pelton AR, DiCello J, Miyazaki S. Optimization of process-ing and properties of medical grade Nitinol wire. Min InvasTher & Allied Technol. 2000; 9:107-118.

Duerig TW, Pelton AR, Stöckel D. The use of superelasticityin medicine. Metalle. 1996; 9: 569-574.

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ContactK. Koop

Institut für Implantat-TechnologieFriedrich-Barnewitz-Strasse 4D-18119 Rostock-WarnemündeGermany

Telephone: +49 381 66 09 413Fax: +49 381 66 09 400

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