The long-term structural integrity of the substrate is critical for the development of medical devices approved for demanding cardiovascular applications such as transcatheter aortic and mitral valve repair (TAVR/TMVR). Understanding the fatigue life of nitinol can help to ensure long-term device efficacy. The high-cycle fatigue life of this unique material is of particular interest.2–5
This article continues a comparison of the effects of tube processing methodologies on the fatigue life of surrogate samples that represent the fundamental closed cell comprising a self-expanding stent or heart valve. As a result of previous work by Robertson et al, it is possible to compare the effects of two tube processing methods (TM-1 and TM-2) on fatigue life.1 The resulting fatigue behaviors are correlated with microstructural aspects of these alloys and discussed in terms of traditional metallurgical tenets and novel computational modeling of the potency of primary inclusions in fatigue crack nucleation. Part 1, which appeared in the August 2019 issue, examined materials, procedures, and results. Part 2 now looks at fatigue behavior, including probabilistic analyses and correlation with microstructural analyses as well as a direct comparison of methods.
To distinguish trends in fatigue behaviors, strain amplitudes, εa, corresponding to 50, 5, and 1 percent probabilities of fracture were determined as a function of number of cycles, Nf, using the open source program R developed for statistical computing.6 Output data are in the form of strain amplitudes and number of cycles, Nf, for a given probability of fracture. Treating intact diamonds at 107 cycles as runouts, the median probabilities, PLN50, were calculated using a log-normal function, while low probabilities, Pw5 and Pw1, were obtained using a 3-parameter Weibull function.7 The general forms of the cumulative distributions, F(x), for both functions are given in Equations 1 and 2, respectively:
with β the shape parameter, α the scale parameter, and λ the location parameter. Often a normal distribution curve does not accurately represent fatigue data at low probabilities, i.e., as P→0. The ability to alter the curve scale, shape, and location with the Weibull function allows a better fit and thus a more accurate arithmetic model for these low probability data.
The fatigue data in the current study shown in Figure 1 along with the 50 percent probability of fracture εa-Nf curves for tube lots TM-1: 1-1 (solid red), 1-2 (dashed red), and, 2-1 (solid green). These median curves demonstrate the central tendency of the fatigue behavior of the tube lots.7 The PLN50 curves for lots 1-1 and 1-2 are essentially identical. This was expected since both were produced from the same ingot using TM-1 processing. The PLN50 curve for lot 2-1 is notably different than those for 1-1 and 1-2, exhibiting better fatigue behavior in the high-cycle fatigue region as indicated by higher strain amplitudes required to fracture half the samples over the majority of Nf.
The εaP-Nf curves corresponding to 50, 5, and 1 percent probabilities of fracture were also determined for the diamond fatigue data from Robertson et al and are compared with those in the current study in Figures 2, 3, and 4, respectively. No raw data is shown in these figures since the curves sufficiently represent probabilistic fatigue behaviors of diamonds in both studies.
Of particular interest in these figures is the difference in the probability of fracture curves between tubing made from Std VIM-VAR nitinol and processed via TM-1, and, the five materials produced via TM-2. Despite using a standard grade of nitinol, diamonds made from TM-1 tubing exhibit markedly superior fatigue lives to those processed using TM-2 for the standard grades of nitinol, and, quite similar fatigue behavior to the cleaner HP-VAR and PO VIM-VAR materials specifically developed to exhibit superior fatigue performance.
In general, comparison of data presented in Table 1 and Figure 2 shows for P=50 percent in the high-cycle fatigue region, for Nf > 105 cycles:
TM-1: 2-1 exhibits superior fatigue life at all probabilities to all materials and processes.
TM-1: 1-1 and 1-2 exhibit the second-best fatigue life and are virtually identical.
TM-2: HP-VAR exhibits the third best fatigue life converging with the TM-1: 1-1 and 1-2 curves at 107 cycles.
TM-2: PO VIM-VAR exhibits the fourth best fatigue life and is slightly inferior to the HP-VAR.
TM-2: Std VIM, TM-2: Std VIM-VAR, and, TM-2: Std VAR exhibit increasingly worse fatigue lives, respectively.
P = 5 percent and 1 percent data in Table 1 and Figures 3 and 4 demonstrate that:
TM-1: 2-1 exhibits the best fatigue life.
TM-1: 1-1, TM-1: 1-2, TM-2: HP VAR, and, TM-2: PO VIM-VAR, exhibit the second-best fatigue lives and are statistically identical.
TM-2: Std VIM, TM-2: Std VIM-VAR, and, TM-2: Std VAR exhibit increasingly worse fatigue lives, respectively.
It is notable that for a given probability the slopes of the εaP-Nf curves are quite similar in the high-cycle fatigue region. The exception is the median probability curves for TM-1: 1-1 and 1-2, which exhibit a more negative slope. Differences in slopes for the different materials and processes diminish with decreased probability with curves becoming nearly parallel over the entire range of Nf at P = 1 percent. Also, slope magnitudes become less negative with decreased probability. These phenomena reflect the similarity in shape of the Weibull distribution curves at these extreme values.7
Direct Comparison of TM-1 and TM-2. Robertson tested the five nitinol materials listed in Table 2 specifically to examine the effects of cleanliness on fatigue life of diamond surrogates. All materials were processed the same to minimize the effects of tube processing on results. Since the standard VIM-VAR nitinol was the same nominal grade used in the current study, it was possible to discern insight into the direct effects of TM-1 and TM-2 tube processing on fatigue behavior by accounting for differences in starting composition and microstructures between these four tube lots (TM-1: 1-1, 1-2, and 2-1, and, TM-2: Std VIM-VAR).
The εaP-Nf curves for the Standard VIM-VAR nitinol tubing made using TM-1 and TM-2 are shown in Figures 2, 3, and 4 for the three probabilities as the solid red line (TM-1: 1-1), dashed red line (TM-1: 1-2), solid green line (TM-1; 2-1), and, solid blue line (TM-2: Std VIM-VAR). Comparing these four curves shows a substantial difference in fatigue behavior between diamonds made from TM-1 and TM-2 tubing over the entire range of Nf for all probabilities. In the high-cycle fatigue region, for 105 cycles < Nf < 107 cycles, on average, the TM-1 curves (for 1-1, 1-2 and 2-1) are between 0.5 and 1.5 percent higher in absolute strain amplitude than the curve for the TM-2: Std VIM-VAR.
For all probabilities, εaP at 107 cycles for the standard VIM-VAR nitinol tubing made using TM-1 is about two to three times greater than those for tubing made using TM-2 processing. This is a substantial difference thought to be a direct result of the differences in tube manufacturing techniques and related effects on resulting microstructure and matrix properties.
Correlation with Microstructural Analyses
Murakami and Beretta have shown that the fatigue limit of materials containing non-metallic inclusions exhibits a very strong correlation with the nucleating defect size as projected onto a plane perpendicular to the maximum principal stress. They show that small cracks, defects, and non-metallic inclusions having the same “projected defect size” normal to the maximum principal stress, have identical influence on the fatigue limit regardless of different stress concentration factors. As such, it can be anticipated that the projected defect size will be useful in prediction of fatigue strength.
It would be expected then that the same inclusion can have different effects on fatigue strength depending on the direction of loading and that size and shape of the inclusion are important factors. Thus, different influences of inclusions appear depending on whether loading produces a tensile stress in the longitudinal direction or the transverse direction of an NMI. In the fatigue testing of diamonds, struts are loaded longitudinally, i.e., along NMI axis, and thus NMI “diameter” as projected onto the transverse plane of a strut would be expected to have the greatest effect on fatigue life of a diamond or stent-like structure subject to pulsatile loading.
Adopting the “projected defect size” model, NMI transverse data for dmedian presented in Table 3 for the TM-1 tubing are deemed suitable for correlating to fatigue lives. Although Robertson et al. did not perform microstructural analyses on transverse sections of samples, estimates for dmedian for the five materials in that study can be obtained from the relationship between Lmedian and dmedian viz., Lmedian = 1.04 dmedian, derived from measurements of L and d on the three tube lots made using TM-1 and the additional 8 mm tubing samples produced using TM-2.
Figure 5 is a plot of εa50 vs. dmedian for all materials from both studies. A best fit curve fit through the six data points for the standard grade materials from both studies, i.e., TM-1: Std VIM-VAR, 1-1, 1-2, and 2-1, and, TM-2: Std VIM, Std VIM-VAR, and Std VAR show that these data follow an inverse power-law function with a negative exponent near unity. The two data points for the high-purity materials from the Robertson study do not fit on this curve. This is thought to be the result of a combination of the differences in sample preparation techniques; a relatively small examination area; and, a microanalytic limit of particle resolution of 0.59 μm in the Robertson study.
This lower bound limit on particulate detection artificially raises the NMI statistical analyses results. The minimum statistical particle length found by Robertson was Lmedian of 1.06 μm, thus limiting the minimal estimated dmedian values shown in Figure 5. With nearly six times greater resolution limit of 0.108 μm of the microanalytical techniques used in the current study and 10–17 times greater surveyed area, a corresponding minimal statistical particulate size of dmedian = 0.44 μm was determined for TM-1: 2-1, and, dmedian = 0.60 mm in the TM-2: Std VIM-VAR tubing.
The power law relationship between the median probabilistic fatigue limits, εa50, and median NMI diameters dmedian for the materials and processes shown in Figure 5 is consistent with data for steels found by Murakami, albeit with a negative exponent of ⅙ or about ⅙ that found for the nitinol materials in the current study. The reduced dependence of fatigue life on nucleating defect size in the steels may be related to the much larger defect sizes that ranged from 25 to 1000 lm compared to the approximately 1 μm size inclusions in the nitinol materials.
The data in Figure 5 comprise the typical relationship between high cycle fatigue limit, σf, and dimension of the defect (part of the Kitagawa-Takahashi diagram).9 Expressing the data in Figure 5 on a log-log plot (not shown), the relation between ε50 and dmedian:
is obtained for the nitinol materials and processes explored in the current study. This equation provides a potential basis for developing a predictive relationship between starting microstructure, tube manufacturing technique, and, probabilistic fatigue strength of a finished component. Further work is needed to develop fatigue relationships with microstructures resulting from specific manufacturing processes especially at low probabilities critical to chronic medical device efficacies.
This study compared the effects of two tube manufacturing techniques, TM-1 and TM-2, on the high-cycle fatigue life of three standard grades and two high-purity grades of superelastic nitinol used in the manufacture of class III cardiovascular medical devices. The results suggest that the tube manufacturing technique has a significant impact on fatigue life of a finished superelastic nitinol component.
Probabilistic fatigue results were correlated to statistical microanalyses performed on samples representative of both tube manufacturing techniques and compared with the following results. For all probabilities, εaP at 107 cycles for the standard VIM-VAR grade of nitinol TM-1 tubing is about two to three times greater than εaP for tubing made using TM-2 processing. For all probabilities, and despite using a standard grade of nitinol, diamonds made from TM-1 tubing exhibit markedly superior fatigue lives to those processed using TM-2 for the standard grades of nitinol, and, quite similar fatigue behavior to the cleaner HP-VAR and PO VIM-VAR materials.
The dearth of fractured diamonds in the high-cycle fatigue region necessitates reliance on the low-cycle fracture data in the determination of probabilities of fracture in the high-cycle fatigue region. This lack of relevant data contributes to the differences noted in probabilistic curve shapes and inaccuracies in the current analyses, although the extent is unknown.
Development of a more meaningful probabilistic model of high-cycle fatigue must utilize either a greater number of test samples or samples with larger stressed volumes such as seen in Robertson’s wire data to facilitate a larger number of fractures in the high-cycle fatigue region.
Such data can also be used as a basis for development of a stressed-volume based probabilistic fatigue model, which when combined with a more mechanistic, less empirical, description of fatigue can be used to more accurately predict device fatigue life to higher Nf and with less need for in-vitro testing.
- Robertson S., Launey M., Shelley O., Ong I., Vien L., Senthilnathan K., Saffari P., Schlegel S., and Pelton. A.; A statistical approach to understand the role of inclusions on the fatigue resistance of superelastic nitinol wire and tubing, Journal of the Mechanical Behavior of Biomaterials, p. 119–131, (2015).
- Schulz, E, Jabs, A. Gori, T. Von Bardeleben, S., Hink, U., Kosper-Konig, W., Vahl, C.F., and Munzel, T.:Transcatheter Aortic Valve Implantation with the New-Generation Evolut RTM – Comparison with CoreValve® in a Single Center Cohort. IJC Heart & Vasculature 12, 52-56 (2016).
- Piazza, N., Martucci, G. Lachapelle, K., de Varennes, B., Bilodeau, L., Buithieu, J., Mylotte, D.: First-in-Human Ex- perience with the Medtronic CoreValve Evolut R; EuroIntervention 9 1260–1263 (2014).
- Zhu, P., Brinson, L.C., Peraza-Hernandez, E., Hartl, D., and Stebner, A.; Comparison of three-Dimensional Shape Memory Alloy Constitutive Models: Finite Element Analysis of Actuation and Suerelastic Responses of a Shape Memory Alloy Tube; From ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems; Snowbird, Utah, USA, (2013).
- Wheeler, R., Othmane, B., Gao, X., Calkins, F., Ghanbari, Z., Garrison, H. Lagoudas, D., Petersen, A., Pless, J. Stebner, A. and Turner, T.; Engineering Design Tools for Shape Memory Alloy Actuators: CASMART Collaborative Best Practices and Case Studies.; From ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Stowe, Vermont (2016).
- R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
- Weibull, W.; A Statistical Distribution Function of Wide Applicability; Journal of Applied Mechanics; 293–297; (1951).
- Murakami, Y., and Beretta, S.; Small Defects and Inhomogeneities in Fatigue Strength: Experiments, Models and Statistical Implications; Extremes; 2:2; 123–147, (1999).
- Kitagawa, H. and Takahashi, S.; Ap- plicability of fracture mechanics to very small cracks or the cracks in the early stage; Proc. 2nd Int. Conf. Mech. Behavior Mater.; Boston, MA 627–631 (1976).
This article was written by Paul Adler, Invariant-Plane Solutions, LLC, Wheeling, IL; Rudolf Frei, Vascotube GmbH, a Cirtec Medical company, Birkenfeld, Germany; Michael Kimiecik, Paul Briant, and Brad James, Exponent, Inc., Menlo Park, CA; and Chuan Liu, Northwestern University, Evanston, CA. For more information, visit here .