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

The fatigue life of nitinol affects tube processing.

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.

Probabilistic Analyses

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.

Fig. 1 - εa-Nf data with PLN50 curves for tube lots 1-1 (solid red), 1-2 (dashed red), and 2-1 (solid green). PLN50 for lots 1-1 and 1-2 are essentially identical. εa50 at 107 cycles are also shown.

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.

Fig. 2 - εa50–Nf curves from the current study redrawn from Figure 8 and TM-2 from Robertson et al. εa50 at Nf = 107 cycles for each material is shown in the blue boxes on the right side of the figure. Vertical double arrowed black line shows difference between TM-1: Std VIM-VAR; 1-1 and 1-2, and, TM-2: Std VIM-VAR probabilistic fatigue curves.
Fig. 3 - εa5-Nf curves for TM-1 from the current study and TM-2 from Robertson et al. εa5 at Nf = 107 cycles for each material is shown in the blue boxes on the right side of the figure. Vertical double arrowed black line shows difference between TM-1: Std VIM-VAR; 1-1 and 1-2, and, TM-2: Std VIM-VAR probabilistic fatigue curves.
Fig. 4 - εa1–Nf curves for TM-1 from the current study and TM-2 from Robertson et al. εa1 at Nf = 107 cycles for each material is shown in the blue boxes on the right side of the figure. Vertical double arrowed black line shows difference between TM-1: Std VIM-VAR; 1-1 and 1-2, and, TM-2: Std VIM-VAR probabilistic fatigue curves.

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.

Table 1. εaP for P = 50, 5, and 1 percent at 107 cycles for the TM-1 and TM-2 tubing. Highlighted cells compare HCF behavior of TM-1 and TM-2 for the same nominal grade of Std VIM-VAR nitinol.

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