# Ultrasonic fatigue of superelastic Nitinol and in situ synchrotron observation of strain and damage

M. Fitzka, H. Rennhofer, D. Catoor, M. Reiterer, S. Checchia, M. Di Michiel,

H.C. Lichtenegger, H. Mayer

► To cite this version:

M. Fitzka, H. Rennhofer, D. Catoor, M. Reiterer, S. Checchia, et al. Ultrasonic fatigue of superelastic Nitinol and in situ synchrotron observation of strain and damage. Journal of Materials Research and Technology, 2024, 33, pp.5160–5169. 10.1016/j.jmrt.2024.10.172. hal-05097689

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# Ultrasonic fatigue of superelastic Nitinol and in situ synchrotron observation of strain and damage

M. Fitzka<sup>a, *, 1</sup>, H. Rennhofer<sup>a</sup>, D. Catoor<sup>b</sup>, M. Reiterer<sup>c</sup>, S. Checchia<sup>d</sup>, M. di Michiel<sup>d</sup>, H.C. Lichtenegger<sup>a</sup>, H. Mayer<sup>a</sup>

## ARTICLE INFO

Handling editor: SN Monteiro

## Keywords:

Nitinol

XRD

Very high cycle fatigue

Ultrasonic fatigue

Strain rate influence

Inclusion

## ABSTRACT

Superelastic Nitinol was tested at ultrasonic frequency in the high and very high cycle fatigue regime. Thin sheet specimens were initially preloaded to mimic crimping and deployment of Nitinol implants, which lead to a sample in a multi-phase state with martensitic phase in the middle and adjacent zones with austenitic phase. In situ synchrotron X-ray diffraction (XRD) was used to monitor cyclic strains over an entire ultrasonic cycle, and to compare the results with low frequency loading. Both austenitic and martensitic regimes showed similar sinusoidal elastic deformation at cycling frequencies 0.1 Hz and 18.3 kHz, and strains were comparable over the entire gauge section of the specimen. XRD data showed progressive growth of austenitic bands in formerly martensitic areas with increasing numbers of ultrasonic cycles. This increased specimen stiffness and cyclic stresses promoting crack initiation, which nearly exclusively occurred at cracked surface inclusions. The strain versus fatigue lifetime diagram shows a pronounced change in slope below $10^6$ cycles. The overlapping properties measured at low and ultrasonic frequency demonstrate that ultrasonic fatigue testing is in principle appropriate for rapid characterization of the cyclic properties of Nitinol.

## 1. Introduction

Nitinol is a nearly equi-atomic intermetallic Ni–Ti alloy that exhibits both shape memory and superelasticity owing to a reversible stress-induced martensitic transformation [1]. A combination of good corrosion resistance and biocompatibility as well as good fatigue performance has made the material a mainstay in medical device applications [2]. Superelastic Nitinol is widely used for self-expandable biomedical implants such as stents and transcatheter heart valve frames. Such devices are compressed into small diameter catheters to be deployed at the target anatomical locations. During crimping, highly stressed regions are subjected to a reversible stress-induced martensitic transformation from B2 austenite to a B19' martensite via an intermediate rhombohedral R-phase [3]. At the implant location, the device partially expands and exerts the necessary force to keep the artery open to restore blood flow. Forward and reverse transformation occur at nearly constant stresses that are commonly referred to as the upper and lower plateau

stresses, respectively. Post-implantation, such devices are often subjected to cyclic loading by the surrounding tissue, resulting from cardiac cycles or musculoskeletal movements. The fatigue properties are, therefore, of great interest for the development and application of Nitinol-based medical devices.

Literature on Nitinol fatigue is dating back to the 1970s where cyclic plastic deformations [4] and high cycle fatigue lifetimes have been explored [5]. Fatigue tests with diamond shaped Nitinol specimens that resemble the maximum loaded region of a stent have been performed up to $10^7$ cycles to study the effect of mean strain on fatigue lifetimes [6]. In the context of structural heart implants, fatigue data up to $4 \times 10^8$ cycles from bending tests and a constant life model were obtained from tube-derived beam specimens [7]. Fatigue properties up to $10^9$ cycles are available from rotary bending fatigue tests [8], and a pronounced change of slope of the strain range versus load cycles curve at approximately $10^5$ cycles was found.

The role of strain inhomogeneities associated with the stress-induced

<footnote><sup>a</sup> Institute of Physics and Materials Science, BOKU University, 1190, Vienna, Austria</footnote>

<footnote><sup>b</sup> Edwards Lifesciences, One Edwards Way, Irvine, CA, USA</footnote>

<footnote><sup>c</sup> Medtronic PLC, Medtronic Energy and Component Center, Brooklyn Center, USA</footnote>

<footnote><sup>d</sup> European Synchrotron Radiation Facility, Grenoble, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: michael.fitzka@boku.ac.at (M. Fitzka).</footnote>

<footnote n="1">¹ Postal address: BOKU University, Institute of Physics and Materials Science, Peter-Jordan-Str. 82, 1190 Vienna, Austria.</footnote>
transformation on cyclic strain distribution and fatigue crack initiation was investigated in Ref. [9]. It was shown that crack initiation occurs at near-surface inclusions within the region undergoing forward and reverse stress induced martensitic transformation. This work also indicates that the tension-tension fatigue strength below $10^7$ cycles is related to the activation of cyclic stress-induced phase transformation. Test with Nitinol wires showed that this relationship holds more generally under tension-tension, while providing more evidence for the importance of pre-strain, mean strain and strain amplitude for Nitinol fatigue [10].

Several investigations show the important role of inclusions acting as a preferential initiation sites for fatigue cracks [9,11–17]. Fatigue properties of Nitinol can be improved by material production leading to smaller and fewer inclusions [15,16], since the largest inclusion in the stressed volume determines cyclic strength [17]. Ageing leading to the production of fine $Ti_3Ni_4$ precipitates considerably improved the cyclic strength of Nitinol [18,19]. Pre-straining the material prior to cycling also increased the fatigue properties [10,20–22]. Fatigue crack propagation studies performed at different temperatures and load ratios with conventional compact-tension fracture mechanics specimens [23] as well as with specimens obtained from thin-sheets [24,25] can also be found in the literature. Review articles [26–28] give an overview of fatigue investigations performed with Nitinol.

Long term implants like heart valve frames and stents are subjected to very high numbers of load cycles during their lifetime. Assuming a heart rate of 72 beats per minute for a typical adult human, 15 years of implant life will roughly lead to $5 \times 10^8$ cycles. Fatigue data up to several hundred million load cycles, however, are rare in the literature [7,8] due to the long time required to perform such tests. Testing times can be shortened by increasing the cycling frequency; however, strain rate sensitivity of deformation and of phase transformation could influence the fatigue damage mechanism and the resultant fatigue lifetimes. For example, in the absence of a suitable heat transfer medium, high strain rates increase the stress for austenitic-martensitic phase transformation [29–31] due to adiabatic heating from the latent heat of transformation. Constant displacement amplitude loading at frequencies between 0.004 Hz and 40 Hz show a narrower cyclic stress-strain curve with higher maximum and lower minimum stresses for the higher frequency [9]. Lower lifetimes were found in cyclic bending tests at cycling frequency 13 Hz compared to 0.6 Hz, fostered by specimen heating at the higher frequency [32]. In fatigue crack propagation tests, however, no influence on fatigue crack propagation rates was found cycling the specimen at 5 Hz or 50 Hz, respectively [24].

Ultrasonic frequency fatigue testing drastically reduces testing times due to the cycling frequency in the 20 kHz range and is ideally suited for investigations in the very high cycle fatigue regime [33,34]. It has been successfully used to investigate a wide range of materials including metals, ceramics, polymers and composites [35]. Ultrasonic fatigue testing has, however, not been applied for fatigue lifetime measurements of Nitinol because of potential rate sensitivity of the fatigue process stemming from rate sensitivity in the stress-induced parameters. Additionally, questions remain regarding an appropriate ultrasonic fatigue testing procedure and if data measured at very high strain rates are truly representative for the material behavior of structural implants where strain rates are four orders of magnitude lower.

In our previous work, we presented a test setup to cyclically stress thin Nitinol sheets at ultrasonic frequency [36]. The specimen is not vibrating in resonance, as would be the case in most ultrasonic fatigue experiments. It is rather cyclically stressed with the aid of an ultrasonic load train, which is built into a miniaturized and transportable load frame. In an in situ synchrotron experiment lattice deformation during an entire ultrasonic load cycle for the specimen in fully austenitic phase was revealed using a frame summation technique [36]. Sinusoidal lattice deformation in the austenitic phase at 18.3 kHz and at 0.1 Hz were found to be similar, which verifies comparable loading conditions in the test setup. It was also confirmed that the forward and reverse

transformation from austenite to R-phase, as well as from austenite to martensite indeed occurred at ultrasonic frequency. Cyclic forward and back transformation, which play a role in fatigue damage in Nitinol [8, 9] can therefore be reproduced in ultrasonic tests.

In the present investigation, we further investigate the applicability of ultrasonic fatigue testing to the characterization of cyclic deformation and fatigue of Nitinol. We pre-deform the specimen to mimic the initial crimp and release deformation of a cardiac implant and to obtain a mixed-phase condition in the specimen consisting of austenite, martensite and two transition zones in between. In a first in situ synchrotron experiment, we compare lattice deformations of the different phases when subjected to the same cyclic amplitude at 0.1 Hz and 18.3 kHz (Chapter 4.1). In a second scanning XRD synchrotron experiment we subject a specimen to ultrasonic fatigue loading and monitor the progress of fatigue damage in-situ (Chapter 4.2). A strain amplitude versus lifetime diagram is measured for lifetimes in the high and very high cycle fatigue regime (Chapter 5.1) and crack initiation locations are investigated (Chapter 5.2). The investigation should reveal differences and similarities of the fatigue properties measured at low and ultrasonic frequencies to gauge the usefulness of ultrasonic frequency testing as a method to rapidly evaluate Nitinol fatigue.

## 2. Material and method

### 2.1. Material and specimen

In the present investigation superelastic Nitinol with 55.9% wt nickel supplied by Johnson-Matthey (San Jose, CA, USA) is used. The austenite finish temperature of the material, $A_f$ is between 13.4 °C and 14.5 °C i.e., the austenitic phase is stable at room temperature in the absence of stress. Tapered dog bone specimens as shown in Fig. 1 were laser cut from sheets with 0.25 mm thickness and subsequently micro blasted and electropolished to remove the recast and heat affected material (~25 µm). The resulting surface finish is smooth and brightly reflective and mimics the surface conditions of actual medical implants.

### 2.2. Mechanical testing procedure

The mechanical setup for performing synchrotron in situ fatigue tests with Nitinol sheets at ultrasonic frequency is shown in Fig. 2. An ultrasonic converter and the attached ultrasonic horn are mounted to the moving crosshead of a purpose-built miniaturized load frame with 500 N load capacity. The crosshead is moved via two synchronously stepper motor driven ball screws, allowing for 0.3 µm step resolution. In addition to providing mean loads the load frame also serves to cycle the specimen at a frequency of 0.1 Hz.

Push-pull resonance vibrations are generated with the ultrasonic converter and are magnified with the ultrasonic horn where one end of

<figure><img src="image_4.png" /><figcaption>Fig. 1. Sheet specimen shape used for ultrasonic fatigue tests and in situ synchrotron XRD investigations (all dimensions in mm), sheet thickness is uniform at 0.25 mm; adapted from Ref. [36].</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Mechanical setup for performing ultrasonic fatigue tests and for in situ synchrotron XRD tests; schematic (left) and in situ at ID15A at the ESRF (right); extended from Ref. [36].</figcaption></figure>

the sheet specimen is bolted to at its lower end (Fig. 2). For this purpose, a flat surface is machined onto one side at the lower end of the ultrasonic horn, and onto a rod stub rigidly mounted to the load cell on the other end in the same fashion. The horn is vibrating in resonance at a frequency of about 18.3 kHz, and the attached specimen is forced to a joint sinusoidal deformation at this frequency. The thin sheet specimen (Fig. 1) does not resonate since it is deliberately shorter than the resonance length as long thin sheet specimens would buckle during high frequency loading. Displacement measurements at the surface perpendicular to the loading direction were intermittently acquired with a fiber-optic sensor during individual tests to confirm that no buckling vibrations of specimens occur.

The amplitude of the ultrasonic resonance vibration is measured with a vibration gauge working on the principle of induction. The lower end of the ultrasonic horn is vibrating in a coil type induction sensor and induces a sinusoidal voltage signal proportional to the horn’s movement. With this feedback signal, the vibration amplitude is controlled in a closed-loop circuit with high accuracy i.e., the maximum deviation between selected and realized vibration amplitude is ±1%. Calibration of displacement amplitude was performed with a Polytec IPV-100 in-plane laser vibrometer. A second closed loop control circuit guarantees that the excitation frequency is kept at the actual resonance frequency of the load train with an accuracy better than ±1 Hz. More details of the setup were described previously [36].

Under ultrasonic frequency cycling, solely the end of the specimen, that is connected to the ultrasonic horn, is oscillating. The other end of the specimen that is connected to the load cell remains motionless due to the inertia of the load cell, which was confirmed by measurements with the laser vibrometer. Cyclic loading of the specimen at low frequency realized via moving the crosshead, however, leads to a deformation of the S-type load cell. The elongation of the specimen as a function of the crosshead displacement is measured with a clip on extensometer between the two clamping locations of the specimen. Due to compliance of the miniaturized load frame and the load cell, this extension is smaller than the applied displacement of the crosshead. Stated vibration amplitudes always refer to the actual extension of the specimens in the following.

All tests were carried out in an air-conditioned laboratory (21 °C, 50% relative humidity). Loading of specimens was realized in pulsed mode with intermittent cooling pauses (pulse length 100 ms, pause lengths between 500 and 700 ms) with additional pressurized air-cooling in place. Specimen surface temperatures at the transition zones between austenitic and martensitic material phases (Fig. 4) were routinely monitored with an infrared thermometer (spot size σ1 mm, <10 ms response time, sampling rate 1024 s⁻¹). Fig. 3 shows surface

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Spot IR-thermometer surface temperature measurements of a specimen cycled at a vibration amplitude of 26 µm with different pause lengths.</figcaption></figure>

temperature measurements for a specimen vibrating with 26 µm displacement amplitude with 100 ms long pulses and different pause lengths. The actual pause lengths in the experiments were adjusted so that no increase by more than 1.5 °C (i.e., beyond 22.5 °C) occurred, which is essential for the experiments with Nitinol due to its strongly temperature dependent mechanical behavior.

## 2.3. *In situ synchrotron XRD during ultrasonic cycling*

In situ synchrotron diffraction experiments were conducted at the ESRF in Grenoble, France, at the beamline ID15A [37], which was specifically chosen for its high-energy X-ray radiation and its fast detector capability. Comparing material behavior at ultrasonic and ordinary loading rates requires adequate temporal resolution of the high frequency vibration movement i.e., very short exposure times (around 1 µs) are necessary for a clear attribution of the diffraction patterns to a specific phase position of the ultrasonic load cycle. ID15A was operated at 60 keV with a beam size of (134 ± 5) µm × (170 ± 5) µm full width at half maximum and at 714 nm sample to detector distance. The detector Dectris CdTe Pilatus 2 M is capable of very short, gated exposures i.e., the detector starts and continues to acquire for as long as an external trigger signal remains at logic high level. The shortest successfully tested exposure time was 170 ns, comfortably permitting the targeted range of
<figure><img src="image_7.png" /><figcaption>Fig. 4. Pre-straining procedure of Nitinol specimens prior to cyclic loading (left); specimen in a multi-phase state after pre-straining (right); extended from Ref. [36].</figcaption></figure>

approximately 1 µs. Sample-detector distance and q-range were calibrated with a LaB6 powder sample; the background was corrected with an air measurement of 40 min duration.

### 2.3.1. Frame summation scheme

In our previous investigation [36] exposure times of about 10 ms were identified to yield diffraction patterns with reasonable intensity. To obtain a clear attribution of a single diffraction pattern to a specific phase position of the ultrasonic cycle and to capture spectra at maximum and minimum displacement, however, a temporal resolution of about 1 µs is required. To this end a frame summation scheme was implemented in Ref. [36], where the diffraction pattern at a specific phase position $ΔΦ_i$ is obtained from repeatedly triggering the detector to expose a ~1 µs long "phase window" $ΔΦ_{frm}$ over subsequent cycles until a total exposure time of 10 ms has accumulated i.e., about $10^4$ exposures are accumulated. This process is then repeated for the next phase position $ΔΦ_{i+1} = ΔΦ_i + ΔΦ_{frm}$ and so forth, until diffraction patterns are acquired at all phase positions of interest. In the present investigation, patterns were acquired at 50 equally spaced phase positions $ΔΦ_i$ i.e., $ΔΦ_{frm} ≈ 1.09$ µs at 18.3 kHz over the entire load cycle.

The gating trigger signal to the detector to commence exposure at a specific $ΔΦ_i$ for the duration of $ΔΦ_{frm}$ is time-referenced to the cycle generation clock of the ultrasonic fatigue test generator. The corresponding absolute time intervals are continuously calculated from and adjusted for changes in resonance frequency. The trigger generation sequence does not start before the pulsed ultrasonic vibration has reached its nominal amplitude. The number of exposures of ~1 µs to accumulate a total exposure time of 10 ms exceeds the number of cycles per 100 ms long pulse (approximately 1600 cycles). Therefore, the sequence must be repeated over a few consecutive pulses (typically seven pulses).

For comparison, specimens were also cycled at the low frequency of 0.1 Hz by means of crosshead movement of the miniaturized load frame, and 10 ms exposures were taken at the same 50 phase positions $ΔΦ_i$ of the load cycle.

### 2.3.2. Effect of incident X-ray beam on specimen temperature

Given the sensitivity of the austenite-martensite transformation stress to temperature, it is of paramount importance that the X-ray beam does not cause specimen heating. With 86% X-ray transmission through a 0.25 mm thick specimen at 60 keV, in situ temperature measurements with an infrared camera demonstrated that there were no discernible changes in specimen surface temperature with a continuously incident beam on the air-cooled specimen over the course of 1 min. This suggests that the mechanical response, phase transformation, and, by extension, diffraction data should remain unaffected by the incident X-ray beam.

## 3. Pre-deformation and multi-phase state of the specimen

Specimens are subjected to a pre-straining procedure prior to cyclic loading that mimics crimping and deployment of actual Nitinol implants. The procedure is realized through crosshead movement at a rate of 15 µm/s. Fig. 4 shows the resulting displacement-stress curve, where clamp extension denotes the elongation of the clamp distance (Fig. 1; clamp distance in load free condition is 32 mm).

In stage (1), elastic deformation of the austenitic phase occurs until at around 200 MPa (2), where the curve starts to deviate from the initially linear course as the R-phase (a rhombohedral distortion of the cubic B2 phase) is formed. At the point at which the maximum stress in the specimen reaches the forward transformation stress (3), a single martensitic (B19' phase) band begins to grow from the narrowest cross-section to an increasingly wider one, and continued deformation to (4) is observed without a significant increase in stress ("upper plateau"). The actual slight increase in stress can be attributed to the taper of the gauge section. Upon unloading starting from (4) first the martensite relaxes elastically and the band narrows gradually as martensite at the larger cross-sections reaches reverse transformation stress and transforms back to austenite (5). The result is a specimen in a multi-phase state (Fig. 4, right): A martensite band is located in the center of the gauge section, with austenite to either side. After this pre-deformation procedure, displacement controlled cyclic loading between (5) and (6) is performed. Cyclic loading resembles pulsatile blood vessel contractions the implant would experience in vivo.

For the specimen in a multi-phase condition after the preloading procedure (5), the local strains over the specimen length are inhomogeneous due to the varying cross-section and the differing stiffness between the austenitic and the martensitic phase. Average strain over the 6 mm long middle section with radius 50 mm has been computed from digital image correlation (DIC) tests. For the deformation between (5) and (6) an average increase of strain of $9 \times 10^{-5}$ was found for every 1 µm of clamp extension. From evaluating DIC measurements, average strain in Fig. 4 is ≈ 5% at (4), and ≈2.5% at (5), respectively.

The pre-strain procedure was performed in situ in the synchrotron. This allows us to obtain XRD patterns and evaluate the phase composition during the procedure. Fig. 5 shows XRD patterns that were obtained at position (1), (2) and (4) with the beam aimed at the center of the gauge section. It is noted that the peak intensities, and therefore the phases, switch sharply between austenite and martensite.

## 4. In situ synchrotron observations at low and ultrasonic frequency

### 4.1. Elastic deformation of a specimen in a multi-phase state at 0.1 Hz and 18.3 kHz

Nitinol dogbone specimens are subjected to a cyclic elongation at
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** XRD patterns of austenitic phase (left column), austenitic plus R-phase (middle column), and martensitic phase (right column); raw patterns (top row) and spectra integrated over the northern azimuthal (81°–99°) sector (bottom row), relevant peaks for fitting to derive lattice parameters are indicated; extended from Ref. [36].</figcaption></figure>

ultrasonic frequency by fixing one end to the ultrasonic horn. The vibration amplitude of the horn is equivalent to the elongation of the specimen as the second end of the specimen is motionless. Cyclic deformation of the specimen also can be performed using the minaturized load frame which allows to apply a sinusoidal load at 0.1 Hz frequency. If comparable loading conditions of the specimen are present at 18.3 kHz and 0.1 Hz, then cyclic straining of the specimen for the same vibration amplitude must be similar. The experiment is performed with the specimen in a multi-phase state with martensitic phase in the middle and austenitic phase to either side at a vibration amplitude of 15

µm at 18.3 kHz. The analogous experiment at 0.1 Hz is conducted with an amplitude of clamping extension of 15 µm. Previous tests have shown that an amplitude of 15 µm is roughly 65% of the amplitude necessary for fatigue fracture, and no failure during the experiment was expected or detected, therefore.

To this end, XRD was employed to observe lattice deformation in both material phases during cyclic loading at ultrasonic frequency at 18.3 kHz and during quasi-static loading at 0.1 Hz. Cycling a sample in the multi-phase state between (5) and (6) as shown in Fig. 4 at displacement amplitude 15 µm is equivalent to a strain amplitude 1.35

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Phase-resolved lattice strain ($\frac{d-d_0}{d_0}$ in A(200) (top row) and M(012) (bottom row) from lattice spacing $d = 2\pi/Q$ for a specimen in multi-phase condition with respect to $d_0$ at tensile mean strain, during cycling at 18.3 kHz at vibration amplitude 15 µm (left column) and during cycling at 0.1 Hz with cyclic clamp extension amplitude 15 µm (right column).</figcaption></figure>
$\times 10^{-3}$, which corresponds to a strain rate of $\approx 8.5 \times 10^{-4} \text{ s}^{-1}$ at 0.1 Hz, and $\approx 1.6 \times 10^2 \text{ s}^{-1}$ at 18.3 kHz. The beam was aimed at the center of the gauge section (i.e., in the martensite band), and 2.5 mm above/below the center (i.e., in the upper/lower austenitic portion), where XRD patterns were acquired at the same 50 phase positions. The beam was at the same positions performing the experiments at both frequencies giving the best possible basis for a comparison.

Lattice strain ($d-d_0$/d₀, where $d = 2\pi/Q$ over entire sinusoidal load cycles for both loading frequencies is shown in Fig. 6. The austenite (200) and the martensite (012) peaks were fitted in patterns integrated over the northern azimuthal (81°-99°) sector, and lattice strain $\Delta d/d_0$ was calculated with respect to lattice spacing $d_0$ at mean load. Evaluating lattice deformation at maximum and minimum strain, respectively, it is found that $\Delta d/d_0$ for loading at 18.3 kHz and at 0.1 Hz agrees within ±5%.

The concept of point observations as in Fig. 6 is extended to a 2D representation of lattice deformation over the gauge section to gain insight into the spatial distribution of material phases and (cyclic) strains. The beam is scanned over the gauge section in a (7.1 $\times$ 2.6) mm grid with 0.1 mm spacing, and lattice deformation is observed at every grid point for both frequencies at the same cyclic displacement amplitude. Diffraction patterns were only captured at maximum and minimum displacement corresponding to maximum and minimum strain. Fig. 7 (left) shows the difference between maximum and minimum lattice strain for ultrasonic cycling at amplitude 15 µm superimposed to a static displacement of 15 µm, i.e. the displacement varies by 30 µm between (5) and (6) in Fig. 4 with a frequency of 18.3 kHz. Difference in lattice strain for moving the crosshead to equivalent maximum and minimum positions is shown in Fig. 7 (right). The maps of $\Delta d/d_0$ in Fig. 7 demonstrate that strains across the gauge section are consistent between the ultrasonic and the quasi-static loading case. Evaluating and averaging $\Delta d/d_0$ over pixels the upper/lower austenitic and the martensitic regions, respectively, reveals <10% deviation between quasi-static and ultrasonic loading conditions.

## 4.2. Progress of fatigue damage visualized with XRD measurements

The main advantage of the ultrasonic fatigue testing technique lies in the vast reduction of testing time i.e., the easy accessibility of the HCF and VHCF regime. This is, among others, of special relevance for in situ synchrotron experiments, where the available beam time is typically limited and prohibits time consuming experiments. The experiment

<figure><img src="image_10.png" /><figcaption>Fig. 7. 2D maps of specimen deformation across the gauge section; difference between maximum and minimum lattice strain $\Delta d/d_0$ for cyclic deformation at ultrasonic frequency by 30 µm (left); difference in lattice strain for moving the crosshead to equivalent maximum and minimum positions (right).</figcaption></figure>

described in the following serves to observe fatigue damage in situ cycling the specimen in the synchrotron until failure and evaluating XRD measurements.

The sample is pre-strained and subsequently cycled at a vibration amplitude 22.5 µm (strain amplitude $2.0 \times 10^{-3}$), where previous ex situ fatigue tests (section 5.1.) had indicated that failures in the high cycle fatigue regime were expected. XRD served to monitor and track phase distribution and lattice deformation across the gauge section as a function of number of load cycles (Fig. 8). Diffraction patterns were acquired over a grid of (7.1 $\times$ 2.9) mm with a spacing of 0.1 mm across the gauge section. To avoid premature specimen failure, and to ensure an unchanged state during individual measurements, XRD patterns were periodically acquired after increasing numbers of load cycles with the specimen at rest during acquisition, with the superimposed static displacement unchanged since the beginning of the experiment.

Fig. 8 shows the spatial distribution of the austenitic and martensitic material phases (top row), and change in lattice strain from fitting the austenite (200) and the martensite (012) peaks, respectively (bottom row), across the gauge section as a function of number of cycles $N$. Lattice strain is presented with respect to $d_0 = d(N=0)$ i.e., after pre-straining before any cycles were applied.

Starting at $N=0$, the specimen shows austenitic zones at the upper and lower end and a martensitic zone in the middle with a sharp transition to austenite on the lower end, and a more inhomogeneous transition area towards the upper end (top row). Already at $N = 3 \times 10^3$ cycles, growth of both austenitic areas is observed close to the transition zone that had been initially martensitic. Subsequently the phase distribution is stable until, at approximately $N = 5 \times 10^5$ cycles, an initially small island of austenitic phase extends to a band over the full width of the gauge section in the formerly martensitic area.

Besides the changes in the spatial distribution of phases, $\Delta d/d_0(N)$ (bottom row) suddenly exhibits a global increase in lattice deformation and even stronger localized increases in the austenitic regions, visible as a change in color coding from green to yellow. XRD patterns are always taken at the same unchanged clamp extension of the specimen. Therefore, increased lattice deformation must be related to an increase of the stiffness of the specimen. This is plausible, since the fraction of relatively stiffer austenite in the gauge section has increased and the fraction of martensite decreased. Soon after a cyclic loading was resumed after acquiring a grid at $N = 1.5 \times 10^6$ cycles the specimen failed. The corresponding fracture surface is shown in Fig. 10 (left).

# 5. High and very high cycle fatigue of Nitinol

## 5.1. Fatigue lifetimes in the HCF and VHCF regime

Fatigue lifetimes were measured ex situ for Nitinol specimens at 18.3 kHz cycling frequency after an initial preloading procedure as shown in Fig. 4 (left). The specimen is in a multi-phase state with martensitic phase in the center of the gauge section and austenitic phase on either end, separated by the upper and lower transition zones (Fig. 4, right). Fatigue lifetimes measured in ultrasonic fatigue tests are presented in Fig. 9 versus strain amplitudes (for computation of strain amplitude from displacement amplitudes for the specimen in multi-phase state see 3). Specimens were cycled at strain amplitudes, $\Delta\epsilon/2$ between $1.35 \times 10^{-3}$ and $2.7 \times 10^{-3}$ at a mean strain of (2.5% + $\Delta\epsilon/2$). As all tests were conducted with a positive mean load, the load frame's load signal was observed to detect specimen failure and stop the ultrasonic equipment i. e., a drop to zero load. Specimens that withstood $10^9$ cycles without failure were labelled runouts.

Failures were observed between $3 \times 10^4$ and $6 \times 10^8$ cycles. The strain versus fatigue life diagram shows a strong change of the slope below $10^6$ cycles. Solely three specimens failed after $2 \times 10^6$ cycles, whereas 22 specimens failed between $3 \times 10^4$ and $2 \times 10^6$ cycles. Runouts as well as failures were found for strain amplitudes between $2.0 \times 10^{-3}$ and $2.3 \times 10^{-3}$. 50% fracture probability for a limiting lifetime
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Evolution of spatial phase distribution (top row) and lattice strain from the austenite (200) and the martensite (012) peaks with respect to the pre-strained specimen before ultrasonic cycling (i.e., *N* = 0) (bottom row) over the course of a complete in situ ultrasonic fatigue test; white pixels either indicate “air”, or phase ambiguity i.e., lattice deformation cannot be calculated because the pixel has undergone phase transformation since *N* = 0.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Strain amplitude versus fatigue lifetime for specimens in multi-phase condition measured at cycling frequency 18.3 kHz.</figcaption></figure>

of $10^9$ cycles evaluated assuming a Gaussian cumulative frequency distribution of failure probabilities according to Ref. [38] is $2.1 \pm 0.3 \times 10^{-3}$.

## 5.2. Fatigue crack initiation

Fracture surfaces of all failed specimens were investigated in the SEM. From the 24 failed specimens, the crack initiated at a surface inclusion in 20 specimens, at an internal inclusion in one specimen, at the surface without an inclusion in two specimens, and in one specimen, the crack initiation region was deformed and could not be identified. The crack initiation locations with respect to their positions along the gauge section were not explicitly observed in real time. However, the extents of the martensitic bands have been marked on some pre-strained samples prior to cyclic loading. The remaining markings on the relaxed samples after fracture imply that cracks initiated from these regions undergoing

forward and reverse stress induced martensitic transformation.

Fig. 10 (left) shows a fractured inclusion at the surface that led to fracture in the HCF regime, and Fig. 10 (right) shows a fractured internal inclusion where the specimen failed in the VHCF regime. Analyzing this inclusion with energy dispersive X-ray spectroscopy (EDX) delivered $59.1 \pm 0.6\%$ wt Ti, $34.1 \pm 1.6\%$ wt Ni, and $6.8 \pm 0.6\%$ wt O, whereas EDX in the matrix adjacent to the inclusion showed $46.8 \pm 0.8\%$ wt Ti and $53.2 \pm 1.3\%$ wt Ni. Based on literature [11,13] it can be assumed that the inclusion is a $Ni_2TiO_x$ type.

Sizes of crack initiating inclusions are in a very narrow range. The square root of the projected area of the inclusion perpendicular to the loading direction i.e., (area)$^{1/2}$ is in the regime between $2.7 \mu m$ and $4.7 \mu m$ (mean value $3.6 \mu m$). All crack initiating inclusions were fractured, and no interface fracture was observed. The fracture surface close to the inclusion is fine structured and relatively even and becomes coarser in some distance from crack initiation.

## 6. Discussion

The aim of the present study is to investigate the applicability of ultrasonic frequency fatigue testing to characterize the fatigue properties of Nitinol used for stents. Sheet specimens are pre-deformed and tested in multiphase condition to simulate the multi-phase state in stents during delivery and deployment. It is shown that specimen heating can be avoided with pulsed loading and air cooling as specimen temperature increase could be limited to $1.5 \,^\circ C$. Effective cycling frequencies in pulsed loading were greater than 2 kHz, which means that $10^9$ cycles are reached in less than one week. This underlines the great saving of testing times using ultrasonic fatigue testing for very high cycle fatigue testing of Nitinol, which can accelerate material development and can be used for rapid material characterization.

It is however necessary to prove that the loading condition of the Nitinol specimen in the developed ultrasonic setup is comparable to that at conventional frequencies. Unlike in most ultrasonic tests, the specimen is not excited to resonance vibrations but forced to cyclic deformation using the ultrasonic equipment as a high frequency cyclic tension equipment. In situ ultrasonic loading of the specimen in the synchrotron and analyzing the XRD patterns serves to verify cyclic loading conditions for the specimen. Comparing the elastic deformation for the same
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Scanning electron micrographs of fracture surfaces with fatigue crack initiation at inclusions; (left) surface inclusion ($\Delta\epsilon/2 = 2.0 \times 10^{-3}$, $1.5 \times 10^6$ cycles to failure); (right) internal inclusion ($\Delta\epsilon/2 = 2.0 \times 10^3$, $1.2 \times 10^8$ cycles to failure).</figcaption></figure>

vibration amplitude for the used ultrasonic frequency of 18.3 kHz and for a of frequency 0.1 Hz shows a deviation of both strain measurements within ±5%. Sinusoidal loading with the same displacement amplitude led to a similar sinusoidal course of strain if loaded at low and ultrasonic frequency in the austenitic as well as the martensitic region of the specimen (Fig. 6). Moreover, capturing maximum-to-minimum lattice deformation over the multi-phase gauge section shows deviations of strain ranges at 0.1 Hz and 18.3 kHz of no more than 10% (Fig. 7). For the elastically loaded specimen it is confirmed therefore, that the displacement amplitude measured between both specimen's clamping locations determines cyclic deformation and is similar if cycled at low and ultrasonic frequency.

We have previously used this technique to investigate the elastic deformation of a Nitinol specimen in purely austenitic state and similarly found good agreement [36]. Ors et al. [39] performed in situ ultrasonic synchrotron measurements of lattice deformation in pure copper and found about 20%–25% difference to strain gauge measurements. Pearlitic steel was tested by Jacquemain et al. [40] and they found comparable strain amplitudes within the ranges of scatter using strain gauge measurements, laser vibrometer measurements with FEM calculations, and evaluating XRD measurements.

At low displacement amplitudes the specimen deforms elastically, whereas high displacement amplitudes lead to a cyclic forward and reverse phase transformation in the center regime of the specimen. As the load cycle approaches the maximum displacement the martensite band in the middle region of the specimen widens whereas it becomes narrower at minimum displacement. In our previous work we verified that the back and forth phase transformation of austenite to martensite via the intermediate R-phase indeed occurred at ultrasonic frequency [36]. A mechanism that causes failure of Nitinol in the high cycle fatigue regime is the cyclic back and forth transformation between austenitic to martensitic phase [8,9], and it was essential for the applicability of ultrasonic testing, that cyclic phase transformation can occur at ultrasonic strain rates.

The process of fatigue damage under ultrasonic frequency loading is investigated in the present work with in situ synchrotron XRD measurements of a specimen subjected to an increasing number of load cycles. After preloading, the specimen shows austenitic zones at the upper and lower end and a martensitic zone in the middle with a rather narrow transition zone at the bottom end and a more inhomogeneous zone at the upper end (Fig. 8). Already in the first $3 \times 10^3$ cycles, an extension of both austenitic areas become visible close to the transition zone that have been initially martensitic. Phase distribution then seems to be stable until, at approximately $5 \times 10^5$ cycles, an initially small island of austenitic phase extends to a band over the full width of the gauge section in the formerly martensitic area. The Young's modulus of austenite is higher than that of martensite. For example Weaver et al. [8]

report 72.5 GPa for the austenitic and 28.5 GPa for the martensitic phase of the Nitinol used in their investigation. For a given vibration amplitude, the martensitic phase accommodates more strain than the austenite due to its lower stiffness. Reducing the martensitic volume thus must be compensated by higher strains in both, the martensite and austenite phase. In Fig. 8 bottom, this becomes apparent as a shift in color coding towards yellow in both phase regions. Increasing cyclic and static strain aggravate fatigue damage and eventually cause failure of the specimen.

In situ ultrasonic testing in the synchrotron has been previously used in several investigations to monitor the progress of fatigue damage. Liu et al. [41,42] measured influences of microstructure, compositional segregations and strains on initiation and growth of cracks in single crystal Ni-base superalloys. Zimmermann et al. [43] performed in-situ experiments with polycrystalline superalloy Nimonic 80A and cp Ni. Istomin et al. [44] investigated the evolution of fatigue damage in duplex stainless steel by analyzing changes in the diffraction patterns. Krupp et al. [45] showed the importance of the first barrier for the fatigue crack for the VHCF properties of duplex stainless steel. Shimamura et al. [46] used synchrotron radiation for µCT imaging of Cr–Mo steel with the aim to observe internal cracks at inclusions. Messager et al. [47] used synchrotron X-ray tomography to study cracks starting at internal defects in AlSi7Mg0.6 cast aluminum, and internal crack propagation in Ti6Al4V was studied by Hebrard et al. [48] using internally notched specimens. This underlines the great advantage of ultrasonic fatigue testing equipment being easily transported. The load train is relatively compact and light, and positioning the specimen into the beam is therefore relatively easily accomplished.

Fatigue cracks leading to fracture start at fractured inclusions in 88% of specimens. Preferred fatigue crack initiation at inclusions is found in several studies of Nitinol [9,11–17]. Crack initiation for the same specimen shape as used in the present investigation subjected to 40 Hz cycling showed crack initiation within the region undergoing forward and reverse stress induced martensitic transformation typically at a near-surface inclusion [9]. The failure mode found in conventional frequency tests i.e., inclusion initiated fracture, is therefore reproduced in ultrasonic tests.

The measured strain versus fatigue lifetime diagram shows a pronounced change of slope below $10^6$ cycles with a steep slope for lower and a shallower slope for higher lifetimes. Such a change of slope in cyclic load versus fatigue lifetime diagrams is reported in several measurements of Nitinol [6–9,13,14,16,17,20,22]. Solely few investigations can be found with fatigue lifetimes tested to beyond $10^8$ cycles. Rahim et al. [13] performed bending rotation fatigue tests with Nitinol wires and found failures above $10^8$ cycles. Weaver et al. [8] subjected Nitinol wires to rotating bending and found a relatively shallow slope, however, several failures above $10^8$ cycles.
Although the shape of strain versus fatigue lifetime diagram measured in ultrasonic tests is in principle similar to conventional tests, it cannot be assumed that the measured lifetimes are equivalent. Experiments with specimens in multi-phase condition by Catoor et al. [9] show that increasing the cycling frequency decreases the width of the stress strain hysteresis loop if loads are above the elastic regime. Additionally, maximum stress during a load cycle increased and minimum stress decreased as the cycling frequency increased from 0.004 Hz to 40 Hz. This suggests that fatigue lifetimes measured at ultrasonic frequency cannot be directly applied for the design of stents, for example, where the loading rate is about a factor 10 000 lower. Influences of strain rate must be investigated further to improve applicability of ultrasonic lifetimes. However, the previous and the present work show that fundamental mechanisms of fatigue damage, such as specimen loading, phase transformation, crack initiation, and shape of the strain lifetime diagram can be reproduced which makes ultrasonic fatigue testing a promising time saving technique to investigate the very high cycle fatigue properties of Nitinol.

## 7. Conclusions

Nitinol thin sheet specimens in multi-phase condition were tested at ultrasonic frequency in the high and very high cycle fatigue regime. In situ synchrotron experiments served to monitor cyclic straining and progress of fatigue damage. The following conclusions may be drawn.

1. Cyclic elastic deformation in the austenitic as well as martensitic regime of the specimen are similar if cycled at the same displacement amplitude at cycling frequencies 0.1 Hz and 18.3 kHz. Comparable strain ranges over the entire gauge section are found at both cycling frequencies. Cyclic straining of the thin sheet specimen in the elastic regime is similar at ultrasonic frequency and quasi-static loading.

2. Fatigue cracks nearly exclusively initiate at relatively small, cracked surface inclusions. Under ultrasonic frequency cycling, austenitic bands in the formerly martensitic regime are formed. This increases the overall stiffness in the gauge section, increases the cyclic stress for constant displacement amplitude cycling and finally leads to failure from inclusions.

3. The strain versus fatigue lifetime diagram shows a much steeper curve below $10^6$ cycles than above. Failures occurred above $10^8$ cycles indicating that Nitinol does not show a fatigue limit.

4. Crack initiation at inclusions is found in both conventional and ultrasonic tests. Cyclic load versus fatigue lifetimes diagrams show a similar trend. Cyclic phase transformations occur at ultrasonic frequency. Specimen heating can be avoided by pulsed loading, and for the elastic regime it could be confirmed that strain amplitudes for low frequency and ultrasonic loading at the same displacement amplitudes are similar. This suggests that ultrasonic frequency testing is in principle appropriate to measure fatigue performance of Nitinol.

## CRediT authorship contribution statement

**M. Fitzka:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. **H. Rennhofer:** Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – review & editing, Visualization. **D. Catoor:** Conceptualization, Methodology, Validation, Investigation, Resources, Writing – review & editing. **M. Reiterer:** Methodology, Resources, Supervision, Project administration, Funding acquisition. **S. Checchia:** Software, Investigation, Supervision, Resources. **M. di Michiel:** Investigation, Resources. **H.C. Lichtenegger:** Conceptualization, Methodology, Investigation, Supervision. **H. Mayer:** Conceptualization, Methodology, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization, Supervision, Project administration.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities, and we would like to thank the beamline staff for assistance and support in using beamline ID15A.

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