Development of a piezo actuator-based fatigue testing machine for miniature specimens and validation of size effects on fatigue properties

2.1 Specification of fatigue testing machine

The specifications of the bidirectional piezo actuator-based fatigue testing machine developed in this study are presented in Table 1. Figure 1 shows (a) a schematic diagram, (b) an overview, and (c) magnified parts of the developed machine. The testing machine dimensions are 1,174 mm in height, 370 mm in length, and 270 mm in width. This machine uses a piezo actuator, enabling the application of tension, compression, and constant torsion loading. The control method is load-controlled, with maximum loading and displacement of ±1 kN and ±0.15 mm, respectively. In addition, once the rotation angle is set via torsion adjustment parts, the torsional load can be maintained at a constant value throughout the testing. The machine’s maximum frequency is 15 Hz. Load measurement is carried out with a highly rigid load cell, with a maximum capacity of ±5 kN, to prevent the displacement generated by the piezo actuator from being absorbed by load cell deformation. Displacement measurement is performed using a cantilever displacement sensor, which has a maximum capacity of ±1 mm and a high responsiveness of up to 110 Hz, accommodating the machine’s maximum loading frequency.

Figure 1

Appearance of fatigue testing machine: (a) schematic diagram, (b) overview, and (c) magnified parts.

The rationale for selecting a piezo actuator as the loading mechanism is as follows. Operating without friction, the piezo actuator enables control at the nanometer level, facilitating precise fatigue testing of miniature specimens with minimal deformation. In addition, its operation is free from wear during rotation, which extends its service life. A standalone piezo actuator can respond on the order of several kHz, making high-frequency fatigue testing feasible. Based on these advantages, a piezo actuator was chosen for this fatigue testing machine.

The control circuit diagram of the fatigue testing machine is presented in Figure 2. In this diagram, the solid arrow denotes the control signal, while the dash arrows indicate the feedback (control) and measurement signals. The control process is as follows: test conditions, such as loading amplitude and frequency, are first input into the PC, from which control signals are transmitted to LabVIEW (2019 version, National Instruments Corporation, USA). These command signals are then sent as control signals from LabVIEW to each piezo actuator through the respective drivers. The piezo actuators expand and contract in response to the command signals. Three measurement signals – loading, Displacement 1, and Displacement 2 – are subsequently sent back to LabVIEW. Notably, the loading signal also functions as a feedback signal. Based on this feedback, LabVIEW generates a new command signal that is transmitted to each piezo actuator through the corresponding actuator.

Figure 2

Control flow of the alternate piezo actuator type fatigue testing machine.

2.2 Testing frequency

To minimize testing time, it is preferable to maximize the testing frequency without compromising the test results. Therefore, this section examines the frequency characteristics of the developed fatigue testing machine.

The evaluation method involved varying the testing frequency across different loading levels to assess whether the loading control and displacement responses were consistent, based on measured loading and displacement data. To verify output loading, the load–time graph and frequency data were used to confirm whether output values reached the intended targets. In addition, abnormal vibrations, such as resonance, were evaluated by analyzing the relationship between the two displacement measurements obtained from the displacement sensors. Displacement 1 represents the upper rod displacement, while Displacement 2 indicates the lower rod displacement (Figure 1). The results of the frequency characteristic analysis are shown in Figure 3, where the horizontal axis represents the frequency f and the vertical axis shows the loading amplitude P _a. For the verification tests, frequencies of 15, 20, and 35 Hz, along with loading amplitudes of 200, 600, and 1,000 N, were used. In Figure 3, Range I represents test conditions where the machine operated normally, while Range II represents conditions where normal operation was not achieved except for one test condition. As shown, the output loads met target values for all conditions at a frequency of f = 0–15 Hz. However, at frequencies of f = 16–35 Hz, the output load only met target values for the condition of f = 20 Hz and a loading amplitude of P _a = 1,000 N. The inability to sustain target loading beyond this frequency range was attributed to resonance in the lower rod, which became more pronounced at frequencies exceeding 20 Hz. Figure 4 provides an example of a specimen tested under an applied load of 200 N at a frequency of 20 Hz. The variation in output load with the increasing number of cycles is shown in Figure 4(a), where it is observed that the output load remained stable. In addition, Figure 4(b) shows the maximum and minimum displacement values for the upper and lower rods. For the upper rod (purple plots), although some scatter is noted, the maximum and minimum values remained within ±0.03 mm, indicating controlled displacement within measurement accuracy. Conversely, displacement in the lower rod exhibited considerable scatter approximately between 2,000 and 5,000 cycles, which was attributed to resonance. Therefore, the maximum applicable frequency for the developed fatigue testing machine was determined to be f = 15 Hz.

Figure 3

Frequency characteristics of the alternate piezo actuator-based fatigue testing machine.

Figure 4

Variation of output values with increasing number of cycles: (a) applied loading and (b) displacement of rods.

2.3 Controlling system

The control software was developed in-house using LabVIEW. Real-time display of various measured values and graphs provides a clear view of test status during operation. The displayed information includes the current, maximum, minimum, range, and average values for loading, Displacement 1 (upper rod displacement), and Displacement 2 (lower rod displacement). In addition, the control software displays graphs showing the displacement–loading relationship and the load variation over time. The system also features automatic load control to maintain the target value, minimizing the risk of specimen deformation due to excessive load during the attachment process.

PID control can be customized by adjusting the gain values. Currently, the test operates under proportional (P) control, with the integral (I) and differential (D) values set near zero. This configuration was selected due to the high responsiveness of the piezo actuator (a single piezo actuator responds on the order of kHz), as employing PI control would likely result in oscillations.

3.1 Specimen design

The specimen was designed using the FEA described below. Figure 5 shows the shape and dimensions of specimen. The gauge section was designed into a cylindrical shape with a diameter of 1.6 mm to enable multiaxial loading such as axial and torsional loadings. The length of the gauge section is limited to 4 mm, because when the length of the gauge section is three times or more than its diameter, there is a risk that deflection will occur during lathe machining, which may affect surface roughness and parallelism. In addition, in consideration of sampling specimen from actual structures or components, the thickness of gripping portion is limited at 2.2 mm.

Figure 5

Shape and dimensions of specimen (mm).

3.2 Chucking jigs

The miniature specimen must be rigidly secured to prevent irregular loading from affecting the jig during fatigue testing. Given the small size of the specimen, precise alignment of the axis is essential. To meet these requirements, a specialized holding jig was developed, as shown in Figure 6. This jig prevents impact loading during testing by applying fixing force to the specimen’s end face and automatically aligns the axis between the jig and the specimen along the R-section. As illustrated in Figure 7, taper blocks A and B are adjusted by sliding bolts, which apply fixing force by pushing in a fixing rod. The specimen is further stabilized in the thickness direction by positioning it between spacers.

Figure 6

Photograph of gripping jig and specimen.

Figure 7

Schematic of the jig used for fixing the specimen.

3.3 Conditions of FEA

In general, the specimen design aims to maximize the von Mises equivalent stress within the gauge section. However, if the specimen has a round gauge section and a square grip section, it may fracture at the corner during fatigue testing. This can occur due to surface roughness from corner machining and the direct loading contact with the jig. A preliminary test was performed with pull–push loading at an amplitude of 250 MPa using a specimen with the same dimensions as shown in Figure 5 but with a diameter of 1.8 mm. Although this specimen was designed to maximize von Mises stress at the gauge section, it ruptured at the R-section, as illustrated in Figure 8(a). Conversely, in a preliminary test with a specimen diameter of 1.6 mm, the fracture occurred at the gauge section, as shown in Figure 8(b). This indicates that the design should not only maximize von Mises stress at the gauge section but also ensure that corner stress is sufficiently lower than that at the gauge section.

Figure 8

Fracture location for specimens with diameters of (a) 1.8 mm at the R-section and (b) 1.6 mm at the gauge section.

Based on these findings, FEA was conducted on two specimen types with gauge diameters of 1.6 and 1.8 mm. The purpose of the analyses was to determine the maximum von Mises equivalent stress at the gauge section and to compare the corner stresses to establish a required safety margin. ANSYS 2021 R2 was used for the analysis.

In the model, a half-symmetrical shape was constructed to leverage symmetry. To account for the jig’s pressure at the R-section, the specimen holding jig was included in the model. The analytical shape is shown in Figure 9, and Table 2 displays the connection settings between the components. The “Contact” setting was applied to model the potential separation between the test specimen and jig under combined tensile–torsion loading. This setting prevents penetration when the distance between the components decreases, ensuring that compressive loads are transmitted, while treating separated components as if no load is transmitted. In addition, the spacer and fixing rod were modeled as bonded to the jig. The specimen’s pressing force was simulated by applying initial stress along the axial (X) direction to the fixing rod, which in turn compresses the specimen against the jig, generating compressive stress at the R-section.

Figure 9

Overview of analysis model.

The material constants are presented in Table 3, and the loading boundary conditions are depicted in Figure 10. The analysis was conducted in two steps: in Step 1, the pressing load was applied, followed by the axial load in Step 2. The axial load was set at 200 MPa for the gauge section, and the fixing load was set at 1.5 times the axial load to ensure secure attachment.

Figure 10

Boundary conditions used for analysis.

4.1 FEA

The FEA results for specimens with diameters of 1.6 and 1.8 mm are illustrated in Figure 11, using von Mises equivalent stress as the metric. Maximum von Mises stresses were observed at both ends of the gauge section for both specimen sizes, with stress differences from the gauge section remaining within 10%. Similar stress differences at the ends of the gauge section are common in non-miniature fatigue specimens and do not typically pose issues for testing. Pretests confirmed that this miniature fatigue specimen could also be tested without complications, as evidenced by the absence of fractures at the ends of the parallel section as shown in Figure 8(b).

Figure 11

FEA results under axial loading for specimens with diameters of (a) 1.6 mm and (b) 1.8 mm.

In the R-section where fractures occurred in the pretest for the 1.8 mm specimen, the stress reached 145.3 MPa (72.6% of the gauge stress). In contrast, for the 1.6 mm diameter specimen, the R-section stress was 114.1 MPa (57.1% of the gauge stress), achieving a stress reduction of over 15%. The maximum stress at the R-section was concentrated at the edge, where the specimen interfaces with the jig, resulting in compressive stress at this contact point. Given the sharp geometry of the edge, this region becomes susceptible to crack initiation. During the pretest of the 1.8 mm specimen, high stress – exceeding 70% of the gauge stress – developed at the R-section edge, promoting crack growth and leading to early failure at the R-section before the gauge section. Although polishing the edges could potentially reduce crack formation, this is not entirely reliable, as the edges remain in contact with the jig. Consequently, reducing the stress ratio in the R-section is essential. For the 1.6 mm diameter specimen, concentrating stress in the gauge section allows for a reduced stress ratio in the R-section. Based on pretest findings, fractures initiated from the R-section for the 1.8 mm diameter specimen but from the gauge section for the 1.6 mm diameter specimen. Therefore, to avoid premature fracture, the stress at the R-section edge should remain below 57.1% of the gauge stress.

To verify the stress distribution for a specimen with a 1.6 mm diameter under combined axial–torsional loading, FEA was conducted. The magnitude of torsional loading was adjusted so that the von Mises stress in the gauge section equaled the axial loading stress (200 MPa). The developed fatigue testing machine allows for cyclic axial loading while maintaining constant torsional loading, so the analysis followed the sequence: Step 1 (pressing load) ⇒ Step 2 (shear load) ⇒ Step 3 (axial load in tension). The resulting stress distribution behaviors are shown in Figure 12. In this analysis, the R-section stress reached 116.0 MPa, approximately 41% of the gauge section stress, which was 282.8 MPa. Even under combined axial–torsional loading, the gauge section is expected to fracture at the R-section. Comparing this result with Figure 11(b) indicates that the addition of torsional loading further reduces the stress ratio in the R-section, significantly lowering the likelihood of fracture in this area compared to purely axial loading conditions (without torsion). Based on these results, the probability of fracture occurring in the gauge section remains higher than in the R-section, even under combined axial–torsional loading conditions.

Figure 12

FEA results under combined loading for the specimen with a diameter of 1.6 mm.

4.2 Verification testing

Verification testing was conducted to investigate the size effect on fatigue life using AISI 304 and AISI 310S. Figure 13 presents a comparison of fatigue life for AISI 304 between miniature and bulk specimens, with additional data from the National Institute for Materials Science (NIMS) [15,16] included for reference. Arrows in Figure 13 indicate specimens that did not fail. At an applied stress amplitude of 300 MPa, the fatigue life of miniature specimens is slightly longer than that of bulk specimens. In contrast, at a lower stress amplitude of 270 MPa, the fatigue life difference between the two specimen types is over an order of magnitude, indicating a clear size effect. Due to the absence of fatigue limit data for bulk specimens, NIMS data were utilized for further analysis. The fatigue limit for miniature specimens is approximately 270 MPa, while the NIMS data indicate a fatigue limit of about 235 MPa for bulk specimens, lower than that of the miniature specimens. Therefore, the size effect is evident in both finite and infinite fatigue life ranges. Additionally, after normalizing the ordinate by tensile strength (σ _UTS of current AISI 304 is 618 MPa and σ _UTS of NIMS AISI 304 is 617 MPa), the gap between the NIMS data and current results narrows. It is well established that even materials from the same manufacturer and batch may show data scatter, making slight inconsistencies unavoidable.

Figure 13

Comparison of fatigue life for AISI 304 between miniature and bulk specimens: (a) conventional S–N curves and (b) S–N curves normalized by tensile strength.

To further investigate whether the size of the fatigue initiation site influences fatigue life for the two specimen types, fracture surface observations were performed. Typical fracture surfaces are shown in Figure 14. As depicted, fatigue cracks initiated from the surface in both specimen types, under both high and low applied stress amplitudes of 300 and 270 MPa. These observations are consistent with those obtained for bulk AISI 316 in the high-cycle regime [17,18]. Thus, while specimen size impacts fatigue life and the fatigue limit, it has minimal effect on fatigue crack initiation behavior.

Figure 14

Fracture surface observations for (a) and (c) miniature, and (b) and (d) bulk specimens.

In addition, the fatigue test results for AISI 310S miniature specimens, along with data from NIMS data sheets, are shown in Figure 15. At relatively high stress levels (320–400 MPa), the fatigue life of both specimen types is nearly equivalent, despite some data scatter. However, as the applied stress amplitude decreases, the fatigue life gap between the two specimen types widens significantly. While NIMS data do not include a specific fatigue limit, the trend of the S–N curve suggests an approximate fatigue limit of 200–220 MPa. In contrast, the fatigue limit of miniature specimens is around 250 MPa. Moreover, after normalizing the ordinate by tensile strength (σ _UTS of current AISI 310S is 534 MPa and σ _UTS of NIMS AISI 310S is 567 MPa), the gap at relatively high stress levels became larger, while at relative low stress levels the trend hardly changed. Based on these results, it can be concluded that a size effect is present in both materials studied, with the fatigue limit of miniature specimens exceeding that of bulk specimens. In austenitic stainless steel, fatigue cracks typically initiate at the surface from a “weak” grain in the high-cycle fatigue region. Larger-diameter specimens are more likely to contain such weak grains, which may increase the likelihood of crack initiation compared to smaller specimens [19]. This contributes to the observed size effect.

Figure 15

Comparison of fatigue life for AISI 310S between miniature and bulk specimens: (a) conventional S–N curves and (b) S–N curves normalized by tensile strength.