Effect of Microscopic Structure on High-cycle Fatigue Damage in Polycrystalline Nano-copper

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ScienceDirect

Available online at Available online at www.sciencedirect.comwww.sciencedirect.com

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Structural Integrity Procedia 00 (2016) 000–000

www.elsevier.com/locate/procedia

Peer-review under responsibility of the Scientific Committee of PCF 2016.

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

Thermo-mechanical modeling of a high pressure turbine blade of an

airplane gas turbine engine

P. Brandão

a

_{, V. Infante}

b

_{, A.M. Deus}

c

_*

a_{Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

b_{IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

c_{CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa,}

Portugal

Abstract

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

Peer-review under responsibility of the Scientific Committee of PCF 2016.

Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

* Corresponding author. Tel.: +351 218419991.

E-mail address: [email protected]

Procedia Structural Integrity 2 (2016) 1375–1382

Peer review under responsibility of the Scientific Committee of ECF21. 10.1016/j.prostr.2016.06.175

10.1016/j.prostr.2016.06.175

Available online at www.sciencedirect.com

ScienceDirect

Peer-review under responsibility of the Scientific Committee of ECF21.

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Effect of Microscopic Structure on High-cycle Fatigue Damage in

Polycrystalline Nano-copper

Takashi Sumigawa

a,

_{*, Kenta Matsumoto}

a

_{, Takayuki Kitamura}

a

a _{Department of Mechanical Engineering and Science, Kyoto University, Kyoto-daigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan}

Abstract

A high-cycle loading method under full load reversal using resonant vibration was developed to investigate the high-cycle fatigue damage of polycrystalline copper in a multi-layered material. A component specimen in which a thin layer of nano-polycrystalline copper was sandwiched between a Si substrate and SiN layer was prepared by the focused ion beam technique, and a cyclic load was applied to the specimen. In order to reduce the resonance frequency of the specimen was reduced to less than several hundred kilohertz to control the loading cycle, a gold weight was attached to the specimen tip by tungsten deposition. The high-cycle fatigue loading induced slip bands associated with extrusion/intrusion of approximately several tens of nanometers in width on the upper surface of the Cu layer. The slip band was formed by the microscopic stress field in the grain, which was generated by the deformation constraint between grains. Although the morphology of the extrusion/intrusion was very similar to that observed in fatigue of the bulk material, the size was significantly different. A crack along the grain boundary was observed and it seemed to be initiated by the collision of slip bands with the grain boundary.

Keywords: Nano-polycrystalline material; high-cycle fatigue; Slip band; Stress field; Resolved shear stress 1. Introduction

Metal fatigue often leads to the catastrophic failure of components, and it has thus been widely investigated [Basinski et al. (1980), Basinski et al. (1992), Laird (1986), Mughrabi (1978), Mughrabi (1983)]. Many studies have specifically focused on persistent slip bands (PSBs) [Basinski et al. (1980), Basinski et al. (1992), Laird (1986),

* Corresponding author. Tel.: +81-75-383-3619; fax: +81-75-383-3619.

Available online at www.sciencedirect.com

ScienceDirect

21st European Conference on Fracture, ECF21, 20-24 June 2016, Catania, Italy

Effect of Microscopic Structure on High-cycle Fatigue Damage in

Polycrystalline Nano-copper

Takashi Sumigawa

a,

_{*, Kenta Matsumoto}

a

_{, Takayuki Kitamura}

a

a _{Department of Mechanical Engineering and Science, Kyoto University, Kyoto-daigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan}

Abstract

A high-cycle loading method under full load reversal using resonant vibration was developed to investigate the high-cycle fatigue damage of polycrystalline copper in a multi-layered material. A component specimen in which a thin layer of nano-polycrystalline copper was sandwiched between a Si substrate and SiN layer was prepared by the focused ion beam technique, and a cyclic load was applied to the specimen. In order to reduce the resonance frequency of the specimen was reduced to less than several hundred kilohertz to control the loading cycle, a gold weight was attached to the specimen tip by tungsten deposition. The high-cycle fatigue loading induced slip bands associated with extrusion/intrusion of approximately several tens of nanometers in width on the upper surface of the Cu layer. The slip band was formed by the microscopic stress field in the grain, which was generated by the deformation constraint between grains. Although the morphology of the extrusion/intrusion was very similar to that observed in fatigue of the bulk material, the size was significantly different. A crack along the grain boundary was observed and it seemed to be initiated by the collision of slip bands with the grain boundary.

Keywords: Nano-polycrystalline material; high-cycle fatigue; Slip band; Stress field; Resolved shear stress 1. Introduction

Metal fatigue often leads to the catastrophic failure of components, and it has thus been widely investigated [Basinski et al. (1980), Basinski et al. (1992), Laird (1986), Mughrabi (1978), Mughrabi (1983)]. Many studies have specifically focused on persistent slip bands (PSBs) [Basinski et al. (1980), Basinski et al. (1992), Laird (1986),

* Corresponding author. Tel.: +81-75-383-3619; fax: +81-75-383-3619.

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1376 Takashi Sumigawa et al. / Procedia Structural Integrity 2 (2016) 1375–1382 2 Author name / Structural Integrity Procedia 00 (2016) 000–000

Mughrabi (1978), Mughrabi (1983), Lukas et al. (1968)], which consist of a characteristic understructure (ladder-like structure) formed by the self-organization of dislocations [Basinski et al. (1992), Laird (1986), Mughrabi (1980)] because they play an important role in crack initiation due to plastic strain accumulation [Winter (1974)] and stress concentration at the resulting extrusions/intrusions [Thompson et al. (1956), Basinski et al. (1983)]. The PSBs and extrusions/intrusions generally have dimensions larger than a few micrometers [Mughrabi (1980), Grosskreutz (1975), Laufer (1966), Woods (1973)].

Electronic devices typically include micrometer- or nanometer-scale polycrystalline metals that are often subjected to mechanical vibration or thermal cyclic loading. However, for components smaller than a few micrometers, there is no space to form PSBs and the extrusion/intrusion during fatigue. Moreover, although the slip behavior is governed by the crystal orientation and the loading direction in a single crystal, it is difficult to describe the slip behavior in a polycrystal by a simple law because of the effect of deformation constraint between grains. Characteristic slip behavior that cannot be defined by the crystal orientation and loading direction has been observed near grain boundaries [Sumigawa et al. (2004)]. Therefore, characteristic fatigue behavior is expected to occur in micrometer/sub-micrometer scale polycrystalline metals.

Many researchers [Schwaiger et al. (2003a), Zhang (2005), Kraft et al. (2001), Schwaiger et al. (2003b), Read (1998)] have investigated the fatigue of low-dimensional materials. The characteristic fatigue behavior was expected because the small volume results in a specific plasticity [Greer et al. (2005), Greer and Nix (2006), Uchic et al. (2004), Volkert (2006), Zhang et al. (2008)] due to dislocation source starvation [Greer and Nix (2006), Budiman et al. (2008)] and the inhibition of dislocation glide by the image force from interfaces and free surfaces [Weertman (1964)]. However, the details of fatigue behavior in nano-polycrystalline metals that are constrained by dissimilar materials have yet to be clarified.

In this work, a fatigue experiment based on resonant vibration was conducted using a nano-component specimen consisting of silicon (Si), titanium (Ti), nano-polycrystalline copper (Cu), and silicon nitride (SiN). The fatigue damage was examined based on detailed observations.

Nomenclature

PSB Persistent slip band

FIB Focused ion beam

f0 Resonant frequency of specimen

w Width of test section

h Height of test section

k Spring constant of test section

m Mass of the weight at the test section tip

lG Length from the test section root to the center gravity of the weight

E Young’s modulus

SEM Scanning electron microscopy EBSD Electron back-scatter diffraction Δδ1 Displacement range at the weight end

Δδ2 Displacement range at the test section root

Δδ1/2 Displacement amplitude at the weight end

Δδ2/2 Displacement amplitude at the test section root

FE-SEM Field emission-scanning electron microscopy ΔVin/2 Input voltage amplitude

Δδ/2 Displacement amplitude

Δτcrss/2 Amplitude of resolved shear stress

Author name / Structural Integrity Procedia 00 (2016) 000–000 3 2. Experimental procedure

2.1. Specimen preparation

Layers of Ti (20 nm thick), Cu (200 nm thick), and SiN (20 nm thick) were continuously deposited by magnetron sputtering on a single crystalline Si(100) substrate, of which the native oxidized layer was removed by argon ion etching. After deposition, the multi-layered material was annealed in a vacuum (1×10-4_{Pa base pressure) at 673 K}

for 1 h.

The specimen for the fatigue experiment was carved out of the multi-layered material by focused ion beam (FIB) processing with an accelerating voltage of 40 kV and a beam current of 1.17 nA. Figure 1 schematically illustrates the concept of the resonant fatigue experiment method. A cantilever-shaped test section is attached to a base (Fig. 1(a)). The test section contains a Si substrate and Cu, Ti and SiN layers. A fully reversed bending load to the test section is realized by applying resonant oscillation to the base in the vertical direction. However, a submicron component generally has a resonant frequency over a few tens of gigahertz, which makes it difficult to control the loading cycle. Therefore, to reduce the resonant frequency of the specimen, a Au weight is attached to the test section tip (Fig. 1(b)). The resonance frequency f0, of a cantilever (cross-section of w (width) × h (height)) with a

weight at the tip is approximately evaluated by the following equation:

m k f 2π 1 0 _       ₃ G 3 4l wh E k

,

(1)

where k, m, E, and lG are the spring constant of the test section in the vibration direction, the mass of the weight, the

Young’s modulus of the test section, and the length from the test section root to the gravity center of weight, respectively. Based on Eq. (1), the shape and size of the weight were designed so that f0 < 300 kHz was achieved.

The fabrication procedure is as follows.

1. A cube block of 25×25×25 μm3_{was carved out of the multi-layered material (Fig. 2(a)).}

2. The end of the microprobe installed in the FIB processing system was fixed on the upper surface of the block by tungsten (W) vapor deposition (Fig. 2(b)), and the block was picked up after cutting the holding part (Fig. 2(c)). 3. The block was fixed on a Si substrate (550 μm thick) (Fig. 2(d)) by W deposition. The microprobe was cut by

FIB and separated (Fig. 2(e)).

4. A Au block for weight was carved out of a polycrystalline Au plate. The Au block was then mounted on the SiN layer of the multi-layered block on the Si substrate by W deposition (Figs. 2(f) and (g)).

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Takashi Sumigawa et al. / Procedia Structural Integrity 2 (2016) 1375–1382 1377

2 Author name / Structural Integrity Procedia 00 (2016) 000–000

Mughrabi (1978), Mughrabi (1983), Lukas et al. (1968)], which consist of a characteristic understructure (ladder-like structure) formed by the self-organization of dislocations [Basinski et al. (1992), Laird (1986), Mughrabi (1980)] because they play an important role in crack initiation due to plastic strain accumulation [Winter (1974)] and stress concentration at the resulting extrusions/intrusions [Thompson et al. (1956), Basinski et al. (1983)]. The PSBs and extrusions/intrusions generally have dimensions larger than a few micrometers [Mughrabi (1980), Grosskreutz (1975), Laufer (1966), Woods (1973)].

Electronic devices typically include micrometer- or nanometer-scale polycrystalline metals that are often subjected to mechanical vibration or thermal cyclic loading. However, for components smaller than a few micrometers, there is no space to form PSBs and the extrusion/intrusion during fatigue. Moreover, although the slip behavior is governed by the crystal orientation and the loading direction in a single crystal, it is difficult to describe the slip behavior in a polycrystal by a simple law because of the effect of deformation constraint between grains. Characteristic slip behavior that cannot be defined by the crystal orientation and loading direction has been observed near grain boundaries [Sumigawa et al. (2004)]. Therefore, characteristic fatigue behavior is expected to occur in micrometer/sub-micrometer scale polycrystalline metals.

Many researchers [Schwaiger et al. (2003a), Zhang (2005), Kraft et al. (2001), Schwaiger et al. (2003b), Read (1998)] have investigated the fatigue of low-dimensional materials. The characteristic fatigue behavior was expected because the small volume results in a specific plasticity [Greer et al. (2005), Greer and Nix (2006), Uchic et al. (2004), Volkert (2006), Zhang et al. (2008)] due to dislocation source starvation [Greer and Nix (2006), Budiman et al. (2008)] and the inhibition of dislocation glide by the image force from interfaces and free surfaces [Weertman (1964)]. However, the details of fatigue behavior in nano-polycrystalline metals that are constrained by dissimilar materials have yet to be clarified.

In this work, a fatigue experiment based on resonant vibration was conducted using a nano-component specimen consisting of silicon (Si), titanium (Ti), nano-polycrystalline copper (Cu), and silicon nitride (SiN). The fatigue damage was examined based on detailed observations.

Nomenclature

PSB Persistent slip band

FIB Focused ion beam

f0 Resonant frequency of specimen

w Width of test section

h Height of test section

k Spring constant of test section

m Mass of the weight at the test section tip

lG Length from the test section root to the center gravity of the weight

E Young’s modulus

SEM Scanning electron microscopy EBSD Electron back-scatter diffraction Δδ1 Displacement range at the weight end

Δδ2 Displacement range at the test section root

Δδ1/2 Displacement amplitude at the weight end

Δδ2/2 Displacement amplitude at the test section root

FE-SEM Field emission-scanning electron microscopy ΔVin/2 Input voltage amplitude

Δδ/2 Displacement amplitude

Δτcrss/2 Amplitude of resolved shear stress

Author name / Structural Integrity Procedia 00 (2016) 000–000 3 2. Experimental procedure

2.1. Specimen preparation

Layers of Ti (20 nm thick), Cu (200 nm thick), and SiN (20 nm thick) were continuously deposited by magnetron sputtering on a single crystalline Si(100) substrate, of which the native oxidized layer was removed by argon ion etching. After deposition, the multi-layered material was annealed in a vacuum (1×10-4_{Pa base pressure) at 673 K}

for 1 h.

The specimen for the fatigue experiment was carved out of the multi-layered material by focused ion beam (FIB) processing with an accelerating voltage of 40 kV and a beam current of 1.17 nA. Figure 1 schematically illustrates the concept of the resonant fatigue experiment method. A cantilever-shaped test section is attached to a base (Fig. 1(a)). The test section contains a Si substrate and Cu, Ti and SiN layers. A fully reversed bending load to the test section is realized by applying resonant oscillation to the base in the vertical direction. However, a submicron component generally has a resonant frequency over a few tens of gigahertz, which makes it difficult to control the loading cycle. Therefore, to reduce the resonant frequency of the specimen, a Au weight is attached to the test section tip (Fig. 1(b)). The resonance frequency f0, of a cantilever (cross-section of w (width) × h (height)) with a

weight at the tip is approximately evaluated by the following equation:

m k f 2π 1 0 _       ₃ G 3 4l wh E k

,

(1)

where k, m, E, and lG are the spring constant of the test section in the vibration direction, the mass of the weight, the

Young’s modulus of the test section, and the length from the test section root to the gravity center of weight, respectively. Based on Eq. (1), the shape and size of the weight were designed so that f0 < 300 kHz was achieved.

The fabrication procedure is as follows.

1. A cube block of 25×25×25 μm3_{was carved out of the multi-layered material (Fig. 2(a)).}

2. The end of the microprobe installed in the FIB processing system was fixed on the upper surface of the block by tungsten (W) vapor deposition (Fig. 2(b)), and the block was picked up after cutting the holding part (Fig. 2(c)). 3. The block was fixed on a Si substrate (550 μm thick) (Fig. 2(d)) by W deposition. The microprobe was cut by

FIB and separated (Fig. 2(e)).

4. A Au block for weight was carved out of a polycrystalline Au plate. The Au block was then mounted on the SiN layer of the multi-layered block on the Si substrate by W deposition (Figs. 2(f) and (g)).

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Fig. 2. Schematic illustration of the specimen preparation method using FIB.

5. A test section that included the Si substrate and layers of Ti, Cu, and SiN was fabricated using a beam with a low current of 0.02 nA (Fig. 2(h)). The upper surface of the test section was flattened by a weak beam to avoid any difference in the level at the interface (Fig. 2(i)).

6. Argon (Ar) ion milling (Hitachi, Gentle Mill-Hi; accelerating voltage: 0.3 kV, current: 8 μA, processing time: 5 min) was performed on the surfaces of the test section to remove damaged layers introduced by FIB.

Figure 3 shows scanning electron microscopy (SEM) images of a specimen prepared for the resonant fatigue experiment. The surface was flat and there were no steps and defects in the test section. In this specimen, only Cu deformed plastically [Sumigawa (2010)] because it possesses the lowest yield stress of the constituent materials. The crystallography on the upper surface of the Cu portion in the test section was analyzed using electron backscatter diffraction (EBSD) analysis.

2.2. Fatigue experiment

Figure 4 shows a diagram of the experimental system, which is composed of a piezoelectric actuator, an operational amplifier, a function generator, a laser Doppler vibrometer, and a control computer. The minimum velocity resolution of the laser Doppler vibrometer is 0.05 μm/s, which is sufficient performance to measure the displacement amplitude of the specimens because they are oscillated in a velocity range of around 1×105_{μm/s. The}

laser beam is narrowed down to approximately 10 μm using a 20× power objective lens.

The specimen is mounted on the piezoelectric actuator with a cyanoacrylate adhesive. The function generator supplies a sinusoidal alternating input voltage ΔVin/2, with a constant amplitude, and the output voltage is amplified

by the operational amplifier. The experiment is performed at room temperature in an air atmosphere. The displacement range at the weight end, Δδ1, and the test section root, Δδ2, are measured with the laser Doppler

vibrometer.

Before the fatigue experiment, the resonant frequency of the specimen was evaluated by oscillation at frequencies between 0 and 200 kHz with a small displacement amplitude. The resonance fatigue test was then conducted at the resonant frequency. If there was no change in Δδ1 during the test, then the oscillation was continued until 107 cycles.

Subsequent oscillation was applied to the specimen with an input voltage amplitude that was approximately 0.3-0.7 V higher

Author name / Structural Integrity Procedia 00 (2016) 000–000 5

Fig. 3. SEM images of specimen fabricated by FIB.

Fig. 4. Schematic diagram of the system used for the resonant fatigue experiment.

than the previous value. This operation was repeated until a significant change in Δδ1 was observed. After the

fatigue test was terminated, the surfaces of the test section were carefully observed using field emission-SEM (FE-SEM).

3. Results and discussion

3.1. Resonant Fatigue

At ΔVin/2 ≤ 1.0 V, the deformation amplitude, Δδ/2, was constant until 107 cycles. However, it suddenly

decreased before 107_{cycles at ΔV}_in_{/2 = 1.60 V and f}₀_{shifted after the sudden decrease, which indicated that the}

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Fig. 2. Schematic illustration of the specimen preparation method using FIB.

5. A test section that included the Si substrate and layers of Ti, Cu, and SiN was fabricated using a beam with a low current of 0.02 nA (Fig. 2(h)). The upper surface of the test section was flattened by a weak beam to avoid any difference in the level at the interface (Fig. 2(i)).

6. Argon (Ar) ion milling (Hitachi, Gentle Mill-Hi; accelerating voltage: 0.3 kV, current: 8 μA, processing time: 5 min) was performed on the surfaces of the test section to remove damaged layers introduced by FIB.

Figure 3 shows scanning electron microscopy (SEM) images of a specimen prepared for the resonant fatigue experiment. The surface was flat and there were no steps and defects in the test section. In this specimen, only Cu deformed plastically [Sumigawa (2010)] because it possesses the lowest yield stress of the constituent materials. The crystallography on the upper surface of the Cu portion in the test section was analyzed using electron backscatter diffraction (EBSD) analysis.

2.2. Fatigue experiment

Figure 4 shows a diagram of the experimental system, which is composed of a piezoelectric actuator, an operational amplifier, a function generator, a laser Doppler vibrometer, and a control computer. The minimum velocity resolution of the laser Doppler vibrometer is 0.05 μm/s, which is sufficient performance to measure the displacement amplitude of the specimens because they are oscillated in a velocity range of around 1×105_{μm/s. The}

laser beam is narrowed down to approximately 10 μm using a 20× power objective lens.

The specimen is mounted on the piezoelectric actuator with a cyanoacrylate adhesive. The function generator supplies a sinusoidal alternating input voltage ΔVin/2, with a constant amplitude, and the output voltage is amplified

by the operational amplifier. The experiment is performed at room temperature in an air atmosphere. The displacement range at the weight end, Δδ1, and the test section root, Δδ2, are measured with the laser Doppler

vibrometer.

Before the fatigue experiment, the resonant frequency of the specimen was evaluated by oscillation at frequencies between 0 and 200 kHz with a small displacement amplitude. The resonance fatigue test was then conducted at the resonant frequency. If there was no change in Δδ1 during the test, then the oscillation was continued until 107 cycles.

Subsequent oscillation was applied to the specimen with an input voltage amplitude that was approximately 0.3-0.7 V higher

Author name / Structural Integrity Procedia 00 (2016) 000–000 5

Fig. 3. SEM images of specimen fabricated by FIB.

Fig. 4. Schematic diagram of the system used for the resonant fatigue experiment.

than the previous value. This operation was repeated until a significant change in Δδ1 was observed. After the

fatigue test was terminated, the surfaces of the test section were carefully observed using field emission-SEM (FE-SEM).

3. Results and discussion

3.1. Resonant Fatigue

At ΔVin/2 ≤ 1.0 V, the deformation amplitude, Δδ/2, was constant until 107 cycles. However, it suddenly

decreased before 107_{cycles at ΔV}_in_{/2 = 1.60 V and f}₀_{shifted after the sudden decrease, which indicated that the}

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3.2. Fatigue damage

Figure 5(a) shows FE-SEM images of the upper Cu surface after the fatigue test. Although no defects were present before the experiment, distinct traces appeared on the Cu surface upon cyclic loading. Figure 5(b) shows magnified SEM images of the upper Cu surface. Distinct traces were observed with a straight line-like appearance and inclined at an angle of approximately 45° to the applied normal stress. Analysis of the crystallographic orientation suggested that the traces were slip bands generated by the activity of the primary slip system. The slip bands were composed of extrusion and intrusion with a width of approximately 15 nm. The extrusion grew in the lower-right direction, which corresponded to the primary slip system, and had a height of approximately 30 nm. Although this was very similar to the extrusion/intrusion observed in fatigue of the bulk material [Mughrabi (1978), Lukas et al. (1968), Basinski et al. (1983)], the width (ca. 15-30 nm) was significantly different from that of the bulk (ca. 1 μm [Winter (1974), Volkert and Lilleodden (2006), Zhang et al. (2008)]). Moreover, a crack was observed along the grain boundary (see Fig. 5(c)), which appeared to have been initiated at the collision point of slip bands with the grain boundary where the stress was concentrated.

3.3. Formation stress of slip bands

The polycrystalline material possesses complex stress distribution due to the deformation constraint [Sumigawa et al. (2004)]. The microscopic stress distribution in the nano-polycrystalline Cu was obtained by an elastic finite element method (FEM) analysis. The exact shape and crystal orientation of grains on the surface of the nano-polycrystalline Cu were reproduced. Taking into account the crystalline orientations of the grains, the elastic

Fig. 5. FE-SEM images of the test section after the fatigue experiment.

Author name / Structural Integrity Procedia 00 (2016) 000–000 7 constants of each grain were determined on the basis of the elastic constants in a single crystal (C11 = 168.0 GPa, C12

= 75.4 GPa, C44 = 121.0 GPa). On the basis of the displacement amplitude at the generation of slip bands, the critical

resolved shear stress amplitude Δτcrss/2 to generate slip bands was evaluated to be approximately 300-400 MPa,

which was much higher than that of PSB formation in Cu bulk single crystal (27 MPa [Melisova et al. (1997)]). 4. Conclusion

A resonance fatigue experiment was conducted using a Si/Ti/Cu/SiN cantilever nano-material to examine the fatigue damage in nano-polycrystalline Cu under fully reverse loading. The results are summarized as follows. 1. The resonance frequency of the cantilever specimen was successfully reduced by attaching a Au weight to the

test part end.

2. At an input voltage amplitude of ΔVin/2≤1.0 V, Δδ1/2 and f0 were unchanged until 107 cycles. However, Δδ1/2

dropped significantly before 107_{cycles at ΔV}_in_{/2 = 1.60 V. The sudden drop is due to the change in f}₀

associated with the formation of fatigue damage.

3. Slip bands with a width of a few tens of nanometers were generated in a grain in the nano-polycrystalline Cu layer after the sudden drop of Δδ/2. Although extrusions/intrusions were observed in the slip bands, the sizes were significantly smaller.

4. The stress concentration induced by the collision of an extrusion with a grain boundary generated a crack along the grain boundary.

Acknowledgements

This work was supported in part by Grants-in-Aid for Young Scientists (A) (No. 24686018), Scientific Research (A) (No. 15H02210), Specially Promoted Research (No. 25000012), and Challenging Exploratory Research (No. 26630009) from the Japan Society for the Promotion of Science (JSPS).

References

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Basinski, Z.S., Pascual, R., Basinski, S.J., 1983. Low Amplitude Fatigue of Copper Single Crystals-I. The Role of the Surface in Fatigue Failure. Acta Metallurgica 31(4), 591-602.

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Lukas, P, Klesnil M, Krejci J., 1968. Dislocations and Persistent Slip Bands in Copper Single Crystals Fatigued at Low Stress Amplitude. Physica Status Solidi 27, 545-558.

Melisova, D., Weiss, B., Stickler, R., 1997. Nucleation of persistent slip bands in Cu single crystals under stress controlled cycling. Scripta Metallurgica 36, 1061-1066.

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Mughrabi, H., 1978. The Cyclic Hardening and Saturation Behaviour of Copper Single Crystals. Materials Science and Engineering 33, 207-223. Mughrabi, H., 1980. in “Strength of metals and alloys”. In: Haasen, P., Gerold, V., Kostorz, G. (Eds.). Oxford: Pergamon Press.

Read, D.T., 1998. Tension-tension fatigue of copper thin films. International Journal of Fatigue 20(3), 203-209.

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