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Multiaxial low-cycle fatigue failure mechanism of super-elastic NiTi shape memory alloy micro-tubes
Materials Science & Engineering A 665 (2016) 17–25
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Multiaxial low-cycle fatigue failure mechanism of super-elastic NiTi shape memory alloy micro-tubes Di Song a, Guozheng Kang b,c,n, Qianhua Kan b,c, Chao Yu c, Chuanzeng Zhang d a
School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China c School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China d Department of Civil Engineering, University of Siegen, Siegen 57068, Germany b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 November 2015 Received in revised form 1 March 2016 Accepted 8 April 2016 Available online 9 April 2016
Based on the microscopic observations on the fracture morphology of the super-elastic NiTi shape memory alloy (SMA) micro-tubes subjected to uniaxial and multiaxial low-cycle fatigue loadings, the common features of the fracture surface under both uniaxial and multiaxial fatigue loadings and the special ones appearing only in multiaxial ones are investigated. From the observed results, the multiaxial low-cycle fatigue failure mechanism of the NiTi SMA micro-tubes is investigated. It is found that for the multiaxial fatigue failure of the super-elastic NiTi SMA micro-tubes, besides the common features such as the fatigue striations, dimples and secondary cracks observed in the uniaxial fatigue tests, some special micro-patterns are observed on the fracture surface of the specimens, i.e., V-shaped troughs, scratches, abundant crack-origins, through-walled steps and slanted rupture. It implies that the multiaxial cyclic loadings result in not only a higher damage level at the stage of the crack initiation, but also the multidirectional and multi-planar modes of the crack propagation during the stress-controlled low-cycle fatigue of the NiTi shape memory alloy micro-tubes. & 2016 Elsevier B.V. All rights reserved.
Keywords: NiTi shape memory alloy Multiaxial low-cycle fatigue Microstructural observation Fracture morphology Failure mechanism
1. Introduction NiTi shape memory alloys (SMAs) are widely used in astronautic and bio-medical applications and so on, due to their unique super-elasticity, shape memory effect and excellent bio-compatibility [1–3]. NiTi SMAs possess an austenite phase (a simple cubic B2 crystal structure) if the ambient temperature is higher than the finish temperature of the austenite phase (Af ), but the austenite phase can be transformed into the martensite one (a monoclinic B19′ crystal structure) if the applied stress load is higher than the start stress of the martensite transformation. This phenomenon is often referred to as the “stress- or strain-induced martensite transformation” of the NiTi SMAs. Such stress- or strain-induced martensite phase of the NiTi SMAs can be also transformed back into the austenite one if the applied stress or stain is in an unloading process. Here, a reverse transformation occurs and a reversible strain of about 8% can be obtained. This special feature is termed as the “super-elasticity” of the SMAs distinctive from that n Corresponding author at: State Keyoratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China. E-mail addresses: [email protected], [email protected] (G. Kang).
http://dx.doi.org/10.1016/j.msea.2016.04.019 0921-5093/& 2016 Elsevier B.V. All rights reserved.
of the ordinary metals [4–6]. Since NiTi SMA devices are often subjected to a cyclic loading in service, their cyclic deformation and fatigue failure are key issues to be investigated. Recently, it was reported that during the cyclic loading, the super-elasticity of the NiTi SMAs is gradually degraded by the repeated martensite transformation and its reverse, and the responding peak and valley strains are progressively accumulated during the stress-controlled cyclic loading [7–12], which was denoted as the “transformation ratchetting” of the SMAs by Kang et al. [10]. Moreover, it is also demonstrated that the cyclic degeneration of the super-elasticity is mainly induced by the transformation induced plasticity arising in the repeated forward/ reverse transformations of the NiTi SMAs [13,14]. As interpreted by Lagoudas and Entchev [15], the mismatch of the elastic and inelastic deformations between the austenite and martensite phases can result in local stress-concentrations at the interfaces of the austenite and martensite phases, which leads to a collection of plenty dislocations at the interfaces and greatly promotes the dislocation slip during the cyclic forward/reverse transformation. It means that the transformation induced plasticity is a dominant mechanism for the cyclic super-elasticity degeneration of the NiTi SMAs [8,14,15]. In the last two decades, many researchers [3,16–24] performed
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experiments to investigate the fatigue failure of the NiTi SMAs. Many previous works demonstrated that, owing to their unique thermo-elastic martensite transformation, the fatigue failure of the NiTi SMAs is remarkably different from that of the ordinary metals, the cyclic stress-strain responses of the NiTi SMAs are gradually stabilized and keep unchanged till the final failure. Although a large inelastic deformation (e.g., 8–10%) occurs during the fatigue loading of the NiTi SMAs, a brittle fracture suddenly happens [3,20–24]. References [4,20] further reported that the NiTi SMAs are the alloys with the lowest crack propagation rate, since the cyclic accumulated residual martensite phase might hinder the propagation of the micro-cracks. Moreover, based on the fatigue tests of the NiTi SMAs, the microscopic fractographic analyses were also performed in references [5,6,18–22,25–28]. The previous investigations revealed that the ductile fracture patterns such as dimples and fatigue striations arise on the fracture surface of the NiTi fatigue specimens, and the dislocations tend to collect at the interfaces between the austenite and martensite phases. However, the previous fatigue tests of the NiTi SMAs were mainly performed under the uniaxial and bend fatigue loading conditions in order to match the service conditions of endovascular stents and dental orthodontic wires in medical applications and others. In despite of many aforementioned previous fatigue tests and related micro-structural observations of the NiTi SMAs, the following three aspects are still not sufficiently addressed: 1) The fatigue tests of the NiTi SMAs with a very small geometrical size such as the micro-tubes (with a wall thickness less than 400 mm as used in the manufacturing of endovascular stents) are still inadequate. It has been demonstrated that the fatigue failure of the NiTi SMA specimens with very small geometrical size cannot be extrapolated from that with a larger size [4,28]. Thus, more detailed fatigue tests with the micro-observations on the fracture surface of the NiTi SMA micro-tubes should be conducted to investigate the damage evolution and failure mechanism of such micro-sized devices. 2) Most of the previous fatigue tests were performed at room temperature (about 293 K), rather than at the temperature of human body. Since the variation of the ambient temperature will seriously affect the transformation start stress of the NiTi SMAs (e.g., with an increasing ambient temperature of 1 K, the start stress of the martensite transformation will be increased by approximately 8 MPa [29]) and then significantly influence the fatigue life, the reported fatigue data obtained at room temperature cannot be directly used to assess the fatigue life of the NiTi devices implanted in the human body. Thus, the fatigue tests and the corresponding micro-observations of the NiTi SMA micro-tubes at the temperature of human body (i.e., 310 K) are extremely necessary. 3) The reported experiments performed under the non-proportionally multiaxial loading conditions are far from sufficient, though some macroscopic fatigue data of the NiTi SMAs were obtained in [24]. The multiaxial fatigue failure mechanism of the NiTi SMAs has not been well understood and addressed in the literature.
Motivated by the aforementioned aspects and based on the macroscopic uniaxial and multiaxial stress-controlled fatigue tests of the super-elastic NiTi SMA micro-tubes done by Song et al. [23,24] at the temperature of human body (i.e., at 310 K), the fracture surfaces of broken specimens obtained under different loading paths are microscopically investigated in this study by scanning electron microscope (SEM). The multiaxial fatigue failure mechanism of the NiTi micro-tubes is analyzed and discussed by comparing the multiaxial results with the uniaxial ones, which is very important to construct an adequate failure model to predict the multiaxial fatigue life and establish the reliability of the NiTi devices. Some new findings are obtained and highlighted.
2. Experimental material and method The super-elastic NiTi SMA micro-tubes made of Nitinol SE508, which meets the ASTM F2063-05 medical Nitinol standard [31] and provided by the Jiangyin Materials Development Co., Ltd., China, are used in this work. The micro-tubes were aged two hours at 823 K and then polished mechanically to certain surface toughness. The grain size is within the range of 10–20 mm, and the austenite start temperature As, austenite finish temperature Af, martensite start temperature Ms, and martensite finish temperature Mf are 271, 302, 285, and 238 K, respectively, which were measured using a differential scanning calorimetry (DSC) by Song et al. [23]. The micro-tubular specimens with an outer diameter of 2.5 mm and an inner diameter of 2.2 mm (i.e., with a thickness of 150 mm) are adopted in the uniaxial and multiaxial fatigue tests. The whole-life transformation ratchetting and the fatigue life obtained from the macroscopic experiments were reported by Song et al. [23,24], while the fracture surfaces of the specimens are investigated in this work by the SEM (JSM-6490LV, JEOL Ltd.). In the microscopic observations, the fracture surfaces from eight specimens in two uniaxial and six multiaxial fatigue tests are used. Here, three kinds of multiaxial loading paths as shown in Fig. 1 are considered. Some details on the load cases and the corresponding fatigue lives are listed in Table 1, where the load cases with 2407 283 MPa and 450 7283 MPa indicate that the applied axial means stresses are 240 and 450 MPa and the stress amplitude is 283 MPa. For the multiaxial loading cases as shown in Fig. 1, the mean equivalent shear stress is zero and the equivalent shear stress amplitude (i.e., 3 τ ) is 283 MPa. Here, the von-Mises criteria is used, and the maximum equivalent stresses in the two prescribed load cases of the multiaxial fatigue tests are 595 and 786 MPa, respectively. It can be observed in Table 1 that the multiaxial fatigue lives are much shorter than that of the corresponding uniaxial ones, which implies that the multiaxial loadings can significantly reduce the fatigue lives of the super-elastic NiTi SMA micro-tubes. The fracture surfaces directly from the broken specimens and without any treatments are observed by the SEM. Before the SEM observation to the fracture surface, an energy depressive spectrometry (EDS) measurement to a selected area of the fracture
Fig. 1. Schematic diagrams of multiaxial loading paths: (a) square; (b) hourglass-typed; (c) butterfly-typed ones.
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Table 1 Load cases and fatigue lives (the number in brackets with c represents the number of cycles) of the specimens used in microscopic observations. Uniaxial
2407 283 MPa 450 7283 MPa
1# (1516c) 2# (735c)
Multiaxial Square
Hourglass
Butterfly
3# (302c) 4# (288c)
5# (375c) 6# (297c)
7# (681c) 8# (240c)
surface was performed and the results are shown in Fig. 2. It is seen that the super-elastic NiTi SMA micro-tubes used in this work are composed of near-equiatomic Ni and Ti elements, as well as some co-existing impurities. From Fig. 2b, it can be observed that some inclusions with different geometrical sizes appear at the bottom of the dimples, which are mainly formed by the Fe and S elements. The ingredient of the NiTi alloys including the inclusions meets the medical Nitinol standard of the ASTM F2063-05 [31].
3. Experimental observations and discussions 3.1. Common patterns in both uniaxial and multiaxial fatigue tests In this section, some common microstructural patterns observed on the fracture surfaces of the specimens in both uniaxial and multiaxial fatigue tests are analyzed and discussed, which are independent of the fatigue loadings. However, the differences caused by the applied stress levels are addressed. 3.1.1. Crack origins It is observed that during the fatigue tests of the super-elastic NiTi SMA micro-tubes, crack origins usually occur at four possible locations: (1) outer surface, (2) inner surface, (3) internal voids, and (4) internal inclusions, as shown in Fig. 3. Since the wallthickness of the NiTi SMA micro-tubes is much smaller than the critical size of the macro-cracks (e.g., 1 mm), the so-called “crack” in this work designates the micro-crack. Fig. 3a shows that the crack origins on the outer surface are usually flabellate-shaped with a number of tiny fatigue steps, which are formed by the extension and intersection of several micro-cracks on various planes. It is also observed that the fatigue steps are usually radially distributed, and become converged at the crack-origin. If the crack origins are relatively bigger along the surface, the fatigue steps become nearly perpendicular to the outer surface. From Fig. 3(b) to (d), it is seen that the crack origins are also prone to occur on the inner surface (especially near the surface defects) or near the internal voids and inclusions (internal
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defects). These three kinds of crack origins are induced by the stress concentrations near the defects during the cyclic loading. The stress concentrations are beneficial to the initiation of microcracks. However, it was demonstrated in [4,32–33] that the defects in the NiTi SMAs hardly influence the obtained fatigue lives, and the fatigue lives of the NiTi SMAs with a normal and extra low contents of defects are essentially the same. This finding can be interpreted as that the crack origins in the NiTi SMAs are mainly due to the transformation-induced plasticity occurring during the repeated martensite transformations and their reverses [15,30]. The stress-induced martensite variants gradually accumulate and change their positions during the cyclic loading [34], and then promote the crack initiation at various locations in the specimen, whose effect on the fatigue life of the NiTi SMAs is much more dominant than that of the pre-existing defects. This specific failure mechanism also leads to the excellent repeatability of the obtained fatigue lives of the NiTi SMA micro-tubes (e.g., a maximum deviation of 4% in the uniaxial fatigue loadings and 6% in the multiaxial ones) as demonstrated by Song et al. [23,24]. It has been verified in [23,30] that the most significant influencing factor on the fatigue life of the NiTi SMAs is their unique thermo-elastic martensite transformation, especially the extents of the martensite transformation and its reverse (i.e., the completeness of the forward/reverse martensite transformation), which are determined by the applied stress or strain levels. The damage accumulated during the repeated martensite transformations and their reverses leads to the final fracture of the NiTi SMAs. This phenomenon is remarkably different from that of the ordinary metals. 3.1.2. Fatigue striations On the fracture surfaces of the NiTi specimens after the fatigue tests, massive fatigue striations were observed in the region of the crack propagation, which is similar to that in ordinary ductile metals. The striations are characterized by various propagation directions, which are deduced from different crack origins and propagate independently with the development of the local stresses. From Fig. 4, it is seen that the fatigue striations with a higher density usually occur near the internal voids or inclusions due to the stress concentrations at such locations, which indicates that internal voids or inclusions are harmful to the crack propagation of the NiTi SMAs during the cyclic loading. It is also found that on the fracture surfaces of the NiTi SMA micro-tubes, the regions of the crack propagation (with striations) and the local fracture (with dimples) alternately appear, and no main-crack propagation is observed. The reason for this special failure feature is that both the martensite transformation occurring ahead the crack-tip and the reverse transformation in the crack-wake can reduce the stress
Fig. 2. Results of the EDS measurement: (a) NiTi matrix; (b) inclusions.
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eq Fig. 3. Typical locations of the crack origins observed on the fracture surfaces: (a) outer surface (1#, σmax ¼523 MPa, Nf ¼ 1516c); (b) inner surface (3#, σmax ¼595 MPa, eq ¼786 MPa, Nf ¼288c); (d) internal inclusion (2#, σmax ¼733 MPa, Nf ¼ 735c). Nf ¼ 302c); (c) internal void (4#, σmax
intensity at the crack-tip, greatly lower the propagation rate of the micro-cracks, and thus significantly hinder the formation of the macro-cracks [35,36]. It implies that the final fracture of the NiTi SMA micro-tubes during the fatigue loading is caused by the coalescence and the growth of the micro-cracks. The micro-cracks initiate and propagate independently, then result in a throughwall micro-crack and finally lead to a sudden fatigue failure as observed by Song et al. [23,24]. 3.1.3. Secondary cracks Another patterns observed in the regions of the crack propagation are the secondary cracks, which initiate and propagate during the fatigue loading, but do not cause the final fracture of
the specimens. From Fig. 5, it is seen that the secondary cracks arising on the fracture surfaces are usually accompanied by the fatigue striations, and their orientations are mostly parallel to the fatigue striations (Fig. 5a). In contrast, some secondary cracks perpendicular to the striations are also observed in certain regions, indicating that the secondary cracks may also develop from the same crack origins as the primary cracks, which are characterized by the striations on the fracture surface and induce the fatigue failure. As shown in Fig. 5b, both the fatigue striations and the secondary cracks develop from the two origins located at the left and right sides of the picture (i.e., the outer and inner surfaces of the specimens), and the secondary cracks are perpendicular to the striations. This feature can be observed more easily in the NiTi
eq Fig. 4. Typical locations of the fatigue striations with a higher density: (a) near the defect (5#, σmax ¼ 595 MPa, Nf ¼375c); (b) near the inclusion (2#, σmax ¼ 733 MPa, Nf ¼ 735c).
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Fig. 5. Secondary cracks on the fracture surfaces: (a) parallel to the fatigue striations (1#, σmax ¼ 523 MPa, Nf ¼ 1516c); (b) perpendicular to the fatigue striations (5#, eq eq ¼595 MPa, Nf ¼ 375c); (c) larger secondary cracks with a higher stress level (8#, σmax ¼ 786 MPa, Nf ¼ 240c). σmax
SMA micro-tubes than in the wire or bar specimens with a larger geometrical size, since the secondary cracks are prone to initiate on both the outer and the inner surfaces of the micro-tubes. Moreover, comparing the secondary cracks observed in the fatigue tests with different stress levels, it shows that more secondary cracks occur on the fracture surfaces of the specimen subjected to a fatigue loading with a lower stress level and their sizes are relatively small as shown in Fig. 5a and b. This phenomenon can be explained by the fact that the energy accumulation driving the crack propagation requires a longer period in the fatigue test with a lower stress level, and the propagations of the micro-cracks in different directions will also hinder the subsequent propagations of other micro-cracks [17]. It should be also noted here that larger secondary cracks are prone to form on the fracture surface of the specimen subjected to a fatigue loading with a higher stress level as shown in Fig. 5c, since a high stress level is beneficial to the propagations of both the primary and the secondary cracks. 3.2. Special microstructural patterns in multiaxial fatigue tests Here, some special microstructural patterns observed only in the multiaxial fatigue test of the NiTi SMA micro-tubes are outlined and discussed, in order to verify the essential differences in the crack initiation and propagation between the uniaxial and the multiaxial fatigue tests. The microstructural patterns observed in the multiaxial fatigue tests are mainly characterized by the following four characteristics: (1) V-shaped troughs, (2) throughwalled fatigue steps and slanted rupture, (3) scratches, and (4) abundant crack origins along the surfaces. These specific
patterns and their formation mechanisms are discussed in this subsection. 3.2.1. V-shaped troughs In the multiaxial loading cases, an important microstructural pattern with a V-shaped trough is observed on the fracture surfaces, as shown in Fig. 6. Such a pattern was also observed by Jensen [37] in the multiaxial fatigue tests of the tubular NiTi SMA specimens, but its formation mechanism was not investigated there. From Fig. 6, it is seen that the V-shaped troughs can be divided into two types: one is the single-form through across the whole wall-thickness of the micro-tubes (Fig. 6a), and the other one presents a continuous wave pattern or tiny saw tooth (Fig. 6b and c). The formation of the V-shaped trough on the fracture surfaces can be explained as follows. Since the direction of the applied stress continuously changes during the multiaxial cyclic loading, the propagations of the micro-cracks are driven in various directions. When the micro-cracks formed in different directions encounter each other, their propagations will stop, and then a V-shaped trough is emerged. For the single V-shaped trough as shown in Fig. 6a, the micro-cracks usually initiate on both the outer and the inner surfaces of the specimens, and then lead to the formation of a through-walled crack which causes the final fracture of the specimens. On the other hand, the V-shaped trough with a continuous wave pattern as shown in Fig. 6b and a saw tooth as shown in Fig. 6c is prone to occur in the multiaxial loading case with a lower stress level, since a larger number of the loading cycles before the fatigue failure will provide more chances for the diversions of the propagating cracks. The V-shaped trough represents the multi-directional mode of the crack propagation in
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eq eq Fig. 6. V-shaped troughs in the multiaxial loading cases: (a) single through-walled shape (4#, σmax ¼ 786 MPa, Nf ¼ 288c); (b) wave pattern (3#, σmax ¼595 MPa, Nf ¼302c); eq (c) saw tooth (7#, σmax ¼ 595 MPa, Nf ¼ 681c).
the multiaxial fatigue cases. 3.2.2. Through-walled fatigue steps and slanted rupture Further typical microstructural patterns observed in the multiaxial fatigue tests of the NiTi SMA micro-tubes are throughwalled fatigue steps and slanted rupture as shown in Fig. 7. It is found that the fatigue steps occurring in the multiaxial loading cases are observed not only in the regions of the crack origins, and they usually propagate across the wall thickness of the specimens independently, which finally leads to the formation of the through-walled fatigue steps on different planes as shown in Fig. 7a. Such a multi-planar propagation of the micro-cracks indicates the occurrence of the mode-II and mode-III crack
propagations, which is different from the single mode-I crack propagation in the uniaxial fatigue of the NiTi SMAs. Moreover, in the region of the final fracture on the fracture surface of the specimens subjected to the multiaxial loadings, the mode-II and mode-III cracks usually result in the formation of the slanted rupture as shown in Fig. 7b. The slanted rupture pattern is induced by the combined action of the tensile stress and the alternating shear stress. The micro-cracks propagate along the direction perpendicular to the maximum tensile normal stress [38], which leads to an angle of approximately 20° between the plane of the slanted rupture and the cross-section of the specimens. It can be also observed from Fig. 7b that the parabolic ductile dimples on different planes occur on the plane of the slanted rupture, which
eq Fig. 7. Through-walled fatigue steps and slanted rupture observed in the multiaxial fatigue tests: (a) through-walled fatigue steps (4#, σmax ¼ 786 MPa, Nf ¼ 288c); eq (b) slanted rupture (5#, σmax ¼595 MPa, Nf ¼375c).
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eq Fig. 8. Scratches on the fracture surfaces in the multiaxial loading cases: (a) uni-directional scratches (3#, σmax ¼ 595 MPa, Nf ¼ 302c); (b) bi-directional scratches (5#, eq ¼595 MPa, Nf ¼ 375c). σmax
are different from the rounded dimples and even-fracture mode (i.e. the fracture surface nearly parallel to the cross-section) appearing in the uniaxial loading cases. 3.2.3. Scratches From the microscopic observations, it can be observed that scratches usually occur on the fracture surfaces of the specimens subjected to the multiaxial fatigue loadings as shown in Fig. 8, while they are not found in the uniaxial fatigue tests. Fig. 8a shows that most scratches are uni-directional, while bi-directional ones can be also observed on the fracture surfaces as shown in Fig. 8b. Such a pattern indicates that a cyclic friction occurs between the two surfaces of the partly fractured specimens during the variation of the stress direction in the multiaxial loading cases, and it is more evident in the cases with a compressive axial stress. The scratches can be also regarded as the evidence for the existence of the mode-II and mode-III cracks during the cyclic loading [38]. It is also observed that the scratches usually develop near the outer and the inner surfaces and in the regions of the crack initiation and propagation. However, other microstructural patterns such as the tiny fatigue steps and the fatigue striations cannot be found at the locations where the scratches appear, because the cyclic friction will wear out the surface morphology during the subsequent cyclic loading. Thus, the scratches can intuitively reflect the relative moving directions of the two fracture surfaces, and the local crack propagation can be estimated from the directions of the scratches.
3.2.4. Abundant crack origins along the surfaces It can be observed that on the fracture surfaces of the specimens in the multiaxial fatigue tests, the amount of the crack origins is much larger than that in the uniaxial ones, and abundant crack origins are induced on the fracture surfaces especially near the outer and the inner surfaces as shown in Fig. 9. The increased crack origins are owing not only to the promotion of the multiaxial stress state to the crack initiation as in the ordinary metals, but also to another more important reason, that is, a unique inelastic deformation mechanism (i.e., martensite re-orientation) occurs in the multiaxial fatigue tests of the NiTi SMAs due to the stress alternation. Also, the mismatch between different martensite variants (there are 24 different variants) will cause a stress concentration and promote the dislocation slip, which is denoted as the “re-orientation induced plasticity” of the NiTi SMAs [24]. Similar to the effect of the transformation induced plasticity, the reorientation induced plasticity is also an important mechanism for the crack initiation in the multiaxial fatigue of the NiTi SMAs, which causes a higher damage level and makes the multiaxial fatigue life much shorter than that of the uniaxial one, even at quite lower equivalent stress levels as listed in Table 1. 3.3. Discussions on the failure mechanism of the multiaxial fatigue From the microscopic observations presented in the previous subsections, it can be concluded that some common microstructural patterns observed on the fracture surfaces of the NiTi SMAs subjected to uniaxial fatigue loadings, such as the fatigue
eq Fig. 9. Abundant crack origins along the surfaces in the multiaxial loading cases: (a) on the outer surface (8#, σmax ¼786 MPa, Nf ¼240c); (b) on both outer and inner eq surfaces (3#, σmax ¼ 595 MPa, Nf ¼ 302c).
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striations, dimples and secondary cracks, are also found on the fracture surfaces under the multiaxial fatigue loadings. However, due to the alternation of the stress state and a novel inelastic deformation mechanism of the NiTi SMAs, i.e., the martensite reorientation arising under the multiaxial loading conditions, some special microstructural patterns, such as the V-shaped troughs, through-walled steps, slanted rupture and scratches, and abundant crack origins, are observed only on the fracture surfaces of the NiTi SMA micro-tubes in the multiaxial fatigue tests. It indicates that the multiaxial fatigue loading will influence both the crack initiation and the crack propagation in the NiTi SMAs. At the stage of the micro-crack initiation, the martensite reorientation induced plasticity occurring only under the multiaxial cyclic loading conditions will initiate a much larger amount of the micro-cracks in the NiTi SMA micro-tubes, which is reflected by the occurrence of the abundant crack origins along the outer/inner surfaces as shown in Fig. 9. It means that a higher damage accumulation occurs at the stage of the crack initiation in the multiaxial fatigue tests of the NiTi SMA micro-tubes than that in the uniaxial loading cases. Since the martensite re-orientation induced plasticity can be also deduced from a dislocation slip similar to the martensite transformation induced plasticity, it can also result in an irreversible residual deformation of the NiTi SMAs during the multiaxial cyclic loading and then promote the cyclic degradation of the super-elasticity of the NiTi SMAs as demonstrated in the previous fatigue tests done by Song et al. [24]. Such macroscopic experimental results and the observed abundant crack origins representing a higher damage level can be mutually confirmed herein. At the stage of the micro-crack propagation, it is found that the crack propagation in the NiTi SMA micro-tubes presents a multiplanar and multi-directional mode in the multiaxial fatigue tests. Under the combined tension-torsion multiaxial cyclic loading conditions, there is not only a mode-I crack propagation as in the uniaxial loading tests, but also the mode-II and mode-III cracks exist in the NiTi SMA micro-tubes, which result in the throughwalled fatigue steps as shown in Fig. 7a, slanted rupture and parabolic-shaped dimples as shown in Fig. 7b, and scratches as shown in Fig. 8. Moreover, the alternation of the stress state caused by the multiaxial cyclic loading also promotes the crack propagation in different directions, and hence leads to wavier crack propagation traces than in the uniaxial loading cases, which are shown in Fig. 6. Thus, it can be concluded that the fatigue failure mechanism of the super-elastic NiTi SMA micro-tubes under the multiaxial loading conditions is significantly different from that under uniaxial loading conditions. This is characterized by both a higher damage level in the crack initiation and a more complex mode in the crack propagation, which will significantly influence the damage evolution and then greatly shorten the fatigue lives of the NiTi SMA micro-tubes. Thus, from the microscopic observations on the microstructural patterns on the fracture surfaces, the multiaxial fatigue failure mechanism of the super-elastic NiTi SMA micro-tubes is characterized by the special features of the crack initiation and propagation mainly caused by the alternation of the stress state and a novel inelastic deformation mechanism of the NiTi SMAs during the multiaxial cyclic loading, i.e., the martensite re-orientation induced plasticity. The damage evolution and the fatigue life of the NiTi SMAs under the multiaxial fatigue loadings are in general very difficult to accurately describe and predict, since the multiaxial fatigue failure mechanism of the NiTi SMAs is much more complex than that in the uniaxial loading cases. It implies that not only the martensite transformation and the re-orientation induced plasticity should be reasonably considered, but also the various crack propagation modes should be taken into account in the construction of adequate multiaxial fatigue failure models, which
demand further extensive investigations. It should be remarked here that a phenomenological uniaxial fatigue failure model for the NiTi SMA micro-tubes was established by Song et al. [30], which can reasonably describe the uniaxial damage evolution and predict fatigue life. In principle, a corresponding multiaxial fatigue failure model can be developed by extending the existing uniaxial one based on the observed multiaxial fatigue failure mechanism in this work, which will be considered in our future work. Moreover, it should be noted here that since only a SEM is used to observe the microstructural patterns on the fracture surfaces of the NiTi SMA micro-tubes, the dislocations and their evolution during the fatigue tests cannot be revealed. The microscopic observations on the dislocations and their evolution by a transmission electron microscope (TEM) will help to understand the fatigue damage of the NiTi SMAs more deeply, which will be also taken into consideration in our future work.
4. Conclusions From the microstructural observations in both uniaxial and multiaxial fatigue tests, such as crack origins, fatigue striations and secondary cracks, the following conclusions can be drawn: 1) The regions of the crack propagation and the final fracture appear alternatively on the fracture surfaces of the super-elastic NiTi SMA micro-tubes, and the fatigue failure is mainly controlled by the initiation and propagation of the micro-cracks. 2) Some special microstructural patterns, such as the V-shaped troughs, through-walled fatigue steps, slanted rupture, scratches, and abundant crack origins along the surfaces are observed only on the fracture surfaces of the NiTi micro-tubes subjected to the multiaxial fatigue loadings. A higher damage level occurs at the stage of the crack initiation, and a multi-directional and multi-planar crack propagation mode appears in the multiaxial fatigue failure, which leads to a much shorter fatigue life in the multiaxial fatigue tests than in the uniaxial loading cases. 3) The distinctive fatigue failure mechanism under multiaxial loading conditions should be considered appropriately in the construction of the adequate multiaxial fatigue failure models to accurately predict the multiaxial fatigue life of the superelastic NiTi SMA micro-tubes.
Acknowledgments Financial supports by the National Natural Science Foundation of China (11532010), Scientific Research Foundation of University of Electronic Science and Technology of China (ZYGX2015KYQD075) and the project for Sichuan Provincial Youth Science and Technology Innovation Team, China (2013TD0004) are gratefully acknowledged.
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Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Multiaxial low-cycle fatigue failure mechanism of super-elastic NiTi shape memory alloy micro-tubes Di Song a, Guozheng Kang b,c,n, Qianhua Kan b,c, Chao Yu c, Chuanzeng Zhang d a
School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China c School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China d Department of Civil Engineering, University of Siegen, Siegen 57068, Germany b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 November 2015 Received in revised form 1 March 2016 Accepted 8 April 2016 Available online 9 April 2016
Based on the microscopic observations on the fracture morphology of the super-elastic NiTi shape memory alloy (SMA) micro-tubes subjected to uniaxial and multiaxial low-cycle fatigue loadings, the common features of the fracture surface under both uniaxial and multiaxial fatigue loadings and the special ones appearing only in multiaxial ones are investigated. From the observed results, the multiaxial low-cycle fatigue failure mechanism of the NiTi SMA micro-tubes is investigated. It is found that for the multiaxial fatigue failure of the super-elastic NiTi SMA micro-tubes, besides the common features such as the fatigue striations, dimples and secondary cracks observed in the uniaxial fatigue tests, some special micro-patterns are observed on the fracture surface of the specimens, i.e., V-shaped troughs, scratches, abundant crack-origins, through-walled steps and slanted rupture. It implies that the multiaxial cyclic loadings result in not only a higher damage level at the stage of the crack initiation, but also the multidirectional and multi-planar modes of the crack propagation during the stress-controlled low-cycle fatigue of the NiTi shape memory alloy micro-tubes. & 2016 Elsevier B.V. All rights reserved.
Keywords: NiTi shape memory alloy Multiaxial low-cycle fatigue Microstructural observation Fracture morphology Failure mechanism
1. Introduction NiTi shape memory alloys (SMAs) are widely used in astronautic and bio-medical applications and so on, due to their unique super-elasticity, shape memory effect and excellent bio-compatibility [1–3]. NiTi SMAs possess an austenite phase (a simple cubic B2 crystal structure) if the ambient temperature is higher than the finish temperature of the austenite phase (Af ), but the austenite phase can be transformed into the martensite one (a monoclinic B19′ crystal structure) if the applied stress load is higher than the start stress of the martensite transformation. This phenomenon is often referred to as the “stress- or strain-induced martensite transformation” of the NiTi SMAs. Such stress- or strain-induced martensite phase of the NiTi SMAs can be also transformed back into the austenite one if the applied stress or stain is in an unloading process. Here, a reverse transformation occurs and a reversible strain of about 8% can be obtained. This special feature is termed as the “super-elasticity” of the SMAs distinctive from that n Corresponding author at: State Keyoratory of Traction Power, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China. E-mail addresses: [email protected], [email protected] (G. Kang).
http://dx.doi.org/10.1016/j.msea.2016.04.019 0921-5093/& 2016 Elsevier B.V. All rights reserved.
of the ordinary metals [4–6]. Since NiTi SMA devices are often subjected to a cyclic loading in service, their cyclic deformation and fatigue failure are key issues to be investigated. Recently, it was reported that during the cyclic loading, the super-elasticity of the NiTi SMAs is gradually degraded by the repeated martensite transformation and its reverse, and the responding peak and valley strains are progressively accumulated during the stress-controlled cyclic loading [7–12], which was denoted as the “transformation ratchetting” of the SMAs by Kang et al. [10]. Moreover, it is also demonstrated that the cyclic degeneration of the super-elasticity is mainly induced by the transformation induced plasticity arising in the repeated forward/ reverse transformations of the NiTi SMAs [13,14]. As interpreted by Lagoudas and Entchev [15], the mismatch of the elastic and inelastic deformations between the austenite and martensite phases can result in local stress-concentrations at the interfaces of the austenite and martensite phases, which leads to a collection of plenty dislocations at the interfaces and greatly promotes the dislocation slip during the cyclic forward/reverse transformation. It means that the transformation induced plasticity is a dominant mechanism for the cyclic super-elasticity degeneration of the NiTi SMAs [8,14,15]. In the last two decades, many researchers [3,16–24] performed
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experiments to investigate the fatigue failure of the NiTi SMAs. Many previous works demonstrated that, owing to their unique thermo-elastic martensite transformation, the fatigue failure of the NiTi SMAs is remarkably different from that of the ordinary metals, the cyclic stress-strain responses of the NiTi SMAs are gradually stabilized and keep unchanged till the final failure. Although a large inelastic deformation (e.g., 8–10%) occurs during the fatigue loading of the NiTi SMAs, a brittle fracture suddenly happens [3,20–24]. References [4,20] further reported that the NiTi SMAs are the alloys with the lowest crack propagation rate, since the cyclic accumulated residual martensite phase might hinder the propagation of the micro-cracks. Moreover, based on the fatigue tests of the NiTi SMAs, the microscopic fractographic analyses were also performed in references [5,6,18–22,25–28]. The previous investigations revealed that the ductile fracture patterns such as dimples and fatigue striations arise on the fracture surface of the NiTi fatigue specimens, and the dislocations tend to collect at the interfaces between the austenite and martensite phases. However, the previous fatigue tests of the NiTi SMAs were mainly performed under the uniaxial and bend fatigue loading conditions in order to match the service conditions of endovascular stents and dental orthodontic wires in medical applications and others. In despite of many aforementioned previous fatigue tests and related micro-structural observations of the NiTi SMAs, the following three aspects are still not sufficiently addressed: 1) The fatigue tests of the NiTi SMAs with a very small geometrical size such as the micro-tubes (with a wall thickness less than 400 mm as used in the manufacturing of endovascular stents) are still inadequate. It has been demonstrated that the fatigue failure of the NiTi SMA specimens with very small geometrical size cannot be extrapolated from that with a larger size [4,28]. Thus, more detailed fatigue tests with the micro-observations on the fracture surface of the NiTi SMA micro-tubes should be conducted to investigate the damage evolution and failure mechanism of such micro-sized devices. 2) Most of the previous fatigue tests were performed at room temperature (about 293 K), rather than at the temperature of human body. Since the variation of the ambient temperature will seriously affect the transformation start stress of the NiTi SMAs (e.g., with an increasing ambient temperature of 1 K, the start stress of the martensite transformation will be increased by approximately 8 MPa [29]) and then significantly influence the fatigue life, the reported fatigue data obtained at room temperature cannot be directly used to assess the fatigue life of the NiTi devices implanted in the human body. Thus, the fatigue tests and the corresponding micro-observations of the NiTi SMA micro-tubes at the temperature of human body (i.e., 310 K) are extremely necessary. 3) The reported experiments performed under the non-proportionally multiaxial loading conditions are far from sufficient, though some macroscopic fatigue data of the NiTi SMAs were obtained in [24]. The multiaxial fatigue failure mechanism of the NiTi SMAs has not been well understood and addressed in the literature.
Motivated by the aforementioned aspects and based on the macroscopic uniaxial and multiaxial stress-controlled fatigue tests of the super-elastic NiTi SMA micro-tubes done by Song et al. [23,24] at the temperature of human body (i.e., at 310 K), the fracture surfaces of broken specimens obtained under different loading paths are microscopically investigated in this study by scanning electron microscope (SEM). The multiaxial fatigue failure mechanism of the NiTi micro-tubes is analyzed and discussed by comparing the multiaxial results with the uniaxial ones, which is very important to construct an adequate failure model to predict the multiaxial fatigue life and establish the reliability of the NiTi devices. Some new findings are obtained and highlighted.
2. Experimental material and method The super-elastic NiTi SMA micro-tubes made of Nitinol SE508, which meets the ASTM F2063-05 medical Nitinol standard [31] and provided by the Jiangyin Materials Development Co., Ltd., China, are used in this work. The micro-tubes were aged two hours at 823 K and then polished mechanically to certain surface toughness. The grain size is within the range of 10–20 mm, and the austenite start temperature As, austenite finish temperature Af, martensite start temperature Ms, and martensite finish temperature Mf are 271, 302, 285, and 238 K, respectively, which were measured using a differential scanning calorimetry (DSC) by Song et al. [23]. The micro-tubular specimens with an outer diameter of 2.5 mm and an inner diameter of 2.2 mm (i.e., with a thickness of 150 mm) are adopted in the uniaxial and multiaxial fatigue tests. The whole-life transformation ratchetting and the fatigue life obtained from the macroscopic experiments were reported by Song et al. [23,24], while the fracture surfaces of the specimens are investigated in this work by the SEM (JSM-6490LV, JEOL Ltd.). In the microscopic observations, the fracture surfaces from eight specimens in two uniaxial and six multiaxial fatigue tests are used. Here, three kinds of multiaxial loading paths as shown in Fig. 1 are considered. Some details on the load cases and the corresponding fatigue lives are listed in Table 1, where the load cases with 2407 283 MPa and 450 7283 MPa indicate that the applied axial means stresses are 240 and 450 MPa and the stress amplitude is 283 MPa. For the multiaxial loading cases as shown in Fig. 1, the mean equivalent shear stress is zero and the equivalent shear stress amplitude (i.e., 3 τ ) is 283 MPa. Here, the von-Mises criteria is used, and the maximum equivalent stresses in the two prescribed load cases of the multiaxial fatigue tests are 595 and 786 MPa, respectively. It can be observed in Table 1 that the multiaxial fatigue lives are much shorter than that of the corresponding uniaxial ones, which implies that the multiaxial loadings can significantly reduce the fatigue lives of the super-elastic NiTi SMA micro-tubes. The fracture surfaces directly from the broken specimens and without any treatments are observed by the SEM. Before the SEM observation to the fracture surface, an energy depressive spectrometry (EDS) measurement to a selected area of the fracture
Fig. 1. Schematic diagrams of multiaxial loading paths: (a) square; (b) hourglass-typed; (c) butterfly-typed ones.
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Table 1 Load cases and fatigue lives (the number in brackets with c represents the number of cycles) of the specimens used in microscopic observations. Uniaxial
2407 283 MPa 450 7283 MPa
1# (1516c) 2# (735c)
Multiaxial Square
Hourglass
Butterfly
3# (302c) 4# (288c)
5# (375c) 6# (297c)
7# (681c) 8# (240c)
surface was performed and the results are shown in Fig. 2. It is seen that the super-elastic NiTi SMA micro-tubes used in this work are composed of near-equiatomic Ni and Ti elements, as well as some co-existing impurities. From Fig. 2b, it can be observed that some inclusions with different geometrical sizes appear at the bottom of the dimples, which are mainly formed by the Fe and S elements. The ingredient of the NiTi alloys including the inclusions meets the medical Nitinol standard of the ASTM F2063-05 [31].
3. Experimental observations and discussions 3.1. Common patterns in both uniaxial and multiaxial fatigue tests In this section, some common microstructural patterns observed on the fracture surfaces of the specimens in both uniaxial and multiaxial fatigue tests are analyzed and discussed, which are independent of the fatigue loadings. However, the differences caused by the applied stress levels are addressed. 3.1.1. Crack origins It is observed that during the fatigue tests of the super-elastic NiTi SMA micro-tubes, crack origins usually occur at four possible locations: (1) outer surface, (2) inner surface, (3) internal voids, and (4) internal inclusions, as shown in Fig. 3. Since the wallthickness of the NiTi SMA micro-tubes is much smaller than the critical size of the macro-cracks (e.g., 1 mm), the so-called “crack” in this work designates the micro-crack. Fig. 3a shows that the crack origins on the outer surface are usually flabellate-shaped with a number of tiny fatigue steps, which are formed by the extension and intersection of several micro-cracks on various planes. It is also observed that the fatigue steps are usually radially distributed, and become converged at the crack-origin. If the crack origins are relatively bigger along the surface, the fatigue steps become nearly perpendicular to the outer surface. From Fig. 3(b) to (d), it is seen that the crack origins are also prone to occur on the inner surface (especially near the surface defects) or near the internal voids and inclusions (internal
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defects). These three kinds of crack origins are induced by the stress concentrations near the defects during the cyclic loading. The stress concentrations are beneficial to the initiation of microcracks. However, it was demonstrated in [4,32–33] that the defects in the NiTi SMAs hardly influence the obtained fatigue lives, and the fatigue lives of the NiTi SMAs with a normal and extra low contents of defects are essentially the same. This finding can be interpreted as that the crack origins in the NiTi SMAs are mainly due to the transformation-induced plasticity occurring during the repeated martensite transformations and their reverses [15,30]. The stress-induced martensite variants gradually accumulate and change their positions during the cyclic loading [34], and then promote the crack initiation at various locations in the specimen, whose effect on the fatigue life of the NiTi SMAs is much more dominant than that of the pre-existing defects. This specific failure mechanism also leads to the excellent repeatability of the obtained fatigue lives of the NiTi SMA micro-tubes (e.g., a maximum deviation of 4% in the uniaxial fatigue loadings and 6% in the multiaxial ones) as demonstrated by Song et al. [23,24]. It has been verified in [23,30] that the most significant influencing factor on the fatigue life of the NiTi SMAs is their unique thermo-elastic martensite transformation, especially the extents of the martensite transformation and its reverse (i.e., the completeness of the forward/reverse martensite transformation), which are determined by the applied stress or strain levels. The damage accumulated during the repeated martensite transformations and their reverses leads to the final fracture of the NiTi SMAs. This phenomenon is remarkably different from that of the ordinary metals. 3.1.2. Fatigue striations On the fracture surfaces of the NiTi specimens after the fatigue tests, massive fatigue striations were observed in the region of the crack propagation, which is similar to that in ordinary ductile metals. The striations are characterized by various propagation directions, which are deduced from different crack origins and propagate independently with the development of the local stresses. From Fig. 4, it is seen that the fatigue striations with a higher density usually occur near the internal voids or inclusions due to the stress concentrations at such locations, which indicates that internal voids or inclusions are harmful to the crack propagation of the NiTi SMAs during the cyclic loading. It is also found that on the fracture surfaces of the NiTi SMA micro-tubes, the regions of the crack propagation (with striations) and the local fracture (with dimples) alternately appear, and no main-crack propagation is observed. The reason for this special failure feature is that both the martensite transformation occurring ahead the crack-tip and the reverse transformation in the crack-wake can reduce the stress
Fig. 2. Results of the EDS measurement: (a) NiTi matrix; (b) inclusions.
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eq Fig. 3. Typical locations of the crack origins observed on the fracture surfaces: (a) outer surface (1#, σmax ¼523 MPa, Nf ¼ 1516c); (b) inner surface (3#, σmax ¼595 MPa, eq ¼786 MPa, Nf ¼288c); (d) internal inclusion (2#, σmax ¼733 MPa, Nf ¼ 735c). Nf ¼ 302c); (c) internal void (4#, σmax
intensity at the crack-tip, greatly lower the propagation rate of the micro-cracks, and thus significantly hinder the formation of the macro-cracks [35,36]. It implies that the final fracture of the NiTi SMA micro-tubes during the fatigue loading is caused by the coalescence and the growth of the micro-cracks. The micro-cracks initiate and propagate independently, then result in a throughwall micro-crack and finally lead to a sudden fatigue failure as observed by Song et al. [23,24]. 3.1.3. Secondary cracks Another patterns observed in the regions of the crack propagation are the secondary cracks, which initiate and propagate during the fatigue loading, but do not cause the final fracture of
the specimens. From Fig. 5, it is seen that the secondary cracks arising on the fracture surfaces are usually accompanied by the fatigue striations, and their orientations are mostly parallel to the fatigue striations (Fig. 5a). In contrast, some secondary cracks perpendicular to the striations are also observed in certain regions, indicating that the secondary cracks may also develop from the same crack origins as the primary cracks, which are characterized by the striations on the fracture surface and induce the fatigue failure. As shown in Fig. 5b, both the fatigue striations and the secondary cracks develop from the two origins located at the left and right sides of the picture (i.e., the outer and inner surfaces of the specimens), and the secondary cracks are perpendicular to the striations. This feature can be observed more easily in the NiTi
eq Fig. 4. Typical locations of the fatigue striations with a higher density: (a) near the defect (5#, σmax ¼ 595 MPa, Nf ¼375c); (b) near the inclusion (2#, σmax ¼ 733 MPa, Nf ¼ 735c).
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Fig. 5. Secondary cracks on the fracture surfaces: (a) parallel to the fatigue striations (1#, σmax ¼ 523 MPa, Nf ¼ 1516c); (b) perpendicular to the fatigue striations (5#, eq eq ¼595 MPa, Nf ¼ 375c); (c) larger secondary cracks with a higher stress level (8#, σmax ¼ 786 MPa, Nf ¼ 240c). σmax
SMA micro-tubes than in the wire or bar specimens with a larger geometrical size, since the secondary cracks are prone to initiate on both the outer and the inner surfaces of the micro-tubes. Moreover, comparing the secondary cracks observed in the fatigue tests with different stress levels, it shows that more secondary cracks occur on the fracture surfaces of the specimen subjected to a fatigue loading with a lower stress level and their sizes are relatively small as shown in Fig. 5a and b. This phenomenon can be explained by the fact that the energy accumulation driving the crack propagation requires a longer period in the fatigue test with a lower stress level, and the propagations of the micro-cracks in different directions will also hinder the subsequent propagations of other micro-cracks [17]. It should be also noted here that larger secondary cracks are prone to form on the fracture surface of the specimen subjected to a fatigue loading with a higher stress level as shown in Fig. 5c, since a high stress level is beneficial to the propagations of both the primary and the secondary cracks. 3.2. Special microstructural patterns in multiaxial fatigue tests Here, some special microstructural patterns observed only in the multiaxial fatigue test of the NiTi SMA micro-tubes are outlined and discussed, in order to verify the essential differences in the crack initiation and propagation between the uniaxial and the multiaxial fatigue tests. The microstructural patterns observed in the multiaxial fatigue tests are mainly characterized by the following four characteristics: (1) V-shaped troughs, (2) throughwalled fatigue steps and slanted rupture, (3) scratches, and (4) abundant crack origins along the surfaces. These specific
patterns and their formation mechanisms are discussed in this subsection. 3.2.1. V-shaped troughs In the multiaxial loading cases, an important microstructural pattern with a V-shaped trough is observed on the fracture surfaces, as shown in Fig. 6. Such a pattern was also observed by Jensen [37] in the multiaxial fatigue tests of the tubular NiTi SMA specimens, but its formation mechanism was not investigated there. From Fig. 6, it is seen that the V-shaped troughs can be divided into two types: one is the single-form through across the whole wall-thickness of the micro-tubes (Fig. 6a), and the other one presents a continuous wave pattern or tiny saw tooth (Fig. 6b and c). The formation of the V-shaped trough on the fracture surfaces can be explained as follows. Since the direction of the applied stress continuously changes during the multiaxial cyclic loading, the propagations of the micro-cracks are driven in various directions. When the micro-cracks formed in different directions encounter each other, their propagations will stop, and then a V-shaped trough is emerged. For the single V-shaped trough as shown in Fig. 6a, the micro-cracks usually initiate on both the outer and the inner surfaces of the specimens, and then lead to the formation of a through-walled crack which causes the final fracture of the specimens. On the other hand, the V-shaped trough with a continuous wave pattern as shown in Fig. 6b and a saw tooth as shown in Fig. 6c is prone to occur in the multiaxial loading case with a lower stress level, since a larger number of the loading cycles before the fatigue failure will provide more chances for the diversions of the propagating cracks. The V-shaped trough represents the multi-directional mode of the crack propagation in
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eq eq Fig. 6. V-shaped troughs in the multiaxial loading cases: (a) single through-walled shape (4#, σmax ¼ 786 MPa, Nf ¼ 288c); (b) wave pattern (3#, σmax ¼595 MPa, Nf ¼302c); eq (c) saw tooth (7#, σmax ¼ 595 MPa, Nf ¼ 681c).
the multiaxial fatigue cases. 3.2.2. Through-walled fatigue steps and slanted rupture Further typical microstructural patterns observed in the multiaxial fatigue tests of the NiTi SMA micro-tubes are throughwalled fatigue steps and slanted rupture as shown in Fig. 7. It is found that the fatigue steps occurring in the multiaxial loading cases are observed not only in the regions of the crack origins, and they usually propagate across the wall thickness of the specimens independently, which finally leads to the formation of the through-walled fatigue steps on different planes as shown in Fig. 7a. Such a multi-planar propagation of the micro-cracks indicates the occurrence of the mode-II and mode-III crack
propagations, which is different from the single mode-I crack propagation in the uniaxial fatigue of the NiTi SMAs. Moreover, in the region of the final fracture on the fracture surface of the specimens subjected to the multiaxial loadings, the mode-II and mode-III cracks usually result in the formation of the slanted rupture as shown in Fig. 7b. The slanted rupture pattern is induced by the combined action of the tensile stress and the alternating shear stress. The micro-cracks propagate along the direction perpendicular to the maximum tensile normal stress [38], which leads to an angle of approximately 20° between the plane of the slanted rupture and the cross-section of the specimens. It can be also observed from Fig. 7b that the parabolic ductile dimples on different planes occur on the plane of the slanted rupture, which
eq Fig. 7. Through-walled fatigue steps and slanted rupture observed in the multiaxial fatigue tests: (a) through-walled fatigue steps (4#, σmax ¼ 786 MPa, Nf ¼ 288c); eq (b) slanted rupture (5#, σmax ¼595 MPa, Nf ¼375c).
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eq Fig. 8. Scratches on the fracture surfaces in the multiaxial loading cases: (a) uni-directional scratches (3#, σmax ¼ 595 MPa, Nf ¼ 302c); (b) bi-directional scratches (5#, eq ¼595 MPa, Nf ¼ 375c). σmax
are different from the rounded dimples and even-fracture mode (i.e. the fracture surface nearly parallel to the cross-section) appearing in the uniaxial loading cases. 3.2.3. Scratches From the microscopic observations, it can be observed that scratches usually occur on the fracture surfaces of the specimens subjected to the multiaxial fatigue loadings as shown in Fig. 8, while they are not found in the uniaxial fatigue tests. Fig. 8a shows that most scratches are uni-directional, while bi-directional ones can be also observed on the fracture surfaces as shown in Fig. 8b. Such a pattern indicates that a cyclic friction occurs between the two surfaces of the partly fractured specimens during the variation of the stress direction in the multiaxial loading cases, and it is more evident in the cases with a compressive axial stress. The scratches can be also regarded as the evidence for the existence of the mode-II and mode-III cracks during the cyclic loading [38]. It is also observed that the scratches usually develop near the outer and the inner surfaces and in the regions of the crack initiation and propagation. However, other microstructural patterns such as the tiny fatigue steps and the fatigue striations cannot be found at the locations where the scratches appear, because the cyclic friction will wear out the surface morphology during the subsequent cyclic loading. Thus, the scratches can intuitively reflect the relative moving directions of the two fracture surfaces, and the local crack propagation can be estimated from the directions of the scratches.
3.2.4. Abundant crack origins along the surfaces It can be observed that on the fracture surfaces of the specimens in the multiaxial fatigue tests, the amount of the crack origins is much larger than that in the uniaxial ones, and abundant crack origins are induced on the fracture surfaces especially near the outer and the inner surfaces as shown in Fig. 9. The increased crack origins are owing not only to the promotion of the multiaxial stress state to the crack initiation as in the ordinary metals, but also to another more important reason, that is, a unique inelastic deformation mechanism (i.e., martensite re-orientation) occurs in the multiaxial fatigue tests of the NiTi SMAs due to the stress alternation. Also, the mismatch between different martensite variants (there are 24 different variants) will cause a stress concentration and promote the dislocation slip, which is denoted as the “re-orientation induced plasticity” of the NiTi SMAs [24]. Similar to the effect of the transformation induced plasticity, the reorientation induced plasticity is also an important mechanism for the crack initiation in the multiaxial fatigue of the NiTi SMAs, which causes a higher damage level and makes the multiaxial fatigue life much shorter than that of the uniaxial one, even at quite lower equivalent stress levels as listed in Table 1. 3.3. Discussions on the failure mechanism of the multiaxial fatigue From the microscopic observations presented in the previous subsections, it can be concluded that some common microstructural patterns observed on the fracture surfaces of the NiTi SMAs subjected to uniaxial fatigue loadings, such as the fatigue
eq Fig. 9. Abundant crack origins along the surfaces in the multiaxial loading cases: (a) on the outer surface (8#, σmax ¼786 MPa, Nf ¼240c); (b) on both outer and inner eq surfaces (3#, σmax ¼ 595 MPa, Nf ¼ 302c).
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striations, dimples and secondary cracks, are also found on the fracture surfaces under the multiaxial fatigue loadings. However, due to the alternation of the stress state and a novel inelastic deformation mechanism of the NiTi SMAs, i.e., the martensite reorientation arising under the multiaxial loading conditions, some special microstructural patterns, such as the V-shaped troughs, through-walled steps, slanted rupture and scratches, and abundant crack origins, are observed only on the fracture surfaces of the NiTi SMA micro-tubes in the multiaxial fatigue tests. It indicates that the multiaxial fatigue loading will influence both the crack initiation and the crack propagation in the NiTi SMAs. At the stage of the micro-crack initiation, the martensite reorientation induced plasticity occurring only under the multiaxial cyclic loading conditions will initiate a much larger amount of the micro-cracks in the NiTi SMA micro-tubes, which is reflected by the occurrence of the abundant crack origins along the outer/inner surfaces as shown in Fig. 9. It means that a higher damage accumulation occurs at the stage of the crack initiation in the multiaxial fatigue tests of the NiTi SMA micro-tubes than that in the uniaxial loading cases. Since the martensite re-orientation induced plasticity can be also deduced from a dislocation slip similar to the martensite transformation induced plasticity, it can also result in an irreversible residual deformation of the NiTi SMAs during the multiaxial cyclic loading and then promote the cyclic degradation of the super-elasticity of the NiTi SMAs as demonstrated in the previous fatigue tests done by Song et al. [24]. Such macroscopic experimental results and the observed abundant crack origins representing a higher damage level can be mutually confirmed herein. At the stage of the micro-crack propagation, it is found that the crack propagation in the NiTi SMA micro-tubes presents a multiplanar and multi-directional mode in the multiaxial fatigue tests. Under the combined tension-torsion multiaxial cyclic loading conditions, there is not only a mode-I crack propagation as in the uniaxial loading tests, but also the mode-II and mode-III cracks exist in the NiTi SMA micro-tubes, which result in the throughwalled fatigue steps as shown in Fig. 7a, slanted rupture and parabolic-shaped dimples as shown in Fig. 7b, and scratches as shown in Fig. 8. Moreover, the alternation of the stress state caused by the multiaxial cyclic loading also promotes the crack propagation in different directions, and hence leads to wavier crack propagation traces than in the uniaxial loading cases, which are shown in Fig. 6. Thus, it can be concluded that the fatigue failure mechanism of the super-elastic NiTi SMA micro-tubes under the multiaxial loading conditions is significantly different from that under uniaxial loading conditions. This is characterized by both a higher damage level in the crack initiation and a more complex mode in the crack propagation, which will significantly influence the damage evolution and then greatly shorten the fatigue lives of the NiTi SMA micro-tubes. Thus, from the microscopic observations on the microstructural patterns on the fracture surfaces, the multiaxial fatigue failure mechanism of the super-elastic NiTi SMA micro-tubes is characterized by the special features of the crack initiation and propagation mainly caused by the alternation of the stress state and a novel inelastic deformation mechanism of the NiTi SMAs during the multiaxial cyclic loading, i.e., the martensite re-orientation induced plasticity. The damage evolution and the fatigue life of the NiTi SMAs under the multiaxial fatigue loadings are in general very difficult to accurately describe and predict, since the multiaxial fatigue failure mechanism of the NiTi SMAs is much more complex than that in the uniaxial loading cases. It implies that not only the martensite transformation and the re-orientation induced plasticity should be reasonably considered, but also the various crack propagation modes should be taken into account in the construction of adequate multiaxial fatigue failure models, which
demand further extensive investigations. It should be remarked here that a phenomenological uniaxial fatigue failure model for the NiTi SMA micro-tubes was established by Song et al. [30], which can reasonably describe the uniaxial damage evolution and predict fatigue life. In principle, a corresponding multiaxial fatigue failure model can be developed by extending the existing uniaxial one based on the observed multiaxial fatigue failure mechanism in this work, which will be considered in our future work. Moreover, it should be noted here that since only a SEM is used to observe the microstructural patterns on the fracture surfaces of the NiTi SMA micro-tubes, the dislocations and their evolution during the fatigue tests cannot be revealed. The microscopic observations on the dislocations and their evolution by a transmission electron microscope (TEM) will help to understand the fatigue damage of the NiTi SMAs more deeply, which will be also taken into consideration in our future work.
4. Conclusions From the microstructural observations in both uniaxial and multiaxial fatigue tests, such as crack origins, fatigue striations and secondary cracks, the following conclusions can be drawn: 1) The regions of the crack propagation and the final fracture appear alternatively on the fracture surfaces of the super-elastic NiTi SMA micro-tubes, and the fatigue failure is mainly controlled by the initiation and propagation of the micro-cracks. 2) Some special microstructural patterns, such as the V-shaped troughs, through-walled fatigue steps, slanted rupture, scratches, and abundant crack origins along the surfaces are observed only on the fracture surfaces of the NiTi micro-tubes subjected to the multiaxial fatigue loadings. A higher damage level occurs at the stage of the crack initiation, and a multi-directional and multi-planar crack propagation mode appears in the multiaxial fatigue failure, which leads to a much shorter fatigue life in the multiaxial fatigue tests than in the uniaxial loading cases. 3) The distinctive fatigue failure mechanism under multiaxial loading conditions should be considered appropriately in the construction of the adequate multiaxial fatigue failure models to accurately predict the multiaxial fatigue life of the superelastic NiTi SMA micro-tubes.
Acknowledgments Financial supports by the National Natural Science Foundation of China (11532010), Scientific Research Foundation of University of Electronic Science and Technology of China (ZYGX2015KYQD075) and the project for Sichuan Provincial Youth Science and Technology Innovation Team, China (2013TD0004) are gratefully acknowledged.
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