Compression fatigue behavior and failure mechanism of porous titanium for biomedical applications

Author’s Accepted Manuscript Compression fatigue behavior and failure mechanism of porous titanium for biomedical applications Fuping Li, Jinshan Li, Tingting Huang, Hongchao Kou, Lian Zhou www.elsevier.com/locate/jmbbm

PII: DOI: Reference:

S1751-6161(16)30344-7 http://dx.doi.org/10.1016/j.jmbbm.2016.09.035 JMBBM2092

To appear in: Journal of the Mechanical Behavior of Biomedical Materials Received date: 16 June 2016 Revised date: 5 September 2016 Accepted date: 27 September 2016 Cite this article as: Fuping Li, Jinshan Li, Tingting Huang, Hongchao Kou and Lian Zhou, Compression fatigue behavior and failure mechanism of porous titanium for biomedical applications, Journal of the Mechanical Behavior of Biomedical Materials, http://dx.doi.org/10.1016/j.jmbbm.2016.09.035 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Compression fatigue behavior and failure mechanism of porous titanium for biomedical applications

Fuping Li, Jinshan Li, Tingting Huang, Hongchao Kou*, Lian Zhou

State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, PR China

*

Corresponding author. Tel.: +86 029 88460568; [email protected]

Abstract Porous titanium and its alloys are believed to be one of the most attractive biomaterials for orthopedic implant applications. In the present work, porous pure titanium with 50-70% porosity and different pore size was fabricated by diffusion bonding. Compression fatigue behavior was systematically studied along the out-of-plane direction. It resulted that porous pure titanium has anisotropic pore structure and the microstructure is fine-grained equiaxed α phase with a few twins in some α grains. Porosity and pore size have some effect on the S-N curve but this effect is negligible when the fatigue strength is normalized by the yield stress. The relationship between normalized fatigue strength and fatigue life conforms to a power law. The compression fatigue behavior is characteristic of strain accumulation. Porous titanium experiences uniform deformation throughout the entire sample when fatigue 1

cycle is lower than a critical value (NT). When fatigue cycles exceed NT, strain accumulates rapidly and a single collapse band forms with a certain angle to the loading direction, leading to the sudden failure of testing sample. Both cyclic ratcheting and fatigue crack growth contribute to the fatigue failure mechanism, while the cyclic ratcheting is the dominant one. Porous titanium possesses higher normalized fatigue strength which is in the range of 0.5-0.55 at 106 cycles. The reasons for the higher normalized fatigue strength were analyzed based on the microstructure and fatigue failure mechanism.

Keywords: Porous Titanium; Diffusion bonding; Compression fatigue; Failure mechanism; normalized fatigue strength

1. Introduction Porous metals have received a considerable amount of attention in recent years because of their properties such as low density and unique functional properties (Freyman et al., 2001). They have wide applications in thermal insulation, packaging, energy/sound absorbing and biomaterials. For biomedical applications, porous titanium alloys are believed to be one of the most favorable choices for orthopedic implants, because they combine both admirable features of titanium alloys and porous structure (Levine, 2008; Marin et al., 2010). On the one hand, titanium alloys possess superior

mechanical

properties,

excellent

corrosion

resistance

and

good

biocompatibility in comparison with other common metallic biomaterials such as 2

stainless steel and Co-based alloys (Chen and Thouas, 2015; Geetha et al., 2009; Gepreel and Niinomi, 2013). On the other, porous structure is favored to reduce the “stress-shielding” effect through decreasing Young’s modulus of titanium alloys by tailoring porosity (Caparrós et al., 2014; El-Hajje et al., 2014; Ryan et al., 2006). Moreover, bone-like porous structure has the benefits to promote body fluid transport and improve osseointegration with surrounding bone tissue (Prado et al., 2015). Porous metals can be successfully fabricated by liquid state processing through gas injection and addition of blowing agent in the melt (Banhart, 2001). However, these methods are not applicable to porous titanium and its alloys because of their high melting point and extremely high reactivity. Previous studies have shown that porous titanium can be fabricated by a solid state processing named diffusion bonding of titanium meshes. This fabrication processing has preferable control of pore structure including porosity, pore size and distribution (Li et al., 2015b), and the obtained pore structure is qualified for cell proliferation, differentiation and bone tissue ingrowth by conducting studies in vitro and in vivo (Chang et al., 2016). The fabricated porous titanium possesses compressive properties compatible with trabecular bone both on the quasi-static condition and in the range of physiological strain rate (Li et al., 2014; Li et al., 2015b). Moreover, in comparison with other solid state processing such as powder sintering (Oh et al., 2003), space holder method (Jha et al., 2013; Li et al., 2013) and additive manufacturing (Li et al., 2009; Zhao et al., 2016), porous pure titanium fabricated by diffusion bonding has high ductility and good biosafty due to the lower diffusion bonding temperature and no addition of 3

space holder (Li et al., 2015b). In brief, porous pure titanium fabricated by diffusion bonding shows huge potential for orthopedic implant applications. It is well known that fatigue properties of metallic biomaterials should be greatly concerned especially for bone implant applications (Niinomi, 2007). Porous biomaterials implanted in human body are usually under cyclic loading conditions during walking and running. Recently, there are some studies regarding the fatigue behavior of porous Ti6Al4V alloys. For instance, Hrabe et al. (Hrabe et al., 2011) and Yavari et al. (Amin Yavari et al., 2013) studied the compression fatigue behavior of porous Ti6Al4V alloys fabricated by selective electron beam melting (SEBM) and selective laser melting (SLM), respectively. The resulted normalized fatigue strength at 106 cycles for porous Ti6Al4V alloys is lower than 0.25 in both studies, which is related to stress concentrations from the defects such as unmelted powders, internal closed pores and texture lines. The normalized fatigue strength is defined as the ratio of maximum fatigue strength to the yield stress obtained from quasi-static compression. Erkan Aşık et al. (Asik and Bor, 2015) investigated the compressive fatigue properties of porous Ti6Al4V alloys fabricated by space holder method and the resulted normalized fatigue strength at 106 cycles is about 0.75. In addition, Li et al. (Li et al., 2012) studied the fatigue failure mechanism of porous Ti6Al4V alloys fabricated by SEBM. The underlying dominant mechanism of fatigue failure is interaction between cyclic ratcheting and fatigue crack formation and growth. However, there are few studies on the compressive fatigue behavior of porous pure titanium for biomedical applications. Pure titanium possesses higher ductility, 4

non-toxicity but lower strength than Ti6Al4V alloy. For biomedical applications, Ti6Al4V alloys would cause allergic reactions after long-term implantation in the human body due to the toxicity of V and Al element (Niinomi, 2008). Wauthle et al. (Wauthle et al., 2015) compared the quasi-static compressive and fatigue properties between porous pure titanium and porous Ti6Al4V ELI alloys. It results that porous pure titanium is an excellent material for cyclically loaded porous implants and the highest normalized fatigue strength at 106 cycles for porous pure titanium is about 0.5. Lefebvre et al. (Lefebvre et al., 2009) and Özbilen et al. (Özbilen et al., 2016) studied the influence of interstitials, especially oxygen, on the compressive fatigue properties of porous pure titanium fabricated by space holder method, but the fatigue failure mechanism was not well deeply analyzed. Therefore, it is urgent to systematically study the compression fatigue behavior of porous pure titanium, including the effect of pore structure and fatigue failure mechanism. In addition, the compressive fatigue strength of porous pure titanium should be enhanced for the long-term clinical applications. In the present work, porous pure titanium samples with 50-70% porosity and different pore size were fabricated by diffusion bonding. Their compression fatigue behavior was systematically investigated. The effect of pore structure including porosity and pore size on fatigue behavior was discussed based on the fatigue failure mechanism. Porous pure titanium possesses higher normalized fatigue strength and the reasons are elucidated.

2. Material and methods 5

2.1 Fabrication of porous pure titanium Porous pure titanium was fabricated by vacuum diffusion bonding of titanium meshes. Three types of titanium meshes with square pore shape were used as starting materials. These three types of titanium meshes have different structure diameters (pore size and wire diameter) which are shown in Table 1. Before diffusion bonding, the titanium meshes were surface-treated by acid solution to remove the oxidized layer. Certain numbers of titanium meshes were stacked layer by layer to form a cuboid sample. Then the cuboid sample was placed in the furnace of diffusion bonding equipment. The diffusion bonding temperature is 850 °C and the holding time at this temperature is 1 h. The vacuum pressure was maintained to about 6.6×10−3 Pa during diffusion bonding process. After diffusion bonding, the samples were furnace cooled to the room temperature. More details of the fabrication process can be found in Ref. (Li et al., 2015a; Li et al., 2015b). Porous titanium with designed porosity of 50%, 60% and 70% was successfully fabricated by above fabrication process. The difference of porosity between designed and measured value is less than ±3%. Porous titanium with different average pore size can be fabricated by using different types of titanium meshes showing in Table 1. 2.2 Structure characterization Microstructure of porous titanium was observed by optical microscopy (Olympus, Japan). Phase composition of porous titanium and titanium mesh was identified by an X-ray diffractometer (XRD, DX-2700) with Cu Kα radiation. The diffraction angle was in the range of 20-90° with a step increment of 0.02°. Pore 6

structure of porous titanium was characterized by scanning electron microscopy (SEM, JEOL-JSM6330F). Porous titanium samples were scanned by the Micro-CT scanner (Siemens Inveon), a high-resolution protocol with a slice of 10 μm. Based on the Micro-CT results, the average pore size was calculated by the reconstruction software Mimics 14.11. Porosity of porous titanium was calculated by a mass-volume method using Eq. (1):  M  P  1   100%  V s 

(1)

where M and V are the mass and volume of porous titanium, respectively, and ρs is the density of solid titanium. 2.3 Mechanical test 2.3.1 Quasi-static compression test Quasi-static compression test of porous titanium was conducted along the out-of-plane direction. The compression in the out-of-plane direction is defined as loading direction parallel to the titanium mesh face. The definition of out-of-plane direction can be also found in Ref. (Li et al., 2015b). All the quasi-static compression tests were performed on a screw-driven load frame (MTS SYSTEMS) at a stain rate of 10-3 s-1. At least three compression tests were conducted for each condition. During quasi-static compression, a series of unloading-reloading cycles at different strains were conducted for porous titanium with different porosity. Compressive properties, including yield stress (σy) and Young’s modulus (E), were calculated from the nominal compressive stress-strain curves. 2.3.2 Compression fatigue test 7

Compression fatigue tests in the out-of-plane direction were conducted on a hydraulic test frame (MTS 858 Mini Bionix II). The sample size for fatigue test was Φ10×15mm. The load frequency was 20 Hz with sinusoidal wave shape and the load ratio (R) is fixed at 0.1. The load ratio (R) is the ratio between minimum compressive fatigue stress (σmin) and maximum fatigue stress (σmax). Six different values of maximum fatigue stress which was in the range of 0.5-0.8σy were chosen for each types of porous titanium. At least two fatigue tests were conducted for each condition. If the difference of fatigue life between two fatigue tests is larger than 40%, a third one was conducted. The displacement at the maximum fatigue stress was measured and recorded as a function of cycles during the fatigue tests. The fatigue test was terminated once the porous sample failed or the number of cycles exceeded 106. The fatigue failure mechanism of porous titanium was discussed according to the SEM (SEM, JEOL-JSM6330F) observation of the testing samples.

3. Results 3.1 Pore structure and microstructure Fig. 1 shows pore structure of porous titanium with 70% porosity fabricated by diffusion bonding of titanium meshes. Porous titanium has homogeneous and anisotropic pore structure. The pore shape of porous titanium is elongated (Fig. 1(b)) and square (Fig. 1(d)) in the out-of-plane and in-plane direction, respectively. Fig. 1(c) depicts the mesh hinges formed during diffusion bonding of two connected mesh wires. Obviously, no cracks and other defects can be observed in the mesh hinge. In addition, the surface of titanium wires is clean and smooth, as shown in Fig. 1. Table 8

2 shows the porosity and average pore size of porous titanium. The average pore size is in the range of 150-650 μm for porous titanium with 50-70% porosity and fabricated by different types titanium meshes. It has been reported that pore size in the range of 100-600 μm is more suited for bone ingrowth into the pore structure (Fukuda et al., 2011; Xue et al., 2007). Therefore, it is indicated that present porous titanium possesses suited pore structure for bone ingrowth. Moreover, average pore size of porous titanium can be adjusted by tailoring pore size of titanium meshes, as shown in Table 2. The average pore size of porous titanium fabricated by type I meshes (Ti-70-I) is about 278 μm, while it increases to about 623 μm for porous titanium fabricated by type III meshes (Ti-70-III). The XRD patterns of titanium mesh and porous titanium are revealed in Fig. 2(a). Both titanium mesh and porous titanium only contain α phase and there are no peaks corresponding to impurities in the XRD patterns. Fig. 2(a) displays the microstructure of porous titanium fabricated by diffusion bonding of titanium meshes. The microstructure of porous titanium is equiaxed α phase and a few twins indicated by arrow in Fig. 2(b) can be observed within some α grains. The twins in some α grains are resulted from the cold drawing process during the fabrication of titanium mesh wires. Moreover, the equiaxed α grains are very fine with size of ~10 μm, as shown in Fig. 2(b). 3.2 Quasi-static compressive properties Fig. 3 shows the quasi-static compressive stress-strain curves of porous titanium with different porosity. The compressive stress-strain curves of porous titanium possess typical features of porous metals, with a long plateau region before 9

densification. In the plateau region, the stress-strain curves are smooth and there is no appearance of any serrations in the curves. Smooth plateau region is a key characteristic of porous metals with high ductility, which indicates that porous titanium fabricated by diffusion bonding has high ductility. Fig. 3 also shows the unloading-reloading curves of porous titanium at different strains. Different from porous titanium in Ref. (Liu et al., 2010), no evident “hysteresis effect” can be observed at any strains for present porous titanium with 50-70% porosity, as shown in Fig. 3. It has been demonstrated that the “hysteresis” between the unloading and reloading curves can characterize the structural damage within porous metals during compression (Imwinkelried, 2007). The overlap between unloading and reloading curves at any strains shows the structural integrity of the deformed porous titanium during compression. The insert graph in Fig. 3 is the Ti-70-I sample at about 45% compressive strain. Obviously, the main deformation mode of porous titanium during quasi-static compression is buckling of titanium meshes. Table 2 displays quasi-static compressive properties of porous titanium calculated from stress-strain curves. The Young’s modulus and yield stress of porous titanium with 50-70% porosity are in the range of about 1-6 MPa and 20-70 GPa, respectively. The quasi-static compressive properties decrease with increase in porosity. It have been shown that compressive Young’s modulus and yield stress of human trabecular bone from distal femur are in the range of 0.01-3 GPa and 2-70 MPa, respectively (Goldstein, 1987). It is obvious that the quasi-static compressive properties of porous titanium with 50-70% porosity are close to those of the trabecular 10

bone, which indicates that present porous titanium has potential application for trabecular bone implants. 3.3 Compression fatigue properties 3.3.1 Strain accumulation It has been demonstrated that gradual strain accumulation which leads to progressive shorten of the tested sample is the main characteristic of porous metals during compression fatigue tests (Li et al., 2012). Relationship between the strain at maximum fatigue stress (εmax) and fatigue cycle (N) at different maximum fatigue stress (σmax) for Ti-70-I sample is plotted in Fig. 4. The other porous samples with different porosity and fabricated by different type of titanium meshes have the same features as the Fig. 4. Obviously, the strain accumulation of porous titanium during compression fatigue tests exhibits three different stages. In the stage I, there is small strain increase in the first few cycles. Thereafter, minimal strain accumulation is observed after large amount of cycles, which is referred as stage II. Finally, after a critical fatigue cycle, there is rapid strain increase and the porous sample fails within limited cycles (stage III). The critical fatigue cycle corresponding to the transition from stage II to stage III is denoted as NT in Fig. 4. When the fatigue cycle (N) is lower than the value of NT during fatigue test, the strain increase is negligible and the porous sample has cyclic stability. However, once the value of N is higher than NT, there is rapid and abrupt increase in strain and the tested sample fails in a few fatigue cycles. The value of NT is defined as the fatigue life of porous sample because the sample fails within a few fatigue cycles after stage II. As shown in Fig. 4, the value of 11

NT is heavily dependent on the maximum fatigue stress (σmax) during fatigue test. Fig. 5 shows strain per cycle plotted as a function of fatigue cycle for Ti-70-I sample tested at different maximum fatigue stress. There are three key characteristics in the (dεmax/dN)-N curves. Take the maximum fatigue stress equal to 0.7σy as an example (as shown in the insert graph in Fig. 5). In the stage I, the value of strain per cycle decreases gradually from about 10-5 to about 5×10-7. In the stage II, the value of strain per cycle is nearly constant until the fatigue number attains the value of NT. The constant value of strain per cycle in this stage is denoted as (dεmax/dN)II and it is equal to about 5×10-7 for σmax equal to 0.7σy. In the stage III, the value of strain per cycle increases rapidly from about 7×10-7 to about 10-4 once the fatigue cycle is beyond the value of NT. 3.3.2 S-N curves The S-N curves of porous titanium with different porosity and fabricated by different types of titanium meshes are shown in Fig. 6 and 7, respectively. Obviously, as shown in Fig. 6(a) and Fig. 7(a), when tested at the same maximum fatigue stress, the fatigue life of porous titanium increases with deceasing porosity and porous titanium fabricated by type II meshes has longer fatigue life. However, as the maximum fatigue stress (σmax) is normalized by the yield stress (σy), the fatigue life of porous titanium with different porosity and fabricated by different types of meshes is almost the same, as shown in Fig. 6(b) and Fig. 7(b). In addition, as the value of σmax/σy equal to 0.5, the fatigue life of porous titanium exceeds 106 and the testing samples do not fail. Therefore, it is indicated that the normalized fatigue strength of 12

porous titanium is in the range of 0.5-0.55 at 106 cycles. 3.3.3 Cyclic stress-strain features The cyclic stress-strain features of porous titanium at different fatigue cycles are shown in Fig. 8. Theses cyclic stress-strain loops of porous titanium with different porosity and pore size exhibit similar characteristics. The hysteresis loops are gradually displaced along the strain axis, indicating that cycle ratcheting is involved in the compression fatigue process (Guo et al., 1994; McCullough et al., 2000). In addition, Young’s modulus decreases during fatigue test especially for porous titanium with 70% porosity, as shown in Fig. 8(b). The reduction of Young’s modulus with increase in fatigue cycles is mainly caused by the fatigue crack formation and growth (Zhou and Soboyejo, 2004). Thus it is indicated that both cyclic ratcheting and fatigue crack growth contribute to the fatigue failure of porous titanium fabricated by diffusion bonding. 3.3.4 Fatigue fracture morphology Fig. 9 depicts the SEM images of Ti-60-I samples at different fatigue cycles during tests. The corresponding maximum fatigue stress is equal to 0.7σy. Before fatigue test, the porous sample is homogeneous. After 5×103 fatigue cycles, the porous sample experiences uniform deformation and no local strain concentration is observed. There is no obvious difference in macrostructure between original sample and sample after 5×103 fatigue cycles. However, after 1.2×104 fatigue cycles, non-uniform deformation appears with the sign of formation of a single collapse band and the porous sample suddenly fails. The single collapse band is at a certain angle to the 13

loading direction, as shown in Fig. 9(c). Formation of collapse band is a common phenomenon during compression fatigue test of porous metals (Harte et al., 1999; Ozbilen et al., 2016; Zhao et al., 2016). It has been shown that the collapse band is caused by regions with high localized stress, where accompanied by high dislocation concentrations (Ozbilen et al., 2016). Moreover, as shown in Fig. 9(d), some cracks are observed in the region of collapse band for porous titanium after 1.2×104 fatigue cycles. Theses cracks are caused by the fracture of mesh hinges which are the bonding interface between adjacent mesh wires.

4. Discussion 4.1 Compression fatigue failure mechanism Compression fatigue behavior of cellular solids has been investigated extensively in previous studies and several fatigue failure mechanism, including cyclic ratcheting, softening and fatigue cracks growth, has been proposed. Cyclic ratcheting is the gradual strain accumulation owing to the plastic deformation of strut during compression fatigue test. As shown in Fig. 8(a) and (b), the cyclic stress-strain loops are gradually displaced along the strain axis and modulus decreases with increase in fatigue cycles, indicating that both cyclic ratcheting and fatigue cracks growth are involved in the failure mechanism of porous titanium. In order to deeply elucidate the effect of cyclic ratcheting and fatigue cracks growth on the fatigue process, fatigue ratcheting strain and fatigue damage strain are calculated based on the cyclic stress-strain loops and method proposed in Ref. (Bowman et al., 1998). Fig. 8(c) is the schematic drawing of calculation of fatigue ratcheting strain and fatigue damage 14

according to cyclic stress-strain loops. As shown in Fig. 8(c), after K fatigue cycles, the fatigue ratcheting strain (εRK) caused by ratcheting effect is the difference of minimum strain between K and first cycles. And the fatigue damage strain (εDK) caused by fatigue cracks growth is the difference of stress-strain loop strain between K and first cycles, which can be expressed as:  DK   K  1

(2)

Based on the cycle stress-strain loops in Fig. 8(a) and (b), the fatigue ratcheting strain and fatigue damage strain of porous titanium with 50% and 70% porosity are calculated and shown in Fig. 10(a) and (b), respectively. Both the fatigue ratcheting strain and fatigue damage strain gradually increase with increase in fatigue cycles, indicating that both cyclic ratcheting and fatigue crack growth contribute to the fatigue failure of porous titanium. However, the fatigue ratcheting strain is much higher the fatigue damage strain. For porous titanium with 50% porosity, the fatigue ratcheting strain is about two orders of magnitude higher than the fatigue damage strain. The much higher fatigue ratcheting strain demonstrates that cyclic ratcheting is the main failure mechanism of porous titanium during compression fatigue test. The less effect of crack formation and growth on fatigue failure of porous titanium also can be proved by the fracture morphology during fatigue test. As shown in Fig. 9(b), after 5×103 fatigue cycles, the porous sample experiences uniform deformation and no fatigue cracks are observed in the macrostructure, revealing that uniform plastic deformation caused by ratcheting effect is main failure mechanism. Some cracks appear in the failed porous sample, as shown in Fig. 9(d). These cracks 15

are caused by fracture of mesh hinges due to the local non-uniform deformation. At the beginning of the fatigue test, the porous sample experiences uniform plastic deformation and the strain at maximum fatigue stress increases at a constant slow rate (as shown in Fig. 5) owing to the homogeneous structure and cyclic ratcheting. Once the fatigue cycle reaches NT, non-uniform deformation caused by fatigue cracks growth appears, leading to the formation of collapse band and sudden failure of porous sample. Therefore, the cyclic ratcheting is the main fatigue failure mechanism and the ratcheting rate in stage II shown in Fig. 5 is the main factor determining the fatigue life of porous titanium. It should be noted that, as shown in Fig. 5, there are no abrupt strain jumps in the (dεmax/dN)-N curves of present porous titanium and the value of dεmax/dN in stage II is constant. The abrupt strain jump has been observed during the compression fatigue test of cellular aluminum alloy (Alporas foam) and it is resulted from the irregular microstructure and non-uniform deformation (Sugimura et al., 1999). The absence of strain jump for present porous titanium is believed to be related with more uniform deformation and homogeneous structure compared to other porous metals. This phenomenon of no strain jump has been also observed in porous Ti6Al4V alloys (Amin Yavari et al., 2013) and aluminum-steel foams (Vendra et al., 2009) that show uniform plastic deformation during fatigue tests. 4.2 Effect of porosity and pore size on fatigue properties The relationship between normalized fatigue strength (σmax/σy) and fatigue cycle (N) conforms to a typical power law which can be expressed as follows: 16

 max  AN b y

(3)

where A is a constant related to the material property, b is exponent which represents the degradation rate. By fitting the experimental values to Eq. (3), as shown in Fig. 6(b) and Fig. 7(b), the values of A and b are determined to be 1.52 and 0.08, respectively. This power law can be used to predict the fatigue life of porous titanium and its alloys fabricated by diffusion bonding. Through conducting quasi-static compression test, the yield stress (σy) can be obtained in the stress-strain curves. Then the fatigue life at certain maximum fatigue stress can be deduced by Eq. (3). Moreover, as shown in Fig. 6(b) and Fig. 7(b), the exponent of b is equal to 0.08 for present porous titanium, which is lower than that for porous Ti6Al4V alloys fabricated by selective laser melting (b=0.301) (Amin Yavari et al., 2013) but a little higher than that for syntactic foam (b=0.041-0.051) (Hossain and Shivakumar, 2011). As the value of b represents the degradation rate during fatigue test, it is indicated that present porous titanium has higher normalized fatigue strength. As shown in Fig. 6(b) and Fig. 7(b), the porosity and pore size has minor effect on the normalized S-N curves. The reason for this minor effect can be illustrated by the failure mechanism of porous titanium during compression fatigue test. As discussed in section 4.1, the main fatigue failure mechanism is cyclic ratcheting and strain accumulation. Thus strain accumulation rate has substantial influence in the compression fatigue behavior. As shown in Fig. 5, the value of strain per cycle is nearly constant in stage II which means strain accumulation rate is unchanged for porous titanium. This constant value is denoted as (dεmax/dN)II). Fig. 11 shows the 17

relationship between the value of (dεmax/dN)II and normalized fatigue strength (σmax/σy) for porous titanium with different porosity and pore size. It can be seen that the value of (dεmax/dN)II is sensitive to the normalized fatigue strength. Their relationship is described by a power law with exponent (n) close to 13.5. The values of n for porous titanium with different porosity and pore size are nearly equivalent to each other, which indicate that porous titanium has similar cyclic ratcheting and strain accumulation behavior during fatigue tests. And that explains why the fatigue life of porous titanium with different porosity and pore size is almost the same when the maximum fatigue stress (σmax) is normalized by the yield stress (σy). 4.3 Normalized fatigue strength As shown in Fig. 6 and 7, the normalized fatigue strength of porous titanium is in the range of 0.5-0.55 at 106 cycles. Table 3 shows normalized fatigue strength of solid/porous/porous-coated titanium and Ti6Al4V alloys at 106 cycles in previous studies (Amin Yavari et al., 2013; Asaoka et al., 1985; Cook et al., 1988; Hrabe et al., 2011; Janeček et al., 2011; Wauthle et al., 2015; Yan et al., 2013). Obviously, the normalized fatigue strength of porous titanium and Ti6Al4V alloys in previous studies is lower than 0.5. The normalized fatigue strength in present work is close to that of the solid Ti6Al4V alloy, but higher than that of porous-coated/porous titanium and Ti6Al4V alloys fabricated by other methods. The higher normalized fatigue strength in present work is discussed based on the microstructure and fatigue failure mechanism. As discussed in section 4.1, the fatigue failure mechanism of porous titanium is 18

cyclic ratcheting and fatigue crack growth, while the former plays a dominant role. Thus the ratcheting rate is the main factor determining the fatigue life of porous titanium. McCullough et al. (McCullough et al., 2000) deeply analyzed the effect of cyclic ratcheting on the compression fatigue behavior of porous metals. As indicated by studies of McCullough et al., the ratcheting rate (dε/dN) of open porous metal can be described as: k

(3 k 1)/2 d p 0.6 1.7(2k  1)  max   C 1  R     dN k 2 k 0 

(4)

where C, p, k and σ0 are material parameters in the ratcheting model. R is the load ratio applied in the compression fatigue test. σmax is the maximum fatigue stress and

 is the relative density of porous metal. The fatigue life (NT) at certain stress level can be estimated on the assumption that the fatigue limit is attained when the accumulated plastic strain has reached to the quasi-static yield strain (εy) of the porous metal. Combing Eq. (4), the fatigue life (NT) of porous metal can be calculated as (McCullough et al., 2000): C 1  R  0.6 1.7(2k  1)  max  (3k 1)/2 1    NT y k 2 k  0  k

p

(5)

According to Eq. (5), the cyclic damage of porous metal is heavily dependent on the maximum fatigue stress, relative density and ductility. For present porous titanium, because the diffusion bonding is a solid state process and the diffusion bonding temperature is about 30 K below the β-transus temperature of pure titanium, no solidification defects such as shrinkage cavity and segregation can be formed in the porous sample. In addition, the oxygen content of present porous titanium fabricated 19

by diffusion bonding is about 0.16 wt.% (Li et al., 2015b) which is much lower than 0.8 wt.%. Previous studies have shown that oxygen content in titanium significantly affects its ductility, reaching near-zero values for 0.8 wt.% oxygen content (Wasz et al., 1996). It is indicated that present porous titanium has higher ductility and thus higher fatigue strength according to Eq. (5). The high ductility of porous titanium also can be demonstrated by the smooth quasi-static stress-strain curves (Fig. 3). Microstructure is also a key factor for the compression fatigue properties. For the porous titanium and Ti6Al4V alloys fabricated by selective laser/electron beam melting, the microstructure is α’ martensite (Table 3) which is a hard and brittle phase. As indicated by Eq. (5), brittleness is harmful to the compressive fatigue properties. The microstructure of porous titanium fabricated by diffusion bonding is fine equiaxed α phase and the grain size is lower than 20 μm, as shown in Fig. 2(b). The equiaxed microstructure can provide higher fatigue resistance, especially high-cycle fatigue resistance, than acicular and lamellar microstructure. Moreover, some defects including unmelted powders, internal pores and inclusions can be observed in the porous samples fabricated by selective laser/electron beam melting and space-holder method. All these defects are against the fatigue resistance of porous samples. Therefore, porous titanium fabricated by diffusion bonding possesses higher normalized fatigue strength. It is also indicated that improvement in ductility of porous titanium and Ti6Al4V alloys is an effective way to improve their fatigue properties. For porous titanium and Ti6Al4V alloys fabricated by selective laser/electron beam melting, post heat-treatment should be employed in order to 20

improve their microstructure, ductility and fatigue properties. For present porous titanium with 50-70% porosity fabricated by diffusion bonding, quasi-static compressive properties are biocompatible with the human trabecular bone and the normalized fatigue strength is relative higher. Moreover, pore structure is qualified for cell proliferation, differentiation and bone tissue ingrowth according to the studies in vitro and in vivo (Chang et al., 2016). Thus present porous titanium has huge potential for trabecular bone implant applications, especially for the segmental bone defect.

5. Conclusions In the present work, compression fatigue behavior of porous titanium fabricated by diffusion bonding of titanium meshes was studied. The main conclusions are as follows. (1) Porous titanium fabricated by diffusion bonding has homogeneous and anisotropic pore structure with elongated pores in the out-of-plane direction. The microstructure of porous titanium is fine-grained equiaxed α phase with a few twins. Porous titanium shows high ductility but less evident “hysteresis effect” during quasi-static compression. (2) Porosity and pore size have some effect on the S-N curve but this effect is negligible when the fatigue strength is normalized by the yield stress. The relationship between normalized fatigue strength and fatigue cycles conforms to a power law, which can be used to predict the fatigue life. The negligible effect of porosity and pore size on normalized S-N curve is related to the identical strain 21

accumulation behavior during compression fatigue. (3) The compression fatigue behavior of porous titanium is characteristic of strain accumulation and a critical fatigue cycle (NT) exists in the εmax-N and (dεmax/dN)-N curves. The fatigue failure mechanism of porous titanium is cyclic ratcheting and fatigue crack growth, while the former plays a dominant role. When the fatigue cycle is lower than NT, the strain accumulation is slow and constant, and porous sample experiences uniform deformation. Once the fatigue cycle exceeds NT, non-uniform deformation caused by fatigue cracks growth appears, leading to the formation of collapse band and sudden failure of porous sample. (4) Porous titanium possesses higher normalized fatigue strength which is in the range 0.5-0.55 at 106 cycles. The higher normalized fatigue strength is related to the low cyclic ratcheting rate resulted from high ductility and fine equiaxed microstructure. Porous titanium has huge potential for trabecular bone implant applications, especially for the segmental bone defect.

Acknowledgements This work was financially supported by National Basic Research Program of China (No. 2012CB619101) and The Program of Introducing Talents of Discipline to Universities (No. B08040).

References 22

Amin Yavari, S., Wauthle, R., van der Stok, J., Riemslag, A.C., Janssen, M., Mulier, M., Kruth, J.P., Schrooten, J., Weinans, H., Zadpoor, A.A., 2013. Fatigue behavior of porous biomaterials manufactured using selective laser melting. Materials Science and Engineering: C 33, 4849-4858. Asaoka, K., Kuwayama, N., Okuno, O., Miura, I., 1985. Mechanical properties and biomechanical compatibility of porous titanium for dental implants. Journal of Biomedical Materials Research 19, 699-713. Asik, E.E., Bor, S., 2015. Fatigue behavior of Ti-6Al-4V foams processed by magnesium space holder technique. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 621, 157-165. Banhart, J., 2001. Manufacture, characterisation and application of cellular metals and metal foams. Progress in Materials Science 46, 559-632. Bowman, S.M., Guo, X.E., Cheng, D.W., Keaveny, T.M., Gibson, L.J., Hayes, W.C., McMahon, T.A., 1998. Creep Contributes to the Fatigue Behavior of Bovine Trabecular Bone. Journal of Biomechanical Engineering 120, 647-654. Caparrós, C., Guillem-Martí, J., Molmeneu, M., Punset, M., Calero, J.A., Gil, F.J., 2014. Mechanical properties and in vitro biological response to porous titanium alloys prepared for use in intervertebral implants. Journal of the Mechanical Behavior of Biomedical Materials 39, 79-86. Chang, B., Song, W., Han, T., Yan, J., Li, F., Zhao, L., Kou, H., Zhang, Y., 2016. Influence of pore size of porous titanium fabricated by vacuum diffusion bonding of titanium meshes on cell penetration and bone ingrowth. Acta Biomaterialia 33, 23

311-321. Chen, Q., Thouas, G.A., 2015. Metallic implant biomaterials. Materials Science and Engineering: R: Reports 87, 1-57. Cook, S.D., Thongpreda, N., Anderson, R.C., Haddad, R.J., 1988. The effect of post-sintering heat treatments on the fatigue properties of porous coated Ti-6Al-4V Alloy. Journal of Biomedical Materials Research 22, 287-302. El-Hajje, A., Kolos, E.C., Wang, J.K., Maleksaeedi, S., He, Z., Wiria, F.E., Choong, C., Ruys, A.J., 2014. Physical and mechanical characterisation of 3D-printed porous titanium for biomedical applications. Journal of Materials Science: Materials in Medicine 25, 2471-2480. Freyman, T.M., Yannas, I.V., Gibson, L.J., 2001. Cellular materials as porous scaffolds for tissue engineering. Progress in Materials Science 46, 273-282. Fukuda, A., Takemoto, M., Saito, T., Fujibayashi, S., Neo, M., Pattanayak, D.K., Matsushita, T., Sasaki, K., Nishida, N., Kokubo, T., Nakamura, T., 2011. Osteoinduction of porous Ti implants with a channel structure fabricated by selective laser melting. Acta Biomaterialia 7, 2327-2336. Geetha, M., Singh, A.K., Asokamani, R., Gogia, A.K., 2009. Ti based biomaterials, the ultimate choice for orthopaedic implants – A review. Progress in Materials Science 54, 397-425. Gepreel, M., Niinomi, M., 2013. Biocompatibility of Ti-alloys for long-term implantation. Journal of the Mechanical Behavior of Biomedical Materials 20, 407-415. 24

Goldstein, S.A., 1987. The mechanical properties of trabecular bone: Dependence on anatomic location and function. Journal of Biomechanics 20, 1055-1061. Guo, X.D.E., McMahon, T.A., Keaveny, T.M., Hayes, W.C., Gibson, L.J., 1994. Finite element modeling of damage accumulation in trabecular bone under cyclic loading. Journal of Biomechanics 27, 145-155. Harte, A.M., Fleck, N.A., Ashby, M.F., 1999. Fatigue failure of an open cell and a closed cell aluminium alloy foam. Acta Materialia 47, 2511-2524. Hossain, M.M., Shivakumar, K., 2011. Compression fatigue performance of a fire resistant syntactic foam. Composite Structures 94, 290-298. Hrabe,

N.W.,

Heinl,

P.,

Flinn,

B.,

Körner,

C.,

Bordia,

R.K.,

2011.

Compression-compression fatigue of selective electron beam melted cellular titanium (Ti-6Al-4V). Journal of Biomedical Materials Research Part B: Applied Biomaterials 99B, 313-320. Imwinkelried, T., 2007. Mechanical properties of open-pore titanium foam. Journal of Biomedical Materials Research Part A 81A, 964-970. Janeček, M., Nový, F., Stráský, J., Harcuba, P., Wagner, L., 2011. Fatigue endurance of Ti-6Al-4V alloy with electro-eroded surface for improved bone in-growth. Journal of the Mechanical Behavior of Biomedical Materials 4, 417-422. Jha, N., Mondal, D.P., Dutta Majumdar, J., Badkul, A., Jha, A.K., Khare, A.K., 2013. Highly porous open cell Ti-foam using NaCl as temporary space holder through powder metallurgy route. Materials & Design 47, 810-819. Lefebvre, L.P., Baril, E., Bureau, M.N., 2009. Effect of the oxygen content in solution 25

on the static and cyclic deformation of titanium foams. Journal of Materials Science-Materials in Medicine 20, 2223-2233. Levine, B., 2008. A New Era in Porous Metals: Applications in Orthopaedics. Advanced Engineering Materials 10, 788-792. Li, B.Q., Wang, C.Y., Lu, X., 2013. Effect of pore structure on the compressive property of porous Ti produced by powder metallurgy technique. Materials & Design 50, 613-619. Li, F., Li, J., Kou, H., Huang, T., Zhou, L., 2015a. Compressive mechanical compatibility of anisotropic porous Ti6Al4V alloys in the range of physiological strain rate for cortical bone implant applications. Journal of Materials Science: Materials in Medicine 26, 1-8. Li, F., Li, J., Kou, H., Xu, G., Li, T., Zhou, L., 2014. Anisotropic porous titanium with superior mechanical compatibility in the range of physiological strain rate for trabecular bone implant applications. Materials Letters 137, 424-427. Li, F., Li, J., Xu, G., Liu, G., Kou, H., Zhou, L., 2015b. Fabrication, pore structure and compressive behavior of anisotropic porous titanium for human trabecular bone implant applications. Journal of the Mechanical Behavior of Biomedical Materials 46, 104-114. Li, S.J., Murr, L.E., Cheng, X.Y., Zhang, Z.B., Hao, Y.L., Yang, R., Medina, F., Wicker, R.B., 2012. Compression fatigue behavior of Ti–6Al–4V mesh arrays fabricated by electron beam melting. Acta Materialia 60, 793-802. Li, X., Wang, C., Zhang, W., Li, Y., 2009. Fabrication and characterization of porous 26

Ti6Al4V parts for biomedical applications using electron beam melting process. Materials Letters 63, 403-405. Liu, P., Tan, Q., Wu, L., He, G., 2010. Compressive and pseudo-elastic hysteresis behavior of entangled titanium wire materials. Materials Science and Engineering: A 527, 3301-3309. Marin, E., Fusi, S., Pressacco, M., Paussa, L., Fedrizzi, L., 2010. Characterization of cellular solids in Ti6Al4V for orthopaedic implant applications: Trabecular titanium. Journal of the Mechanical Behavior of Biomedical Materials 3, 373-381. McCullough, K.Y.G., Fleck, N.A., Ashby, M.F., 2000. Stress-life fatigue behaviour of aluminum alloy foams. Fatigue and Fracture of Engineering Materials and Structures 23, 199-208. Niinomi, M., 2007. Fatigue characteristics of metallic biomaterials. International Journal of Fatigue 29, 992-1000. Niinomi, M., 2008. Biologically and Mechanically Biocompatible Titanium Alloys. MATERIALS TRANSACTIONS 49, 2170-2178. Oh, I.H., Nomura, N., Masahashi, N., Hanada, S., 2003. Mechanical properties of porous titanium compacts prepared by powder sintering. Scripta Materialia 49, 1197-1202. Özbilen, S., Liebert, D., Beck, T., Bram, M., 2016. Fatigue behavior of highly porous titanium produced by powder metallurgy with temporary space holders. Materials Science and Engineering: C 60, 446-457. Prado, R.F., Rabêlo, S.B., Andrade, D.P., Nascimento, R.D., Henriques, R.V.A., 27

Carvalho, Y.R., Cairo, C.A.A., Vasconcellos, L.M.R., 2015. Porous titanium and Ti– 35Nb alloy: effects on gene expression of osteoblastic cells derived from human alveolar bone. Journal of Materials Science: Materials in Medicine 26, 1-11. Ryan, G., Pandit, A., Apatsidis, D.P., 2006. Fabrication methods of porous metals for use in orthopaedic applications. Biomaterials 27, 2651-2670. Sugimura, Y., Rabiei, A., Evans, A.G., Harte, A.M., Fleck, N.A., 1999. Compression fatigue of a cellular Al alloy. Materials Science and Engineering: A 269, 38-48. Vendra, L., Neville, B., Rabiei, A., 2009. Fatigue in aluminum–steel and steel–steel composite foams. Materials Science and Engineering: A 517, 146-153. Wasz, M.L., Brotzen, F.R., McLellan, R.B., Griffin, A.J., 1996. Effect of oxygen and hydrogen on mechanical properties of commercial purity titanium. International Materials Reviews 41, 1-12. Wauthle, R., Ahmadi, S.M., Amin Yavari, S., Mulier, M., Zadpoor, A.A., Weinans, H., Van Humbeeck, J., Kruth, J.-P., Schrooten, J., 2015. Revival of pure titanium for dynamically loaded porous implants using additive manufacturing. Materials Science and Engineering: C 54, 94-100. Xue, W., Krishna, B.V., Bandyopadhyay, A., Bose, S., 2007. Processing and biocompatibility evaluation of laser processed porous titanium. Acta Biomaterialia 3, 1007-1018. Yan, Y., Nash, G.L., Nash, P., 2013. Effect of density and pore morphology on fatigue properties of sintered Ti–6Al–4V. International Journal of Fatigue 55, 81-91. Zhao, S., Li, S.J., Hou, W.T., Hao, Y.L., Yang, R., Misra, R.D.K., 2016. The influence 28

of cell morphology on the compressive fatigue behavior of Ti-6Al-4V meshes fabricated by electron beam melting. Journal of the Mechanical Behavior of Biomedical Materials 59, 251-264. Zhou, J., Soboyejo, W.O., 2004. Compression–compression fatigue of open cell aluminum foams: macro-/micro-mechanisms and the effects of heat treatment. Materials Science and Engineering: A 369, 23-35.

Fig. 1 Pore structure of porous titanium with 70% porosity fabricated by diffusion bond of type I titanium meshes: (a) Porous sample for mechanical test; (b) Pore structure in the out-of-plane direction; (c) Mesh hinge formed during diffusion bonding of connected mesh wires; (d) Pore structure in the in-plane direction. Fig. 2 (a) XRD patterns of titanium mesh and porous titanium; (b) Microstructure of porous titanium showing fine equiaxed α grains and twins. Fig. 3 Quasi-static compressive stress-strain curves of porous titanium with different porosity fabricated by type I titanium meshes. The insert graph represents Ti-70-I sample at 45% compressive strain. Fig. 4 Strain at maximum fatigue stress (εmax) plotted as a function of the fatigue cycle (N) for Ti-70-I sample tested at several values of maximum fatigue stress (σmax). Fig. 5 Relationship between strain per cycle (dεmax/dN) and fatigue number (N) for Ti-70-I sample tested at different maximum fatigue stress Fig. 6 The S-N curves of porous titanium with different porosity and fabricated by 29

types I meshes. (a) Based on the absolute maximum fatigue stress (σmax). (b) Based on the normalized fatigue strength (σmax/σy). Fig. 7 The S-N curves of porous titanium with 70% porosity and fabricated by different types of meshes. (a) Based on the absolute maximum fatigue stress (σmax). (b) Based on the normalized fatigue strength (σmax/σy). Fig. 8 Cyclic stress-strain loops of porous titanium with different porosity: (a) 50% porosity; (b) 70% porosity. (c) Schematic drawing of calculation of fatigue ratcheting strain and fatigue damage according to cyclic stress-strain loops. Fig. 9 SEM images of Ti-60-I samples at different fatigue cycles during tests: (a) before fatigue test; (b) N=5×103; (c) Failed sample (N=1.2×104) showing formation of collapse band; (d) SEM image showing the formation of fatigue crack in the mesh hinge. Fig. 10 Fatigue ratcheting strain and fatigue damage strain of porous titanium with different porosity: (a) 50% porosity; (b) 70% porosity. Fig. 11 Relationship between strain per cycle in stage II ((dεmax/dN)II) and normalized fatigue strength for porous titanium with different porosity and fabricated by different types of meshes.

Table 1 Pore size and wire diameter of three types of titanium meshes. Type

Pore size, L (μm)

Wire diameter, D (μm)

30

I

400±8

80±3

II

650±13

200±7

III

900±17

200±8

Table 2 Pore structure and quasi-static compressive properties of porous titanium fabricated by diffusion bonding of titanium meshes.

Sample

Mesh type

Average pore size

σy

E

(μm)

(MPa)

(GPa)

Porosity

Ti-70-I

I

69.4%

278

22.3±1.4

1.51±0.06

Ti-60-I

I

61.1%

227

35.9±2.4

2.09±0.15

Ti-50-I

I

50.8%

186

68.1±2.7

5.51±0.22

Ti-70-II

II

70.5%

495

52.5±1.6

2.34±0.14

Ti-70-III

III

70.1%

623

27.1±1.4

1.66±0.12

Trabecular bone (distal femur)

-

-

-

~2-70

~0.01-3

Table 3 Normalized fatigue strength of solid/porous-coated/porous titanium and Ti6Al4V alloys. Normalized fatigue Sample

Fabrication method

Microstructure

strength

Ref.

(N=106) Porous Titanium

Diffusion bonding

Fine equiaxed 31

0.5-0.55

Present work

~0.2 (surface Janeček et al., Solid Ti6Al4V alloy

-

Bi-modal

electro-eroded) 2011 ~0.6 (surface polished)

Porous-coated

Coarse/fine Powder sintering

Ti6Al4V alloy Porous Titanium

~0.15-0.2

Cook et al., 1988

0.3

Asaoka et al., 1985

acicular Powder sintering

-

Wauthle et al., Porous Titanium

Selective laser melting

-

0.32-0.5 2015

Porous Ti6Al4V alloy

Powder sintering

Lamellar

0.1-0.3

Yan et al., 2013

Acicular α’

0.15-0.25

Hrabe et al., 2011

Selective electron Porous Ti6Al4V alloy beam melting Amin Yavari et al., Porous Ti6Al4V alloy

Selective laser melting

Acicular α’

<0.2 2013

Fig. 1

32

Fig. 2

Fig. 3

33

Fig. 4

Fig. 5

34

Fig. 6

Fig. 7

35

Fig. 8

Fig. 9

Fig. 10

36

Fig. 11

37