Evaluation of near-threshold fatigue crack propagation in Ti-6 Al-4 V Alloy with harmonic structure created by Mechanical Milling and Spark Plasma Sintering

Titanium alloy (Ti-6Al-4V) having a bimodal “harmonic structure”, which consists of coarsegrained structure surrounded by a network structure of fine grains, was fabricated by mechanical milling (MM) and spark plasma sintering (SPS) to achieve high strength and good plasticity. The aim of this study is to investigate the near-threshold fatigue crack propagation in Ti-6Al-4V alloy with harmonic structure. Ti-6Al-4V alloy powders were mechanically milled in a planetary ball mill to create fine grains at powder’s surface and the MM-processed powders were consolidated by SPS. K-decreasing fatigue crack propagation tests were conducted using the DC(T) specimen (ASTM standard) with harmonic structure under the stress ratios, R, from 0.1 to 0.8 in ambient laboratory atmosphere. After testing, fracture surfaces were observed using scanning electron microscope (SEM), and crack profiles were analyzed using electron backscatter diffraction (EBSD) to discuss the mechanism of fatigue crack propagation. Threshold stress intensity range, Kth, of the material with harmonic structure decreased with stress ratio, R, whereas the effective stress intensity range, Keff, showed constant value for R lower than 0.5. This result indicates that the influence of the stress ratio, R, on Kth of Ti6Al-4V with harmonic structure can be concluded to be that on crack closure. Compared to the compact prepared from as-received powders with coarse acicular microstructure, Kth value of the material with harmonic structure was low. This was because the closure stress intensity, Kcl, in the material with harmonic structure was lower than that of the coarse-grained material due to the existence of fine grains. In addition, the effects of the grain size on the fatigue crack propagation behaviors of Ti-6Al-4V alloy were investigated for the bulk homogeneous material. The effects of the stress ratio and the grain size on the fatigue crack propagation of the material with harmonic structure were quantified.


INTRODUCTION
i-6Al-4V has been widely used for structural applications such as bio-implants and aerospace components due to its high specific strength and excellent corrosion resistance.Recently, improving mechanical properties of materials are required to increase structural reliability and reduce the size and weight of various components.Since mechanical properties of metallic materials are determined by their microstructural factors, the grain-refinement process is effective to improve their yield strength [1,2] and fatigue strength.However, a homogeneous fine-grained structure generally leads to decrease the ductility of materials due to their plastic instability.Previous investigations have reported the microstructural design which improves both of strength and ductility of materials [3][4][5][6].Wang et al. [3] reported that pure copper with a bimodal grain size distribution created by a thermomechanical treatment exhibited stable tensile deformation leading to a high tensile ductility.The author's group [7][8][9][10][11][12][13] has developed an exquisite microstructural design, called "harmonic structure", which consists of coarse-grained structure surrounded by a network structure of fine grains.In the previous studies, metallic materials with harmonic structure, such as pure copper [7], stainless steel [8][9][10], Co-Cr-Mo alloy [11], commercially pure titanium [12] and Ti-6Al-4V alloy [13,14] exhibited high strength and high ductility compared to their homogeneous counterparts.The authors have focused on the fatigue properties of the Ti-6Al-4V alloy with harmonic structure and reported that a fatigue crack was initiated from the coarse-grained structure in the harmonic structure in 4-points bending [14].However, fatigue crack growth changes depending on the stress ratio and grain size of materials [15][16][17] so that the fatigue crack propagation of the material with a bimodal harmonic structure should be examined to achieve the practical use of it.The present work deals with the evaluation of the near-threshold fatigue crack propagation of the Ti-6Al-4V alloy with a bimodal harmonic structure, which exhibits superior mechanical properties.Furthermore, the effects of the stress ratio and the grain size on the fatigue crack propagation of the material with harmonic structure were investigated on the basis of the crack closure concept, and its mechanism is discussed from viewpoints of fractography and crystallography.

Material
he material used in the present study was a Ti-6Al-4V alloy with the chemical composition shown in Tab. 1.This Ti-6Al-4V powder (186 m diameter) was produced using the plasma rotating electrode process (PREP).The powders were mechanically milled (MM) in a Fritch P-5 planetary ball mill with tungsten carbide vial and SUJ2 steel balls in the argon gas atmosphere at room temperature.Mechanical milling was performed at a rotational speed of 200 rpm for 90 ks under the condition of the ball-to-powder mass ratio 1.8 : 1.After mechanical milling, the powders were consolidated by a spark plasma sintering (SPS) at 1123 K for 1.8 ks under vacuum and 50 MPa applied stress using a graphite die with 25 mm internal diameters (Harmonic series).In addition, the compact prepared from the as-received initial (IP) powders were also prepared as a coarse-grained material (IP series).The Harmonic series exhibits higher strength and ductility compared to the IP series as shown in Tab. 2 [13].Fig. 1 shows the image quality (IQ) maps obtained by EBSD for the (a) IP and (b) Harmonic series [14].The IP series has a coarse acicular microstructure, whereas the Harmonic series two different microstructures; fine-grained and coarsegrained structures.The fine-grained structure formed a network structure and the coarse-grained structure was surrounded by the fine-grained structure network.Minimum grain size in the Harmonic is about 1.

Fatigue testing
The specimen used in the present study was the disk-shaped compact DC(T) specimen (2 mm thick, 25.2 mm wide).The sintered compacts (7.5 mm thickness, 25.2 mm wide) were cut to about 2.5 mm thickness and machined into the specimen.Then, specimen sides were polished with emery papers (#80 to #4000) and mirror-finished using SiO 2 .Fig. 2 shows the schematic illustration showing the specimen preparations.Fatigue crack propagation tests were conducted in an electro-dynamic fatigue testing machine under the condition of five values of the stress ratio, R, ranging from 0.1 to 0.8.To approach the threshold, K-decreasing tests were conducted under the constant-R loading regimen.Specimens were first fatigue pre-cracked for a minimum of 1 mm from the notch tip.The frequency of stress cycling was 30 Hz and the tests were carried out in ambient laboratory atmosphere.The value of the fatigue threshold, K th , was defined as the maximum value under a crack growth rate of 10 -11 m/cycle.Crack lengths were monitored by unloading elastic compliance method [18].The magnitude of crack closure was also monitored; closure stress intensity, Kcl, was obtained from the closure load, Pcl.Based on such measurements, an effective stress intensity range, K eff = K max -K cl , was estimated.Where K max is the maximum value of stress intensity factor.

Microscopic observations
After testing, fracture surfaces were observed using scanning electron microscope (SEM) and crack profiles were observed and analyzed using electron backscatter diffraction (EBSD).

Crack propagation behavior
he relation of the crack growth rate, da/dN, against the stress intensity range, K, is shown in Fig. 3 for the IP and Harmonic series.In each series, the threshold stress intensity range, Kth, decreased and crack growth rate, da/dN, increased at a given applied K value with increasing stress ratio, R. Furthermore, in the Harmonic series, crack growth rates were constantly higher at comparable K levels and thresholds were lower at comparable stress ratios compared to the IP series.Fig. 4 shows the relationship between Kth and R for each series.The value of Kth tended to be decreased approximately linearly with increasing R and the K th value of the IP series was higher than that of the Harmonic series at comparable stress ratios.The relation between Kth and R in the IP and Harmonic series are expressed as Eqs.( 1) and (2), respectively.

Crack closure
The role of stress ratio at near-threshold levels is generally attributed to crack closure [17].Fig. 5 shows the relationship between da/dN and Keff.In each series, the value of Keff tended to normalize the stress ratio onto a single curve near threshold under R = 0.5.This result indicates that the effect of the stress ratio on the K th disappears.However, when R is greater than 0.5, Kth value still decreased with increasing stress ratio, R. Same tendency was observed in the previous IP series Harmonic series study [16].Ritchie et al. [16] has proposed the superposition model that the measured fatigue crack growth rate results from contributions from both mechanical fatigue cracking and sustain load cracking at high stress ratio.
To examine the magnitude of crack closure, the ratio of closure stress intensity factor, K cl , to maximum stress intensity factor, Kmax, was calculated.Fig. 6 shows the relationship between Kcl/Kmax and Keff under various stress ratios.In this figure, K cl /K max = R when crack closure does not occur.At low stress ratios, the value of K cl /K max tended to be decreased with increasing Keff and then was saturated to the constant value which is equal to stress ratio, whereas Kcl/Kmax showed constant value independent of K eff at high stress ratios.These results mean that crack closure occurs near the threshold at low stress ratios.Moreover, the Kcl/Kmax value of the Harmonic series was lower than that of the IP series at low stress ratios (0.1, 0.3).Especially, at stress ratio of 0.5, crack closure occurred in the IP series, but the Harmonic series showed constant K cl /K max value.Consequently, the harmonic structure reduced the K cl value of Ti-6Al-4V alloy, resulting in decreasing the value of Kth.

Effects of grain size on the fatigue crack propagation of Ti-6Al-4V alloy
To clarify the reason for decreasing Kth values of Ti-6Al-4V alloy by creating a harmonic structure as mentioned in the previous section, effects of grain size on the fatigue crack propagation were investigated for the bulk homogeneous material.Fig. 7 shows the relation of the crack growth rate, da/dN (R = 0.1), against the stress intensity range, K, in the bulk homogeneous Ti-6Al-4V alloys with different grain size [19].The K th value of the coarse-grained bulk homogeneous material (d =5.7 m) was high compared to the fine-grained one (d =2.2 m).In contrast, as results of calculating the effective threshold stress intensity range, K eff,th , the effect of grain size on the value of K th disappears.The values of Kcl of the bulk homogeneous Ti-6Al-4V alloys are shown in Fig. 8.The Kcl value of the coarse-grained bulk material (d =5.7 m) was higher than that of the fine-grained one (d =2.2 m).In the case of the fine-grained material (d =2.2 m), the value of K cl decreased with increasing K and was saturated to approximately 0.6 MPam 1/2 .The grain size strongly influences the behaviors of fatigue crack propagation and crack closure of Ti-6Al-4V alloy; the fine grains reduce the value of Kcl.

Fractography and crack profiles
The role of crack closure at near-threshold levels is generally attributed to the roughness-induced mechanism [20].To characterize the surface topography of fracture surfaces, the three dimensional axonometric drawing was produced.
Examples of axonometric drawings for the (a) IP and (b) Harmonic series are shown in Fig. 9.The surface topography of the IP series was rougher compared to the Harmonic series.Nalla et al. [15] has reported that the structure sensitivity of fatigue crack growth changes depending on the microstructure of Ti-6Al-4V alloy.Moreover, the coarser microstructure showed a more tortuous and deflected crack path than the finer microstructure, resulting in increasing the fatigue crack growth resistance due to the roughness-induced crack closure.The present study exhibited the same trend of the previous study [15].Fig. 10 shows the inverse pole figure (IPF) maps obtained by EBSD at specimen's surface.In this figure, crack profiles are represented by black lines.In Fig. 10(a), crack profile of the Harmonic series showed very smooth and a fatigue crack was arrested at the coarse-grained structure, represented by the arrow mark.However, in some areas, a crack profile was influenced by the microstructure of the Harmonic series.Fig. 10(b) showed that a fatigue crack avoided propagating the coarse-grained structure of the Harmonic series, and propagated across the fine-grained structure.where d is an average grain size of the bulk homogeneous material (m).The gradient obtained from the data of R = 0.1 was higher than that of the R = 0.5.This result means that effect of grain size on the value of K th is remarkable at low stress ratio.Furthermore, the K th value of the Harmonic series was estimated.Fig. 12 shows a schematic diagram explaining the estimation of threshold stress intensity range, Kth, of the Harmonic series based on the data of the bulk homogeneous materials.Assuming that the threshold stress intensity range decreases linearly with decreasing the square root of the grain size, we obtain the estimated Kth by substituting the grain size of fine-grained structure, dmin, of the Harmonic series into the Eqs.( 3) and ( 4) for each R: Estimated values of Kth of the Harmonic series are shown in Tab. 3. Comparing to values of Kth estimated and obtained by tests for each R, there were no obvious differences.This result indicates that the value ofK th of the Harmonic series can be estimated based on the fatigue crack propagation of the bulk homogeneous material and was determined by the crack propagation behavior of the fine-grained structure in the harmonic structure.Consequently, a bimodal harmonic structure reduced the fatigue crack propagation resistance of Ti-6Al-4V alloy due to the existence of the fine-grained structure, which decreased the closure intensity factor, Kcl.However, there were little differences in K eff,th values between the Harmonic series and the IP series so that additional mechanisms and factors may exist.This reason should be clarified in future works.

2 )Figure 3 :
Figure 3: Relationship between crack growth rate and stress intensity range for the (a) IP and (b) Harmonic series.

Figure 4 :
Figure 4: Relationship between threshold stress intensity range and stress ratio for the IP and Harmonic series.

Figure 5 :
Figure 5: Relationship between crack propagation rate and effective stress intensity range for the (a) IP and (b) Harmonic series.

Figure 6 :
Figure 6: Relationship between Kcl/Kmax and effective stress intensity range for the IP and Harmonic series.

Figure 7 :Figure 8 :
Figure 7: Relationship between crack growth rate and stress intensity range for the bulk specimen with homogeneous microstructure Figure 8: Relationship between crack closure intensity and stress intensity range for the bulk specimen with homogeneous microstructure.

Figure 10 :
Figure 10: Inverse pole figure (IPF) maps of the crack profiles in the Harmonic series ((a) R = 0.1 and (b) R = 0.5).Estimation of the threshold stress intensity range of the material with harmonic structureBased on these results obtained in the present study, one might expect that a fine-grained structure in the harmonic structure dominates the fatigue crack propagation of the Harmonic series.To quantify the effects of fine-grained structure on the fatigue crack propagation of Ti-6Al-4V alloy, the threshold values of K obtained from the bulk homogeneous materials are re-plotted against the square root of the grain size, d in Fig.11.For each R value, the value of Kth increased with square root of the grain size.The relation between K th and d in the bulk homogeneous material are expressed as Eqs.(3) and (4), respectively.Kth = 2.86 + 0.578d 1/2 : R = 0.1(3) Kth = 2.61 + 0.259d 1/2 : R = 0.5(4)

Figure 11 :
Figure 11: Relationship between threshold stress intensity range and grain size for the bulk specimen with homogeneous microstructure.

Figure 12 :Table 3 :
Figure 12: Schematic diagram explaining the estimation of threshold stress intensity range of the Harmonic series based on the data of the bulk specimen with homogeneous microstructure.