Fatigue Property of Additively Manufactured Ti-6Al-4V under Non-proportional Multiaxial Loading

Low cycle fatigue strength properties of additively manufactured Ti-6Al-4V alloy were experimentally investigated under proportional and non-proportional multiaxial loading. Fatigue tests have been conducted by means of hollow cylinder specimens with and without heat treatments, at room temperature in air. Fatigue tests with proportional loading represented by a push-pull strain path and nonproportional loading represented by a circle strain path were conducted, respectively. The fatigue lives of additively manufactured specimens were drastically reduced obviously by internal voids and defects in comparison with the specimens used in the previous study [1]. In addition, the defect size is measured, and the defect does not cause fatigue strength reduction above some size. The fracture surface was observed using SEM to investigate fracture mechanism of additively manufactured specimens under two types of strain path. Different fracture patterns are recognized for the two strain paths; however, both showed the retention of the crack propagation in spite of the presence of numerous defects. The crack propagation properties of the materials with numerous defects under non-proportional multiaxial loading were elucidated to increase the reliability of additive manufactured components.


Introduction
Additive manufacturing (AM) has enabled to fabricate complex geometry parts, to lighten weight, and to shorten processing time due to the creation of subsequent thin cross-sections of a component and represents one of the most innovative fabrication technologies in recent years [2][3][4]. However, AM has a lot of process parameters, and the process control is extremely di cult. Moreover, the defects and residual stresses are arisen by thermal expansion or thermal contraction in a manufacturing process [2][3][4][5][6][7][8]. Therefore, AM mostly is not recognized practicable because strength reliability of AM parts is inferior to traditional manufacturing technologies such as casting, forging and rolling in general [9][10].
Accordingly, to widen the applicability of AM parts, fatigue strength properties of additively manufactured components need to be accurately understood.
The titanium alloy Ti-6Al-4V is currently employed, mostly in the aeronautical and medical elds, because it has the properties of high strength, excellent thermal and corrosion resistance and biocompatibility. On the other hand, material cost is expensive, and the machinability is worse. From the above, Ti-6Al-4V is considered to be a good material for AM [11]. Uniaxial high cycle fatigue tests for AM Ti-6Al-4V have been widely analyzed; however the research on low cycle fatigue strength under non-proportional multiaxial loading in which principal direction of stress or strain changes in a cycle has not yet been reported [12][13][14][15][16][17][18].
In this study, low cycle fatigue tests under non-proportional multiaxial loading were conducted by means of additively manufactured specimen. In addition, the fracture mechanism of AM components with defects was investigated by the fracture surface observation. Then, the factor of the decrease in fatigue strength was discussed focusing on internal defects, that have hardly been clari ed in the previous study [1].

Laser Powder Bed Fusion
The laser powder bed fusion (L-PBF) is the most employed technique for fabrication of additively manufactured components. The steps of the fabrication technique are represented schematically in Figure 1 [19], and manufacturing processes are shown below: 1. Layer of powdered material is applied to building platform; 2. Powdered material is solidi ed into a cross-section of a 3D model with laser; 3.
Building platform is lowered. The next layer of powder is applied; 4. The process repeats itself until the creation of the part is complete; 5. The part is removed from the unused powder.
As the advantages, L-PBF can economically fabricate ideal parts with complex geometries in a rapid design to manufacturing cycle. However, as the disadvantages, the components fabricated by L-PBF have voids, residual stresses and surface roughness due to the in uence of different process parameters. For the improvement, performing HIP and sandpapering can remove voids and surface roughness, respectively. Thus, fatigue strength of AM components can be improved. Figure 2 and Figure 3 show a schematic view and a photo of the electrical servo-controlled tension torsion fatigue testing machine. The testing machine is equipped with 2 types of cylinders for axial and torsion loading, and it enables to generate non-proportional loading. The maximum axial load is 50 kN, and maximum torque is 500 Nm. The load cell was equipped for load measurement, and the extensometer which has equipped the eddy current sensor was employed to detect axial strain and shear strain, simultaneously. Figure 4 shows a schematic view of the extensometer attached onto the specimen.

Material and Specimen
The material tested was titanium alloy Ti-6Al-4V. Figure 5 show the shape and dimensions with no machining process and the resultant hollow cylinder specimen which has a 9 mm inner diameter, an 11 mm outer diameter, and 12 mm parallel part. The types of specimens were with (HT) and without (NHT) heat treatment to remove the residual stresses. The layer was laminated perpendicular to the longitudinal direction of the specimen. The specimens were polished with an alumina powder solution (particle size 1 μm) on the external surface and with a sand paper with #2000 grit on the internal surface to avoid the in uence of surface roughness on fatigue life. A parallel part of the specimens has numerous defects; However, the number of defects differs for each of them.

Test Condition
The testing machine that can perform tensile and torsion tests was used to apply both proportional and non-proportional loading paths to the specimens. The proportional loading path is represented by push-pull strain path (PP), whereas the non-proportional loading path is represented by circle strain path (CI) in which axial and shear strain have 90 degrees-out-of-phase. In the CI, the intensity of the von Mises' equivalent strain was constant while the direction of the principal strain changes during the cycle. The axial and shear strain were measured using an extensometer with a 12 mm strain gage length connected to the specimens. The applied strains are visualized in Figure 6. The test temperature was room temperature in air, and strain rate ε eq = 0.2 %/s was applied. Fatigue tests were conducted under strain control. Number of cycles to failure (failure life) was de ned when axial and shear stress amplitude  Figure 8 shows the generated hysteresis loops for 0.5N f and the maximum stress behavior during the tests in each test condition.
The results (Fig. 7) of fatigue tests under PP clearly show that the data scatter is not so drastic and were within the factor of 3 bands. Moreover, they were no difference between heat treatment and no heat treatment. It is considered the temperature for heat treatment was not su cient to remove residual stresses. However, the data of PP HT (Δε eq = 1.3 %) exhibited lower failure lives and out of the factor of 3 bands. In Fig. 8 (a), (b) and (e), the hysteresis loops and the maximum stress amplitude at Δε eq = 1.3 % were compared. The hysteresis loops indicated the almost same elastic deformation. The maximum stress amplitude for NHT remains almost constants. Then probably, the crack initiated from the vicinity of N f , and the failure occurred very quickly after the crack initiation. On the other hand, for HT, the maximum stress amplitude decreased instantly from around 0.3N f . Therefore, the crack was considered to initiate from 0.3N f , and after some crack propagation, the failure took place.
Failure life (Fig. 7) under CI was reduced compared to PP resulting in 10% decrease in fatigue life. The scattering of data was also very small; however, it cannot be con rmed due to limited data (the presence of the only one data of CI NHT (Δε eq = 0.5%)), the reduction in failure life for NHT cannot be seen. For the other material such as stainless steel and carbon steel, in case of low strain level, the failure life is the almost same as PP, but it is not clear for this study due to limited data. In Fig. 8 (c), (d) and (f), the hysteresis loops and the maximum stress amplitude of Δε eq = 0.5% were compared. In case of low strain level, the hysteresis loops also exhibited the almost same elastic deformation. The maximum stress amplitude for two data was similar in deformation behavior. Although the overload was seen in the data of HT, it is estimated that there is almost no effect because it could be adjusted in 10 cycles. Therefore, why this data shows the longer life than other data remains as question. The previous test results are also shown in Fig. 7 [1]. In the previous study data, failure lives were longer than that of this study. The specimens of the previous study were the same material (Ti-6Al-4V) but were fabricated with a different manufacturing condition. Based on the above-mentioned, the internal defects were investigated to quantify the size of defects. Figure 9 compares the internal defects between the previous study and this study. In the previous study, the small defects were observed inside, but in this study, the internal defects depend on the observation site. AM components have usually the defects inside, and fatigue strength of the material depends on size and density of the defect; however, the defects size does not affect the fatigue life above a certain size because the results of fatigue tests (Fig. 7) shows a clear correlation regardless of various defect size. It is necessary to investigate the dependence of fatigue strength reduction on defect size. Figure 10 shows the pictures of fracture surface after fatigue tests, and the observation surface is perpendicular to the specimen axis. It is di cult for main crack initiation site to be analyzed as for specimens of this study. The cracks were initiated from the boundary of partly melted defects regardless of strain range and strain paths, and the stress concentration in the defects causes premature rupture in comparison to the results which were obtained with the same material [1]. From Figure 10 (a2) and (b2), the crack propagation patterns were divided into the rst phase (from the crack initiation site to the crack middle site) and the second phase (form the crack middle site to the crack end site) during test. In the rst phase of the test, the propagation path was different due to strain paths, and it is possible that high stress existed evidenced by rougher fatigue fracture surfaces. In PP, the crack propagated simply, but in the CI, it became complicated. Basically, due to the change of the principal direction of stress and strain during the cycle in CI, maximum shear stress plane is changed in the cycle. Thus, there is a possibility for the crack to initiate and propagate to many directions. In the second phase of the test, fatigue fracture surfaces were with the similar pattern, and the crack propagation seems to be suppressed. It is estimated that a local non-propagating effect under multiaxial stress took place. Thus, it is possible that the change of the crack propagation pattern in each phase of the test is a characteristic of AM components with numerous defects, and it is noticeable under non-proportional multiaxial loading.

Fracture Surface
From this study, the fatigue strength is absolutely inferior to that of the previous study and traditionally manufactured components; however, there is a possibility that AM technology is used for the mechanical structure because the non-propagating effect of cracks was veri ed under non-proportional multiaxial loading.

Conclusions
(1) The failure lives under PP and CI were almost not affected by heat treatment performed to remove residual stresses due to insu cient temperature. In PP, the data scatter is not so drastic and almost all data were within the factor of 3 bands. In CI, although the scattering of data was also very small, failure life under CI was reduced compared with PP resulting in 10% decrease in failure life.
(2) The small defects were observed inside in previous study, and the defects were larger in this study. Stress concentration at the boundary of defects was generated, and the results of fatigue test shows a clear correlation, so the size of defects above a certain size does not affect the failure life.
(3) Regardless of strain range and strain paths, the cracks were initiated from the boundary of partially melted defects, indicating that stress concentration in the defect caused premature rupture compared to the results obtained with the same material.
(4) In the rst phase of the test, the propagation path was different due to strain paths; however, in the second phase of the test, fatigue fracture surfaces were with the similar pattern, and the crack propagation seems to be suppressed. Figure 3 Photo picture of fatigue testing machine State of lever type extensometer during fatigue test