1. Introduction
Metal component additive manufacturing (AM) is the general designation for a series of advanced manufacturing processes based on a three-dimensional digital model that are used to fabricate metal components by melting and depositing metal powders or wires layer upon layer. AM can be divided into two main categories according to the different supply methods of the raw metal materials: powder bed fusion (PBF) and direct energy deposition (DED). PBF processes, such as selective laser melting (SLM), use thermal energy to selectively fuse regions of a powder bed, while DED processes use focused thermal energy to fuse materials by melting during deposition [
1]. DED methods, including laser metal deposition (LMD), are more suitable for fabricating large titanium structural components than PBF processes [
2,
3,
4,
5,
6]. Large titanium structural components have been successfully fabricated by many researchers and research institutions by using LMD and have been widely used as load-bearing structures in aeronautical engineering [
7,
8].
Aeronautical structures experience repeat loads over their long periods of service, and fatigue is one of the main damage phenomena in aerospace metallic structures [
9]. Therefore, the fatigue behavior of LMD titanium components must be further elucidated, and fatigue performance characterization methods must be established. The major factors causing the fatigue failure of LMD and other AM titanium alloys include the microstructure, internal defects, and residual stresses [
10].
The specific thermodynamic process used during manufacturing, i.e., cyclic heating and rapid cooling, results in the unique microstructure of the LMD titanium alloy, which includes relatively large columnar grains, multiple melt layers between the processing layers and unique microstructures [
11]. These specific characteristics in the microstructures may have some influence on the fatigue performance of the parts [
12,
13,
14,
15]. Wang et al. [
12] studied the fatigue strength of LMD TC18(
Ti-5Al-5Mo-5V-1Cr-1Fe) titanium alloy and determined that its strength is much lower than that of wrought TC18 titanium alloy. Sterling et al. [
13] reported that the fatigue lives of LMD Ti-6Al-4V specimens, including as-built and annealed specimens, are shorter than those of wrought specimens. Zhai et al. [
14,
15] also determined that LMD Ti-6Al-4V has a lower fatigue crack growth threshold than wrought Ti-6Al-4V. Studies have also been conducted on the fatigue mechanism and the effects of the microstructures of titanium alloys manufactured by LMD and other AM processes. The studies of Rafi et al. [
16] and Zhai [
13] et al. showed that, compared to EBM Ti-6Al-4V, LMD and SLM Ti-6Al-4V parts have a higher fatigue strength but lower fatigue toughness, and this phenomenon may result from the presence of fine α’ martensite.
Internal defects are another major factor affecting the fatigue performance. Such defects introduce a stress concentration around them and easily become a nucleation site of crack [
17]. Biswas et al. [
18] and Li et al. [
19] revealed that the internal defects, such as lack of fusion (LOF) and pores, are likely to become nucleation sites for shear bands and micro-cracks. The presence of internal defects may also lead to mixed failure behaviors that were observed in many studies [
12,
13,
17,
20,
21,
22,
23,
24,
25,
26], inconsistent with the case of traditionally manufactured titanium alloy. The crack may initiate from both surface and internal defects of specimens. The influences of different types of defects are also investigated. Akerfeldt et al. [
20] stated that the internal LOF is more likely to result in cracks than pores, and this phenomenon is particularly significant in specimens with a force directed parallel to the powder deposition direction. Prabhu et al. [
21] showed that unmelted particles in LMD titanium alloy specimens have a significant effect on the fatigue life, while the pores have a minimal effect. Leuders et al. [
22] considered that the pores within specimens have a drastic effect on the fatigue behavior of SLM titanium alloys in the high-cycle-fatigue (HCF) regime.
The location and size of internal defects also affect the fatigue properties to a great extent. Many investigations have shown that the nearer pores are to the surface, the shorter the fatigue life [
13,
23,
24,
25,
26]. This phenomenon can be partly explained by Xu et al.’s [
27] study. The cross-sectional area of a defect normal to the applied stress has a large effect on the fatigue life properties [
28]. Several studies reported that fatigue failure occurs first at the largest defect, so there is a shorter fatigue life for AM specimens in the presence of larger internal defects [
13,
23,
24,
25]. However, He et al. [
26] indicated a different conclusion that a larger pore may lead to a longer fatigue life when the pores have similar distances to the surface.
Residual stresses are also a direct cause of crack initiation that can affect the fatigue properties of AM specimens. AM processes, particularly LMD and other laser-based AM processes, are prone to induce significant residual stresses due to their large inherent temperature gradients [
29]. Different process parameters and deposition strategies may lead to different residual stress distributions. Tensile residual stresses are always distributed at the surface and near-surface zone of as-built AM titanium alloy parts and may have a significant influence on the fatigue properties [
30]. Although the residual stress can be partly relieved by some heat treatment processes, it is hardly eliminated completely [
22,
31,
32,
33].
The fatigue behaviors of AM materials are usually complicated due to their unique microstructure, internal defects, and residual stress distributions. As a new manufacturing method, the fatigue life properties must be precisely described. The experimental techniques and description methods for
S-N curves have long been a concern [
34]. The
S-N curves of materials show the pre-conditions and inputs for anti-fatigue structure design. Fatigue life data always have significant variations, and the fatigue life under a specific stress level is closely related to the survival rate,
P. In many cases, especially for the reliability design of components, the relationships between the fatigue stress and life at different survival rates, namely, the
P-S-N curves, must be determined. The previously mentioned
S-N curve is the median fatigue life curve, i.e., the
P-S-N curve with a 50% survival rate. Scholars have conducted studies on the fatigue properties of AM materials in recent years, and the
P-S-N curves (
S-N curves) of different materials manufactured by several different AM processes have been tested [
35,
36,
37,
38,
39,
40]. Regulations and standards such as ASTM E739-10 [
41] and ISO 12107:2012 [
42] have been issued with test procedures and method descriptions for
P-S-N curves (
S-N curves) based on a lognormal distribution. However, the unique AM fabrication process leads to various failure behaviors, and the fatigue life of AM materials therefore displays significantly greater uncertainty and variation than that of their conventionally manufactured counterparts [
26,
40,
43,
44]. The mixed failure behaviors and large variation make the existing description methods unable to accurately describe the fatigue properties of AM materials, and the following problems may occur when the existing description method is used to determine the fatigue
P-S-N curves of AM materials:
(i) Because of the complex fatigue failure behaviors, the fatigue life distribution of AM materials may be different from that of traditional materials, and the traditional distribution model thus cannot accurately describe the fatigue life variation under specific stress levels.
(ii) Due to the large variation in the fatigue life, the reliability life in the high-reliability region will be very short using the traditional P-S-N curve model to describe the fatigue properties of AM materials.
(iii) The large fatigue life variation requires a larger number of fatigue test specimens to determine the P-S-N curve, which will inevitably increase the time and economic cost of the process.
In this paper, two sets of fatigue tests under peak stresses of 720 and 760 MPa were conducted, and fatigue life data under three different stress levels were obtained, including the data under 800 MPa published in [
26]. Sufficient data, no fewer than 15 specimens under each stress level, were used to develop and prove the conclusions. Compared with the existing research, especially the previous study ([
26]), there are four main innovations and contributions in this paper:
(i) This paper examines more data (at least 15 specimens under each stress level) than in previous studies, which generally reported the data of 5–10 specimens under the same stress [
23,
26,
35,
37,
38,
39,
40,
45]; the data herein were used to illustrate the mixed failure behavior and fatigue life properties.
(ii) A P-S-N curve description method of the LMD Ti-6.5Al-2Zr-1Mo-1V titanium alloy was established based on a bimodal lognormal distribution (BLG).
(iii) Considering the disadvantages of the parameter estimation method based on rank distribution theory developed in [
26], especially the weakness in robustness, the maximum likelihood estimation (MLE) method was used to estimate the parameters, and the Newton–Raphson algorithm was used to solve the equations.
(iv) Compared to previous studies [
13,
23,
24,
25,
26], the mixed failure behavior and the influence of internal pores on the fatigue life of LMD Ti-6.5Al-2Zr-1Mo-1V specimens were discussed in more detail, and the conclusion regarding the influence of the size and location of the pore defects on the fatigue life was corrected by analyzing the greater amount of data in this paper.
7. Conclusions and Recommendations for Further Work
In this paper, fatigue tests of standard smooth Ti-6.5Al-2Zr-1Mo-1V specimens were conducted, and abundant data were obtained. The mixed failure behavior and the influence of internal pores on the fatigue life of LMD Ti-6.5Al-2Zr-1Mo-1V specimens were discussed in detail, and a novel P-S-N curve method based on a BLG was established to describe the fatigue properties of LMD titanium alloys. Through the method, the fatigue life at a high reliability value is increased. This result may promote the application of LMD titanium alloys in engineering and can significantly improve the structural design flexibility and reduce the structure weight. From the test results and analyses, the following conclusions can be drawn:
(i) Mixed failure behaviors of Ti-6.5Al-2Zr-1Mo-1V titanium alloy, with cracks initiating from both internal pores and the surface or subsurface, are observed in the medium- and high-cycle fatigue regimes. These mixed failure behaviors may be an intrinsic characteristic of LMD titanium alloys under CA stress and independent of the stress level. However, the proportion of SII in the overall population may be related to the stress level: the proportion decreases with an increase in the stress level.
(ii) For the internal pore failure model, there is no significant positive or negative correlation between the fatigue life and the size and location of the pore defects.
(iii) The BLG is reasonable for the fatigue life description in the medium- and high-cycle fatigue regimes of LMD titanium alloys. The Newton–Raphson algorithm was used to estimate the BLG parameters based on the MLE method, and the Basquin equation can be used to describe the P-S-N curve of the LMD titanium alloy.
There are also some recommendations for further investigations:
(i) In-depth research on the relationship between the proportion of SII and the stress level is needed. This phenomenon may be caused by the combined influences of the microstructure, the types and geometric parameters of the defects, and the local stress state.
(ii) The influence of the sizes and locations of the pore defects on the fatigue life requires further research to arrive at a more general conclusion.