Data-driven evaluation of fatigue performance of additive manufactured parts using miniature specimens

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1138

2. Size effect on fatigue properties for conventionally-fabricated metallic materials. . . . . . .1138

2.1. Fatigue data collection of pure Cu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1138

2.2. Fatigue data collection of engineering alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139

2.3. General trends and dominated factors for fatigue size effect . . . . . . . . . . . . . . . . . . . . . .1140

3. Influencing factors on evaluating fatigue properties of AM parts using miniature specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1141

3.1. Effect of surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1141

3.2. Effect of process-induced internal defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142

3.3. Effect of build thickness of AM parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142

4. Recent efforts to evaluate fatigue performance of AM parts using miniature specimens and resultant new challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142

4.1. Tensile properties of AM parts using miniature specimens . . . . . . . . . . . . . . . . . . . . . . .1143

4.2. New testing methods to evaluate fatigue performance using miniature specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1143

4.3. Building confidence to evaluate fatigue performance of AM parts using miniature specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1143

4.4. Application of machine learning to fatigue properties prediction from miniature specimen tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1144

5. Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144

5.1. Data collection through a large number of miniature specimen-based experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144

5.2. Data augmentation for miniature specimen tests via machine learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144

5.3. Data analysis and model establishment for miniature specimen tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144

6.Summary . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1145

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . 1146

1. Introduction

Metal additive manufacturing (AM) has gathered tremendous attention from multiple industries, including aerospace, automotive and medical devices, which is able to fabricate geometrically complex parts in near-net-shape form on demand in days rather than months [1,2]. Although General Electric (GE) company recently announced that it has developed a laser-printed fuel nozzle with 25% weight reduction and part count reduction from 18 to 1, as compared with traditional counterparts, and would be installed in the next-generation LEAP engines, the mechanical behavior and overall trustworthiness of AM parts are not yet fully documented due to strong material anisotropy and unavoidable processing-induced defects [3]. In addition, as the metal AM technologies is becoming mature towards industrial application, especially the fracture-critical components, the need for a comprehensive understanding of process-structure-properties-performance (PSPP) relationships, qualification and certification of metallic AM parts in terms of fatigue performance as well as its dependence on process variables becomes even more urgent [4].

It is well known that any change in the AM processing parameters, e.g. laser energy density, building orientation, scanning strategy in selective laser melting (SLM), build thickness and build orientation can significantly affect the thermal history, which ultimately results in the location-specific defect distribution and microstructure heterogeneities as well as anisotropic mechanical properties [5,6]. Traditional material definitions assume that mechanical properties of specimens excised from a wide range of spatial locations within manufactured components are uniform, all the results are considered as one population. In fact, such practice neglects the process path- and location-specific microstructure variables and generates scatter to the population. This makes the design allowable be conservative, leaving substantial margin or material capability underutilized [7]. In addition, the mechanical properties of the topologically optimized AM parts with a gradient in the build thickness can hardly be evaluated by the standard specimens due to the dimension restriction [8]. According to the draft of the new NASA standard for the qualification of AM parts for spaceflight, all the service components need to be fabricated together with a series of witness specimens for mechanical evaluation, which aims at material control [8,9]. However, it is unlikely that a complex part could be validated with a few tests since the effective correspondence between theses witness specimens and the final part must be established and confirmed. Therefore, one of the effective approaches is to establish a new mechanical testing standard on miniature specimens, which would be helpful in rapidly evaluating such build thickness-, location- and orientation-dependent mechanical properties of AM parts.

Recently, some efforts were devoted to developing the miniature specimen-based tensile testing methods [10], [11], [12], [13], [14] and extending these methods to evaluate tensile properties of AM parts [8,15]. However, some ongoing challenges still need to be addressed [4,16]. For example, the so-called ‘Size effect’ should be considered in the use of the miniature specimens when the specimen dimension scales down to a certain level [17]. Compared with the tensile properties, a major concern for AM parts in application is their fatigue properties. Whereas much less work is conducted to investigate the fatigue properties of miniature specimens of AM parts so far. Therefore, the establishment of a new fatigue testing method or even a standard related to miniature specimens would be of great significance and impact on the evaluation of fatigue performance of AM parts. Moreover, this new standard may have an extensive meaning that can be used for evaluating the residual life of in-service components, determining the performance of newly-developed nano-structured materials and local properties of weld joints and so on when only small volume of a material is available [18,19].

The motivation of this paper is to address reasons, necessities and potential strategies to correctly evaluate and qualify fatigue properties of the AM parts (if there is no special statement, AM parts refer to SLMed metal parts in this overview) with location-specific defects, microstructure heterogeneities as well as mechanical anisotropy using miniature specimen testing technique. Therefore, an outline of the paper is as follows. Section 2 firstly introduces the research progress in size effects on fatigue performance of a couple of conventionally-fabricated metals, such as pure Cu (one of the most representative and well-investigated polycrystalline metals), and two kinds of typical engineering alloys (CA6NM martensite stainless steel and Ti alloy) with the specimen thickness ranging from millimeter to dozens of micrometers. These data reported in literature were highlighted to summarize some general rules for size effects. Then, Section 3 switches to some influencing factors in evaluating the fatigue properties of AM parts including the defect-sensitive variables (surface roughness and process-induced defects) and the specimen thickness. Furthermore, Section 4 reports recent efforts to evaluate fatigue performance of AM parts using miniature specimens and resultant new challenges. In view of these new challenges, Section 5 presents an outlook for possible strategies to establish a data-driven evaluation workflow about the fatigue performance of AM parts using miniature specimens. Finally, Section 6 gives the main summary.

2. Size effect on fatigue properties for conventionally-fabricated metallic materials

In general, it has been recognized that the size effect was mainly related to the geometrical scale such as specimen thickness/diameter and the microstructural scale, such as grain or phase size in the material [20], [21], [22], [23], [24]. When taking account of the combined effect of the geometrical and the microstructrual scales, one would introduce an aspect ratio (t/d) of the specimen thickness or diameter (t) to the grain size (d), which exhibits a significant role in the size effect on mechanical properties when t and d values are in the same order [25]. In order to figure out possible trends and dominated factors for the size effect on fatigue properties of conventionally-fabricated metallic materials, fatigue data of a representative polycrystalline metal (Cu) as well as two kinds of engineering alloys (CA6NM martensite stainless steel and Ti alloy) with the specimen thickness ranging from millimeters to dozens of micrometers are summarized.

2.1. Fatigue data collection of pure Cu

Fig. 1(a) presents S-N curves of bulk Cu and Cu polycrystalline foils/wires as a function of the specimen thickness/wire specimen diameter ranging from 20 μm to 4 mm [26], [27], [28]. Fatigue strengths of the micrometer-scale Cu polycrystalline foils are higher than that of bulk Cu, and decrease with decreasing t in the range of 20-190 μm. Furthermore, the relationship between the specimen thickness and the low-cycle fatigue (LCF) and high-cycle fatigue (HCF) strengths (the total strain amplitude corresponding to fatigue life of 1 × 10⁴ and 1 × 10⁶ cycles, respectively) of all kinds of polycrystalline Cu specimens is presented in Fig. 1(b) [26], [27], [28], [29], [30], [31], [32]. When t>3 mm, the HCF strength of coarse grain (CG) Cu (0.078%) is lower than that of ultrafine grain (UFG) Cu (0.121%), but the LCF strength (0.3%) is higher than that of UFG Cu (0.241%). This result is reasonable because the HCF strength is known to be dominated by the strength of the material and the LCF strength is dominated by the ductility of the material. When 20 μm<t<190 μm, both the LCF and HCF strengths of all kinds of polycrystalline Cu, including the as-rolled Cu foils (t/d = 10-95), annealed Cu foils (t/d = 6-24) and Cu wires (t/d = 0.4-2.5) decrease with decreasing t (Fig. 1(b) and (c)). When 190 μm<t<2 mm, limited experimental data on the size effect of polycrystalline Cu specimens can be available, as shown in Fig. 1(b).

2.2. Fatigue data collection of engineering alloys

Fig. 2 presents the size effect on fatigue properties of a couple of engineering alloys with t ranging from 2.5 mm to about 40 μm [33,34]. Ma et al. [34] recently investigated the size effect on fatigue properties of the CA6NM martensite stainless steel with the specimen thickness ranging from 40 μm to 2.5 mm and found that the HCF strength was almost same as t > 230 um, and then reached a peak value at t = 100 μm, but then sharply decreased with decreasing t. Zhang et al. [33] also investigated the effect of specimen thickness on fatigue properties of the Ti alloy with t ranging from 100 μm to 2 mm and found the similar results (Fig. 2(b)). The fatigue strength kept constant until t scales down to 400 μm, but then increased with decreasing t. Furthermore, Dzugan et al. [18] investigated the effect of temperature on the size effect on LCF properties of four kinds of steels, including 34CrNiMo6, 30CrNiMrV9, 08CH18N10T and Custom465. It was found that the LCF properties of miniature specimens (the gauge diameter is 2 mm) were comparable with that of the standard specimens (the gauge diameter of 6-10 mm) even though at elevated temperature (798 K). From above, we can conclude that the size effect on fatigue properties of conventionally-fabricated alloys may only appear when t< 400-600 μm.

2.3. General trends and dominated factors for fatigue size effect

To obtain a deep insight into the mechanism for the size effect on fatigue properties, the normalized HCF strength (corresponding to 1 × 10⁶ cycles) and LCF strength (corresponding to 1 × 10⁴ cycles) of polycrystalline Cu, as a function of t are summarized in Fig. 3(a) and (b), respectively [1,26,[28], [29], [30], [31], [32],35,36]. The normalized fatigue strength can be expressed by:

σ_norm=(σ_max-σ) /(σ_max-σ_min) (1)

where σ_norm is the normalized fatigue strength, σ is the HCF or LCF strength, σ_max and σ_min are the maximum and the minimum values of the fatigue strength, respectively. In addition, the data points with different t/d ratios are scaled by the size of bubble, which can be expressed by

Bubble size=log(t/d)+1 (2)

From Fig. 3(a) and (b), we may have general trends as follows,

(1)As t>2 mm (Fig. 3(a) and (b)), both HCF and LCF strengths do not exhibit evident thickness dependence, but they gradually increase with decreasing grain size (small bubble: small value of t/d, big bubble: large value of t/d) at the same thickness, demonstrating the fatigue strength of Cu polycrystalline only depends on the grain size regardless of LCF or HCF loading. However, this grain size strengthening effect (Hall-Petch relationship [37,38]) would become unremarkable if the number of grains across the thickness is less than one (t/d<1). It is because that most of the GBs will be normal to the loading direction, resulting in the interaction between the mobile dislocations and GBs was limited to a local region close to the GBs [25].

(2) However, when 20 μm<t<200 μm (the left data in Fig. 3(a) and (b)), the fatigue strengths of all kinds of Cu polycrystalline specimens decrease with decreasing t, indicating than the size effect is mainly dominated by the specimen thickness. But the mechanism may be different which depends on the t/d ratio. When t/d<25, such as for the annealed Cu wires (t/d = 0.4-2.5) and annealed Cu foils (t/d = 6-24), the role of the surface grains becomes increasingly noticeable and dislocations can easily escape from the surface, resulting in the decrease in the strength [39]. Such a size effect is in agreement with that found in Cu single crystal specimens [40,41]. It is expected that the development of cyclic strain localization in the surface grains through the formation of fatigue extrusions/intrusions dominates the fatigue life [27]. Whereas as t/d >25, such as for the as-rolled Cu foils (t/d = 40-380), a reduction in the fatigue strength with decreasing t would be due to a possible change in fracture mechanisms from plain strain to plane stress [31].

(3) When 200 μm<t<2 mm (Fig. 3(c)), it is believed that fatigue properties are dominated by the t/d ratio when t and d in the same order [25]. This can be evidenced by a summary of the LCF and HCF strengths of the CA6NM martensite stainless steel (t/d = 0.5-12.5) as well as the Ti alloy (t/d = 0.14-2.79) as a function of t/d, as shown in Fig. 3(c) [33,34]. Generally, the variation in the LCF and HCF strengths has an opposite trend and the fatigue strengths have an extreme value when t/d = 3. In the case of t/d>3, the fatigue life mainly depends on the crack growth life. Resistance to the fatigue crack growth will increase with increasing t due to more GBs being involved in resisting crack growth. However, as t/d<3, the role of surface grains becomes crucial and the fatigue life will be dominated by the crack initiation life [27].

Fig. 4 schematically summarizes the size effect on fatigue properties of metallic materials, which can be divided into three regimes.

Regime I: when t>2 mm, both the LCF and HCF strengths are dominated by d and located between the upper bound (the fatigue strength corresponding to small d) and the lower bound (the fatigue strength corresponding to large d). This grain size strengthening effect (Hall-Petch effect) is believed to be only valid as t/d>>1.

Regime Ⅱ: when 200 μm<t< 2 mm, the LCF and HCF strengths are dominated by t/d and have an opposite variation trend. As t/d<3, the fatigue life depends on the crack initiation life, whereas depends on the crack propagation life when 3<t/d<25. Actually, owing to the variation in material, fabrication process, loading mode and so on, the size effect in the range of 200 μm to 2 mm is likely to exhibit other trends shown by two dashed lines in Fig. 4, which need to be investigated further.

Regime Ⅲ: when 20 μm<t<200 um regardless of the t/d ratio, both the LCF and HCF strengths are controlled by t and decrease with decreasing t.

3. Influencing factors on evaluating fatigue properties of AM parts using miniature specimens

Contrary to the evaluation of fatigue properties of conventionally-fabricated metallic materials with miniature specimens, the randomness of surface roughness and process-induced internal defects introduce significant scatter into the fatigue data of AM specimens. Therefore, in addition to microstructural variables (d, t, t/d), another two defect-sensitive factors such as the surface roughness and the process-induced internal defects would contribute to the build thickness effect on fatigue performance of AM parts.

3.1. Effect of surface roughness

AM parts in the as-built state always possess significantly large surface roughness and many sub-surface defects due to the layer-upon-layer build strategy during the AM processing. Surface roughness acts as a stress raiser and has an adverse effect on the fatigue properties, especially the HCF properties [8]. Pegues et al. [42] reported that the fatigue strength of L-PBF produced Ti-6Al-4V parts in the as-built condition (75-120 MPa) is in stark contrast to that of wrought counterparts (550-750 MPa). Therefore, post processing, such as mechanical milling, electropolishing and vibratory grinding, is applied to remove the rough surface for improving the durability of AM parts. After machining and polishing treatments, the fatigue performance of L-PBF 316L increased by 50% compared with that of as-built ones [43]. Similar results were also reported for other AM metallic materials [44]. However, one of the most outstanding advantages of AM is the ability to manufacture net shape parts without the need of any post processing. Additionally, the biomedical AM parts, such as bone implants may benefit from surface roughness due to the better implant integration [45]. For this reason, it is imperative to have a deeper understanding of fatigue performance of AM parts fabricated in the net shape condition without any surface treatment before testing.

For the as-built specimens, the circumferential surface roughness would introduce a measuring error for the specimen gage section area [46]. The difference between the load-bearing and nominal stress amplitudes caused by such error would increase with decreasing the specimen diameter/thickness [42]. The more accurate measurement of the load-bearing cross-sectional area was conducted by using digital image software after fatigue fracture. Additionally, Pegues et al. [42] systematically investigated the effect of surface area and gauge diameter on fatigue behavior of as built L-PBF Ti-6Al-4V parts, indicating that fatigue behavior of AM parts is more sensitive to gauge diameter than surface area. The number of fatigue crack initiation sites increases and the effect of surface roughness on the fatigue behavior becomes more evident with decreasing the gauge diameter. Therefore, the surface to volume ratio should be considered as a significant parameter influencing the specimen thickness-dependent fatigue properties of AM parts.

3.2. Effect of process-induced internal defects

Similar to surface roughness, the process-induced internal defects generated by vapor recoil and surface tension or sub-optimal processing parameters, are the dominant factors on shortening the fatigue life of AM parts used in machined/polished state, which can hardly be removed even by hot isostatic pressing (HIP) treatment [46], [47], [48]. As discussed previously, lack of fusion defects and porosity are the most common internal defects seen in the AM parts. The location, shape and size of internal defects are the primary variables for the decrease in the HCF life of AM metallic materials, and the location is considered to have a more adverse effect contrary to the shape and size due to the fact that crack initiation sites are mostly observed close to the specimen surface [49].

3.3. Effect of build thickness of AM parts

By comprehensively considering the abovementioned microstructure- and defect-sensitive factors, the build thickness effect on fatigue performance of AM parts may not follow the rule derived from that of conventionally-fabricated metallic materials shown in Fig. 4. For example, the critical specimen thickness (t = 200 μm) corresponding to the maximum fatigue strength of conventionally-fabricated metallic materials shown in Fig. 4 may shift toward the right direction of the map. Additionally, the variation trend of the HCF strength of AM parts with the thickness ranging from 200 μm to 2 mm may be changed into that indicated by dashed lines shown in Fig. 4. Thus, the build thickness effect on fatigue performance of AM parts still needs to be elucidated.

Fig. 5 illustrates a general flowchart to model the build thickness effect on fatigue performance of AM parts. These influencing factors not only include the intrinsic factors related to microstructures (t, d, t/d) but also the extrinsic factors associated with defects (surface roughness and process-induced internal defects) [48]. Regarding the intrinsic factors, fatigue life can be modeled by the microstructure-sensitive fatigue model (e.g. multistage fatigue model proposed by McDowell et al.), while as for the extrinsic factors, Berretta and Romano successfully used the area (the square root of the equivalent defect area projected onto the loading plane) model in conjunction with the Kitagawa-Takahashi diagram modeling the effect of surface roughness and process-induced internal defects on fatigue strength of AM metallic materials [9,50]. In addition, numerical models (e.g. Finite element analysis) have been applied to determine the crack propagation threshold, which then can help to evaluate the actual fatigue performance of parts [51].

In general, a reasonable model can hardly be attained by simply incorporating all of the abovementioned models together. A more practical model for predicting fatigue performance of AM parts may rely on establishment of a data-driven evaluation platform, which will be discussed in the last section.

4. Recent efforts to evaluate fatigue performance of AM parts using miniature specimens and resultant new challenges

Compared with the mechanical properties of conventionally-fabricated metallic materials, the mechanical properties of geometrically complex AM parts may vary with the build thickness, location and orientation due to varying temperature gradient and cooling rate introduced by the fabrication process. Thus, the conventional testing procedures using the standard testing specimens fail to characterize such local mechanical properties due to the restriction of the specimen dimensions as well as the defect distribution and microstructure heterogeneities. Whereas using miniature specimens can bring immense advantages [5,6]. Furthermore, although the standard specimen tests have always been used to provide fundamental data for products’ design and manufacturing, miniature specimens can also be used to determine the relevant mechanical properties of in-service components without affecting their functionality when the volume of materials is limited. Obviously, it is beneficial to use miniature specimens to evaluate the mechanical properties of AM parts. However, many ongoing challenges are still remaining.

4.1. Tensile properties of AM parts using miniature specimens

Dzugan et al. [15] firstly employed the miniature specimens (the total length of specimen is only 15.5 mm) to assess the location- and orientation-dependent tensile properties of SLM-fabricated Ti-6Al-4V used as the hip replacement set and the experimental results exhibited a good reliability compared with that of standard specimens. Furthermore, they attempted to develop a systematic approach for evaluating the effects of the thickness, the location and the orientation on the microstructure and resulting tensile properties using miniature specimens taken from SLMed and SEBMed Ti-6Al-4V alloys [8]. Fig. 6 shows a comparison of yield strength (YS) and ultimate tensile strength (UTS) of the as-built specimens with t = 0.5, 1.0, 1.5, 2.0, 2.5 mm and the ground specimens with t = 0.5 mm (t >1 mm specimens were symmetrically grounded from both sides to a final thickness of 0.5 mm) fabricated by SLM [8]. It appears that the YS and UTS of the as-built specimens reach saturated values with increasing the build thickness, whereas the ground specimens with t = 0.5 mm exhibit similar YS and UTS regardless of the original thickness. This suggests that the surface defects play a significant role in the size effect on tensile properties of SLMed parts. A thick specimen with the small surface area to volume ratio may reduce the effect of specimen surfaces on the tensile properties, but this may not be true for fatigue properties, which still needs to be investigated carefully.

4.2. New testing methods to evaluate fatigue performance using miniature specimens

Recently, most of the testing methods, equipment and gripping fixtures are developed for ASTM standard specimens. As for the miniature fatigue specimens, many technical difficulties still need to be addressed [10,13,19]. For example, assessment of LCF properties in the strain-controlled mode at room and high temperature using miniature specimens is very difficult since these miniature specimens are apt to buckle during fatigue loading. Recently, Dzugan et al. [18,52] has successfully used cylindrical miniature specimens (the minimum diameter of the gauge section is 2 mm) to evaluate the LCF properties of four types of steels at temperature ranging from room to 525 ℃. In addition, under the necessity for light-weight design of automobile, Martin et al. [53] firstly attempted to use dumb-bell shaped miniature specimens (the gauge length, width and thickness are 0 mm, 6.35 mm and 1.78 mm, respectively) to determine the LCF properties of thin sheet parts. The above work has paved the way for evaluating the LCF properties by using miniature specimens, more extensive studies on fatigue properties of the miniature specimens with smaller dimensions at higher temperature are necessary prior to standardization of the testing methods.

4.3. Building confidence to evaluate fatigue performance of AM parts using miniature specimens

A survey of the literatures indicates that a great range of dog-bone specimens with different dimensions and shapes have been used to measure the static tensile and fatigue properties [54]. The thickness or width of the dog-bone shaped miniature specimens usually scales from hundreds of micrometer [55] to several millimeters [56], the gauge length ranges from several millimeters [57] to dozens of millimeters [56]. This situation naturally causes concern as to whether any change in the shape or dimension of the gauge area of the miniature specimens would have a significant effect on the measured fatigue properties and how to judge the reasonability of the miniature specimen dimensions? Thus, it is necessary to have a systematic investigation on the effect of specimen dimension/geometry on fatigue properties of metallic materials.

In addition, it is inevitable to adopt miniature specimens with different thicknesses due to the existence of gradient in the build thickness at various locations of geometrically complex AM parts. Therefore, the effect of geometrical scale on the correlation relationship between the location-specific microstructure and fatigue properties of AM parts needs to be clarified [16].

As for the size effect on fatigue properties of conventionally-fabricated structural materials, a series of work has been carried out by Zhang’s group [27,33,58,59]. Although the possible trends for the size effect have been shown in Fig. 4, accessible data are still rather limited, especially for the specimen with the thickness ranging from 200 μm to 2 mm, and the underlying mechanism is far from being understood. Additionally, the size effect on fatigue properties at high temperature is an uncultivated region needing to be investigated.

In the case of AM materials, Seifi and Dzugan are working on the item aimed at establishing a new guideline for evaluating the orientation- and location-dependent mechanical properties of AM parts (ASTM WK49229). This work item initiated from 2015 and the draft is now under development. Recently, they attempted to use miniature specimens to evaluate the effects of the specimen thickness, the location and the orientation on the microstructure and resulting tensile properties [8]. Their preliminary work is a successful case in qualifying tensile properties of AM parts using miniature specimens. In addition, Nicoletto et al. [60,61] firstly quantified the effects of notch and directionality of materials on fatigue performance of the SLMed Ti-6Al-4V by using the specific miniature specimens. However, using miniature specimens to qualify the fatigue performance of AM parts is just beginning. A large number of fatigue data generated by using miniature specimens are required. On this basis, machine learning (ML) is expected to be a feasible approach to construct a bridge between the fatigue data attained by the standard and miniature specimen tests. The advantage is the fact that this linkage is purely data-driven without using traditional computational methods and no need to know the intrinsic but complex physical mechanism. Once the quantitative correlation between these two types of data is attained by using the well-trained ML algorithm, the confidence in using miniature specimens to evaluate fatigue properties of AM parts would be established.

4.4. Application of machine learning to fatigue properties prediction from miniature specimen tests

The combination of big data and artificial intelligence (AI) is referred to as the forth paradigm in materials science [62]. ML as one of the subfields of AI has evolved rapidly for recent years, which is suitable for handling complex problems that involve massive combinatorial spaces or non-linear processes. Recently, ML has been tried to predict fatigue properties of metallic materials from the standard specimen tests and static mechanical properties from miniature specimen tests [63], [64], [65], [66]. Partheepan et al. [65] proposed a neural network to predict the yield strength from the data obtained by conducting tensile tests of dumb-bell shaped miniature specimen. The input to the neural network is the yield load obtained from the miniature specimen tests, and the output is yield strength, which is convinced to be in good agreement (<5% error) with the actual value from the standard tests according to the ASTM E8-03. In addition, Abendroth et al. [66] used neutral network to identify the deformation, damage, and fracture properties of ductile materials by small punch tests (SPT) with miniature specimens. Firstly, they used finite element method (FEM) for SPT to generate a data base in various material parameters conditions. Then, this data base is utilized to train a neural network with three hidden-layers. Finally, the network can be used to predict the load displacement curve of the SPT for a set of given material parameters, which can be performed much faster than a FEM model and also can be extended into the identification of the unknown material parameters. Furthermore, artificial neural networks (ANN) were employed to predict the fracture toughness of in-service materials based on dumb-bell shaped miniature specimens, the value is close to that determined by the standard tests [67]. However, up to now there is limited research regarding the prediction of fatigue properties of miniature specimens using neutral network, especially for the AM parts, which still needs to be further investigated.

5. Outlook

With the gradual maturity of the AM technology towards industrial application, how to rapidly evaluate fatigue properties of AM parts is always of concern. A potential approach may be the combination of a large amount of data collected via a large number of miniature specimen tests and theoretical computations as well as the ‘big data’ analysis with ML. Fig. 7 conceptually depicts a data-driven evaluation workflow for fatigue performance of AM parts using miniature specimens.

5.1. Data collection through a large number of miniature specimen-based experiments

As shown in the left part of Fig. 7, in order to correlate the location-specific and orientation-dependent fatigue properties to corresponding microstructure and defect distribution features in a geometrically complex AM parts, such as the blade used in Siemens SGT-400 industrial gas turbine, a series of individual miniature specimens would be extracted from various locations (including the top, center and bottom of AM parts, the thin-walled sections with gradient thickness, the corners of the AM parts with different stress concentrations, the loading bearing sections of AM parts etc.) and corresponding orientations (building/scanning/transverse direction etc.). The aim of this practice is to document the variation in fatigue properties from all featured locations and orientations. After the microstructure characterization and fatigue tests using these miniature specimens, numerous kinds of materials data, including images taken by optical microscope, scanning electron microscope and transmission electron microscope, electron backscatter diffraction data, defects information detected by 3D-high resolution transmission X-ray tomography, macro residual stress characterized by neutron diffraction technique and location-specific fatigue properties (LCF and HCF properties at room and high temperatures, fatigue crack growth rates etc.) and even fracture surface morphologies can be collected into a data set. In addition, the new data stream including the output of simulation techniques, published patterns, existing database also will be stored in such ‘big data’.

5.2. Data augmentation for miniature specimen tests via machine learning

ML can also be regarded as a powerful tool to realize data augmentation for miniature specimen tests, since its great non-linear fitting capacity can help to establish a complex data relationship. For example, as demonstrated in Zhang’s work [68], their ANN model takes three sets of experimental data with stress ratios of 0.02, 0.33 and 0.75 as the training sets, and the other experimental data with stress ratios of 0.1 and 0.5 as the testing sets. After training and testing, a model with satisfactory fitting accuracy is obtained. Moreover, the model has the capacity to predict the fatigue crack growth of the material whose stress ratio lies between 0.02 and 0.75. From this viewpoint, ML algorithm can be used to extend the original data sets attained by miniature specimen tests into a wide data range.

5.3. Data analysis and model establishment for miniature specimen tests

It is fair to say that so large quantities of structural and mechanical data have greatly surpassed our capability to analyze it. ML would play a key role in large-scale data analysis and ultimately produce predictable statistical models on the material behavior. The process of ML generally includes following steps: data preprocessing such as sampling, attribute-type conversion and normalization, data representation, model selection for training data (supervised, semi-supervised or unsupervised model depending on the type and amount of available data), model establishment and optimization by training and testing data with ML algorithms such as ANN and deep neural networks (DNN) [69,70].

The final knowledge will be given in the form of PSPP relationship of AM metallic materials. From the left to the right of the PSPP relationship, the deductive relationship of cause and effect flow can help to build data-driven forward models and shorten the time for experiments and simulations. More importantly, the inverse models from the right to the left of the PSPP relationship is expected to be realized for materials design and performance optimization of AM parts. A good inverse model should be able to provide multiple options, so as to maximize the performance with the most cost-effective approach [62]. Under the umbrella of this qualification platform, the current materials research and development (R&D) time may be reduced to half [71].

6. Summary

(1) A thorough summary on the length scale-related fatigue performance of conventionally-fabricated metallic materials, correlating with the geometrical scales (specimen thickness, etc.), the microstructural scales (grain size, etc.) and their coupling effects (t/d) was presented.

(2)

Owing to the restriction of dimensions, the defect distribution and microstructure heterogeneities of the geometrically complex AM parts, the location-specific and orientation-dependent fatigue performances should be evaluated and qualified by miniature specimens rather than standard specimens.

(3) In order to build confidence in using miniature specimens to evaluate fatigue performance of AM parts, both the microstructural and defect-sensitive factors need to be taken into consideration.

(4) New challenges in documenting the location-specific and orientation-dependent fatigue properties evaluated by the miniature specimens and analyzing a large amount of the data with ML are becoming prevailed.

(5) A potential roadmap to establish a data-driven evaluation platform in terms of a large number of miniature specimen-based experiment data, the theoretical computation and the ‘big data’ analysis with ML is proposed.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC, Grant Nos. 51771207 and 51571199).

The authors have declared that no competing interests exist.

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