Additive manufacturing: effects of defects

Additive manufacturing: effects of defects

18

Additive manufacturing (AM) is expected to be a promising new manufacturing process for components having complex geometry; for example see Fig. 18.1 [1]. High-strength or hard steels and also light metals such as Ti and Al alloys are expected to be used for aerospace and automotive industry components having complex shapes which need special costly casting and welding processes if traditional manufacturing methods are applied. The recent flood of publications on AM reflects the high expectation of industries for a revolution in the manufacturing process. Many review papers [2
6] on AM have also been published. The topics of publications and review papers change year by year, reflecting the progress in manufacturing processes and experimental analysis based on strength parameters. Due to the many publications and the rapid progress, it is almost impossible for the author of this book to make a thorough survey covering all of them. The advantages of AM have been emphasised, especially for high-strength or hard steels, which are difficult and costly to manufacture by traditional machining to complex shapes. However, a disadvantage or challenge of AM is the presence of defects which are inevitably produced by the manufacturing process. Until now, the papers which have focused on the quantitative evaluation of defects are relatively sparse among the flood of publications. Without strict and reliable quality control of components regarding defects, we cannot positively admire the advantages of AM as the new technology. In this chapter, the method of quantitative evaluation of defects for two typical AM materials, Ti
6Al
4V and nickel-based superalloy 718, will be explained.

Figure 18.1 Example of a spherical cage manufactured by AM. (a) Overall view, (b) magnification of (a). Source: Courtesy: H. Masuo, Introductory Slides for Additive Manufacturing, Metal Technology Co. Ltd, 2017 [1]. Metal Fatigue. DOI: https://doi.org/10.1016/B978-0-12-813876-2.00018-2 © 2019 Elsevier Ltd. All rights reserved.

454

Metal Fatigue

This chapter focuses on the effects of defects, surface roughness and the hot isostatic pressing (HIP) process on the fatigue strength of Ti
6Al
4V and on the effects of build-up direction and defects of the nickel-based superalloy 718 manufactured by AM. Practical guides will be presented for the fatigue design and development of high-quality and high-strength AM materials, based on the combination pffiffiffiffiffiffiffiffiffi of the statistics of extremes on defects, and the area parameter model. Experimental procedures and results for both Ti
6Al
4V and nickel-based superalloy 718 will be explained in detail, because the study on AM materials is currently in the early stage of development, so we need to pay attention to every influencing factor before we can find a relevant direction for the future development of AM.

18.1

Ti
6Al
4V

Much literature on the fatigue properties of AM Ti
6Al
4V has been published in recent years [2,7
11]. For example, Beretta and Romano [2] reviewed papers related to the fatigue strength of AlSi10Mg and Ti
6Al
4V from the viewpoint of small cracks. Gu¨nther et al. [7] carried out precise experimental investigations on Ti
6Al
4V in high cycle fatigue, and very high cycle fatigue, and discussed the problems from the viewpoint of statistical scatter of defect size based on microstructural observations. They pointed out the problem raised by the interaction between defects and a specimen surface. They also pointed out the advantages of HIP on the improvement of fatigue properties of Ti
6Al
4V. Currently, it seems that there is no common consensus for the definition of defect size for complex configurations of AM defects and, additionally, there is still a misconception that a constant ΔKth for long cracks can be applied to small defects such as AM defects. This section discusses the fatigue properties of a Ti
6Al
4V manufactured by AM in terms of the effect of defects, surface roughness and HIP. In this chapter, the study on Ti
6Al
4V by Masuo et al. [12] is first introduced. The raw materials and as-built specimens having the final shape were prepared by AM processes: electron beam melting (EBM) and direct metal laser sintering (DMLS) methods. The particle size is about 80 μm for EBM and about 40 μm for DMLS. The specimens were built in the direction of the specimen axis. Preheating was applied to EBM in every layer and stress relief heat treatment was applied to DMLS after building specimens. HIP was applied to several series of specimens and as-built specimens in order to separate the effects of surface roughness and defects. Table 18.1 classifies the specimens by AM methods (EBM or DMLS), surface polishing (as-built or surface polish) and HIP. Table 18.2 shows the mechanical properties of the Ti
6Al
4V manufactured by AM. Fig. 18.2 shows the shape and dimensions of fatigue test specimens for rotating bending fatigue. Rotating bending fatigue tests were carried out at 60 Hz. The surfaces of machined specimens were polished with #600 emery paper. Fig. 18.3 shows the

Additive manufacturing: effects of defects

455

Table 18.1 Specimen classifications Process

Surface condition

HIP No

As-built Yes EBM No Surface polish (#600) Yes AM type No As-built Yes DMLS No Surface polish (#600) Yes No Rolled material

Surface polish (#600) Yes

Table 18.2 Mechanical properties AM process

EBM

DMLS Yes

No

Yes

σUTS (MPa)

1046

986

1176

980

Elongation (%)

20

22

14

22

HV 0.3

369

345

378

340

R18

(10)

12

R18

25

φ6

No

φ12º–0.02

HIP

(10)

25

82

Figure 18.2 Shape and dimension of specimen (in mm).

microstructures made by different processing. It can be confirmed that most of the defects which are visible before HIP disappeared due to the effect of HIP. The Vickers hardness HV (P 5 0.3 kgf) was measured at 6 points. The scatters of HV are summarized as follows. EBM without HIP: 369 6 1.9%, EBM with HIP: 345 6 2.6%

456

Metal Fatigue

DMLS without HIP: 378 6 0.8%, DMLS with HIP: 340 6 2.1% Rolled material without HIP: 310 6 6.1%, Rolled material with HIP: 300 6 7.0% The fatigue fracture origins were mostly at surface or at defects near surface (Fig. 18.10
12).

Figure 18.3 Microstructures produced by different processes.

Additive manufacturing: effects of defects

18.2

457

Tests, results and discussion for Ti
6Al
4V

When we discuss the fatigue properties of materials manufactured by AM, we should first pay attention to the ideal or upper bound of fatigue strength which we can expect for the case without the influence of defects. It is well known that there is a very good correlation between fatigue limit and Vickers hardness HV up to HV 5 B400. For HV . 400, the fatigue limit drops drastically due to the presence of small defects (see Figs. 1.6 and 1.7). There is a robust empirical formula (Eq. (1.2)) between the fatigue limit σw and HV for HV , 400 (Fig. 1.6 (Garwood et al.) and Fig. 1.7 (Nishijima, S.)). σw; ideal 5 1:6HV 6 0:1HV

(18.1)

where the units are σw, ideal in MPa and HV in kgf/mm2. Since the Vickers hardness of the material investigated in this study ranges from HV 5 340 to 378, the ideal upper bound of fatigue strength can be estimated to be around σw, ideal 5 544
605 MPa if Eq. (18. 1) is valid also for Ti alloys. Fig. 18.4 summarises S
N data for EBM specimens. Fig. 18.5 summarises S
N data for DMLS specimens. From Figs. 18.4 and 18.5, the common trend of fatigue strength for all series of specimens is expressed as follows: As-built without HIP , As-built with HIP , Surface polish without HIP , Surface polish with HIP: 800

Surface polish without HIP (HV = 369) Surface polish with HIP (HV = 345) As built without HIP (HV = 369) As built with HIP ( HV = 345)

700

σa (MPa)

600 500 400 300 200 100 0 104

105

106

107

Nf (cycles)

Figure 18.4 S
N data for EBM specimens.

108

458

Metal Fatigue

800

Surface polish without HIP (HV = 378) Surface polish with HIP ( HV = 340) As built without HIP ( HV = 378) As built with HIP ( HV = 340)

700

σa (MPa)

600 500 400 300 200 100 0 104

105

106

107

108

Nf (cycles)

Figure 18.5 S
N data for DMLS specimens.

The surface-polished specimens with HIP have a fatigue limit close to the ideal upper bound. On the other hand, the fatigue limits of as-built specimens are only about 27% of the ideal fatigue limit expected from HV. Thus, the surface polish and HIP are definitely effective in improving the fatigue properties of AM materials. Table 18.3 summarises all the experimental results and the basic material properties. The fatigue limits cited in Table 18.3 are the values determined approximately from the S
N data of Figs. 18.4 and 18.5. Since individual specimens contain defects having different sizes and shapes, we cannot determine the exact fatigue limit for individual specimens prior to a fatigue test. Even if a specimen ran out at a stress for N 5 107 cycles, we cannot define the stress as the fatigue limit of the specimen. The fatigue limit of a specimen varies depending on the most detrimental defect in the specimen, which is difficult to identify prior to a fatigue failure test. Figs. 18.6 and 18.7 show the surface morphologies of as-built specimens for EBM and DMLS, respectively. The surface roughness is different between EBM and DMLS due to the different particle sizes: 80 μm for EBM and 40 μm for DMLS. Fig. 18.8 shows the microstructure and defects of a transverse cross-section for an as-built specimen of EBM without HIP. Many defects are visible in Fig. 18.8. Fig. 18.9 shows the microstructure and defects of a transverse section for an as-built specimen of EBM with HIP. Most of the defects disappeared due to the effect of HIP. Figs. 18.10 and 18.11 show defects which were observed at fracture origins in contact with specimen surfaces. Compared to rolled steels, the direction of defects in AM materials is random and not aligned in an identical direction. The varieties of defect shapes are mostly due to lack of fusion or to various sizes of particle.

Additive manufacturing: effects of defects

459

Table 18.3 Summary of fatigue data and other properties

Process

Surface condition

Surface roughness

HIP

Approximate fatigue limit (MPa)

HV

No

140

Yes

Ra (μm)

Rz (μm)

369

32
42

219
290

195

345

30
41

212
254

No

240
260

369

Yes

590

345

No

155

378

10
13

75
90

Yes

195
220

340

12
13

86
96

No

370

378

Yes

610

340

No

530
540

310

Yes

440

300

As-built EBM


Surface polish AM As-built DMLS Surface polish Rolled material

Surface polish

Figure 18.6 Surface morphology for EBM specimens.

Figure 18.7 Surface morphology for DMLS specimens.







460

Metal Fatigue

Figure 18.8 Defects observed on the section of an as-built EBM specimen without HIP.

Figure 18.9 Disappearance of defects from the section of an as-built EBM specimen with HIP.

Fig. 18.12 shows the fatigue fracture surface near specimen surfaces of as-built specimens. The surface roughness in both EBM and DMLS is much larger in size than the defects shown. It must be noted that defects (surface roughness) opening to a specimen surface cannot be eliminated by HIP as shown in Fig. 18.12. Since defects have various shapes, we need to define the relevant rule for estimating the effect of defects. In this regard, the representative dimension of a defect pffiffiffiffiffiffiffiffiffi can be expressed with area in terms of a fracture mechanics concept (see Chapter 2: Stress concentration).

Additive manufacturing: effects of defects

461

Figure 18.10 Fatigue fracture origins of surface-polished EBM specimens without HIP and estimation of the effective defect size.

Figure 18.11 Fatigue fracture origins of surface-polished DMLS specimens without HIP and estimation of the effective defect size.

Figure 18.12 Surface morphology of as-built specimens after HIP. HIP does not improve the surface condition of as-built specimens.

462

Metal Fatigue

Fig. 18.13 illustrates various possible configurations of defects for which we need pffiffiffiffiffiffiffiffiffi to consider the effective defect size, areaeff, which differs from the real defect size. Initial fatigue crack growth for irregularly shaped cracks and defects, as shown in Fig. 18.14, starts from the deepest concave corner point due to the extremely high stress intensity factor at that point. As the crack grows, and the shape of the crack front becomes rounded, the stress intensity factor decreases (see Fig. 18.14 [13]). The crack continues growing to failure if the value of ΔK exceeds the threshold stress intensity factor range ΔKth. If the value of ΔK is lower than ΔKth, the crack stops growing and becomes a nonpropagating crack (see Chapter 13: Ti Alloys). Therefore, if defects have configurations such as the examples in Fig. 18.13, we must pffiffiffiffiffiffiffiffiffi consider the effective size of defects areaeff, rather than the real size of defects. In this regard, when we apply the statistics of extreme analysis of defect size to fatigue design of AM materials, we need to consider the modification pffiffiffiffiffiffiffiffiffiof defect size. Based on the values of the effective defect sizes, areaeff, at fracture origins and the Vickers hardness HV, the normalised S
N data were derived as in Fig. 18.15. The applied stress σa is normalised by the estimated fatigue limit σw. In deriving Fig. 18.15, it must be noted that we cannot determine the fatigue limit σw of individual specimens of this kind of material by the conventional fatigue test to N 5 107, because individual specimens contain defects with different size which can be identified only after fatigue failure testing. In other words, individual specimens have individually different fatigue limits. Therefore, the specimens which have runout for N 5 107 were tested again at a higher stress and the size of defects

Figure 18.13 Estimation method for the effective size (dotted line) of irregularly shaped defects and defects near surface (see Chapter 2: Stress concentration and Ref. [13]). (a) Irregularly shaped internal defect. (b) Irregularly shaped surface defect. (c) Irregularly shaped internal defect in interaction with surface. (d) Interacting adjacent two defects. (e) Inclined defect in contact with surface.

Additive manufacturing: effects of defects

463

Figure 18.14 Estimation method for the effective size (dotted line) of irregularly shaped defects and defects near surface. (see Chapter 2: Stress concentration and Ref. [13]).

2.4 EBM Surface polish without HIP EBM Surface polish without HIP A EBM Surface polish without HIP B DMLS Surface polish without HIP DMLS Surface polish without HIP C DMLS Surface polish without HIP D

2.2 2.0 1.8

σa /σw

1.6 1.4 1.2

C3

A3

D2

1.0

C2 D1 C1 A2 B1 A1

B2

0.8 0.6 0.4 0.2 0.0

104

105

106

107

108

Cycles to failure Nf (cycles)

Figure 18.15 Normalised S
N curve: σ a/σ w
Nf specimens runout for N 5 107 were tested at higher stress and the defects at fracture origin were identified for the calculation of σw. It must be noted that the fatigue limit is different in individual specimens due to the presence of defects with different size.

464

Metal Fatigue

at fracture origins was identified. The marks A1, B1, C1 and D1 in Fig. 18.15 mean the specimens runout for N 5 107 by the first test and the marks A2, B2, C2 etc., mean the specimens tested at a stress higher than the previous tests. It can be seen that the values of σa/σw for failed specimens are mostly larger than B0.9 and the values of σa/σ for runout specimens are mostly smaller than pwffiffiffiffiffiffiffiffiffi 1.0, so estimation based on the area parameter model (Eq. (18.2)) works well (see also Chapter 13: Ti Alloys). σw 5 1:43ðHV 1 120Þ=

pffiffiffiffiffiffiffiffiffi 1=6 areaeff

(18.2)

pffiffiffiffiffiffiffiffiffi where the units are σw: MPa, HV: kgf/mm2, areaeff : μm. However, Fig. 18.15 shows failures of some EBM specimens at σ/σw , 1.0. The reason may be larger particle size EBM specimens than in DMLS. In EBM specipin ffiffiffiffiffiffiffiffiffi mens the effective defect size areaeff with large irregularity might not be correctly identified due to the larger particle size than for DMLS, as seen in Fig. 18.10. Gu¨nther et al. [7] reported similar results in which theypestimated σw by ffiffiffiffiffiffiffiffiffi using the constant 1.41 instead of 1.43, and the direct value of area instead of pffiffiffiffiffiffiffiffiffi areaeff in Eq. (18.2), including consideration of Fig. 6.15b and Eq. (6.2). However, if we pay attention to the defect configurations shown in Figs.p18.10 ffiffiffiffiffiffiffiffiffi and 18.13, a better estimate might be made by modifying the defect size by areaeff. It may be necessary to investigate in more detail the configuration of defects, and the possible heterogeneous microstructure surrounding defects produced by lack of fusion. Thus, since the fatigue limit of AM specimens is influenced by the size of defects contained in individual specimens, it must be noted that we cannot define a definite fatigue limit for a material in question from the usual S
N data. The definition of the effective defect size is p not evident in cases such as ffiffiffiffiffiffiffiffiffi Figs. 18.16 and 18.17, so the effective defect size areaeff must be estimated by the equivalent elliptical area. This is because, in the case of adjacent defects within the critical distance, fatigue cracks emanating from one defect are likely to be connected with neighbouring defects (see Fig. 2.16 and Ref. [14]). Therefore, when we apply the statistics of extremes to fatigue design of AM materials, we need to consider the modification of defect size as shown in Figs. 18.16 and 18.17. Fig. 18.18 shows the statistics of extreme analysis of the largest defects which appeared on the sections cut from a specimen with an inspection area S0 5 28 mm2.

Figure 18.16 Estimation of

pffiffiffiffiffiffiffiffiffi areaeff for EBM without HIP.

Additive manufacturing: effects of defects

Figure 18.17 Estimation of

465

pffiffiffiffiffiffiffiffiffi areaeff for DMLS without HIP.

S0

7

EBM 6

28 mm2 without HIP

DMLS without HIP

5

Reduced variate yi

4

3

2

1

0

–1

–2 0

100

200

300

400

500

√areamax (µm) Figure 18.18 Statistics of extremes analysis for the largest defects observed on specimen pffiffiffiffiffiffiffiffiffi section. areamax was calculated based on the rule of Figs. 18.16 and 18.17.

466

Metal Fatigue

V0

65 mm3

F(%) T

7

EBM Surface polish without HIP 6

DMLS Surface polish without HIP

5

Reduced variate yi

4

3

2

1

0

–1

–2 0

100

200

300

400

500

600

area max (μm) Figure 18.19 Statistics of extremes analysis for the defects observed at fracture origin. pffiffiffiffiffiffiffiffiffi areamax was calculated based on the rule of Figs. 18.10, 18.11 and 18.13. V0 5 65 mm3: Control volume of surface annular zone of specimen under stress higher than 90% of nominal stress.

Fig. 18.19 shows the statistics of extreme analysis of the defects which pffiffiffiffiffiffiffiffiffiwere observed at fatigue fracture origins. In this analysis, the modification of area was applied based on the rule of Fig. 18.13. Figs. 18.18 and 18.19 indicate that material DMLS is graded higher than material EBM within the current processing conditions, so particle sizes and the data of Figs. 18.18 and 18.19 can be used as the measure for quality control of AM materials. Inserting the approximate values of fatigue limit for as-built specimens pffiffiffiffiffiffiffiffiffi of Figs. 18.4 and 18.5 into Eq. (18.2), we can estimate the equivalent area for

Additive manufacturing: effects of defects

467

Figure 18.20 Average defect size for failure type by Weibull probability plot [7].

pffiffiffiffiffiffiffiffiffi surface roughness. The estimated values of area exceed 1000 μm for all the cases pffiffiffiffiffiffiffiffiffi of EBM and DMLS. Since Eq. (18.2) is valid for area ,1000 μm, it can be inferred that the surface roughness produced by AM is much larger and more detrimental than other defects, and cannot be categorised as a small crack problem. Therefore, it will be of practical importance to eliminate the effect of surface roughness by polishing or other technique, such as shot peening, at least at critical locations, or by chemical etching [15]. From the above discussion, it is necessary for the safe fatigue design of AM components to consider the method of the statistics of extremes analysis based on Figs. 18.13, 18.18 and 18.19. By considering the volume p and numbers produced of ffiffiffiffiffiffiffiffiffi the components in question, the effective largest defect, areaeffmax, contained in large or manypcomponents can be predicted. The lower bound of the fatigue limit ffiffiffiffiffiffiffiffiffi σwl based on areaeffmax can be determined by the following equation. σwl 5 1:43ðHV 1 120Þ=

pffiffiffiffiffiffiffiffiffi 1=6 areaeffmax

(18.3)

pffiffiffiffiffiffiffiffiffi where the units are σwl: MPa, HV: kgf/mm2, areaeffmax: μm. Gu¨nther et al. [7] investigated the influence of the internal failure types by porosity, lack of fusion and α-phase on the fatigue life in the VHCF regime. Fig. 18.20 shows the Weibull probability plot of each failure type. Fig. 18.21 shows the S
N data obtained for materials manufactured by SLM and EBM. The horizontalffiffiffiffiffiffiffiffiffi lines in Fig. 18.21 are the estimates of fatigue limits by the application of the p area parameter model using the average size of porosity, α-phase and lack of fusion in Fig. 18.20. It is evident that lack of fusion is more detrimental than other possible failure origins.

18.3

Nickel-based superalloy 718 [16]

Many studies on Ni-based superalloy 718 produced by AM have also been reported [17]. It is well known that high-strength metallic materials with Vickers hardness

468

Metal Fatigue

Figure 18.21 S
N data by Gu¨nther et al. [7] and the average fatigue limits estimated pffiffiffiffiffiffiffiffiffi by the area parameter model applied to each defect.

HV . 400 are very sensitive to small defects (see Fig. 1.6). The Vickers hardness of the Ni-based superalloy 718, which was manufactured by AM and is discussed in this chapter, is HV 5 B470 [16], which is approximately a common value for this material after the standard heat treatment. Defects of the material reported by the work of Ref. [16] on Ni-based superalloy 718 were mostly gas porosity and those produced by lack of fusion. The guide for the fatigue design and development of high-quality Ni-based superalloy 718 by AM processing will be presented. This is based on the similar method for Ti
6Al
4V, with the combination of the statistics of extremes on pffiffiffiffiffiffiffiffiffi defects and the area parameter model.

18.4

Tests, results and discussion for nickel-based superalloy 718

The material data and testing method will be explained in detail, because this information will be useful for the future study of Ni-based superalloy 718. The material was made by the selective laser melting (SLM) method. Solution treatment is based on AMS5663. Specimens were machined from two kinds of raw plate materials, denoted A and B, produced by AM. Specimens were cut in two directions, that is the as-built direction (L direction) and the transverse direction (T direction) to asbuilt direction, as shown in Fig. 18.22 (case for Material A and similarly for Material B). Fig. 18.23 shows the microstructure of the both materials A and B. It has been found from the microstructure observation that the granulometry of the powder particle of material B is smaller than that of material A. Also the materials A and B were produced by different selective laser melting machine systems based

Additive manufacturing: effects of defects

469

A-T1 A-T2

65

A-T3 A-T4 A-T5 A-T6 A-T7 65 A-L2

A-L3

A-L4

A-L5

A-L6

A-L7

15

A-L1

Figure 18.22 Raw plate material (Material A) and cutting layout for specimens.

Figure 18.23 Microstructure of Ni-based superalloy 718 produced by SLM.

Metal Fatigue

φ5

R40

(18)

(φ 6.8)

470

12

(18)

(64)

Figure 18.24 Shape and dimension of tension
compression specimen.

on the recommended processing parameters of the machine fabricators. Fig. 18.24 shows the shape and dimensions of the specimen. The mechanical properties were measured using the same specimen. The 0.2% proof stress ranged from 1227 MPa to 1329 MPa, and the ultimate tensile strength ranged from 1306 MPa to 1499 MPa. The elongation with an 8 mm gauge length ranged from 13.6% to 31.8%, and the reduction in area from 8.6% to 30.7%. Observation of fracture surfaces revealed that the scatter of the mechanical properties was caused by various defects contained in specimens. Specimen surfaces were polished using #600 emery paper. Material offcuts remaining after cutting specimens in accordance with Fig. 18.22 were used to investigate the microstructure and the statistical distribution of defects. The analysis of statistics of extremes was applied to the largest defects observed on nine sections, with the unit observation area S0 5 80.97 mm2 for Material A, and S0 5 116.49 mm2 for Material B. The largest defects were separately analysed as pores, linear defects and equivalent elliptical defects for interactive adjacent defects. The Vickers hardness HV (P 5 5 kgf) was measured at five points. HV 5 465% 6 1.7% for A
T, and HV 5 474% 6 1.2% for B
T. Tension compression fatigue tests were carried out with a hydraulic tension
compression testing machine at 30 Hz, with strict specimen alignment within 6 5% for the values of four strain gauges attached to each specimen at 6 500 με and 6 1000 με. The fatigue fracture origins were mostly at defects. Accurate specimen and testing machine alignment are very important to avoid obtaining incorrect data related to nonuniform stress distribution, for statistical size distribution of defects and spatial configurations of defects in specimens. When we discuss the fatigue properties of materials made by AM, we should first pay attention to the ideal or upper bound of fatigue strength to be reached for the case without influence of defects (see Figs. 1.6 and 1.7). For HV . 400, the fatigue limit drops drastically due to the presence of small defects (Fig. 1.6). There is a robust empirical formula (Eq. (18.1)) between the ideal fatigue limit, σw, ideal, and HV for HV , 400 (Fig. 1.7). Since the Vickers hardness of the material investigated in this study ranges from HV 5 465 to 474, the ideal fatigue strength can be estimated to be around σw, ideal 5 744
758 MPa. Fig. 18.25 shows the S
N data for Material A. There is no apparent difference in fatigue strength between the T and L directions. All specimens fractured from

Additive manufacturing: effects of defects

471

800 ： Material A (direction–L) ： Material A (direction–T)

Stress amplitude σa [MPa]

700 600 500

B3 A2

C2

400

B2 C1

300

B1

A1

200 100

Runout 0 10 4

10 5

10 6

10 7

10 8

Cycles to failure Nf [cycles]

Figure 18.25 S
N data of Material A.

Figure 18.26 Defects at fatigue fracture origin of Material A.

defects, and fatigue failure results show a large scatter due to scatter of the defects at fracture origins. The locations of defects of fracture origins are mostly in contact with specimen surfaces. The specimens which ran out for N 5 107 cycles were tested again at a higher stress to identify the fatal inclusion which led to specimen failure. A second or third test was carried out at a stress 40 MPa higher than the previous test in order to avoid the coaxing effect. Fig. 18.26a and c are typical defects at fracture origins in Material A. Fig. 18.26b is identified as a pore. Fig. 18.27 shows S
N data for Material B. Fig. 18.28 shows the defects observed at fracture origin for Material B. These defects have various kinds and irregular shapes. Fig. 18.28 shows a defect which was observed at a fracture origin in contact with the specimen surface in Material B. It was very common at fracture origins to

472

Metal Fatigue

800

：Material B (direction–L) ：Material B (direction–T)

Stress amplitude σa [MPa]

700 600 500 b2

400

a2

300 b1

200 a1

100

Runout 0 10 4

10 5

10 6

10 7

10 8

Cycles to failure N f [cycles]

Figure 18.27 S
N data of Material B.

Figure 18.28 Defects at fatigue fracture origin of Material B.

observe defects inclined to the specimen surface. Compared to rolled steels, the direction of defects in AM materials is random and not aligned in the same direction. The varieties of defects are due to lack of fusion or various qualities of powders. Since it is very difficult to identify the presence, shape and size of defects in advance of a fatigue test, it is extremely difficult to predict the fatigue limit of individual specimens prior to fatigue testing. Nevertheless, in order to quantify the fatigue limit, we need to pay attention to the mechanics p aspect ffiffiffiffiffiffiffiffiffi of defects. The representative dimension of a defect can be expressed with area in terms of the fracture mechanics concept. From the viewpoint of the statistics of extremes, defects

Additive manufacturing: effects of defects

473

Figure 18.29 Inclined defect in contact with specimen surface and the effective defect size (dotted line).

larger than the defect observed at the fracture origin should possibly exist in the specimen. The defects at fracture origins pffiffiffiffiffiffiffiffiffi appear mostly in contact with specimen surfaces, because the effective size areaeff for a defect is larger when it exists in contact with a surface, as shown in Figs. 18.26 and 18.27. Thus, in case of Figs. 18.28 and 18.29, the effective equivalent crack size pffiffiffiffiffiffiffiffiffi areaeff can bepapproximately estimated by the dotted line, though a better estimaffiffiffiffiffiffiffiffiffi tion method of areaeff must be studied in future works. Another detrimental factor which increases the probability of fracture from surface defects is discussed from the viewpoint of stress intensity factors for surface and subsurface cracks in Appendix A. As shown in Fig. 18.25, the specimen A1 which ran out N 5 2 3 107 and B1, B2 and C1 which ran out N 5 107 were tested again at higher stress to identify the fatal defect. The data for tests at higher stresses are denoted by A2, B2, B3 and C2 in Fig. 18.25. Similar tests were carried out for the specimens a1, b1, a2 and b2 of pffiffiffiffiffiffiffiffiffi Material B in Fig. 18.27. Based on the values of the effective defect size areaeff and the Vickers hardness HV, the fatigue limit σw can be estimated by Eq. (18.2). Normalised S
N data are shown in Fig. 18.30a and b, where the applied stress σ is normalised by the estimated fatigue limit σw. It can be seen that the values of σ/σ w for failed specimens are mostly larger than B0.9 and estimation based on the p ffiffiffiffiffiffiffiffiffi area parameter model works well. However, some specimens of Material B failed at the values σ/σw close to 0.8 at around Nf 5 106. At present, the reason for this is not clear. Although the Vickers hardness of Material B is almost the same as that of Material A, the fatigue strength is lower than in Material A. As explained in the previous section, the same trend was observed for the additively manufactured Ti
6Al
4V with larger particles. pffiffiffiffiffiffiffiffiffi These results suggest that more precise estimation of the effective size areaeff is necessary for the complex configuration of multidefects as shown in Fig. 18.13. Another factor to be considered is the upper limit of the size of defects for materials having high HV. Chapetti et al. [18]

474

Metal Fatigue 2.0

2.0 : Material A (direction-L) : Material A (direction-T)

1.8

1.6

1.4

1.4 A2

1.0

C2

0.8

B3

σa /σw

σa/σw

b2

1.2

1.2

C1

a2 1.0 0.8

A1

B2

0.6

b1

0.6

B1

a1

0.4

0.4 0.2 0.0 10 4

: Material B (direction-L) : Material B (direction-T)

1.8

1.6

0.2

Runout 10 5

10 6

10 7

Cycles to failure Nf [cycles]

(a) Material A

10 8

0.0 10 4

Runout 10 5

10 6

10 7

10 8

Cycles to failure Nf [cycles]

(b) Material B

Figure 18.30 Normalised S
N curve: σ/σw
Nf [16].

Figure 18.31 ƒKI versus

pffiffiffiffiffiffiffiffiffi areaeff of defects at fracture origins [16].

pffiffiffiffiffiffiffiffiffi reported that the slope of the parea ffiffiffiffiffiffiffiffiffiparameter model, 1/3, for hard steels should converge at p a ffiffiffiffiffiffiffiffiffi critical value of area smaller than 100 μm to a horizontal line as the value of area increases. This is because ΔKth for long cracks in hard steels is smaller than for soft steels due to decrease in the crack closure effect (see Section 15.4 for VHCF). If the data of Fig. 18.27 are plotted in the same style as Fig. 5.7, we obtain Fig. 18.31. The values of ƒKth for long crack of conventionally manufactured Ni-based superalloy 718 were estimated using the database in reference manual of FATIGUE CRACK GROWTH COMPUTER PROGRAM “NASGRO” [19]. The values of σ/σw for A1, B1, B2 and C1 in Fig. 18.30a and a1 and b1 in Fig. 18.30b, which ran out for N 5 107, are confirmed to be lower than 1.0 by calculation using the defect sizes obtained by the subsequent tests at higher stress. For example, the values of σ/σw for the specimens of Material A which ran out longer than N 5 107 were summarised as follows: G

G

G

pffiffiffiffiffiffiffiffiffi Applied stress σ 5 300 MPa, N 5 2 3 107, area 5 179 μm. σw 5 352 MPa. σ/σw 5 0.85. p ffiffiffiffiffiffiffiffiffi Applied stress σ 5 365 MPa, N 5 107, area 5 19 μm. σw 5 512 MPa. σ/σw 5 0.71. pffiffiffiffiffiffiffiffiffi Applied stress σ 5 350 MPa, N 5 107, area 5 74 μm. σw 5 408 MPa. σ/σw 5 0.86.

Additive manufacturing: effects of defects

Pore

Elliptical

Linear

Pore

8.0

8.0

7.0

7.0

6.0

6.0

5.0 4.0

Elliptical defect

3.0 2.0 1.0 0.0

S0 = 80.97 mm2 –2.0 20

40

60

√area max (μm) or (a) Material A

80

Linear

Elliptical defect

4.0 3.0 2.0 1.0 0.0

Linear defect –1.0

0

Elliptical

Pore

5.0

Pore

Reduced variate yj

Reduced variate yj

475

100

Linear defect

–1.0

S0 = 116.49 mm2 –2.0 0

50

100

150

200

√area max (μm) or

(b) Material B

Figure 18.32 Statistics of extremes of the defects of the raw plate materials.

Thus, it is confirmed that these previous tests were carried out below the fatigue limit of each specimen (see Fig. 18.30). Since the fatigue limit of AM specimens is influenced by the size of defects contained in individual specimens, we must understand that we cannot define a constant fatigue limit for a material in question from the usual S
N data. Fig. 18.32 shows the statistics of extremes analysis of the largest defects which appeared on the sections cut from the raw plate materials within the area S0 5 80.97 mm2 for Material A and S0 5 116.49 mm2 for Material B. Regarding pffiffiffiffiffiffiffiffiffi linear defects, the length of linear defects was also plotted in addition to area. This pffiffiffiffiffiffiffiffiffi is because the effective value of area must be estimated by using the length of defect, based on the concept explained in Figs. 18.28 and 18.29. Although these analyses are based on 2D measurement, the statistics of extremes analysis, such as Fig. 18.32, will be useful to improve the quality of AM processes. From the viewpoint of the quality control of AM materials based on defect size, A is graded higher than B. From the above discussion, it is necessary for the fatigue design of AM components to consider the method of the statistics of extremes based on not only Fig. 18.32 (even with the 2D measurement) but also the concept of Fig. 18.33. Considering the volume andpnumbers of production of the components in question, ffiffiffiffiffiffiffiffiffi the effective largest defect areaeffmax contained in large or many components can pffiffiffiffiffiffiffiffiffi be predicted. The lower bound of the fatigue limit σwl based on areaeffmax can be determined by Eq. (18.3).

476

Metal Fatigue

8.0 7.0 6.0

Material A Reduced variate yj

5.0 4.0

Material B 3.0 2.0 1.0 0.0 –1.0 –2.0

V0 = 235.6 mm3 0

100

200

300

400

500

√area effmax (μm) Figure 18.33 Statistics of extremes of the defects at fracture origin of Materials A and pffiffiffiffiffiffiffiffiffi B in terms of areaeffmax (V0: specimen volume).

Fig. 18.33 shows the statistics of extremes analysis of the defects which pffiffiffiffiffiffiffiffiffiwere observed at fatigue fracture origins. In this analysis, the modification of pffiffiffiffiffiffiffiffiffi area was applied based on the rule of Figs. 18.28 and 18.29, and then the areaeffmax was estimated. Regarding the fatigue limit of Ni-based superalloy 718, a supplementary description may be necessary in terms of VHCF. There are several publications which report fatigue failure at cycles longer than 107 cycles from subsurface grain showing a facet at a fracture origin [20]. Thus, the possibility of ‘no fatigue limit’ has arisen for this alloy. Similar results were also reported on Ti
6Al
4V [21]. However, this phenomenon can be understood as the failure from a large grain or cluster of grains preferentially oriented to the applied stress (see Section 15.5) as the extreme value of grain size distribution, which is preferentially oriented to the applied stress, and is eventually regarded as equivalent to a defect with delayed pffiffiffiffiffiffiffiffiffi crack initiation in the interior of a specimen. Actually, the application of the area parameter model to these large grains with facet works quite well. This problem is explained in Section 15.5 in terms of the statistical nature of VHCF.

Additive manufacturing: effects of defects

18.5

477

Summary and perspectives

Major factors which influence the fatigue strength of AM materials can be summarised as follows: 1. Microstructure Phases Grain size Texture 2. Build direction As-built direction Direction transverse to build direction 3. Defects Surface roughness Pores Lack of fusion Shrinkage Inclusions 4. Residual stress

18.5.1 Defects All these factors are mutually correlated to each other. However, if we pay attention to the fatigue strength and quality control of AM components, the strongest focus must be put on defects: surface roughness, pores and lack of fusion. Although surface roughness is usually not categorised as defects in conventional machined components, decreasing the effect of surface roughness is crucially important, as seen in the results for Ti
6Al
4V. The fatigue strength of as-built specimens is decreased to the level of 1/3 of the fatigue strength of the ideal fatigue strength as shown in Figs. 18.4 and 18.5. Shrinkage is relatively rare in AM materials compared to conventional cast components. The presence of inclusions is caused by the quality of the original particles. However, the size of inclusions is relatively smaller than other defects in AM. Thus, other factors such as microstructure and building direction must be analysed from the viewpoint of controlling these defects. Defects in AM materials are mostly gas porosity and those made by lack of fusion. From the viewpoint of size, defects made by lack of fusion are more detrimental than gas porosity. Many defects which are formed at the subsurface can be eliminated by HIP. Eventually HIP improved the fatigue strength of Ti
6Al
4V drastically to the level of the ideal fatigue limit to be expected from the hardness. Surface roughness has a strong detrimental influence on fatigue strength. However, HIP does not improve the surface roughness. There was no apparent difference in fatigue strength between the built directions, T and L directions, both for Materials A and B of nickel-based superalloy 718. This is because the influence of defects is more crucial than the microstructural difference made by built direction [22].

478

Metal Fatigue

18.5.2 Goal to ideal fatigue strength Fig. 18.34 shows the overall data of fatigue strength of AM specimens compared with the ideal fatigue limit expected from the Vickers hardness. When we discuss the quality of components manufactured by AM, we need to note the gap between the ideal fatigue strength and the real data. Considering the current status of AM technology related to the above-cited influential factors, we need to develop new techniques such as microshot peening and chemical etching [15] to overcome the surface roughness effect and new processes, in combination with HIP, to diminish the remaining defects produced by lack of fusion.

Figure 18.34 Relationship between fatigue strength σw and Vickers hardness HV. There is a big gap between the fatigue strength of specimens manufacture by AM and the ideal fatigue limit expected from HV.

Additive manufacturing: effects of defects

479

18.5.3 Standardisation of defect size The real size of individual defects does not reflect the true effect of defects. The tenpffiffiffiffiffiffiffiffiffi tative method for estimating the effective size areaeff of irregularly shaped defects and interacting adjacent defects was explained from the viewpoint of fracture mechanics. It is necessary pffiffiffiffiffiffiffiffiffi to establish a more accurate standard definition of the effective defect size areaeff based on thepextended 3D analysis ffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiwith consideration of the surface effect. By combination with areaeff and the area parameter model the fatigue limit can be estimated with fairly good accuracy.

18.5.4 Surface effect Although the statistics of extremes analysis is useful for the quality control of AM, the particular surface effect and interaction effect of adjacent defects must be carefully considered. The effective defect size of multiple adjacent defects is much larger than a single defect. It must be noted that surface defects are more detrimental than subsurface defects. Romano et al. [23,24] discussed this problem in detail on Ti
6Al
4V and AlSi10Mg manufactured by AM. Fig. 18.A1 and 18.A2 compare the stress intensity factors for surface cracks and subsurface cracks. The stress intensity factor KI for a central crack with length 2a in a plate with width 2W and a/W 5 0.5, is only 18% (F(λ) 5 1.18) larger than the pffiffiffi KI0 (5σ0 πa) for a crack in an infinite plate. If there exists an edge crack with the same length in the same plate with width 2W and a/W 5 0.5, we have the high value of KI as F(λ) 5 2.827. Likewise, the stress intensity factor KI for a penny-shaped crack with radius a in the centre of a cylinder with diameter d and 2a/d 5 0.5 (Fig. 18.A2b) is only 8% pffiffiffi larger than the KI0 (5(2/π)σ0 πa) for a penny-shaped crack in an infinite body. If there exists a semicircular crack with the same size in the same cylinder with width diameter d and a/d 5 0.5, we can easily imagine the big difference compared to the crack of Fig. 18.A2b. This is the surface effect of defects in AM materials. Therefore, even if the size of a surface crack is smaller than a subsurface crack and the crack growth rate is slower at the beginning, the growth rate of the surface crack quickly overtakes the growth of a larger subsurface crack. We have to pay attention to another reason for frequent fatigue fractures from surface layer in AM materials even under tension-compression fatigue. In case of high strength steels, internal fracture from inclusions is observed in very high cycle fatigue. This is due to the low population of large inclusions in high strength steels. On the other hand, in case of AM materials, the population of large defects is very high compared to high strength steels.

18.5.5 Quality control of AM components Since the configurations of defects in AM materials are random and complex, a defect in contact pffiffiffiffiffiffiffiffiffiwith a specimen surface has a higher influence (termed the effective defect size areaeff) than the real size of the defect from the viewpoint of fracture

480

Metal Fatigue

mechanics (see also Appendix A). The statistics of extremes analysis based on the fracture mechanics evaluation of defects is useful for the quality control of AM. X-ray computed tomography (X-CT) has been actively applied for the 3D identification and measurement of all defects contained in a component. The data obtained by X-CT will be useful for the statistics of extremes analysis [2,23
25]. However, the surface effect must be carefully considered for the use of the data [2,23
25]. Considering the volume and number ofpproductions of components, the lower ffiffiffiffiffiffiffiffiffi bound of the fatigue limit σ based on area can be determined by the wl effmax pffiffiffiffiffiffiffiffiffi area parameter model.

References [1] H. Masuo, Introductory Slides for Additive Manufacturing, Metal Technology Co. Ltd, 2017. [2] S. Beretta, S. Romano, A comparison of fatigue strength sensitivity to defects for materials manufactured by AM or traditional processes, Int. J. Fatigue 94 (2017) 178
191. [3] U. Zerbst, K. Hilgenberg, Damage development and damage tolerance of structures manufactured by selective laser melting
a review, Proc. Struct. Integr. 7 (2017) 141
148. [4] R. Molael, A. Fatemi, Fatigue design with additive manufactured metals: issues to consider and perspective for future research, Proc. Eng. 213 (2018) 5
16. [5] J.J. Lewandowski, M. Seifi, Metal Additive Manufacturing: A Review of Mechanical Properties (Postprint), AFRL-RX-WP-JA-2017-0156, Interim Report, 19 April (2016). [6] M. Seifi, A. Salem, J. Beuth, O. Harrysson, J.J. Lewandowski, Overview of materials qualification needs for metal additive manufacturing, JOM 68-3 (2016) 747
764. [7] J. Gu¨nther, D. Krewerth, T. Lippmann, S. Leuders, T. Tro¨ster, A. Weidner, et al., Fatigue life of additively manufactured Ti
6Al
4V in the very high cycle fatigue regime, Int. J. Fatigue 94 (2017) 236
245. and References included in this paper. [8] G. Kasperovich, J. Hausmann, Improvement of fatigue resistance and ductility of Ti6Al-4V processed by selective laser melting, J. Mater. Process. Technol. 220 (2015) 202
214. [9] H. Gong, K. Rafi, H. Gu, T. Starr, B. Stucker, Analysis of defect generation in Ti-6Al4V parts made using powder bed fusion additive manufacturing processes, Addit. Manufact. 1 (2014) 87
98. [10] P. Li, D. Warner, A. Fatemi, N. Phan, Critical assessment of the fatigue performance of additively manufactured Ti-6Al-4V and perspective for future research, Int. J. Fatigue 85 (2016) 130
143. [11] S. Leuders, M. Vollmer, F. Brenne, T. Troster, T. Neindorf, Fatigue strength prediction for titanium alloy Ti6Al4V manufactured by selective lase melting, Metall. Mater. Trans. A 46A (2015) 3816
3822. [12] H. Masuo, Y. Tanaka, S. Morokoshi, H. Yagura, T. Uchida, Y. Yamamoto, Y. Murakami, Effects of defects, surface roughness and HIP on fatigue strength of Ti-6Al4V manufactured by additive manufacturing, Proc. Struct. Integr. 7 (2017) 19
26. And also, H. Masuo, Y. Tanaka, S. Morokoshi, H. Yagura, T. Uchida, Y. Yamamoto, Y. Murakami, Influence of defects, surface roughness and HIP on the fatigue strength of Ti-6Al-4V manufactured by additive manufacturing, International Journal of Fatigue 117 (2018) 163
179.

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481

[13] Y. Murakami, S. Nemat-Nasser, Growth and stability of interacting surface flaws of arbitrary shape, Eng. Fract. Mech. 17-1 (1983) 193
210. [14] M. Aman, S. Okazaki, H. Matsunaga, G.B. Mariquis, H. Remes, Interaction effect of adjacent defects on the fatigue limit of a medium carbon steel, Fatigue Fract. Eng. Mater. Struct. 40-1 (2017) 130
144. [15] T. Persenot, J. Buffiere, E. Maire, R. Dendievel, G. Martin, Fatigue properties of EMB as-built and chemically etched thin parts, Proc. Struct. Integr. 7 (2017) 158
165. [16] Y. Yamashita, T. Murakami, R. Mihara, M. Okada, Y. Murakami, Defect analysis and fatigue design basis for Ni-based superalloy 718 manufactured by additive manufacturing, Proc. Struct. Integrity 7 (2017) 11
18 and Y. Yamashita, T. Murakami, R. Mihara, M. Okada, Y. Murakami, Defect analysis and fatigue design basis for Ni-based superalloy 718 manufactured by selective laser melting, Int. J. Fatigue 117 (2018) 485
495. [17] For example, R. Konecna, L. Kunz, G. Nicoletto, A. Baca, Long fatigue crack growth in Inconel 718 produced by selective laser melting, Int. J. Fatigue, 92 (2016), 499
506. [18] M. Chapetti, T. Tagawa, T. Miyata, Ultra-long cycle fatigue of high-strength carbon steels part II: estimation of fatigue limit for failure from internal inclusions, Mater. Sci. Eng. A356 (2003) 236
244. [19] National Aeronautics and Space Administration. Fatigue Crack Growth Computer Program “NASGRO” version 3.0 reference manual; 2000. [20] K. Kobayashi, K. Yamaguchi, M. Hayakawa, M. Kimura, T. Ogata, S. Matsuoka, High-cycle fatigue properties of alloy 718 for space use, J. Jpn. Inst. Met. 68-8 (2004) 523
525. [21] F. Yoshinaka, T. Nakamura, S. Nakayama, D. Shiozawa, Y. Nakai, K. Uesugi, Int. J. Fatigue 93 (2016) 397
405. [22] J.N. Domfang Ngnekou, Y. Nadot, G. Henaff, J. Nicolai, L. Ridosz, Influence of defect size on the fatigue resistance of AlSi10Mg alloy elaborated by selective laser melting (SLM), Proc. Struct. Integr. 7 (2017) 75
83. [23] S. Romano, J. Gumpinger, M. Gschweiitl, S. Beretta, Qualification of AM parts: extreme value statistics applied to tomographic measurements, Mater. Des. 131 (2017) 32
48. [24] S. Romano, A. Bruckner-Foit, A. Bradao, J. Gumpinger, T. Ghindini, S. Beretta, Fatigue properties of AlSi10Mg obtained by additive manufacturing: defect-based modelling and prediction of fatigue strength, Eng. Fract. Mech. 187 (2018) 165
189. [25] I. Serrano-Munoz, J.-Y. Buffiere, R. Mokso, C. Verdu, Y. Nadot, Location, location & size: defects close to surfaces dominate fatigue crack initiation, Sci. Rep. (2017) 1
9. Available from: https://doi.org/10.1038/srep45239. www.nature.com/scientificreports, | 7:45239 |.

Appendix A

High probability of fatigue fracture from surface defects due to difference of stress intensity factor for surface cracks and subsurface cracks

By comparing the viewpoint of stress intensity factors for an edge crack and a penny-shaped crack, we can understand the higher probability of fatigue fracture from surface defects. As shown in Fig. 18.A1, the stress intensity factor KIA for an pffiffiffiffiffiffiffiffi edge crack with length aA is KIA 5 1.12σ πaA , while KIB for a penny-shaped

482

Metal Fatigue

Figure 18.A1 Stress intensity factor for 2D crack. (a) Edge crack in a semi-infinite plate, (b) Edge crack in a finite width plate, (c) Central crack. KI 5 F(λ)σ0Oπa, (a) F(λ) 5 1.1215, (b) F(λ) 5 2.827 for λ 5 a/W 5 0.5, (c) F(λ) 5 1.0 for λ 5 a/W 5 0, F(λ) 5 B1.189 for λ 5 a/W 5 0.5 [A2]

Figure 18.A2 Stress intensity factor for (a) semielliptical crack and (b) pennyshaped crack in a cylinder, F(λ) 5 2/π for λ 5 a/W 5 0, and F(λ) 5 B1.08 3 2/π for λ 5 a/W 5 0.5 [A1].

pffiffiffiffiffiffiffiffi crack (Fig. 18.A2) is KIB 5 (2/π)σ πaB . The ratio aA/aB for KIA 5 KIB is 0.323. Thus, a small edge crack having the size aA 5 BaB/3 has an equivalent stress intensity factor with a large penny-shaped crack. Moreover, as shown in Fig. 18.A2, the

Additive manufacturing: effects of defects

483

stress intensity factor for a penny-shaped crack with diameter 2aB (5d/2, λ 5 0.5) at the centre of a cylindrical specimen with diameter d is only 1.08 times larger [A1] compared to that of a penny-shaped crack in an infinite body, pffiffiffiffiffiffiffiffi KI 5 (2/π)σ πaB . For reference, in the 2D case the stress intensity factor for a crack with length 2aB (5W, λ 5 0.5) at the centre of a plate with width W is only 1.18 times larger [A2] compared to that of a 2D crack in an infinite plate, pffiffiffiffiffiffiffiffi KI 5 σ πaB . It follows that the growth of an internal crack due to the increase in the size is relatively slower than for surface cracks. If we guess the risk of a crack only based on its size, the analysis would lead us to a misconception. Thus, we need to analyse the problems of AM material from the viewpoint of stress intensity factors for both surface cracks and subsurface cracks. Moreover, if we compare the size of cracks having the identical value of stress pffiffiffiffiffiffiffiffiffi intensity factors K at crack front for a surface crack with area andffi Imaxffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi ps ffiffiffiffiffiffiffiffiffi KImax 5 0.65σ π areas, a subsurface crack with areai and K 5 0.5σ π area i pffiffiffiffiffiImax ffi and a penny-shaped crack pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiwith radius a and KI 5 (2/π)σ πa, we can estimate as areasD(0.54
0.59) areai. This is the major cause of the surface effect of defects in AM materials. [A1] Y. Murakami (Editor-in-chief), Stress Intensity Factors Handbook, vol. 2, Pergamon Press (1987), p. 653. [A2] M. Isida, Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions, Int. J. Fract. 7-3 (1971), 301
316. See also Y. Murakami (Editor-in-chief), Stress Intensity Factors Handbook, vol. 1, Pergamon Press (1987), p. 68, and Y. Murakami, Theory of Elasticity and Stress Concentration, John Wiley and Sons, Ltd, (2017), p. 81.