Experimental Study of VHCF Fractographic Features of Conventionally and Additively Manufactured Steels

Abstract Materials produced by additive manufacturing (AM) have been extremely related to literature. However, there is still unconsolidated knowledge about the fatigue life and respective mechanisms of initiation of cracks predominant in the VHCF regime for these materials. What has been observed in materials produced by conventional routes is that fatigue cracks tend to nucleate from intrinsic defects of the material located internally or in subsurface regions. The change in the evolution process of fatigue cracks leads to the formation of a characteristic morphology on the fracture surface, known as “fish-eye”. Another widespread aspect observed on the fracture surfaces is the formation of a fine granular area (FGA) nearby the initiation sites. This work aims to investigate the mechanisms of crack nucleation in VHCF of two distinct materials: conventional steel, DIN 34CrNiMo6 and AISI 316L stainless steel produced by L-DED. The ultrasonic tests were carried out at a frequency of 20±0,5 kHz and R= -1. The S-N curves were obtained and fracture surfaces were analyzed, fish-eye and FGA formation was verified. FGA sizes were compared to values estimated by empirical equations. FGA and fish-eye sizes were related to stress amplitude and maximum stress intensity factor (SIF).


Introduction
Very high cycle fatigue (VHCF) has assumed a relevant role in recent years.Due to technological development, the fatigue life of structural and mechanical components usually exceeds the high cycle regime (10 6 -10 7 cycles) 1 .
Recently, a growing study of additive manufacturing (AM) applied to ultrasonic fatigue tests has been observed.AM is becoming a promising technique for a number of applications in aerospace, automotive and medical industries.This technique is used to repair high-value-added components or manufacture new 3D parts.The process offers great flexibility in terms of the feed material (metallic powder or filler wire), it also allows the manufacture of multifunctional 3D components from different materials simultaneously [2][3][4][5][6] .Several materials can be used in this process, but AISI 316L stainless steel is one of the most studied and processed by these techniques due to the excellent properties (weldability, corrosion resistance and tensile properties) that are preserved in the final parts 6 .
Phenomena belonging to the VHCF regime, such as "fish-eye" and fine granular area (FGA) are commonly observed on the specimens' fracture surface, mainly highstrength steel manufactured by conventional routes [6][7][8][9][10][11][12] (the expression means -conventional steel manufacturing and casting process with subsequent forging and quenching and tempering treatment).However, there is still no consolidated knowledge about these features in AM materials.
This study compares the fracture surfaces of the specimens that present subsurface or internal crack nucleation after VHCF tests.The proposed steels were manufactured by conventional route (DIN 34CrNiMo6) and additively (AISI 316L).The main aims of this study were to measure the fish-eye and FGA regions and compare them with the values obtained by empirical equations available in the literature.

Fracture surface aspects
The fracture surface in VHCF can present different characteristics in comparison to other regimes.Many researchers have observed internal or subsurface crack initiation usually at non-metallic inclusions, indicating that VHCF is more sensitive to internal defects [7][8][9][10][11][12] .The fracture surface exhibits a circular fatigue crack propagation, called fish-eye and an FGA nearby the inclusion responsible for the nucleation of the crack.These phenomena occur mainly in high-strength steels and result in a fracture surface with four stages for crack formation, as presented in Figure 1: crack initiation (i), crack growth into the fish-eye (ii), crack growth outside the fish-eye (iii) and final fracture (iv) 7,10,11 .
Figure 2 presents the crack stages and their aspects with a transverse sectional view.FGA (2) region is the appearance vicinity of the internal defects (1 -e.g.inclusion) and exhibits a rough surface.Sakai 13 attributes its formation to a sequence of three stages: polygonization, nucleation and coalescence of micro debonding and complete formation of the FGA.The fish-eye region (3) presents a smooth surface and finally (4) representing the crack growth stage exhibits again a high roughness region.The figure on the right represents schematically the regions indicated in the figure on the left and their respective roughness.

FGA size equations
It is known that FGA is an important phenomenon on fracture surfaces in the VHCF regime.The stress intensity factor (SIF) value of the FGA boundary can be related to the threshold for short crack growth.The crucial role of the FGA in the VHCF regime led some authors to investigate the FGA formation mechanisms and FGA size.Empirical equations to estimate the FGA size (diameter) are available in the literature.Murakami 14,15 , Liu et al. 16 and Yang 17 proposed that the FGA size increases with the decreasing the stress amplitude and its size is dependent on the mechanical properties of the material and the applied stress amplitude (σ a ).The following are the presented empirical equations (Equations 1-3) proposed by these authors.
Yang 17 obtained an empirical equation in which FGA size by fracture mechanics.The FGA is dependent on the material's yield strength (σ y ) and σ a .The FGA size is given in meters and it is represented by φ FGA An equation proposed by Murakami and coauthors 14,15 indicates the FGA size is dependent on the Vickers hardness (HV) and σ a and the crack initiation site.The constant (C) is modified according to the crack nucleation origin, being 1.43 for subsurface crack initiation and 1.56 for internal crack initiation [18][19][20] .
( ) Equation 3, as follows, is similar to Equation 2. Therefore, Liu and co-authors 16 proposed a single value for C. In this way, the constant C becomes independent of the crack initiation site [18][19][20] .

Materials
The materials used for this study was high-strength steel manufactured from a conventional route, DIN 34CrNiMo6 21 and stainless steel by additive manufacturing, AISI 316L 22 .Table 1 shows the chemical composition with main elements and Table 2 presents the mechanical properties of both materials.The chemical characterization was performed with the Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) technique and the tension tests were conducted in an Instron 5988 equipment according to ASTM A370 23 .For the tension tests, a laser extensometer was applied to measure the deformation and the 0.2% offset method was used to calculate the elastic modulus and yield strength.
The AISI 316L stainless steel produced by additive manufacturing was produced using metallic powder by L-DED (direct energy deposition by laser) process in an RPM Innovations 535 machine with a 25° nozzle.The metallic powder used for the manufacture of all specimens was a gas atomized 316L stainless steel powder (code 316L-5520), made by Höganäs company.The powder particles are predominantly spherical, with a granulometric distribution of 53-150 µm 24,25 .The process parameters used in the manufacturing procedure were defined by prior empirical knowledge of the equipment and processing of this alloy 22 .All specimens were vertically built in the form of cylindrical bars using the same process parameters, which are indicated in Table 3.For each specimen, the outer boundary was primarily deposited and then the filling.For that, in each layer was used the zigzag deposition strategy and the direction of the filling passes was rotated 45° incrementally (0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°,0°).
After the fabrication process, the samples were subjected to heat treatments of stress relief followed by solubilization.In the stress relief treatment, the samples were kept at 550°C for 6 hours and cooled in air (cooling rate equal to 5° C/ min).In the solubilization, they were kept at 1070°C for 2 hours, considering 1 hour for a soak and 1 hour for the treatment, and later they were cooled in two stages: initially in the saline solution until 260°C and soon after in air until the room temperature.The cooling rate in air was equivalent to 5° C/min and in the saline solution was equal to 100° C/ min, respectively.And then, all the specimens for the VHCF test were machined.

VHCF test
Both materials tests were performed in an ultrasonic fatigue machine (frequency = 20 kHz) with loading conditions R=-1 and controlled temperature.Figure 3 presents the schematic drawing of the displacement and stress distribution along the system with the main four components of the machine.In the absence of standardization, the ultrasonic test machines differ from laboratory to laboratory, but the main components are: A power generator responsible to transform 50 to 60 Hz voltage signal into 20 kHz ultrasonic electrical sinusoidal signal, a piezoelectric converter that transforms the electrical signal into longitudinal ultrasonic waves and vibration (mechanical loading) of the same frequency, an ultrasonic horn that amplifies the vibration coming from the piezoelectric converter in order to obtain the required strain amplitude in the middle section of the specimen (necessary to perform the tests) and a computer for data acquisition.

S-N curves
Figures 6 and 7 present the plotted S-N data for both groups of specimens.As shown, all the experiments were carried out aiming for 10 9 cycles (run out).Both materials show a tendency of higher life for lower stresses in the VHCF regime even with considerable scatter in the results.In the two situations, an equation was obtained to predict the fatigue life based on the plotted data of specimens that failed during the tests.For the DIN 34CrNiMo6 specimens, the applied stresses that caused fatigue failure are shown to be higher than expected for the VHCF regime, achieving levels almost equivalent to half of the ultimate tensile strength of the   material under study.In fact, two of the run-out specimens did not fail under the action of stress higher than 450 MPa.The high dispersion observed in the results of AISI 316L (AM), Figure 7, is due to the number of internal defects that exist and that are not replicated in all samples.Fatigue strength for 1.0E+09 corresponds to stress values equivalent to 35% of the ultimate tensile strength (σ u ), which is consistent with the literature (the literature mentions that fatigue strength for 1.0E+07 cycles is equivalent to this percentage of σ u ) 7 .In addition, for the specimens that failed before 1.0E+07, the crack initiation site was pore and surface defects.As for the specimens that failed within the VHCF regime, the non-metallic inclusions were the mandatory defect for crack nucleation.

FGA size and estimates
Two specimens for each material were investigated by scanning electron microscopy (SEM).Table 4 summarizes the information about the material, applied stress amplitude (σ a ), corresponding fatigue life (N f ) and the crack nucleation site (CNS) of each specimen labeled from 1 to 4.
Details of fish-eye and FGA formation are observed in Figures 8-11.It was observed that in all cases the crack nucleation sites were from non-metallic inclusions.
After investigating the fracture surface and measuring the FGA sizes with the aid of a digital image program (DIP), the measured values were compared to the estimated ones by Equations 1, 2 and 3, as shown in Figure 12.
Based on this comparison, the measured FGA size of DIN 34CrNiMo6 specimens agrees well with Liu´s formula.However, for the AISI 316L (AM) specimens, the measures of FGA size presented a greater agreement with the results estimated by Yang's model.Although the result estimated by Yang's equation presented a large variation compared to the FGA size measured in specimen 3, considering the two situations it was the most suitable.The difference between these models is related to the mechanical property used as a calculation parameter for estimating the FGA size.While the Yang model considers the yield stress as the mandatory parameter, the others consider Vickers hardness.Considering these two mechanical properties, it is assumed that the Yang Model presented better results due to the lower dispersion between the values obtained for the yield stress.This is more noticeable in Figure 13, where is shown the percentage difference (error index) between measured and calculated values of FGA size for all specimens in question.The results obtained by Murakami's equation presented the worst agreement with the measured values for the four situations.
It was also verified that the measured FGA size (≈ 700 µm) in specimen nº3 by DIP for subsurface fish-eye agrees well with the literature 26 .
The fish-eye size was also measured and compared with FGA size in function of the stress amplitude, as shown in Figure 14.It was noticed that FGA and fish-eye sizes rise with the increasing stress amplitude for AISI 316L (AM) specimens.However, for DIN 34CrNiMo6 specimens the opposite happens.FGA and fish-eye sizes decrease with the increase of stress amplitude.
Moreover, the maximum stress intensity factor (SIF) at FGA and fish-eye boundaries were calculated using the Equation 4 27,28 to identify the threshold for internal short crack propagation and the threshold for circular crack propagation.Table 5 presents the     For AISI 316L (AM) specimens these values differ briefly.This is explained because the crack propagation to form the FGA consumes a large part of the area inside the fish-eye   region, which is in line with the literature 26 for the same material and build direction of the AM process.

Conclusions
The following conclusions can be drawn:

Figures 4 and 5
Figures 4 and 5 present the geometry and dimensions of the specimens according to Bathias book 7 .The resonance length of DIN 34CrNiMo6 specimens is 15.38 mm and for AISI 316L (AM) is 15.89 mm.

Figure 3 .
Figure 3. Schematic drawing of the displacement and stress distribution along the system the main components of an ultrasonic fatigue machine 7 .Table 3. L-DED process parameters.Laser power (W)

Figure 4 .
Figure 4. DIN 34CrNiMo6 specimen hourglass shape with dimension in mm.

Figure 8 .
Figure 8. SEM of fracture surface of Specimen n°1: a) Fish-eye formation and its border in the magnification; b) Magnification inside the Fish-eye and FGA regions 20,21 .

Figure 10 .
Figure 10.SEM of fracture surface of Specimen n° 3: a) Fish-eye formation; b) Magnification of FGA area with fine grain detailed.
• The crack nucleation in the VHCF regime for AM materials follows the same behavior and the cracks tend to start internally; • The FGA size measured on the fracture surface agrees well with the results estimated by Liu et al. for DIN 34CrNiMo6 specimens and the relationship proposed by Yang et al. was better suitable for AISI 316L (AM) measures; • Murakami's expression underestimated the FGA size measures for both materials;

Figure 11 .
Figure 11.SEM of fracture surface of Specimen nº 4: a) Fish-eye and FGA formations; b) Magnification of FGA area.

Figure 12 .
Figure 12.Comparison between measured and estimated FGA size.

Figure 13 .
Figure 13.Error index for each model and steel.

Figure 14 .were found around 4 9
Figure 14.Fish-eye and FGA size x stress amplitude.

Table 2 .
Mechanical properties with average/standard deviation.Experimental Study of VHCF Fractographic Features of Conventionally and Additively Manufactured Steels
a (MPa) f N (cycles) Experimental Study of VHCF Fractographic Features of Conventionally and Additively Manufactured Steels Based on calculated values of FGA K ∆ and fish eye K − ∆ , it is noticeable that for DIN 34CrNiMo6 specimens the