Improving fatigue properties of normal direction ultrasonic vibration assisted face grinding Inconel 718 by regulating machined surface integrity

Damage mechanics considers fatigue failure as a process of damage variable D evolution [19]. When material accumulates damage variable D from the initial damage D₀ to the critical damage D_c with a certain damage evolution law, fatigue failure ensues because of low residual strength [20]. Moreover, the damage evolution law is closely related to alternating loads (for a uni-axial fatigue problem: σ= σ_m + σ_asinωt), and stress amplitude σ_a is a primary dominant factor of damage evolution [21].

Within the S-N curve of metal material, the fatigue life N_f approaches infinity when the applied σ_a is lower than fatigue strength σ_f [22]. Consequently, the N_f tends to be infinite, signifying that damage D does not produce in material when σ_a < σ_f. In the condition of σ_a < σ_f, it has been proposed that there is fatigue damage D accumulation in very high-cycle fatigue; however, within the field of engineering applications, the fatigue damage D accumulation can be negligible due to its extremely slow accumulation rate [23]. Therefore, the σ_f is regarded as a critical criterion in assessing damage accumulation of metal materials. Furthermore, the precise calculation of σ_f is important for the prediction of N_f.

The mean stress σ_m within any region of the machined surface layer will vary due to different surface statuses, subsequently influencing the fatigue strength [24]. Thus, it is extremely important to establish a model that can accurately reflect the σ_f under any σ_m. Cai and Xu [25] established a fatigue strength σ_f prediction model that could accurately describe the relationship between σ_f and σ_m of materials, which was expressed by

$$\begin{align}{\sigma _{\text{f}}} = \frac{{{\sigma _r} - {\sigma _{\text{m}}} + \sqrt {{{\left( {{\sigma _r} - {\sigma _{\text{m}}}} \right)}^2} + 4\eta {\sigma _{\text{m}}}{\sigma _r}} }}{2}\end{align} \tag{ 1 }$$

where σ_r is the fatigue strength under the cycle ratio R= r; for engineering applications, the critical components are required to be non-plastic deformation, so the Soderberg relation is widely used. Thus, (σ_r)_mod is the modification of σ_r in equation (1) based on the Soderberg linear equation, it can be expressed as

$$\begin{align}{\left( {{\sigma _{\text{r}}}} \right)_{{\text{mod}}}} = {\sigma _{ - 1}}\left[ {1 - {{\left( {\frac{{{\sigma _{\text{m}}}}}{{{\sigma _{\text{s}}}}}} \right)}^\alpha }} \right]\end{align} \tag{ 2 }$$

where σ₋₁ is the fatigue strength corresponding to symmetrical cyclic loadings (R= −1); σ_s is the yield strength of the material; η is the material constant, which can be expressed by

$$\begin{align}\eta = \frac{{1 + \lambda }}{{1 - \lambda }}\end{align} \tag{ 3 }$$

where λ and α are material constants. Combining equations (1)–(3), the σ_f of the material under any σ_m can be obtained.

The fatigue strength of ground affected layer (GAL) is affected by surface topology, residual stress, and microhardness. Therefore, the influence of SI on σ_f should be considered to modify the fatigue strength σ_f model. The ground surface topography can be regarded as composed of numerous micro-notches, which produce a stress concentration under external loading. The stress concentration can precipitate the elevation in local surface stress and the concomitant reduction in fatigue strength σ_f, ultimately resulting in the initiation of fatigue cracks [26]. The stress concentration factor K_t reflects the degree of stress concentration in the notch, while the fatigue notch factor K_f evaluates the impact of stress concentration on fatigue strength σ_f. The relationship between K_t and K_f [27, 28] can be expressed as

$$\begin{align}{K_{\text{f}}} = 1 + q\left( {{K_t} - 1} \right) = \frac{{{\sigma _{\text{f}}}}}{{{\sigma _{{\text{f}},{\text{notched}}}}}}\end{align} \tag{ 4 }$$

where, σ_f and σ_{f, notched} represent the fatigue strength of material and fatigue strength considering surface topography; q is the notch sensitivity coefficient, which relates to material and machined surface topography. In engineering applications, due to the difficulty in obtaining q, the conservative calculations using K_t instead of K_f are acceptable (that is, q= 1, K_t = K_f) [29]. The σ_{f, notched} can be determined by dividing the nominal fatigue strength σ_f of the smooth specimen by the K_t, which can be expressed by

$$\begin{align}{\sigma _{{\text{f}},{\text{notched}}}} = \frac{{{\sigma _{\text{f}}}}}{{{K_{\text{t}}}}} = \frac{{{\sigma _1}}}{{{\sigma _{{\text{nom}}}}}}\end{align} \tag{ 5 }$$

where σ₁ is the principal stress of each point of surface topography along the loading direction, and σ_nom is nominal stress.

The residual stress in the machined surface layer is usually equivalent to local mean stress, which is an effectively equivalent method in the calculation of fatigue life or fatigue strength considering residual stress [30]. The equivalent mean stress σ_mr (that is, σ_mr = σ_m + σ_res) is recognized and used in the numerical calculation process in the impact of residual stress σ_res on fatigue performance, which indicates that σ_res changes the actual σ_m of component.

The refined grains can enhance the mechanical properties of metal materials by improving yield strength [31]. The work-hardening mechanism of GAL is mainly divided into fine grain strengthening and dislocation strengthening. Our previous work [32] established a quantitative relationship between microhardness and microstructure (refined grain region and high-density dislocation region) of Inconel 718. The increment of yield strength Δσ_s could be converted to the microhardness increment ΔH via equation (6) [33]:

$$\begin{align}{{\Delta }}H = {\alpha _T}{{\Delta }}{\sigma _s}\end{align} \tag{ 6 }$$

where α_T is the Tabor factor of Inconel 718 and its value is 2.918 [34]. Substituting σ_mr and equations (5) and (6) into equations (1) and (2), a fatigue strength (σ_f)_sur considering multiple SI indexes can be defined by

$$\begin{align}{\left({\sigma _{\text{f}}}\right)_{{\text{sur}}}} &= {K_{\text{t}}}\frac{{{{\left( {{\sigma _{\text{r}}}} \right)}_{{\text{sur}}}} - {\sigma _{{\text{mr}}}} + \sqrt {{{\left( {{{\left( {{\sigma _{\text{r}}}} \right)}_{{\text{sur}}}} - {\sigma _{{\text{mr}}}}} \right)}^2} + 4\eta {\sigma _{{\text{mr}}}}{{\left( {{\sigma _{\text{r}}}} \right)}_{{\text{sur}}}}} }}{2}\end{align} \tag{ 7 }$$

$$\begin{align}{\left({\sigma _{\text{r}}}\right)_{{\text{sur}}}} &= {\sigma _{ - 1}}\left[ {1 - {{\left( {\frac{{{\sigma _{{\text{mr}}}}}}{{{\sigma _{\text{s}}} + \left( {{{\Delta }}H/{\alpha _T}} \right)}}} \right)}^\alpha }} \right].\end{align} \tag{ 8 }$$

All material constants in the fatigue strength (σ_f)_sur model need to be determined. Based on the relationship between N_f and σ_a [35], the S-N curve of the Inconel 718 polished sample (without being influenced by SI) can be calculated under any σ_m and R. The relationship between N_f and σ_a can be expressed by

$$\begin{align}{\sigma _{\text{a}}}^{\beta + 1}{N_{\text{f}}} &= {C_{ - 1}}{\left( {\frac{{{\sigma _{\text{f}}}}}{{{\sigma _{ - 1}}}}} \right)^{\kappa + \beta + 1}}\mathop \int \nolimits_{{D_0}}^{{D_C}} \frac{{{{\left( {1 - D} \right)}^{\beta + 1}}dD}}{{t\left( {{\sigma _{\text{a}}}} \right)}}\end{align} \tag{ 9 }$$

$$\begin{align}t\left( {{\sigma _{\text{a}}}} \right) &= \mathop \int \nolimits_0^{2\pi } \left( {1 - {{\left( {\frac{{1 - D}}{{{\sigma _{\text{a}}}\left| {{\text{sin}}\theta } \right|}}{\sigma _{\text{f}}}} \right)}^\gamma }} \right){\left| {{\text{sin}}\theta } \right|^\beta }\left| {{\text{cos}}\theta } \right|d\theta \end{align} \tag{ 10 }$$

where κ, β, γ, and C₋₁ are material constants; t(σ_a) is an integral related to the cyclic waveform, and it represents the form of damage accumulation in a sinusoidal cycle. The S-N curves of Inconel 718 were calculated under R= −1 and R= 0.1 using equations (1)–(3), (9) and (10). Zhong et al [36] and Xu and Lei [37] obtained the S-N curve of the polishing samples of Inconel 718 alloy with R= −1 and R= 0.1, respectively. By comparing with the experimental values from Zhong et al and Xu et al the material constants of Inconel 718 were obtained (table 1). As shown in figure 1, the predicted N_f under R = −1 and R = 0.1 fitted the experimental value well.

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The ground surface topography exhibits the characteristics of geometric self-similarity and self-affinity [38], indicating that a length of 200 μm suffices to represent the entirety of ground surface topography. Given that the depth of GAL typically does not exceed 150 μm, an area with a size of 200 μm × 200 μm can be deemed representative of the GAL. The calculation process of (σ_f)_sur distribution in GAL is shown in figure 2(a). The precision of (σ_f)_sur calculation was set as 1 μm, that is, the GAL was divided into elements with a size of 1 μm × 1 μm in the calculation process. Combined with equations (7) and (8), the (σ_f)_sur distribution could be calculated after obtaining the K_t, σ_res, and microhardness data in GAL.

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The radius of curvature, micro-notches spacing, and micro-notches depth presented considerable challenges in acquisition due to their inherent randomness and the complexity involved in their measurement. Consequently, the K_t caused by the machined surface was calculated using the FEM in tandem with the actual surface topography data. In figure 2(b), a two-dimensional (2D) geometric model of the machined surface was established, and the plane strain hypothesis was supposed for this 2D calculation. The mesh was structured hex elements with a size of 1 μm × 1 μm. The reason for the 2D calculation of K_t was that this work focused on the fatigue strength distribution in the grinding depth direction. As for the transversal position, the ground surface topography was self-similar, which made it impossible (and unnecessary) to determine the exact location of the maximum value of K_t in the transverse direction. Surface node coordinates were altered utilizing a Python script based on the measured ground topography data. According to the σ_m of high-cycle fatigue tests in this work, a uniform load (σ_nom = 467.5 MPa) was applied as boundary conditions for the calculation of K_t. The principal stresses σ₁[i,j] of all elements were extracted, and then divided by the σ_nom to obtain a matrix of K_t [i,j].

The distribution of σ_res within GAL was calculated using FEM. Ordinarily, a CBN abrasive grain manifested as a polyhedral shape with 8–14 faces [39]. To obtain a polyhedral abrasive grain, a parametric Python script was used to randomly cut a cube abrasive grain. The calculation steps included the grinding step, cooling step, and boundary unloading step, which were consistent with the formation process of grinding residual strain (more details provided in Supplementary material A). Since the simulation was based on a single abrasive particle, the calculated σ_res had a periodic characteristic of abrasive grain trajectory. In the actual grinding process, the periodic characteristic was not significant because there were countless abrasive grains to remove the material. Therefore, it was assumed that the σ_res distribution of the same depth from the grinding surface was uniform. As shown in figure 2(c), the σ_res for all elements equidistant from the ground surface was extracted and their average value was computed. Taking the extraction results of σ_res, the distribution of equivalent average stress σ_mr within GAL could be obtained. Based on the material constants in table 1 and the calculation method in figure 2, the (σ_f)_sur distribution of GAL under different SI characteristics could be obtained.

Material subjected to the fatigue test is Nicked-based superalloy Inconel 718. Chemical compositions and mechanical properties of Inconel 718 are shown in tables 2 and 3 respectively. Fatigue test plate samples were obtained by diamond wire saw cutting and then processed by ND-UVAFG to investigate the effect of SI on fatigue characteristics.

Table 3. Mechanical properties of Inconel 718 (T = 25 °C).

Ultimate tensile strength ${\sigma _{\text{u}}}$/MPa	Yield strength ${\sigma _{\text{s}}}$/MPa	Elastic modulus E /GPa	Elongation $\delta$/%
1 430	1 263	200	24

As shown in figures 3(a) and (b), the fatigue test plate samples were ground using a three-axis high-precision machine (KMC600S UMT). The grinding tool was a resin-bonded CBN grinding wheel with a diameter of 20 mm and a barrel radius of 10 mm, and the grit size was 100#. Ultrasonic amplitude was applied in the axial direction of the grinding wheel by self-developed ultrasonic equipment, and grinding parameters were shown in table 4. In the experiment, the ultrasonic amplitude was set to 4 μm, and the corresponding ultrasonic frequency was 25.6 kHz. Hand-polishing was conducted on the polishing surfaces of the fatigue samples along the fatigue load direction to ensure the fatigue crack preferentially initiated on the ground surface. The size of the polishing abrasive was 2000 #. After the grinding tests, surface topography, surface residual stress, and surface microhardness were characterized. The surface topography was characterized via ZYGO 3D surface optical profilometer, and the surface roughness R_a along the fatigue load direction was measured. The residual stress was measured by Bruker D8 ADVANCEX x-ray diffractometer (Homoclination method: Φ= 0°, and ψ was $\pm$ 45°, $\pm$ 36°, $\pm$ 27°, $\pm$ 18°, $\pm$ 9°, and 0°, respectively.). The x-ray scanning range was 2θ within [−87.5°, 93.5°]; the scanning angle step interval was 0.03°; the scanning crystal plane was <311> crystal plane, and the x-ray tube target material was copper. The residual stress was measured at five positions in the middle of the fatigue samples and the measured results were averaged. A Vickers microhardness measurement apparatus (Feima) was used for measuring the surface microhardness, and the test force and keeping time were set to 5 g and 10 s. The microhardness at the same depth was measured five times and measured results were averaged.

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Table 4. Grinding parameters of fatigue samples.

Sample number	Rotation speed $n$/rpm	Feed rate vf /(mm·min−1)	Grinding depth ap/ μm	Ultrasonic amplitude A/μm
#1/#2	4 000	40	20	0/4
#3/#4	2 000	20	20	0/4
#5/#6	2 000	40	40	0/4
#7/#8	1 000	60	40	0/4

Room temperature fatigue tests were performed using an SDS-200 electro-hydraulic servo static/dynamic testing machine and repeated five times for each group. A sinusoidal waveform circle load was applied with a frequency of 20 Hz. The maximum circle load σ_max was set to 850 MPa and the cyclic stress ratio R= 0.1. It should be emphasized that the machined surface textures and orientations would affect the fatigue life, but fatigue failure tended to occur in the most dangerous situations. Therefore, the ground surface texture direction with the lowest fatigue life was selected in obtaining surface topography data and in designing the fatigue test. Chen et al [40] found that the fatigue life of surface texture transverse to the fatigue loading direction samples and surface texture obliques 45° to the fatigue loading direction samples was relatively lower. Due to the circular arc texture of the ground surface, all fatigue samples in this work were carried out based on the surface texture transverse to the fatigue loading direction. After the fatigue test, the microscopic analysis of the fatigue fracture was performed using a SEM.

3.2.1. Surface integrity of ND-UVAFG.

As shown in figure 4, the trajectories of abrasive grains in CG were the superpositions of rotation motion and feed motion, resulting in the ground surface presenting a typical gully feature. Then, ND-UVAFG introduced an additional hammering effect that produced a fish-scale texture to the ground surface. The ND-UVAFG also extended the arc length of the abrasive grain, resulting in more serious plastic deformation than CG [41]. Consequently, the combined effects of harming effect and severe plastic deformation during ND-UVAFG deteriorated the ground surface quality by comparing the R_a of CG and ND-UVAFG. Sample #2 exhibited a 67% increase in R_a over Sample #1 due to an amplified arc length at higher rotation speed n in ND-UVAFG. The plastic deformation of sample #2 was serious, and deep pits appeared on the surface of ND-UVAFG under the action of axial vibration, as shown in figure 4(a). Conversely, the decrease of rotation speed n reduced the plastic deformation significantly of ND-UVAFG during material removal, improving the deterioration of R_a. As a result, sample #6 displayed only a 33.5% increase in R_a compared to sample #5, and the R_a of sample #4 increased by only 10% compared to sample #3 due to a lower feed rate. The correlation between R_a and rotation speed n was inversely proportional; hence, the R_a was larger at n= 1000 rpm, leading to a slight difference (9.8%) in R_a between samples # 7 and # 8. In conclusion, a decrease in rotation speed n could reduce the deterioration degree of R_a for NA-UVAFG, but excessively low spindle speed (1000 rpm) would still lead to poor ground surface quality (R_a > 0.2 μm).

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In figure 5(a), as d increased, the microhardness first increased and reached its maximum value in the high-density dislocation region, then gradually decreased to the bulk material value (410 HV_0.05). This phenomenon was attributed to dynamic recrystallization caused by high temperature and high strain near the ground surface region, culminating in the formation of a refined grain region. The temperature in the region adjacent to the refined grain region was lower, which restrained the dynamic recrystallization, resulting in the formation of a high-density dislocation region. According to the Hall–Petch formula, the microhardness increment ΔH in the refined grain region was 150.4 HV due to grain boundary strengthening. The main mechanism of the high-density dislocation region was dislocation strengthening, and the calculated microhardness increment ΔH was 189 HV. The extrusion and impact of abrasive grain on the ground surface were enhanced under the action of ultrasonic vibration, resulting in the increase in the degree of ground surface plastic deformation and its influence depth; in addition, the ultrasonic vibration reduced the grinding temperature, which weakened the softening effect of grinding heat on the ground surface [18]. Therefore, ND-UVAFG increased microhardness, surface hardening depth, and surface hardening degree.

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As shown in figure 5(b), the ND-UVAFG improved the compressive σ_res on the ground surface compared to CG. The increase in compressive σ_res was attributed to ultrasonic vibration enhancing squeezing effect [42] and work-hardening degree [43] in GAL. Additionally, the high-frequency separation of the abrasive grain from the workpiece led to a reduction in grinding temperature, thereby decreasing the tensile σ_res induced by thermal effects [44, 45]. Given that the penetration depth of x-ray was generally 20 μm, the surface σ_res measured by XRD was the average value within 0–20 μm from the ground surface. Therefore, the average simulation value of σ_res within the L < 20 μm was compared with the experimental value. Since the simulation was based on a single abrasive grain grinding, the ratios of the simulation values of σ_res to the measured values were in the range of 1.9–2.8 (further details in supplementary material A3). After introducing the equivalent transformation coefficient k_eq = 2.45, the average error between the simulation values and the experimental values of σ_res was 8.81%. Therefore, the simulation value of σ_res obtained by the FEM in section 2.2 could be used for fatigue strength calculation. It should be noted that the σ_res would be released when the material was plastically deformed under alternating loading [46]. However, all of the σ_res obtained from the grinding experiments in this work were compressive σ_res (σ_res < 0) and the K_t < 1.2, indicating that the maximum stress σ_1max = K_t(σ_max + σ_res) during fatigue loading was less than σ_s. Therefore, the release of σ_res in this work could be ignored [47], and the main reason why this work did not consider σ_res release during FCI was due to the σ_res release law at the crack tip requiring further investigation.

3.2.2. Fatigue performance of samples machined with ND-UVAFG.

The fatigue fracture morphology is usually divided into three typical regions, i.e. fatigue source (fatigue crack initiation region), fatigue crack propagation region, and transient fracture region. The initiation mechanism of fatigue cracks includes surface initiation and internal initiation, corresponding to surface fatigue source and interior fatigue source. In figure 6, the machining flaw on the ground surface was identified as the fatigue source for samples #7 (figure 6(b)) and #8 (figure 6(d)), and the fatigue crack propagated radially. For samples #1 (figure 7(a)) and #3 (figure 7(c)) with R_a < 0.1 μm, the fatigue sources were also located on the ground surface. In figure 7(b), it was shown that the fatigue source of sample #2 located in GAL was within 50 μm from the ground surface. Although sample #2 exhibited a higher R_a compared to samples #1 and #3, its ground surface defects were less prone to initiate fatigue crack due to significant compressive σ_res. According to the SI data, the GAL depth of sample #4 was about 170 μm, and the fatigue source of sample #4 was located in bulk material far away from the ground surface. The fatigue sources of samples #5 and #6 were also located in the bulk material.

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The fatigue life N_f of CG samples (#1, #3, #5, and #7) and ND-UVAFG samples (#2, #4, #6, and #8) was shown in figure 8(a). Except for samples #7 and #8, the ND-UVAFG samples generally exhibited a higher N_f compared to the CG samples. Specifically, ND-UVAFG samples #2 and #4 both demonstrated an increase in N_f exceeding 90% when contrasted with CG samples #1 and #3. The N_f of ND-UVAFG sample #6 was the highest, which was 22% higher than that of CG sample #5. However, the N_f of ND-UVAFG sample #8 was lower than that of CG sample #7.

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In figure 8(b), the N_f of samples #1, #3, #7, and #8, of which feature fatigue sources located on the ground surface, was comparatively low. For high-cycle fatigue, the fatigue crack initiation life N_i and fatigue crack growth life N_p accounted for more than 80% of the total fatigue life N_f, especially the N_i would consume a lot of time. The propensity for machining flaws on the ground surface to act as nucleation sites for fatigue cracks meant the acceleration of the fatigue crack initiation process. This acceleration resulted in the fatigue life of samples #1, #3, #7, and #8 being relatively low due to the surface fatigue source. Conversely, samples (#2, #4, #5, and #6) with interior fatigue sources were less susceptible to early fatigue crack initiation attributable to machining defects. Therefore, samples #2, #4, #5, and #6 had a higher fatigue life than samples with surface fatigue sources.

Fatigue cracks were prone to initiate at the location with the minimum fatigue strength, which was [(σ_f)_sur]_min or (σ_f)_bm. Thus, FCI sites could be predicted by the location of the minimum fatigue strength. For the polishing surface of the fatigue sample, the R_a of the polishing surface was less than 0.03 μm, and the calculated minimum fatigue strength was about 368 MPa, which was nearly equivalent to the fatigue strength of bulk material ((σ_f)_bm = 375 MPa). As a result, the influence of the polished surface on fatigue strength was deemed negligible, and the polished surface was representative of the bulk material. Taking samples #1 and #4 as examples, the accuracy of the fatigue strength model needed to be verified. In figure 9, the (σ_f)_sur distribution of sample #1 indicated that minimum fatigue strength in the GAL [(σ_f)_sur]_min appeared at the stress concentration position caused by the surface topography, and the fatigue crack was easily initiated on the ground surface. For sample #4, the compressive σ_res introduced by ND-UVAFG could restrains the stress concentration effect on the ground surface, resulting in the [(σ_f)_sur]_min greater than the (σ_f)_bm. Therefore, the fatigue crack was initiated in the bulk material of sample #4 and on the ground surface of sample #1, respectively. The predicted FCI sites with different SI characteristics were consistent with the location of the fatigue source in experimental results, which verified the developed fatigue strength model.

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In conclusion, the location of the fatigue source was directly related to SI and indirectly determined the fatigue life of the sample. According to the above results, a strategy for improving the fatigue life was proposed in this work, which was to transfer the fatigue source from the machined surface to the bulk material by controlling the SI indexes. To achieve this strategy, it was necessary to analyze the influence mechanism of SI on FCI sites based on the (σ_f)_sur distribution of GAL in detail.

Elements with (σ_f)_sur below σ_a (382.5 MPa) would accumulate fatigue damage D. The rate of damage accumulation for D was inversely proportional to the fatigue strength, indicating that elements with the minimum fatigue strength were most susceptible to becoming fatigue sources due to their higher rates of damage accumulation. The minimum fatigue strength could be either the minimum fatigue strength of ground surface [(σ_f)_sur]_min or the fatigue strength of bulk material (σ_f)_bm. Under the experimental conditions of this work, the fatigue strength (σ_f)_bm of bulk material was calculated to be 375 MPa. When [(σ_f)_sur]_min < (σ_f)_bm, the FCI sites tended to appear on the ground surface, otherwise FCI sites would locate in the bulk material. Owing to the σ_res simulation values used in calculating the (σ_f)_sur, the σ_res on the ground surface in subsequent analyses was based on the average values of simulations within 0–5 μm close to the ground surface.

The ground surface topography was composed of countless micro-notches, and the (σ_f)_k represented the fatigue strength considering only the stress concentration caused by surface micro-notch. As shown in figure 10, the K_t at the trough of the surface micro-notches could reach 1.19, while the K_t at the peak of surface micro-notches was all less than 1. This localized stress concentration at the troughs of the surface micro-notch led to the FCI sites ([(σ_f)_k]_min) on the ground surface, resulting in the fatigue cracks easily initiating on the ground surface (surface fatigue source). In figure 11, without the influence of the σ_res and the microhardness, the stress concentration led the [(σ_f)_k]_min to appear easily on the ground surface, even for samples #1, #3, and #4 with R_a < 0.1 μm. For samples #2, #5, #6, #7, and #8, the [(σ_f)_k]_min was relatively lower due to the severe stress concentration effect induced by the greater surface roughness (R_a > 0.13 μm). In essence, micro-notches-induced stress concentrations invariably led to FCI sites appearing on the ground surface of all samples, which deviated from the experimental results of actual fatigue source locations. Therefore, an evaluation of ground surface fatigue properties could not be limited to considering only ground surface topographical influences. The σ_res and the microhardness of GAL also played crucial roles by enhancing fatigue strength and thus altering the location of FCI sites.

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After considering the impact of residual stress and microhardness on fatigue strength, the fatigue strength (σ_f)_sur distribution of samples with FCI sites on the ground surface was shown in figure 12. The FCI sites ([(σ_f)_sur]_min) were located on the ground surface for samples #7 and #8, despite their compressive σ_res both exceeding 300MPa, owing to their large surface roughness (R_a > 0.2 μm). A high compressive σ_res did not guarantee that FCI sites would avoid locating on the ground surface. Indeed, the effect of compressive σ_res and microhardness on improving fatigue strength was not significant at poor surface roughness R_a. Similarly, a minimum R_a did not ensure an absence of FCI sites from the ground surface either. It is important to recognize that although the surface roughness R_a of samples #1 and #3 was less than 0.1 μm, FCI sites were still located on the ground surface because of the lower compressive σ_res. The beneficial impacts of compressive σ_res and microhardness on fatigue strength were insufficient to offset the deterioration of fatigue strength caused by the stress concentration effect, resulting in the FCI sites ([(σ_f)_sur]_min) located at the micro-notches on the ground surface. The predicted locations for FCI sites of samples #1, #3, #7, and #8 were consistent with the experimental observations where the fatigue source was located on the ground surface. The above conclusion indicated that the stress concentration had a more substantial negative effect on fatigue strength than the positive influence exerted by residual stress or microhardness, which explained why the FCI sites were located on the ground surface.

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Although the significantly higher R_a of sample #2 (Ra = 0.149 μm) compared to sample #1, the [(σ_f)_sur]_min of sample #2 was 377.8 MPa due to the introduction of large compressive σ_res by ND-UVAFG. Therefore, the [(σ_f)_sur]_min of sample #2 surpassed its (σ_f)_bm, resulting in the FCI sites being transferred to the bulk material. For sample #4, the surface roughness R_a (0.082 μm) was almost equivalent to that of sample #1, but the [(σ_f)_sur]_min (387 MPa) was higher than the (σ_f)_bm (375 MPa) due to the improvement of (σ_f)_sur by compressive σ_res (−387 MPa) and work hardening. As a result, the bulk material of sample #4 easily initiated fatigue cracks compared with the GAL at σ_a = 382.5 MPa, unifying with observed fatigue source location in fatigue fracture morphology. For sample #5 (R_a = 0.134 μm), the [(σ_f)_k]_min was located on the ground surface, and compressive σ_res transferred the FCI sites from the ground surface ([(σ_f)_sur]_min = 378.07 MPa) to the bulk material. In figure 11(f), it was evident that the stress concentration of sample #6 was obvious due to its rougher ground surface (R_a = 0.155 μm), and the difference between the [(σ_f)_k]_min of samples #6 and #7 was not significant. However, under the action of compressive σ_res, the FCI sites of sample #6 were not presented on the ground surface but rather located in the bulk material. As shown in figure 13, the compressive σ_res ultimately strengthened the fatigue strength of the ground surface, resulting in the minimum fatigue strength of (σ_f)_bm, and FCI sites were located in the bulk material. For samples #2, #4, #5, and #6, the prediction results of FCI sites were consistent with fatigue source in experimental observation, which indicated that the larger compressive σ_res could transfer the FCI sites from the ground surface to the bulk material, thus improving the fatigue life of the sample.

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In conclusion, the FCI sites were determined by SI indexes (stress concentration, σ_res, and microhardness). The fatigue strength of the ground surface was a result of competition between the deteriorating effect caused by stress concentration and the strengthening effect by compressive σ_res, microhardness. When the deteriorating effect was greater than the strengthening effect, the ground surface became the FCI sites ([(σ_f)_sur]_min < (σ_f)_bm), and the ground surface would initiate fatigue crack. In contrast, when the strengthening effect was greater than the deteriorating effect, the ground surface was strengthened ([(σ_f)_sur]_min > (σ_f)_bm) and did not become the FCI sites, resulting in the bulk material was prone to initiate fatigue crack. Therefore, a strategy for improving the fatigue life could be proposed, which was to transfer the FCI sites from the machined surface to the bulk material by controlling the SI indexes. Effectively controlling this transition of FCI sites depended on quantifying the competitive relationship between strengthening and deteriorating effects. Following this strategy required calculating an SI field where FCI sites were more likely to be located in bulk material based on this developed model.

In figure 14, the trends of (σ_f)_sur to the σ_m were analyzed under varying conditions of microhardness increment ΔH (K_t = 1, σ_res = 0 MPa). It was observed that the increment of (σ_f)_sur caused by work-hardening was only 1.03% at σ_m = 467.5 MPa (experiment value). For ND-UVAFG Inconel 718, the influence of microhardness on (σ_f)_sur proved to be minimal at this specific σ_m level; therefore, when calculating the SI field for improving fatigue life, only K_t and σ_res were taken into account. In this work, the microhardness was not a key indicator for calculating the SI field improving fatigue life, which only represented the microhardness was not the main influencing factor for the (σ_f)_sur of ND-UVAFG Inconel 718 at σ_m = 467.5 MPa. However, whether microhardness was the main influencing factor on fatigue strength still requires to be determined by materials, mean stress, and machining processing [48].

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The (σ_f)_sur was a result of competition between K_t and compressive σ_res. Due to the stress concentration, the [(σ_f)_sur]_min was generally located on the ground surface and was lower than (σ_f)_bm, which led to the FCI sites appearing on the ground surface. On the contrary, the [(σ_f)_sur]_min would be greater than the (σ_f)_bm because of compressive σ_res, and then FCI sites were located in the bulk material. To quantify this competitive relationship in (σ_f)_sur, the fatigue strength difference Δσ_f between [(σ_f)_sur]_min and (σ_f)_bm was introduced, that was, Δσ_f = [(σ_f)_sur]_min—(σ_f)_bm. Subsequently, the influence of K_t and σ_res on the Δσ_f was analyzed. A positive Δσ_f (Δσ_f > 0, [(σ_f)_sur]_min > (σ_f)_bm) suggested that the fatigue cracks were easier initiated in bulk material, which would prolong the fatigue life; a negative Δσ_f (Δσ_f < 0, [(σ_f)_sur]_min < (σ_f)_bm) indicated that the fatigue cracks were prone to be initiated at stress concentration on the ground surface, and the fatigue life reducing. Therefore, a critical condition of SI indexes that FCI appeared in the ground surface or bulk material was Δσ_f = 0. The SI field with Δσ_f > 0 was defined as the fatigue life improving region, and the SI field with Δσ_f < 0 was defined as the fatigue life deteriorating region.

In figure 15(a), a compressive σ_res of −150 MPa was required to achieve the fatigue life improving region at K_t = 1.05; however, this became challenging at K_t = 1.3, where a much higher compressive σ_res of −550 MPa was required. For samples #7 and #8, with maximum values of K_t on the ground surface were 1.176 and 1.196 respectively, their compressive σ_res values were both less than −350 MPa. As a result, samples #7 and #8 were in fatigue life deteriorating region with FCI sites emerging on the ground surface, which led to them exhibiting the lowest N_f. The fatigue life improving region could be achieved when the compressive σ_res on the ground surface reached −350 MPa for samples #1—#6 (K_t < 1.15). Specifically, when analyzed samples #1 and #3 with the maximum K_t on their ground surfaces being 1.13 and 1.126 respectively, the FCI sites was still located on the ground surface due to insufficient compressive σ_res (−227 MPa and −307 MPa). This resulted in relatively low N_f for both samples #1 and #3 due to compressive σ_res did not reach the requirement, but sample #3 demonstrated higher N_f than sample #1. On the other hand, the FCI sites of samples #2, #4, #5, and #6 were located in bulk material because these samples exhibited substantial compressive σ_res (−387 MPa, −395 MPa, −356 MPa, and −423 MPa) at the ground surface. The overall comparison revealed that average fatigue life increased by approximately 140% for samples in the fatigue life improving region compared to samples in the fatigue life deterioration region. The calculation results were consistent with the experimental results, which verified the effectiveness of the critical condition.

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The ND-UVAFG process has been successful in introducing significant compressive σ_res, but it would also bring the issue of increasing K_t caused by impact pits on the ground surface. Previously, the process parameters of ND-UVAFG that could improve the fatigue life were not unclear. To improve N_f effectively, the SI field should be within the fatigue life improving region. In figure 15(b), the σ_res and K_t were calculated when the Δσ_f = 0, and the relation of Δσ_f = 0 was obtained by fitting, that was σ_res = 778.3 × K_t ^−4.398–786.3. The fatigue life improving region could be achieved corresponding to conditions where σ_res and K_t satisfied the equation: 778.3 × K_t ^−4.398–σ_res > 786.3. Rotation speed n is an important factor that determines the R_a and its deterioration degree. Since R_a inversely correlates with n, a smaller K_t can be obtained with a higher rotation speed (n > 1 000 rpm). Nonetheless, ND-UVAFG induces greater arc length than CG at n= 4 000 rpm, resulting in serious plastic deformation during material removal processes. Under the action of high-frequency ultrasonic vibration, the obvious pits will be formed on the ground surface, leading to the K_t > 1.15. In addition, the compressive σ_res is positively correlated with the rotation speed n. To introduce a larger compressive σ_res, the rotation speed n should be controlled within 2000–3000 rpm considering the K_t and σ_res. To fully utilize the advantages of compressive σ_res introduced by ND-UVAFG while ensuring that K_t remains below critical levels (<1.15), a small grinding depth a_p (20–40 μm) and feeding speed v_f (20 mm·min⁻¹) are recommended for grinding the Inconel 718.