Fatigue life investigation of notched TC4 specimens subjected to different patterns of laser shock peening

of view. Proposed LSP pattern allowed one to increase the fatigue life of specimens with semi-circular notch by an order of magnitude. The numerical simulation of the LSP was performed to visualize the residual stress field of treated specimen after loading and to give the interpretation of the experimentally observed improvement of fatigue life.


INTRODUCTION
he key benefit of Laser Shock Peening (LSP) treatment is enhancement of fatigue properties in metallic materials. Therefore, it has been widely applied to commercial alloys used in aerospace industry (especially aluminum and titanium) to increase fatigue life of aircraft components and engineering structures weakened by stress concentrators. A. G. Sanchez et al. [1] studied the effect of LSP with and without protective coating on the fatigue performance of AA7075-T651 aluminum samples with pre-corroded pits in them. They found that generated residual stresses effectively suppress the influence of corrosion pits and improve fatigue life up to 160 000 cycles for LSP without coating and 80 000 cycles for LSP with coating. J. G. Pretorius et al. [2] simulated residual stresses due to LSP in fillet radii step region on a high-speed gas turbine engine shaft made of AISI 4340 steel and estimated fatigue life in Fe-safe software. The results demonstrated substantial improvement by 553% in the case of LSP. Ren et al. [3] studied the effect of double-sided LSP of a thin Ti-6Al-4V dog-bone specimen on fatigue properties in presence of foreign object damage. They obtained that double-sided LSP increases fatigue performance of the sample by the introduction of compressive residual stresses. Similar results were obtained by J.-M. Yang et al. [4]. They applied LSP to the open hole specimens made of 2024-T3 aluminum alloy. The obtained results have shown significant improvement in fatigue performance for the various notch configurations when both sides of the samples were treated simultaneously. Jan Kaufman et al. [5] performed corrosion fatigue tests on rectangular specimens made of AA5083 aluminum alloy. The specimens subjected to LSP without protective coating and fully submersed into the water have better improvement of fatigue life (+69%) than samples with protective coating in standard laminar flow conditions (+59%). Several studies compared the effectiveness of LSP with traditional surface improvement techniques although not all of them showed that LSP has better performance. For instance, A. Clauer [6] compared the fatigue life of AA7075-T7351 notched specimens treated by LSP with shot-peened (SP) specimens. He obtained that LSP induces a higher increase in the number of cycles to failure than SP. However, in [7] it was found that for fretting fatigue tests of Ti-6Al-4V dogbone specimen SP gives better results than LSP. At the same time, the authors obtained deeper compressive residual stresses in the case of LSP but with a lower magnitude. J. Epp and H.-W. Zoch [8] compared LSP with Water Jet Peening (WJP) and Shot Peening (SP) with regard to the microstructure, surface topography, residual stresses, and fatigue properties for gear teeth-like specimens made of case-hardened steel. They have found that LSP has minimal effect on surface topology while WJP induces surface damage. SP is characterized by the presence of the strong plastic deformation. Regarding the fatigue properties, SP shows the highest improvement (+37%), while LSP and WJP demonstrate lower results (+15% and +23% respectively). In terms of the residual stresses, LSP has shown the deepest penetration of the compressive residual stresses but the magnitude is lower than SP, which is in agreement with the results presented in [7]. In addition to these findings, some works presented an insignificant or even deteriorating influence of LSP on fatigue life. Abdul-Jabar H. Ali [9] reported minor improvement (up to 1.534 times) in the fatigue life of AA7075 aluminum alloy specimens treated with LSP which were tested at a constant amplitude stress range from 0.3σ u up to 0.8σ u , where σ u is the ultimate strength. G. Ivetic et al. [10] studied the effect of laser shots treatment on the fatigue performance in open-hole aluminum specimens. They carried out residual stress measurements, fractographic analysis, and numerical simulation. The results have shown presence of tensile residual stresses in the mid-section of the specimens after the treatment. Therefore, the positive effect of LSP was found when the hole was cut after the LSP and negative effect was encountered when the hole was already presented. P. Ouyang et al. [11] studied the effect of LSP on the fatigue life of Ti-6Al-4V titanium alloy experimentally and by means of numerical simulation. Numerical results have shown an improvement in the fatigue life of the peened specimen in more than 17 times in comparison with the non-treated one. However, experimental results haven't confirmed such significant enhancement. The authors explained that fact by the presence of local stress concentrators in the samples exposed by laser shots treatment which can cause a negative influence on the fatigue life. Zhao et al. [12] analyzed crack propagation rates for the CT-samples with a V-shape notch subjected to LSP with two different patterns obtained experimentally and by FEM simulation. They concluded that the considered LSP patterns (peening of the area near the notch root and peening of the area at some distance from the root) had led to a decrease in fatigue performance in comparison with the untreated sample. M. Achintha et al. [13] also concluded that laser shots treated open hole specimens can have low fatigue performance. They carried out fatigue tests on two aerospacegrade aluminum samples with two different thicknesses (thin and thick) and two different peening schemes as well as a numerical simulation of residual stress distribution in them. The experiments demonstrated some improvement in the fatigue life for thin specimens after LSP in the area around the hole and no effect for the thick ones. The numerical simulation explained these observations by the presence of tensile stresses in the mid-plane of the thick specimens. In the present work, the influence of LSP patterns on the fatigue life of notched TC4 specimens is studied experimentally. Two LSP patterns different from each other by their location relative to the notch are used to form the residual stress T field in the notched area. The fatigue life of treated and untreated specimens is determined during fatigue tests. Numerical simulation of LSP allows us to visualize the created residual stress field and to interpret fatigue test results.

MATERIALS AND EXPERIMENTAL CONDITIONS
itanium alloys are widely used in the aerospace industry and in engineering to produce structures, semi-finished products, and aircraft components. Alpha-beta titanium alloys are typically medium of high-strength materials (tensile strength ranging from 620 to 1250 MPa). However, their fatigue characteristics (fatigue life, fracture toughness, and so on) can be significantly improved by surface treatment processes such as LSP. In this work, specimens of TC4 (Ti-6Al-4V) titanium alloy with a semi-circular notch ( Fig. 1) were investigated under fatigue loading conditions after laser shots treatment. LSP was carried out on the basis of the original Laser Pinning Complex assembled in the Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences. It includes a Nd:YAG high energy laser Beamtech SGR-Extra-10, industrial robotic manipulator STEP SR50 and residual stress measurement system SINT MTS3000 RESTAN. Additional optic system can produce the laser beam with a square-form profile of 1 mm side. The pulse duration and energy of laser impact were 10 ns and 1 J, respectively. The aluminum foil of 80μm was used as an ablative layer. Two LSP patterns shown in Fig. 2 were realized. In the case of the LSP pattern №1 (Fig. 2 (a)), the treatment area was on the surface of the front and back side of specimen and includes the semi-circular notch zone. The LSP pattern №2 ( Fig. 2 (b)) assumed the LSP treatment directly in semi-circular notch along a curved path. The laser beam was directed along the normal to the surface in both cases. Two series of specimens treated by above mentioned two patterns were tested under uniaxial cyclic loading conditions. Fatigue experiments were carried out on a 100kN servo-hydraulic testing machine Bi-00-100 under constant maximum loading of 10 kN at a stress ratio R=0.1 and loading frequency 10 Hz. The number of cycles before fracture of specimens in two parts was registered for treated specimens and untreated ones (base material).

EXPERIMENTAL RESULTS
s a result of LSP, the residual stress field was formed on the specimen surface and under the surface up to a depth of 1 mm. The maximum value of compressive residual stress and the depth of its formation are the main characteristics that show the efficiency of laser shots treatment for the mechanical properties improvement. The T A measurement of the residual stresses values versus the depth of the treated layer was carried out by the hole drilling method using an automatic system MTS3000-Restan (according to ASTM E837-13a). This method has a number disadvantages such as flat surface of the specimen, measurements only in one point of the surface, selection of suitable strain gauge sizes if specimen is small enough, providing only two components of residual stress and etc. Due to these restrictions, the drilling method allows us to measure the residual stress profile only in the case of the LSP pattern №1. A high curvature of the treated surface in the pattern №2 and its small size did not allow us to use the hole drilling method for residual stress profile determination. However, it is fair to assume that a laser impact of the same power density forms in the same material the residual stresses field with the similar magnitude and configuration. The dependence of residual stress components (σ x , σ y ) on the subsurface layer depth (Fig. 3) was obtained for following characteristics of laser shot: 1 J energy impact, 10 ns pulse duration, 1 mm 2 beam profile area, 10GW/cm 2 power density.  According to the results of the fatigue test, the LSP pattern №1 doesn't have a significant influence on the fatigue life of the treated specimens. The average number of cycles before fracture of the base material and specimens treated by LSP pattern №1 is 130·10 3 cycles and 142·10 3 cycles, respectively. At the same time, the LSP pattern №2 induces a significant grow in the fatigue life (more than 10 6 cycles). Two specimens were broken near the grip (i.e. not in the treated semicircular notched area). Another two specimens indicated by arrow in Fig.4 weren't broken at all. This experimental observation is probably related to the most optimal configuration of residual stress field generated by LSP in the stress concentrator region. In this case, the applied stress level, at which the fatigue crack grows in the base material, is not enough for a fatigue crack initiation in specimens after LSP by the pattern №2. To confirm this assumption, it is necessary to analyze the residual stress distribution in the stress concentrator region. Experimental measurements of residual stress distribution in this region are difficult. Therefore, to analyze the distribution of residual stresses in the specimen after the application of the LSP pattern №2 and explain the fatigue life improvement after LSP a numerical simulation has been carried out.

NUMERICAL SIMULATION
s it was shown above, LSP pattern № 1 didn't improve the fatigue life of the notched specimens. Similar results were obtained by other researchers [10,13]. They obtained no improvement in the fatigue life of samples with stress concentrators. These results were related to the deteriorating effect of tensile residual stresses which occur in the specimen after the treatment. It was observed [10,13] that tensile residual stresses produced in the mid-section of the specimen with stress concentrator during LSP of its front and rear sides contribute to negative effect on its fatigue performance. The LSP scheme № 2 is different and laser shots are applied directly at the concentrator. This peening pattern leads to a significant improvement in the fatigue performance of specimens. To analyze distribution of residual stresses in the sample after application of this pattern and explain these results the numerical simulation has been carried out. The numerical simulation was conducted using a finite-element model of a multi-shot LSP process which was developed in [14].

Finite-element model
In this work, only a brief description of the material model and numerical simulation process is given. More detailed information can be found in [14]. Similar to [15][16][17][18][19], LSP was considered as a purely mechanical process. Therefore, the formation of high-pressure plasma and surface ablation were neglected during the simulation. The effect of the laser pulse was taken into account by imposing mechanical pressure on the treated surface. Numerical simulation was performed in finite-element software Abaqus. Fig. 5 shows the geometry of the computational domain. The geometry corresponds to the tested samples. Boundary conditions were assigned according to the experimental procedure. The half-circled zone near both ends of the gage at the front side (shaded areas at Fig. 5(a)) as well as half of the opposite side of the sample (without stress concentrator) (shaded area at Fig. 5(b)) were fixed. These conditions correspond to the gripping of the specimen by robotic arm in the LSP process. The specimen was discretized by 8-node linear brick elements with reduced integration (C3D8R). A more refined mesh was applied at the peened area. Convergence study had shown that optimum size of the sample in this region was equal to 0.1 mm. In other regions mesh size was increased with the maximum element size which didn't exceed 2.5 mm. The peening strategy was the same as in the LSP pattern № 2. Only the bore of the notch was subjected to LSP. The peening zone was a semicircular domain with chords at a distance of 4 mm from the external stress concentrator edges. Each laser shot was modeled by the two-step approach. The first step was dynamic which simulated elasto-plastic stress wave propagation induced by pulse loading. At this step, an explicit time integration scheme was applied. Laser pulse was imposed as a pressure boundary condition acting at the square region with an edge size of 1 mm of the stress concentrator surface. Following [16,20,21], it was assumed that pressure function for square spots is spatially homogeneous. A simple triangular approximation of dependence of the pressure P on time t was used as it has been proved to be valid for LSP simulation [15,22,23]: where t  τ is the time of pressure increase, t 2 τis the time of pressure decrease, τ=10 ns is the laser pulse duration, P peak is the peak pressure value. Parameters t 1 and t 2 for TC4 alloy were determined in our previous work [14] and verified for a large range of laser peak intensities from 3.3 GW/cm 2 to 40 GW/cm 2 . The total duration of time at this step was equal to 10 μs to ensure that no further plastic strain had occurred. Peak pressure was calculated according to Fabbro model of ablation in a confined medium [24]: where Z=(2·Z water ·Z t )/( Z water +Z t ) is the combined acoustic impedance of water (Z water = 0.17·106 g/(cm 2 ··s)) and target (Z t = 1.7·106 g/(cm 2 ··s) for aluminum foil [25]), α is the efficiency coefficient which is typically equal to 0.33, I is the maximum energy density (10 GW/cm 2 in our case). As the dynamic step had finished, the static step was calculated using an implicit time integration scheme. Stress tensor components, strain tensor components, and the displacement vector components were transferred from the previous (dynamic) step as the initial values for the static step. This step is aimed to simulate a stress-strain state after a laser shock impact. The stresses at the static equilibrium state are the residual stresses. This procedure was repeated for each shot until all stress concentrator area was peened.

Material model
As LSP induces propagation of elasto-plastic waves in the material, the strain-rate sensitive model should be applied for its simulation. In our previous study [14] it has been shown that the Johnson-Cook plasticity model is effective for LSP modeling: where σ eq is the equivalent stress, ε pl eq is the equivalent plastic strain, έ pl eq is the equivalent plastic strain rate, A is the yield stress, B is the strengthening coefficient, n is the strain hardening exponent, C defines strain-rate sensitivity, έ 0 is the reference (quasistatic) stain rate. It should be noted that effects related to the thermal softening are negligible during LSP. Therefore, these effects are not considered in the present work [25][26][27]. Johnson-Cook material parameters and elastic constants for TC4 are presented in Tab. 1 [14]. The elastic material behavior was isotropic and described by Hook's law with two parameters (Young modulus and Poisson's ratio). Johnson-Cook material parameters were determined in [14] as a result of an identification procedure. Uniaxial stress-strain data obtained in the strain rate range from 5·10 -3 s -1 to 2.2·10 3 s -1 were used for this purpose. A, B, n parameters were defined using experimental quasistatic tensile diagram. Strain-sensitive material parameter C was obtained by dynamic stress-strain curves measured in a split-Hopkinson-bar testing system. The above-described model was verified in [14] for a wide range of peak energy densities (from 3.3 GW/cm 2 to 40 GW/cm 2 ) and square spots with edge sizes varied from 1 mm to 3 mm. The verification was performed by comparison of the numerical in-depth residual stress profiles with the experimental data provided by the hole drilling method. The predicted results were in reasonable agreement with the experimental measurements for all considered cases. Fig. 6(a) shows the distribution of  22 stress tensor component which is parallel to a longitudinal direction of the sample whose notch is subjected to the treatment with the LSP regime № 2. To present a more detailed distribution of residual stress near the stress concentrator, the results have been restricted by the cross sectional planes, one of which is located in the middle of the sample and the other one is at a distance of 1.25 cm from it. It can be seen that compressive residual stress is formed in the peening zone as expected. However, due to the complex geometry of the sample notch the distribution is non-homogeneous. The maximum compressive value is about -700 MPa and it is located in the middle of the stress concentrator surface. This part of the sample is the one where fatigue crack is expected to initiate. Therefore, it is important to produce compressive residual stress throughout the entire thickness of the sample and do not let the tensile stress within it. With the increase in the distance from the middle of the stress concentrator the compressive stress gradually declines. As the peening zone doesn't include the whole stress concentrator, compressive residual stress is absent in the area near the external edge of the concentrator. The figure shows that tensile stress in the middle part of the concentrator is located only under the peened surface and at the sample faces adjacent to the notch. Fig. 6(b) illustrates the distribution of mechanical pressure, which gives us information about the mean value of three main stress tensor components. It can be seen that this value is also heterogeneous owing to the curvature of the stress concentrator. However, the maximum value of compressive residual stress is achieved along the whole peening zone. The location of tensile stress in the middle part of the concentrator is the same as for  22 . Fig. 6(c) presents the distribution of effective plastic strain after LSP with pattern №2. Due to the high curvature of the notch and the complex interaction between the residual stress generated by the first shots and elasto-plastic stress waves induced by each subsequent laser shot, the distribution of the plastic strain is non-homogenous. Only in the middle of the stress concentrator, a small zone with enough uniform strain distribution can be distinguished. On average, the magnitude of effective plastic strain is 1-3% which is explained by a high value of TC4 yield stress (Tab. 1). On the whole, it can be seen that the LSP strategy №2 leads to favorable residual stress distribution. The tensile residual stress is located under the sample surface or in regions subjected to low loading during the fatigue test, while the highly loaded part of the sample under the fatigue test is surrounded by compressive residual stress.

Results of simulation
To analyze the effect of the LSP pattern №2 on the stress state during uniaxial loading the peened sample was stretched with the maximum force applied in the fatigue experiment which was equal to 10 kN. Fig. 7 illustrates the distribution of  22 stress tensor component over the whole sample. This component has been chosen as it is directed along the loading of the specimen. The tensile stress is localized in the middle part of the notch at the front surface. The same conclusion is valid for the opposite side of the specimen. The shape of the tensile zone is typical for this type of loading. The compressive residual stress is still can be seen at the inner surface of the stress concentrator.  For the detailed analysis of the stress state near the notch, the same part of the specimen as in Fig. 6 has been chosen. Fig.  8(a) presents the distribution of  22 . The maximum tensile stress is still under the surface of the sample. However, the compressive residual stress near the edges of the notch converts into tensile. Also, the value of compressive residual stress in the middle part of the notch surface diminishes due to the tensile loading. The compressive residual stress becomes more homogeneous near the chords bounding the peening zone. This part is less loaded than the middle part of the sample under mode I loading. restricted by two vertical planes (the first one located at the middle of the sample and the second one is at the distance of 1.25 cm from it) after tension with the loading equal to 10 kN. Fig. 9 gives results in a more suitable for comparison purposes way. Fig. 9(a) presents profiles of residual stresses induced by LSP pattern №2 along the specimen thickness at the three different positions of the notch surface. The first curve is located in the middle of the notch, the second curve is at the quarter of the notch radius, and the third curve is near the chord of the peening zone. All curves show that there is a compressive stress state at the surface of the notch after LSP.
The values near the edges of the notch are lower than values at the middle of the thickness. As it was mentioned above, the maximum compressive residual stress is observed in the middle part of the notch. For the considered location of the curve, its value is -700 MPa. With the increase in the distance from the center, the compressive stress declines. At the quarter of the notch radius, its absolute value decreases by 1.6 times and is about -430 MPa. The lowest value is near the boundary of the peening zone and it is equal to -160 MPa. Fig. 9(b) shows profiles of  22 stress tensor component in the peened specimen subjected to tension. The profiles are obtained for the same locations as in Fig. 9(a). The significant increase in the  22 for the first and the second curve can be observed. For the third curve the results are nearly the same as after LSP pattern №2 without any loading. This indicates that this zone is only slightly affected by the loading. Due to the rise in stress all curves have similar values which varies from -230 MPa to -150 MPa for the thickness interval from 1 to 2 mm. However, the second curve demonstrates that the stress level near the front and rear faces of the sample is close to zero. Moreover, the third profile indicates tensile stress state of the sample near the boundary chord of the peening zone.
The minimum value of the stress component in the middle of the notch shown by the first profile is equal to -150 MPa ( Fig. 9(b)). Therefore, the external loading induces a decline in compressive stress in this region about 4.7 times in comparison with the unloaded case ( Fig. 9(a)). Nevertheless, the stress state in the notch remains compressive. Although the tensile stress occurs in the other two considered regions due to the external loading, its maximum value at the surface does not exceed 300 MPa which is significantly lower than the yield stress of TC4 alloy (Tab. 1). Consequently, during cyclic loading, the sample in the notch area undergoes only elastic deformation. Thus, the LSP pattern №2 leads to the improvement in the fatigue life observed in the test, as the largest tensile stress is located only under the peened surface as it is shown in Fig. 9. The first line corresponds to the residual stress after pattern №2 in the absence of the external loading. The second line shows the stress profile in the peened sample after the tension of it with a force equal to 10 kN. From the first curve, it can be seen that the penetration depth of the compressive residual stress after LSP pattern №2 is about 0.6 mm. The minimum value is around -700 MPa similar to the Fig. 9(a). The maximum tensile stress is at the depth of 0.9 mm and it is equal to 90 MPa. The difference in minimum value of residual stress between experimental results presented in Fig. 3 and numerical results given in Fig. 10 is nearly 16%. This minor disagreement can be explained by possible measurement inaccuracies of the incremental hole drilling method due to its incremental and destructive character. Difference in the penetration depth of compressive residual stresses is explained by the different conditions of elastic-plastic stress wave propagation. Experimental results presented in Fig. 3 correspond to the LSP pattern №1, where the plane surface of the sample has been treated, while numerical results given in Fig. 10 correspond to the LSP pattern №2, where curvilinear surface of the stress concentrator has been peened. It should be noted also that numerical results demonstrate the effect of stress drop on the peened surface. It can be seen that the maximum value of compressive stress is observed not at the material surface, but in the near-surface zone. This effect is associated with the generation of surface relaxation waves from the perimeter of the laser spot, which results in a decrease of compressive stresses at the treated surface [28][29][30]. A specific feature of the hole drilling method is the averaging of the obtained data over the drilled area. Therefore, it can affect the ability of it to register properly the above-described effect.
After the tension the stress component increases (the second curve in Fig. 10). The minimum value becomes equal to -180 MPa which indicates the substantial effect of the loading though at the notch surface stress is still compressive. At the same time, the penetration depth of compressive stress is declined by 60% and has a value of 0.2 mm. The maximum subsurface tensile stress is at the same depth and is around 500 MPa which is 5.5 times higher than after LSP pattern №2.
Despite the fact, that there is a substantial increase in subsurface tensile stress this value is also lower than the yield stress of TC4. Thus, it can be concluded that LSP regime №2 is effective because it contributes to the decrease in the stress value in the highly-loaded regions of the sample.

CONCLUSIONS
he work presented experimental results on the fatigue life of the notched TC4 specimens subjected to LSP. Two LSP patterns were examined in the context of fatigue life improvement. The experimental study has shown that different LSP schemes with the same characteristics of laser impact have a discrepant effect on the fatigue life. An important role is played not only by laser impact characteristics but also configuration and place of LSP of sample surface relative to the stress concentrator region and loading conditions. In the present case, it has been found that LSP of the stress concentrator area leads to a more significant improvement of fatigue properties of the sample in comparison with the conventional approach when the front and rear surfaces of the sample near the notch are peened. The proposed LSP pattern increases the fatigue life of specimens with a semi-circular notch by an order of magnitude. The numerical simulation of the LSP regime was performed to visualize the residual stress field in the treated specimen after loading and to give the interpretation of the experimentally observed improvement of the fatigue life. The applied LSP model was based on a two-step approach according to which dynamic and static problems were solved to obtain residual stress distribution after each shot. Although this method is characterized by substantial computational costs, it provides an accurate representation of the residual stress field. The numerical results have shown that the chosen treatment regime let us avoid the formation of the tensile stress at the middle section of the sample notch. Since the tensile stress increases during subsequent fatigue test and causes a crack initiation, reduction of it due to LSP contributes to the fatigue life improvement. When the semi-circular notch of the sample is subjected to LSP, the bore of the notch is in compressive stress state and the maximum tensile residual stress is located under the surface of the sample. Subsequent tension of the sample with the loading corresponding to the maximum force in the fatigue experiment induces decrease in the compressive stress in the middle part of the stress concentrator as well as the rise in the tensile stress inside the sample. However, the surface tensile stress is far from the yield stress and the specimen deforms in the elastic range during fatigue loading. Therefore, the substantial improvement in fatigue life is observed in the experiment.