Study on fatigue crack growth property of abrasive waterjet peened aluminum alloy

Abrasive waterjet peening is a favorable surface treatment method for improving the fatigue resistance of metal materials. An insight into the fatigue crack growth properties of AWJ peened specimens is meaningful for obtaining better strengthening performance. In present work, a numerical model of AWJ peening was established and experimentally validated for investigating the fatigue crack growth characteristics of Aluminum specimens. The effect of peening and loading conditions on the fatigue performance was also analyzed. The results indicated that the stress intensity factor at the peened region was enhanced and the crack propagation was significantly inhibited by the compressive residual stress. The influence of compressive residual stress on the effective stress factor range is greater under lower external load and higher loading ratio. The fatigue life for reaching the crack length of 40 mm is increased by 37%, 60% and 98% after peening by using the intensity of 0.6 mmA, 0.8 mmA and 1 mmA, respectively.


Introduction
Fatigue is a common reason for the failure of metal components.This phenomenon generally occurs after the bearing of alternating loads, and the stress for the fracture initiation is much lower than the yield strength of the material.The fracture usually initiates at the inherent defect on surface, and therefore the surface strengthening is important for prevention of the fatigue failure.Shot peening is a commonly used surface strengthening method for metal components, which can introduce microstructure modification and compressive residual stress to the surface layer.The compressive residual stress can inhibit the subsurface crack initiation and development, and therefore improve the fatigue performance of materials [1][2][3].
Among the various derivative methods of shot peening, abrasive waterjet peening has the advantage of lower thermal effect and less surface damage [4][5][6].Wang et al [7] investigated the plastic deformation of the nickel based alloy induced by abrasive waterjet peening and found that the near surface grains were refined with a depth larger than 100 μm.Song et al [8] studied the treatment performance of submerged abrasive waterjet on the titanium alloy.The result showed that refined grain hardening layer and the compressive residual stress field can effectively prevent the crack initiation.Yao et al [9] used abrasive waterjet peening on TA19 alloy and found that nanoscale grains and abundant dislocations were generated on the work-hardened layer.
The improvement of fatigue resistance mainly results from the deceleration of crack propagation induced by the strain hardening.The fatigue crack growth of the peened specimen therefore raised concerns.Wang et al [10] investigated the fatigue crack property of titanium alloy after the treatment of shot peening.The result indicated that the formation of cracks was delayed by 64% and the fatigue life was prolonged by 34%.The fatigue performance of components after shot peening depends significantly on the conducting parameters such as coverage rate and peening intensity, etc. Liu [11] used the cohesive zone model for analyzing the fatigue crack growth of nickel based alloy treated by shot peening, and found that the crack initiation position depended on the shot peening intensity.Hatamleh et al [12] investigated the fatigue crack growth of shot peened aluminum alloy and found that the growth rate depended strongly on the external load ratio.Qin et al [13] studied the effect of peening coverage on fatigue crack growth property of aluminum.The result indicated that da/dN-ΔK curve changed little under constant loads and the growth rate reached minimum at 300% coverage.He et al [14] studied the fatigue behaviors of shot peened turbine blade material under different conditions and found that intense intensity can lead to crack retardation and longer fatigue life for the well finished specimen.Cerny et al [15] investigated the effect of shot peening on short fatigue cracks of Al-alloys, and the results indicated that an extensive plastic deformation zone localized in the cladding layer.The critical defect length for the reliable arrest is 0.35 mm by using shot peening.
The researches on abrasive waterjet peening mentioned above detailed the compressive deformation and the microstructure modification, whereas the crack growth characteristics have not been fully inspected.This paper aims to investigate the fatigue crack growth behavior of AlSi10Mg alloy, which is commonly used for elaborate parts in aeronautic industry and strengthened by traditional shot peening currently.The crack propagation rate and the stress intensity factor under different peening and loading conditions were analyzed by implementing the established numeric model.

FE modeling of the peening
The peening simulation is essential for obtaining the residual stress field before the fatigue crack growth analysis of the specimen.The finite element model established in ANSYS LS-DYNA 19.0 is shown in figure 1.The abrasive particles are assumed to be randomly distributed in the horizontal dimension, and impact on the surface layer-by-layer.Considering that excessive exposure has little effect on the strain hardening, full coverage was applied for each trial [16].The alumina particle was taken as rigid body due to its high hardness.The velocity of the particle was considered to be the same with the laden water flow, which can be calculated by: Where P is the water pressure and ρ is density of the water.All impacts were assumed to be vertical for better deforming effect.
A small part of the peened region on the aluminum specimen was modeled with the size of 8 mm × 8 mm × 3 mm.8-node hexahedral elements were used to mesh the model.The mesh number was finalized as 344956 after evaluating the computation dependency on the mesh accuracy.Johnson-Cook constitutive model was used to describe the dynamic behavior of the specimen material under impacts.The relevant parameters are listed in table 1.
In order to verify the validity of the model, experiments were performed by using the previously developed abrasive waterjet equipment depicted in [18].The chemical composition of the target material is shown in table 2. The experimental operating conditions were determined based on the simulation conditions and listed in table 3.For easier quantifying the exposure degree to the shots, the conducting parameters were transferred to Almen intensity according to the method described in [19].After the processing, the specimen surface was cleaned and observed using SEM.As the section shown in figure 2, the dimples introduced by abrasive particles spread over the surface.The surface roughness was slightly increased from 2.4 μm to 3.7 μm.The measurement of residual stress induced by the abrasive waterjet peening was performed by using XRD method.Cu-Kα radiation under 30 KV and 20 mA was employed.The ψ angles was ranged from 0°to 45°.The residual stress distribution along depth was measured with the assistance of electrochemical delamination.The residual stress profile along the vertical direction of the impacted aluminum target is shown in figure 3. Compressive residual stress layer was located at the sub-surface region.Higher peening intensity can lead to increases of the compression depth and magnitude.The result of the simulation corresponds well with that of the experiment.The deviation is under 17%, which shows an acceptable reliability of the numerical model.

Modeling of fatigue crack
Compact tension specimen is commonly used for evaluating the crack propagation behavior.The geometry of the specimen modeled in ANSYS 19.0 is shown in figure 4, which has the same dimensions with that in [20].The model is meshed with the higher-order tetrahedral element SOLID 187.The tensile alternating load was applied at the holes.The loading amplitude was ranged from 1 KN to 2 KN, and the load ratio R was ranged from 0.1 to 0.3 with a frequency of 25 Hz.The stress-strain curve is shown in figure 5.The square areas close to the tip on both sides of the specimen were peened for generating residual stress.The peened area dimension is 20 mm × 30 mm.The vertical distribution of residual stress field obtained in the preceding numerical analysis was polynomial fitted, and then implemented on elements of the peening area with the utilization of INISTATE function.
A singularity always exists around the crack tip, and the stress and strain adjacent to the crack tip usually have high gradients.The crack tip mesh is crucial for the stress-analysis and fracture-parameters calculation accuracy.To record the sharply changing stress and strain fields, the mesh adjacent to the crack tip was refined and shown in figure 6.
Interaction integral method is used to calculate the stress intensity factor.Local crack tip coordinate system is set up for establishing crack-tip field in interaction integral formulation.The local coordinate system should keep the consistency through entire nodes of the crack front.The inconsistency of coordinate systems will lead to independency of the calculated stress intensity factor on path, as well as the disordered distribution of stress intensity factor around the crack front.
During the crack growth simulation, the mesh is updated based on crack shape variations arised from crack growth at each calculation step.The crack propagation calculation starts subsequent to the stress calculation in the solution stage.In other words, the stress intensity factor is solved prior to the crack propagation.The crack growth increment is solved with the usage of the maximal dimension of the element at the crack front.The increment for each iteration is calculated with the crack propagation, as well as the maximal stress intensity factor at the crack front.

Fundamentals of fatigue crack growth
Crack growth represents the detachment of the separated fracture surfaces.Energy-release-rate method is commonly used to treat this problem.The actuation of the crack growth demands an increment of the surface  energy for detachment of the fracture surfaces.A threshold exists for the surface energy to meet the requirement of crack surface detachment and the further crack growth.
Under the background of linear elastic fracture mechanics, a threshold should be exceeded for the stress at the crack tip.For the case of fatigue crack, the growth occurs before reaching the threshold of stress under the static case.The stress intensity factor represents the stress amplitude at the crack tip under a certain geometrical and loading condition.The stress situation adjacent to the crack tip can be described by the linear superposition of stresses induced by the external load and the residual plastic deformation.The overall stress intensity factor can be therefore expressed as: Where K ex and K res are the stress intensity factors related to the applied loading amplitude and the residual stress condition, respectively.The overall stress intensity factor range and the stress ratio can be therefore expressed as: For considering the effect of stress ratio, effective stress intensity factor range ΔK eff is adopted and the crack growth rate can be derived as [21]: Where γ is the sensitivity coefficient to stress ratio of the material, C and m are material constants.

Results and discussion on fatigue crack properties
The fracture crack growth rate curve as a function of effective stress intensity factor range of the untreated specimen is shown in figure 7. The comparison was made with the experimental data in [20], and shows an acceptable consistency.The model can therefore be considered as valid.
The crack propagation under different loading conditions were investigated.Figure 8 shows the variation of the stress intensity factor with the crack length under different load amplitudes.It is depicted that the stress intensity factor increases with an increase of the external load.The stress intensity factor at the front end of the peened region is higher compared with that of the untreated region.However, the stress intensity factor within the peened region decreases with an increment of the crack length.This can be attributed to the compressive residual stress at the deformation zone and the balancing tensile residual stress outside the deformation zone.Overall stress intensity factor, which is comprised of the external load stress intensity factor and the residual stress intensity factor, directly influences the crack growth rate.The crack propagation can be enhanced by the tensile residual stress and inhibited by the compressive residual stress.With further increment of crack length, the overall stress intensity factor of peened specimen approaches to the same with that of the untreated one.The effective stress intensity factor range under different loads is shown in figure 9.It can be inferred that the compressive residual stress has greater influence on the effective stress intensity factor range under lower external load.The effective stress intensity factor range at the tip front after peening is higher than that of the untreated one.The effective stress intensity factor range decreases with an increment of the crack length, and finally converge to that of the untreated specimen.The crack growth rate shown in figure 10 has a similar variation tendency with the effective stress intensity factor range.
The effective stress intensity factor range and the crack growth rate under different load ratios are shown in figures 11 and 12.It is depicted that the effective stress intensity factor range is lower under high external load.The compressive residual stress has less influence on the effective stress intensity factor range when the load ratio increases.The reduction of the applied mean force by the compressive residual stress at the peened zone is unapparent under higher external load ratio.For the untreated specimen, the stress ratio at the crack tip is equal to the external load ratio.The results indicated that the crack growth retardation by shot peening is insignificant under high load ratio.
The variation of the fatigue crack propagation rate with the stress intensity factor range is shown in figure 13.It can be found that the propagation rate of crack after peening is lower than that of the untreated when the stress intensity factor range is relatively low.This can be attributed to the inhibition on the crack propagation by the compressive residual stress at the early stage.With the increase of the stress intensity factor range, the gap between crack propagation rates of peened and untreated samples diminishes.The variation of the crack length with the number of load cycles is shown in figure 14.The fatigue life for reaching the crack length of 40 mm is increased by 37%, 60% and 98% after peening by using the intensity of 0.6 mmA, 0.8 mmA and 1 mmA, respectively.It can be inferred that the fatigue life and the final crack length are both higher after peening.The crack length sharply increases with the load cycle number after exceeding about 20 mm, which indicates a fast growth phase of the crack.The compressive residual stress left by the peening can significantly delay the fast growth of the crack.

Conclusions
In present study, the fatigue crack growth properties of abrasive waterjet peened aluminum alloy specimens have been analyzed with the implementation of numerical models.Conclusions can be drawn as follow: 1.The stress intensity factor increases with an increase of the external load.The stress intensity factor increases and then decreases with an increment of the crack length in the peened region.
2. The effective stress intensity factor range at the tip front after peening is higher than that of the untreated one, and finally converge to that of the untreated specimen with an increment of the crack length.Compressive residual stress has greater influence on the effective stress intensity factor range under lower external load.3. The crack growth retardation by shot peening is insignificant under high load ratio.The compressive residual stress has less influence on the effective stress intensity factor range when the load ratio increases.
4. The fatigue life for reaching the crack length of 40 mm is increased by 37%, 60% and 98% after peening by using the intensity of 0.6 mmA, 0.8 mmA and 1 mmA, respectively.The compressive residual stress can significantly arrest the fast crack propagation.

Figure 1 .
Figure 1.FE model of the target with one-layer of particles.

Figure 4 .
Figure 4. Geometry model for the compact tension specimen.

Figure 5 .
Figure 5.The stress-strain curve of the specimen.

Figure 6 .
Figure 6.Refined zone of the mesh around the crack tip.

Figure 8 .
Figure 8. Overall stress intensity factor with respect to the crack length under different loads (Almen intensity = 0.6 mmA, R = 0.1).