metals

Article

Investigation of Laser Treatment as a Method for Fatigue CrackGrowth Retardation in Aluminum Alloy 2198-T851

Cauê Pettermann Carvalho 1 , Milton Sergio Fernandes de Lima 2 , Viktor Pastoukhov 1

and Carlos Antonio Reis Pereira Baptista 1,*

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Citation: Carvalho, C.P.; de Lima,

M.S.F.; Pastoukhov, V.; Baptista,

C.A.R.P. Investigation of Laser

Treatment as a Method for Fatigue

Crack Growth Retardation in

Aluminum Alloy 2198-T851. Metals

2021, 11, 2034. https://doi.org/

10.3390/met11122034

Academic Editor: John Campbell

Received: 4 November 2021

Accepted: 11 December 2021

Published: 15 December 2021

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4.0/).

1 Engineering School of Lorena, University of São Paulo (EEL/USP), Lorena 12602-810, SP, Brazil;caue.pc@usp.br (C.P.C.); vpastouk@usp.br (V.P.)

2 Photonics Division, Institute for Advanced Studies (IEAv/DCTA), São José dos Campos 12242-150, SP, Brazil;msflima@gmail.com

* Correspondence: carlos.baptista@usp.br

Abstract: Among the third-generation Al-Li alloys, AA2198 stands out for its lower density, formabil-ity and increased stiffness, being suitable for use in aircraft fuselage sheets and other inner structuresin order to reduce weight and improve performance. An important topic related to damage tolerantstructures is the development of techniques to retard fatigue crack propagation, such as the localizedheating by a laser source. The aim of the present work was to find the most suitable parameters forthe production of laser heating lines in 2198-T851 alloy sheets in order to reduce the fatigue crackgrowth rate in this material. Laboratory tests using C(T) specimens under two loading conditions(R = 0.1 and 0.5) provided a useful dataset on the laser heated material. The experimental resultsindicate a 200 W laser beam power at treatment speeds of 1 and 10 mm/s was sufficient to retardcrack growth in the current setup. The more expressive results were obtained for 200 W laser powerwith a speed of 1 mm/s and cyclic loading with stress ratio R = 0.1.

Keywords: laser surface treatment; laser heating; fatigue crack growth; AA2198-T851

1. Introduction

The growing demand for lighter structures and for manufacturing and operating costsreduction has driven research into materials and processes for the aeronautical industry.A current trend in these projects is comprised of hybrid structures combining compositematerials and advanced aluminum alloys, of which the latest to find general use in theaircraft industry is the aluminum-lithium (Al-Li) alloy. Lithium is the lightest known metaland the addition of Li to aluminum alloys offers the promise of substantially reducing theweight of aeronautical alloys. Just 1 wt.% Li added to aluminum reduces the density by 3%and increases the elastic modulus by about 6%. Al-Li alloys are fairly weldable, possesshigh fracture toughness and present high resistance to fatigue crack propagation [1,2].

The third generation of Al-Li was developed from the 1990s with reduced Li con-centrations, aiming to solve the anisotropy and thermal stability problems presented bythe previous Al-Li alloys. An emphasis was given on the 2xxx system, resulting in anessentially ternary Al-Cu-Li with Li contents generally being between 1 and 2 wt.% and Cucontents between 2 and 4 wt.%, although other elements can also be added to the alloys.The typical intermetallic precipitates formed during thermo-mechanical processing, andwhich respond for the main hardening mechanisms, are δ’ (Al3Li), θ’ (Al2Cu), T1 (Al2CuLi),β’ (Al3Zr) and S’ (Al2CuMg). Among the developed alloys, the AA2198 class stands out forits lower density, good formability and increased stiffness, being suitable for use in fuselageskins and other inner structures aiming to reduce weight and improve performance [3,4].

In damage tolerant metallic structures, the adoption of less conservative projects ismade possible by enhancing the reliability of the life predictions of cracked components.Much study has been conducted on the fatigue crack growth (FCG) of metallic materials.

Metals 2021, 11, 2034. https://doi.org/10.3390/met11122034 https://www.mdpi.com/journal/metals

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However, an important topic related to this subject that needs more research is the develop-ment of techniques to mitigate or retard FCG. Over time, various efforts have been made,ranging from drilling holes near to the crack tip causing its temporary stop [5], to methodssuch as shot peening, cold expansion, overloads, adhesive bonded coatings and variouslaser treatments [6–11]. Most of them are based on the introduction of compressive residualstresses favoring retardation or even crack arrest. Even if the positive effects of the inducedresidual stresses are not taken into account in a project, manufacturers and operators usesuch techniques because they help to reduce the maintenance costs. Recently developedmethods like the localized heating by a laser source are promising tools to improve thedamage tolerance approach [7,12–14].

The localized heating gives rise to residual stress fields due to the differential thermalexpansion and contraction between the heated volume and the base metal, similarly tothe residual stresses developed upon welding, and it seems to be more feasible for use inthin sheets. Yee and Sidhu [7] evaluated the claim previously made by Parker [12] in hispatent, that the residual tensile stress induced by heating a narrow strip of sheet materialalong the crack path and ahead of the crack can reduce the shear stress at the crack tipresulting from fatigue loading and thus effectively retard the FCG rate. They pointedout the need for further research to determine the laser absorbent coating for aluminumalloys and for a more accurate control of process parameters such as the duration of laserbeam exposure and the speed of laser scanning. Schnubel et al. [13] used an Nd:YAGlaser to produce heating lines perpendicular to the crack growth direction in AA2198-T3C(T)100 specimens. The tensile residual stresses generated in the direction of the heatingline were compensated for by compressive residual stresses near the heating line. Thesecompressive stresses retarded FCG, enabling a 100% increase in the propagation life of5 mm thick sheets. Cunha and Lima [14] applied laser heating lines in AA2024-T3 alclad1.6 mm thick specimens using a Yb:fiber laser. The laser power was maintained at 200 Wand a combination of laser speed, number of heating lines and surface coating were appliedto the specimens. The best results in terms of increased FCG lifetime for tests conductedat a stress ratio of 0.1 were achieved by applying two laser heat lines to carbon blackspray-painted specimens and were in the range of 44% to 64%, depending on laser speed.Kashaev et al. [15] used a 2.2-kW Nd:YAG laser to apply a defocused laser beam power of600 W with a spot diameter of 3.5 mm and an advance speed of 1.6 m/min to the surfaceof 2 mm thick AA20204-T3 sheets. Two different treatment designs were investigatedregarding their potential to retard FCF: lines and circles. The highest FCG life extension of285% was achieved by the application of four laser beam heating lines or two circles oneach specimen side. Although some advances have been made, more research is neededregarding the optimization of laser heating treatments and the quantification of their effects.

The aim of the present work was to find the most suitable parameters for the produc-tion of laser heating lines in 2198-T851 alloy sheets in order to reduce the FCG rate in thismaterial. Laboratory tests using C(T) specimens under diverse loading conditions provideda useful dataset on the laser heated material. The experimental data were analyzed in orderto describe and explain the effect of laser heating on the FCG behavior of the alloy.

2. Material and Methods

The material used in this work was an AA2198-T851 sheet with 2.0 mm thickness. Thisthird-generation Al-Li alloy patented by Constellium (formerly Alcan) with the trademark“Airware” is one of the most advanced Al-Li alloys commercially available currently. TheT851 temper corresponds to solution heat treatment followed by quenching, stress relievingby stretching and then artificial aging. The chemical composition of the alloy, determined viainductively coupled plasma mass spectrometry (ICP Vista MPX, Varian, Palo Alto, CA, USA)in a previous work [16], conforms to AMS 4412 standard and includes, as main elements, thefollowing (wt. %): 1.01 Li, 3.68 Cu, 0.305 Mg, 0.12 Zr, 0.03 Si, 0.027 Ti, 0.08 Fe and 0.01 Zn(Al–remainder). The tensile properties of the AA2198-T851 sheet material are: Young’smodulus = 81 GPa, yield stress = 439 MPa and ultimate tensile strength = 480 MPa [16].

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The local heating treatments were performed using an IPG Photonics (Oxford, MA,USA) Yb:fiber laser model YLR-2000, with a maximum power of 2 kW. The optical headwas positioned 12.2 mm above the focal length, resulting in a Gaussian spot diameter of2 mm on the surface of the aluminum sheet samples, which were previously spray paintedwith carbon black to ensure uniform absorption of the laser heating. The laser irradiationexperiments were performed in a computerized numerical control (CNC) table. In orderto find the most promising process parameters, some preliminary tests were conductedin which various combinations of the laser powers (150, 200 and 250 W) and the opticalhead displacement speed over the sheet surface (1, 2.5, 5 and 10 mm/s) were set. Theobjective of these tests was to determine laser energy densities that produce visible heatinglines without undesirable effects such as excessive melting of the material (as in welding)or visible bending of the sheet samples. By means of visual inspection, the resultinginteraction between the laser beam and the sheet material was rated as weak (any effect),ideal, or destructive (too much melting). Some combinations considered optimal wereperformed in quadruplicate for statistical purposes.

Microstructural analyses and hardness measurements were performed in cross sectionsamples taken from the preliminary test sheets. The samples were sectioned transverselyto the heating lines by abrasive cutting with a low-speed diamond saw, cold mounted inepoxy resin and then mechanically polished and etched (10 s) with Keller reagent (190 mLdistilled water, 5 mL nitric acid, 3 mL hydrochloric acid and 2 mL hydrofluoric acid) formicrostructure visualization using a Leica (Wetzlar, Germany) DM4000 optical microscope.The hardness measurements, taken approximately 100 µm below the laser treated surface,were performed using a Buehler (Lake Bluff, IL, USA) Micromet 2004 Vickers hardnesstester with 50 gf load and 10 s dwell time.

Compact tension C(T) specimens, cut in the T-L orientation, were adopted for the FCGtests. The specimens were manufactured by electrical discharge machining including thenotch with a root radius of 0.25 mm. From the preliminary tests, two laser beam heatingconditions were selected for the fatigue specimens, namely, the displacement speeds of1 mm/s and 10 mm/s, both with a laser power level of 200 W. Just like the preliminary testsheets, the FCG specimens were spray painted with carbon black prior to laser irradiation.Each specimen was irradiated with two heating lines on the same side and each heatingline was produced by a single laser pass. The position and number of the heating lines werebased on the previous work by Cunha and Lima [14]. For comparison, some of the FCGspecimens were left in the “as-received” condition (i.e., without laser beam heating line).The specimen dimensions, including the heating lines position, are shown in Figure 1.

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Figure 1. Geometry and dimensions (mm) of the FCG specimens, including laser lines positioning.

The FCG tests, conducted in accordance with the ASTM E647-15e1 standard at room temperature in laboratory air, were performed with constant load amplitude under force control using an MTS (Eden Prairie, MN, USA) 810 servo-hydraulic machine. The fatigue pre-cracking of the specimens was performed prior to the FCG tests, by letting a pre-crack to grow about 15 mm from the notch tip and ensuring that the final maximum load during pre-crack was less than the maximum load of the test, for which the data were obtained. The test frequency was kept constant at 5 Hz and the loading waveform was sinusoidal. Two load ratios (min/max) were adopted for the tests: R = 0.1 and 0.5. The compliance method of crack length monitoring was used during the tests. The crack growth rate was calculated using both the secant and the seven-point incremental polynomial methods.

3. Results 3.1. Microstructural Examination and Hardness Measurements

Figure 2 presents cross section optical micrographs of samples treated with 200 W laser power and four laser speeds, showing the influence of the laser treatments on the microstructure beneath the laser irradiated surfaces. It can be seen that, for the laser speeds of 2.5 and 5 mm/s, the material was melted, resulting in a porous resolidified layer. It is noteworthy that, for both the highest and lowest adopted speeds, no surface melting occurred. The heating marks are visible and distinguished by their coarser microstructure resulting from grain growth. While the absence of a fusion zone in the 10 mm/s sample can be attributed to a lower heat input, it is somewhat surprising to find the same feature in the material treated with 1 mm/s laser speed. One possible reason for this is that the higher heat input resulted in a more intense oxidation of the carbon black, thus reducing the ablative layer. The direct interaction of the laser beam with the aluminum sheet due to the higher reflectivity results in less energy absorption. All of the tests with laser power 250 W resulted in fusion zones with high porosity. On the other hand, the tests with laser power of 150 W resulted in almost indistinguishable microstructural changes. These con-ditions (150 W and 250 W) were not presented here.

Figure 1. Geometry and dimensions (mm) of the FCG specimens, including laser lines positioning.

The FCG tests, conducted in accordance with the ASTM E647-15e1 standard at roomtemperature in laboratory air, were performed with constant load amplitude under forcecontrol using an MTS (Eden Prairie, MN, USA) 810 servo-hydraulic machine. The fatigue

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pre-cracking of the specimens was performed prior to the FCG tests, by letting a pre-crackto grow about 15 mm from the notch tip and ensuring that the final maximum load duringpre-crack was less than the maximum load of the test, for which the data were obtained.The test frequency was kept constant at 5 Hz and the loading waveform was sinusoidal.Two load ratios (min/max) were adopted for the tests: R = 0.1 and 0.5. The compliancemethod of crack length monitoring was used during the tests. The crack growth rate wascalculated using both the secant and the seven-point incremental polynomial methods.

3. Results3.1. Microstructural Examination and Hardness Measurements

Figure 2 presents cross section optical micrographs of samples treated with 200 Wlaser power and four laser speeds, showing the influence of the laser treatments on themicrostructure beneath the laser irradiated surfaces. It can be seen that, for the laser speedsof 2.5 and 5 mm/s, the material was melted, resulting in a porous resolidified layer. Itis noteworthy that, for both the highest and lowest adopted speeds, no surface meltingoccurred. The heating marks are visible and distinguished by their coarser microstructureresulting from grain growth. While the absence of a fusion zone in the 10 mm/s sample canbe attributed to a lower heat input, it is somewhat surprising to find the same feature in thematerial treated with 1 mm/s laser speed. One possible reason for this is that the higherheat input resulted in a more intense oxidation of the carbon black, thus reducing theablative layer. The direct interaction of the laser beam with the aluminum sheet due to thehigher reflectivity results in less energy absorption. All of the tests with laser power 250 Wresulted in fusion zones with high porosity. On the other hand, the tests with laser powerof 150 W resulted in almost indistinguishable microstructural changes. These conditions(150 W and 250 W) were not presented here.

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(a) (b)

(c) (d)

Figure 2. Light optical micrographs of cross sections of heating lines produced with laser power of 200 W and displacement speeds of: (a) 1 mm/s; (b) 2.5 mm/s; (c) 5 mm/s; (d) 10 mm/s (etchant: Keller). The arrows indicate the beam axes.

The hardness profiles for the samples treated with 200 W laser power are shown in Figure 3, in which the horizontal axis corresponds to the distance from the laser beam centerline. For the samples corresponding to laser speeds of 2.5 mm/s and 5 mm/s, the hardness values at the fusion zone dropped from 155 HV (base metal) to levels of about 60 HV with a high dispersion in hardness values, which may be due to the porosity observed in the fusion zone. Naturally the conditions where pores appeared were considered of no interest for the fatigue crack growth experiments. The unmelted samples, that is, laser speeds of 1 mm/s and 10 mm/s, presented distinct hardness profiles, which will be discussed in the next section.

Figure 3. Hardness profiles beneath the 200 W laser irradiated surfaces.

3.2. Fatigue Crack Growth Tests

Figure 2. Light optical micrographs of cross sections of heating lines produced with laser power of200 W and displacement speeds of: (a) 1 mm/s; (b) 2.5 mm/s; (c) 5 mm/s; (d) 10 mm/s (etchant:Keller). The arrows indicate the beam axes.

The hardness profiles for the samples treated with 200 W laser power are shown inFigure 3, in which the horizontal axis corresponds to the distance from the laser beamcenterline. For the samples corresponding to laser speeds of 2.5 mm/s and 5 mm/s, the

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hardness values at the fusion zone dropped from 155 HV (base metal) to levels of about60 HV with a high dispersion in hardness values, which may be due to the porosity ob-served in the fusion zone. Naturally the conditions where pores appeared were consideredof no interest for the fatigue crack growth experiments. The unmelted samples, that is,laser speeds of 1 mm/s and 10 mm/s, presented distinct hardness profiles, which will bediscussed in the next section.

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(a) (b)

(c) (d)

Figure 2. Light optical micrographs of cross sections of heating lines produced with laser power of 200 W and displacement speeds of: (a) 1 mm/s; (b) 2.5 mm/s; (c) 5 mm/s; (d) 10 mm/s (etchant: Keller). The arrows indicate the beam axes.

The hardness profiles for the samples treated with 200 W laser power are shown in Figure 3, in which the horizontal axis corresponds to the distance from the laser beam centerline. For the samples corresponding to laser speeds of 2.5 mm/s and 5 mm/s, the hardness values at the fusion zone dropped from 155 HV (base metal) to levels of about 60 HV with a high dispersion in hardness values, which may be due to the porosity observed in the fusion zone. Naturally the conditions where pores appeared were considered of no interest for the fatigue crack growth experiments. The unmelted samples, that is, laser speeds of 1 mm/s and 10 mm/s, presented distinct hardness profiles, which will be discussed in the next section.

Figure 3. Hardness profiles beneath the 200 W laser irradiated surfaces.

3.2. Fatigue Crack Growth Tests

Figure 3. Hardness profiles beneath the 200 W laser irradiated surfaces.

3.2. Fatigue Crack Growth Tests

The two promising laser heating conditions (laser power 200 W and speeds of 1 mm/sand 10 mm/s), from here referred to as L01 and L10, were adopted for the fatigue crackgrowth tests in a comparative study with the as-received (AR) material. The raw fatiguecrack growth data obtained in the tests with load ratios R = 0.1 (with Pmax = 800 N) andR = 0.5 (with Pmax = 1.1 kN) are plotted in Figures 4 and 5, respectively.

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The two promising laser heating conditions (laser power 200 W and speeds of 1 mm/s and 10 mm/s), from here referred to as L01 and L10, were adopted for the fatigue crack growth tests in a comparative study with the as-received (AR) material. The raw fatigue crack growth data obtained in the tests with load ratios R = 0.1 (with Pmax = 800 N) and R = 0.5 (with Pmax = 1.1 kN) are plotted in Figures 4 and 5, respectively.

Figure 4. FCG test results: crack length vs. number of cycles for R = 0.1.

It is noticeable that a crack arrest occurred in L01-R01 FCG test (Figure 4), which was interrupted after approximately 115,000 cycles and 3 mm crack length increase. A deviation of 12° was observed in the arrested crack growth direction, after an initial growth normal to the loading direction. The other test conditions did not show significant crack deflection. The drop in the crack growth rate can be also observed in Figure 6, in which da/dN calculated by the secant method is plotted against crack size for the R = 0.1 tests. The maximum load in that test was then increased from 800 N to 1.1 kN and the test was resumed. Another L01-R01 test with increased load (Pmax = 1.6 kN) was also performed from the beginning for the da/dN-ΔK analyzes. The calculations of ΔK were done according to ASTM E647-15e1.

Figure 5. FCG test results: crack length vs. number of cycles for R = 0.5.

Figure 4. FCG test results: crack length vs. number of cycles for R = 0.1.

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The two promising laser heating conditions (laser power 200 W and speeds of 1 mm/s and 10 mm/s), from here referred to as L01 and L10, were adopted for the fatigue crack growth tests in a comparative study with the as-received (AR) material. The raw fatigue crack growth data obtained in the tests with load ratios R = 0.1 (with Pmax = 800 N) and R = 0.5 (with Pmax = 1.1 kN) are plotted in Figures 4 and 5, respectively.

Figure 4. FCG test results: crack length vs. number of cycles for R = 0.1.

It is noticeable that a crack arrest occurred in L01-R01 FCG test (Figure 4), which was interrupted after approximately 115,000 cycles and 3 mm crack length increase. A deviation of 12° was observed in the arrested crack growth direction, after an initial growth normal to the loading direction. The other test conditions did not show significant crack deflection. The drop in the crack growth rate can be also observed in Figure 6, in which da/dN calculated by the secant method is plotted against crack size for the R = 0.1 tests. The maximum load in that test was then increased from 800 N to 1.1 kN and the test was resumed. Another L01-R01 test with increased load (Pmax = 1.6 kN) was also performed from the beginning for the da/dN-ΔK analyzes. The calculations of ΔK were done according to ASTM E647-15e1.

Figure 5. FCG test results: crack length vs. number of cycles for R = 0.5. Figure 5. FCG test results: crack length vs. number of cycles for R = 0.5.

It is noticeable that a crack arrest occurred in L01-R01 FCG test (Figure 4), whichwas interrupted after approximately 115,000 cycles and 3 mm crack length increase. Adeviation of 12◦ was observed in the arrested crack growth direction, after an initial growthnormal to the loading direction. The other test conditions did not show significant crackdeflection. The drop in the crack growth rate can be also observed in Figure 6, in whichda/dN calculated by the secant method is plotted against crack size for the R = 0.1 tests.The maximum load in that test was then increased from 800 N to 1.1 kN and the test wasresumed. Another L01-R01 test with increased load (Pmax = 1.6 kN) was also performedfrom the beginning for the da/dN-∆K analyzes. The calculations of ∆K were done accordingto ASTM E647-15e1.

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Figure 6. Crack growth rate vs. crack length for R = 0.1 tests.

Figures 7 and 8 present, in bi-logarithmic scale, the fatigue crack growth rate in terms of the stress intensity factor range (ΔK) nominal values. In both loading conditions (R = 0.1 and R = 0.5) it was observed that FCG rates of L01 specimens started from lower levels.

Figure 7. FCG test results: da/dN vs. ΔK plots for R = 0.1.

Figure 6. Crack growth rate vs. crack length for R = 0.1 tests.

Figures 7 and 8 present, in bi-logarithmic scale, the fatigue crack growth rate in termsof the stress intensity factor range (∆K) nominal values. In both loading conditions (R = 0.1and R = 0.5) it was observed that FCG rates of L01 specimens started from lower levels.

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Figure 6. Crack growth rate vs. crack length for R = 0.1 tests.

Figures 7 and 8 present, in bi-logarithmic scale, the fatigue crack growth rate in terms of the stress intensity factor range (ΔK) nominal values. In both loading conditions (R = 0.1 and R = 0.5) it was observed that FCG rates of L01 specimens started from lower levels.

Figure 7. FCG test results: da/dN vs. ΔK plots for R = 0.1. Figure 7. FCG test results: da/dN vs. ∆K plots for R = 0.1.

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Figure 8. FCG test results: da/dN vs. ΔK plots for R = 0.5.

4. Discussion For clearness purposes, Vickers hardness profiles for the laser speeds of 1 mm/s and

10 mm/s are plotted again in Figure 9. In these conditions, the hardness was also reduced, although not so much as in the samples presenting a fusion zone (see Figure 3). Moreover, the two conditions resulted in clearly distinct hardness profiles. These features may be discussed based on the premise that hardness in AA2198 depends effectively on the density and size of the strengthening precipitates, which can be strongly affected by the local thermal cycles experienced by the samples during the laser heating.

(a) (b)

Figure 9. Hardness profiles beneath the laser irradiated surfaces with laser speeds of (a) 1 mm/s; (b) 10 mm/s.

Zhao et al. [17] evaluated the effect of laser pressure weld in AA2198, showing the relationship between hardness and precipitation evolution in the weld metal and in the heat affected zones (HAZ). By means of transmission electron microscopy analyses, they found that the base material AA2198 with 155–170 HV contained a high density of T1 phase, medium density of needle-shaped θ’ and spherical δ’ phases and a low density of spherical β’ and needle-shaped S’ phases. The distribution of the hardening precipitates significantly changed, in different ways, in the weld metal and in various positions of the HAZ. This was attributed to the fact that these phases are formed and dissolve at distinct

Figure 8. FCG test results: da/dN vs. ∆K plots for R = 0.5.

4. Discussion

For clearness purposes, Vickers hardness profiles for the laser speeds of 1 mm/s and10 mm/s are plotted again in Figure 9. In these conditions, the hardness was also reduced,although not so much as in the samples presenting a fusion zone (see Figure 3). Moreover,the two conditions resulted in clearly distinct hardness profiles. These features may bediscussed based on the premise that hardness in AA2198 depends effectively on the densityand size of the strengthening precipitates, which can be strongly affected by the localthermal cycles experienced by the samples during the laser heating.

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Figure 8. FCG test results: da/dN vs. ΔK plots for R = 0.5.

4. Discussion For clearness purposes, Vickers hardness profiles for the laser speeds of 1 mm/s and

10 mm/s are plotted again in Figure 9. In these conditions, the hardness was also reduced, although not so much as in the samples presenting a fusion zone (see Figure 3). Moreover, the two conditions resulted in clearly distinct hardness profiles. These features may be discussed based on the premise that hardness in AA2198 depends effectively on the density and size of the strengthening precipitates, which can be strongly affected by the local thermal cycles experienced by the samples during the laser heating.

(a) (b)

Figure 9. Hardness profiles beneath the laser irradiated surfaces with laser speeds of (a) 1 mm/s; (b) 10 mm/s.

Zhao et al. [17] evaluated the effect of laser pressure weld in AA2198, showing the relationship between hardness and precipitation evolution in the weld metal and in the heat affected zones (HAZ). By means of transmission electron microscopy analyses, they found that the base material AA2198 with 155–170 HV contained a high density of T1 phase, medium density of needle-shaped θ’ and spherical δ’ phases and a low density of spherical β’ and needle-shaped S’ phases. The distribution of the hardening precipitates significantly changed, in different ways, in the weld metal and in various positions of the HAZ. This was attributed to the fact that these phases are formed and dissolve at distinct

Figure 9. Hardness profiles beneath the laser irradiated surfaces with laser speeds of (a) 1 mm/s; (b) 10 mm/s.

Zhao et al. [17] evaluated the effect of laser pressure weld in AA2198, showing therelationship between hardness and precipitation evolution in the weld metal and in theheat affected zones (HAZ). By means of transmission electron microscopy analyses, theyfound that the base material AA2198 with 155–170 HV contained a high density of T1phase, medium density of needle-shaped θ’ and spherical δ’ phases and a low density ofspherical β’ and needle-shaped S’ phases. The distribution of the hardening precipitatessignificantly changed, in different ways, in the weld metal and in various positions of theHAZ. This was attributed to the fact that these phases are formed and dissolve at distincttemperature ranges. Besides, the softening in the welded region was essentially due to thereduced density of fine T1 precipitates, associated with their dissolution or coarsening [17].The presence of significantly coarsened β’, re-precipitated δ’ (during cooling) and Cuand Li solutes in a region of dissolved precipitates, among others, also contributed to thevariations observed in the hardness profile. Although the present work does not deal withlaser welding, the material beneath the irradiated surface is subjected to thermal cyclesthat can transform the hardening precipitates as well. As shown in Figure 2, the laserheating at 1 mm/s caused a lower hardness drop in a wider area than the laser heating at10 mm/s. Moreover, there is a hardness peak (120 HV) in the middle of the heating lineproduced at 1 mm/s. These features are the result of the thermal cycles experienced by thematerial, which in turn depends basically on the laser speed and eventually the oxidationcharacteristics of the carbon black layer. A detailed precipitates investigation is beyond thescope of this work.

The distinct hardness profiles observed in Figure 2 are therefore a consequence oftemperature differences in the heating lines and may also be related to differences inresidual stresses and, consequently, in the fatigue crack growth behavior as previouslyshown. On the other hand, the effect of laser heating on the FCG rate depends also on thestress ratio, being more evident for R = 0.1 than for R = 0.5 (Figures 4 and 5). In tests underthe same conditions (R and Pmax), the life increases due to crack retardation at subcriticalcrack growth were approximately the following: 5% for L10-R05, 32% for L01-R05 and30% for L10-R01. The L01-R01 test under the same Pmax resulted in crack arrest and wasresumed with a higher load. Another test with increased Pmax = 1.6 kN was conducted forthe simulation purposes. The reason for the R-effect on the performance of laser treatedmaterial regarding FCG resistance may lie in how the residual stresses affect the drivingforce for crack growth, as discussed in the following paragraphs. Beyond that, it was thecombination of the more favorable laser heating parameters and loading condition that ledthe L01-R01 condition to show a better effect on restraining the fatigue crack growth.

The stress intensity factor K is a parameter of Linear Elastic Fracture Mechanics thatreflects the elastic stress field in the vicinity of the crack tip as a function of the crack size

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itself and the nominal stress applied to the part. Bearing in mind that stress tends to infinityin the elastic asymptote, the formation of a plastic zone at the tip of the crack is considered,limiting the stress values. In a loading cycle, ∆K relates to the difference between the stressfields acting on loading and unloading and is accepted as the driving force for fatigue crackgrowth as described, for example, by the well-known Paris model [18]:

da/dN = C (∆K)n, (1)

where C, n are fitting constants. For a given maximum load in the loading cycle, the elasticstresses in the unloading increase with the increase of R [19]. On the other hand, in the caseof laser-treated samples, there are compressive residual stresses along the crack line, in equi-librium with the resultant tractive residual stresses acting on the heating lines. The intensityof these stresses depends, among other factors, on the laser treatment parameters, on thematerial properties and geometry of the specimen. For example, compressive residualstresses of −30 MPa were found in AA2198-T8 CT(100) specimens by Schnubel et al. [13]and values between −30 MPa and −22 MPa were observed along the crack line in AA2024-T3 CT(50) specimens by Cunha and Lima [14]. However, these measurements do not takein account possible residual stress relaxation and/or redistribution as the crack grows,which makes it difficult to model fatigue crack propagation.

A straightforward way to get around this issue when modeling FCG is to assumea constant value for residual stress along the crack path. Thus, it is considered that thiscompressive static field, superimposed on the applied load, acts by reducing the normalstresses ahead of the crack described by the stress intensity factor range. Two possiblesituations may arise from this superposition when considering the effective K values. If theresidual stress is sufficient only to reduce the effective values of Kmax and Kmin withoutzeroing the latter, we have a situation where ∆Kef = ∆K, but with an effective stress ratioless than the nominal, that is, Ref < R, and, in this case, the reduction in the crack growthrate tends to be modest or negligible. On the other hand, if the compressive residual stressis sufficient to make Kmin negative, the zero value is adopted for this parameter, resultingin the effective stress intensity factor range also being smaller than the nominal one, that is,∆Kef < ∆K, leading to a more expressive reduction in the crack growth rate, as observedhere for the R = 0.1 tests.

In order to model FCG for this loading condition, numerical simulations of crackgrowth were performed. To do so, initially the fitting parameters for the Paris equationwere determined for the AR-R01 test condition, resulting in C = 1.57 × 10−10 and n = 2.318.Then the crack length versus number of cycle curves can be determined by numericalintegration and fits very well to experimental data, as shown in Figure 10. For the lasertreated conditions L10-R01 (Pmax = 800 N) and L01-R01 (Pmax = 1.6 kN), the crack growthcurves were obtained by adopting the AR-R01 fitting parameters and superposing in ∆Kcalculations a uniformly distributed compressive stress acting from the initial crack lengthup to a = 27.5 mm. The compressive stresses for each condition were determined by atrial-and-error bisection method in which the effective ∆K and R values were determinedby subtracting a chosen compressive load Prc from Pmax and Pmin and adopting the valuezero for the latter in case of negative result. The obtained results were Prc = −180 N forL10-R01 and Prc = −390 N for L01-R01 condition. The numerical simulations resultingfrom this simple method are shown in Figures 11 and 12 and proved suitable to reproducethe experimental results. Note that, by superposing the compressive load −390 N onthe loading condition that resulted in crack arrest (Figure 4), the corresponding apparentthreshold observed in ∆K (see Figure 6) would be recalculated as about 6.0 MPa·m0.5,which is a reasonable value. Additionally, the individual fitting parameters for all of thetest conditions to the Paris model were calculated and presented in Table 1 to allow acomparative view.

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residual stress is sufficient only to reduce the effective values of Kmax and Kmin without zeroing the latter, we have a situation where ΔKef = ΔK, but with an effective stress ratio less than the nominal, that is, Ref < R, and, in this case, the reduction in the crack growth rate tends to be modest or negligible. On the other hand, if the compressive residual stress is sufficient to make Kmin negative, the zero value is adopted for this parameter, resulting in the effective stress intensity factor range also being smaller than the nominal one, that is, ΔKef < ΔK, leading to a more expressive reduction in the crack growth rate, as observed here for the R = 0.1 tests.

In order to model FCG for this loading condition, numerical simulations of crack growth were performed. To do so, initially the fitting parameters for the Paris equation were determined for the AR-R01 test condition, resulting in C = 1.57 × 10−10 and n = 2.318. Then the crack length versus number of cycle curves can be determined by numerical integration and fits very well to experimental data, as shown in Figure 10. For the laser treated conditions L10-R01 (Pmax = 800 N) and L01-R01 (Pmax = 1.6 kN), the crack growth curves were obtained by adopting the AR-R01 fitting parameters and superposing in ΔK calculations a uniformly distributed compressive stress acting from the initial crack length up to a = 27.5 mm. The compressive stresses for each condition were determined by a trial-and-error bisection method in which the effective ΔK and R values were determined by subtracting a chosen compressive load Prc from Pmax and Pmin and adopting the value zero for the latter in case of negative result. The obtained results were Prc = −180 N for L10-R01 and Prc = −390 N for L01-R01 condition. The numerical simulations resulting from this simple method are shown in Figures 11 and 12 and proved suitable to reproduce the experimental results. Note that, by superposing the compressive load −390 N on the loading condition that resulted in crack arrest (Figure 4), the corresponding apparent threshold observed in ΔK (see Figure 6) would be recalculated as about 6.0 MPa⋅m0.5, which is a reasonable value. Additionally, the individual fitting parameters for all of the test conditions to the Paris model were calculated and presented in Table 1 to allow a comparative view.

Figure 10. Crack length vs. number of cycles for AR-R01: experimental results and modeling. Figure 10. Crack length vs. number of cycles for AR-R01: experimental results and modeling.

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Figure 11. Crack length vs. number of cycles for L10-R01: experimental results and simulation.

Figure 12. Crack length vs. number of cycles for L01-R01: experimental results and simulation.

Table 1. Fitting parameters for the Paris model.

Material Condition Load Ratio C (mm/cycle)/(Mpa. √m)n n

AR 0.1 1.57 × 10−10 2.318 0.5 7.06 × 10−13 3.289

L01 0.1 6.24 × 10−20 5.456 0.5 5.44 × 10−13 3.270

L10 0.1 1.38 × 10−12 3.050 0.5 6.59 × 10−12 2.876

5. Conclusions For the laser line heating treatments of AA 2198-T851 2 mm thick sheets, the suitable

process conditions were 200 W laser power with speeds of 1 mm/s or 10 mm/s. The distinct hardness profiles observed beneath the laser irradiated surfaces were attributed to thermal cycle differences in the heating lines. The effects of laser heating on fatigue crack growth behavior depend not only on the process parameters, but also on the loading

Figure 11. Crack length vs. number of cycles for L10-R01: experimental results and simulation.

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Figure 11. Crack length vs. number of cycles for L10-R01: experimental results and simulation.

Figure 12. Crack length vs. number of cycles for L01-R01: experimental results and simulation.

Table 1. Fitting parameters for the Paris model.

Material Condition Load Ratio C (mm/cycle)/(Mpa. √m)n n

AR 0.1 1.57 × 10−10 2.318 0.5 7.06 × 10−13 3.289

L01 0.1 6.24 × 10−20 5.456 0.5 5.44 × 10−13 3.270

L10 0.1 1.38 × 10−12 3.050 0.5 6.59 × 10−12 2.876

5. Conclusions For the laser line heating treatments of AA 2198-T851 2 mm thick sheets, the suitable

process conditions were 200 W laser power with speeds of 1 mm/s or 10 mm/s. The distinct hardness profiles observed beneath the laser irradiated surfaces were attributed to thermal cycle differences in the heating lines. The effects of laser heating on fatigue crack growth behavior depend not only on the process parameters, but also on the loading

Figure 12. Crack length vs. number of cycles for L01-R01: experimental results and simulation.

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Table 1. Fitting parameters for the Paris model.

Material Condition Load Ratio C (mm/cycle)/(Mpa.√

m)n n

AR0.1 1.57 × 10−10 2.3180.5 7.06 × 10−13 3.289

L010.1 6.24 × 10−20 5.4560.5 5.44 × 10−13 3.270

L100.1 1.38 × 10−12 3.0500.5 6.59 × 10−12 2.876

5. Conclusions

For the laser line heating treatments of AA 2198-T851 2 mm thick sheets, the suitableprocess conditions were 200 W laser power with speeds of 1 mm/s or 10 mm/s. Thedistinct hardness profiles observed beneath the laser irradiated surfaces were attributedto thermal cycle differences in the heating lines. The effects of laser heating on fatiguecrack growth behavior depend not only on the process parameters, but also on the loadingconditions. The more expressive results were obtained for heating with laser speed of1 mm/s and cyclic loading with stress ratio R = 0.1.

Author Contributions: Conceptualization, C.A.R.P.B. and M.S.F.d.L.; methodology, C.P.C., M.S.F.d.L.,V.P. and C.A.R.P.B.; investigation, C.P.C., V.P. and C.A.R.P.B.; writing—original draft preparation,C.A.R.P.B. and C.P.C.; writing—review and editing, M.S.F.d.L.; supervision, C.A.R.P.B. and M.S.F.d.L.;project administration, C.A.R.P.B. and M.S.F.d.L.; funding acquisition, C.A.R.P.B. All authors haveread and agreed to the published version of the manuscript.

Funding: This research was funded by the São Paulo State Research Support Foundation (FAPESP),grant number 2018/16438-9.

Institutional Review Board Statement: Not applicable.

Acknowledgments: C.P.C. acknowledges the Coordination of Superior Level Staff Improvement(CAPES) and C.A.R.P.B. acknowledges the National Council for Scientific and Technological Devel-opment (CNPq) for the research grants.

Conflicts of Interest: The authors declare no conflict of interest.

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