Influence of Temperature-Dependent Properties of Aluminum Alloy On

metals

Article Inﬂuence of Temperature-Dependent Properties of Aluminum Alloy on Evolution of Plastic Strain and Residual Stress during Quenching Process

Yuxun Zhang 1,2, Youping Yi 1,2, Shiquan Huang 1,2,* and Hailin He 1

1 State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China; [email protected] (Y.Z.); [email protected] (Y.Y.); [email protected] (H.H.) 2 School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China * Correspondence: [email protected]; Tel.: +86-135-4898-1584

Received: 31 March 2017; Accepted: 15 June 2017; Published: 21 June 2017

Abstract: To lessen quenching residual stresses in aluminum alloy components, theory analysis, quenching experiments, and numerical simulation were applied to investigate the inﬂuence of temperature-dependent material properties on the evolution of plastic strain and stress in the forged 2A14 aluminum alloy components during quenching process. The results show that the thermal expansion coefﬁcients, yield strengths, and elastic moduli played key roles in determining the magnitude of plastic strains. To produce a certain plastic strain, the temperature difference increased with decreasing temperature. It means that the cooling rates at high temperatures play an important role in determining residual stresses. Only reducing the cooling rate at low temperatures does not reduce residual stresses. An optimized quenching process can minimize the residual stresses and guarantee superior mechanical properties. In the quenching process, the cooling rates were low at temperatures above 450 ◦C and were high at temperatures below 400 ◦C.

Keywords: aluminum alloy; quenching process; material property; cooling rate; plastic strain; residual stress

1. Introduction Heat-treatable aluminum alloys are widely used to fabricate forged components used in aerospace and aircraft industry for weight reduction. Solution quenching and aging treatments are applied to the aluminum alloy components to obtain high mechanical properties [1]. For this purpose, fast cooling rates are required to avoid or limit precipitation during the quenching process [2]. However, high cooling rates result in serious inhomogeneous deformations and lead to high residual stresses [3], which deteriorates the mechanical properties and dimensional stability [4,5], and also have important impact on fatigue properties [6–8]. Therefore, it is important to study how to control the residual stresses. Residual stresses can be relieved by plastic deformation. For example, Koç et al. [9] found that compression and stretching processes could reduce the residual stress of 7050 forged blocks by more than 90%. However, this technique cannot be used for complicated cross-section components [10]. Many researchers employed vibration methods to release the residual stresses [11,12] and studied their mechanisms [13]. However, this technique is conﬁned to large components since the high amplitude of vibration deforms the thinner or smaller components [5]. Heat treatment methods are also applied to relieve the residual stresses. Dong et al. [10] successfully lowered the residual stress with uphill quenching and thermal-cold cycling processes. Sun et al. [14] relieved the residual stress by repeated heating of the samples at high heating rates and subsequent artiﬁcial aging treatment.

Metals 2017, 7, 228; doi:10.3390/met7060228 www.mdpi.com/journal/metals Metals 2017, 7, 228 2 of 13

Although the technologies described above are effective in relieving the residual stresses, the need of special tools and procedures increases their costs. Therefore, an economical approach is to minimize the residual stresses during quenching. Residual stresses decrease with reducing cooling rates. Our previous work showed that, as compared to the mechanical properties, the residual stress decreased faster with decreasing cooling rates [15]. Dong et al. [10] balanced the residual stress and mechanical properties of the thin aluminum alloy plates with warm water at 80 ◦C. The mechanical performances are mainly determined by the cooling rates in the quenching sensitivity temperature range. The quenching sensitivity can be studied by time-temperature- transformation/properties (TTT/TTP) curves. For example, by using of TTP curves, Li et al. [16] showed that the mechanical performances of the 6063 aluminum alloy are determined by the cooling rates during the quenching sensitivity temperature range from 410–300 ◦C. Based on the results, they proposed a step quenching method to balance the mechanical properties and residual stresses. Its cooling rates are high in the quenching sensitivity temperature range to guarantee mechanical performances, and they are low in the others ranges to reduce residual stresses. Our previous work [15] showed that such a step quenching method could balance the residual stress and mechanical performances. However, the step quenching technology is mainly designed based on the characteristics of the quench-induced phase transformation of the material. It is best to utilize the characteristics of quenching residual stress evolution and quench-induced phase transformation during quenching to design the quenching technology. Nallathambi et al. [17] studied the inﬂuence of thermal, metallurgical, and mechanical properties on the ﬁnal distortion and residual stresses during quenching. However, the effect of material properties on the evolution of residual stress at different temperatures is still unclear. This information is needed to guide the designing of quenching technology. This work investigated the effect of temperature-dependent material properties of forged 2A14 aluminum alloy on the evolution of stress and plastic strain during quenching process using a constructed model and numerical simulation methods. Moreover, the effect of cooling rates on residual stresses was studied by quenching the samples with different quenching technologies. Table1 listed all the nomenclatures used in this paper.

Table 1. Nomenclature.

T Temperature ∆T temperature difference between the temperature of the unit and reference temperature 0 ◦C Tg temperature difference between the two units of the model α thermal expansion coefﬁcient E elastic modulus Ep plastic modulus σ0.2 yield strength i number of the unit εT thermal expansion strain ε total strain εe elastic strain εp plastic strain σ thermal stress PEEQ equivalent plastic strain PE22 plastic strain in y direction S22 stress in y direction

2. Methods

2.1. Theoretical Analysis Residual stresses are determined by inhomogeneous plastic strains. They usually increase with increasing magnitude of plastic strain. During quenching, inhomogeneous temperature distribution causes inhomogeneous thermal expansion strain (εT), which causes the thermal stresses and strains to Metals 2017, 7, 228 3 of 13 maintain the force and shape balance. When thermal stress exceeds the yield strength, plastic strain occurs. Material properties change with temperatures. The yield strengths and elastic moduli of 2A14 aluminum alloy decrease with increasing temperatures. This implies that the characteristics of evolution of thermal stresses and plastic strains may be different at different temperatures during quenching. In this work, a model with two units was proposed to investigate these characteristics (Figure1). As shown in Figure1a, the temperatures of the two units are initially the same, leading to the same thermal expansions. The thermal expansion was obtained using Equation (1), where 0 ◦C was taken as the reference temperature. As quenching proceeded, a temperature difference (Tg) between the two units appeared, as shown in Figure1b; it resulted in strains to balance the unequal thermal expansions. To simplify the analysis, we presumed that the ﬁnal heights of the two units are the same (Equation (2)). Moreover, the two units have the same magnitude of thermal stresses. The strain comprises elastic strain and plastic strain, which are described by Equation (4) in reference [18]. In this model, we presumed that the thermal stress always exceeds the yield strength (Equation (3)). Combining Equations (1)–(4), the plastic strain of unit i is obtained from Equation (5). Equations (6)–(8) proposed three variants, A, B, and C, to simplify the formation of Equation (5). Equation (9) was obtained by combining Equations (5)–(8), and was used to investigate the inﬂuence of temperature-dependent material properties on plastic strains at different temperatures, but with the same temperature difference. As shown in Table2, the plastic moduli were obtained from a previous work [19]. The other material properties are described in Section 2.3.

εT = α∆T (1)

αiTi − εi = αi+1Ti+1 + εi+1; σi = σi+1 (2) e p εi = εi + εi (3)

e σi p (σi − σ0.2,i) εi = ; εi = (4) Ei Ep,i ! σ + σ (α T − α T ) + 0.2,i 1 + 0.2,i i i i+1 i+1 E E p p,i+1 p,i σ0.2,i εi = ! − (5) 1 1 1 1 Ep,i + + + Ep,i Ep,i+1 Ep,i Ei+1 Ei

A = (αiTi − αi+1Ti+1) (6) ! σ + σ B = 0.2,i 1 + 0.2,i (7) Ep,i+1 Ep,i ! 1 1 1 1 C = + + + (8) Ep,i+1 Ep,i Ei+1 Ei

p A + B σ0.2,i εi = − (9) CEp,i Ep,i where α, E, Ep, and σ0.2 are the thermal expansion coefﬁcient, elastic modulus, plastic modulus, and yield strength, respectively. T is the temperature of the unit. ∆T is the temperature difference between T and reference 0 ◦C. εT, ε, εe, εp, and σ are the thermal expansion, total strain, elastic strain, plastic strain, and thermal stress, respectively. The subscript i is the number of the unit. Metals 2017, 7, 228 4 of 13 Metals 2017, 7, 228 4 of 13

FigureFigure 1.1.Two-unit Two-unit model: model: (a) uniform(a) uniform temperatures temperatures at the beginningat the beginning of quenching; of quenching; and (b) temperature and (b) differencetemperature appeared difference during appe quenching.ared during quenching.

TableTable 2.2. PlasticPlastic modulimoduli atat differentdifferent temperatures.temperatures.

TemperatureTemperature (°C) (◦C) 30 30 130 130 230 230 330 330 430 430 530 530 EP (MPa) 9000 5000 2000 1000 400 200 Ep (MPa) 9000 5000 2000 1000 400 200 2.2. Quenching Experiment: Material and Heat Treatment 2.2. Quenching Experiment: Material and Heat Treatment Quenching residual stresses are affected by products’ material properties, structure and inhomogeneousQuenching residualtemperature stresses distribution are affected during by products’quenching. material The temperature properties, distribution structure and is inhomogeneousdetermined by temperaturethe cooling distributionrates; increasing during cool quenching.ing rate Theincreases temperature the temperature distribution gradient. is determined The byinfluence the cooling of cooling rates; increasingrates on residual cooling ratestress increases was investigated the temperature by quenching gradient. the The forged inﬂuence 2A14 of coolingaluminum rates alloy on samples residual with stress different was investigated quenching bytechnologies. quenching The the samples forged 2A14were machined aluminum from alloy a samplescommercial with forged different component quenching 78 mm technologies. in thickness; The their samples chemical were compositions machined fromare listed a commercial in Table 3. forgedAs shown component in Figure 78 2a, mm the in thickness;size of the theirsamples chemical is 110 compositions mm × 100 mm are × listed 70 mm, in Table and3 its. As thickness shown indirection Figure2 isa, along the size the ofz-axis. the samples Their x, isy, 110and mmz directions× 100 mmare along× 70 mm,the long and transverse its thickness direction, direction short is alongtransverse the z -axis.direction, Their andx, y thickness, and z directions direction are of alongthe component, the long transverse respectively. direction, Similar short to our transverse previous direction,work [15], and the thicknesstwo end surfaces direction (110 of themm component, × 100 mm) were respectively. taken as Similarthe main to heat-dispersing our previous work surfaces, [15], thewhile two the end other surfaces four surfaces (110 mm were× 100 encapsulated mm) were wi takenth about as the 20-mm-thick main heat-dispersing asbestos. As surfaces,shown in whileTable the4, the other samples four surfaceswere quenched were encapsulated immediately with after aboutthe so 20-mm-thicklution treatment asbestos. at 500 °C As for shown 4 h. Sample in Table A14, ◦ thewas samples quenched were with quenched room temperature immediately water after (about the solution 20 °C). treatmentSample A2 at was 500 firstC for quenched 4 h. Sample in room A1 ◦ wastemperature quenched water with until room the temperature temperature water at the (about central 20 pointC). SampleP0 decreased A2 was to ﬁrstabout quenched 410 °C, and in room then ◦ temperatureit was cooled water in room until thetemperature temperature air. at The the centraltransfer point time P0 was decreased smaller to than about 1 410s. SampleC, and A3 then was it wasquenched cooled by in rooma step temperaturequenching technology air. The transfer using timea spray-quenching was smaller than device 1 s. Sampledesigned A3 by was us, quenchedas shown byin Figure a step quenching3. Detailed technologyinformation using of the a device spray-quenching is present in device our submitted designed patent by us, (CN as shown 201710016344.5). in Figure3. DetailedAs shown information in Figure 2a, of thethe devicetemperatures is present at inpoints our submittedP0 and P1 patentduring (CN quenching 201710016344.5). were monitored As shown by inusing Figure Φ12 a,mm the naked temperatures type K thermocouples at points P0 and deeply P1 during embedded quenching into were the samples. monitored The by cooling using Φ history1 mm nakedof P0 was type used K thermocouples to stand for the deeply cooling embedded rates of into the thesamples samples. with The different cooling quenching history of technologies. P0 was used toThe stand temperature for the cooling difference rates ofbetween the samples points with P0 differentand P1 was quenching used to technologies. estimate the Theinhomogeneous temperature differencetemperature between distribution points P0of the and samples. P1 was used to estimate the inhomogeneous temperature distribution of the samples. Table 3. Chemical composition of the studied material (wt %). Table 3. Chemical composition of the studied material (wt %). Cu Mg Mn Si Fe Ni Zn Ti Al 4.28Cu 0.6 Mg 0.81 Mn 0.94 Si 0.15 Fe 0.003 Ni Zn0.01 Ti0.04 Balance Al 4.28 0.6 0.81 0.94 0.15 0.003 0.01 0.04 Balance

Metals 2017, 7, 228 5 of 13 MetalsMetals2017 2017, ,7 7,, 228 228 55 of of 13 13

Figure 2. Schematic of quenching of a sample: (a) sizes and measured points (the unit used in this FigureFigure 2.2.Schematic Schematic ofof quenchingquenching ofof aa sample:sample: ((aa)) sizessizes andand measuredmeasured pointspoints (the(the unitunit usedused inin thisthis figure is “mm”); and (b) cutting plane of slitting method. ﬁgurefigure is is “mm”); “mm”); and and ( b(b)) cutting cutting plane plane of of slitting slitting method. method.

FigureFigure 3. 3. SchematicSchematic of of spray spray quenching quenching experiment. experiment. Figure 3. Schematic of spray quenching experiment. TableTable 4. 4. HeatHeat treatments treatments applied applied to to 2A14 2A14 aluminum aluminum alloy alloy samples. samples. Table 4. Heat treatments applied to 2A14 aluminum alloy samples. SamplesSamples Solution Solution Treatment Treatment Quenching Quenching Technology Technology Ageing Ageing Treatment Treatment Samples Solution Treatment Quenching Technology Ageing Treatment A1 500 °C/4◦ h 20 °C◦ 165 °C/9◦ h A1A1 500 500 C/4°C/4 hh 20 °CC 165 165 °C/9C/9 h h Step 1: 20 °C◦ A2 500 °C/4◦ h Step 1: 20 20 °CC 165 °C/9◦ h A2A2 500 500 C/4°C/4 hh Step 2: air 165165 °C/9C/9 h h StepStep 2: air air A3A3 500 °C/4◦C/4 h h Spray Spray quenching quenching 165 165 °C/9◦C/9 h h A3 500 °C/4 h Spray quenching 165 °C/9 h Refering to References [10,20], the residual stresses of the as-quenched samples were measured ReferingRefering toto ReferencesReferences [[10,20],10,20], thethe residualresidual stressesstresses of of the the as-quenched as-quenched samplessamples werewere measured measured by the slitting method. As shown in Figure 2b, a wire-electrode cutting machine was used to cut byby thethe slittingslitting method.method. AsAs shownshown inin FigureFigure2 b,2b, a a wire-electrode wire-electrode cutting cutting machine machine was was used used to to cut cut incrementally along the cutting plane. With the incremental increase in the depth (aj) of the cutting incrementallyincrementally alongalong thethe cuttingcutting plane.plane. WithWith thethe incrementalincremental increaseincrease inin thethe depth depth ( a(aj)j) ofof thethe cutting cutting plane, the residual stresses of the blocks were released. The strains (εy)y in the y direction were plane,plane, the the residual residual stresses stresses of theof blocksthe blocks were released.were released. The strains The (strainsεy) in the (εy) directionin the y weredirection measured were measuredby using foilby using strain foil gauges strain (BX120-5AA) gauges (BX120-5AA) with 5 mm with gauge 5 mm lengths, gauge lengths, which werewhich connected were connected in 1/4 measured by using foil strain gauges (BX120-5AA) with 5 mm gauge lengths, which were connected inbridging 1/4 bridging mode. mode. The central The central line of line the of gauge the gauge was at was the at mid-length the mid-length of the of sample. the sample. Thestrains The strains were in 1/4 bridging mode. The central line of the gauge was at the mid-length of the sample. The strains were the functions of cutting depths (aj). We presumed that the residual stress σy(z) along the cutting the functions of cutting depths (aj). We presumed that the residual stress σy(z) along the cutting plane were the functions of cutting depths (aj). We presumed that the residual stress σy(z) along the cutting plane is the function of z. As in Equation (10), it can be described by the polynomial Pi (70 − z) and is the function of z. As in Equation (10), it can be described by the polynomial Pi (70 − z) and the plane is the function of z. As in Equation (10), it can be described by the polynomial Pi (70 − z) and theundetermined undetermined coefﬁcient coefficientAi. At Ai the. At same the same time, astime, in Equationas in Equati (11),on the (11), measured the measured stains (ε ystains) at different (εy) at the undetermined coefficient Ai. At the same time, as in Equation (11), the measured stains (εy) at differentdepths (a depthsj) can be (a describedj) can be described by the undetermined by the undetermined coefﬁcient coefficientAi and compliance Ai and compliance function C functioni (aj). Ci (Caji) different depths (aj) can be described by the undetermined coefficient Ai and compliance function Ci (isaj). the Ci strain(aj) is atthe the strain measured at the point measured with thepoint depth with (a jthe) of thedepth cutting (aj) of plane the cutting increasing plane incrementally, increasing (aj). Ci (aj) is the strain at the measured point with the depth (aj) of the cutting plane increasing incrementally,when Pi (70 − whenz) stress Pi (70 was − z applied) stress was along applied the z direction along the of z direction the sample. of the The sample. numerical The simulationnumerical incrementally, when Pi (70 − z) stress was applied along the z direction of the sample. The numerical simulationmethod was method used towas calculate used toC calculatei (aj). As C showni (aj). As in shown Equation in Equation (12), the (12), least the square least methodsquare method is used simulation method was used to calculate Ci (aj). As shown in Equation (12), the least square method isto used obtain to Aobtaini using Aithe using measured the measured strains strains and calculated and calculated strains strains given ingiven Equation in Equation (11). In (11). this In paper, this is used to obtain Ai using the measured strains and calculated strains given in Equation (11). In this

Metals 2017, 7, 228 6 of 13 the residualMetals 2017 stress, 7, 228 (Equation (10)) was not calculated, and, instead, the measured strains were6 of used 13 to estimate the residual stress of the samples, which underwent different quenching treatments. paper, the residual stress (Equation (10)) was not calculated, and, instead, the measured strains were used to estimate the residual stress of the sampn les, which underwent different quenching treatments. σy(z) = ∑ AiPi(70 − z) = PA (10) i=1 =70 − = (10) n εy aj = ∑ AiCi aj = CA (11) =i=1 = (11) " #2 ∂ m n ∑ ε aj − ∑ AkCk aj, Pk = 0 i = 1, 2, . . . , n (12) ∂Ai −, =0 = 1,2, ⋯ , (12) j=1 k=1 The tensileThe tensile test test samples samples in inx directionx direction were were machinedmachined from from the the mid-thickness mid-thickness part part of the of aged the aged samples,samples, and and were were used used to evaluateto evaluate the the mechanical mechanical properties. Three Three test test specimens specimens were were taken taken from from 2 everyevery sample sample with with dimensions dimensions of 2 of× 82 mm× 8 mmand2 and a gauge a gauge length length 30 mm,30 mm, utilizing utilizing a 25a 25 mm mm gauge gauge length extensometerlength extensometer according according to GB/T 1685-2013.to GB/T 1685-2013. The samples The samples were testedwere tested at a strainat a strain rate rate of 0.0011 of 0.0011 s− 1. s−1. 2.3. Numerical Simulation 2.3. Numerical Simulation The numerical simulation software ABAQUS standard with coupled temperature–displacement analysis wasThe usednumerical to further simulation study software the inﬂuence ABAQUS of stan materialdard with properties coupled temperature–displacement and cooling rates at different temperaturesanalysis was on used plastic to further strain andstudy residual the influence stress of during material quenching. properties and The cooling size of rates the modelat different was the temperatures on plastic strain and residual stress during quenching. The size of the model was the same as that of the samples used for the heat treatment experiments. Only the two end surfaces same as that of the samples used for the heat treatment experiments. Only the two end surfaces (110 × (110 mmmm × 100100 mm) mm exchanged) exchanged heat heat with with water water during during quenching. quenching. Due to the Due symmetry, to the symmetry, only an eighth only an eighthof ofthe the sample sample was was used used to reduce to reduce calculating calculating time, time,as shown as shown in Figure in Figure4. The 4displacement. The displacement in the in the normalnormal direction direction ofof thethe three symmetry planes planes was was restricted. restricted. Similar Similar to the to theexperiments, experiments, only onlyend end surfacesurface of this of modelthis model exchanged exchanged heat heat with with the the environment. environment. The The elementelement type used used in in this this model model is is an 8-nodean thermally8-node thermally coupled coupled brick, brick, trilinear trilinear displacement displacement and and temperature element element (C3D8T), (C3D8T), and andthe the numbernumber of the of elementsthe elements was was 6160. 6160. The The incremental incremental time in in the the analysis analysis is chosen is chosen automatically automatically by the by the computercomputer program program and and the the solution solution technique technique is is fullfull Newton method. method.

FigureFigure 4. 4.Numerical Numerical simulation model. model.

The density of this material is set constant at a value of 2800 kg m−3. Figure 5 shows the yield −3 Thestress density at different of this plastic material strains is used set constant in the simu at alation value model, of 2800 where kg· mthe yield. Figure points5 shows at different the yield stresstemperatures at different are plastic the strainssmall value used of in the the curves simulation. As shown model, in whereTable 5, the the yield thermal points expansion at different temperaturescoefficients, are elasticity the small moduli, value ofconductivities, the curves. Asand shown specific in Tableheat capacities5, the thermal were expansionobtained from coefficients, the elasticity moduli, conductivities, and specific heat capacities were obtained from the literature [21,22]. − − The convective heat transfer coefficient of aluminum/air was set constant at 0.2 kW·m 2·s 1. MetalsMetals 2017 2017, 7, ,228 7, 228 7 of7 of13 13

Metalsliteratureliterature2017, [21,22].7, 228[21,22]. The The convective convective heat heat transfer transfer coeffic coefficientient ofof aluminum/air waswas set set constant constant at at 0.2 0.2 7kW ofkW 13 −2 −1 m−2m·s−1.·s .

FigureFigure 5. 5.Yield Yield strengths strengths at atdifferent different temperatures.temperatures. Figure 5. Yield strengths at different temperatures. TableTable 5. 5.Thermal Thermal properties. properties. Temperature (°C) Table 205. Thermal 100 properties. 200 300 400 500 ◦ Temperature ( −C)1 −1 20 100 200 300 400 500 ConductivitiesTemperature (W·m (°C) ·K ) 114.3 20 122.3 100 130.8 200 145.1 300 124.5 400 122.7 500 −1 −1−1−1 SpecificConductivitiesConductivities heat capacities (W·m (W·−m 1(J·kg·K−·1K) ·K) ) 114.3809114.3 122.3860 122.3 130.8 897 130.8 145.1 922 145.1 124.5 872124.5 122.7 985122.7 Elasticity moduli (GPa)· − 1· −1 81.5 66.2 49.3 31.0 25.3 -- SpecificSpecific heat heat capacities capacities (J·kg (J kg−1·K−1K) ) 809 809860 860 897 897 922 922 872 872 985 985 ThermalElasticity expansion moduli coefficients (GPa) (10−5) 2.08 81.5 2.19 66.2 2.61 49.3 2.70 31.0 2.68 25.3 2.73– Elasticity moduli (GPa) 81.5 66.2 49.3 31.0 25.3 -- Thermal expansion coefficients (10−5) 2.08 2.19 2.61 2.70 2.68 2.73 Thermal expansion coefficients (10−5) 2.08 2.19 2.61 2.70 2.68 2.73 The temperature-dependent material properties changed with temperature, and affected the evolution of thermal stress and plastic strain at different temperatures during the quenching process. TheThe temperature-dependenttemperature-dependent material properties changed with temperature,temperature, and affectedaffected thethe The thermal expansion coefficient, elastic modulus, and yield strength play key roles in the evolution evolutionevolution ofof thermal stress and plasticplastic strain at different temperatur temperatureses during the quenching process. of thermal stress and plastic strain. Numerical simulation was used to analyze the effect by TheThe thermalthermal expansionexpansion coefficient,coefficient, elasticelastic modulus,modulus, andand yieldyield strengthstrength playplay keykey rolesroles inin thethe evolution comparing the properties of samples M0–M3 with different material properties, as shown in Table 6. ofof thermalthermal stress stress and and plastic plastic strain. strain. Numerical Numerical simulation simulation was used was to used analyze to theanalyze effect bythe comparing effect by theSample properties M0 ofused samples the measured M0–M3 material with different properties material of the properties, studied material, as shown as shown in Table in6 .Table Sample 5 and M0 comparingFigure 5. theFor properties samples M1–M3, of samples only oneM0–M3 kind withof measured different material material properties properties, was as adjusted shown andin Table they 6. used the measured material properties of the studied material, as shown in Table5 and Figure5. Sampleare the M0 thermal used the expansion measured coefficient, material elastic properties modulu ofs, the and studied yield strength, material, respectively. as shown inThe Table material 5 and For samples M1–M3, only one kind of measured material properties was adjusted and they are the Figureproperties 5. For sampleswere adjusted M1–M3, by onlytaking one the kind value of ofmeasured the corresponding material properties material properties was adjusted at 20 and °C theyas thermal expansion coefficient, elastic modulus, and yield strength, respectively. The material properties arereference the thermal values, expansion and multiplying coefficient, elasticthe reference modulu valuess, and yieldwith thestrength, multiplier respectively. factors atThe different material were adjusted by taking the value of the corresponding material properties at 20 ◦C as reference values, propertiestemperatures were (asadjusted shown by in takingFigure 6)the to value obtain of th thee corresponding corresponding values material at different properties temperatures. at 20 °C as andreferenceThe multiplying Mises values, stress the and reference equivalentmultiplying values plastic withthe strainreference the multiplier (PEEQ) values along factors thewith atcentral the different multiplierline (L0) temperatures were factors used (astoat estimate showndifferentin Figuretemperaturesthe 6level) to obtain of (asresidual theshown corresponding stresses in Figure and plastic 6) values to obtainstrains at different thofe the corresponding samples. temperatures. values The Mises at different stress and temperatures. equivalent plasticThe Mises strain stress (PEEQ) and alongequivalent the central plastic line strain (L0) (PEEQ) were used along to the estimate central the line level (L0) of were residual used stresses to estimate and plasticthe level strains of residual of the samples.stresses and plasticTable strains 6. Simulation of the samples. scheme.

Samples Material PropertiesTable 6. Simulation M0 scheme. M1 M2 M3 Thermal expansion coefficientsTable 6. Simulation -- adjusting scheme. -- -- Elasticity moduli -- -- adjusting -- SamplesSamples Material Material Properties Properties M0 M0 M1 M1 M2 M2 M3 M3 Yield strengths ------adjusting ThermalThermal expansion expansion coefﬁcients coefficients – -- adjusting adjusting -- – -- – ElasticityElasticity moduli moduli – -- – -- adjusting adjusting -- – YieldYield strengths strengths – -- – -- -- – adjusting adjusting

Figure 6. Multiplier factors of thermal expansion coefficient, elastic modulus, and yield strength at different temperatures.

FigureFigure 6.6. MultiplierMultiplier factorsfactors ofof thermalthermal expansionexpansion coefﬁcient,coefficient, elasticelastic modulus,modulus, and yieldyield strengthstrength atat differentdifferent temperatures.temperatures.

Metals 2017, 7, 228 8 of 13 Metals 2017, 7, 228 8 of 13 ABAQUS was also used to study the influence of cooling rates on the residual stresses by simulating the quenching process. Prior to this, the heat transfer coefficients of aluminum/water were obtainedABAQUS by using was the also Deform used 2D to studyinverse the heat inﬂuence transfer ofmodule. cooling The rates measured on the temperature residual stresses vs. time by simulatingcurves at point the quenchingP0 were used. process. The Mises Prior tostresses, this, the prin heatcipal transfer stresses coefﬁcients in the y direction of aluminum/water (S22), equivalent were obtainedplastic strain by using (PEEQ), the and Deform plastic 2D strains inverse in heatthe y transfer direction module. (PE22) Thealong measured the central temperature line (L0) were vs. used time curvesto estimate at point the P0plastic were strains used. and The Misesstresses stresses, of the samples. principal stresses in the y direction (S22), equivalent plastic strain (PEEQ), and plastic strains in the y direction (PE22) along the central line (L0) were used to3. Results estimate and the Analysis plastic strains and stresses of the samples.

3. Results and Analysis 3.1. Influence of Material Properties at Different Temperatures on the Evolution of Stress and Strain 3.1. InﬂuenceMaterial of properties Material Properties change with at Different temperatures. Temperatures Thus, on the the evolutio Evolutionn ofof Stressstress and and Strain plastic strain are differentMaterial at properties different temperatures. change with temperatures. This section will Thus, investigate the evolution the evolut of stression of and plastic plastic strain strain at aredifferent different temperatures at different during temperatures. quenching, This and section study will how investigate the changing the evolutionof material of properties plastic strain affect at differentthe evolution temperatures of residual during plastic quenching, strain and andstress study after how quenching the changing treatment. of material properties affect the evolutionFirst, the of two-unit residual model plastic strain(Figure and 1) stresswas used after quenchingto investigate treatment. the plastic strains at different temperatures with the same temperature differences (Tg). Replace the coefficients of Equation (9) with First, the two-unit model (Figure1) was used to investigate the plastic strains at different the material properties and set Tg as 50 °C, 100 °C, and 150 °C, respectively. The plastic strains ( ) at temperatures with the same temperature differences (Tg). Replace the coefﬁcients of Equation (9) with different temperatures of unit i were obtained.◦ As◦ shown in◦ Figure 7, the plastic strain increases withp the material properties and set Tg as 50 C, 100 C, and 150 C, respectively. The plastic strains (εi ) at differentincreasing temperatures temperature of difference unit i were and obtained. temperature. As shown The in results Figure indicate7, the plastic that strainto produce increases a certain with increasingplastic strain, temperature the temperature difference anddifference temperature. should The be results increased indicate with that todecreasing produce a certaintemperature. plastic strain,Consequently, the temperature the temperature difference differences should be at increased high temperatures with decreasing should temperature.be reduced to Consequently, minimize the theresidual temperature stresses. differences at high temperatures should be reduced to minimize the residual stresses.

Figure 7. Plastic strains of unit i of the model at different temperaturestemperatures with a certaincertain temperaturetemperature difference (Tgg).

Figure 8 shows the simulation results for the samples (M0–M3) with different material Figure8 shows the simulation results for the samples (M0–M3) with different material properties. properties. Equivalent plastic strain (PEEQ) and Mises stresses along the central line (L0) represent Equivalent plastic strain (PEEQ) and Mises stresses along the central line (L0) represent the plastic the plastic strains and residual stresses of the samples, respectively. As shown in Figure 8b,c, the strains and residual stresses of the samples, respectively. As shown in Figure8b,c, the plastic strains plastic strains and residual stresses of the samples M1–M3 are lower than those of the sample M0. and residual stresses of the samples M1–M3 are lower than those of the sample M0. Figure8a compares Figure 8a compares the adjusting material properties used for samples M1–M3 with the ones for the adjusting material properties used for samples M1–M3 with the ones for sample M0. Like the sample M0. Like the treatments in Section 2.3, the values of every kind of measured material treatments in Section 2.3, the values of every kind of measured material properties at 20 ◦C were properties at 20 °C were considered to be reference values, and the material properties at different considered to be reference values, and the material properties at different temperatures were divided temperatures were divided by the corresponding reference value. Compared with the material by the corresponding reference value. Compared with the material properties used for sample M0, properties used for sample M0, the thermal expansion coefficients used for sample M1 are smaller, the thermal expansion coefﬁcients used for sample M1 are smaller, the elastic moduli used for sample the elastic moduli used for sample M2 are smaller, and the yield strengths for sample M3 are bigger. M2 are smaller, and the yield strengths for sample M3 are bigger. Reducing thermal expansion Reducing thermal expansion coefficients reduced thermal expansion and thermal stresses during coefﬁcients reduced thermal expansion and thermal stresses during quenching, which resulted in the quenching, which resulted in the decrease of plastic strains. Reducing the elastic modulus resulted in decrease of plastic strains. Reducing the elastic modulus resulted in an increase in the allowable elastic an increase in the allowable elastic strain at a certain thermal strain, and this led to the reduction in strain at a certain thermal strain, and this led to the reduction in the plastic strain during quenching. the plastic strain during quenching. The increase in the yield strength reduced the plastic strain at a

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Thecertain increase thermal in thestress. yield Therefore, strength reducedthe plastic the st plasticrains and strain residual at a certain stresse thermals of samples stress. M1–M3 Therefore, are thesmaller plastic than strains the ones and residualof sample stresses M0. of samples M1–M3 are smaller than the ones of sample M0.

FigureFigure 8.8. ResidualResidual equivalentequivalent plasticplastic strainstrain (PEEQ)(PEEQ) andand MisesMises stressesstresses alongalong thethe centralcentral lineline L0L0 ofof thethe samplesample (110 (110 mm mm× × 100 mm × 7070 mm) mm) in in Figure Figure 2a2a using different thermalthermal expansionexpansion coefﬁcients,coefficients, elastic elastic moduli,moduli, andand yieldyield strengths:strengths: ((aa)) normalizednormalized measuredmeasured andand adjustingadjusting materialmaterial properties;properties; ((bb)) PFEQ;PFEQ; andand ((cc)) MisesMises stresses.stresses.

3.2.3.2. InfluenceInfluence ofof CoolingCooling RatesRates atat DifferentDifferent TemperaturesTemperatures on on Residual Residual Stress Stress TheThe sectionsection aboveabove indicatesindicates thatthat toto produceproduce aa certaincertain plasticplastic strain,strain, thethe magnitudemagnitude ofof temperaturetemperature differencedifference should should be be increased increased with with decreasing decreasing temperatures. temperatures. For real For components, real components, the residual the residual stresses arestresses determined are determined by inhomogeneous by inhomogeneous plastic deformations. plastic deformations. The evolution The evolution of plastic of plastic strain andstrain stress and isstress affected is affected by the temperature by the temper distributionsature distributions in the components in the components during quenching. during Thequenching. temperature The differencetemperature increased difference with increased increasing with cooling increasing rate. cooling At the rate. same At time, the thesame cooling time, the rates cooling determine rates mechanicaldetermine properties,mechanical and properties, this relationship and this has relati beenonship studied has using been time-temperature- studied using time-temperature- properties (TTP) curvesproperties in our (TTP) previous curves work in our [15 ].previous To optimize work the [15]. quenching To optimize process, the thisquenching section willprocess, investigated this section the influencewill investigated of cooling the rates influence at different of cooling temperatures rates at ondifferent the evolution temperatures of plastic on strainthe evolution and final of residual plastic stressstrain byand quenching final residual the samples stress by with quenching different the quenching samples with technologies. different quenching technologies. FigureFigure9 9 shows shows the the cooling cooling rates rates at at P0, P0, temperature temperature differences differences between between points points P0 P0 and and P1, P1, strains strains measuredmeasured by by the the slitting slitting method, method, and and tensile tensile properties properties of the of samples. the samples. The results The show results that show reducing that thereducing cooling the rates cooling in a low rates temperature in a low temperature range does notrange reduce does residual not reduce stresses. residual However, stresses. an optimizedHowever, stepan optimized quenching step process quenching can minimize process the residualcan minimi stressesze the and residual result in stresses good mechanical and result properties. in good Asmechanical shown in Figureproperties.9a,b, theAs coolingshown ratesin Figure and temperature 9a,b, the cooling differences rates between and temperature P0 and P1 ofdifferences Samples A1between and A2 P0 are and almost P1 of the Samples same inA1 the and temperature A2 are almost range the from same 500 in to the 420 temperature◦C, and the range cooling from rates 500 and to temperature420 °C, and differencesthe cooling ofrates Sample and A2temperature are much lowerdifferences than thoseof Sample of Sample A2 are A1 much at temperatures lower than below those 400of Sample◦C. However, A1 at temperatures the residual stresses below 400 of the °C. two Howeve samplesr, the are residual almostthe stresses same, of as the shown two insamples Figure 9arec. Thisalmost means the thatsame, changing as shown the coolingin Figure rates 9c. at lowThis temperatures means that doeschanging not change the cooling the residual rates stressesat low fortemperatures the Samples does A1 andnot A2.change In the the case residual of Sample stresses A3, for the the cooling Samples rates A1 are and lower A2. at In temperatures the case of Sample above 300A3,◦ theC, especially cooling rates above are 450 lower◦C, thanat temperatures those of Sample above A1. 300 The °C, cooling especially rates above are higher 450 °C, than than those those of the of sampleSample A1A1. at The temperatures cooling rates below are high abouter than 300 those◦C. The of the temperature sample A1 differencesat temperatures of Sample below A3about are 300 lower °C. The temperature differences of Sample A3 are lower at temperatures above 400 °C and slightly higher at temperatures below 350 °C. However, the residual stresses of Sample A3 are much lower than

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Metals 2017, 7, 228 10 of 13 at temperatures above 400 ◦C and slightly higher at temperatures below 350 ◦C. However, the residual thosestresses of ofSample Sample A1 A3 due are to much the lower lower cooling than those rates of atSample high temperatures. A1 due to the This lower is because cooling plastic rates at strain high occurredtemperatures. more easily This isat becausehigh temperatures, plastic strain according occurred to the more results easily and at analysis high temperatures, presented in Section according 3.1. Moreover,to the results as shown and analysis in Figure presented 9d, the tensile in Section properti 3.1.es Moreover, of sample asA3 shown are close in to Figure those9 d,of Sample the tensile A1, propertiesbecause the of cooling sample rates A3 areare closehigh toin thosethe quenching of Sample sensitivity A1, because range the from cooling 300 rates to 400 are °C high [15]. in This the quenchingmeans that sensitivity residual rangestresses from and 300 mechanical to 400 ◦C[ 15performances]. This means can that residualbe balanced stresses by andemploying mechanical an performancesoptimized quenching can be balancedtechnology by with employing low cooling an optimized rates in high quenching temperature technology range withand high low cooling rates in highother temperaturetemperature range ranges. and high cooling rates in other temperature ranges.

Figure 9.9. ResultsResults of of Samples Samples A1–A3 A1–A3 with with different different quenching quenching technology: technology: (a) cooling (a) cooling rates atrates P0 during at P0 duringthe quenching the quenching process; process; (b) temperature (b) temperature differences differences between pointsbetween P0 points and P1 P0 during and theP1 during quenching the process;quenching (c) strainsprocess; measured (c) strains by measured the slitting by method the slitting after quenching method after treatment; quenching and ( dtreatment;) tensile properties and (d) tensileafter aging properties treatments. after aging treatments.

The numerical simulation method was used to further study the influence of cooling rates on The numerical simulation method was used to further study the inﬂuence of cooling rates on the the evolution of residual stress. Figure 10 shows the evolution of the plastic strain at P0, plastic strains evolution of residual stress. Figure 10 shows the evolution of the plastic strain at P0, plastic strains and and residual stresses along L0. As shown in Figure 10a, the plastic strains (plastic strains in the y residual stresses along L0. As shown in Figure 10a, the plastic strains (plastic strains in the y direction direction (PE22) and equivalent plastic strain (PEEQ)) at P0 of Sample A1 and A2 vs. temperature (PE22) and equivalent plastic strain (PEEQ)) at P0 of Sample A1 and A2 vs. temperature curves are curves are almost the same. The plastic strains reached the magnitudes at about 490 °C and remained almost the same. The plastic strains reached the magnitudes at about 490 ◦C and remained unchanged unchanged thereafter; even the cooling rates of Sample A2 are much lower below 400 °C. According thereafter; even the cooling rates of Sample A2 are much lower below 400 ◦C. According to the results to the results and analysis presented in Section 3.1, to produce a certain plastic strain, the temperature and analysis presented in Section 3.1, to produce a certain plastic strain, the temperature difference difference should be increased with decreasing temperatures. This explains that reducing the cooling should be increased with decreasing temperatures. This explains that reducing the cooling rates at low rates at low temperature range does not reduce the plastic strains at P0. Consequently, as shown in temperature range does not reduce the plastic strains at P0. Consequently, as shown in Figure 10b,c, Figure 10b,c, the plastic strains (PE22 and PEEQ) and residual stress (Mises stress and principal the plastic strains (PE22 and PEEQ) and residual stress (Mises stress and principal stresses in the y stresses in the y direction (S22)) along L0 of the two samples are almost the same. Moreover, in the direction (S22)) along L0 of the two samples are almost the same. Moreover, in the case of Sample A3, case of Sample A3, the step quenching technology produces lower plastic strains and residual stresses the step quenching technology produces lower plastic strains and residual stresses along L0 due to along L0 due to the low cooling rates at high temperatures. The results coincide with the experimental the low cooling rates at high temperatures. The results coincide with the experimental results in the results in the above paragraph. above paragraph.

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FigureFigure 10.10. SimulationSimulation resultsresults ofof thethe quenchingquenching samples:samples: ((aa)) evolutionevolution ofof thethe plasticplastic strainstrain (plastic(plastic strainsstrains inin thethe yy directiondirection (PE22)(PE22) andand equivalentequivalent plasticplastic strainstrain (PEEQ))(PEEQ)) atat pointpoint P0;P0; ((bb)) plasticplastic strainsstrains (PE22(PE22 andand PEEQ)PEEQ) alongalong thethe centralcentral lineline L0;L0; andand ((cc)) residualresidual stressesstresses (Mises(Mises stressstress andand principalprincipal stressesstresses inin thethey ydirection direction (S22))(S22)) alongalong L0.L0.

4.4. DiscussionDiscussion TheThe influenceinfluence ofof temperature-dependenttemperature-dependent materialmaterial propertiesproperties onon thethe evolutionevolution ofof plasticplastic strainstrain atat differentdifferent temperaturestemperatures duringduring thethe quenchingquenching processprocess waswas investigated,investigated, andand thethe influenceinfluence ofof coolingcooling ratesrates atat differentdifferent temperaturestemperatures onon thethe evolutionevolution ofof plasticplastic strainstrain andand residualresidual stressstress forfor forgedforged 2A142A14 aluminumaluminum alloyalloy componentscomponents duringduring thethe quenchingquenching processprocess waswas also also analyzed. analyzed. DuringDuring quenching process, process, the the thermal thermal expansions expansions at high-temperature at high-temperature locations locations than than at low- at low-temperaturetemperature locations. locations. The The difference difference in inthe the th thermalermal expansions expansions resulted resulted in in thermal strains andand stressesstresses toto balancebalance thethe inhomogeneousinhomogeneous thermalthermal expansions.expansions. ThisThis usuallyusually producedproduced inhomogeneousinhomogeneous plasticplastic strains,strains, whichwhich resultedresulted inin residualsresidualsstress stress after after the the quenching quenching treatment. treatment. EquationEquation (9)(9) showsshows thatthat thethe thermalthermal expansionexpansion coefficients,coefficients, elasticelastic moduli,moduli, andand yieldyield strengthsstrengths playplay keykey rolesroles inin determiningdetermining thethe magnitudemagnitude ofof plasticplastic strains.strains. FigureFigure8 8 shows shows that that compared compared with with thethe samplesample M0,M0, decreasingdecreasing thethe thermalthermal expansionexpansion coefficientscoefficients andand increasingincreasing yieldyield strengthsstrengths atat highhigh temperaturestemperatures decreases decreases the the residual residual plastic plastic strains strains and and stressesstresses alongalong thethe centralcentral lineline L0L0 ofof thethe samplesample M1M1 andand M3,M3, respectively;respectively; further,further, decreasingdecreasing thethe elasticelastic modulimoduli decreasesdecreases thethe residualresidual plasticplastic strainsstrains andand stressesstresses alongalong lineline L0L0 ofof thethe samplesample M2.M2. ThisThis cancan bebe explainedexplained asas follows:follows: DuringDuring thethe quenchingquenching process,process, decreasingdecreasing thermal thermal expansion expansion coefficient coefficien decreasedt decreased the thermalthe thermal expansion expansion and thermal and thermal stress, whichstress, resultedwhich resulted in a decrease in a decrease in the plastic in the strain. plastic Further, strain. increasing Further, in yieldcreasing strength yield reduced strength the reduced plastic strainthe plastic at a certain strain thermalat a certain stress; thermal reducing stress; the elastic reducing modulus the elastic resulted modulus in the riseresulted of allowable in the elasticrise of strainallowable at a certainelastic strain thermal at strain,a certain and thermal then led strain, to the and reduction then led in to the the plastic reduction strain. in the The plastic reduction strain. in theThe plastic reduction strains in duringthe plastic quenching strains during decreased quench residualing decreased plastic strains residual and stressesplastic strains of the components.and stresses of theThe components. paragraph above implies that increasing thermal expansion coefficient and decreasing the yieldThe strength paragraph causes above an increase implies in thethat plastic increasing strain. th However,ermal expansion decreasing coefficient elastic modulusand decreasing decreases the theyield plastic strength strain. causes For an the increase studied in the material, plastic strain. the thermal However, expansion decreasing coefficient elastic modulus increase decreases with the increasingthe plastic temperature; strain. For the elasticstudied modulus material, and the yield thermal strength expansion decrease coefficient with increasing increase temperature. with the increasing temperature; the elastic modulus and yield strength decrease with increasing temperature. Using the model in Section 2.1, the evolution of the plastic strain at different temperatures during Using the model in Section 2.1, the evolution of the plastic strain at different temperatures during quenching process was studied. Figure 7 shows that the plastic strain increases with increasing

Metals 2017, 7, 228 12 of 13 quenching process was studied. Figure7 shows that the plastic strain increases with increasing temperature at the same temperature difference between the two units; the plastic strain increases with increasing temperature difference at the same temperatures. This means that the influence of the thermal expansion coefficients and yield strengths changing with temperatures on plastic strains are more serious than the effect of the changes in the elastic moduli. Thus, the plastic strains increase with temperature. Quenching residual stress of aluminum alloy components are caused by the inhomogeneous temperature distribution. Decreasing the temperature gradients decreases the plastic strain during the quenching process, resulting in lower residual stresses. Decreasing the cooling rates decreases the temperature gradient. Many papers reported that reducing the cooling rate can minimize residual stresses [10,15,23]. However, the above paragraphs in this section imply that for this material component, the residual plastic strains and stresses are mainly determined by the cooling rates in a high-temperature zone. Figure9 shows that compared with the sample A1, reducing the cooling rates at low temperatures below 400 ◦C does not reduce the measured strains of the sample A2, as indicated by the slitting method results; in contrast, reducing the cooling rates at high temperatures above about 450 ◦C reduces the strains of sample A3 sharply, as per measurement results of the slitting method. The strains are in proportion with the residual stress of the samples. Figure 10 shows the residual strains and stresses simulation results along the central line L0 of the samples A1–A3, and they show a similar trend as the quenching experiment results. These results confirmed that the cooling rate at the high-temperature zone insignificantly affects the residual stress of this studied material component. Time-temperature-properties (TTP) curves of this studied material [15] show that mechanical performances are mainly determined by cooling rates in the quenching sensitivity temperature range. According to this conclusion and the results presented above, an optimized step quenching technology was proposed to balance the residual stresses and mechanical properties. By quenching sample A3 with this cooling path, the residual stresses were reduced significantly and the tensile properties changed slightly, compared with sample A1 quenched with water at 20 ◦C, as shown in Figures9 and 10. In this quenching treatment, the cooling rates were low at high temperatures above 450 ◦C to minimize the residual stresses, and they increased in the other temperature ranges, resulting in good mechanical properties.

5. Conclusions After analyzing and summarizing the results above, several main conclusions were inferred. Plastic strains increase with the temperature when the temperature difference remains unchanged. The cooling rates at high temperatures play a key role in determining the magnitude of residual stresses. Only reducing the cooling rates at low temperatures cannot reduce the residual stress and plastic strains. Residual stresses and mechanical properties can be balanced with an optimized quenching technology. The cooling rates of the sample are low at high temperatures to reduce residual stress and are high at the other temperatures to improve mechanical properties.

Acknowledgments: This work was financially supported by State Key Laboratory of High Performance Complex Manufacturing (zzyjkt2014-02) and the fund of Jiangsu Province for the transformation of scientific and technological achievements (BA2015075). Author Contributions: Yuxun Zhang, Shiquan Huang and Youping Yi conceived and designed the model, numerical simulation and experiments; Yuxun Zhang performed the experiments; Yuxun Zhang, Shiquan Huang and Hailin He analyzed the data; Youping, Yi contributed reagents/materials/analysis tools; Yuxun Zhang wrote the paper; Youping Yi, Shiquan Huang and Hailin He helped modify the manuscript. Conflicts of Interest: The authors declare no conflict of interest. Metals 2017, 7, 228 13 of 13

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