metals Article
Damage in Creep Aging Process of an Al-Zn-Mg-Cu Alloy: Experiments and Modeling Chao Lei, Heng Li *, Jin Fu, Nian Shi, Gaowei Zheng and Tianjun Bian State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China;
[email protected] (C.L.);
[email protected] (J.F.);
[email protected] (N.S.);
[email protected] (G.Z.);
[email protected] (T.B.) * Correspondence:
[email protected]; Tel.: +86-029-8846-0212 (ext. 808) Received: 13 March 2018; Accepted: 16 April 2018; Published: 20 April 2018
Abstract: In creep age forming (CAF), large integral panel components of high-strength aluminum alloy can be shaped and strengthened under external elastic loading at an elevated temperature through creep deformation and age hardening, simultaneously. However, the high ribbed structure on panel may induce stress concentration, inhomogeneous plastic deformation and even damage evolution on the bending rib, leading to the difficulty in controlling forming precision and material properties. Therefore, the generation and evolution of damage are necessary to be considered in the design of CAF. Taking 7050 aluminum alloy as the case material, the continuous and interrupted creep aging tests at 165 ◦ C and three stress levels (300, 325, and 350 MPa) were conducted, and the corresponding material properties, precipitate, and damage microstructures were studied by mechanical properties tests, transmission electron microscope (TEM) and scanning electron microscope (SEM) characterizations. With the increase of stress level, the creep deformation occurs easier, the precipitates grow up faster, the creep damage occurs earlier, the growth rate and the size of microvoids increase, the mechanical properties decrease more rapidly, and the dominant mechanism of creep fracture changes from shear to microvoid coalescence. To simulate creep aging behavior with damage, a continuum damage mechanics (CDM) based model is calibrated and numerically implemented into ABAQUS solver via CREEP subroutine. The CAF of 7050 aluminum alloy panels with different height ribs were conducted by experiment and FE simulation. The forming process presents a typical stress relaxation phenomenon. The creep damage mainly occurs on the bending rib due to the severe stress concentration. With the increase of rib height, the creep strain and damage degree increase, but the springback decreases. Keywords: creep age forming; damage evolution; constitutive model; finite element simulation; Al-Zn-Mg-Cu alloy
1. Introduction Aim at the integrated manufacturing of shape forming and performance tailoring, creep age forming (CAF), as a novel and promising sheet metal forming technology, has been developed and applied to manufacturing the integral panel components in the aerospace field [1]. In general, the high strength aluminum alloy panel is elastic loaded to fit the die for obtaining the target shape under the artificial aging temperature. Under this specific thermal-mechanical field of CAF, the elastic deformation is gradually changed into permanent deformation by creep, and in the meantime, the material can be strengthened by aging [2]. The greatest advantage of CAF technology lies in the synchronous process of shape forming and material strengthening, then the traditional separate forming and heat treatment processes can be combined [3–5]. However, due to the complex structure of the integral panels, such as high rib, non-uniform thickness, and variable curvature, an uneven Metals 2018, 8, 285; doi:10.3390/met8040285
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complex stress distribution will be produced on the panels in CAF. Especially, when the ribbed panel fits the die closely, the severe stress concentration can even produce local inhomogeneous plastic deformation on the bending rib. In this condition, irreversible creep damage is usually brought out with the increase of the creep deformation degree [6]. The production of damage will inevitably bring difficulties to the control of forming accuracy and product performance. In recent years, many experimental and numerical studies about CAF mainly focused on the optimization of thermal-mechanical parameters, the selection of material initial tempers, the characterization of microstructures and properties, and the prediction of springback and performance. Arabi Jeshvaghani et al. [7,8] studied the effects of time and temperature on the springback and mechanical properties of 7075 aluminum alloy in CAF, and discussed the dominant mechanisms of age hardening and creep deformation. Lei et al. [9–11] investigated the effects of material initial tempers and the thermal-mechanical loading sequences on creep aging behaviors, and revealed that the 7050 aluminum alloy with re-solution temper creep aged under the sequence of loading prior to heating will obtain the desired creep deformation and material properties. Chen et al. [12–14] tested the microstructures, mechanical properties, and corrosion resistances of age-formed 7050 aluminum alloy, and found that, when compared with the stress-free aging, the precipitate coarsening and the grain boundary precipitation free zone widening, respectively, lead to the decrease of mechanical properties and the improvement of corrosion resistance in the creep aging condition. Ho et al. [15,16] established a set of physically-based unified creep constitutive equations to model aging hardening and creep deformation behaviors of 7010 aluminum alloy sheet in CAF, and obtained agreement well between the predicted and experimental results of yield strength and springback. These studies provide beneficial knowledge for the revelation of deformation mechanism, the optimization of technological parameters and the simulation of forming process. However, the experiments in the above studies were carried out by using the creep tensile tests under creep aging conditions and the simple CAF tests of flat panels. The complex structures of the ribbed panel and the induced stress concentration problems have not been involved. Lam et al. [17] studied the effect of different rib stiffener designs on the springback of 2219 aluminum alloy ribbed panel in CAF, and found that the highest elastic stress is more likely to occur within and around the bending rib, taking up a greater proportion of the creep strain. Yang et al. [18] investigated the CAF of pre-deformed 2219 aluminum alloy ribbed panel by experiment and modeling, and pointed out that the final shape of the panel that was contributed from plastic deformation and creep deformation concurrently, with corresponding percentages of 33% and 67%, respectively. Although above studies have been carried out on the effects of the complex structures of ribbed panels, there are less reports aimed at the creep damage that is caused by stress concentration and inhomogeneous deformation. To simulate the creep deformation and aging hardening behaviors in CAF, a lot of constitutive models have been developed [1], however, the existing creep aging models did not involve the creep damage. Kowalewski et al. [19] proposed a creep constitutive model based on continuous damage mechanism (CDM), which contains two damage state variables to model the process of softening. However, the ability of the CDM based model to simulate damage in CAF is still to be studied. In this work, taking an Al-Zn-Mg-Cu alloy AA7050 as the case material, the experimental studies on the creep aging behavior with damage were carried out using uniaxial tensile creep aging tests, mechanical property tests, precipitate and microvoid microstructures characterizations, and fracture morphology analyses. A CDM based creep aging model was calibrated and embedded into the commercial FE solver ABAQUS by CREEP subroutine to numerically investigate the CAF process of AA7050 ribbed panel, and the real CAF tests were carried out to verify the accuracy of the model.
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2. Experimental Procedures Procedures 2. Experimental 2.1. As-Received Material Material and and Specimen 2.1. As-Received Specimen Preparation Preparation A alloy hot A 12.7 12.7 mm mm thick thick commercial commercial 7050-T7451 7050-T7451 (AMS (AMS 4050) 4050) aluminum aluminum alloy hot rolled rolled plate plate that that was was provided by CORUS Aluminum was used in this work. The chemical composition is listed in 1. provided by CORUS Aluminum was used in this work. The chemical composition is listed inTable Table The creep aging test specimens were machined out from the hot rolled plate by wire electrical discharge 1. The creep aging test specimens were machined out from the hot rolled plate by wire electrical machining (EDM), along the rolling 1 shows the geometry and geometry the dimensions of discharge machining (EDM), along direction. the rollingFigure direction. Figure 1 shows the and the the specimens. In order to regain the supersaturated solid solution state of alloy, the specimens were dimensions of the specimens. In order to regain the supersaturated solid solution state of alloy, the subjected solution treatment at 470 ◦ C treatment for 50 min at and subsequent Before water creep specimenstowere subjected to solution 470 °C for 50water min quenching. and subsequent aging, all of the specimens were room temperature exposed for more than 24 h to obtain stable natural quenching. Before creep aging, all of the specimens were room temperature exposed for more than aging 24 h totemper obtain [20]. stable natural aging temper [20]. Table 1. Nominal chemical composition of AA7050 (wt. %). Table 1. Nominal chemical composition of AA7050 (wt. %). Zn Zn
Mg Mg
Cu Cu
Zr Zr
Si Si
Fe Fe
5.93 1.91 1.91 5.93
2.45 2.45
0.11 0.11
0.05 0.05
0.14 0.14
Ti Ti
Mn Mn
Al Al
0.03 0.03 0.01 0.01 Bal. Bal.
Figure 1. 1. Geometry dimensions of of creep creep aging aging test test specimens specimens (unit: (unit: mm). mm). Figure Geometry and and dimensions
2.2. Creep Tests 2.2. Creep Aging Aging Tensile Tensile Tests The creep creep aging aging tests tests were were conducted conducted under under 300, 300, 325 and 350 350 MPa MPa until until the the specimens specimens The 325 and fractured. The testing apparatus is a specialized 100 kN electronic creep testing machine with aa fractured. The testing apparatus is a specialized 100 kN electronic creep testing machine with ◦ C. thermal environment furnace, which can control the testing temperature fluctuation less than thermal environment furnace, which can control the testing temperature fluctuation less than 11 °C. The specimen testing temperature was heated to The specimen was was fitted fitted in inthe themiddle middleofofthe thefurnace, furnace,and andthen thenthe the testing temperature was heated ◦ 165 °C and detected around the top, middle, and bottom of specimen. After heating to the target to 165 C and detected around the top, middle, and bottom of specimen. After heating to the target temperature, the the tensile tensile stress stress was was applied applied on on the the specimen specimen under under the the loading loading speed speed of of 0.5 0.5 mm/min, mm/min, temperature, and then then the the stress stress was was kept kept constant constant during during subsequent subsequent creep creep aging aging process. process. The The elongation elongation of of the the and specimen was measured by a probe-type grating line displacement transducer with the accuracy of specimen was measured by a probe-type grating line displacement transducer with the accuracy of5 −4 − 4 mm. 1010 mm. To To study the mechanical 5× × study theevolutions evolutionsofofcreep creepdamage, damage,precipitate precipitate microstructure, microstructure, and and mechanical property during the above creep aging tests, a series of interrupted tests were performed the property during the above creep aging tests, a series of interrupted tests were performed underunder the same same testing conditions. For each experimental condition, the total number of creep aging tensile testing conditions. For each experimental condition, the total number of creep aging tensile tests was testslimited was not limited until obtaining four sets of highly creepthe data ensure the not until obtaining four sets of highly repetitive creeprepetitive data to ensure testto credibility. Onetest of credibility. One of the four sets of creep data was selected to analyze creep deformation, and the four the four sets of creep data was selected to analyze creep deformation, and the four creep aged specimens creepused agedfor specimens were used for the properties subsequent mechanical propertiescharacterization. tests and microstructure were the subsequent mechanical tests and microstructure In detail, characterization. In detail, three creep aged specimens were used in tensile tests to obtain the three creep aged specimens were used in tensile tests to obtain the average values of yield strength (YS), average values of yield strength (YS), tensile strength (TS), and elongation. The gauge section on the tensile strength (TS), and elongation. The gauge section on the fourth one was divided into three parts fourth wasand divided intowere threeused partsfor byhardness wire EDM, then they were used forand hardness test, by wireone EDM, then they test,and precipitate characterization, microvoid precipitate characterization, and microvoid observation, respectively. observation, respectively. 2.3. Mechanical Tests and and Microstructure Microstructure Characterization Characterization 2.3. Mechanical Properties Properties Tests For the the creep creep aged aged specimen, specimen, the the room room temperature temperature tensile carried out by aa MTS MTS For tensile tests tests were were carried out by CMT5205 universal universalmaterial material testing machine a speed tensileof speed of 2 and mm/min, and the CMT5205 testing machine underunder a tensile 2 mm/min, the deformation deformation of specimen was by the same extension meter asaging in thetensile creep test. agingUsing tensile of specimen was measured by measured the same extension meter as in the creep a test. Using a THV-1MD digital micro-Vickers hardness tester, the micro-hardness of each creep aged specimen was measured ten times in order to calculate an average hardness value.
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THV-1MD digital micro-Vickers hardness tester, the micro-hardness of each creep aged specimen was Theten precipitate of an creep aged specimens were characterized by a TECNAI G2 measured times in microstructures order to calculate average hardness value. F30The transmission electron microscope (TEM) 200 kV. were In the preparationbyprocess of TEM precipitate microstructures of creep agedat specimens characterized a TECNAI G2 F30 specimens, a slice was cut away from the selected creep aged specimen by wire EDM and then transmission electron microscope (TEM) at 200 kV. In the preparation process of TEM specimens, a slice frictional thinned to selected 60 μm thickness. Some 3 mm by diameter disksand were blanked outthinned from the was cut away from the creep aged specimen wire EDM then frictional toslice 60 µm and twin-jet electro-polished in a solution of 20% perchloric acid and 80% ethanol (in volume) at −20 thickness. Some 3 mm diameter disks were blanked out from the slice and twin-jet electro-polished in °C and 20 V. The morphologies of fractures and microvoids were observed by a JEOL JCM-6000 a solution of 20% perchloric acid and 80% ethanol (in volume) at −20 ◦ C and 20 V. The morphologies scanning electron microscope (SEM). of fractures and microvoids were observed by a JEOL JCM-6000 scanning electron microscope (SEM). 2.4. CAF Tests for Ribbed Panels
2.4. CAF Tests for Ribbed Panels
Figure 2 shows the geometries and the dimensions of the ribbed panels and the dies used in Figure 2 shows the geometries and the dimensions of the ribbed panels and the dies used in CAF CAF tests. The thickness (t) of baseplate and rib is 3 mm, and the rib heights (h) are 0, 3, 6, and 9 mm. tests. The thickness (t) of baseplate and rib is 3 mm, and the rib heights (h) are 0, 3, 6, and 9 mm. The ribbed panels were also machined out from the hot rolled plate by NC milling, and then the The ribbed panels were also machined out from the hot rolled plate by NC milling, and then the solution treated under 470 °C for 50 min, followed by water quenching, and their length direction ◦ C for 50 min, followed by water quenching, and their length direction was solution treated under 470 was parallel to the rolling direction. In the assembly stage, the ribbed panel was placed between the parallel thelower rolling direction. assembly stage, thefailure ribbedthat panel placed between upper upperto and dies. In orderIn to the avoid the compression waswas caused by the direct the contact and lower dies. In order to avoid the compression failure that was caused by the direct contact of the rib and upper die, some pure aluminum pads were placed around the ribs to fill the gap of thebetween rib and the upper die, some pads were placed around the to fill the panel gap between baseplate and pure upperaluminum die. The upper die was pressed down to ribs fit the ribbed with thethe baseplate and upper die.and The upper diewas wasmaintained pressed down fit the ribbed panel with the and lower lower die completely, this fitting usingtobolts at each end of the upper dielower completely, and this fitting was maintained using bolts at each end of the upper and lower dies. dies. The whole set of device was placed in the aging furnace and was heated to 165 °C. After ◦ The whole of set12ofh,device was placed in the aging and and was the heated to 165 After holding holding the device was removed from furnace the furnace, ribbed panelC.was cooled and of 12 unloaded. h, the device was removed from the furnace, and the ribbed panel was cooled and unloaded.
Figure 2. Geometries and dimensions of (a) upper and lower dies and (b) ribbed panels (unit: mm). Figure 2. Geometries and dimensions of (a) upper and lower dies and (b) ribbed panels (unit: mm).
3. Creep Aging Behaviors with Damage Evolution
3. Creep Aging Behaviors with Damage Evolution 3.1. Creep Deformation
3.1. Creep Deformation
Figure 3 shows the creep strain and creep rate curves of AA7050 under 165 °C and various Figure 3 shows the creep strain and creep rate curves of AA7050 under 165 ◦ C and various applied stresses. In the creep strain curves, it can be seen that the creep strain in the tertiary creep
applied stresses. In the creep strain curves, it can be seen that the creep strain in the tertiary creep
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stage accounts accounts for for aa large With the the increase increase of of applied stage large proportion proportion of of total total creep creep strain. strain. With applied stress, stress, the the steady creep stage In the steady creep stage and and fracture fracture time time obviously obviously shorten, shorten, but but the the total total creep creep strain strain increases. increases. In the creep rate curves, the the typical typical three three stages stages of of creep creep deformation are presented presented clearly. clearly. The The creep creep rate creep rate curves, deformation are rate reduces sharply in inthe theprimary primarycreep creepstage stageand andit itremains remains stable steady creep stage. to reduces sharply stable in in thethe steady creep stage. DueDue to the the occurrence of damage, creep rate increases drasticallyafter afterentering enteringthe thetertiary tertiarycreep creep stage, stage, occurrence of damage, thethe creep rate increases drastically leading to to the the final final fracture. fracture. With With the the increase increase of of stress, stress, the the steady steady creep creep rate rate becomes becomes larger, larger, but leading but the the steady creep stage steady creep stage shortens shortens and and even even disappears. disappears.
Creep Creepstrain strain(%) (%)
44
33
300 MPa MPa 300 325 MPa MPa 325 350 MPa MPa 350 Fracture Fracture
1.0 (b)1.0
300 MPa MPa 300 325 MPa MPa 325 350 MPa MPa 350
0.8 0.8 -1 Creep Creeprate rate(h (h-1))
(a) 55
22 11 00
0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0
00
44
12 88 12 h) Time (h Time
16 16
20 20
00
44
12 88 12 Time (h) (h) Time
16 16
20 20
◦ C and Figure 3. Creep Creep deformation deformation behaviors behaviors of AA7050 during creep aging tensile tests under 165 and Figure 3. and Figure 3. Creep deformation behaviors of of AA7050 AA7050 during during creep creep aging aging tensile tensile tests tests under under 165 165 °C different stress levels: (a) creep strain curves; and, (b) creep rate curves. different stress levels: levels: (a) (a) creep creep strain strain curves; curves; and, and, (b) (b) creep creep rate rate curves. curves. different stress
3.2. 3.2. Age Age Hardening Hardening Figure shows the the evolutions evolutions of of mechanical mechanical properties AA7050 during aging Figure 44 shows properties of of AA7050 during the the creep creep aging ◦ tensile tests under 165 °C and different applied stresses, including hardness, YS, TS, and elongation. tensile tests under 165 C and different applied stresses, including hardness, YS, TS, and elongation. The mechanical mechanical strengths strengths (hardness, increase firstly firstly and and then then decrease decrease with with creep creep aging aging The (hardness, YS YS and and TS) TS) increase time. mechanical strength earlier the the time. The The higher higher the the applied applied stress, stress, the the faster faster the the mechanical strength improves, improves, and and the the earlier material obtains peak mechanical strength. This shows that the increase of the applied stress material obtains peak mechanical strength. This shows that the increase of the applied stress accelerates accelerates the age hardening. Guo et al. [21] applied stress can theand formation the age hardening. Guo et al. [21] verified the verified applied the stress can promote thepromote formation growth and growth ofinprecipitates in an Al-Zn-Mg-Cu alloy.discussion The detailed willdrawing be carried of precipitates an Al-Zn-Mg-Cu alloy. The detailed willdiscussion be carried out on out the drawing on the microstructure observation below. microstructure observation below. 600 (b)600
200 (a) 200
Yield Yieldstrength strength(MPa) (MPa)
Hardness Hardness(HV) (HV)
180 180 160 160 140 140 300 MPa MPa 300 325 MPa MPa 325 350 MPa MPa 350
120 120 100 100
00
44
12 88 12 Time (h) (h) Time
16 16
500 500
400 400 300 MPa MPa 300 325 MPa MPa 325 350 MPa MPa 350
300 300 20 20
Figure 4. Cont.
00
44
12 88 12 Time (h) (h) Time
16 16
20 20
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600 600
Elongation (%)(%) Elongation
Tensile strength (MPa) Tensile strength (MPa)
(c) 650 (c) 650
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550 550 500 500
300 MPa 300 325 MPa 325 350 MPa 350 MPa
24 24 18 18 12 12 6 6
450 450 0 0
4 4
8 12 Time (h)12 8 Time (h)
16 16
20 20
0 0
4 4
8 12 Time (h) 12 8 Time (h)
16 16
20 20
Figure 4. 4. Mechanical Mechanical properties properties evolutions evolutions of during creep aging tensile tensile tests tests under under 165 165 ◦°C Figure of AA7050 AA7050 during creep aging C Figure 4. Mechanical properties evolutions of AA7050 during creep aging tensile tests under 165 °C and different stress levels: (a) hardness; (b) yield strength; (c) tensile strength; and, (d) elongation. and different stress levels: (a) hardness; (b) yield strength; (c) tensile strength; and, (d) elongation. and different stress levels: (a) hardness; (b) yield strength; (c) tensile strength; and, (d) elongation.
Based on the evolutions of mechanical properties, some creep aged specimens were selected to Based on on the the evolutions evolutionsof ofmechanical mechanicalproperties, properties,some somecreep creep aged specimens were selected Based aged specimens were selected to observe corresponding precipitate microstructures. The precipitation sequence of Al-Zn-Mg-Cu to observe corresponding precipitatemicrostructures. microstructures.The Theprecipitation precipitation sequence sequence of of Al-Zn-Mg-Cu observe corresponding precipitate Al-Zn-Mg-Cu alloys has been confirmed as: supersaturated solid solution → GP zone → η’ phase → η phase [22]. alloys has been confirmed as: solid → GP zone zone → →η’ η’ phase phase →ηη phase phase [22]. [22]. alloys confirmed as: supersaturated supersaturated solid solution solution → GP Under has thebeen creep aging condition, the metastable η’ phase and stable η phase→are the main Under the creep aging condition, the metastable η’ phase and stable η phase are the main precipitates Under the creep aging metastable η’ phase and of stable η phase are themainly main precipitates to affect the condition, mechanicalthe strengths, and the difference the hardening effect to affect the mechanical strengths, andstrengths, the difference of the hardening effect mainly depends on the precipitates to affect the mechanical and the difference of the hardening effect mainly depends on the size of the two precipitates. The small-sized η’ phase can only be cut by moving size of theontwo The small-sized η’The phase can only bephase cut bycan moving dislocation, which depends theprecipitates. size two precipitates. small-sized onlyinto be cut moving dislocation, which hasofa the stronger hardening effect. While the η’η’ phase transforms the by big-sized η has a stronger hardening effect. While the η’ phase transforms into the big-sized η phase that can dislocation, a strongerby hardening While the phase transforms into the η phase that which can behasbypassed moving effect. dislocation, theη’mechanical strengths willbig-sized decrease. be bypassed by moving dislocation, the mechanical strengths will decrease. Therefore, they are not phase thatthey can benot bypassed by moving Therefore, are distinguished here. dislocation, the mechanical strengths will decrease. distinguished here. Therefore, are not Figurethey 5 shows thedistinguished intragranularhere. precipitates of creep aged AA7050 under 165 ◦°C and 300 MPa Figure 5 shows the intragranular precipitates of creep aged under 165 C and 300 300 MPa Figure 5 shows the intragranular creep aged AA7050 AA7050 underexist 165 °C MPa for 2, 4 and 12 h, and 350 MPa for 3 h.precipitates Many fine of and dispersive precipitates in and the matrix of for 2, 4 and 12 h, and 350 MPa for 3 h. Many fine and dispersive precipitates exist in the matrix of for 2, 4 and 12 h, and 350 MPa for 3 h. Many fine and dispersive precipitates exist in the matrix of alloy after creep aging of 2 h under 300 MPa. It can be seen from the mechanical properties curves alloy after creep of 300 It be seen the mechanical properties curves alloy after creep aging aging of 22 h h under under 300 MPa. MPa. It can can seen from fromthat the the mechanical curves that the hardness and strength are rising at this time,beindicating alloy hasproperties not yet obtained that the the hardness hardness and and strength strength are are rising at this time, indicating that the the alloy has not yet obtained that rising at this time, indicating that alloy has not yet obtained the peak strength, still in the under-aging temper. After creep aging of 4 h, the precipitates grow up the peak peak strength, strength, still still in the the under-aging under-aging temper. temper. After After creep creep aging aging of of 4 h, h, the the precipitates precipitates grow grow up up the obviously, and the peakinstrength appears, indicating that the alloy is in 4the peak-aging temper. With obviously, and the peak strength appears, indicating that the alloy is in the peak-aging temper. With obviously, the peak appears, that thecoarsen alloy isseverely, in the peak-aging temper. With the furtherand extension of strength creep aging time,indicating the precipitates so the alloy enters the the further further extension extension of of creep creep aging aging time, time, the the precipitates precipitates coarsen coarsen severely, severely, so so the alloy enters the the the alloy enters the over-aging temper and the mechanical strengths decrease. Under 350 MPa, although the precipitates over-aging temper temper and and the the mechanical mechanical strengths strengths decrease. Under 350 350 MPa, MPa, although although the the precipitates precipitates over-aging decrease.decreased. Under are still small, the mechanical strengths have obviously This indicates that the cause of are still mechanical strengths have obviously decreased. This indicates thatthat the cause of the are still small, small,the the mechanical strengths have obviously decreased. This cause of the decreasing mechanical strengths of the alloy is not over-aging, but theindicates occurrence of the damage. decreasing mechanical strengths of the alloy is not over-aging, but the occurrence of damage. the decreasing mechanical strengths of the alloy is not over-aging, but the occurrence of damage.
Figure 5. Cont.
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Figure 5. 5. Transmission Transmission electron electron microscope(TEM) (TEM) brightfield field imagesfor for intragranularprecipitates precipitatesof Figure Figure 5. Transmission electron microscope microscope (TEM)bright bright fieldimages images forintragranular intragranular precipitates of creep aged AA7050 under 165 °C and different stress levels: (a) 300 MPa for 2 h; (b) 300 MPafor for4 4h; ◦ and different stress levels: (a) 300 MPa for 2 h; (b) 300 MPa creep aged AA7050 under 165 of creep aged AA7050 under 165C°C and different stress levels: (a) 300 MPa for 2 h; (b) 300 MPa for 4 h; (c) 300 MPa for 12 h; and, (d) 350 MPa 3 h. (c) 300 MPa forfor 1212 h; h; and, (d)(d) 350350 MPa forfor 3 h. h; (c) 300 MPa and, MPa for 3 h.
3.3. Damage Evolution 3.3. Damage Evolution Evolution 3.3. Damage Figure 66 shows the evolution ofofmicrovoid in in AA7050 during creep aging under 165 °C and ◦ C 350 Figure showsthe theevolution evolutionof microvoid AA7050 during creep aging under and Figure 6 shows microvoid in AA7050 during creep aging under 165 165 °C and 350 MPa. After creep aging of 1 h, the damage cavity appears due to the chipping and separating of the 350 MPa. After creep aging of 1 h, the damage cavity appears due to the chipping and separating of MPa. After creep aging of 1 h, the damage cavity appears due to the chipping and separating of the second phase from the matrix. As the creep proceeds, the microvoid gradually grows because it the second phase from matrix. creep proceeds,the themicrovoid microvoidgradually graduallygrows growsbecause because it it second phase from thethe matrix. AsAs thethe creep proceeds, captures a large number of moving dislocations. When the microvoid becomes larger and larger and captures a large number captures number of of moving moving dislocations. dislocations.When Whenthe themicrovoid microvoidbecomes becomeslarger largerand andlarger largerand andit it eventually becomes a crack, the specimen fractures quickly after entering the tertiary creep stage. eventually becomes a crack, the specimen fractures quickly after entering the tertiary creep stage. it eventually becomes a crack, the specimen fractures quickly after entering the tertiary creep stage.
Figure electron microscope microscope (SEM) (SEM) images images for for evolution evolutionof ofmicrovoid microvoidin inAA7050 AA7050during during Figure 6. 6. Scanning Scanning electron ◦ C and Figure 6. Scanning electron microscope (SEM) evolution creep under 350 (a) 11 h; h;images (b) 22 h; h; for and, (c) 33 h. h. of microvoid in AA7050 during creep aging aging under 165 165 °C and 350 MPa: MPa: (a) (b) and, (c) creep aging under 165 °C and 350 MPa: (a) 1 h; (b) 2 h; and, (c) 3 h.
Figure the comparison comparison of of microvoids microvoids in in AA7050 AA7050 during duringthe thetertiary tertiarycreep creepstage stageunder under Figure 7 7 shows shows the ◦ C and different stress levels. The greater the applied stress, the bigger the microvoid. It is 165 Figure 7 shows the comparison of microvoids in AA7050 during the tertiary creep stage under 165 °C and different stress levels. The greater the applied stress, the bigger the microvoid. It is mentioned that stress the size size of microvoid microvoid gradually grows with with thethe creep deformation, butthe thesize 165 °C andabove different levels. The greater the applied stress, bigger the microvoid. Itsize is mentioned above that the of gradually grows the creep deformation, but of microvoids in the tertiary creep stage is very different under different stress levels. This indicates mentioned above that the size of microvoid gradually grows with the creep deformation, but the size of microvoids in the tertiary creep stage is very different under different stress levels. This indicates that the important factor affecting the sizedifferent ofmicrvoid micrvoid applied stress rather than creep time. of microvoids in the tertiary creep stage the is very under different stress levels. This indicates that the most most important factor affecting size of isisapplied stress rather than creep time. The increase of stress significantly promotes the movement of dislocation, and then causes more that most important factor affecting the size of movement micrvoid isof applied stress and rather than creepmore time. The the increase of stress significantly promotes the dislocation, then causes dislocation to participate in the growth of the microvoid. The increase of stress significantly promotes the movement of dislocation, and then causes more dislocation to participate in the growth of the microvoid. dislocation to participate in the growth of the microvoid.
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Figure SEM for comparison of microvoids in in AA7050 AA7050 during during tertiary tertiarycreep creepstage stageunder under165 165 Figure7. SEMimages images Figure 7.7. SEM imagesfor forcomparison comparisonofofmicrovoids microvoids in AA7050 during tertiary creep stage under °C and different stress levels: (a) 300 MPa for 18 h; (b) 325 MPa for 8 h; and, (c) 350 MPa for 4 h. ◦ °C and different stress levels: (a) 300 MPa for 18 MPaMPa for 8for h; 8and, (c) 350 for 4for h. 4 h. 165 C and different stress levels: (a) 300 MPa forh; 18(b) h; 325 (b) 325 h; and, (c) MPa 350 MPa
The aging tensile tensile tests, tests,and andobvious obviousnecking neckingcan can Thespecimens specimensare areeventually eventually ruptured ruptured in the creep aging The specimens are eventually ruptured in the creep aging tensile tests, and obvious necking can be parallel to to the the maximum maximum shear shear stress stressdirection, direction, befound foundnear near the the fracture. fracture. The The fracture fracture surface is parallel be found near the fracture. The fracture surface is parallel to the maximum shear stress direction, and with the principal stress This fracture mode can be summarized andhas hasan anangle angleof of45° 45° with the principal direction. This fracture mode can be summarized asas and has an angle of 45◦ with the principal stress direction. This fracture mode can be summarized as ductile ductilefracture. fracture. ductile fracture. Figure during creep creep aging agingtensile tensiletests testsunder under165 165 Figure88shows showsthe the fracture fracture morphologies morphologies of AA7050 during Figure 8 shows the fracture morphologies of AA7050 during creep aging tensile tests under 165 ◦ C °C and are are composed composed with withdimples dimplesof ofdifferent different °Cand anddifferent differentstress stress levels. levels. The The fractures fractures are spongy and and different stress levels. The fractures are spongy and are composed with With dimples of different sizesand andshear shearplanes. planes. Such Such this this fracture fracture mode is a typical ductile sizes ductile fracture fracture [23]. [23]. Withthe theincrease increaseofof sizes andstress, shear planes. Suchmode this fracture mode is a from typical ductile fracture [23]. With the increase applied the fracture fracture gradually shear applied stress, the mode gradually varies shear fracture fracture to to microvoid microvoid coalescence coalescence offracture. appliedThe stress, the fracture mode gradually varies from shear fracture to microvoid coalescence increasing stress stress is is conducive conducive to the generation fracture. The increasing generation of of internal internal necking, necking, and and the theshear shear fracture. The increasing stress is conducive to the generation of internal necking, and the shear between betweenthe thematrix matrixand and microvoid microvoid is is reduced. The stress has between has little little effect effecton onthe thedimple dimplediameter, diameter,but but the microvoid is reduced. The stressSome has little effect on thecan dimpleseen diameter, but the thematrix dimpleand deepens with the the increase of broken the dimple deepens with increase stress. broken particles particles can be be seen clearly clearlyininthe the dimple deepens with the increase of stress. Some broken particles can be seen clearly in the dimples, dimples, and proved to be the insoluble second phase Al 7 Cu 2 Fe, which is a high temperature stable dimples, and proved to be the insoluble 7Cu2Fe, which is a high temperature stable and proved to be the insoluble second Al7 Cuconcentration high temperature stable phase and 2 Fe, which is a phase andwill will be dissolved above 500phase °C. Stress occurs phase and be dissolved above 500 concentration occurs around around these thesesecond secondphases phases ◦ C. Stress concentration occurs around these second phases during creep will be dissolved above 500 duringcreep creep deformation, deformation, and and aa large large number number of during of micro-cracks micro-cracks are are produced, produced, leading leadingtotothe thefinal final deformation, and a large number of micro-cracks are produced, leading to the final fracture. fracture. fracture.
Figure 8. Cont.
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Figure of AA7050 AA7050 during duringcreep creepaging agingtensile tensiletests testsunder under Figure8.8. SEM SEM images images for for fracture fracture morphologies morphologies of 165 C and MPa; (b) (b) 325 325 MPa; MPa; (c) (c)350 350MPa; MPa;and, and,(d) (d)component componentanalysis analysis 165◦°C anddifferent differentstress stresslevels: levels: (a) (a) 300 300 MPa; of ofsecond secondphase phase particle. particle.
Tofurther furtherclarify clarify the the damage damage mechanism mechanism in To in creep creep aging aging process, process,the theroom roomtemperature temperaturetensile tensile fracture experiments experiments were were conducted conducted on on AA7050 AA7050 with with two two states. states. Figure fracture Figure9a9ashows showsthe theroom room temperature tensile fracture morphology of the alloy with solution temper, and Figure 9b represents temperature tensile fracture morphology of the alloy with solution temper, and Figure 9b represents ◦ C and thatof ofthe thealloy alloy creep creep that that is is aged aged under under 165 that 165 °C and 300 300 MPa MPafor for12 12h. h.The Thealloy alloywith withsolution solutiontemper temper has aa comparatively comparatively high high elongation, elongation, and has and there there are are aa large largenumber numberofofshear shearplanes planesininthe thefracture, fracture, showingaatypical typicalshear shearfracture. fracture.The Theroom roomtemperature temperaturetensile tensilefracture fractureofofcreep creepaged agedalloy alloyhas hasa alot lotof showing of glide steps, showing a ductile fracture dominant by shear fracture. It can be seen that the glide steps, showing a ductile fracture dominant by shear fracture. It can be seen that the difference of difference of fracturebetween mechanisms roomtension temperature tension andiscreep aging because theof fracture mechanisms roombetween temperature and creep aging because theisproduction production of damage microvoids during the creep aging process. damage microvoids during the creep aging process.
Figure tensile fracture fracture morphologies morphologiesofofAA7050 AA7050with withdifferent different Figure9.9.SEM SEM images images for for room room temperature temperature tensile ◦ states: aged under under 165 165 °C C and and 300 300 MPa MPa for for12 12h. h. states: (a) (a) solution solution temper; temper; and, and, (b) (b) creep creep aged
Material and and Process Process Modeling Modeling 4.4.Material
4.1. Model 4.1.Calibration Calibration of of CDM CDM Based Based Constitutive Constitutive Model Kowalewski sinh function function to to describe describethe thestress stresslevel leveldependence dependenceofofcreep creeprate, rate, Kowalewski et et al. al. [19] [19] used used aa sinh and to characterize the tertiary tertiary creep creep softening. softening.This ThisCDM CDM and introduced introduced two two damage damage state state variables variables to characterize the basedequation equation set set is is expressed expressed as: as: based (11− HH) ddε = AA sinh BBσ = (1 − ωn)nsinh (1 − ϕ) (1)(1) ddt t 1
dt
1 dH
h dε
1 H
ddt H = hσ dt d 1 − HH∗ 1 dt dt H *
(2) (2)
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d K C 4 (3) 1 dt 3 KC dϕ 4 = (3) d (1d− ϕ) dt 3C = (4) dt dt dω dε =C (4) n B 1 H / 1 dt cothdt B 1 H / 1 (5) n = [ Bσ (1 − H )/(1 − ϕ)]coth[ Bσ (1 − H )/(1 − ϕ)] (5) where A, B, C, h, H*, and KC are material constants, which can be divided into three groups: (a) h and where A, B, C, h,the H*, primary and KC are material which can divided into three groups: h and H* characterize creep; (b) Aconstants, and B describe thebe secondary creep; and, (c) C(a) and Kc H* characterize the primary creep; (b) A and B describe the secondary creep; and, (c) C and Kc represent represent the damage evolution. The parameter H reveals the influence of hardening in the early the damage evolution. The parameter H0reveals the influence of saturation hardening value in the of early stageequation of creep, stage of creep, and its value varies from to H*, where H* is the H. This andcontains its valuetwo varies from 0state to H*, where H* the saturation value of of softening H. This equation set contains two set damage variables to is present the influence in tertiary creep stage. damage state variables to present the influence of softening in tertiary creep stage. The first variable The first variable φ reflects the effect of precipitation on the material mechanical property during theϕ reflectsprocess, the effect of precipitation on the material property during the aging and aging and its value varies from 0 to 1.mechanical The second variable ω describes theprocess, cavitation its value varies from 0 to 1. The second variable ω describes the cavitation induced damage during induced damage during creep process. creep process. The determination of material constants is an important part for establishing an accurate The determination constants is an genetic important part for establishing accurate constitutive model [24,25].ofInmaterial this work, a simplified algorithm (GA) is taken toan determine constitutive model [24,25]. In this work, a simplified genetic algorithm (GA) is taken to determine the the constitutive parameters. The error between experimental and calculated values of the creep constitutive parameters. The error between strain ε is taken as the optimization objectiveexperimental function: and calculated values of the creep strain ε is taken as the optimization objective function: m n1
ijc ije / ijei f ( ) n1 m j h 2 j
1 i 1 f (ε) = j∑ ∑
2
(6) (6)
εcij − εeij /εeij
j =1 i =1
where ij and ij represent the calculated and experimental values of creep strain, respectively. where εc and εeij represent the calculated and experimental values of creep strain, respectively. n1 is the n1 is the ijnumber of experimental creep curves, and mj is the number of experimental data on the jth number of experimental creep curves, and mj is the number of experimental data on the jth creep curve. creep curve. Fourth Order Gill Formula is selected as the numerical integration method for GA to solve the Fourth Order Gill Formula is selected as the numerical integration method for GA to solve the above problem. The GA parameters are defined as follows: population size 400, crossover probability above problem. The GA parameters are defined as follows: population size 400, crossover 0.8, mutation probability 0.05, and iterative algebra 1500. The optimized constitutive parameters of probability 0.8, mutation probability 0.05, and iterative algebra 1500. The optimized constitutive AA7050 are obtained, as listed in Table 2. Figure 10 shows the comparison between experimental and parameters of AA7050 are obtained, as listed in Table 2.◦ Figure 10 shows the comparison between calculated creep strains of AA7050 creep aged under 165 C and different stresses. The well agreement experimental and calculated creep strains of AA7050 creep aged under 165 °C and different stresses. indicates that the CDM based creep aging model is suitable for describing the creep aging behavior The well agreement indicates that the CDM based creep aging model is suitable for describing the with damage. creep aging behavior with damage. c
e
Table 2. Material constants of AA7050 in continuous damage mechanism (CDM) model. Table 2. Material constants of AA7050 in continuous damage mechanism (CDM) model. 1) −1 ) A (h−A −1) h (MPa) (h−1) B (MPa B (MPa h (MPa) − 8 4.00014.0001 × 10 × 10−8 0.0343 1.3127 × 10×5 105 0.0343 1.3127
1.0
Creep strain (%)
0.8
H* (-) H* (-) 0.2000 0.2000
Symbol: experimental value Line: fitting curve
−1 )
(h) C −1 KCK(h
C (-) C (-)
−5 −5 10
4.0996 4.0996 ×× 10
66.3721 66.3721
200 MPa 250 MPa 300 MPa
0.6 0.4 0.2 0.0
0
2
4
6 Time (h)
8
10
12
Figure10. 10.Comparison Comparisonbetween betweenexperimental experimentaland andcalculated calculatedcreep creepstrains strainsof ofAA7050. AA7050. Figure
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4.2. FE 4.2. FE Modeling Modeling for for CAF CAF of of Ribbed Ribbed Panels Panels The CDM based based model model has has been been implemented implemented into commercial FE solver ABAQUS ABAQUS via a The CDM into commercial FE solver via a user-defined subroutine and an an implicit implicit FE FE model model has has been been developed developed for for CAF CAF of of AA7050 AA7050 user-defined subroutine CREEP, CREEP, and ribbed panel. Figure 11 shows the FE models of ribbed panels and dies, and CAF simulation ribbed panel. Figure 11 shows the FE models of ribbed panels and dies, and CAF simulation procedure. procedure. 8-node tetrahedral reduced integral three-dimensional solid element is The 8-node The tetrahedral reduced integral three-dimensional solid element (C3D8R) is (C3D8R) used in FE used in FEofmodeling of thealloy aluminum alloymesh panel. Theonmesh sizes and on baseplate and× rib5 are ×5 modeling the aluminum panel. The sizes baseplate rib are 5 mm mm5×mm 1 mm mm 5×mm 1 mm andmm 5 mm 1.5 respectively. mm × 1 mm,The respectively. concave die with of bending of 300 and × 1.5 × 1 ×mm, concave dieThe with bending radius 300 mmradius is composed mm is composed rigid elements, andthroughout completely the fixed throughout theContact formingbetween process.the Contact of rigid elements, of and completely fixed forming process. rigid between theand rigid die surface and the deformable aluminum panel is defined as a friction die surface the deformable aluminum panel is defined as a friction coefficient of 0.3.coefficient Since the of 0.3.isSince the panel is completely symmetrical, forofconvenience, 1/4 ofasthe is taken panel completely symmetrical, for convenience, 1/4 the panel is taken thepanel research object as in the the research object in the A subsequent discussion. locatedsurface at theofcenter the upper subsequent discussion. feature point located atAthefeature center point of the upper the ribof is selected to surface of the rib is selected to analyze the simulation results. The whole simulation process is analyze the simulation results. The whole simulation process is divided into three steps: (1) Loading: divided into is three steps: (1) Loading: pressure is gradually increased 10 MPa, leading to the the pressure gradually increased tothe 10 MPa, leading to the panel touchtowith the die completely; panel touch with the die completely; (2)hHolding: the the pressure forand 12 hdie; to maintain the fitting (2) Holding: the pressure is held for 12 to maintain fittingisofheld panel and, (3) Unloading: of panel and is die; and, (3) Table Unloading: is removed. Table 3 lists the mechanical properties the pressure removed. 3 lists the the pressure mechanical properties of the AA7050 with solution temper ◦ of the AA7050 under 165 C. with solution temper under 165 °C.
Figure 11. FE models and creep age forming (CAF) simulation procedure. Figure 11. FE models and creep age forming (CAF) simulation procedure. Table 3. Mechanical property of AA7050 under 165 ◦°C. Table 3. Mechanical property of AA7050 under 165 C.
Heat Treatment Condition Heat Treatment Condition Solution temper Solution temper
Yield Strength (MPa) Yield Strength 284.90 (MPa) 284.90
Elastic Modulus (GPa) Poisson’s Ratio Elastic Modulus Poisson’s Ratio 62.24 (GPa) 0.33 62.24
0.33
5. FE Simulation and Experimental Verification for CAF of Ribbed Panels
5. FE Simulation and Experimental Verification for CAF of Ribbed Panels 5.1. FE Model Validation Based on Springback 5.1. FE Model Validation Based on Springback The deflection method is selected to measure the springback (S) as shown in Figure 12 The deflection method selected to measure the when springback (S) asisshown in Figure according according to Equation (7). δis0 is the initial deflection the panel attached to the 12 die. δf is the to Equation (7). after δ0 is the initial deflection when the panel is attached to the die. δf is the final deflection final deflection panel springback. after panel springback. SS(δ) = (11 − δ f/δ00) ×100% 100% (7) (7) f
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Figure 12. Schematic diagram of springback measurement. Figure Figure 12. 12. Schematic Schematic diagram diagram of of springback springback measurement. measurement.
Figure 13 shows the predicted final deflection of AA7050 ribbed panel with h/t = 1 after Figure 13 shows the predicted final deflection of AA7050 ribbed panel with h/t = 1 after Figure 13 shows predicted finalexperimental deflection of AA7050 ribbedInpanel springback and the the corresponding verification. this with case,h/t δ0 =is1 after 34.60springback mm, the springback and the corresponding experimental verification. In this case, δ0 is 34.60 mm, the and the corresponding experimental verification. In this case, δ is 34.60 mm, the predicted δf is predicted δf is 24.01 mm and corresponding experimental results is 0 23.72 mm. That is, the predicted predicted δf is 24.01 mm and corresponding experimental results is 23.72 mm. That is, the predicted 24.01experimental mm and corresponding experimental results is 23.72 That is, theTable predicted and S are 30.61% and 31.45%, and the errormm. is only 2.67%. 4 listsand theexperimental comparison and experimental S are 30.61% and 31.45%, and the error is only 2.67%. Table 4 lists the comparison S are 30.61% and 31.45%, and and predicted the error δisf and onlyS 2.67%. Table 4 lists the comparison between the between the experimental of AA7050 ribbed panels with different h/t. It can between the experimental and predicted δf and S of AA7050 ribbed panels with different h/t. It can experimental S of AA7050 panelsand withthe different h/t. It decreases can be seenwith that the the be seen that and the predicted rib limits δthe occurrence of ribbed springback, springback f and be seen that the rib limits the occurrence of springback, and the springback decreases with the rib limitsofthe and thethan springback decreases themodel increase rib height. increase riboccurrence height. Allofofspringback, the errors are less 3%, indicating thatwith the FE hasofsatisfactory increase of rib height. All of the errors are less than 3%, indicating that the FE model has satisfactory All of the errors are less than 3%, indicating that the FE model has satisfactory prediction accuracy. prediction accuracy. prediction accuracy.
Figure 13. FE FE simulation simulation and and experimental experimental verification verification based springback of of creep creep aged aged AA7050 AA7050 Figure 13. based on on springback Figure 13. FE simulation and experimental verification based on springback of creep aged AA7050 ribbed panel with with h/t h/t ==11(unit: ribbed panel (unit:mm). mm). ribbed panel with h/t = 1 (unit: mm). Table 4. Comparison between experimental experimental and and predicted predicted values values of of springback. springback. Table 4. Comparison between Table 4. Comparison between experimental and predicted values of springback.
Predicted Value Experimental Value Value Value Predicted Value Experimental Experimental ValueErrorError h/t Predicted (%) h/t δf (mm) S (%) h/t Error (%) δf (mm) S (%) δ (mm) δ (mm) S (%) S (%) (%) f f δf (mm) S (%) δf (mm) S (%) 0 19.57 43.44 19.19 44.54 2.47 19.57 43.44 43.44 19.19 19.19 44.54 2.472.47 00 19.57 44.54 11 24.01 30.61 23.72 31.45 2.67 24.01 30.61 30.61 23.72 23.72 31.45 2.67 2.67 1 24.01 31.45 22 27.19 21.42 26.98 22.02 2.76 27.19 21.42 26.98 22.02 2.76 2 27.19 21.42 26.98 22.02 2.76 27.93 19.28 19.28 27.73 19.86 2.91 33 27.93 27.73 19.86 2.91 3 27.93 19.28 27.73 19.86 2.91 5.2. and Damage Damage 5.2. Evolutions Evolutions of of Stress, Stress, Strain Strain and 5.2. Evolutions of Stress, Strain and Damage Figure 14shows showsthe theMises Mises stress distribution of AA7050 ribbed panels different h/t.CAF The Figure 14 stress distribution of AA7050 ribbed panels withwith different h/t. The Figure 14 shows the Mises stress distribution of AA7050 ribbed panels with different h/t. The CAF process when the are panels are attached the die At the thismaximum point, theMises maximum process beginsbegins when the panels attached to the dietoclosely. Atclosely. this point, stress CAF process begins when the panels are attached to the die closely. At this point, the maximum Mises the =panel of h/t = 0which is 242isMPa, which less than the yield 284 MPa for on the stress panel on of h/t 0 is 242 MPa, less than theisyield strength of 284strength MPa forof AA7050 under Mises stress on the panel of h/t = 0 is 242 MPa, which is less than the yield strength of 284 MPa for ◦ AA7050 under 165 °C, while the maximum Mises stress on the panel of h/t = 3 is 377 MPa. It can be 165 C, while the maximum Mises stress on the panel of h/t = 3 is 377 MPa. It can be seen that there AA7050 under 165 °C, while the maximum Mises stress on the panel of h/t = 3 is 377 MPa. It can be seen that there severe stresswithin concentration within around the rib the CAF high are severe stressare concentration and around the and rib of the panel dueoftothe thepanel high due h/t. to After seen that there are severe stress concentration within and around the rib of the panel due to the high h/t. CAF of 12 h, Mises the maximum Mises on both ofreduced, the panels are reduced, which of 12After h, the maximum stresses on bothstresses of the panels are which are 226 MPa of are h/t 226 =0 h/t. After CAF of 12 h, the maximum Mises stresses on both of the panels are reduced, which are 226 MPa of h/t = 0 and 228 MPa of h/t = 3, respectively. The stress relaxation phenomenon is more and 228 MPa of h/t = 3, respectively. The stress relaxation phenomenon is more obvious on the panel MPa of h/t = 0 and 228 MPa of h/t = 3, respectively. The stress relaxation phenomenon is more obvious the panel with high h/t. with highonh/t. obvious on the panel with high h/t.
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Figure 14. 14. Mises Mises stress stress distribution distribution of of AA7050 AA7050 ribbed ribbedpanels: panels: (a) (a)h/t h/t = = 0, creep aged aged 00 h; h; (b) (b) h/t h/t = = 3, Figure 0, creep 3, Figure 14. Mises stress distribution of AA7050 ribbed panels: (a) h/t = 0, creep aged 0 h; (b) h/t = 3, creep aged aged 00 h; h; (c) (c) h/t h/t ==0,0,creep creep creepaged aged 12 12 h; h; and, and, (d) (d) h/t h/t==3,3,creep creepaged aged1212h.h. creep aged 0 h; (c) h/t = 0, creep aged 12 h; and, (d) h/t = 3, creep aged 12 h.
Figure 15 shows the creep strain distribution of AA7050 ribbed panels creep aged for 12 h. The Figure 15 shows showsthe thecreep creepstrain straindistribution distribution AA7050 ribbed panels creep forh.12 h. Figure 15 of of AA7050 ribbed panels creep agedaged for 12 The creep deformation of the panel of h/t = 0 is homogeneous, and the maximum creep strain is 0.04%. The deformation the panel 0 is homogeneous, and the maximum creep is strain is creepcreep deformation of theofpanel of h/tof= h/t 0 is = homogeneous, and the maximum creep strain 0.04%. For the panel of h/t = 3, the creep deformation is the most obvious in the middle of the rib, and 0.04%. the of panel 3, the deformation creep deformation the obvious most obvious the middle theand rib, For theFor panel h/t =of3,h/t the= creep is the is most in theinmiddle of theofrib, gradually decreases toward the both ends and the surrounding area. The maximum creep strain for and gradually decreases toward the both the surrounding area. maximum creep strain gradually decreases toward the both endsends andand the surrounding area. TheThe maximum creep strain for h/t = 3 is 0.59%, which is much bigger than that for h/t = 0. This is because the plastic deformation for h/t = 3 is 0.59%, which is much bigger than that for h/t = 0. This is because the plastic deformation h/t = 3 is 0.59%, which is much bigger than that for h/t = 0. This is because the plastic deformation produced during loading stage is equivalent to a pre-deformation for the material, promoting the produced equivalent to atopre-deformation for the promoting the creep produced during duringloading loadingstage stageis is equivalent a pre-deformation formaterial, the material, promoting the creep deformation during the creep aging stage [26]. deformation duringduring the creep creep deformation the aging creep stage aging [26]. stage [26].
Figure 15. Creep strain distribution of AA7050 ribbed panels creep aged for 12 h: (a) h/t = 0; and, (b) Figure 15. 15. Creep 1212 h:h: (a)(a) h/th/t = 0;=and, (b) Figure Creep strain strain distribution distributionofofAA7050 AA7050ribbed ribbedpanels panelscreep creepaged agedfor for 0; and, h/t = 3. h/t = 3. (b) h/t = 3.
Figure 16 shows the evolutions of the Mises stress, creep strain and damage variable on the Figure 16 shows the evolutions of the Mises stress, creep strain and damage variable on the feature point AA7050 ribbed panels during of the ribbed different h/tfeature show Figure 16of shows the evolutions of the MisesCAF. stress,All creep strain and panels damagewith variable on the feature point of AA7050 ribbed panels during CAF. All of the ribbed panels with different h/t show typical stress relaxation phenomena, and the higher the rib, the more obvious the relaxation. The point of AA7050 ribbed panels during CAF. All of the ribbed panels with different h/t show typical typical stress relaxation phenomena, and the higher the rib, the more obvious the relaxation. The creep relaxation strains increase with the creep time, but ratesobvious decrease gradually. higher rib, stress phenomena, and the higher thethe rib,creep the more the relaxation.The The creep the strains creep strains increase with the creep time, but the creep rates decrease gradually. The higher the rib, the more serious the damage. increase with the creep time, but the creep rates decrease gradually. The higher the rib, the more the more serious the damage. serious the damage.
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(b)
H/t=0 H/t=1 H/t=2 H/t=3
350
300
250
H/t=0 H/t=1 H/t=2 H/t=3
0.4 0.3 0.2 0.1 0.0
0
2
4
6 8 Time (h) (c) 0.4
Damage variable (-)
200
0.6 0.5
Creep strain (%)
Mises stress (MPa)
(a)400
10
12
0
2
4
6 8 Time (h)
10
12
H/t=0 H/t=1 H/t=2 H/t=3
0.3 0.2 0.1 0.0 0
2
4
6 8 Time (h)
10
12
Figure Figure 16. 16. Evolutions Evolutions of of (a) (a) Mises Mises stress, stress, (b) (b) creep creep strain, strain, and and (c) (c) damage damage variable variable on on feature feature point point of of AA7050 ribbed panels. AA7050 ribbed panels.
6. 6. Conclusions Conclusions Taking 7050aluminum aluminumalloy alloy case material, combining experiment and simulation, the Taking 7050 asas thethe case material, combining experiment and simulation, the creep creep aging damage behavior of the alloy was studied. The major conclusions can be drawn, aging damage behavior of the alloy was studied. The major conclusions can be drawn, as follows: as follows: (1) The effects of applied stress on the creep deformation, evolutions of precipitates and microvoids, (1) The effects property, of applied on themechanism creep deformation, evolutions of the precipitates and mechanical andstress the damage were studied. The greater applied stress, microvoids, mechanical property, and the damage mechanism were studied. The greater the the bigger the creep strain, the faster the growth rates of precipitates and microvoids, the more applied stress, the bigger the creep strain, the faster the growth rates of precipitates and rapid the decrease of mechanical property. The dominant mechanism of creep fracture changes microvoids, the more rapid the decrease mechanical The dominant mechanism of from shear to microvoid coalescence withofthe increase ofproperty. applied stress. creep fracture changes from shear to microvoid coalescence with the increase of applied stress. (2) The CDM based creep aging constitutive model was calibrated, and the material constants were (2) The CDM based creep aging constitutive model was and the constants were determined by GA. Two damage state variables werecalibrated, used to model thematerial tertiary creep softening determined by GA. Two damage state variables were used model the tertiary creep softening that is caused by the damage and over-aging. Then, the to constitutive model was verified by that is caused by the damage and over-aging. Then, the constitutive model was verified by comparison between the experimental and calculated creep strains, and the well-fitting results comparison between the experimental calculated creep aging strains, and thewith well-fitting indicated that the model is suitable for and describing the creep behavior damage.results indicated that the model is suitable for describing the creep aging behavior with damage. (3) Implementing the creep aging model into ABAQUS solver via CREEP subroutine and combining (3) Implementing the and creep aging model intoprocess ABAQUS solverpanels via CREEP subroutine and the FE simulation experiment, the CAF of ribbed was studied. The creep combining the place FE simulation and the CAF process of ribbed panels wasthe studied. damage takes mainly on theexperiment, bending rib, and with the increase of rib height, creep The creep damage takes place mainly on the bending rib, and with the increase of rib height, the deformation, and damage degree increase but the springback decreases. creep deformation, and damage degree increase but the springback decreases. Acknowledgments: The research is supported by the National Natural Science Foundation of China for Key Acknowledgments: supported by for the Excellent National Natural Science Foundation Key Program (51235010),The theresearch Nationalis Science Fund Young Scholars (51522509) of theChina MarieforCurie Program (51235010), National Science Fund for Excellent Youngproject Scholars the Marie Curie International Researchthe Staff Exchange Scheme (IRSES, MatProFuture, No.:(51522509) 318968) within the 7th EC International Research Staff Exchange Scheme (IRSES, MatProFuture, project No.: 318968) within the 7th EC Framework Programme (FP7). Framework Programme Chao (FP7).Lei performed the study and wrote the paper under the guidance of Heng Li; Author Contributions: Nian ShiContributions: and Jin Fu assisted experiments Zheng andunder Tianjun assisted editing Author Chaothe Lei performed and the modeling; study andGaowei wrote the paper theBian guidance of in Heng Li; the manuscript. Nian Shi and Jin Fu assisted the experiments and modeling; Gaowei Zheng and Tianjun Bian assisted in editing the manuscript.
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Conflicts of Interest: The authors declare no conflict of interest.
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8.
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