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CDRX modelling in friction stir welding of AA7075-T6 aluminum alloy: Analytical approaches
Journal of Materials Processing Technology 191 (2007) 356–359
CDRX modelling in friction stir welding of AA7075-T6 aluminum alloy: Analytical approaches G. Buffa a,∗ , L. Fratini a , R. Shivpuri b a
Dipartimento di Tecnologia Meccanica, Produzione e Ingegneria Gestionale Universit`a di Palermo, Viale delle Scienze 90128 Palermo, Italy b The Ohio State University, Department of Industrial, Welding and Systems Engineering 1971 Neil Avenue, 210 Baker Systems, Columbus, OH 43210, USA
Abstract Friction stir welding (FSW) is an energy efficient and environmentally “friendly” (no fumes, noise, or sparks) welding process, during which the workpiece are welded together in a solid-state joining process at a temperature below the melting point of the workpiece material under a combination of extruding and forging. Significant microstructural evolution takes place during FSW: in particular continuous dynamic recrystallization (CDRX) phenomena result in a highly refined grain structure in the weld nugget and strongly affect the final joint resistance. In the paper two different analytical models aimed to the determination of the average grain size due to continuous dynamic recrystallization phenomena in FSW processes of AA7075-T6 aluminum alloys have been implemented in a 3D FEM model and numerical analyses of the welding processes have been performed to verify their effectiveness. © 2007 Elsevier B.V. All rights reserved. Keywords: Friction stir welding; Continuous dynamic recrystallization; FEM
1. Introduction Friction stir welding (FSW) of butt joints is obtained inserting a specially designed rotating pin into the adjoining edges of the sheets to be welded and then moving it all along the welding line [1]. The tool is characterized by a rather small nuting angle (θ) limiting the contact between the tool shoulder and the sheets to be welded just to about one half of the shoulder surface. As the pin is inserted into the sheets, the blanks material undergoes to a local backward extrusion process up to reach the tool shoulder contact. The tool rotation determines an increase of the material temperature due to the friction forces work. As a consequence the material mechanical characteristics are locally decreased and the blanks material reaches a sort of “soft” state; no melting is observed, a circumferential metal flow is obtained all around the tool pin and close to the tool shoulder contact surface. As such material softening is obtained, the tool is moved along the joint avoiding the pin fracture due to excessive material reaction. The tool movement determines heat generation due to both friction forces work and material deformation one. Furthermore,
∗
Corresponding author. Tel.: +39 091 665 7051; fax: +39 091 665 7039. E-mail addresses: [email protected] (G. Buffa), [email protected] (L. Fratini), [email protected] (R. Shivpuri). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.033
the composition of the tool spin vector and of the feed rate vector determines a peculiar metal flow all around the tool contact surface [2,3]. What is more, considering a section of the joint normal to the tool movement direction, an asymmetric metal flow is obtained. An advancing side and a retreating one are observed in the joint section: the former is characterized by the “positive” composition of the tool feed rate and of the peripheral tool velocity; on the contrary, in the latter the two velocity vectors are opposite. Overall, the tool action determines the material softening and, what is more, the metal flux which allows the blanks welding. Recently, a few research activities have been developed on the numerical simulation of FSW processes [4,5]. In previous papers [6,7] the authors presented a 3D fully coupled thermo-mechanical FEM model in which the tool–workpiece interaction in FSW of butt joints was investigated. In particular in Ref. [7] the material microstructure evolution was taken into account through a proper model of grain size evolution due to recrystallization phenomena. It should be observed that in FSW processes a continuous dynamic recrystallization phenomenon (CDRX) [8] occurs due to the tool pin action. The tool stirring action generates fine, equiaxed, recrystallized grains; such new microstructure determines the local material mechanical properties and the overall joint resistance [9].
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
357
In the present paper in order to predict the average grain size occurring in FSW of AA7075-T6 sheets due to the CDRX phenomena and to all the metallurgical effects occurring due to the welding process, two different analytical approaches have been followed. In particular, two analytical models of grain size evolution have been implemented in the FE model. The models, once characterized for the utilized materials, are able to calculate the local value of the average grain size on the basis of the most relevant process field variables, namely temperature, strain and strain rate. The effectiveness of the two proposed tools was tested on the basis of experimental evidences, i.e. the measured grain sizes, for further welding processes. Fig. 2. The FEM model.
2. Experiments and FE model The FSW of butt joints between 3 mm thick AA7075-T6 blanks were considered. The utilized alloy was characterized at room temperature by a yield stress of 460 MPa and an ultimate tensile stress (UTSb) of 530 MPa. At room temperature the blank material showed a microhardness equal to 160 HV and grains of about 72 m (D0 ). Square specimens of 100 mm edges were jointed. The utilized tool was made in H13 steel quenched at 1020 ◦ C, characterized by a 52 HRc hardness; a cylindrical pin was used with a pin diameter of 3.00 mm and a pin height equal to 2.80 mm; the shoulder diameter was equal to 10 mm. During the tests a tool sinking of 2.90 mm has been utilized. Fig. 1 shows the developed experimental plane: six different tests, namely FSW1–6, characterized by different values of rotating speed (R) and advancing speed (Vf ), were carried out on a milling machine. Each experiment was repeated three times and macro and micrography were developed on the joints transverse sections. The commercial FEA software DEFORM-3DTM , Lagrangian implicit code designed for metal forming processes, has been utilized to model the FSW process (Fig. 2). The workpiece was modelled as a rigid viscoplastic material, and the welding tool was assumed rigid. It should be observed that the rigidviscoplastic finite element formulation is based on the variational approach; a few details on the equations governing the material behavior can be found in Ref. [6]. The FSW numerical simulation was divided into two stages: the sinking stage, in order to reach high enough temperature for the subsequent welding process, and the welding (advancing) one, modeled to investigate the thermo-mechanical phenomena in the formation of the weld nugget. As far as the mechanical properties of the material are regarded, a tabular material flow stress data at the varying of the temperature and of the strain rate were utilized on the basis of literature data [6]. Furthermore, for the thermal characteristics of the considered AA7075-T6 aluminum alloy, the following values were utilized: thermal conductivity k = 180 N/s ◦ C and thermal capacity c = 2.4 N/mm2 ◦ C taken from literature; no variation of k and c with temperature was taken into account. A
Fig. 1. The investigated processes.
constant interface heat exchange coefficient of 11 N/mm s ◦ C was utilized for the tool sheet contact surface. The tool was modeled as rigid body and meshed, for the thermal analysis. As far as the modeling of the workpiece is regarded, a “single block” continuum model (sheet blank without a gap) is used in order to avoid contact instabilities due to the intermittent contact at the sheet–sheet and sheet–tool interfaces. The rotating tool moves forward and welds a crack left behind the pin as it advances along the welding line. The sheet blank, 3 mm in thickness, was meshed with about 10,000 tetrahedral elements with single edges of about 0.75 mm (Fig. 2); in this way about four elements were placed along the sheet thickness. A nonuniform mesh with adaptive re-meshing was adopted with smaller elements close to the tool and a re-meshing referring volume was identified all along the tool feed movement. A constant shear friction factor of 0.46 was used for the tool–sheet interface [6].
3. The CDRX phenomenon modeling It is well known that a detailed observation of the material microstructure of a friction stir welded joint section allows to distinguish a few different areas: starting from the parent material, the heat affected zone (HAZ), characterized by an enlarged average grain size, is first found out. Then the so-called thermomechanically affected zone (TMAZ) is encountered: in this area, the material has been plastically deformed by the tool, and the heat flux has also exerted some influence on the material. Finally, close to the welding line, the nugget area is discovered: a recrystallized area in which the original grain and subgrain boundaries appear to be replaced with fine, equiaxed recrystallized grains characterized by a nominal dimension of few m [8]. In the present research two different analytical formulations have been taken into account to predict the final recrystallized grain dimension. The first analytical model was implemented by the authors and used for AA6082-T6 alloys in Ref. [7]. The model takes into account the local value of strain, strain rate and temperature as well as a few material constants: Q DCDRX = C1 εk ε˙ j D0h exp − (1) RT where DCDRX is the average grain size due to the continuous dynamic recrystallization phenomena, ε the equivalent plastic strain, ε˙ the strain rate, D0 the initial grain size, Q the material continuous recrystallization activation energy, R the gas constant, T the absolute temperature and C1 , k, j and h are the material constants. In the technical literature a few references were found out on the metallurgical phenomena occurring in
358
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
Fig. 3. Comparison between the measured and the calculated average grain sizes at y = 1 mm for: (a) FSW5 and (b) FSW6.
aluminum alloys at high temperatures. In such papers a recurring value of 140 kJ/mole referred to the aluminum alloys continuous recrystallization activation energy (Q) was found out. In order to characterize the AA7075-T6 aluminum alloy, for each of the four experimental tests FSW1–4, a grain size map was traced considering 65 different loci of measurement referred to a x–y coordinate system [8]. The numerical simulations of the FSW processes characterized by the investigated operative conditions (FSW1–4) permitted to highlight the temperature, strain and strain rate distributions occurring during the processes; the field variables values obtained by the numerical simulations in section AA (Fig. 2), in the positions corresponding to the ones considered in the experiments, were acquired for each test. A matrix of results was then obtained made of the experimental values of the grain size and of the numerical values of the considered field variables. A constant D0 value of 72 m was considered. An inverse approach permitted to determine the proper material coefficients (C1 , k, j, h) to be introduced in the model minimizing the error between the predicted grain size and the experimentally measured one leading to the following grain size evolution model for the AA7075-T6 material: Q DCDRX = 100ε−0.1648 ε˙ −0.322 D0−0.104 exp − (2) RT The second analytical model takes into account the ZenerHollomon parameter and a few material constants as follows: DCDRX =
1 a + b ln(Z)
(3)
being a = 3.63, b = −1.62, Z = ε˙ eQ/RT , and Q the gas constant [10]. The local values of the grain size were then calculated for each weld test on the basis of the local values of the field variables derived from the numerical model. 4. The obtained results Both the models were implemented as subroutine in the FEM code; in order to test their effectiveness the FSW5 and FSW6 processes indicated in Fig. 1 were developed both experimentally and numerically. The obtained numerical results were compared with the experimental ones in terms of grain sizes: for each of the 2 tests, 65 different measurement loci with 5 depths through the specimen thickness were then considered, both in the experiment and in the numerical simulation. Fig. 3a and b shows the average grain size for FSW5 and FSW6 considered at a height of y = 1 mm from the bottom of the blanks. As it can be seen from the figure, both the models are able to correctly predict the grain size close to the welding line, i.e. at a distance of about 1 mm. As far as the distance from the welding line increases, the prediction becomes less accurate, especially for FSW5. Experimental evidence demonstrates that the operative parameters that characterize FSW5 (R and Vf , see again Fig. 1) result in a smaller nugget area of the welded joint. At a distance of 2 mm from the welding line, no more CDRX phenomena are observed, resulting in a poorer performance of both the analytical model. In turn, the presence of a wider nugget area in FSW6 results in a better performance of both the analytical models, even at a distance from the welding line of 2 mm.
Fig. 4. Comparison between the measured and the calculated average grain sizes at y = 2.5 mm for: (a) FSW5 and (b) FSW6.
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
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Fig. 4a and b shows the average grain size for the same two tests at y = 2.5 mm from the bottom of the blanks, i.e. close to the upper surface of the joint. Again, an overall good agreement between the measured and the calculated results is found for both the analytical models. However, a slightly worse performance is obtained by the A2 model in FSW6. In order to quantitatively compare the obtained results of the two analytical models for the investigated material, a simple evaluation of the total quadratic error between the numerical data (num) – evaluated with the FEM code either utilizing the A1 model or the A2 – and the experimental ones (exp) was utilized as expressed in the next Eq. (4): Err = (expij − numij )2 (4)
lead to an even more accurate grain size prediction. What is more, the use of an artificial intelligence tool could be particularly effective in correlating simple field variables, easily deliverable from the FEM model, and the average material grain size, tanking into account both static and dynamic metallurgical phenomena occurring in FSW and thus resulting in an overall grain size prediction in the welded joint section.
where j is the index indicating the measurement loci of the nugget area (j = 1–65) and i is the index indicating the FSW test process conditions (i equal to 5 or 6). The calculated total quadratic error was equal to 899 for the A1 model, and 1548 for the A2 model. The better overall performance of the A1 model is due to the fact that it takes into account also the local value of the average effective strain, resulting both in a more accurate characterization of the considered measurement loci, and in a larger robustness of the model to small oscillations of the process variables values due to the FEM simulation.
References
i
j
5. Conclusions In the paper two different analytical models, namely A1 and A2, are implemented in a FE model in order to calculate the final average grain size due to the CDRX phenomena in FSW of AA7075-T6 aluminum alloys. A quadratic error has been utilized in order to compare the performances of the two utilized approaches. Both the models returned calculated average grain size values in the nugget area close to the experimental ones. The A1 model showed better performances due to the presence of the effective strain, which results in a better characterization of the considered locus and in a larger robustness of the model itself. It can be easily predicted that further improvements in the FEM model and in the specific grain size evolution model would
Acknowledgments This work has been performed with funding from MIUR (Italian Ministry for Instruction, University and Research) and supported from the Center for Excellence in Forging Technology at the Ohio State University.
[1] H.J. Liu, H. Fujii, M. Maeda, K. Nogi, Tensile properties and fracture locations of friction-stir-welded joints of 2017-T351 aluminum alloy, J. Mater. Process. Technol. 142 (2003) 692–696. [2] I. Shigematsu, Y.J. Kwon, K. Suzuki, T. Imai, N. Saito, Joining of 5083 and 6061 aluminum alloys by friction stir welding, J. Mater. Sci. Lett. 22 (2003) 343–356. [3] W.B. Lee, Y.M. Yeon, S.B. Jung, The improvement of mechanical properties of friction-stir-welded A356 Al alloy, Mater. Sci. Eng. A355 (2003) 154–159. [4] M. Song, R. Kovacevic, Thermal modeling of friction stir welding in a moving coordinate system and its validation, Int. J. Mach. Tools Manuf. 43 (2003) 605–615. [5] W.D. Lockwood, A.P. Reynolds, Simulation of the global response of a friction stir weld using local constitutive behavior, Mater. Sci. Eng. A339 (2003) 35–42. [6] G. Buffa, J. Hua, R. Shivpuri, L. Fratini, A continuum based FEM model for friction stir welding—model development, Mater. Sci. Eng., A419/1–2 (2006) 381–388. [7] G. Buffa, L. Fratini, CDRX modeling in friction stir welding of aluminum alloys, J. Mach. Tools Manuf. 45 (10) (2005) 1188–1194. [8] K.V. Jata, S.L. Semiatin, Continuous dynamic recrystallization during friction stir welding of high strength aluminum alloys, Scr. Mater. 43 (2000) 743–749. [9] A. Barcellona, G. Buffa, L. Fratini, Process parameters analysis in friction stir welding of AA6082-T6 sheets, in: VII ESAFORM Conference, Trondhaim, 2004, pp. 371–374. [10] E. Cerri, E. Evangelista, A. Forcellese, H. McQueen, Comparative hot workability of 7012 and 7075 alloys after different pretreatments, Mater. Sci. Eng. A197 (1995) 181–198.
CDRX modelling in friction stir welding of AA7075-T6 aluminum alloy: Analytical approaches G. Buffa a,∗ , L. Fratini a , R. Shivpuri b a
Dipartimento di Tecnologia Meccanica, Produzione e Ingegneria Gestionale Universit`a di Palermo, Viale delle Scienze 90128 Palermo, Italy b The Ohio State University, Department of Industrial, Welding and Systems Engineering 1971 Neil Avenue, 210 Baker Systems, Columbus, OH 43210, USA
Abstract Friction stir welding (FSW) is an energy efficient and environmentally “friendly” (no fumes, noise, or sparks) welding process, during which the workpiece are welded together in a solid-state joining process at a temperature below the melting point of the workpiece material under a combination of extruding and forging. Significant microstructural evolution takes place during FSW: in particular continuous dynamic recrystallization (CDRX) phenomena result in a highly refined grain structure in the weld nugget and strongly affect the final joint resistance. In the paper two different analytical models aimed to the determination of the average grain size due to continuous dynamic recrystallization phenomena in FSW processes of AA7075-T6 aluminum alloys have been implemented in a 3D FEM model and numerical analyses of the welding processes have been performed to verify their effectiveness. © 2007 Elsevier B.V. All rights reserved. Keywords: Friction stir welding; Continuous dynamic recrystallization; FEM
1. Introduction Friction stir welding (FSW) of butt joints is obtained inserting a specially designed rotating pin into the adjoining edges of the sheets to be welded and then moving it all along the welding line [1]. The tool is characterized by a rather small nuting angle (θ) limiting the contact between the tool shoulder and the sheets to be welded just to about one half of the shoulder surface. As the pin is inserted into the sheets, the blanks material undergoes to a local backward extrusion process up to reach the tool shoulder contact. The tool rotation determines an increase of the material temperature due to the friction forces work. As a consequence the material mechanical characteristics are locally decreased and the blanks material reaches a sort of “soft” state; no melting is observed, a circumferential metal flow is obtained all around the tool pin and close to the tool shoulder contact surface. As such material softening is obtained, the tool is moved along the joint avoiding the pin fracture due to excessive material reaction. The tool movement determines heat generation due to both friction forces work and material deformation one. Furthermore,
∗
Corresponding author. Tel.: +39 091 665 7051; fax: +39 091 665 7039. E-mail addresses: [email protected] (G. Buffa), [email protected] (L. Fratini), [email protected] (R. Shivpuri). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.03.033
the composition of the tool spin vector and of the feed rate vector determines a peculiar metal flow all around the tool contact surface [2,3]. What is more, considering a section of the joint normal to the tool movement direction, an asymmetric metal flow is obtained. An advancing side and a retreating one are observed in the joint section: the former is characterized by the “positive” composition of the tool feed rate and of the peripheral tool velocity; on the contrary, in the latter the two velocity vectors are opposite. Overall, the tool action determines the material softening and, what is more, the metal flux which allows the blanks welding. Recently, a few research activities have been developed on the numerical simulation of FSW processes [4,5]. In previous papers [6,7] the authors presented a 3D fully coupled thermo-mechanical FEM model in which the tool–workpiece interaction in FSW of butt joints was investigated. In particular in Ref. [7] the material microstructure evolution was taken into account through a proper model of grain size evolution due to recrystallization phenomena. It should be observed that in FSW processes a continuous dynamic recrystallization phenomenon (CDRX) [8] occurs due to the tool pin action. The tool stirring action generates fine, equiaxed, recrystallized grains; such new microstructure determines the local material mechanical properties and the overall joint resistance [9].
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
357
In the present paper in order to predict the average grain size occurring in FSW of AA7075-T6 sheets due to the CDRX phenomena and to all the metallurgical effects occurring due to the welding process, two different analytical approaches have been followed. In particular, two analytical models of grain size evolution have been implemented in the FE model. The models, once characterized for the utilized materials, are able to calculate the local value of the average grain size on the basis of the most relevant process field variables, namely temperature, strain and strain rate. The effectiveness of the two proposed tools was tested on the basis of experimental evidences, i.e. the measured grain sizes, for further welding processes. Fig. 2. The FEM model.
2. Experiments and FE model The FSW of butt joints between 3 mm thick AA7075-T6 blanks were considered. The utilized alloy was characterized at room temperature by a yield stress of 460 MPa and an ultimate tensile stress (UTSb) of 530 MPa. At room temperature the blank material showed a microhardness equal to 160 HV and grains of about 72 m (D0 ). Square specimens of 100 mm edges were jointed. The utilized tool was made in H13 steel quenched at 1020 ◦ C, characterized by a 52 HRc hardness; a cylindrical pin was used with a pin diameter of 3.00 mm and a pin height equal to 2.80 mm; the shoulder diameter was equal to 10 mm. During the tests a tool sinking of 2.90 mm has been utilized. Fig. 1 shows the developed experimental plane: six different tests, namely FSW1–6, characterized by different values of rotating speed (R) and advancing speed (Vf ), were carried out on a milling machine. Each experiment was repeated three times and macro and micrography were developed on the joints transverse sections. The commercial FEA software DEFORM-3DTM , Lagrangian implicit code designed for metal forming processes, has been utilized to model the FSW process (Fig. 2). The workpiece was modelled as a rigid viscoplastic material, and the welding tool was assumed rigid. It should be observed that the rigidviscoplastic finite element formulation is based on the variational approach; a few details on the equations governing the material behavior can be found in Ref. [6]. The FSW numerical simulation was divided into two stages: the sinking stage, in order to reach high enough temperature for the subsequent welding process, and the welding (advancing) one, modeled to investigate the thermo-mechanical phenomena in the formation of the weld nugget. As far as the mechanical properties of the material are regarded, a tabular material flow stress data at the varying of the temperature and of the strain rate were utilized on the basis of literature data [6]. Furthermore, for the thermal characteristics of the considered AA7075-T6 aluminum alloy, the following values were utilized: thermal conductivity k = 180 N/s ◦ C and thermal capacity c = 2.4 N/mm2 ◦ C taken from literature; no variation of k and c with temperature was taken into account. A
Fig. 1. The investigated processes.
constant interface heat exchange coefficient of 11 N/mm s ◦ C was utilized for the tool sheet contact surface. The tool was modeled as rigid body and meshed, for the thermal analysis. As far as the modeling of the workpiece is regarded, a “single block” continuum model (sheet blank without a gap) is used in order to avoid contact instabilities due to the intermittent contact at the sheet–sheet and sheet–tool interfaces. The rotating tool moves forward and welds a crack left behind the pin as it advances along the welding line. The sheet blank, 3 mm in thickness, was meshed with about 10,000 tetrahedral elements with single edges of about 0.75 mm (Fig. 2); in this way about four elements were placed along the sheet thickness. A nonuniform mesh with adaptive re-meshing was adopted with smaller elements close to the tool and a re-meshing referring volume was identified all along the tool feed movement. A constant shear friction factor of 0.46 was used for the tool–sheet interface [6].
3. The CDRX phenomenon modeling It is well known that a detailed observation of the material microstructure of a friction stir welded joint section allows to distinguish a few different areas: starting from the parent material, the heat affected zone (HAZ), characterized by an enlarged average grain size, is first found out. Then the so-called thermomechanically affected zone (TMAZ) is encountered: in this area, the material has been plastically deformed by the tool, and the heat flux has also exerted some influence on the material. Finally, close to the welding line, the nugget area is discovered: a recrystallized area in which the original grain and subgrain boundaries appear to be replaced with fine, equiaxed recrystallized grains characterized by a nominal dimension of few m [8]. In the present research two different analytical formulations have been taken into account to predict the final recrystallized grain dimension. The first analytical model was implemented by the authors and used for AA6082-T6 alloys in Ref. [7]. The model takes into account the local value of strain, strain rate and temperature as well as a few material constants: Q DCDRX = C1 εk ε˙ j D0h exp − (1) RT where DCDRX is the average grain size due to the continuous dynamic recrystallization phenomena, ε the equivalent plastic strain, ε˙ the strain rate, D0 the initial grain size, Q the material continuous recrystallization activation energy, R the gas constant, T the absolute temperature and C1 , k, j and h are the material constants. In the technical literature a few references were found out on the metallurgical phenomena occurring in
358
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
Fig. 3. Comparison between the measured and the calculated average grain sizes at y = 1 mm for: (a) FSW5 and (b) FSW6.
aluminum alloys at high temperatures. In such papers a recurring value of 140 kJ/mole referred to the aluminum alloys continuous recrystallization activation energy (Q) was found out. In order to characterize the AA7075-T6 aluminum alloy, for each of the four experimental tests FSW1–4, a grain size map was traced considering 65 different loci of measurement referred to a x–y coordinate system [8]. The numerical simulations of the FSW processes characterized by the investigated operative conditions (FSW1–4) permitted to highlight the temperature, strain and strain rate distributions occurring during the processes; the field variables values obtained by the numerical simulations in section AA (Fig. 2), in the positions corresponding to the ones considered in the experiments, were acquired for each test. A matrix of results was then obtained made of the experimental values of the grain size and of the numerical values of the considered field variables. A constant D0 value of 72 m was considered. An inverse approach permitted to determine the proper material coefficients (C1 , k, j, h) to be introduced in the model minimizing the error between the predicted grain size and the experimentally measured one leading to the following grain size evolution model for the AA7075-T6 material: Q DCDRX = 100ε−0.1648 ε˙ −0.322 D0−0.104 exp − (2) RT The second analytical model takes into account the ZenerHollomon parameter and a few material constants as follows: DCDRX =
1 a + b ln(Z)
(3)
being a = 3.63, b = −1.62, Z = ε˙ eQ/RT , and Q the gas constant [10]. The local values of the grain size were then calculated for each weld test on the basis of the local values of the field variables derived from the numerical model. 4. The obtained results Both the models were implemented as subroutine in the FEM code; in order to test their effectiveness the FSW5 and FSW6 processes indicated in Fig. 1 were developed both experimentally and numerically. The obtained numerical results were compared with the experimental ones in terms of grain sizes: for each of the 2 tests, 65 different measurement loci with 5 depths through the specimen thickness were then considered, both in the experiment and in the numerical simulation. Fig. 3a and b shows the average grain size for FSW5 and FSW6 considered at a height of y = 1 mm from the bottom of the blanks. As it can be seen from the figure, both the models are able to correctly predict the grain size close to the welding line, i.e. at a distance of about 1 mm. As far as the distance from the welding line increases, the prediction becomes less accurate, especially for FSW5. Experimental evidence demonstrates that the operative parameters that characterize FSW5 (R and Vf , see again Fig. 1) result in a smaller nugget area of the welded joint. At a distance of 2 mm from the welding line, no more CDRX phenomena are observed, resulting in a poorer performance of both the analytical model. In turn, the presence of a wider nugget area in FSW6 results in a better performance of both the analytical models, even at a distance from the welding line of 2 mm.
Fig. 4. Comparison between the measured and the calculated average grain sizes at y = 2.5 mm for: (a) FSW5 and (b) FSW6.
G. Buffa et al. / Journal of Materials Processing Technology 191 (2007) 356–359
359
Fig. 4a and b shows the average grain size for the same two tests at y = 2.5 mm from the bottom of the blanks, i.e. close to the upper surface of the joint. Again, an overall good agreement between the measured and the calculated results is found for both the analytical models. However, a slightly worse performance is obtained by the A2 model in FSW6. In order to quantitatively compare the obtained results of the two analytical models for the investigated material, a simple evaluation of the total quadratic error between the numerical data (num) – evaluated with the FEM code either utilizing the A1 model or the A2 – and the experimental ones (exp) was utilized as expressed in the next Eq. (4): Err = (expij − numij )2 (4)
lead to an even more accurate grain size prediction. What is more, the use of an artificial intelligence tool could be particularly effective in correlating simple field variables, easily deliverable from the FEM model, and the average material grain size, tanking into account both static and dynamic metallurgical phenomena occurring in FSW and thus resulting in an overall grain size prediction in the welded joint section.
where j is the index indicating the measurement loci of the nugget area (j = 1–65) and i is the index indicating the FSW test process conditions (i equal to 5 or 6). The calculated total quadratic error was equal to 899 for the A1 model, and 1548 for the A2 model. The better overall performance of the A1 model is due to the fact that it takes into account also the local value of the average effective strain, resulting both in a more accurate characterization of the considered measurement loci, and in a larger robustness of the model to small oscillations of the process variables values due to the FEM simulation.
References
i
j
5. Conclusions In the paper two different analytical models, namely A1 and A2, are implemented in a FE model in order to calculate the final average grain size due to the CDRX phenomena in FSW of AA7075-T6 aluminum alloys. A quadratic error has been utilized in order to compare the performances of the two utilized approaches. Both the models returned calculated average grain size values in the nugget area close to the experimental ones. The A1 model showed better performances due to the presence of the effective strain, which results in a better characterization of the considered locus and in a larger robustness of the model itself. It can be easily predicted that further improvements in the FEM model and in the specific grain size evolution model would
Acknowledgments This work has been performed with funding from MIUR (Italian Ministry for Instruction, University and Research) and supported from the Center for Excellence in Forging Technology at the Ohio State University.
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