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Finite element modelling of isothermal forging of a high strength aluminium alloy
Journal of Materials Processing Technology, 34 (1992) 77-84
77
Elsevier
Finite element modelling of isothermal forging of a high strength aluminium alloy A. Forcellese°, F. Gabrielli °, F. Micari °°, O. Zurla °°° ° oo ooo
Dipartimento di Meccanica, Universit~ di Ancona Dipartimento di Tecnologia e Produzione Meccaniea, Universi~ di Palermo DIEM, Universi~ di Bologna
Abstract
In the present paper the isothermal forging has been computer simulated by finite element modelling in order to rationalize and optimize the process. The isothermal forging of AA 7012 aluminium alloy was investigated at temperatures ranging from 250 to 400°C, with strain rate of 0.05 s-1. Hot workability of the material was investigated and constitutive equations were defined using torsion tests. Such equations were used in finite element modelling of isothermal forging. The numerical predictions were compared with isothermal experimental test results at the same conditions; an excellent agreement was observed.
1. INTRODUCTION The application of finite element (FE) techniques to model bulk forming processes as forging, extrusion, and rolling, in order to predict working loads and material flow patterns between deforming tools [1-5] is receiving continuously increasing attention. Recent developments in FE methods offer several benefits including significant reductions in the cost of both the design and the analysis of hot working operations. Among hot working processes, isothermal forging is becoming increasingly important for forming of high strength materials. It involves keeping both dies and workpiece at the same temperature for forging. This allows to maintain good formability of the material throughout the entire forging operation and permits a significantly better process control than is possible with conventional metalworking operations. The dimensional accuracy is improved as well as reproducibility while the deformation conditions can be manipulated in order to obtain controlled microstructural evolution. The disadvantage deriving from production rates, that in an isothermal forging are lower than those of conventional one, is offset by the fact that isothermal forging is a one-shot operation and there is no need for a series of shaping stages with their associated reheating and die changes. The slow squeezing operations also enable pieces to be forged to near net shape. This can give significant savings on material cost in forging and on subsequent machining operations. Since the technique of isothermal forging is very expensive owing to intrinsic cost of both the material being forged and the dies, any failure during the process could be very costly. Therefore, mathematical modelling techniques, based on finite element methods, are used in 0924-0136/92/$05.00 © 1992ElsevierSciencePublishers B.V. All rights reserved.
78 isothermal forging [3,4,6-8] to predict: a) the maximum load on press during forging operations, b) the local stresses both in workpiece and die, c) the metal flow patterns, and d) the microstructural evolution. The correct application of FE technique requires an accurate description of the material behaviour in the hot working regime, the development of computational procedures to be implemented into finite element programs, and the verification of the numerical predictions by means of experimental tests. In the present paper, an analysis of the isothermal axisymmetric forging of a high strength aluminium alloy, intended for aerospace applications, has been performed at different temperatures, with a low strain rate. In particular, hot formability studies were performed by simulative methods based on the analysis of torsion test since it allows to assess the flow behaviour in extended strain ranges that are comparable with strain values in most metalworking operations [9] and permits the relatively easy application of programmed deformation to simulate rolling or forging schedules [10,11]. Such results have lead to definition of constitutive equations describing the material plastic flow in the hot working regime. These equations were used in finite element modelling of isothermal forging. The numerical prediction results were compared with experimental data. The local distribution of the hot metalworking parameters has been obtained in different working conditions.
2. EXPERIMENTAL PROCEDURES The material used in the present investigation, supplied by Alures ISML, Italy, is the AA 7012 aluminium alloy with chemical composition shown in table I. Such alloy was developed in order to obtain mechanical properties that are comparable with those of the AA 7075 alloy but, by means of a suitable composition control, with better hot formability.
Table I: Chemical composition of the AA 7012 A1 alloy (wt. %) Zn
Mg
Cu
Zr
Mn
Fe
Si
Ti
6.27
1.85
1.07
0.11
0.14
0.10
0.058
0.016
The heat treatment of the extruded ingot was performed in two stages; a homogenization treatment at 460°C for 6 h was followed by a solution treatment at 480°C, 16 h. The hot formability studies, used for defining the constitutive equations, were performed by means of torsion tests carried out on a servohydraulic closed loop torsion machine in the range of temperatures from 250 to 400°C, with strain rates from 0.05 to 4 s"1. The specimens, machined in the extrusion direction, were torsioned until rupture. Surface shear stresses r and shear strains "t were derived by means of the relationships [12]: nFR (a+n:+m')
= 2
a
v
2~RN
(l)
L
where P is the measured torque, R and L the radius and the gauge length of the specimen
79 respectively, N the revolution number, n' the hardening rate coefficient that in the experimental condition of the present investigation can be neglected, and m' is the revolution rate sensitivity for the torque; m', being independent of strain rate, results equal to the strain rate sensitivity m calculated at different strains and temperatures [13]. Equivalent stresses a and strains e were obtained by von Mises criterion: o = ~
~ = ~
(2)
The above conversion to equivalent values according to the von Mises criterion and idealwork concept has been generally accepted and gives reasonable agreement between results obtained in torsion and in tension or compression at high temperatures [14-16]. Compression tests, used for the experimental verification of the model, were performed on a servohydraulic closed loop material testing machine, equipped for high temperature tests, at 0.05 s"l, with temperatures varying from 250 to 400°C. The tests were carried out in isothermal conditions with temperature of deforming tools equal to that of cylindrical specimens. They were characterized by initial height of 20 mm and diameter of 12 ram. During the tests the temperature was monitored in the specimen and in different points of the tools.
3. THE NUMERICAL CODE The analysis of the axisymmetric upsetting process was carried out employing an incremental approach in order to follow the whole transient process: a variational method, based on the "Upper-Bound" theorem, has been used and the material behaviour has been considered as rigid visco-plastic, neglecting the elastic component of the deformation. This approximation, which allows a remarkable reduction of the required computations, can surely be accepted when hot forming processes are studied. Moreover, in order to take into account the incompressibility condition, the Lagrange multipliers technique has been introduced; thus the minimum condition required by the "Upper-Bound" theorem can be written as:
min[fvo~dV ÷ fvx~vdV_fs(t)r(u)dS]
(3)
being ~ the equivalent plastic strain rate, ~. the Lagrange multiplier, i v the volumetric strain rate, (t) the vector of the traction on the surface S where they known, and finally (u) the vector of the velocity components. The discretization of the above functional is carried out following the usual finite element procedures: a set of non linear stiffness equations is then generated with the nodal velocity component as unknowns, which is iteratively solved by means the Newton-Raphson technique. At the end of each step of the deformation path the nodal coordinates are updated on the basis of the calculated nodal velocities and of the employed time step increment At. At the same way, the equivalent plastic strain rate is integrated along the deformation path. The above described mechanical analysis was applied to the axisymmetric upsetting process. The forging system (Fig. 1) was discretized employing 100 four-nodes isoparametric bilinear elements for the workpiece and 71 elements for the die. Calculations were performed up to
80 66% reduction in height, with 1% reduction for each step. The temperature of the billet was equal to 250, 300, 350, and 400°C in the four analyzed conditions respectively, and the mechanical properties of the workpiece were calculated according to the initial temperature value. Finally, at the die-workpiece interface sticking friction conditions were assumed owing to the expected behaviour affected by lubrication conditions and by the height/diameter ratio of the specimens used.
200 = 0.05 s -~
J.50
~
~
250' C
IIIIIJ ~-
iO0
300' C -
~
350' C
50 400° C
Z
,
,
0.0 0~1)10Y.P. -0.1~t01 0,(l[I*00 0.1~*01
.
.
,
0.5
.
.
.
.
i
1.0
.
.
.
.
i
t .5
.
.
.
.
2.0
e
Fig. 2: Influence of temperature on flow curves.
Fig. 1: Forging system.
4. RESULTS AND DISCUSSION Experimental torsion test results show that, at given temperature and strain rate, flow stress increases with strain up to a maximum and then decreases to the fracture value. At constant strain, flow stress decreases with increasing temperature and decreasing strain rate. In particular, the flow stress maximum value occur at strain values that decrease when temperature increases and strain rate decreases (Fig. 2). The study of hot formability on the alloy under investigation permitted to evaluate the mechanical state equation a=f(e,~,T) that is of extreme utility in the prediction of the load involved in forming process. The material flow behaviour of the AA 7012 aluminium alloy described by the relationship among flow stress, strain rate, and temperature, at a given strain, was supplied by Sellars and Tegart [17] by means of the equation:
Z = ~exp(~T) = A/o"
(4)
where Z is the Zener-Hollomon parameter, Q the activation energy, T the absolute
81 temperature, R the universal gas constant, A' and n material parameters. The dependence of the temperature compensated strain rate Z on flow stress, at E=0.2, is shown in fig. 3. It is apparent that flow stress increases when Z increases. The activation energy value used was Q=205 kJ/mol [18]; the material parameters, calculated in the strain range investigated, are summarized in table II.
10a3 6=0.2
c ~021
Table II: Constitutive parameters
D
e
A' (s.MPa) -1
n
0.1
1.73.10 l
9.35
0.2
5.28" 10-2
9.49
0.4
1.93-10 -3
10.21
0.6
1.74" 10-4
10.77
O.8
7.56" 10-5
10.98
~019 D_
E 0
1017
-0c "
L 10Is C
N 1013
.
.
.
.
.
.
.
.
,
•
.
,
102 Equivalent stress, MPa
,
,
,
,
,
103
Fig. 3: Effect of temperature compensated strain rate on flow stress.
The constitutive equation (4) was used to perform the numerical simulation of isothermal axisymmetric upsetting of the AA 7012 alloy by means of a finite element program. Such thermal-mechanical analysis, performed with strain rate of 0.05 sl , in the temperature range from 250 to 400°C, has allowed the prediction of the load-ram travel curves in isothermal condition. They were compared with the isothermal experimental curves obtained in the same temperature and strain rate conditions (Fig. 4). The comparison shows that, at a given values of ram travel, the numerical predictions are systematically lower than experimental data. This seems to be inconsistent with FE modelling that is based on "Upper-Bound" theorem and that should lead to predicted curves higher than experimental ones. However, metal flow input data for modelling derive from torsion tests. It has been shown that, mainly at low strains, flow stress curves obtained in torsion are lower than those obtained by tension or compression tests owing to the different texture developing during deformation [19,20], different thermal profiles [21], etc. At higher strains, flow stresses obtained by torsion tests tend to approach the values in tension and compression tests owing to the prevailing effects of dynamic restoration processes. Consequently, the difference between predicted and experimental load-ram travel curves, in general, decreases with increasing strain. In the present study, this is observed in a significant extent in curves at 250°C. On increasing temperature such aspect becomes less and less remarkable. This may sound inconsistent with results of a previous paper [22] dealing with modelling of forging in
82
70000
70000 T=250' C
T=300° C
// Z
1= ~3 0 -J
Z
35000
/
=
¢0 0 --J
J
35000
I
I
i
,
,
,
,
~
,
,
,
,
I
,
,
,
5 I0 Ram travel, mm
.
,
.
.
.
I
.
.
.
.
I
.
.
.
.
5 I0 Ram travel, mm
15
15
70000
70000
T=400'C
T=350 ° C
Z
ro o
35000
35000
.
0
.
.
.
i
.
.
.
.
5 Ram travel,
I
10 mm
.
.
.
.
0
15
,
,
,
,
I
.
.
.
.
i
,
,
,
,
5 10 Ram travel, mm
Fig. 4: Comparison between experimental ( ) and predicted (- - -) load versus ram travel curves at different temperatures, 0.05 s -l.
15
83 anisothermal conditions and at high strain rates. In the present case, test conditions refer to very low strain rates; it derives from fig. 2 that the strain to peak is much lower and becomes comparable with peak strain from compression tests [14,17]. This is much truer, the higher the temperature is.
1) 0.368DO0
l) 0.535[@0
2) 0.61~,00
2) O.lql[~O0 3)
~--~
3t4o.851[,0oo.10~[,ot ~ ;
O.ICb[,01
~
~
,
/
,
/
4) 0.}32[,01
5) 0.133D01
5> 0,]~[+01
b)0.}58[,01
5
6
"~
I) 0.182D01
1~O.?]]UOI X
Y~
,4
X
~oi~ [mlv pL~suc
~R,
QRII(JV.P. -O.ID~DI 0.000D00O.]O'~'Ot
a)
STRR
[gHv PLASl][ 0RIH0LP. -0,100D01D.QOOD00 0.l~01
~T
b)
Fig. 5: Predicted accumulated plastic strain distribution after 66% reduction in height: a) T=250°C, b) T=400°C.
The distribution of accumulated plastic strain at 250 and 400°C, after 66% height reduction, is shown in fig. 5. It is apparent that the distribution is slightly temperature sensitive. At constant temperature, the accumulated strain is not uniform. Equivalent strain varies from 0.53 to 2.11 at 250°C, and from 0.37 to 1.82 at 400°C. The lower values were observed under the central part of material-tool interface. The higher values were found in the core region of the specimen and next to initial edge of the specimen where folding processes take place. The strain distribution and its variation during the process of the specimen forged in isothermal condition at 400°C, 0.05 S "l , a r e very similar to the strain distribution observed in hot die forging in the same strain rate and initial temperature conditions [13]. This indicates that strains are predominantly determined by the preform geometry and the die configuration.
5. CONCLUSIONS Isothermal forging of the AA 7012 Aluminium alloy was investigated at temperatures
84 from 250 to 400°C keeping a constant strain rate of 0.05 sq. The material flow behaviour was studied by means of torsion tests that provided the plastic flow equation for the forging simulation. The analysis has shown that: i) forging loads decrease when temperature increases due to high temperature softening mechanisms occurring during deformation, ii) the load-ram travel curves predicted by FE modelling are in good agreement with the experimental results particularly at higher strains where softening mechanisms are prevailing, and iii) the accumulated equivalent strain distribution does not change significantly with temperature.
6. ACKNOWLEDGEMENTS The authors thank Dr. P. Fiorini, ISML-ALURES, Novara, Italy, for supplying the material and for suggestions during this work. The financial support of Italian Ministry of Scientific and Technological Research is acknowledged.
7. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22
O.C. Zienkiewicz, E. Onate, J.C. Heinrich: Int. J. Num. Meth. Eng., 17 (1981), p. 1497. C.R. Bo~r, G. Schr&ter: Proceedings of 21th. MTDR Conference, (1980), p. 209. N. Rebelo, S. Kobayashi: Int. J. Mech. Sci., 22 (1980), p. 699. N. Rebelo, S. Kobayashi: Ref. 3, p. 707. N. Alberti, L. Cannizzaro, F. Micari: Annals of the CIRP, 39 (1990), p. 231. S. Kobayashi: "Numerical Analysis of Forming Processes", J.F.T. Pittman et al. eds., John Wiley and Sons Ltd., (1984), p. 45. K. Ohuchi, Y. Nakazawa, K. Matsuno: Mat. Trans. JIM, 30 (1989), p. 67. L. Anand, A. Zavaliangos: Annals of the CIRP, 39 (1990), p. 235. P. Moore: "Deformation Under Hot Working Conditions", The Iron and Steel Institute, London, (1968), p. 103. M.M. Farag, C.M. Sellars and W.J. McG. Tegart: Ref. 7, p. 60. J. Cotner, W.J. McG. Tegart: J. Inst. Metals, 97 (1969), p. 73. D.S. Fields, W.A. Backofen: Proc. Amer. Soc. Test. Mat., 57 (1957), p. 1259. A. Forcellese, F. Gabrielli, F. Micari and O. Zurla: Atti del XX Convegno AIAS, Palermo, (1990), p. 593. J.J. Jonas, C.M. Sellars and W.J. McG. Tegart: Met. Rev., 14 (1969), p. 130. C. Rossard, P. Blain: M6m. Sci. Rev. M6t., 56 (1959), p. 285. F.A. Hodierne: J. Inst. Metals, 91 (1962-63), p. 267. C.M. Sellars, W.J. McG. Tegart: M6m. Sci. Rev. M6t., 63 (1966), p. 731. H.J. McQueen, E. Evangelista, A. Forcellese, I.C. Smith and E. Di Russo: Proceedings of the Symposium "Modelling the Deformation of Crystalline Solids", TSM-AIME, New Orleans, (1991), in print. E. Aernoudt, J.G. Sevillano: J. Iron and Steel Inst., 211 (1973), p. 718. D.B. Holt: Acta Met., 7 (1959), p. 466. G.D. Lahoti, T. Altan: J. Eng. Mat. Tech., (1975), p. 113. A. Forcellese, F. Gabrielli, L. Micari, O. Zurla: J. Mat. Process. Tech., (1992), submitted for publication.
77
Elsevier
Finite element modelling of isothermal forging of a high strength aluminium alloy A. Forcellese°, F. Gabrielli °, F. Micari °°, O. Zurla °°° ° oo ooo
Dipartimento di Meccanica, Universit~ di Ancona Dipartimento di Tecnologia e Produzione Meccaniea, Universi~ di Palermo DIEM, Universi~ di Bologna
Abstract
In the present paper the isothermal forging has been computer simulated by finite element modelling in order to rationalize and optimize the process. The isothermal forging of AA 7012 aluminium alloy was investigated at temperatures ranging from 250 to 400°C, with strain rate of 0.05 s-1. Hot workability of the material was investigated and constitutive equations were defined using torsion tests. Such equations were used in finite element modelling of isothermal forging. The numerical predictions were compared with isothermal experimental test results at the same conditions; an excellent agreement was observed.
1. INTRODUCTION The application of finite element (FE) techniques to model bulk forming processes as forging, extrusion, and rolling, in order to predict working loads and material flow patterns between deforming tools [1-5] is receiving continuously increasing attention. Recent developments in FE methods offer several benefits including significant reductions in the cost of both the design and the analysis of hot working operations. Among hot working processes, isothermal forging is becoming increasingly important for forming of high strength materials. It involves keeping both dies and workpiece at the same temperature for forging. This allows to maintain good formability of the material throughout the entire forging operation and permits a significantly better process control than is possible with conventional metalworking operations. The dimensional accuracy is improved as well as reproducibility while the deformation conditions can be manipulated in order to obtain controlled microstructural evolution. The disadvantage deriving from production rates, that in an isothermal forging are lower than those of conventional one, is offset by the fact that isothermal forging is a one-shot operation and there is no need for a series of shaping stages with their associated reheating and die changes. The slow squeezing operations also enable pieces to be forged to near net shape. This can give significant savings on material cost in forging and on subsequent machining operations. Since the technique of isothermal forging is very expensive owing to intrinsic cost of both the material being forged and the dies, any failure during the process could be very costly. Therefore, mathematical modelling techniques, based on finite element methods, are used in 0924-0136/92/$05.00 © 1992ElsevierSciencePublishers B.V. All rights reserved.
78 isothermal forging [3,4,6-8] to predict: a) the maximum load on press during forging operations, b) the local stresses both in workpiece and die, c) the metal flow patterns, and d) the microstructural evolution. The correct application of FE technique requires an accurate description of the material behaviour in the hot working regime, the development of computational procedures to be implemented into finite element programs, and the verification of the numerical predictions by means of experimental tests. In the present paper, an analysis of the isothermal axisymmetric forging of a high strength aluminium alloy, intended for aerospace applications, has been performed at different temperatures, with a low strain rate. In particular, hot formability studies were performed by simulative methods based on the analysis of torsion test since it allows to assess the flow behaviour in extended strain ranges that are comparable with strain values in most metalworking operations [9] and permits the relatively easy application of programmed deformation to simulate rolling or forging schedules [10,11]. Such results have lead to definition of constitutive equations describing the material plastic flow in the hot working regime. These equations were used in finite element modelling of isothermal forging. The numerical prediction results were compared with experimental data. The local distribution of the hot metalworking parameters has been obtained in different working conditions.
2. EXPERIMENTAL PROCEDURES The material used in the present investigation, supplied by Alures ISML, Italy, is the AA 7012 aluminium alloy with chemical composition shown in table I. Such alloy was developed in order to obtain mechanical properties that are comparable with those of the AA 7075 alloy but, by means of a suitable composition control, with better hot formability.
Table I: Chemical composition of the AA 7012 A1 alloy (wt. %) Zn
Mg
Cu
Zr
Mn
Fe
Si
Ti
6.27
1.85
1.07
0.11
0.14
0.10
0.058
0.016
The heat treatment of the extruded ingot was performed in two stages; a homogenization treatment at 460°C for 6 h was followed by a solution treatment at 480°C, 16 h. The hot formability studies, used for defining the constitutive equations, were performed by means of torsion tests carried out on a servohydraulic closed loop torsion machine in the range of temperatures from 250 to 400°C, with strain rates from 0.05 to 4 s"1. The specimens, machined in the extrusion direction, were torsioned until rupture. Surface shear stresses r and shear strains "t were derived by means of the relationships [12]: nFR (a+n:+m')
= 2
a
v
2~RN
(l)
L
where P is the measured torque, R and L the radius and the gauge length of the specimen
79 respectively, N the revolution number, n' the hardening rate coefficient that in the experimental condition of the present investigation can be neglected, and m' is the revolution rate sensitivity for the torque; m', being independent of strain rate, results equal to the strain rate sensitivity m calculated at different strains and temperatures [13]. Equivalent stresses a and strains e were obtained by von Mises criterion: o = ~
~ = ~
(2)
The above conversion to equivalent values according to the von Mises criterion and idealwork concept has been generally accepted and gives reasonable agreement between results obtained in torsion and in tension or compression at high temperatures [14-16]. Compression tests, used for the experimental verification of the model, were performed on a servohydraulic closed loop material testing machine, equipped for high temperature tests, at 0.05 s"l, with temperatures varying from 250 to 400°C. The tests were carried out in isothermal conditions with temperature of deforming tools equal to that of cylindrical specimens. They were characterized by initial height of 20 mm and diameter of 12 ram. During the tests the temperature was monitored in the specimen and in different points of the tools.
3. THE NUMERICAL CODE The analysis of the axisymmetric upsetting process was carried out employing an incremental approach in order to follow the whole transient process: a variational method, based on the "Upper-Bound" theorem, has been used and the material behaviour has been considered as rigid visco-plastic, neglecting the elastic component of the deformation. This approximation, which allows a remarkable reduction of the required computations, can surely be accepted when hot forming processes are studied. Moreover, in order to take into account the incompressibility condition, the Lagrange multipliers technique has been introduced; thus the minimum condition required by the "Upper-Bound" theorem can be written as:
min[fvo~dV ÷ fvx~vdV_fs(t)r(u)dS]
(3)
being ~ the equivalent plastic strain rate, ~. the Lagrange multiplier, i v the volumetric strain rate, (t) the vector of the traction on the surface S where they known, and finally (u) the vector of the velocity components. The discretization of the above functional is carried out following the usual finite element procedures: a set of non linear stiffness equations is then generated with the nodal velocity component as unknowns, which is iteratively solved by means the Newton-Raphson technique. At the end of each step of the deformation path the nodal coordinates are updated on the basis of the calculated nodal velocities and of the employed time step increment At. At the same way, the equivalent plastic strain rate is integrated along the deformation path. The above described mechanical analysis was applied to the axisymmetric upsetting process. The forging system (Fig. 1) was discretized employing 100 four-nodes isoparametric bilinear elements for the workpiece and 71 elements for the die. Calculations were performed up to
80 66% reduction in height, with 1% reduction for each step. The temperature of the billet was equal to 250, 300, 350, and 400°C in the four analyzed conditions respectively, and the mechanical properties of the workpiece were calculated according to the initial temperature value. Finally, at the die-workpiece interface sticking friction conditions were assumed owing to the expected behaviour affected by lubrication conditions and by the height/diameter ratio of the specimens used.
200 = 0.05 s -~
J.50
~
~
250' C
IIIIIJ ~-
iO0
300' C -
~
350' C
50 400° C
Z
,
,
0.0 0~1)10Y.P. -0.1~t01 0,(l[I*00 0.1~*01
.
.
,
0.5
.
.
.
.
i
1.0
.
.
.
.
i
t .5
.
.
.
.
2.0
e
Fig. 2: Influence of temperature on flow curves.
Fig. 1: Forging system.
4. RESULTS AND DISCUSSION Experimental torsion test results show that, at given temperature and strain rate, flow stress increases with strain up to a maximum and then decreases to the fracture value. At constant strain, flow stress decreases with increasing temperature and decreasing strain rate. In particular, the flow stress maximum value occur at strain values that decrease when temperature increases and strain rate decreases (Fig. 2). The study of hot formability on the alloy under investigation permitted to evaluate the mechanical state equation a=f(e,~,T) that is of extreme utility in the prediction of the load involved in forming process. The material flow behaviour of the AA 7012 aluminium alloy described by the relationship among flow stress, strain rate, and temperature, at a given strain, was supplied by Sellars and Tegart [17] by means of the equation:
Z = ~exp(~T) = A/o"
(4)
where Z is the Zener-Hollomon parameter, Q the activation energy, T the absolute
81 temperature, R the universal gas constant, A' and n material parameters. The dependence of the temperature compensated strain rate Z on flow stress, at E=0.2, is shown in fig. 3. It is apparent that flow stress increases when Z increases. The activation energy value used was Q=205 kJ/mol [18]; the material parameters, calculated in the strain range investigated, are summarized in table II.
10a3 6=0.2
c ~021
Table II: Constitutive parameters
D
e
A' (s.MPa) -1
n
0.1
1.73.10 l
9.35
0.2
5.28" 10-2
9.49
0.4
1.93-10 -3
10.21
0.6
1.74" 10-4
10.77
O.8
7.56" 10-5
10.98
~019 D_
E 0
1017
-0c "
L 10Is C
N 1013
.
.
.
.
.
.
.
.
,
•
.
,
102 Equivalent stress, MPa
,
,
,
,
,
103
Fig. 3: Effect of temperature compensated strain rate on flow stress.
The constitutive equation (4) was used to perform the numerical simulation of isothermal axisymmetric upsetting of the AA 7012 alloy by means of a finite element program. Such thermal-mechanical analysis, performed with strain rate of 0.05 sl , in the temperature range from 250 to 400°C, has allowed the prediction of the load-ram travel curves in isothermal condition. They were compared with the isothermal experimental curves obtained in the same temperature and strain rate conditions (Fig. 4). The comparison shows that, at a given values of ram travel, the numerical predictions are systematically lower than experimental data. This seems to be inconsistent with FE modelling that is based on "Upper-Bound" theorem and that should lead to predicted curves higher than experimental ones. However, metal flow input data for modelling derive from torsion tests. It has been shown that, mainly at low strains, flow stress curves obtained in torsion are lower than those obtained by tension or compression tests owing to the different texture developing during deformation [19,20], different thermal profiles [21], etc. At higher strains, flow stresses obtained by torsion tests tend to approach the values in tension and compression tests owing to the prevailing effects of dynamic restoration processes. Consequently, the difference between predicted and experimental load-ram travel curves, in general, decreases with increasing strain. In the present study, this is observed in a significant extent in curves at 250°C. On increasing temperature such aspect becomes less and less remarkable. This may sound inconsistent with results of a previous paper [22] dealing with modelling of forging in
82
70000
70000 T=250' C
T=300° C
// Z
1= ~3 0 -J
Z
35000
/
=
¢0 0 --J
J
35000
I
I
i
,
,
,
,
~
,
,
,
,
I
,
,
,
5 I0 Ram travel, mm
.
,
.
.
.
I
.
.
.
.
I
.
.
.
.
5 I0 Ram travel, mm
15
15
70000
70000
T=400'C
T=350 ° C
Z
ro o
35000
35000
.
0
.
.
.
i
.
.
.
.
5 Ram travel,
I
10 mm
.
.
.
.
0
15
,
,
,
,
I
.
.
.
.
i
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Fig. 4: Comparison between experimental ( ) and predicted (- - -) load versus ram travel curves at different temperatures, 0.05 s -l.
15
83 anisothermal conditions and at high strain rates. In the present case, test conditions refer to very low strain rates; it derives from fig. 2 that the strain to peak is much lower and becomes comparable with peak strain from compression tests [14,17]. This is much truer, the higher the temperature is.
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Fig. 5: Predicted accumulated plastic strain distribution after 66% reduction in height: a) T=250°C, b) T=400°C.
The distribution of accumulated plastic strain at 250 and 400°C, after 66% height reduction, is shown in fig. 5. It is apparent that the distribution is slightly temperature sensitive. At constant temperature, the accumulated strain is not uniform. Equivalent strain varies from 0.53 to 2.11 at 250°C, and from 0.37 to 1.82 at 400°C. The lower values were observed under the central part of material-tool interface. The higher values were found in the core region of the specimen and next to initial edge of the specimen where folding processes take place. The strain distribution and its variation during the process of the specimen forged in isothermal condition at 400°C, 0.05 S "l , a r e very similar to the strain distribution observed in hot die forging in the same strain rate and initial temperature conditions [13]. This indicates that strains are predominantly determined by the preform geometry and the die configuration.
5. CONCLUSIONS Isothermal forging of the AA 7012 Aluminium alloy was investigated at temperatures
84 from 250 to 400°C keeping a constant strain rate of 0.05 sq. The material flow behaviour was studied by means of torsion tests that provided the plastic flow equation for the forging simulation. The analysis has shown that: i) forging loads decrease when temperature increases due to high temperature softening mechanisms occurring during deformation, ii) the load-ram travel curves predicted by FE modelling are in good agreement with the experimental results particularly at higher strains where softening mechanisms are prevailing, and iii) the accumulated equivalent strain distribution does not change significantly with temperature.
6. ACKNOWLEDGEMENTS The authors thank Dr. P. Fiorini, ISML-ALURES, Novara, Italy, for supplying the material and for suggestions during this work. The financial support of Italian Ministry of Scientific and Technological Research is acknowledged.
7. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22
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