Determination of the strain-rate sensitivity and the activation energy of deformation in the superplastic aluminium alloy Al-Mg-Mn-Sc Določevanje indeksa občutljivosti na preoblikovalno hitrost in aktivacijske energije za deformacijo superplastične aluminijeve zlitine Al-Mg-Mn-Sc Anton Smolej1, *, Brane Skaza1 Matevž Fazarinc1 University of Ljubljana, Faculty of Natural Science and Engineering, Department of Materials and Metallurgy, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia Corresponding author. E-mail: anton.smolej@ntf.uni-lj.si Received: July 30, 2009 Accepted: August 20, 2009 Abstract: This paper deals with determining the strain-rate sensitivity m and the activation energy for the superplastic deformation Q of a cold rolled aluminium Al-Mg-Mn-Sc alloy. The experiments were carried out under uniaxial tension over the temperature range 390 °C to 550 °C and at a constant strain rate or constant cross-head speed between 1 • 10-4 s-1 and 2 • 10-2 s-1. The m-values were determined on the basis of the true stress, true strain curves and also using the jump-test method. The m-values varied from 0.35 to 0.70, which depended upon the forming conditions. The activation energy for the deformation was determined by the flow curves at various temperatures and at an initial strain rate of 7.5 • 10-4 s-1. Izvleček: Članek obravnava določanje indeksa občutljivosti na preoblikovalno hitrost m in aktivacijsko energijo za superplastično preoblikovanje aluminijeve zlitine Al-Mg-Mn-Sc. Preizkusi so bili narejeni z nateznim preizkusom pri temperaturah od 390 °C do 550 °C pri konstantnih preoblikovalnih hitrostih med 1 • 10-4 s1 in 2 • 10-2 s1 in konstantnih hitrostih raztezanja. Vrednosti m so bile določene na osnovi krivulj dejanska napetost - dejanska deformacija in tudi s skokovitim spreminjanjem preoblikovalne hitrosti. Vrednosti m so bile v mejah 0,35 do 0,70, kar je bilo odvisno od preoblikovalnih razmer. Aktivacijska energija za deformacijo je bila določena s krivuljami tečenja pri različnih temperaturah in konstantni začetni preoblikovalni hitrosti 7,5 • 10-4 s1. Key words: strain-rate sensitivity, activation energy, superplasticity, Al-Mg-Mn-Sc alloy Ključne besede: indeks občutljivosti na preoblikovalno hitrost, aktivacijska energija, superplastičnost, zlitina Al-Mg-Mn-Sc Introduction Superplasticity is the ability of certain polycrystalline materials to achieve large elongations in a tensile test without necking prior to failure. These elongations are up to 1000 %, and in some cases even more. The superplastic forming (SPF) of aluminium-alloy sheets has been commercially established for more than 30 years, and the mechanisms of SPF and the requirements for achieving the superplasticity of materials are now well known.[1, 2] In general, three important conditions are needed to attain the SPF of the material: (i) the grain size should be very fine and stabile, typically less than 10 p,m; (ii) the flow stresses must be low compared with those of conventional materials; and, (iii) the strain-rate sensitivity values m must lie in the range of 0.4 to 0.8.[3] The strain-rate sensitivity index m is considered to be the most important parameter that characterises superplastic deformation.[2] The characteristic equation that describes superplastic behaviour is usually written as a" = K. è"\ I1"6] where o is the flow stress, K is a material constant, è is the strain rate and m is the strain-rate sensitivity index of the flow stress. The m-value is a function of the forming parameters, such as the strain rate and the temperature, and is also connected with the microstructural characteristics.[7] There are a number of reports where the various experimental methods for determining the value of m are described.[2-6] The most convenient method is a uniaxial tensile test at a particular constant temperature and at different strain rates. The simplest method is reflected in the relation ship between the flow stress (er) and the strain rate (¿). The m-value is then defined as the slope of the curve lg o vs. lg s. The jump test is also quite often used.[2] Different variations of this method are distinguished by the way the results are handled. A knowledge of the activation energy enables the evolution of the deformation mechanism of SPF.[8] For aluminium SPF alloys this energy is usually within the range anticipated for grain-boundary diffusion in pure aluminium and interdiffusion in Al-Mg alloys.[9] The activation energy is usually obtained from an Arrhenius plot of In £ vs. the reciprocal absolute temperature 1/T at a constant stress or from a plot of lna vs. 1/T at a constant strain rate.[2, 3] The purpose of this paper is an experimental survey of two methods to determine the strain-rate sensitivity index and to determine the activation energy of the superplastic forming. The examined material was a slightly modified AA5083 (Al-Mg-Mn) alloy with the addition of scandium. Experimental procedure The strain-rate sensitivity index m and the activation energy Q of the SPF were determined for a Al-4.5Mg-0.46Mn-0.44Sc alloy. The alloy was produced by ingot casting and conventionally processed to a sheet with a thickness of 1.9 mm. The superplastic parameters m and Q were determined using a uniaxial tensile test. The samples for this test are shown in Figure 1. H- 21 13 21 R3 (|>6 I , uri I 11 I 10 11 —J Figure 1. Sample for the tensile test The tensile tests were carried out using a Zwick Z250 universal testing machine with 0.5 kN load cell. The machine was equipped with a three-zone electrical resistance furnace. A photograph of the tested equipment is shown in Figure 2. The testing procedure and the evolutions of the results were controlled by the TestXpert II software system. The measurements included a determination of the flow stresses as a function of the true strain and of the strain rate at various strain rates and forming temperatures, which ranged from 1 • 10-4 s-1 to 2 • 10-2 s-1 and from 390 °C to 550 °C, respectively. The data from these experiments were used for a calculation of the strain-rate sensitivity indexes and the activation energy. The strain-rate sensitivity index m as a function of the strain rate was estimated from the stress-strain plots and from the multi- Figure 2. The test equipment strain-rate jump test. The tensile tests were conducted at a constant strain rate with a continuous change of cross-head speed and with a constant cross-head speed, where the initial strain rate decreased with the increased strain. Results and disscusion Strain-rate sensitivity index m The m-values are usually calculated from the logarithmic plot of the flow stress vs strain rate (method I). Figure 3 shows stress-strain rate plots at 550 °C covering the true strains from 0.7 to 1.4. The constant strain rates were in the range from 5 • 10-4 s-1 to 1 • 10-2 s-1. The curves exhibit the sigmoid shapes. The m-values at several strain rates and strains were calculated from the slopes of the plots; these values are presented in Figure 4. The highest m-values for all the strains were in the range of strain rates from 5 • 10-4 s-1 to 1 10-3 s-1. The other method (method II) for determining the m-value is the multi-strain-rate jump test. The jump test was conducted by increasing and decreasing the strain rate by 20 % at every 100 % increment of elongation. The strain rate was constant during the single jumps, which was controlled by software for a continuously changing cross-head speed. The change of cross-head speed is shown in Figure 5 as an example of increasing the strain rate from " = 2.5 • 10-3 s-1 (downward strain rate) to s = 3 • 10~3 s 1 (upward strain rate) for a progressive elongation, and the corresponding simultaneous change of the TOO ro Q. S I Ž 10 0.1 0.0001 ■ I ........I True strain -5- 0.7 -o- 1.1 -o- 1.4 ........i .........I ........ 0.001 0.01 'Ki. s-1 0.1 Figure 3. Stress-strain rate plots for various strains at a temperature of 550 °C Figure 4. Strain-rate sensitivity index m as a function of constant strain rate for various strains at a temperature of 550 °C calculated from the stress-strain rate curves in Figure 3 force. The m-values for various strains or elongations, respectively, were calculated according to the equation: (1) where ox and o2 are the flow stresses, ¿J ¿2 are the corresponding instantaneous strain rates, F1, F2 are the forces and vp v2 are the cross-head speeds before and after the jump. By convention, the m-value is attributed to the downward strain rate ¿i ,[2] The multi-strain jump test makes possible to examine the m values at various progressing strains or elongations m fit» Boflgartun, fc'f!il Figure 5. The change of cross-head speed (red line) and force (green line) during the multi-strain-rate jump test Table 1. Cross-head speeds, forces and m-values for the investigated alloy during the jump test at a downward strain rate s = 2.5 • 10 3 s 1 and at 550 °C E e/% v1/(mm s 1) v2/(mm s 1) F1/N f2/n m 0.69 100 0.0501 0.0602 2.722 3.082 0.68 1.10 200 0.0752 0.0901 2.411 2.711 0.65 1.38 300 0.1000 0.1203 2.031 2.259 0.58 1.61 400 0.1248 0.1498 1.654 1.838 0.58 1.79 500 0.1502 0.1803 1.356 1.491 0.52 1.95 600 0.1755 0.2096 1.072 1.179 0.53 2.08 700 0.1990 0.2403 0.877 0.959 0.47 at a fixed strain rate during a single test. The experimental data of the cross-head speeds v1 and v2 with the corresponding forces F1 and F2 and the calculated m-values at a single strains during the jump test from Figure 5 are given in Table 1. Indexes m, calculated from the jump test, are plotted as a function of strain rate for strains over the range from 0.7 (100 %) to 2.6 (1300 %) at temperature of 550 °C in Figure 6. The index m is changed at all the strains with the strain rates; the data demonstrate the bell-shape curvature that is typical of superplastic materials. The m-values also change with the increased strain. The highest m-values were achieved in the range of constant strain rates 3.5 • 10-4 s1 to 1 • 103 s1 (Figure 6). The maximum m-value was in accordance with the largest elongation of about 2000 % (Figure 7). 0.00001 0.0001 0.001 iii J,vi ufe. ,.s"1 Figure 6. Strain-rate sensitivity index m as a function of the constant strain rate for various strains at 550 °C (jump test with a 20 % increase of the strain rate) Figure 7. Untested and tested sample of Al-4.5%Mg-046%Mn-0.44Sc alloy at 550 °C and an initial strain rate of 7.5 • 10-4 s1 Table 2. Indexes m of the investigated al- In £ — In 1 Q loy at a true strain of 0.7, various strain ln