SISTEMAS DEL VEHICULO

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(6.1)

where a coefficient of a =8.714 [µm] was obtained for type C specimens under PSC at 100°C according to Fig. 4.4.8.

During simulation, the predicted flow curve was fitted to the experimental curve by varying the strain hardening related parameters, systematically. The final result is listed in Table 6.4.1At each deformation step i for one fitting attempt k, the difference between the experimental stress _!exp and simulated one!sim was calculated and then summed as deformation proceeded:

!k=

(

)

i=1 nstep

#

After several thousand times of random parameter choices, a set of fitting parameters giving the lowest difference, i.e.! = min was obtained and then applied for after simulations at this temperature. In this work, two sets of parameters were obtained for simulations at T=100°C and T=400°C. Here should be mentioned that, in the GIA-TW-HD model, no elastic deformation has been considered, and therefore the fitting of the experimental flow curve was started at the initiation of plastic deformation with an offset strain, for instance != !0.005 at 100°C.

6.2   Contributions   of   various   deformation   modes   to   texture   evolution  of  AZ31  

In Mg alloys, at least four slip modes and two twinning modes are involved. The contributions of the various deformation modes to texture evolution were tested by varying the relative CRSS ratios of these modes to that of basal slip. In order to test the contribution of one particular mode to texture evolution, in one set of tests, the CRSS ratio of the deformation mode of interest was changed, whereas of the other modes the CRSSs were kept constant.

89 Fig. 6.2.1 Predicted textures of Mg with random texture under plane strain compression at a strain of ! = !0.45, the relative CRSS values employed in the GIA-TW model for basal slip and extension twinning were !ba: !etw= 1: X : (a) X=1.6; (b) X=4.

A random texture was discretized into 4000 discrete orientations and employed as the input texture for simulations. In the first set of tests, only extension twinning and basal slip were allowed to be activated to certify the relative contributions of these most easily activated modes in Mg alloys. The CRSS for basal slip was kept constant, whereas the one for extension twinning was varied from 1.6 to 4 (!ba: !_etw= 1: X ). The predicted textures at a true strain of -0.45 are shown in Figs. 6.2.1a-b in the form of (0002) PFs. It can be seen that the activations of basal slip and extension twinning, regardless of their relative CRSS ratios, led to a sharp basal texture. This is because both basal slip and extension twinning try to rotate the c-axis of a grain towards the loading direction, i.e.

ND in PSC.

90

Fig. 6.2.2 Predicted textures of Mg with random texture under plane strain compression at a strain of != !0.45, the relative CRSS values employed in the GIA-TW model for basal and pyramidal <c+a> slip as well as extension twinning were

!_ba: !_py: !_etw= 1 : X : 2: (a) X=1; (b) X=2; (c) X=8; (d)-(f) the predicted mode activitiy evolutions for (a)-(c), respectively.

In the second set of tests, pyramidal <c+a> slip was additionally activated. The CRSS ratios of basal slip and extension twinning were set to be 1 and 2, respectively and kept constant for each test, whereas the one of pyramidal <c+a> slip varied from 1 to 8 ( _{!ba: !py: !etw} = 1 : X : 2 ). The predicted textures at the strain of -0.45 and the corresponding evolving mode activities are shown in Figs. 6.2.2 a-f. It can be seen that, when the CRSS of pyramidal <c+a> slip was lower than that of extension twinning, for instance _{!ba : !py: !etw = 1 :1 : 2} , the resulting texture consisted of three components, namely the RD component and the two components symmetrically located between RD and ND. The mode activities in Fig. 6.2.2d suggested that extension twinning was deactivated completely, whereas pyramidal <c+a> slip accommodated most of the deformation at all strains. With a lower CRSS (as given) than that of twinning, pyramidal slip is easier to be activated, since both pyramidal slip and extension twinning accommodate strains along the axis. Meanwhile, pyramidal <c+a> slip rotates the c-axes of random grains towards RD, whereas basal slip tries to rotate them towards ND.

As a result of the competition between basal and pyramidal <c+a> slip, part of the initially randomly distributed orientations were rotated towards ND by basal slip, which led to the orientations between ND and RD, whereas the rest were rotated towards RD by pyramidal <c+a> slip. This resulted in the RD component in Fig. 6.2.2a. With increasing the CRSS ratio (for instance _{!ba: !py: !etw}= 1 : 2 / 8 : 2), the contribution of pyramidal

<c+a> slip decreased rapidly, accompanied by an increase in extension twinning activity (Figs. 6.2.2e-f). The corresponding (0002) PFs shown in Figs. 6.2.2b-c exhibit a strong basal texture at the strain of -0.45.

91 Fig. 6.2.3 Predicted textures of Mg with random initial texture under plane strain compression at a strain of != !0.45, the relative CRSS values employed in the GIA-TW model for basal, prismatic and pyramidal <c+a> slip as well as extension twinning were

!ba : !pr: !py: !etw= 1 : X : 5 : 2: (a) X=3; (b) X=5; (c) X=7; (d)-(f) are the predicted mode activities for (a)-(c), respectively.

In the third set of tests, the influence of prismatic slip on texture evolution was tested by varying its CRSS ratio from 3 to 7, while keeping the others constant (_{!ba: !pr : !py: !etw}= 1 : X : 5 : 2). The predicted textures and mode activities are shown in Fig. 6.2.3a-f. It can be seen that by reducing the CRSS ratio of prismatic slip, the basal texture was rotated towards TD, increasingly so at lower CRSS. Since prismatic slip rotates crystals about their c-axes, it weakens the basal texture and stabilizes orientations with basal poles aligning to TD. However, when prismatic slip becomes more difficult than pyramidal <c+a> slip (for instance _!ba: !_pr: !_py: !_etw = 1 : 7 : 5 : 2), its activity was completely suppressed and a basal texture was obtained again, as shown in Figs. 6.2.3c and f.

92

Fig. 6.2.4 Predicted textures of Mg with random texture under plane strain compression at a strain of != !0.45, the relative CRSS values employed in the GIA-TW model for basal, prismatic and pyramidal <c+a> slip as well as extension twinning were

!ba: !pr: !py: !etw= 1 : X₁: X₂: 2 (a) X₁= X₂ = 1.5 _{; (b)} X₁= 5,!X₂= 1.5 ; (c) X₁= 1.5,!X₂= 2; (d)-(f) are the predicted mode activities for (a)-(c), respectively.

In the fourth set of tests, the relative contributions of non-basal slip, i.e. pyramidal and prismatic slip, were tested by varying their CRSSs, while keeping the ones of basal slip and extension twinning at constant values of 1 and 2, respectively (_{!ba: !pr : !py: !etw = 1 : X1}: X₂: 2). The predicted textures and mode activities are shown in Figs. 6.2.4a-f. When the CRSS ratio of extension twinning was larger than that of non-basal slip ( X₁= X₂ = 1.5 ), extension twinning was completely suppressed. Three components at RD and RD-ND were observed in the (0002) PF, except for a rotation of the RD-ND components towards TD due to prismatic slip. When the CRSS of prismatic slip was larger than that of pyramidal <c+a> (X₁= 5,!X₂= 1.5), prismatic slip was deactivated and the rotation of RD-ND components towards TD was vanished. By contrast, when the CRSS of prismatic slip was lower than that of pyramidal <c+a>

(X₁= 1.5,!X₂ = 2), pyramidal <c+a> slip became less active and the RD orientations disappeared in the (0002) PF in Fig. 6.2.4c.

In conclusion, the influence of various deformation modes on texture evolution under rolling can be summarized as: i) both basal slip and twinning rotate orientations towards ND, regardless of their CRSS ratios; ii) pyramidal <c+a> slip rotates orientations towards

93 RD; iii) prismatic slip rotates crystals about their c-axes and leads to a rotation of the basal texture towards TD; iv) once the CRSS for prismatic slip is larger than that of pyramidal, prismatic slip becomes deactivated.