Elasto-Visco behavior of Al7075-T6 using a numerical technique

The Steinberg Guinan equation is based on the assumption that if the strain rate reaches the critical state (∼10⁵ s⁻¹) , materials become independent of strain rate due to strain rate saturation [15]. The parameters are pressure (P), temperature (T), compression (η) (a dimensionless parameter), and strain (ε). This model was considered, being the expansion of the first-order Taylor expansion in temperature and pressure with a work hardening factor and a small correction for compression. The mathematical expressions are shown in equations (1)–(3), with its usual notation as follows: σ -material strength or flow stress (GPa), σ₀ -ambient strength, $\mathop{G\,}\limits_{{\rm{o}}}$ -shear modulus, Ǵ $P\,=\,\partial G/\partial P$ and Ǵ $T\,=\,\partial G/\partial T$ are the partial derivatives of shear modulus with pressure and temperature, respectively [15].

$$\begin{eqnarray}&&\sigma \,=\,{\sigma }_{0}\unicode{x00192}\left(\varepsilon \right)\left(1+\left(\displaystyle \frac{\unicode{x001F4}P}{\mathop{G\,}\limits_{{\rm{o}}}}\right)\displaystyle \frac{P}{{\eta }^{\displaystyle \frac{1}{3}}}+\left(\displaystyle \frac{\unicode{x001F4}T}{\mathop{G\,}\limits_{{\rm{o}}}}\right)\left(T-300\right)\right.\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\rm{G}}\,=\,{{\rm{G}}}_{0}\left(1+\left(\displaystyle \frac{\unicode{x001F4}P}{\mathop{G\,}\limits_{{\rm{o}}}}\right)\displaystyle \frac{P}{{\eta }^{\displaystyle \frac{1}{3}}}+\left(\displaystyle \frac{\unicode{x001F4}T}{\mathop{G\,}\limits_{{\rm{o}}}}\right)\left(T-300\right)\right.\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\unicode{x00192}\left(\varepsilon \right)\,=\,{\left(1+\beta \left({\varepsilon }_{{\rm{i}}}+\varepsilon \right)\right)}^{{\rm{n}}}\end{eqnarray} \tag{ 3 }$$

Chip formation history helps in understanding the process mechanism under quasi-static conditions [16]. In the simulation study, two distinct types of chip form was noticed in the orthogonal turning operation of Al7075-T6 alloy, at different depths of cut, namely tearing chips and shearing chips. Tearing chips or rupture chips were found to be formed at 0.5 and 0.6 mm and shearing chips formed at 0.7 and 0.8 mm depth of cut. An earlier study has reported that tearing chips most often formed in a low formable material like lamellar graphite cast iron [17]. At a low depth of cut (0.5–0.6 mm), tearing chips were identified as irregular fractured interfaces generated rapidly between the workpiece and the tool rake face (refer figures 2(a) and (b)). It has been understood that the fragmented tearing chips are formed in the shorter shear plane in the secondary shear zone along the length of the chip. The other reason for the formation of a short length chip is due to crack nucleation at twin intersections [18]. At a higher depth of cut (0.7–0.8 mm), relatively longer chips were formed and were characterized by alternate shear bands in the continuous shearing chips. The important characteristics related to the shearing chip have been identified and mainly resulted from the edge dislocation refer figures 2 and 3. [19].

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In the present study, an attempt has been made to predict the temperature history at different depths of cut, ranging from 0.5 to 0.8 mm. It has been noticed that there was no significant rise in temperature up to 0.7 mm depth of cut. However, a sudden rise in average temperature ∼551.59 °C was found at 0.8 mm depth of cut in the secondary shear zone figure 4(a). It has been noticed, with the increasing depth of cut, there was an increase in temperature, with a rise up to 586.22 °C at 0.8 mm depth of cut (figure 5(d)). The major temperature concentration was found to be near the tool-chip interface in the secondary shear zone. The escalation in temperature at this depth of cut can be attributed to the movement of the dislocation slips caused by the movement, accumulation, and agglomeration of bulk grains (here FEA elements) at the local shear boundaries. This occurred majorly in the secondary shear zone, which resulted in greater work hardening. This leads the bulk material/grains to behave stiffer, linked with a local rise in the stress field. The variation of residual stress at different depths of cut is shown in figure 4(b). The local rise in temperature can be also understood as follows: At a higher depth of cut, a dislocation slip was found to be initiated within the secondary shear plane, with the same burger vector, repelling each other and serves as a mutual barrier for their individual motion during the plastic deformation. The highly compressed region in the secondary shear zone was found to suffer a maximum strain hardening effect. The strain hardened region was mainly found to carry a maximum load in the present machining process. An envelope over which plasticity was found to be sustained for a long duration of time supplemented with a sudden local rise in temperature, was noticed mainly at 0.8 mm depth of cut. Not much change in temperature was observed from 0.5 to 0.7 mm depth of cut (figure 4(a)). Moreover, dislocation of the grain boundary was assisted by the rise in localized stresses due to compression and elongation of grains in the secondary shear zone. This mechanism was found to facilitate more fracture energy dissipation in the material compared to any other shear zone. Similar reasons were noticed in the study of steel grades, AISI S-1006, S-7, and S-4340, based on the Johnson–Cook Model [20]. The temperature change, equivalent stress and total deformation history of the Al7075-T6 alloy has been shown in figure 5.

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At a lower depth of cut (0.5 mm), it was noticed that flow/residual stresses had a much higher value (7.68 × 10⁸ Pa) compared to 0.8 mm depth of cut, with a least value of 7.33 × 10⁸ Pa (figure 5). Approximate constant flow stress behaviour can be anticipated during the actual machining process that has been observed between 0.6 to 0.7 mm in the simulation study. An average deformation and residual stress in the material flow was found to be maximum at 0.5 mm and found to be constant from 0.6 mm depth of cut refer figures 4(c) and (b) respectively. An inverse relationship was found to exist between average temperature change and residual stress at a given rake angle 12°. As the temperature increases, the flow stress decreases. The reason for such behaviour is attributed to softening of material at 551.59 °C, which facilitated easy gliding of slip dislocation in its own slip plane.