Formability of Tri-layered IF240/AZ31/IF240 Composite with Strong Bonding: Experimental and Finite Element Modeling

Abstract

In this work, the formability of a hybrid material of Interstitial-Free 240 (IF240) steel and AZ31 magnesium alloy as IF240/AZ31/IF240 tri-layered sheets was investigated. For this purpose, the bonding feasibility of the high-formability IF240 steel and low-formability AZ31 sheets was first assessed. Then, the hot formability behavior of the manufactured laminated composite was evaluated. The rolling of the preheated samples established the layer bonding. The bonding strength was determined using the shear punch test. The texture and its effects on the forming behavior were studied using the x-ray Goniometry method. Nakazima dome tests were employed at ambient and elevated temperatures to determine formability and forming limit curves. The forming process simulation was performed by ABAQUS/Explicit solver, and the results were compared with the experimental data. The results showed that post-annealing time and thickness reduction have significant impacts on the bond strength. The formability of the composite laminate improved significantly by an increase in the temperature. Simulation results of the composite forming behavior were in fair agreement with the experimental results.

Appendix: Hill’s Yield Function

$$f\left( \sigma \right) = \sqrt {F\left( {\sigma _{{22}} - \sigma _{{33}} } \right)^{2} + G\left( {\sigma _{{33}} - \sigma _{{11}} } \right)^{2} + H\left( {\sigma _{{11}} - \sigma _{{22}} } \right)^{2} + 2L\sigma _{{23}} + 2M\sigma _{{31}} + 2N\sigma _{{12}} }$$

(A-1)

F, G, H, L, M, and N are constants determined by the testing of the material in altered orientations, which can be defined using Eqs. (A-2)–(A-7).

$$F = \frac{{\left( {\sigma ^{0} } \right)^{2} }}{2}\left( {\frac{1}{{\sigma _{{22}}^{2} }} + \frac{1}{{\sigma _{{33}}^{2} }} - \frac{1}{{\sigma _{{11}}^{2} }}} \right) = \frac{1}{2}\left( {\frac{1}{{R_{{22}}^{2} }} + \frac{1}{{R_{{33}}^{2} }} - \frac{1}{{R_{{11}}^{2} }}} \right)$$

(A-2)

$$G = \frac{{\left( {\sigma ^{0} } \right)^{2} }}{2}\left( {\frac{1}{{\sigma _{{33}}^{2} }} + \frac{1}{{\sigma _{{11}}^{2} }} - \frac{1}{{\sigma _{{22}}^{2} }}} \right) = \frac{1}{2}\left( {\frac{1}{{R_{{33}}^{2} }} + \frac{1}{{R_{{11}}^{2} }} - \frac{1}{{R_{{22}}^{2} }}} \right)$$

(A-3)

$$H = \frac{{\left( {\sigma ^{0} } \right)^{2} }}{2}\left( {\frac{1}{{\sigma _{{11}}^{2} }} + \frac{1}{{\sigma _{{22}}^{2} }} - \frac{1}{{\sigma _{{33}}^{2} }}} \right) = \frac{1}{2}\left( {\frac{1}{{R_{{11}}^{2} }} + \frac{1}{{R_{{22}}^{2} }} - \frac{1}{{R_{{33}}^{2} }}} \right)$$

(A-4)

$$L = \frac{3}{2}\left( {\frac{{\tau ^{0} }}{{\sigma _{{23}} }}} \right)^{2} = \frac{3}{{2R_{{23}}^{2} }}$$

(A-5)

$$M = \frac{3}{2}\left( {\frac{{\tau ^{0} }}{{\sigma _{{13}} }}} \right)^{2} = \frac{3}{{2R_{{13}}^{2} }}$$

(A-6)

$$N = \frac{3}{2}\left( {\frac{{\tau ^{0} }}{{\sigma _{{12}} }}} \right)^{2} = \frac{3}{{2R_{{12}}^{2} }}$$

(A-7)

In the above equations, $\sigma _{{ij}}$ is the measured yield stress value; $\sigma ^{0}$ is the user-defined reference yield stress specified for the plasticity definition; $R_{{11}}$, $R_{{22}}$, $R_{{33}}$, $R_{{12}}$, $R_{{13}}$, and $R_{{23}}$ are the anisotropic yield stress ratios; and $\tau ^{0} = \frac{{\sigma ^{0} }}{{\sqrt 3 }}$ . The six yield stress ratios are, therefore, defined in the following Eqs.:

$$R_{{ii}} = \frac{{\sigma _{{ii}} }}{{\sigma ^{0} }},i = 1 - 3$$

(A-8)

$$R_{{ij}} = \frac{{\sigma _{{ij}} }}{{\tau ^{0} }},i \ne j,i = 1,2j = 2,3$$

(A-9)

If $\sigma ^{0}$ in the metal plasticity model is defined to be equal to $\sigma _{{11}}$; therefore, $R_{{11}} = 1$, and given the relationships above, $R_{{ij}}$ is obtained using Eq. (A-9):

$$[R_{{ij}} ] = \left[ {\begin{array}{*{20}l} {R_{{11}} = 1} \hfill & {R_{{12}} = \sqrt {\frac{{3r_{{90}} \left( {r_{0} + 1} \right)}}{{\left( {2r_{{45}} + 1} \right)\left( {r_{{90}} + r_{0} } \right)}}} } \hfill & {R_{{13}} = 1} \hfill \\ \vdots \hfill & {R_{{22}} = \sqrt {\frac{{r_{{90}} \left( {r_{0} + 1} \right)}}{{r_{0} \left( {r_{{90}} + 1} \right)}}} } \hfill & {R_{{23}} = 1} \hfill \\ {{\text{SYM}}} \hfill & \cdots \hfill & {R_{{33}} = \sqrt {\frac{{r_{{90}} \left( {r_{0} + 1} \right)}}{{\left( {r_{{90}} + r_{0} } \right)}}} } \hfill \\ \end{array} } \right]$$

(A-9)