Formability and failure response of AA5052-H32 thin sheets with friction stir spot welds during the shock tube-based impact forming

Abstract

In the present study, both the experimental and numerical investigations are carried out to understand the dynamic forming behavior of friction stir spot-welded (FSSW) sheet made of AA 5052-H32 sheets of 1 mm thickness using a shock tube. A hemispherical end nylon striker is propelled at high velocity to deform the FSSW sheet in biaxial mode of deformation. Furthermore, the effect of tool rotational speed and plunge speed on the FSSW joint is studied. During this analysis, a new strategy is followed to evaluate the rate-dependent flow stress–strain properties, which are incorporated during FE simulation using FE code, DEFORM-3D. Tensile test data obtained from the unwelded section of the deformed FSSW sheet is fit to Modified Johnson–Cook (MJC) model, and the rate-dependent properties are identified. In the case of the spot-welded region, a hardness-based multiplying factor is generated to evaluate the stress–strain data by fitting to MJC model. The effect of tool rotational speed and plunge speed on the welding and forming outputs are presented. Temperature evolution during FSSW is validated with the experimental data, and good correlation is obtained. The predicted material flow visualization during FSSW gives insight into the mixing of the material during the joint formation. The results agree with available findings. Various forming outputs such as effective strain distribution, necking height, and the failure pattern are predicted using MJC model in combination with Freudenthal damage model, and the results have good agreement with the experimental data.

Appendix: Identification of stress ratio and strain ratio for plane strain condition with no planar anisotropy

Hill’s 1948 yield criterion for anisotropic materials in principal coordinate system is expressed as [39]:

$$F{\left( {{\sigma_2} - {\sigma_3}} \right)^2} + G{\left( {{\sigma_3} - {\sigma_1}} \right)^2} + H{\left( {{\sigma_1} - {\sigma_2}} \right)^2} = \frac{2}{3}\left( {F + G + H} \right){\bar \sigma^2}$$

(9)

where F, G, and H are the anisotropy parameters; ${\sigma_i}$ represents the principal stress.

During plastic deformation, the stress and the strain are related by the flow rule,

$$d{\varepsilon_{ij}} = d\lambda \frac{{\partial f({\sigma_{ij}})}}{{\partial {\sigma_{ij}}}}$$

(10)

where $d\lambda$ is an arbitrary constant.

The principal strains ($d{\varepsilon_1},d{\varepsilon_2},d{\varepsilon_3}$) for plane stress condition can be obtained by differentiating Eq. (10) with respect to the principal stresses and substituting into the flow rule.

$$\begin{array}{l}d{\varepsilon_1} = d\lambda \left[ {G\left( {{\sigma_1} - {\sigma_3}} \right) + H\left( {{\sigma_1} - {\sigma_2}} \right)} \right]\\d{\varepsilon_2} = d\lambda \left[ {F\left( {{\sigma_2} - {\sigma_3}} \right) + H\left( {{\sigma_2} - {\sigma_1}} \right)} \right]\\d{\varepsilon_3} = d\lambda \left[ {G\left( {{\sigma_3} - {\sigma_1}} \right) + F\left( {{\sigma_3} - {\sigma_2}} \right)} \right]\end{array}$$

(11)

Assuming plane stress condition for thin sheet, Hill’s 1948 yield criterion can be demonstrated as:

$$F{\left( {\sigma_2} \right)^2} + G{\left( {\sigma_1} \right)^2} + H{\left( {{\sigma_1} - {\sigma_2}} \right)^2} = \frac{2}{3}\left( {F + G + H} \right){\bar \sigma^2}$$

(12)

By substituting principal stress ratio, $\alpha = {{\sigma_2} \mathord{\left/ {\vphantom {{\sigma_2} {\sigma_1}}} \right. \kern-\nulldelimiterspace} {\sigma_1}}$ into Eq. (12)

$$F{\left( \alpha \right)^2} + G + H{\left( {1 - \alpha } \right)^2} = \frac{2}{3}\left( {F + G + H} \right)\frac{{{{\bar \sigma }^2}}}{\sigma_1^2}$$

(13)

The principal strain ratio, $\beta = {{d{\varepsilon_2}} \mathord{\left/ {\vphantom {{d{\varepsilon_2}} {d{\varepsilon_1}}}} \right. \kern-\nulldelimiterspace} {d{\varepsilon_1}}}$ for plane stress condition, can be expressed as:

$$\beta = \frac{{F(\alpha ) - H\left( {1 - \alpha } \right)}}{{G + H\left( {1 - \alpha } \right)}}$$

(14)

Assuming plane strain condition (β = 0), α will be expressed as:

$$\alpha = \frac{H}{F + H}$$

(15)

For no planar anisotropy condition ($r = {r_0} = {r_{45}} = {r_{90}}$), Hill’s anisotropic constants (F, G, and H) can be correlated as F = G and H = rG.

Substituting F, G, and H into Eq. (12), the stress ratio can be obtained as:

$$\frac{{\sigma_1}}{\bar \sigma } = \sqrt {\frac{{2\left( {2 + r} \right)\left( {1 + r} \right)}}{{3\left( {1 + 2r} \right)}}}$$

(16)

The principle of equivalent plastic work for plane stress condition is defined as:

$$\bar \sigma d\bar \varepsilon = {\sigma_1}d{\varepsilon_1} + {\sigma_2}d{\varepsilon_2}$$

(17)

The ${\raise0.7ex\hbox{${d\bar \varepsilon }$} \!\mathord{\left/ {\vphantom {{d\bar \varepsilon } {d{\varepsilon_1}}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${d{\varepsilon_1}}$}}$ can be derived as:

$$\frac{d\bar \varepsilon }{{d{\varepsilon_1}}} = \sqrt {\frac{{2\left( {2 + r} \right)\left( {1 + r} \right)}}{{3\left( {1 + 2r} \right)}}}$$

(18)