The Role of Fracture Properties on Lap Joint Strength of Friction Stir Welded AA7055-T6 Sheets

Abstract

Friction stir lap welded (FSLW) joints have weight-saving potential in aluminum-intensive automotive assembly. However, friction stir welding (FSW) also modifies the material microstructure close to the joint. Optimizing the FSLW joint strength requires understanding the relationship between the strength and the joint’s local properties or microstructure. In previous studies, efforts have been dedicated to determining the effects of local softening, the shape of the oxide line, and porosity. However, the role of changes in fracture properties on the joint’s strength has not been studied. In this work, fracture test procedures to characterize the fracture properties within the weld were proposed. The data from these fracture tests has been utilized to calibrate the parameters of the Gurson-tvergard-needleman (GTN) damage model within finite element analysis simulations. Using the weld fracture data, the simulation of a 3-sheet (aluminum alloys 7055–7055-6022) FSLW joint successfully predicted the lap shear strength to be within 10% of the experimental value. Comparison with strength prediction using only the base metal properties indicates that fracture property in the nugget region is crucial in determining the strength of AA7055 FSLW joints.

Appendix

Gurson-Tvergard-Needleman (GTN) Damage Model

The yield condition in the Gurson-Tvergard-Needleman (GTN) damage model [24] is given as

$$ {\Phi } = \left( {\frac{q}{{\sigma_{y} }}} \right)^{2} + 2q_{1} f^{*} \cosh \left( { - q_{2} \frac{3p}{{2\sigma_{y} }} } \right) - \left( {1 + q_{3} f^{*2} } \right) = 0, $$

(A1)

where $q$ is the effective mises stress, $p$ is the hydrostatic pressure, $\sigma_{y}$ is the yield stress of the fully dense matrix material as a function of the equivalent plastic strain, and $q_{1} ,q_{2} ,{\& } q_{3}$ are material parameters. $f^{*} \left( f \right)$ is a function of the void volume fraction $f$ used to model the loss of stress-carrying capacity accompanying void coalescence, and it is defined as

$$ f^{*} = \left\{ {\begin{array}{*{20}l} f \hfill & {{\text{if}} f \le f_{c} } \hfill \\ {f_{c} + \frac{{\overline{f}_{F} - f_{c} }}{{f_{F} - f_{c} }}\left( {f - f_{c} } \right)} \hfill & {{\text{if}} f_{c} < f < f_{F} } \hfill \\ {\overline{f}_{F} } \hfill & {{\text{if}} f \ge f_{F} } \hfill \\ \end{array} ,} \right. $$

(A2)

where $\overline{f}_{F} = \frac{{q_{1} + \sqrt {q_{1}^{2} - q_{3} } }}{{q_{3} }}$. In Eq. A2, $f_{F}$ is the void volume fraction beyond which the material fails to carry any load and $f_{c}$ is the critical value of the void volume fraction. The change in void volume fraction $\dot{f}$ is

$$ \dot{f} = \dot{f}_{N} + \dot{f}_{G} , $$

(A3)

where $\dot{f}_{N}$ is the change due to void nucleation and $\dot{f}_{G}$ is the change due to void growth. These two kinds of change in void volume fraction are defined as

$$ \begin{aligned} \dot{f}_{G} = & \left( {1 - f} \right)\mathop \sum \limits_{k = 1}^{3} \dot{\varepsilon }_{kk}^{pl} , \\ \dot{f}_{N} = & A\dot{\varepsilon }_{{{\text{eff}}}}^{{{\text{pl}}}} , \\ \end{aligned} $$

(A4)

where $\dot{\varepsilon }_{{{\text{kk}}}}^{{{\text{pl}}}}$ denotes the diagonal components of the plastic strain rate matrix and $\dot{\varepsilon }_{{{\text{eff}}}}^{{{\text{pl}}}}$ denotes the effective plastic strain rate. $A$ is a proportionality constant that is defined as

$$ A = \frac{{f_{N} }}{{s_{N} \sqrt {2\pi } }}\exp \left( { - \frac{1}{2}\left( {\frac{{\varepsilon_{{{\text{eff}}}}^{p} - \varepsilon_{N} }}{{s_{N} }}} \right)^{2} } \right), $$

(A5)

where $f_{N}$ is the volume fraction of the nucleating voids, $\varepsilon_{N}$ is the mean nucleation strain and $s_{N}$ is the standard deviation of the nucleation strain. All these three constants are material parameters.

In total, the GTN model has nine material parameters. Some of these parameter values were taken from the literature. For instance, $q_{1} ,q_{2} ,\& q_{3}$ were set to be 1.5, 1 & 2.25, respectively [25]. The initial void volume fraction $f$ is assumed to be zero, and $s_{N}$ is assumed to be equal to $\varepsilon_{N}$. The rest of the parameters, $f_{N} ,\varepsilon_{N} ,f_{c} {\text{and }}f_{F}$ are to be determined from calibration to the test data.