Genetic effects of dynamic recrystallization on ductile fracture at elevated temperature for AA7075 alloy with various stress states: modeling and simulation

Abstract

Temperature and strain rate related dynamic recrystallization (DRX) and its inherited effects on ductile fracture have become an urgent issue which impede accurate prediction of fracture strain and restrict formability for 7075 aluminum alloy in hot deformation process. In order to precisely elaborate the ductile fracture behavior of 7075 aluminum alloy during hot forming process and accurately predict the initiation of ductile fracture, an extended ductile fracture criterion (DFC) at elevated temperature was established considering DRX effects and various stress states. The relationship between fracture strain and Z parameter is revealed in DRX and DRX-free region, respectively. It is noted that fracture strain decreases with the increasing Z parameter in DRX region, while Z parameter has little effect on the fracture behavior in DRX-free region. Consequently, the Z parameter embedded DRX model is introduced into the modified Mohr–Coulomb (MMC) DFC under distinct stress states at elevated temperatures for 7075 aluminum alloy. Based on the Abaqus/Explicit platform, the proposed ductile fracture model is implemented in finite element simulation via VUMAT. Hot forming of T-shaped parts is carried out, and the predicted fracture scenarios including damage evolution, volume fraction of DRX are validated by experimental results.

Appendix A. Z parameter calibration process

In order to determine the characteristic parameters of critical values and peaks applicable to all flow curves studied for 7075 aluminum alloy, a work hardening rate $\theta$ ($\theta =\partial \sigma /\partial \varepsilon$) $-\sigma$ curve should be plotted, shown in Fig. 27. The work hardening-stress curves at different temperatures and strain rate are shown in Fig. 28. Using the method proposed in the literature, ${\sigma }_{c}$ is determined as the second derivative of $\theta$ relative to $\sigma$, that is, the stress value when ${\partial }^{2}\theta /\partial {\sigma }^{2}$ is 0. The peak stress ${\sigma }_{p}$ is defined as the point at $\theta =0$. Then, according to the stress–strain curve, the corresponding turning strain ${\varepsilon }_{c}$ and peak strain ${\sigma }_{p}$ are obtained.

Fig. 27

$\theta -\sigma$ schematic diagram

Fig. 28

Work hardening curves of 7075 under different conditions

The dynamic recovery softening coefficient $\Omega$ is solved by the equation for the work hardening-dynamic recovery stage before the transition strain:

$${\sigma }_{WH}={\left[{\sigma }_{s}^{2}+\left({\sigma }_{0}^{2}-{\sigma }_{s}^{2}\right){e}^{-\Omega \varepsilon }\right]}^{0.5},\varepsilon <{\varepsilon }_{c}$$

(A.1)

Starting from Eq. (A.1), the $\mathrm{ln}\Omega -\mathrm{ln}Z$ relationship diagram is drawn as shown in Fig. 29, and the data in Fig. 29 is fitted, then the mathematical model of $\Omega$ can be determined as:

$$\Omega =14.4846{Z}^{-0.02851}$$

(A.2)

Fig. 29

$\ln\Omega - \ln Z$ schematic diagram

The dynamic recrystallization percentage ${X}_{drx}$ is usually expressed as:

$${X}_{drx}=1-\mathit{exp}\left[{k}_{d}{\left(\frac{\varepsilon -{\varepsilon }_{c}}{{\varepsilon }_{p}}\right)}^{{n}_{d}}\right]$$

(A.3)

where ${X}_{drx}$ is the recrystallization volume fraction, ${k}_{d}$ and ${n}_{d}$ are constants, ${\varepsilon }_{c}$ is the critical strain, and ${\varepsilon }_{p}$ is the peak strain. By fitting the experimentally obtained $\mathit{ln}\left(-\mathit{ln}\left(1-{X}_{drx}\right)\right)$ and $ln(\varepsilon -{\varepsilon }_{c}/{\varepsilon }_{p})$, the values of ${k}_{d}$ and ${n}_{d}$ can be determined: ${k}_{d}$=$-$ 0.1906, ${n}_{d}$=1.6121.