Interaction of the Portevin–Le Chatelier phenomenon with ductile fracture of a thin aluminum CT specimen: experiments and simulations

Abstract

An attempt is made here to capture numerically slant ductile fracture and its early slant strain precursors via combining a dynamic strain aging (DSA) model with ductile damage models. In recent experimental studies it has been shown that in an AA2XXX alloy strain localization in slant bands preceded the onset of damage, originating slant fracture ahead of a notch. Here tensile tests are performed at different strain rates revealing some negative strain rate sensitivity which is an indication of DSA effect for AA2198-T8. A McCormick-type DSA model in conjunction with a Rousselier damage model, a reduced polycrystalline plasticity model and a Coulomb fracture criterion for slip systems have been used. Full 3D finite element simulations using this model and typical parameters for aluminum alloys capture the early strain localization in slanted bands, their intermittent activity and the final slant fracture. Prior simulation results without the DSA model and others using the von Mises plasticity or the GTN model did not capture the early slant strain localization thereby suggesting that DSA may well be the physical origin of the early slant strain localization and final slant fracture phenomena in this alloy.

Appendices

Appendix 1

Smaller values $P_1=40$ and 30 MPa have been investigated using the coarse mesh, with $\omega ~=$ 0.0005–0.0003 and 0.0001, respectively (the calculations diverge early for smaller values of $\omega$). The parameter R is increased from 101 to 141 and 151 MPa (same $R+P_1$), respectively, to account for the smaller PLC amplitudes $P_1$. Although they assume completely pinned dislocations, these corrections approximately give the same load levels in Fig. 18 up to $\hbox {Uy}\sim 0.580~\hbox {mm}$. Therefore, the damage models (porous plasticity and mainly the Coulomb fracture criterion which is very sensitive to the stress level) are not much impacted and the crack growth is almost the same. Note that for $\omega =0.0003$ and 0.0001 (pink and red curve), the maximum time step had to be reduced (from $\Delta t = 1$ s to $\Delta t = 0.1~\hbox {s}$) to catch the sharp variations of the aging time, Eq. (7). With this small time increment, the CPU time already is 24 days for the coarse mesh. (The clock time is 13.5 days with two cores. It is not significantly reduced with 4 or 8 cores.) Although the coarse mesh only gives poor images of the strain rate band patterns, fine mesh calculations have not been attempted with these small values of the $\omega$ parameter.

Small load decreases are obtained for $P_1=30\,\hbox {MPa}$ and $\omega = 0.0001$ (red curve in Fig. 18). For example, the load decreases from 1.0551 to 1.0531 kN for Uy $=$ 0.4129 to Uy $=$ 0.4139 mm. Four or five crossing incremental PLC bands can be guessed in the L-section $x=37$ mm, from Uy $=$ 0.4115 to Uy $=$ 0.4145 mm, although they are smeared by the coarse mesh (left inset in Fig. 18). The band pattern and spacing are similar to the ones in Fig. 13. In these bands, the von Mises equivalent strain rate in the 0.4129–0.4139 interval is approximately $0.004~\hbox {s}^{-1}$ in a few integration points of the L-section; it is about twice the average value in the full thickness. At Uy $=$ 0.4127 and 0.4130 mm, two additional integration points are broken in the lower T-section $\hbox {y}<0$ (left inset in Fig. 18), forming a small “triangular” crack with the prior six broken points at the notch tip. (The configuration is the same in the upper T-section $\hbox {y}>0$.) There are no other “broken point events” in the large interval from Uy $=$ 0.3878 to Uy $=$ 0.4544 mm. It shows that the intermittent PLC bands and the broken point events are strongly related also for $P_1=30~\hbox {MPa}$ and $\omega = 0.0001$. The load decreases because of simultaneous ductile damage (microvoids and/or microcracks, crack propagation) and DSA softening (dislocation unpinning) tentatively modeled by the porous plasticity, Coulomb fracture and KEMC models, respectively.

Fig. 19

Fine MESH 2 calculation, J versus $\Delta$a_max (red curve) and J versus COD (black curve)

Appendix 2

In the J-$\Delta$a curve of Fig. 19, J is computed from the numerical load–displacement curve, according to ASTM1820 standard. Maximum crack growth length $\Delta \hbox {a}_{\mathrm{max}}$ is measured in the deformed geometry by taking the position of the farthest broken integration point in the fine mesh flat crack. The stepwise curve is due to the incremental crack propagation in FE simulations. The variation of J versus crack opening displacement (COD $=$ 2 Uy $=$ time/500) is also shown in Fig. 19. It can be noticed that the J-COD curve shows some oscillations after 0.6 mm. It corresponds to the oscillations in the load–displacement curve of Fig. 12. (These oscillations are not representative of the PLC effect because of the large maximum time step $\Delta \hbox {t}=1$ s in the fine mesh simulations. Also, $\Delta \hbox {a}_{\mathrm{max}}$ is not representative of the complex crack growth shape that can be seen for example in Fig. 17b. The present numerical J-$\Delta$a curve is given for information purposes only.)