Strain hardening effect on ductile tearing under small scale yielding plane strain conditions

Abstract

The effect of strain-hardening on ductile crack growth is explored based on a small scale yielding finite element approach using an advanced nonlocal Gurson model. A focus is put on considering high strain hardening exponent $n$ up to 0.5, while classical literature is often limited to $n=0.2$, in order to encompass materials like stainless steels as well as several modern TRIP-TWIP alloys and high entropy alloys. First, $J_2$ plasticity-based simulations are performed to set the static crack reference. These simulations provide a hint about the origin of the increase of fracture toughness with increasing $n$, connected to much smaller finite strain zones at a given loading level quantified by the value of the $J$ integral. In addition, it is found that above $n\sim 0.3$, the opening stress does not attain a maximum value at a distance equal to one to two crack openings but keeps increasing towards the surface of the blunted crack tip. Then, Gurson-based simulations are used to determine the $J_R$ curve for different $n$ and initial porosity, and associated quantities related to crack initiation such as $J_{Ic}$, critical crack tip opening displacement ${\delta }_c$, and fracture process zone length. As already found in earlier studies, both $J_{Ic}$ and ${\delta }_c$ increase with increasing $n$, although the effect is much more marked on $J_{Ic}$. The origin of this first-order effect is unraveled by looking at the stress triaxiality, damage, and plastic strain fields. Even though the near crack tip stress triaxiality increases with $n$, the associated lower plastic strain at a fixed distance to the crack front leads to much lower void growth rates and delays void coalescence. As a important side result, the simulations appear very sensitive to an accurate fine-tuning of the adjustment factors entering the Gurson model at high strain hardening, pointing towards the intrinsic limitations of the model when $n$ is large. This study confirms the interest in developing alloys with large strain hardening capacity, not only with respect to tensile properties but also in view of enhancing the ductile fracture toughness.