International Journal of Fracture 56: 209-231, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands. 209 A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel M. JHA 1 and R. NARASIMHAN 2 i Warhead Group, ARDE, Pune 411021, India; 2 Mechanical Engineerin9 Department, IISc Bangalore 560012, India Received 1 July 1990; accepted in revised form 30 October 1991 Abstract. In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, Jn, at this time, compare reasonably well with experiments.This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever Jd increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J,~. The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail. I. Introduction Dynamic fracture initiation occurs under rapidly varying loads such as that produced by impact or explosive detonation. In such situations, the loading rates (measured in terms of the stress intensity rate /() are much higher (more than 104 times) than in a conventional quasi-static fracture test [1]. For many metallic materials, the dynamic fracture toughness Kid depends strongly on /( (see, for example, the experimental results given in [2, 3]). There are several factors that can influence the functional dependence of Kid on /£ [2-4]. These include rate sensitivity, adiabatic heating near the crack tip, and most importantly, the dominant failure mechanism. Dynamic fracture can occur on the micro-scale by nucleation, growth and coalescence of voids (ductile failure) or due to coalescence of planar micro cracks (brittle failure) [I]. In a recent study, Zehnder et al. [5] have performed drop-weight impact tests with three-point bend specimens of 4340 steel. The specimens used in these experiments were 1 cm thick and impact speeds of 5 m/s and 10 m/s were employed. The fracture surface of the broken specimens (see photograph Fig. 9 in [5]) shows that considerable crack tunneling occurs in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments (portion between the tunneled core and the free surfaces) happens because of formation of shear lips which are inclined at 45 ° to the free surfaces. The tunneled region is a fibrous, flat-fracture zone near the center-plane of the specimen, which has the shape of a thumb-nail and is about 0.6 cm in length. It is characterized by the ductile failure mechanisms of micro-void nucleation and growth. Based on optical measure- ments near the crack tip, Zehnder et al. [5] have estimated the times at which tunneling and gross fracture initiation (on the free surfaces) occurred in their experiments. For an impact test