A comparative study of the dynamic fragmentation of non-linear elastic and elasto-plastic rings: The roles of stored elastic energy and plastic dissipation

Abstract

We develop a comparative analysis of the processes of dynamic necking and fragmentation in elasto-plastic and hyperelastic ductile rings subjected to rapid radial expansion. For that purpose, finite element simulations have been carried out using the commercial code ABAQUS/Explicit. Expanding velocities which range between 25 m/s and 600 m/s have been investigated. The elasto-plastic material and the hyperelastic material are modelled with constitutive equations which provide nearly the same stress-strain response during monotonic uniaxial tensile loading, and fracture is assumed to occur at the same level of deformation energy. The computations have revealed that, while the number of necks nucleated in the elasto-plastic and hyperelastic rings is similar, the mechanisms which control their development are significantly different. In the elasto-plastic rings several necks are arrested due to the stress waves which travel the specimen after the localization process has started, and thus the number of fractures in the ring is significantly lower than the number of incepted necks. On the contrary, these stress waves do not stop the development of any neck in the hyperelastic rings. The elastic energy released from the sections of the ring which are unloading during the localization process fuels the development of the necks. Hence, for the whole range of investigated velocities, the proportion of necks that develop into fracture sites is much greater for the hyperelastic rings than for the elasto-plastic ones. The comparison between the numerical results obtained for both materials brings to light the roles of elastic unloading and plastic dissipation in multiple necking and fragmentation processes.

Finite element analysis to determine the role of porosity in dynamic localization and fragmentation: Application to porous microstructures obtained from additively manufactured materials

“…Similar specimen dimensions were used in the ring expansion experiments performed by Zhang and Ravi-Chandar (2006). The loading condition is a radial velocity, V r , applied in the inner surface of the ring which remains constant throughout the entire analysis (Rusinek and Zaera, 2007; Vadillo et al, 2012; Rodríguez-Martínez et al, 2013b;Vaz-Romero et al, 2019). The initial condition is a radial velocity of the same value V (t = 0) = V r applied to all the nodes of the finite element mesh (Vaz-Romero et al, 2019;Marvi-Mashhadi and Rodríguez-Martínez, 2020).…”

Multiple necking patterns in elasto-plastic rings subjected to rapid radial expansion: The effect of random distributions of geometric imperfections

“…In order to obtain statistically significant results, for each number of imperfections, the computations have been run with five random distributions of imperfection wavelengths (as mentioned in Section 2). We have also performed calculations with N = 0 for which, in absence of geometric defects, the necking pattern is triggered by the numerical perturbations introduced by the software [34,32,42].…”

“…If theε p −P curve is shifted upwards with increasing time (e.g., the dashed green curve t = 69 µs is above the solid red curve t = 55 µs) is that the equivalent plastic strainε p has increased more than the background strainε p b at the corresponding material point, which indicates the development of the localization process. Similarly, if increasing the loading time shifts theε p −P curve downwards (e.g., the dashed green curve is below the solid red curve) is that the material is unloading elastically (see also Vaz-Romero et al [42]). For t = 5 µs the normalized equivalent plastic strain is virtually constant (the fluctuations of the equivalent strain are not noticeable in the graph), meaning that the strain field in the specimen is largely homogeneous and localization has not occurred yet.…”

“…3 display a succession of peaks and valleys. Similarly to N'souglo et al [30] and Vaz-Romero et al [42], we consider that necks are all the excursions of strain that fulfill the conditionε p = 1.1 when the maximum value ofε p reaches ≈ 2.5.…”

“…approximates the background equivalent strain in the ring (the background strain corresponds to the fundamental solution of the problem in absence of imperfections and before necking localization [42]). Therefore, before the necking pattern is formed, the normalized equivalent plastic strain is ≈ 1.…”