Finite element analysis of AISI 304 steel sheets subjected to dynamic tension: The effects of martensitic transformation and plastic strain development on flow localization

Abstract

b s t r a c tThe paper presents a finite element study of the dynamic necking formation and energy absorption in AISI 304 steel sheets. The analysis emphasizes the effects of strain induced martensitic transformation (SIMT) and plastic strain development on flow localization and sample ductility. The material behavior is described by a constitutive model proposed by the authors which includes the SIMT at high strain rates. The process of martensitic transformation is alternatively switched on and off in the simulations in order to highlight its effect on the necking inception. Two different initial conditions have been applied: specimen at rest which is representative of a regular dynamic tensile test, and specimen with a prescribed initial velocity field in the gauge which minimizes longitudinal plastic wave propagation in the tensile specimen. Plastic waves are found to be responsible for a shift in the neck location, may also mask the actual constitutive performance of the material, hiding the expected increase in ductility and energy absorption linked to the improved strain hardening effect of martensitic transformation. On the contrary, initializing the velocity field leads to a symmetric necking pattern of the kind described in theoretical works, which reveals the actual material behavior. Finally the analysis shows that in absence of plastic waves, and under high loading rates, the SIMT may not further increase the material ductility.

Dynamic necking in materials with strain induced martensitic transformation

“…Actually, at high deformation rates, inertia may take the dominant role in stabilizing the material, on top of the hardening effects. As reported in the theoretical work by Rodríguez-Martínez et al (2013a), at high loading rates, a strong strain hardening may not provide the expected material ductility increase. The cause of this behavior, specifically observed in steels showing SIMT, requires further analysis.…”

“…The perturbation becomes unstable when ReðηÞ 4 0. According to Rodríguez-Martínez et al (2013a) the perturbation growth η þ is assumed to represent the onset of diffuse necking. The term diffuse necking describes the stage of the loading process at which the local plastic flow deviates from the background value.…”

“…A mesh convergence study has been performed, and the time evolution of different critical output variables, namely stress, strain and necking inception, were compared against a measure of mesh density until the results converged satisfactorily. Neither geometrical nor material imperfections were introduced into the model, being the numerical round-off sufficient to perturb the stress and the strain fields (Rusinek and Zaera, 2007;Vadillo et al, 2012;Rodríguez-Martínez et al, 2013a). The imposed loading conditions can be formulated as V z ðr; L=2; tÞ ¼ _ ɛ 0 L 0 =2, V z ðr; 0; tÞ ¼ 0.…”

“…However, most energy absorbers are usually made up of materials that are (i) capable of keeping a high value of the stress upon deformation, and (ii) able to show a large value of strain at failure ɛ f , the second requirement being strongly dependent on the onset of necking which triggers material failure. Although necking and fracture are essentially different events, the first one is an early indication of ultimate structural failure and therefore it is commonly used as a reference for evaluating the energy absorption capacity (Rodríguez-Martínez et al, 2013a), combined with the fact that determination of the stress and strain states after necking presents some difficulties.…”

Investigation and Mechanical Modelling of Pure Molybdenum at High Strain-Rate and Temperature

“…In a lot of works the attention was focused on Zerilli-Armstrong model, but also more physically-based and micromechanical models were identified, usually by using data interpolation techniques. Differently from analytical approaches, the inverse procedure, as that it is proposed here, can be applied for the strength model calibration also in case of necking/instability up to fracture [17][18][19][20]: a Finite Element (FE) based approach allows to take into account the effect of the geometry changes during the necking phase. The stress versus strain curve after necking starts cannot be derived using nominal relation starting from engineering data: the stress state is no longer uniform and uniaxial as a consequence of the increased triaxiality which implies the logarithmic stress differs from the Von Mises stress.…”