Modeling Bauschingher's effect in planar impact

Bauschinger's effect (BE) was first noticed as a decrease in yield stress upon unloading from a plastic state in standard tension-compression tests. It was later established that BE is quite general in terms of materials and modes of loading. Generalizing, BE may be regarded as anisotropic plasticity (in stress space) caused by the plastic flow itself. BE was extensively researched as part of an ongoing effort to understand and model cyclic plasticity. Cyclic plasticity models are based on the concept of kinematic hardening, are usually very complex, and contain many material parameters to be calibrated from tests. Here we're concerned with modeling BE in dynamic situations, specifically planar impact tests. In these tests BE is manifested by the so called Quasi-Elastic (QE) response upon unloading from the shock plateau level. Our approach is based on ideas put forward since the 1930s. First we show that our model, which we call Effective Grains Model (EGM), can reproduce the main modes of response in the plastic range, including BE. Then we apply it to planar impact tests and show that it can reproduce the QE response

Calibrating a material model for AD995 alumina from plate impact VISAR profiles

Nous présentons une validation/calibration d'un modèle de matériau pour l'alumina AD995. Nous utilisons les résultats de cinq expériences d'impact de plaques symétrique menées par Grady [1], désignées CE 56 à 60. Notre modèle de matériau est semblable à celeu employé par Johnson et Holmquist [5]. Il a une courbe de rupture fragile pour le matériau sans endommagement, et une courbe d'écoulement pour le matériau ruiné (granuleux). La réponse iriscoplastique de matériau endommagé aux contraintes de cisaillement, au de la courbe d'écoulement quasistatique, est maxwellienne. Nous calibrons la réponse viscoplastique pour correspondre au test CE 58, puis vérifions la validité du modèle de matériau, en prédisant les résultats pour les quatre autres tests. Un assez bon accord est obtenu.We present a validation/calibration of a material model for AD995 alumina. We use five of Grady's symmetric impact test data designated CE56 to CE60. Our material model is similar to that employed by Johnson and Holmquist [5]. It has a fracture surface for the intact material, and a flow surface for the fractured (granular-like) material. The viscoplastic response of the fractured material to shear stresses beyond the quasistatic yield surface is Maxwellian. We calibrate the viscoplastic response to match test CE58, and then check the validity of the material model by predicting the results for the four other tests. Agreement is quite good

Modeling stress upturn at high strain rates for ductile materials

Ductile materials (mainly metals) exhibit a sharp upturn of stress at strain rates around 103 to 104/s, which is not specific to a certain type of material. It is important to consider stress high rate upturn when dealing with high rate loading, such as shock loading and unloading. Using classical strength models, usually calibrated at not so high rates, may lead to errors with high rate loading and not so high pressures. Here we model high rate upturn on the macroscale. We assume that the upturn mechanism is also responsible for the 4th power law mechanism put forward by Swegle and Grady. In the past we calibrated our overstress dynamic viscoplasticity model for aluminium from 4th power law data. Here we use this calibration to predict the high rate stress upturn

Overstress and flowstress approaches to dynamic viscoplasticity

Viscoplasticity is mostly modelled by the flowstress approach, where the flowstress (Y) is a function of pressure, temperature, plastic strain and strain rate Y(P,T, εp, ε̇). For dynamic Viscoplasticity the flowstress approach is used in hydrocodes together with the radial return algorithm, to determine deviatoric stress components in each computational cell and for each time step. The flowstress approach assumes that during plastic loading, the flowstress in stress space follows the current stress point (current Y). Unloading of a computational cell is therefore always elastic. The overstress approach to dynamic viscoplasticity was used in various versions in the 1950s and early 1960s, before the advent of hydrocodes. By the overstress approach a state point may move out of the quasistatic flow surface upon loading, and hence the term overstress. When this happens, the state point tends to fall back (or relax) onto the quasistatic flow surface through plastic flow, and the rate of this relaxation is an increasing function of the amount of overstress. In the paper we first outline in detail how these two approaches to dynamic viscoplasticity work, and then show an example for which the overstress approach has an advantage over the flowstress approach. The example has to do with elastic precursor decay in planar impact, and with the phenomenon of anomalous thermal strengthening, revealed recently in planar impact tests. The overstress approach has an advantage whenever plastic flow during unloading is of importance

Acceleration of the plates of an ERA cassette using a rigid plastic Gurney model

An Explosive Reactive Annor (ERA) cassette is a sandwich of an explosive layer between two steel plates. To assess the performance of an ERA cassette against a shaped charge metal jet, we need to estimate the velocity and shape of the moving plates interacting with the jet. This is usually done with the classical Gurney model or by computer simulation. The Gurney model assumes that the accelerated plates are rigid, and is able to predict their final velocity quite accurately. But tests and computer simulations show that because of their plasticity, the plates become curved as they accelerate. In this paper we revisit Gurney's derivation and extend it to include the plasticity of the plates. We assume that the plates are rigid-plastic and we model the symmetric case as well as the asymmetric case. To check the model we perform computer simulations with AUTODYN for the same two problems. We find a fair agreement between the model predictions and the computer simulation results

Revisiting the L/D effect at high L/D

Previous computer simulations of the L/D effect (L/D = projectile aspect ratio) demonstrated that reduction in penetration efficiency at large L/D should be explainable within the framework of plasto-dynamic theory. But those simulations did not show what could be the mechanism responsible for penetration velocity deceleration and the reduction in penetration efficiency. Based on computational work that we did some years ago, we assume that the deceleration mechanism has to do with accumulation of projectile material at the bottom of the crater, and that this mechanism is controlled by the flow stress of the projectile (Yp). We conducted four simulations in which we changed Yp from 1.0 to 2.5 GPa. From the results we draw several conclusions. 1. The penetration velocity deceleration rate is proportional to Yp. 2. The deceleration mechanism seems to be caused by projectile material accumulation at the bottom of the crater. 3. We've not shown this, but it seems that projectile material accumulation and penetration velocity deceleration would decrease when Do/D increases (where Dc = crater diameter). 4. Looking at material location plots, we see that after a long time, material flow near the bottom of the crater becomes somewhat unstable. This would indicate that rods with L/D>40 may become inefficient, unless they are shot at velocities of 2 km/s or higher

Surface-burn model for shock initiation

An investigation of a surface-burn of the shock-induced decomposition initiation and detonation of heterogeneous explosives is described. The model assumes a microscale process with hot spots ignited by viscoplastic heating at the boundaries of collapsing pores. A relatively thin reaction zone, or burn surface, is driven by the conduction of the heat of reaction, and has a surface-burn velocity with an Arrhenius dependence on the temperature of the unreacted solid component. Global reaction rates are derived from the microscale model with an empirical burning topology function and a macroscopic reactant-product mixture defined by pressure equilibrium, ideal mixing of specific volume and internal energy,and isentropic response of the unreacted constituents. With simplifying assumptions, the model is extended to treat multi-component explosives. The model is implemented into a method of characteristics hydrocode and shown to be effective in simulating several examples of initiation experiments on TATB explosives. 10 refs., 9 figs