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

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

Crater formation dynamics in long rod (or jet) penetration

Szendrei (and others) proposed a model for the dynamics of crater formation in long rod or jet penetration. We ran computer simulations, with AUTODYN2D/Euler, of a strength-less tungsten long rod penetrating an RHA steel target, to check the performance of Szendrei's model. From the simulations, and by comparing simulations to the model, we draw the following conclusions : 1. The basic assumption behind the model that the crater grows radially from the projectile boundary is simplistic. Simulations show that material points on the crater boundary originate from the initial projectile/target interface. 2. Simulations do not confirm the crater dynamics implied by the model. In the model, the crater starts growing at a high velocity that monotonically decreases to zero. In simulations, the radial velocity starts at a low value, reaches a maximum and then decreases asymptotically to zero. 3. The model prediction of the final crater radius underestimates simulation results quite substantially

Simulating rate dependent spalling with an overstress model

It has been known for a long time that spalling (dynamic tensile failure) is a rate dependent process. Spall strength of metals is determined from the pullback velocity of the free surface velocity history in planar impact spalling tests. Conducting these tests for different volume strain rates in the tension zone, it was established that spall strength increases with strain-rate according to a power law: Strengthspall = A∗(rate)m, where the power m is a small number compared to unity. Nevertheless, standard spall models in commercial and propriety hydrocodes use constant spall strength, and are not able to predict the rate dependence. We propose here a rate dependent spalling model which is based on the overstress concept. In a constant spall strength model, when the negative pressure reaches the negative spall-strength value, pressure is put to zero within a single time step. In our rate dependent model we allow the negative pressure to go above the current negative spall-strength according to specified rate coefficients (calibrated from tests), while the negative pressure is decreased proportional to the amount of overstress above the current negative strength value. We calibrate our rate coefficients according to experimental data for a Stainless Steel and demonstrate how the model works using a 1D hydrocode for planar impacts with different strain rates in the tension zone

A simple model for dynamic shear failure of stainless steel

We propose a simple model to reproduce ductile failure by shear localization in simulations of perforations tests. The model incorporates a positive feedback process of shear strain localization which results in a catastrophic decrease of flow stress. We use the model for perforation tests with 304L stainless steel. It succeeds in reproducing perforation thresholds as well as qualitative features of the perforation process, including shear band formation in some of the projectiles

Simulating rate dependent spalling with an overstress model

It has been known for a long time that spalling (dynamic tensile failure) is a rate dependent process. Spall strength of metals is determined from the pullback velocity of the free surface velocity history in planar impact spalling tests. Conducting these tests for different volume strain rates in the tension zone, it was established that spall strength increases with strain-rate according to a power law: Strengthspall = A∗(rate)m, where the power m is a small number compared to unity. Nevertheless, standard spall models in commercial and propriety hydrocodes use constant spall strength, and are not able to predict the rate dependence. We propose here a rate dependent spalling model which is based on the overstress concept. In a constant spall strength model, when the negative pressure reaches the negative spall-strength value, pressure is put to zero within a single time step. In our rate dependent model we allow the negative pressure to go above the current negative spall-strength according to specified rate coefficients (calibrated from tests), while the negative pressure is decreased proportional to the amount of overstress above the current negative strength value. We calibrate our rate coefficients according to experimental data for a Stainless Steel and demonstrate how the model works using a 1D hydrocode for planar impacts with different strain rates in the tension zone