Dynamic Cavity Expansion Model Research Articles

Inversion method of soil Mohr-Coulomb parameters based on dynamic cavity expansion model

Inversion method of soil Mohr-Coulomb parameters based on dynamic cavity expansion model

A novel dynamic cavity expansion model to predict the resistance of reactive powder concrete (RPC) against projectile impact

The dynamic cavity expansion (DCE) model is a commonly used analytical model to predict the resistance of concrete materials subjected to projectile impact. In this paper, a modified Griffith strength criterion was proposed for reactive powder concrete (RPC), which has a form easy to solve and can well capture the tensile, compressive and triaxial strength of RPC. Combined with the Murnaghan equation of state, the proposed strength criterion was used as the material model for RPC. The cavity expansion resistance was calculated numerically and analytically. It indicates that the numerical and analytical solutions are almost consistent under the same material response. Then, the strain softening behavior that cannot be resolved analytically was further introduced into the material model, and the numerical solution of the DCE model was obtained using LS-DYNA. To verify the present method, the 122.6 MPa RPC targets were tested using 14.5 mm diameter ogival nose projectiles at impact velocities of from 286 to 942 m/s. Combined with previous penetration model, the penetration depth of the present test was predicted. In addition, numerical simulation of this penetration test adopting the HJC model was also performed. It shows predictions of the present model are in good agreement with test and simulation results. Furthermore, the present model was used to predict the existing test date of RPCs with compressive strength of between 67.5 and 140 MPa, and the effectiveness of the present method was verified by comparing with predictions of previous empirical formulas.

A Dynamic Cavity Expansion Model for Rigid Projectile Penetration into Concrete considering the Compressibility and Nonlinear Constitutive Relations

The P-α equation of state (EOS) and a nonlinear yield criterion are utilized to characterize the dynamic constitutive behavior of concrete targets subjected to projectile normal penetration. A dynamic cavity expansion model considering the compressibility and nonlinear constitutive relations for concrete material is developed. Then, a theoretical model to calculate the depth of penetration (DOP) for rigid projectile is established. Furthermore, the proposed model is validated based on the available test data as well as the calculation results by the linear compressible EOS and linear yield criterion. This study shows that the proposed model derived using the P-α EOS and nonlinear yield criterion can effectively reflect the plastic mechanical properties of concrete and is also suitable for predicting the DOP of concrete targets. In addition, the influence law of concrete constitutive parameters such as the cohesion strength, shear strength, internal friction coefficient, and elastic limit pressure on the DOP is revealed.

The combined effect of size, inertia and porosity on the indentation response of ductile materials

Herein, we present a self-similar cavity expansion model that follows from the work of Cohen and Durban (2013b) to analyze the dynamic indentation response of elasto-plastic porous materials while accounting for the plastic strain gradient induced size effect. The incorporation of the plastic strain gradient induced size effect in the dynamic cavity expansion model for elasto-plastic porous materials is the key novelty of our model. The material hardness predicted using the cavity expansion model for a wide range of indentation depths and speeds is compared against the available experimental results for OFHC copper, for strain rates varying from 10−4s−1 to 108s−1. We note that despite several simplifying assumptions, the predictions of our cavity expansion model show a reasonable agreement with the experimentally measured material hardness over a wide range of indentation depths and speeds. In addition, we have also carried out parametric analysis to elucidate the specific roles of indentation speed, size effect and initial porosity, on the material hardness and cavitation fields that develop during the indentation process. In particular, our parametric analysis shows that there exists a critical value of the indentation speed beyond which the contribution of inertial effect becomes extremely important and the material hardness increases rapidly. While the influence of the initial porosity on the material hardness is found to increase with increasing indentation speed and decrease with increasing size effect.

Penetration resistance and the critical cavitation velocity for an ogive-nosed rigid projectile penetrating into a semi-infinite metallic target

This paper studies penetration resistance and projectile-target separation for an ogive-nosed rigid projectile penetrating into a metallic target. A prescribed normal velocity field is introduced to determine the contact stress on the projectile nose, based on which the dynamic equation of a rigid projectile is formulated. Projectile-target separation occurs when the impact velocity of the projectile is greater than the critical cavitation velocity according to Hill's cavitation criterion. Target material is assumed incompressible in both elastic and rigid, perfectly plastic regions in order to simplify the analyses. It shows that the penetration resistance derived from the prescribed velocity field has a different form from that based on the dynamic cavity expansion model. When the impact velocity is greater than the critical cavitation velocity, the projectile-target separation point moves further to the nose tip, leading to the reduction of the contact area between the projectile nose and the target and a large increase of the inertia term (velocity square term) in penetration resistance. The predicted penetration depth and critical cavitation velocity agree reasonably with experimental and numerical results.

Projectile penetration into mortar targets with a broad range of striking velocities: Test and analyses

Eighteen shots of flat nosed cylindrical 45# steel projectiles penetrating into mortar targets with cubic compressive strength of 50MPa are conducted, where the striking velocities are ranged from 510m/s to 1850m/s. By examining the damages of targets, linear dependences of the cratering diameter and depth on the initial striking velocity, as well as the cratering volume on the initial kinetic energy of projectile are found. Three penetration regimes, i.e., rigid projectile penetration, deforming projectile penetration without eroding and eroding projectile penetration are observed successively with the increase of striking velocity. Furthermore, the experimental depths of penetration are compared with the predictions of our recently established rigid and eroding penetration models based on an extended dynamic cavity expansion model (Kong et al. 2017). The rigid projectile penetration model is further validated, and the eroding projectile penetration model is further justified, improved and validated by considering the succeeding rigid penetration stage. Finally, the analytical expressions for the upper limit velocity of rigid projectile penetration and the lower limit velocity of eroding projectile penetration are given and validated, respectively.

Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model

A hyperbolic yield criterion and Murnaghan equation of state were introduced to describe the plastic behavior of concrete material under projectile penetration, and an extended dynamic cavity expansion model was proposed. Then, a unified one-dimensional resistance of concrete target to projectile penetration was formulated, in which the projectile nose shape influences were taken into account by three non-dimensional coefficients. Furthermore, combined with the Newton's second law and Alekseevskii-Tate equations, both rigid and eroding projectile penetration models into concrete targets were established. By comparing with the existing tests data as well as prediction results of previous model based on the linear yield criterion and equation of state, the proposed models were verified. Besides, a series of practical parameters of hyperbolic yield criterion and Murnaghan EOS for the extended dynamic cavity expansion model were given and verified.

Analyses of rigid projectile penetration into UHPCC target based on an improved dynamic cavity expansion model

Ultra-high performance cement based composite (UHPCC) has prominent projectile impact resistance. Aiming to theoretically predict the depth of penetration for rigid projectile penetrating UHPCC target, an improved dynamic cavity expansion model was proposed to describe the plastic behavior of UHPCC material under projectile penetration with a hyperbolic yield criterion and nonlinear equation of state (EOS). Then, combined with the Newton’s second law, rigid projectile penetration model into UHPCC target was established, which was verified by comparing with the previous penetration test data, classic empirical formula and prediction of previous cavity expansion model based on linear yield criterion and EOS. Besides, a series of practical parameters of the hyperbolic yield criterion and nonlinear EOS for the improved dynamic cavity expansion model were given and validated.

PENETRATION ANALYSIS OF ALUMINUM ALLOY FOAM

Aluminum alloy foam offers a unique combination of good characteristics, for example, low density, high strength and energy absorption. During penetration, the foam materials exhibit significant nonlinear deformation. The penetration of aluminum alloy foam struck transversely by cone-nosed projectiles has been theoretically investigated. The dynamic cavity-expansion model is used to study the penetration resistance of the projectiles, which can be taken as two parts. One is due to the elasto-plastic deformation of the aluminum alloy foam materials. The other is dynamic resistance force coming from the energy of the projectiles. The penetration resistance expression is derived and applied to analyze the penetration depth of cone-nosed projectiles into the aluminum alloy foam target. The effect of initial velocity, the geometry of the projectiles on the penetration depth is investigated.

On perforation of ductile metallic plates by blunt rigid projectile

Abstract In order to enhance the theoretical modeling of Chen and Li [Chen X.W., Li Q.M., 2003a. Shear plugging and perforation of ductile circular plates struck by a blunt projectile. Int. J. Impact Engng. 28 (5), 513–536], an intensive numerical study was performed on the perforation of ductile metallic plates by blunt rigid projectiles. The results of this numerical study agree with the modeling by Chen and Li [Chen X.W., Li Q.M., 2003a. Shear plugging and perforation of ductile circular plates struck by a blunt projectile. Int. J. Impact Engng. 28 (5), 513–536] and with the experimental observations of Borvik et al. [Borvik T., Langseth M., Hopperstad O.S., Malo K.A., 1999. Ballistic penetration of steel plates. Int. J. Impact Engng. 22, 855–886; Borvik T., Leinum J.R., Solberg J.K., Hopperstad O.S., Langseth M., 2001b. Observations on shear plug formation in Weldox 460E steel plates impacted by blunt-nosed projectiles. Int. J. Impact Engng. 25, 553–572; Borvik T., Hopperstad O.S., Langseth M., Malo K.A., 2003. Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates. Int. J. Impact Engng. 28 (4), 413–464]. The effect of target thickness on its ballistic performance is discussed by accounting for their structural response. Our study confirms the validity of the assumption of constant shear force during plugging perforation. In addition we show that the dynamic cavity expansion model is suitable for description of flat projectile impacting a thick plate, with lateral material flow.

Shear plugging and perforation of ductile circular plates struck by a blunt projectile

Shear plugging and perforation of ductile circular plates struck by a blunt rigid projectile is studied in the present paper. Effects of transverse shear, bending and membrane deformations on the perforation process are included in a rigid-plastic analysis while the local indentation/penetration is estimated using the dynamic cavity expansion model. Analytical formulae for the perforation ballistic limit and the residual velocity are obtained for a range of plate thickness, which agree with the available experimental results on the perforation of metallic plates.

Penetration Into Concrete Targets By A Hard Projectile

Two dimensionless numbers, termed impact function I and geometry function N, are introduced as dominant parameters to control the penetration depth into concrete targets subjected to a hard projectile impact [1,2]. A definition of nose shape factor is defined quantitatively to eliminate the vagueness of the nose shape deftitions in empirical formulae. A unified formula on penetration depth into concrete target, proposed based on dimensional analysis and dynamic cavity expansion model in [1,2] is applicable for a wide range of impact velocities, nose shapes and concrete strengths and reinforcements, The validity of the proposed penetration formula is verified through comparison with all major empirical formulae, e.g., modified NDRC, ACE, LJKAEA, and experimental results. There exists an upper limit of the rigid projectile assumption, beyond which, the penetration is dominated by semi-hydrodynamic regime. The proposed formula can also be extended to metallic and earth targets.

Deep penetration of a non-deformable projectile with different geometrical characteristics

A general non-dimensional formula based on the dynamic cavity-expansion model is proposed to predict penetration depth into several mediums subjected to a normal impact of a non-deformable projectile. The proposed formula depends on two dimensionless numbers and shows good agreement with penetration tests on metal, concrete and soil for a range of nose shapes and impact velocities. The validity of the formula requires that the penetration depth is larger than the projectile diameter and the projectile nose length while projectile remains rigid without noticeable deformation and damage.

A dynamic cavity expansion model for rocks

A dynamic cavity expansion model for rocks