Dynamic Cavity Expansion Research Articles

Optimization analysis of state equation and failure criterion for concrete slab subjected to impact loading

Concrete slabs are typically subjected to impact loading, and the selection of the equations of state and failure criteria has significant effects on the dynamic mechanical behavior of concrete. One of the most commonly adopted impact loading is projectile impact. In this study, the optimization analysis of the equation of state and failure criterion for rigid projectile penetration, which are often available for theoretical models, were analyzed using regression evaluation methods. Subsequently, based on the analysis results, a multi-phase model for the penetration of rigid projectiles into concrete was established which combined with the dynamic cavity expansion theory. Finally, the prediction results of the proposed model were compared with existing experimental data and prediction results of existing penetration models. The results showed that the prediction model has a wide range of applicability and high accuracy.

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

High-speed penetration of cast Mg-6Gd-3Y-0.5Zr alloy: Experiments and modeling

Ballistic impact experiments are conducted on a cast Mg-6Gd-3Y-0.5Zr alloy using spherical projectiles under a wide range of impact velocities. Penetration processes are captured by high-speed camera. Postmortem target samples are characterized via three-dimensional laser scanning, metallographic microscopy, scanning electron microscopy and electron backscatter diffraction. Shear bands and twinning dominate the deformation of Mg-6Gd-3Y-0.5Zr near the crater, and texture changes due to compression caused by cavity expansion. For instance, a finite element model based on Johnson–Cook constitutive model and Mie–Grüneisen equation of state is established. Four dimensionless quantities related to craters and projectiles are defined. An analytical model based on dynamic cylindrical cavity expansion model is applied considering projectile deformation, and consistent well with experimental and simulated results over the entire incident velocity range.

Rate-Dependent Dynamic Cylindrical Cavity Expansion Equations for Conical- and Ogival-Nosed Projectiles

Rate-Dependent Dynamic Cylindrical Cavity Expansion Equations for Conical- and Ogival-Nosed Projectiles

Cavity expansion in nonlinear viscoelastic solids: A nonlinear dynamic study

Dynamic cavity expansion has been studied for hyperelastic materials since the work of Knowles and Jakub in 1965. It has recently drawn new attention for potential applications in measuring the mechanical properties of soft polymer or biological tissues. These soft materials, however, are intrinsically rate-dependent, and the study of dynamic cavitation in nonlinear viscoelastic solid is relatively scarce. In this article, we utilize the established two-potential nonlinear viscoelastic framework to study the cavity behavior in infinite solid. Differently, we further introduced the surface energy into account and pay extra attention to the oscillation of the cavity surface based on nonlinear dynamics. The cavity behavior and stress change under a monotonically increasing pressure, creep experiment, and relaxation experiment are investigated. Considering surface effects, we notice the cavity surface has an oscillation process of expansion and shrink before infinitely large expansion before rupture. The oscillation amplitude gradually diminishes with time due to the energy consumption of viscosity. Regarding the viscoelastic material as a system with diminishing shear modulus, we analyze the stability of the cavity surface and find it can be either a stable center point or an unstable saddle point. The results of this study are helpful for understanding the cavitation phenomenon in viscoelastic solids caused by dynamic loading.

Dynamic cavity-expansion penetration model of elastic-cracked-crushed response for reinforced-concrete targets

Herein, an improved dynamic cavity-expansion model for penetration of reinforced-concrete targets is proposed. The circumferential restriction effect derived from reinforcing bars in both the cracked and crushed regions has been considered in the proposed model, and the theoretical solutions for the cavity radial stress in compressible and incompressible reinforced concrete are obtained. Through the analysis of concrete strength and reinforcement ratio, we establish a simplified formula to calculate the penetration resistance of reinforced-concrete targets. Moreover, the calculation method of a direct impact resistance for the projectile on the reinforcing bars is developed, and thus, the engineering model for penetration of reinforced-concrete target is constructed. By comparing with the experimental data and empirical formula, the validity of this new model is further verified.

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.

A Dynamic expansion of a cylindrical cavity in a compressible elastic-plastic medium. The Analysis of medium resistance to dynamic penetration of a sharp-nosed impactor

This paper presents the solution of the problem related to the dynamic cylindrical cavity expansion in a compressible elastic-plastic medium. Finite strains, nonlinear compressibility and dependence of the yield stress versus pressure are taken into account in the problem formulation. The study targets at developing a new engineering model on the penetration of a sharp-nosed impactor in the range of middle impact velocities based on the problem analysis results of the cylindrical cavity expansion in a half-space (cylindrical cavity expansion approximation). Based on the analytical approach a model is obtained that determines the resistance of the medium to dynamic cavity expansion. The main parameters of the model depend on the mechanical properties of the medium. For these dependences we proposed approximating relations based on manipulation of the mechanical properties of a number of materials (some alloys and soils). To derive the dynamic penetration model the A.Ya. Sagomonyan assumption of the radial expansion of the hole is used. It is assumed that particles of the medium material move in a radial direction from the surface of the impactor penetrating into the shield. Such assumption can be applied for the class of impactors in the form of slender sharp-nosed bodies of revolution. Based on the assumptions we obtained a model of the medium resistance to the dynamic penetration of a slender sharp-nosed body of revolution. The new model, in addition to the "standard" strength and inertial components, contains the "attached mass", which changes during the penetration process. The experimental validation of the new penetration model using a series of experimental studies on the penetration of various forms of impactors into aluminum alloys is considered. The influence of the “attached mass” and inertial forces of the medium resistance to the penetration is estimated. The conditions of applicability of the new model are obtained: the penetration model is applicable for estimation of the resistance of a compressible medium to penetration of a thin sharp-nosed body of revolution at impact velocities of 200-800 m/s.

Theoretical Investigation on Failure Behavior of Ogive-Nose Projectile Subjected to Impact Loading.

Experimental and theoretical investigations on the failure behaviors of projectile during high-speed impact into concrete slabs were performed in this study. The ogive-nose projectiles after impact experiments were recovered and their microstructures were observed by scanning electron microscope and metallographic microscope. Mass abrasion and nose blunting are the typical failure models of steel projectile. Furthermore, thermal melting and cutting are the two main failure mechanisms. Based on the microscopic experimental results, a theoretical model of ogive-nose projectile subjected to impact loading considering the melting and cutting mechanisms was proposed. A modified cap model is introduced for describing the failure behavior of concrete targets, and then the dynamic cavity expansion theory is used to determine the resistance of projectiles during penetration. Besides, combining with the two-dimensional heat conduction equation and abrasive wear theory, the two main abrasion mechanisms of melting and cutting are included in the proposed model, which breaks through the framework of previous abrasion models with single abrasion mechanism. The predicted results of the present abrasion model are in good agreement with the experimental data, which indicates that the proposed model can effectively predict the failure behavior and penetration performance parameters of high-speed projectiles during penetration into concrete targets, such as mass loss, nose blunting, and depth of penetration.

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.

Rigid elliptical cross-section ogive-nose projectiles penetration into concrete targets

The elliptical cross-section ogive-nose projectile (ECOP) has recently attracted attention because it is well suited to the flattened shape of earth-penetrating weapons. However, the penetration performance of ECOPs has not been completely understood. The objective of this study was to investigate the penetration performance of ECOPs into concrete targets using a theoretical method. A general geometric model of ECOPs was introduced, and closed-form penetration equations were derived according to the dynamic cavity-expansion theory. The model was validated by comparing the predicted penetration depths with test data, and the maximum deviation was 15.8%. The increment in the penetration depth of the ECOP was evaluated using the proposed model, and the effect of the major–minor axis ratio on the increment was examined. Additionally, the mechanism of the penetration-depth increment was investigated with respect to the caliber radius head, axial stress, and resistance.

Penetration characteristics of pyramidal projectile into concrete target

The mechanisms governing penetration of pyramidal projectile into concrete medium were studied. The relationship of normal stress and normal velocity on the surface of the projectile nose was modified based on the assumption that the shape of the tunnel section is the same as that of the projectile. Then, in the low velocity range, a formula for predicting the final penetration depth of the pyramidal projectile is proposed, and the penetration ability of pyramidal projectiles with and without a shank is discussed. The results showed that the penetration depth decreases with the increasing side numbers of the projectile section shape, and the maximum depth of penetration corresponds to the triangular cross-section. In addition, the penetration processes of triangular and circular projectiles into concrete targets were simulated by employing the finite element software LS-DYNA. The Mises stress, tunnel shape, depth of penetration and velocity were investigated. It suggested the triangular projectile has a slight penetration advantage over the circular projectile when the penetration velocity is less than threshold velocity, and this advantage gradually disappears with the increase of impacting velocity. Finally, the shear weakening effect is used to explain the resistance characteristics of the triangular projectile in various velocity ranges, and a method to estimate the upper limit of threshold velocity is given by using the dynamic cavity expansion theory.

Modeling dynamic spherical cavity expansion in elasto-viscoplastic media

In this paper, we extend the dynamic spherical cavity expansion model for rate-independent materials developed by Durban and Masri (Int J Solids Struct 41(20):5697–5716, 2004), Masri and Durban (J Appl Mech 72(6):887–898, 2005), and Cohen et al. (J Appl Mech 77(4):041009, 2010) to viscoplastic media. For that purpose, we describe the material behavior with an isotropic Perzyna-type overstress formulation (Perzyna in Q Appl Math 20:321–332, 1963; Adv Appl Mech 9:243–377, 1966) in which the material rate dependence is controlled by the viscosity parameter $$\eta $$. The theoretical predictions of the cavity expansion model, which assumes that the cavity expands at constant velocity, are compared with finite element simulations performed in ABAQUS/Explicit (Abaqus Explicit v6.13 User’s Manual, ABAQUS Inc., Richmond). The agreement between theory and numerical simulations is excellent for the whole range of cavitation velocities investigated, and for different values of the parameter $$\eta $$. We show that, as opposed to the steady-state self-similar solutions obtained for rate-independent materials (Durban and Masri 2004; Masri and Durban 2005; Cohen et al. 2010), the material viscosity leads to time-dependent cavitation fields and stress relaxation as the cavity enlarges. In addition, we also show that the material viscosity facilitates to model the shock waves that emerge at the highest cavitation velocities investigated, controlling the amplitude and the width of the shock front.

Dynamic spherical cavity expansion analysis of concrete/rock based on Hoek-Brown criterion

Cavity expansion theory has been widely applied to predict the penetration depth of projectiles into geological materials, in which the yield criterion and the constitutive model are combined to describe the shear and compaction of the material, separately. For a precise description of the material behaviors in plastic for geological materials with varied compressive strength, in this present manuscript, the Hoek-Brown yield criterion and the Dilatant-Kinematic equation were introduced into the plastic region. A response region called elastic-cracking-dilatant-compaction region for concrete and rock was established. Then the effects of various parameters, including brittleness coefficient, material integrity coefficient and dilatant coefficient, on the relationship between cavity pressure and normal expansion velocity were discussed. Finally, a penetration depth formula of rigid projectiles into semi-infinite concrete and rock targets was established. It showed that, compared with the classical Forrestal model, the proposed model had a well-being as well as higher accuracy prediction of the penetration depth of concrete and rock materials with various strengths.

A rigid elliptical cross-sectional projectile with different geometrical characteristics penetration into concrete target

Elliptical cross-sectional projectiles have recently attracted attention because they fit the flattened shape of earth-penetrating weapons. This study aims to investigate a rigid elliptical cross-sectional projectile with different geometrical characteristics penetration into the semi-infinite concrete targets by implementing a theoretical method. The general geometric models of four types of elliptical cross-sectional projectiles are introduced; closed-form penetration equations are then derived based on the dynamic cavity-expansion theory. Furthermore, the present models are validated by comparing the predicted penetration depths with the predictions obtained using the semi-empirical formulae and test data; the maximum deviation from the test data is 15.8%. In addition, the deceleration, velocity, and displacement of the projectiles during the penetration process are obtained based on the present models, and the penetration performance of the four types of elliptical cross-sectional projectiles is discussed by comparing the penetration depths. The conical-nose elliptical cross-sectional projectile exhibits the best penetration performance than the other three types if the nose length is sufficiently large, and the ogive-nose elliptical cross-sectional projectile gradually exhibits its penetration performance advantage with the increase in the nose length.

Revising the penetration behavior of concrete-like and metal-like materials against the rigid projectile impact

Many studies indicate that projectile deceleration exhibits a quasi-constant behavior in the tunneling penetration stage of the rigid penetration mode for both metal-like and concrete-like materials. As to the issue, in the present paper the penetration process under the rigid penetration mode was revised, where a two-phase penetration theory is proposed including the ‘Squeeze and Push’ penetration phase and the dynamic spherical cavity expansion penetration phase. When the striking velocity is below the critical striking velocity, the ‘Squeeze and Push’ effect is generated since the cavitation size is less than the projectile diameter, where the quasi-static term overshadows the dynamic term. The interaction from the surface friction between projectile and target and the penetration force due to the main quasi-static term contributes to the occurrence of the quasi-constant phenomenon. Conversely, when the striking velocity is above the critical velocity, the penetration enters into the dynamic spherical cavity expansion penetration phase, the accompanying feature is that the tunnel becomes large beyond the projectile diameter, meanwhile the friction effect between the projectile and target disappears, the deceleration shows a well-defined peak with the rise of the striking velocity. Following the features, semi-empirical formulas are obtained. Finally, the semi-empirical formulae are discussed and validated by comparing with the typical penetration experiments including concrete-like and metal-like materials.

A nonlinear rate-dependent model for predicting the depth of penetration in ultra-high performance fiber reinforced concrete (UHPFRC)

Ultra-high performance fiber reinforced concrete (UHPFRC) is increasingly utilized in protective structures because of its ultra-high compressive strength and excellent toughness. Nevertheless, there is still a lack of model for predicting the depth of penetration (DOP) in UHPFRC against projectile penetrations. This study proposes an analytical predicting model for UHPFRC on the basis of the dynamic cavity expansion theory. The Hoek-Brown criterion is utilized to account for the nonlinear response of UHPFRC, and its rate dependency is also addressed in the model. The developed predicting model is validated against penetration experimental data, and its effectiveness is further compared with previous predicting formulae. The comparison results indicate that the proposed model can achieve more reasonable DOP predictions in UHPFRC targets. Finally, a number of influential parameters are discussed based on the proposed model. It is observed that the DOP is affected by the target compressive strength, while the tensile strength influences the cracked region radius. The developed DOP predicting model provides an accurate estimation of the UHPFRC impact resistance and promotes an effective approach to design UHPFRC protective structures.

Theoretical considerations on cavity diameters and penetration depths of concrete materials generated by shaped charge jets using the targets response modes described by a modified HJC model

The traditional dynamic cavity expansion theory generally deals with the problem of penetrator penetration into targets at lower velocity, which is considered that the materials near the penetrator/target interface are in the plastic state. For shaped charge jets penetration, the concrete materials in a certain distance away from the jet/target interface are in the fluid state. Thus, the radial stress at the cavity surface derived from the dynamic cavity expansion theory cannot be directly applied as the target resistance. The current paper aims to establish a theoretical model for shaped charge jets penetration into concrete targets based on the cavity expansion idea, assuming that the cavity expansion stress is the stress at the flow/fully dense interface. Firstly, the hydrostatic pressure-volume strain relationship described by the HJC concrete constitutive model was analyzed; result indicated that four response regions were produced when concrete subjected to load: the elastic region, the cracked region, the plastic-like (the “plastic” behavior of concrete is named as “plastic-like” since the behavior has nothing to do with the dislocation movement of metals that reflects the plastic behavior) transitional region and the fully dense region. The HJC yield surface equation was then modified by discussing the elastic-cracked-transitional-fully dense response in front of the flow/fully dense interface. With the changing particle velocity at the flow/fully dense interface, it showed that another three response modes were produced in front of the flow/fully dense interface, i.e., the elastic-transitional-fully dense response, the elastic-fully dense response, and the fully dense response. The applications of the equations of state in different response modes were analyzed. Secondly, the calculation model of the radial stress at the flow/fully dense interface was proposed based on the modified HJC model. Thirdly, the shaped charge jets penetration theories were analyzed. In the end, the depth of penetration (DOP) experiments for three different shaped charges into C200 reactive powder concrete (RPC) targets were carried out to verify the theoretical model. Results showed that the cavity diameters and penetration depths predicted by the elastic-cracked-transitional-fully dense response, the elastic-transitional-fully dense response and the elastic-fully dense response exhibited good agreement with the experimental data, whereas that by the fully dense response existed relatively large errors comparing with the other three response modes.

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.