Theoretical And Numerical Study On Failure Modes Of Metal Plates Under Normal Impact By Conical-Nosed Projectiles

A combined numerical and theoretical study is presented in this thesis to examine the penetration and perforation of ductile metal plates subjected to impact by conical-nosed projectiles.Failure modes of metal plates under normal impact by conical-nosed projectiles are discussed,and for different failure modes corresponding theoretical models are established to predict ballistic limits of the plates,residual velocities of the projectiles and perforation energies.Based on the analysis of critical conditions for the transition of different failure modes,a simplified failure (mechanism) diagram for metallic plates under normal impact by conical-nosed projectiles is proposed.Numerical simulations with ABAQUS/VUMAT in which a modified JC constitutive relation with damage is adopted are performed to study the influence of various parameters on the perforation behaviour of metal plates.The findings and conclusions of the investigations conducted in the thesis are helpful for the design of kenietic energy projectiles,protective structures and safety assessment. This paper mainly consists of the following parts:Analytical equations for the perforation of fully-clamped thin metallic plates are derived based on the assumption that plate deformation consists of local piercing as well as global response.Local piercing is analyzed by using quasi-static cylindrical cavity expansion theory with free surface effects whilst global deformation is evaluated by adopting the method employed in the Wen-Jones model.Simple analytical equations are obtained to predict the perforation energy and the ballistic limits.Furthermore,the range of applicability of the model is discussed and a criterion for differentiating a thin plate from a thick target is proposed by comparing the collapse load with the maximum local piercing load.For thick plates,based on the assumption that the deformation is localized and that the impact energy is dissipated only by penetration,Modified Wen's semi-empirical equation is applied to the perforation of thick metallic plates,It is further assumed that the mean pressure offered by the target materials to resist the projectiles consists of two parts:a quasi-static part due to the elastic-plastic deformation of the target materials and a dynamic part due to penetration velocity.Equations are obtained for the residual velocity and ballistic limit.It transpires that the present model predictions are in good agreement with available experimental data for metallic plates struck normally by conical-nosed projectiles. The plugging failure of metallic plates struck normally by a rigid conically-nosed projectile is studied in detail.A modified Bai-Johnson model is suggested herein for the adiabatic shear plugging of a ductile metal plate struck transversely by a flat-ended projectile based on the theories of adiabatic shear instability and thermo-viscoplastic constitutive relationship of ductile metals.By assuming that at post-instability the plate continues to deform the total energy absorbed in the adiabatic shear plugging is analyzed and an expression for the ballistic limit is derived. Furthermore,a critical condition is obtained for differentiating localized adiabatic shear plugging from simple shear plugging failure with global deformations by comparing the model suggested in this paper and the Wen-Jones model.It transpires that the present theoretical predictions are in good agreement with available experimental data in terms of the ballistic limits,perforation energies,residual velocities and the critical transition condition for the modes of plugging failure of ductile metal plates subjected to impact by flat-nosed missiles.For the plugging failure of thick metallic plates struck by rigid conical-nosed projectiles,two theoretical models are suggested depending on the perforation process. There are two cases for the perforaton process,viz.(1) indentation of conical nose, followed by adiabatic plugging formation;(2) indentation of conical nose,penetration (ductile hole enlargement) and then followed by final adiabatic shear plugging. Equations are obtained for residual velocity and ballistic limit for both cases and are compared with available experiments.It is shown tha the present model predictions are in good agreement with the available experimental resultsThe effects of projectile nose shape,properties of plate material,and ratio of plate thickness to projectile diameter on the failure modes are discussed.Based on the analysis of critical conditions for the transition between ductile hole enlargement (piercing) and plugging failure,a simplified failure(mechanism) diagram for the perforation of metallic plates subjected to impact by conical-nosed projectiles at normal incidence is proposed.Numerical simulations with ABAQUS/VUMAT into which a modified JC constitutive relation with damage is incorporated are performed to study the perforaion and penetration of metallic plates struck normally by flat-ended and conical-nose projectiles.Transient deformation and perforation process are obtained. It is shown that with increasing target thickness,target deformation becomes more and more localized and that the present numerical model is capable of reproducing the experimental observations including the "kink" effect.It is also shown that projectile cone angle has significant effect on the perforation modes of ductile metal plates and that for smaller cone angles plates fail by piercing or ductile hole growth and for larger cone angles plates fail by shear plugging or ductile hole enlargement plus shear plugging depending upon the ratio of plate thickness to projectile diameter.Numerical results are found to be in good agreement with available test data for the perforation of steel plates struck normally by flat-ended projectiles.