Numerical modeling of response of monolithic and bilayer plates to impulsive loads

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Abstract

In this paper, we present and discuss the results of our numerical simulation of the dynamic response and failure modes of circular DH-36 steel plates and DH-36 steel–polyurea bilayers, subjected to impulsive loads in reverse ballistic experiments. In our previous article, we reported the procedure and results of these experiments [MR Amini, JB Isaacs, S Nemat-Nasser. Experimental investigation of response of monolithic and bilayer plates to impulsive loads. accepted]. For the numerical simulations, we have used physics-based and experimentally-supported temperature- and rate-sensitive constitutive models for steel and polyurea, including in the latter case the pressure effects. Comparing the simulation and the experimental results, we focus on identifying the potential underpinning mechanisms that control the deformation and failure modes of both monolithic steel and steel–polyurea bilayer plates.

The numerical simulations reveal that the bilayer plate has a superior performance over the monolithic plate if the polyurea layer is cast on its back face (opposite to the blast-receiving side). The presence of the polyurea layer onto the front face (blast-receiving side) amplifies the initial shock loading and thereby enhances the destructive effect of the blast, promoting (rather than mitigating) the failure of the steel plate. In addition, the interface bonding strength between polyurea and steel is examined numerically and it is observed that the interface bonding strength has a significant effect on the performance of the steel–polyurea bilayer plates. The numerical simulations support the experimentally observed facts provided the entire experiment is simulated, employing realistic physics-based constitutive models for all constituents.

Introduction

The response of plates under distributed dynamic impulsive loads has been numerically and analytically studied by a number of researchers. A review of the relevant literature is given by Nurick and Martin [2]. A momentum conservation approach, eigenvalue expansion methods, and wave form approaches are among the various analytical–numerical methods previously used to investigate the response of plates under dynamic loads [3], [4], [5]. In a recent research conducted by Balden and Nurick [6], full scale numerical simulations of the post-failure motion of steel plates subjected to blast loads have been conducted using the finite-element code ABAQUS. Another investigation of this kind has been conducted by Lee and Wierzbicki [4], [5] in which they examine the fracture of thin plates under localized impulsive loads and the possible dishing, disking, and petaling of the plates. Finite-element calculations of Xue and Hutchinson [7] seek to explore the ability of the bilayer plates to sustain intense impulses and assess the results by comparing to the estimated performance of monolithic steel plates of the same total mass, using the finite strain version of the ABAQUS Explicit code. The significance of these full-scale numerical simulation codes is that they allow first, to study the transient response of the plate, second, to incorporate complex temperature-, pressure-, and rate- dependent constitutive models in the finite-element code, and finally, to conduct parametric studies to gain insight into the dynamic deformation mechanisms.

The objective of this paper is to numerically simulate the results of our experiments, presented in a recent paper [1]. To this end, we use the explicit version of the commercially available finite-element code, LS-DYNA, within which physics-based constitutive models of the involved materials, DH-36 steel and polyurea are incorporated. A comprehensive mechanical testing program is used to characterize and model these materials. A temperature and strain-rate sensitive constitutive model, developed by Nemat-Nasser and Guo [7] on the basis of the kinetics and kinematics of dislocation motion, is employed and implemented into LS-DYNA through a user-defined FORTRAN subroutine for the steel plates. Moreover, an experimentally-based viscoelastic, rate-, pressure-, and temperature-sensitive constitutive model, developed by Amirkhizi et al. [8] and implemented into LS-DYNA by Amirkhizi, is used for modeling the polyurea. After validating the numerical model, the model is employed to investigate various aspects of the effects of polyurea coating on the response of the steel plates. The main focus of the calculations is to understand the effects of (1) the relative position of the polyurea layer with respect to the loading direction (i.e., either on the back or the front face), (2) the polyurea–steel interface bonding strength, and (3) the polyurea layer thickness relative to that of the steel layer.

Section snippets

Numerical simulation procedures

In this section, the reverse ballistic experimental setup is briefly explained and the finite-element model is detailed. The material constitutive models used for steel, polyurea, and polyurethane are discussed, and finally, the details of the deformed plate's measurement method are presented.

Numerical simulation results

In this section, we compare the three measured principal stretches and thickness profiles of a selected set of tested monolayer and bilayer samples with their corresponding finite-element model predictions. We also discuss the effect of the polyurea–steel interface bonding strength on the dynamic response of the bilayer plates. The details of the finite-element model parameters are tabulated in Table 2, Table 3.

Summary and conclusions

A finite-element method is employed to study the impulsive response of monolithic steel and bilayer steel–polyurea plates. The entire experimental setup explained in a previous article [1] is modeled using the commercially available finite-element code, LS-DYNA, integrating into this code physics-based and experimentally-supported temperature- and rate-sensitive constitutive models for steel and polyurea, including in the latter case the pressure effects. Comparing the simulation and the

Acknowledgment

This work has been supported by ONR (MURI) grant N000140210666 to the University of California, San Diego, under Dr. Roshdy G. Barsoum's research program. The authors wish to acknowledge Mr. Jeff Simon, a former undergraduate student at UCSD in the Department of Mechanical and Aerospace Engineering, for his help to develop and code the program which has been used to digitally map the scanned images of the cut steel samples and estimate their 3D deformation gradient.

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