Impact response of layered steel–alumina targets
Highlights
► We investigate experimentally the impact response of steel/alumina/steel trilayers. ► We assess the utility of the Deshpande–Evans constitutive law for ceramic deformation. ► The DE model has good predictive capability at moderately high impact velocities. ► We propose a modification to DE to allow for dilatational softening after comminution. ► The proposed modification gives better agreement between experiment and model.
Introduction
Modern armor systems incorporate ceramics in order to improve their resistance to penetration by high-velocity bullets and fragments accompanying detonation of improvised explosive devices. Because of their high hardness, ceramics are capable of imposing large amounts of deformation on an impacting projectile. This causes blunting of the projectile tip, spreading of the impact load, and reduction of the stresses transmitted to underlying layers. Even simple bilayer systems comprising ceramic plates and metal sheets exhibit improved ballistic efficiencies relative to monolithic steel armors of equivalent areal density (Wilkins, 1978, Ben-Dor et al., 2009). Real armor systems, such as those used for protecting military ground vehicles, are geometrically far more complex and must protect against a wide range of high-energy threats while also providing electromagnetic shielding and flammability protection (Vaidya et al., 2001, Rimoli et al., 2011). The capability to numerically simulate ceramic deformation during impact and penetration is needed in order to efficiently design such systems.
To address this need, a mechanism-based continuum model of deformation and damage in ceramics was developed and later extended by Deshpande, Evans and their co-workers (Deshpande and Evans, 2008, Deshpande et al., 2011). The model – hereafter referred to as the Deshpande–Evans (DE) model – has been used with finite element (FE) simulation tools to study dynamic cavity expansion, spherical and spheroconical indentation, and dynamic penetration initiation (Deshpande et al., 2011, Wei et al., 2008, Gamble et al., 2011, Compton et al., 2012) (Fig. 1(a)). It has also been used in constructing failure initiation maps for ceramics impacted by spherical projectiles (Compton et al., 2012). Through comparisons of FE results with experimental measurements of quasi-static indentation (Gamble et al., 2011) and confined impact of alumina tiles by steel spheres (Compton et al., 2012), a set of calibrated material properties have been obtained for one specific armor alumina (Corbit 98, Bittosi Industries). The comparisons indicate that the DE model predictions capture with reasonable accuracy the trends in the spatial extent of sub-surface damage with the magnitude of loading (either dynamic or quasi-static). Such comparisons are useful in assessing the model predictions during the initial stages of impact, wherein the amount of inelastic deformation is small.
In the present study, we seek to expand our assessment of the predictive capability of the DE model to the domain of nearly through-penetration of ceramic/metal trilayers (Fig. 1(c)). This loading scenario differs from that employed in previous studies (cited above) in that it involves large amounts of inelastic strain of the ceramic layer. The emphasis in the present study is on the efficacy of the ceramic in protecting the back face sheet, as manifested in the permanent (plastic) deformation of the back-sheet following impact. Although assessments of this type have, in the past, been made on the basis of ballistic limits, (Hetherington, 1992, Zaera and Sanchez-Galvez, 1998, Lee and Yoo, 2001, Dey et al., 2007, Naik et al., 2012) back-face deformation at velocities below the ballistic limit has been used by others, (Gonçalves et al., 2004, López-Puente et al., 2005) in part because prediction of metal rupture is significantly more difficult than prediction of its plastic deformation. Consequently, in the present study, we make no attempt to predict rupture (and hence penetration) of the back sheet. (The latter is a challenging problem in its own right, even for monolithic metal sheets.) We also make use of the resulting distributions in back-face through-thickness strain: a metric that reveals subtle discrepancies between model predictions and experimental measurements not evident from the distributions in back-face displacement alone.
Previous experimental and numerical studies indicate that the resistance to deformation of a comminuted ceramic during penetration is an important determinant of armor performance(Shockey et al., 1990, Shockey et al., 2010). Immediately after comminution occurs, the ceramic takes the form of a collection of densely-packed granular particles constrained between the projectile, the back sheet and the surrounding undamaged ceramic. The constitutive response of this granular medium is therefore expected to have an important influence on the loads transferred to the back-sheet. In the present study, we show that the extended DE model for one specific ceramic in its current (calibrated) form adequately predicts the behavior of the alumina layer and the metal back-sheet at lower impact velocities. However, at higher velocities, the model tends to under-estimate the peak back-face displacement. To mitigate the discrepancies, we propose a modification to the constitutive law for ceramic deformation in the granular state, allowing for dilatational softening following full comminution. With this modification, the model predictions more closely match the experimental observations. Nevertheless, some salient features in the strain variations in the back-sheet remain unresolved.
Section snippets
Materials and test methods
Impact tests were performed on three target types, each 100 mm by 100 mm in size. The first comprised trilayers of: (i) 1 mm-thick sheets of rolled 4130 steel (obtained from McMaster Carr); (ii) 6 mm-thick tile of an armor alumina (Corbit 98, Bitossi Industries); and (iii) 2 mm-thick sheet of 4130 steel (also from McMaster Carr). The microstructure of the alumina and its response to quasistatic indentation and dynamic impact by steel spheres when confined in a steel fixture are detailed in Gamble et
Geometry and mesh
Finite element (FE) calculations of the tensile tests were performed on a 3-D model of the dog-bone specimen using Abaqus Explicit v.6.9-EF1. The elements were 8-noded linear bricks with reduced integration. The brick edge length was 500 μm in the plane of the sheet. The element thickness was selected to yield 10 elements in the through-thickness direction (Fig. 3 (a)). No mesh-sensitivity of the engineering stress–strain curve up to final necking was observed when the element sizes were
Steel sheets
Engineering stress–strain curves for representative tensile tests at several strain rates are shown in Fig. 4(a). The same results are presented in an alternate format – as the change in flow stress from that at the reference strain rate as a function of strain rate – in Fig. 4(b). As noted earlier, the flow stress follows an additive-type dependence on strain and strain rate, in accord with Eq. (3). Furthermore, for both sheet thicknesses, the strain-rate sensitivity is bilinear over the
Summary and conclusions
Comparisons have been made of measured profiles of the back sheets of impacted metal/ceramic trilayers with corresponding FE simulations using the extended DE model for the ceramic phase, with most material parameters obtained from previous studies of quasi-static indentation and dynamic penetration initiation. Although the two correlate well at moderate impact velocities, the agreement diminishes at higher velocities. In addition, the experimentally-observed localization in the
Acknowledgements
Support from the Office of Naval Research through a Multidisciplinary University Research Initiative Program on “Cellular Materials Concepts for Force Protection,” Prime Award No. N00014-07-1-0764 is gratefully acknowledged. EAG was supported in part by a National Defense Science and Engineering Graduate Fellowship and in part by a National Science Foundation Graduate Fellowship.
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2020, Materials Science and Engineering: ACitation Excerpt :At lower speeds this means that a blunt projectile can make the minimum traversal to penetrate the target by having a path through damaged material, but at higher speeds this means that more energy is spent damaging the ceramic than damaging what is behind the ceramic [46]. The importance of shear on failure was also found by Holland et al. [47] and Gamble et al. [48]. Their work found that when designing composite ceramic and metal armor systems, moving metal from the back face of the target to the front face impaired performance, due to the metal layer failing in shear and transferring that shear into the ceramic, which is less capable of resisting shear.
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2015, International Journal of Impact EngineeringCitation Excerpt :An additional benefit is that microstructural features, such as the initial flaw size and flaw density, can be modeled and their effects assessed. The capability of the model has been demonstrated in a number of recent studies comparing finite element simulation results to experimental measurements; these include quasistatic indentation [1], impact on confined ceramic tiles [33], and projectile penetration of ceramic-metal trilayers [34]. The objectives of the present study are to (i) determine the relationships between the mechanical and microstructural properties of ceramics and the characteristics of their rate-dependent strength in uniaxial compression, and, in doing so, (ii) to probe the Deshpande-Evans (DE) model in a regime of microcrack dominated failure.