With the development of advanced cement-based composites, conventional penetration models based primarily on uniaxial compressive strength have become increasingly inadequate. Although many empirical or semi-empirical models have been refined for specific concrete types, their accuracy levels are mostly limited to narrow material classes. This study introduces a novel penetration resistance model that uses the macroscopic effective hardness as the key parameter input. The use of hardness is motivated by the mechanical similarity between the static resistance component encountered during projectile penetration and the force response in indentation hardness tests. Drawing on this analogy, the effective hardness serves as a unified index that implicitly reflects the combined contributions of mortar, aggregates, and steel fibers within the cement-based matrix. The model integrates both previously published data and new experimental results for deep penetration, spanning a wide range of cement-based materials, including normal-strength concrete (NSC), fiber-reinforced cement paste (FRCP), fiber-reinforced mortar (FRM), engineered cementitious composites (ECC), fiber-reinforced concrete (FRC), fiber-reinforced high-strength mortar and concrete (FRHSM and FRHSC), as well as ultra-high-performance fiber-reinforced concrete (UHPFRC), with aggregate volume fractions up to 52% and compressive strengths from 37.9 to 238.5 MPa. Validation was performed using penetration depth data from ogive-, conical-, and spherical-nosed projectiles impacting at 372.0 to 833.1 m/s, with higher velocities excluded due to potential projectile failure, and prediction errors generally within 15%, demonstrating both accuracy and robustness. Compared to existing empirical formulas, the proposed model shows significantly improved generalizability and offers a practical, non-destructive approach for assessing and designing impact-resistant cement-based materials.
The RLSCJ represents a novel type of shaped charge jet that produces coupled penetration and explosion (or deflagration) effects, which poses a significant threat to concrete structures. In this work, experimental and numerical investigations are performed to analyze this coupled behavior as well as the resultant failure characteristics of concrete targets. Six groups of experiments were conducted using Al/PTFE liners at various standoff distances (S = 50–75 mm) against concrete targets. The experimental results show that, in comparison with inert metal jets, the RLSCJ produces a shallower crater depth yet a larger overall crater area. The target damage decreases with increasing S. Numerical simulations successfully reproduce the entire process of RLSCJ formation, penetration, and explosion. Additionally, parametric analyses were performed to evaluate the effects of liner cone angle θ and liner thickness η on target damage. The results reveal that the RLSCJ exhibits obvious axial density gradients and radial divergence during jet formation, which inherently reduces its penetration capability. The RLSCJ mass inside the penetration hole is positively correlated with the severity of concrete damage, and this mass strongly depends on θ, S, and η. Finally, an empirical formula for crater dimensions induced by the RLSCJ is established based on dimensional analysis. These findings can provide valuable references for assessing RLSCJ performance and optimizing the design of concrete protective structures.
Stochastic fracture of expanding cylindrical shells under explosive loading into numerous fragments is a fundamental and ubiquitous phenomenon. Densely distributed Photon Doppler Velocimetry testing probes are generally used to measure the critical time of penetrating crack of metal shells. Because of the inevitable mismatch between the specifically random crack position and the corresponding nearest testing probe at the space distance, it is still an enigma to generate the accurate fracture time as well as the important intrinsic fracture time spectrum. Here, to address this issue, we formulate a numerical protocol integrating both random penetrating crack and its mismatch with testing probes to model the hidden correlation between them. Then, one machine learning strategy informed by such numerical protocol, and also by an extremely wide space of determined distribution of fracture time is proposed. The synergy of this sequential approach gives rise to a quantitative reconstruction of inherent fracture time spectrum, with the predictive capacity extending significantly beyond the unmodified result from purely velocity measurement. The obtained intrinsic distribution of penetrating fracture can be used not only as an efficient demonstration of fracture capacity of metal shell, but is also transferable to detect both crack at inner surface as well as the crack propagation to build crack network. The generated intrinsic fracture spectrum is instrumental to build the long-sought fracture mechanism in expanding metal shells.
3D-printed graded cellular projectiles (GCPs) can serve as an explosive-free and controllable laboratory technique to generate blast-like pressure pulses, but meeting the demand for high-intensity loads remains challenging due to the coupled material-mesostructural-manufacturing constraints. To address this issue, we develop metallic graded cellular projectiles with open-cell mesostructures through a multiscale design strategy. The macroscopic density distribution of the projectile is inversely solved based on one-dimensional shock wave theory and the prescribed blast-like load profile. This theoretical density design is realized by customizing an irregular open-cell mesostructure using the 3D Voronoi technique, ensuring precise physical fabrication via selective laser melting (SLM). Experimental and numerical validations demonstrate that SLM-fabricated aluminum GCPs can reproduce exponentially decaying blast loads with high fidelity across diverse peak loads and decay rates. Under comparable impact conditions and relative density ranges, the SLM-fabricated aluminum GCPs developed in the present study increased the maximum experimentally validated peak pressure from 20 MPa for ABS-based GCPs to 80 MPa. Theoretical analysis elucidates the key influence of the projectile mass and initial velocity on load simulation performance, and a practical strategy is proposed to determine the two parameters. Furthermore, by systematically evaluating the mechanical properties of foams composed of various 3D-printable matrix materials, a model-predicted envelope map of achievable blast loads is constructed to guide the matrix material selection of GCPs for desired blast scenarios, covering an extensive range of peak loads (3–800 MPa) and decay time constants (0.05–0.65 ms). Ultimately, this work significantly expands the valid simulation range and applicable scenarios of graded cellular projectiles, providing a highly reliable and controllable experimental paradigm for assessing structural survivability under extreme blast threats.
