Plate Impact Tests Research Articles

On the role of the retained porosity on the shock response of additively manufactured high-performance steel: Experiments, constitutive model and finite-element predictions

Experiments have shown that for quasi-static and moderate strain-rates (of the order of 102–103/s) the mechanical response of additively manufactured (AM) and traditionally processed high-strength steels is similar whereas the impact behavior is markedly different. In this paper, we reveal that the main reason for this difference is the retained porosity in the AM material. Fully-implicit finite element calculations are presented in which we simulate both the launching of the impact plate and the impact between the two plates. The constitutive model used is the elastic/plastic model for porous ductile materials with matrix displaying tension-compression asymmetry and Johnson-Cook hardening law that accounts for both strain-rate effects and plastic history. It is shown that even a very small initial porosity changes the wave front, decreases the Hugoniot while increasing the shock rise time, when compared to a void free material. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 steel are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured.Additive manufacturing (AM) of metals is rapidly advancing as a robust method for production of geometrically complex parts. To enhance understanding of material performance and open up additional application opportunities, dynamic characterization of newly printed alloys is required to validate their effectiveness. In this paper, we present results from plate impact testing of AF9628 steel, a newly developed high-strength low alloy martensitic steel for structural applications which require resistance to high-rate deformation. We put into evidence differences in the shock structure between the AM and the traditionally processed material. To gain understanding, we conduct fully-implicit finite element (FE) calculations in which we model both the launching of the impact plate and the impact between the two plates, respectively. An elastic/plastic damage model that accounts for the effects of the tension-compression asymmetry in plastic deformation and its influence on porosity evolution is used. The FE results reveal that even a very small amount of initial porosity leads to an increase in the shock rise time, explaining the observed trends. Furthermore, quantitative comparisons between simulation results and plate impact data for both the AM and the wrought AF9628 are provided. The good agreement show that the model captures the impact response and illustrates the model capabilities to provide information on field variables that cannot be directly measured.

Influence of phase stability on postshock mechanical properties and microstructure evolution in Ti-17 alloy

There has been a growing surge of interest in examining the shock response of titanium alloys, owing to their considerable potential for military applications. The present study aims to reveal the influence of phase stability on the shock-induced mechanical response and substructure evolution of a metastable β titanium alloy, namely, Ti-17. This investigation included extensive work, such as plate impact tests, quasi-static reloading compression tests, and electron microscope analyses. The microstructural evaluations following the shock-wave loading unveil planar slip as the prevailing deformation mechanism in Ti-17 with a bimodal microstructure with stable α and β phases. However, when the shock stress exceeds 10 GPa, the activation of {101¯1}α nano-sized twins was observed, leading to improved reloading ductility. This implies a novel strategy to achieve excellent strength-plasticity compatibility in titanium alloys through appropriate shock-wave loading. Conversely, in Ti-17 with an equiaxed β microstructure, the metastability of the β phase leads to the activation of shock-induced α″ martensite, shock-induced ω, and planar slip. Two distinct forms of interaction involving the α″ laths, i.e., shear and truncation, were also observed. Phase stability greatly influences substructure evolution, which ultimately controls the reloading mechanical properties of the postshock Ti-17 alloy.

Numerical design and experimental validation of shockless plate impact configurations for the Lagrangian analysis of armor ceramics

Ceramic materials are widely used in armor or protective structures, providing weight saving at equivalent performance in comparison to their steel counterparts. Plate-impact experiments are commonly used to investigate the dynamic behavior of ceramics under compressive loading. Using the particle velocity measured at the back of the target, some mechanical properties such as the Hugoniot elastic limit (HEL) as well as the Hugoniot curve of the material can be deduced. Nevertheless, these tests do not provide a direct measurement of the plastic hardening (post-HEL) behavior of the target. In the present work, an experimental shockless plate-impact configuration was developed and implemented to conduct a Lagrangian analysis. This configuration relies on the use of a wavy-machined flyer plate impacting a target made of a buffer, two ceramic plates of different thicknesses, and two window plates as backing. First, the use of wavy flyer plates to generate a loading ramp was validated by considering the impact of the wavy-machined flyer plate against a target, both made of 316L steel. A numerical analysis of this test was developed to confirm the pulse-shaping effect observed experimentally. Next, a ceramic, F99.7 alumina was subjected to the shockless plate impact test in Lagrangian configuration considering the same steel as a buffer and flyer plate material. These tests coupled with Lagrangian analysis enable the curve of axial-stress vs axial-strain beyond the isentropic elastic limit (IEL) to be deduced. The experimental data allow identifying the parameters of an elastoplastic with strain-hardening model to describe the behavior of the tested alumina.

A simulation approach for quantifying ballistic impact damage in ultra-high-performance concrete

In this work, we provide a hydrocode simulation model for high-velocity projectile impact against ultra-high-performance concrete targets and establish a methodology to extract damage quantities from the simulation results. In the parameter derivation process, published and own data stemming from material experiments, such as uniaxial, triaxial, and planar plate impact tests, are used as a starting point. To fill the systematic gaps of strength data for pressures of 1 GPa to 5 GPa and for fractured concretes, residual velocities of projectiles and qualitative target damage information from ballistic experiments with high-hard steel spheres are additionally used as a reference in parametric simulations. All criteria from the comparatively broad data basis are successfully reproduced by the simulation model simultaneously. The simulated damage quantities derived by the proposed extraction procedure are reasonable counterparts to the corresponding experimental measures from earlier published works, allowing a new quality of comparison between both worlds.

Design of multi-stable metamaterial cell with improved and programmable energy trapping ability based on frame reinforced curved beams

Curved beams are a class of elements capable of bi-stability and can be used to construct multi-stable metamaterials. These materials leverage elastic snap-through in curved beams to transition between multiple stable states, effectively achieving energy absorption and trapping. The elastic deformation allows the structure to be used repetitively. However, the conventional curved beam unit cells design process omits the influence of supporting frames, resulting in inadequate constrains of the beam in the fabricated metamaterials. Its mechanical properties and number of stable states can be significantly diverged from theoretical predictions. This paper presents a novel multi-stable metamaterial with improved and consistent energy trapping ability based on frame reinforced curved beams. Comparative finite element analysis of three unit-cell types demonstrates the superior bi-stability of the proposed cell. Moreover, parametric analysis reveals the proposed cell has a wider range of parameters that can achieve bi-stability. The mechanical properties of the single cell and the 2 × 2 metamaterial are obtained by compression tests. The results validate the linear mechanical response that correlates with the number of unit cells which allows optimal programming of multi-stable metamaterials. Finally, plate impact test is conducted to investigate and analyze the cushioning performance of the multi-stable metamaterial.

Vibration response difference of caving mechanism under coal rock impact based on mechanical–hydraulic coupling

Top coal caving in fully mechanized caving mining will cause an irregular impact on the caving mechanism of hydraulic support. The vibration response of the caving mechanism varies under different forms of impact. This response difference is a prerequisite for new coal rock identification technology in intelligent mining. Therefore, this work studies the difference in vibration response of the caving mechanism under different forms of impact. An innovative mechanical–hydraulic coupling system model of the caving mechanism impact by coal rock is established. The metal plate impact test proved the significant difference in vibration response of the caving mechanism under coal rock impact of different materials. Afterward, a more improved mechanical–hydraulic co-simulation model analyzed the difference in the vibration response of the caving mechanism under different rock materials, volumes, velocities and impact positions. The results show that the vibration response is more intense under rock impact than under coal impact. A lower position, a faster velocity and a larger volume correspond to a more noticeable response difference in the caving mechanism. The vibration and fault sensitive areas of the caving mechanism are determined. This study has a reference significance for improving the caving mechanism's structural design and failure prevention. The conclusions provide guidance for a new intelligent coal rock identification technology based on vibration signals.

A re-usable negative stiffness mechanical metamaterial composed of Bi-material systems for high energy dissipation and shock isolation

Mechanical metamaterials with negative stiffness (NS) effects are able to dissipate mechanical energy repeatedly according to the “snap-back” strategy. Nevertheless, the strategy is merely efficient when a plethora of NS cells are lined together in series. Limitations of the strategy bring challenges to ameliorate the capacity of energy dissipation for the NS. In the present research, an unique re-usable NS mechanical metamaterial made up of Bi-material systems was suggested and fabricated, which is able to dissipate energy even supposing such metamaterial was merely made up of a single unit. To get a thorough knowledge of the metamaterial’s quasi-static mechanical characteristics, a combination of loading-unloading experiments and finite element method (FEM) has been conducted. The effects of structural arguments on the mechanical characteristics were then revealed employing the experimentally authenticated numerical model. The metamaterial possesses outstanding re-usability and a large capacity for energy dissipation, according to the findings of quasi-static tests. Finally, plate-impact tests were executed to explore the cushion performances of this metamaterial. The presented Bi-material NS mechanical metamaterial demonstrated notable potential in energy dissipation and shock isolation.

Exploding wire method for the characterization of dynamic tensile strength of composite materials

In the presented study a wire electric explosion method is adopted for the shock loading test of wound T700/LY113 carbon/epoxy composite. The advantage of the proposed test method is a possibility to reach strain rate ∼104 s−1, exceeding upper limit of split Hopkinson pressure bar, but matching lower limits of plate impact test. Compared to the latter test method, a promising feature is a capability to measure in-plane tensile strength of the laminated composite. To implement the proposed method, test samples were fabricated by winding of carbon fiber layers over a polymethyl methacrylate (PMMA) cylinder. Electric explosion of wire inserted in the channel inside the cylinder generates a shock wave, which propagates towards the outer composite shell, and free surface velocity history is recorded using a laser interferometer. It allows estimation of failure strain and tensile strength of the composite in circumferential direction. However, incident shock wave and reverberations are also critical for out-of-plane strength, including delamination, so finite element analysis is used to elaborate what type of failure mode is critical.

Experimental study on Hugoniot parameters of U71Mn steel under high pressure

The Hugoniot parameters of U71Mn steel under high pressure were studied by hypervelocity impact test of U71Mn steel with two-stage light gas gun. The plate impact test of U71Mn steel sample was carried out by means of symmetrical impact. The minimum impact speed was 1.843km/s and the maximum impact speed was 5.018km/s. The Hugoniot relation and Hugoniot parameter C and λ, then the accuracy of Hugoniot parameters of U71Mn steel under high pressure is verified according to Hugoniot equation of state (the relationship curve between impact pressure and density). The research results can provide reference for the application of U71Mn steel in the field of hypervelocity impact.

Theoretical and experimental investigation on teeth impacts between the inner hub and the friction plate of the planetary transmission system's clutch

When the friction plate and the steel plate of a planetary transmission system's clutch are detached, there will be continuous teeth impacts between the clutch friction plate and the inner hub (i.e. the floating ring gear). These impacts exhibit strong nonlinear and stochastic characteristics, especially under variable operating conditions, which have significant effects on the reliability of the friction plate. In this paper, an original dynamic impact model considering the coupling of several stochastic factors (backlash, eccentricity, impact position, etc.) is established to study the impact characteristics between the mating teeth of the clutch friction plate and the inner hub. The changes in impact features such as the total number and position of impact teeth, and the impact force are discussed by the coupling effect between different parameters such as backlash, speed fluctuation amplitude and speed fluctuation frequency. A friction plate impact test bench is designed to measure the dynamic impact force, which is directly compared to the simulation results to verify the proposed dynamic impact model. The analysis results of this study can provide a theoretical basis for improving the service performance and life of the friction plate of the planetary transmission system's clutch.

Shock and Spallation Behavior of a Compositionally Complex High-Strength Low-Alloy Steel under Different Impact Stresses

The shock and spalling behavior of a compositionally complex high strength low-alloy steel (HSLA) was studied using plate impact testing. The free surface velocity of the specimen in the range of 194~938 m/s was measured by a displacement interferometer system for any reflector (DISAR). The Hugoniot elastic limit (HEL), spallation fracture and microstructural evolution of the HSLA under an impact stress of 3.04~18.66 GPa were analyzed. Shock Hugoniots were obtained from the measured particle velocities and calculated shock velocities. The velocity curves show clear signs of HEL and velocity fallback, indicating a transition from elastic to plastic and spalling behavior. When the impact velocity exceeds 757 m/s, the particle velocity rises to the peak and then increases again, indicating that an α→ε phase transition occurred, with a threshold of 13.51 GPa. It was found that the impact velocity is linearly related to the particle velocity of the HSLA. As the impact stress increased, the HEL remained within the range of 1.32~1.50 GPa, while the spalling strength presented an upward trend with the increasing impact stresses. Metallographic analysis shows that the impact failure is dominated by brittle fracture at lower velocities, while more ductile fracture occurs at higher velocities.

A modified p∼α equation of state for concrete-like materials

The p∼α equation of state has been widely used in dynamic constitutive models for concrete-like materials. However, the latest study (J Build Eng 2022; 61: 105262) has shown that its accuracy at low pressures is much compromised. In this note, a modified p∼α equation of state for concrete-like materials is presented herein on the basis of the analysis of recently obtained plate impact test data (J Build Eng 2022; 61: 105262) for cement mortar. Comparison is then made between the plate impact test data for the cement mortar and the predictions from the two equations of state (i.e. the modified p∼α equations of state and the p∼α equations of state) in terms of αp′∼p relationship, α∼p relationship and pressure-volumetric strain relationship. Furthermore, the plate impact test data available for normal concrete is also compared with the predictions from the two equations of state. It is found that the modified p∼α equation of state is in good agreement with the plate impact test data for concrete-like materials and is advantageous over the p∼α equation of state below full compaction pressure.

Effect of reflected stress wave on dynamic crack propagation and arrest behavior of sandstone specimens under impact loading

The interaction of stress waves generated by blasting or excavation disturbance with cracks or joints significantly affects the mechanical behavior of rock masses with some pre-existing cracks. To better understand the dynamic damage evolution mechanism of fractured rock mass, the influence of stress waves on cracks in rock mass must be investigated. Thus, to study the effect of reflected stress wave on dynamic fracture behavior of fissured rock mass, a large-size arc-shape boundary single cleavage triangle (ABSCT) configuration sandstone specimen was proposed in the present study. A series of impact tests were performed on the specimen with 0°, 65°, 95°, and 125° ABSCT using the drop plate impact testing system to determine dynamic fracture properties. The test was numerically simulated using the modified finite difference software and the traditional finite element software. The effect of the reflected stress wave caused by the arc-shape boundary of the ABSCT specimen on the crack propagating speed, crack fracture toughness, and compressive stress along the crack trajectory under dynamic loads was analyzed and discussed. The results show that the ABSCT specimen has a crack arresting effect on a propagating crack. The average crack propagation speed of three specimens with arc-shape boundaries is almost 0.63 times that of the flat-bottom specimen, indicating that the arc boundary has an obvious effect on the crack propagating velocity. The average crack propagating speed decreases with the increase in arc boundary radian. The compressive stress on the crack path of three arc boundary specimens is found to be greater than that of the flat-bottom specimen. Furthermore, the crack arrest toughness is greater than the average crack propagating toughness at the arc-shape boundary specimen.

Structural response and energy absorption assessment of corrugated wall mechanical metamaterials under static and dynamic compressive loading

Mechanical metamaterials, especially corrugated wall structure with negative Poisson's ratio, have received much attention since it offers more options for energy absorption. Herein, the effects of structure factors, wall thickness, and gradient design on the structural response and energy absorption performance of corrugated wall metamaterials have been explored using finite element simulations, quasi-static compression tests and dynamic plate-impact tests. The energy absorption performance was evaluated using indexes such as energy absorption efficiency, specific energy absorption, plateau stress, etc. The results show that the difference in the deformation and interaction mechanism between corrugated walls leads to different mechanical responses of the structure. Compared with the normal sample, the gradient setting of the wall thickness (t) increases the negative Poisson's ratio by 44.6%, and the gradient setting of the structure factor (h/L) increases the maximum energy absorption efficiency to 80.52% (an increase by 14.7%). Finally, plate-impact tests demonstrate that the corrugated gradient structure has better energy dissipation performance than the corrugated normal structure. Compared with the normal sample, the thickness gradient sample and the structure factor gradient sample reduce the impact load of the structure by 42.89% and 34.56%, respectively. This work can strengthen our capability of engineering tunable energy-absorbing device for a wide range of application.

Experimental Research on Dynamic Response of Layered Medium under Impact Load

Stress waves propagating through multiple parallel fractures are attenuated due to the multiple wave reflections and transmissions at the fractures. The dynamic response of a layered medium under an impact load is systematically studied by a model test in this paper. The effects of the impact energy, number of joints, thickness of the medium and joint layer, material properties of the cementation layer, and other factors of the dynamic stress propagation and attenuation of layered media are analyzed. Studies have shown that Sadovsky’s empirical formula fits the attenuation law of vertical peak velocity well, and the obtained attenuation coefficient k and index b can be used for reflecting the dynamic response characteristics of layered media. The attenuation coefficient k is positively correlated with the impact height and negatively correlated with the plate thickness in a single-layer plate impact test. The thickness of the medium layer is the main factor affecting the vibration response of the layered medium in the impact test of the multi-layer slab. The medium thickness, the number of medium layers, and the number of joints have little influence. The different cementation materials and the change of cementation thickness will have a great influence on the dynamic response of layered media, when the cementation layer is filled with joint surfaces for the impact test of multi-layer plates.

On the equation of state for concrete-like materials

This paper presents a systematic study on the equation of state for concrete-like materials. A new method is first proposed to analyze plate impact test data by considering the effects of both wave structures and strength surface; plate impact tests are then performed on cement mortar with impact velocities ranging from 45 m/s to 3050 m/s and experimental results are analyzed by using the newly proposed method; Subsequently, the accuracy of the existing equations of state (i.e. the p∼α equation of state and the equation of state of HJC) is evaluated and similarities and differences are also discussed. Finally, a new equation of state is proposed based on the previous work and the newly acquired test data. The numerical results using the three equations of state are compared with plate impact test data in terms of particle velocity-time history, longitudinal wave velocity and HEL. It is found that the newly proposed equation of state is in good agreement with plate impact test data of concrete-like materials and is advantageous over the existing equations of state.

Dynamic increase factors of concrete-like materials at very high strain rates

Strain rate effects on the compressive and tensile strengths of a concrete-like material play an important part in the construction of its dynamic constitutive model. So far no data for the same material covering a wide range of strain rates were reported in the literature, not to mention the data for compression at strain rates greater than 103 s−1. This paper presents a combined theoretical and experimental study on the dynamic increase factors of concrete-like materials at very high strain rates. First, a method is proposed to determine dynamic increase factor for a concrete-like material in compression due to strain rate effect only (that is to say to eliminate the inertial (containment) effect) at very high strain rates (>103 s−1) by in-depth analysis of its Hugoniot elastic limit (HEL). Then, various material tests (i.e. quasi-static uniaxial compression and tensile tests, SHPB and SHTB tests, plate impact test and dynamic compression-shear test) were performed on a certain type of cement mortar in a wider range of strain rates (i.e. 10-5 s−1 ∼ 106 s−1). Finally, the test data are compared with the previously proposed semi-empirical equations for dynamic increase factors. Furthermore, the plate impact test results for ultra high performance concrete (UHPC) available in the literature are also analyzed using the proposed method. Dynamic increase factor for tension at strain rate of 103 s−1 is obtained indirectly by the relationship between dynamic uniaxial tensile strength and dynamic shear strength through the shear wave tracking (SWT) technique which is based on dynamic compression-shear test. It is found that dynamic increase factor for concrete-like materials in compression due to strain rate effect only can be regarded as a constant at very high strain rates. It is also found that the previously proposed semi-empirical equations can accurately describe the strain rate sensitive behavior of concrete-like materials in both tension and compression.

Constitutive model for fibre reinforced composites with progressive damage based on the spectral decomposition of material stiffness tensor

Complex nature of the fibre reinforced composites, their non-homogeneity and anisotropy make their modelling a challenging task. Although the linear – elastic behaviour of the composites is well understood, there is still a significant uncertainty regarding prediction of damage initiation, damage evolution and material failure especially for a general loading case characterised with triaxial state of stress or strain. Consequently, simplifying assumptions are often unavoidable in development of constitutive models capable of accurately predicting damage. The approach used in this work uses decomposition of the strain energy based on spectral decomposition of the material stiffness tensor and an assumption that each strain energy component represent free energy for a characteristic deformation mode. The criteria for damage initiation are based on an assumption that the damage corresponding to a deformation mode is triggered when the strain energy for that mode exceeds a specified critical limit. In the proposed model the deformation modes are not interacting at continuum scale due to orthogonality of the eigenvectors, i.e. the stiffness tensor symmetry. Damage and its evolution are modelled by reduction of the principal material stiffness based on the effective stress concept and the hypothesis of strain energy equivalence. The constitutive model was implemented into Lawrence Livermore National Laboratory (LLNL) Dyna3d explicit hydrocode and coupled with a vector shock Equation of State. The modelling approach was verified and validated in a series of single element tests, plate impact test and high velocity impact of hard projectile impact on an aerospace grade carbon fibre reinforced plastic. The model accurately predicted material response to impact loading including the test cases characterised by presence of shock waves, e.g. the plate impact test. It was also demonstrated that the model was capable of predicting damage and delamination development in the simulation of the high velocity impact tests, where the numerical results were within 5% of the post impact experimental measurements.

Continuous carbon fiber reinforced composite negative stiffness mechanical metamaterial for recoverable energy absorption

This study investigated negative stiffness (NS) mechanical metamaterials, which are potential in the energy absorption field. However, critical drawback of low specific energy absorption in traditional NS mechanical metamaterials limits them to be applied. In this paper, a reusable continuous carbon fiber reinforced polymer (CFRP) composite NS mechanical metamaterial was proposed and fabricated. A combination of compression tests and numerical simulations have been carried out to gain a comprehensive understanding of the structural quasi-static mechanical properties. Repeatability of the metamaterial was then verified by cyclic compression. The results of quasi-static test show that the metamaterial has excellent reusability characteristics and good energy absorption capability. In addition, the effect of the structural parameters on the mechanical properties was revealed using the experimentally verified numerical model. Moreover, by dint of the numerical model, the effect of stacking sequence of the metamaterial on the mechanical properties was also investigated, and the correctness of the curved beams adopted 0° stacking sequence in this paper was proved. Finally, plate-impact tests were performed to investigate the cushion performance of this metamaterial. The metamaterial structure shows good impact resistance without the occurrence of any plastic deformation. The research has guiding significance for the design of impact-resistant metamaterials.

Molecular dynamics study on the shock induced spallation of polyethylene

Macroscopic experimental results of the plate impact tests of polymers are generally interpreted using the free surface approximation and the acoustic approximation. However, their validity over a range of shock pressures has not been thoroughly investigated yet. We conducted molecular dynamics simulations of plate impact tests of polyethylene to obtain molecular-level insights on those two common approximations associated with the interpretation of shock pressure and spall strength. Our results revealed that the free surface approximation could slightly underpredict the shock pressure in the polymer. The spall strength computed from the free surface velocity history can be significantly smaller than the actual tensile stress in the region of spallation.