High-velocity Impact Experiments Research Articles

Impact response of additively manufactured density-graded open-cell foams

Additive manufacturing has made it possible to fabricate materials that were unachievable with traditional methods. This study focuses on understanding the deformation behavior and energy absorption mechanics of additively manufactured cellular materials with gradually varying densities. Foams have unique deformation behavior due to their intricate topology and composition, resulting in excellent energy dissipation capability. Varying the density can significantly influence their deformation response and improve energy absorption and impact resistance. Voronoi tessellation is employed to model the foams, as it effectively captures the cell morphology in foam structures and produces stochastic cellular topologies accurately. Resin-based additive manufacturing techniques are employed to fabricate cellular materials with varying density configurations for low-velocity and high-velocity impact experiments. The study demonstrates that density-graded foams effectively dissipate a broad spectrum of impact energies, surpassing uniform counterparts by transmitting reduced stress, especially at lower energy levels. This characteristic enhances their suitability for advanced energy absorption applications. The results also show that at high impact velocities, the direction of density gradation influences energy dissipation and peak stress transmission.

Failure analysis of additively manufactured AuxHex and hierarchical honeycomb-core sandwich panels subjected to projectile impact

Honeycomb sandwich panels (HSPs) are extensively employed across various industries owing to their outstanding strength and capacity for energy absorption. Despite their widespread use, the potential of additively manufactured (AM) honeycombs in ballistic protection remains relatively unexplored. This study aims to comprehensively assess the energy absorption performance of two distinct HSP configurations, namely AuxHex and Hierarchical, through high-velocity impact tests spanning velocities ranging from 220 to 270 m/s. The high-velocity impact experiments are conducted using a single-stage pneumatic gun, complemented by simulations executed via Abaqus/Explicit. Our findings reveal that the hierarchical HSP demonstrated a notable 9.6 % enhancement in energy absorption compared to panels featuring an AuxHex honeycomb. Interestingly, the hierarchical panels also necessitated 4.8 % more energy for perforation. In terms of failure mechanisms, both sheets of the HSPs experienced ductile shearing, with the formation of characteristic petal-like structures. Concurrently, the honeycomb core underwent fragmentation on the side facing the projectile, while plugs were ejected from the back sheet. Moreover, our analysis indicates that the residual deflection of the back sheet surpassed that of the striking sheet by 15–20 %. This disparity can be attributed to prolonged contact duration and variations in interaction forces between the sheets. Overall, this investigation provides valuable insights into the energy absorption capabilities of AM honeycomb-based HSPs under high-velocity impact conditions, shedding light on their potential for enhanced ballistic protection in various applications.

High-velocity oblique impact experiments on ice and snow spheres: Implications for the collisional evolution of icy planetesimals at different thermal evolution stages

In order to determine the effect of impact angle on the impact strength of icy planetesimals, we conducted a range of oblique impact experiments for spherical ice and snow targets simulating icy planetesimals at different thermal evolution stages. The ice targets had no porosity and the snow targets had a porosity of 0.5. A polycarbonate or glass sphere impacted the ice targets at 744–1747 m s−1 and the snow targets at 938–5085 m s−1 over a range of impact angles from grazing to head-on collisions. All experiments were conducted using a two-stage light gas gun and a target chamber set in a cold room of −15 °C at Kobe University, Japan. The impact strength, which is a specific energy, Q, when the largest fragment mass is a half of the original target mass, for the ice and snow targets in a head-on collision was determined to be 12 and 520 J kg−1, respectively, whereas it was found that the impact strength depended on the impact velocity. Thus, the normalized largest fragment mass, ml/Mt, could well scale with the velocity dependent Q, that is, Qviγ (where ml and Mt are the masses of largest fragment and target, respectively, and vi is the impact velocity). At high Q, ml/Mt increased drastically with the decrease of impact angle when the impact angle was smaller than a critical angle, θc, and θc~30° for the ice targets and θc~45° for the snow targets. At small Q, ml/Mt continued to increase as the impact angle became smaller for both types of targets. The ml/Mt for oblique impacts had a good correlation with the effective specific energy, Qeff=Qsin2θ, where θ is the impact angle, and the effective impact strength was determined to be 16 J kg−1 and 499 J kg−1 for the ice and snow targets, irrespective of the impact angle. Furthermore, the scaling parameter, Πs_eff, which was proposed by Housen and Holsapple (1990) but includes Qeff instead of Q, multiplied by 1−ϕλ, where ϕ is the porosity, showed even better correlation with ml/Mt, and all ml/Mt data of ice and snow targets could be merged, irrespective of impact velocity and ϕ. Based on our experimental results and a theory on the oblique impact of solar system bodies proposed by Shoemaker (1962), we could estimate the degree of disruption (ml/Mt) at any impact energy and any impact angle for icy planetesimals. Our findings demonstrate that the degree of disruption for icy planetesimals that have experienced sufficient thermal evolution was larger than that for those that did not experience significant thermal evolution.

High-velocity impact performance of sandwich panels with additively manufactured hierarchical honeycomb cores: An experimental and numerical study

The honeycomb sandwich panel presents a highly promising solution for enhancing ballistic behavior owing to its excellent strength-to-weight ratio and impact resistance. This study focuses on investigating the shock mitigation properties of honeycomb sandwich panels through experimentation and numerical simulation of high-velocity impact tests. Single-scale and double-scale hierarchical honeycomb cores are manufactured using selective laser melting with AlSi10Mg powder, combined with a pair of stainless steel (SS 316) sheets. High-velocity impact experiments were conducted within a velocity ranging from 100 to 270 m/s to examine the effects of different cores and projectile nose shapes on the dynamic response of the panels. Numerical simulations using ABAQUS/Explicit software were performed and validated against the experimental results. The sandwich panel with a double-scale hierarchical honeycomb core exhibited 7.8% and 6.1% more energy absorption compared to the single-scale hierarchical honeycomb core against conical and hemispherical nose projectiles, respectively. Additionally, the ballistic limit for the hemispherical projectile was found to be 8.9% higher than the conical-nose projectile under the same impact velocity and panel thickness. Moreover, an increase in panel thickness from 12 mm to 25 mm prompted a significant improvement of approximately 39% in specific energy absorption and a 44% increase in ballistic limit velocity. These findings highlight the considerable potential of single-scale and double-scale hierarchical honeycomb sandwich panels for the development of threat-resistant structures in critical dynamic loading applications.

Collisions between Drones and Rotorcraft: Modeling of the Crash Response of Battery Packs

Drones operating in an urban environment pose a potential collision threat to rotorcraft. In this paper, the battery pack of the DJI MAVIC 2 ZOOM is analyzed since the battery is considered to be the greatest threat due to its high weight and stiffness. Following a pyramid-type building block approach, a high-fidelity model simulation was developed for LSDYNA based on a wide range of experiments, ranging from quasi-static material tests to quasi-static component tests up to high-velocity impact experiments. The high-fidelity model allows the prediction of damage in potential collision scenarios between a high-speed rotorcraft and the battery pack of the drone. For the particular impact configuration analyzed within this paper, the drone battery does not cause catastrophic failure of the windshield of the rotorcraft.

Preservation of pristine materials under impact craters formed on comet nuclei

Comet nuclei are the most primitive small bodies in the solar system, and would contain highly volatiles and amorphous water ice. However, comet nuclei may lose their primordial properties after high-velocity impacts with other small bodies. Such high-velocity impacts might also cause the characteristic circular structures and pinnacles on the comet-nucleus surface. However, the true origin of these geological structure remains uncertain. We here sought to clarify the shape of impact craters and the effects of post-shock heating on the comet surfaces. We conducted high-velocity impact experiments at velocities of 3–5.8 km s−1 on porous-ice targets with 40%, 50% and 60% porosity, and measured the post-shock temperature around the impact crater. The hard, dense refrozen layer formed on the crater wall resembled the pinnacles and sharp pit rims observed on comet nuclei, suggesting that such structures on comets may originate from impacts. In addition, the crater size scaling law for porous ice targets was successfully obtained in the strength-dominated regime. From the temperature profiles obtained, the energy partition coefficient of the projectile kinetic energy to the post-shock heat, γ, was estimated as follows: γ=0.08, 0.27 and 0.63 for 40%, 50% and 60% porosity at 4.2 km s−1 impact velocity, and γ=0.58 and 0.22 for 50% porosity at 3 km s−1 and 5.8 km s−1 impact velocities. These results, together with our crater size scaling law for porous ice, were used to estimate the temperature distribution induced by post-shock heat on the comet-nucleus surface. Volatile depletion and crystallization of amorphous water ice can occur at distances less than twice the crater radius from the crater center—that is, the post-shock heat effects are confined to the area around the crater. This might suggest that the comet nucleus surface remains relatively primitive after impacts.

High-velocity impact experiments and quantitative damage evaluation for finite ultra-high-performance concrete targets

In this work, we aim at improved characterization of target damage occurring as the result of projectile impact against ultra-high-performance concrete (UHPC). For this purpose, we present the results of high-velocity impact experiments with spherical steel projectiles and finite-thickness UHPC targets of approximately 115 MPa compressive cylinder strength in the impact velocity range from approximately 600 m/s to 1500 m/s. The data set obtained from these experiments includes residual projectile velocities as well as qualitative and quantitative information on damage. Quantitative damage information is mainly extracted from digital 3D post mortem targets, which are produced by 3D-scanning. For all damage quantities, a dependence on the impact velocity and the target thickness is discussed and used to provide possible explanations for the origin of the particular type of damage. The large data set presented in this work can constitute the basis for a comprehensive and quantitative verification and validation of analytical, empirical, and numerical models that describe the perforation of UHPC targets in the investigated impact velocity range.

Experimental and Numerical Study on the Perforation Behavior of an Aluminum 6061-T6 Cylindrical Shell.

The modified Johnson-Cook (MJC) material model is widely used in simulation under high-velocity impact. There was a need to estimate a strain rate parameter for the application to the impact analysis, where the method typically used is the Split Hopkinson bar. However, this method had a limit to the experiment of strain rate. This study proposed to estimate the strain rate parameter of the MJC model based on the impact energy and obtained a parameter. The proposed method of strain rate parameter calculation uses strain parameters to estimate from the drop weight impact and high-velocity impact experiments. Then, the ballistic experiment and analysis were carried out with the target of the plate and cylindrical shape. These analysis results were then compared with those obtained from the experiment. The penetration velocities of plates could be predicted with an error of a maximum of approximately 3.7%. The penetration shape of the cylindrical target has a similar result shape according to impact velocity and had an error of approximately 6%.

Impact experiments on granular materials under low gravity: Effects of cohesive strength, internal friction, and porosity of particle layers on crater size

Impact craters on the surface of asteroids provide information about their surface properties and evolutionary processes. Investigating how crater size depends on these physical properties is important for establishing a crater-size scaling law. We conducted high-velocity impact experiments at 1 G and at simulated low gravity on dry particle layers with different physical properties. The crater diameter was larger for targets with smaller internal friction. Also, for similar internal friction, the crater diameter was larger for targets with lower porosity. The crater diameter for targets with particle diameters of several hundred micrometers was proportional to the gravitational acceleration to the power of −0.16 to −0.18. However, the crater diameters for targets with particle sizes of ∼40 μm showed little or no difference between 1 G and low gravity. Although the results for targets with particle sizes of ∼40 μm at 1 G showed a relationship in the gravity regime, the results under low gravity deviated from this tendency. We obtained the condition for the transition between the gravity- and strength-dominated regimes: the ratio of the cohesion Ycoh to the term ρtgD, or the ratio of the effective strength YEFF to ρtgD, where ρt, g, and D are the target bulk density, gravitational acceleration, and crater diameter, respectively. The values of Ycoh/ρtgD and YEFF/ρtgD for targets with particle sizes of ∼40 μm were 0.22–0.27 and 0.11–0.60, respectively. This study provides basic experimental data for comparison with numerical simulations.

An efficient computational framework for hailstone impacts on composite plates utilizing a semi-empirical viscoplastic contact law

The dynamic response of composite structures under impact loading conditions is a complex problem which is attracting substantial attention. Specifically, the case of hailstone impact introduces additional challenges that are urging to be encountered. Hence, the main goal of this paper is to present the development and validation of a computationally efficient impact model that encompasses a novel semi-empirical viscoplastic contact law for crushable ice impactors together with a new time domain spectral shear plate finite element formulation including nonlinear effects due to large displacements and rotations. The new viscoplastic contact law, which provides the coupling between the hailstone impactor and the targeted composite plate, is derived from analytical expressions and observations based on experiments and high-fidelity finite element simulations which utilize a fully integrated ice failure material model. High-velocity spherical hailstone impact experiments on woven glass/epoxy composite plate target structures are conducted using a high pressure pre-charged gas gun Obtained results are validated against high fidelity finite element models and experimental measurements. The results demonstrate the adequacy of the proposed contact law to capture the impact loading, as well as the accuracy, computational efficiency and additional benefits of the presented computational framework compared to other well-established numerical tools.

High-velocity impact fragmentation of additively-manufactured metallic tubes

In this paper, we have developed and demonstrated a novel high-velocity impact experiment to study dynamic fragmentation of additively-manufactured metals. The experiment consists of a light-gas gun that fires a conical nosed cylindrical projectile, that impacts axially on a thin-walled cylindrical tube fabricated by 3D printing. The diameter of the cylindrical part of the projectile is approximately twice greater than the inner diameter of the cylindrical target, which is expanded as the projectile moves forward, and eventually breaks into fragments. The experiments have been performed for impact velocities ranging from ≈180m/s to ≈390m/s, leading to strain rates in the cylindrical target that vary between ≈9000s-1 and ≈23500s−1. The cylindrical samples tested are printed by Selective Laser Melting out of aluminum alloy AlSi10Mg, using two printing qualities, with two different outer diameters, 12 mm and 14 mm, and two different wall thicknesses, 1 mm and 2 mm. A salient feature of this work is that we have characterized by X-ray tomography the porous microstructure of selected specimens before testing. Three-dimensional analysis of the tomograms has shown that the initial void volume fraction of the printed cylinders varies between 1.9% and 6.1%, and the maximum equivalent diameter of the 10 largest pores ranges from 143μm to 216μm, for the two different printing conditions. Two high-speed cameras have been used to film the experiments and thus to obtain time-resolved information on the mechanics of formation and propagation of fractures. Moreover, fragments ejected from the samples have been recovered, sized, weighted and analyzed using X-ray tomography, so that we have obtained indications on the effect of porous microstructure, specimen dimensions and loading velocity on the number and distribution of fragment sizes. To the authors’ knowledge, this is the first paper (i) providing a systematic experimental study (34 impact tests) on the fragmentation behavior of printed specimens, and (ii) including 3D reconstructions of dynamic cracks in porous additively-manufactured materials.

Damage analysis of typical structures of aircraft under high-velocity fragments impact

In this paper, by establishing a fragmented field of a prefabricated fragment warhead and simulating the intersection of the aircraft and the fragment field under dynamic conditions, the determination of the distribution of the vulnerable parts of a specific aircraft is realized. On this basis, the structural characteristic test pieces of the vulnerable parts were tested with the high-velocity impact experiments based on the two-stage light-gas gun. Based on the FEM-SPH self-adaptive method, a numerical simulation model with a high reduction degree was established. Combined with the experimental results, the damage mode of high-velocity prefabricated spherical fragments to typical vulnerable structures, especially the characteristics of secondary damage caused by debris clouds were studied. This paper verified the feasibility of methods for the vulnerable structure distribution of the aircraft by combing the shooting-line method and the Monte Carlo method. The FEM-SPH adaptive method simulates the damage mode and secondary damage caused by debris clouds on vulnerable aircraft structures. The study in this paper can be severed as an analysis tool in specific aircraft design and damage mode analysis under different threat sources.

Optimization of target thickness and investigation on the effect of heat treatment on the ballistic performance of aluminium alloy 7075 targets against hard steel core projectile

Optimization of target thickness and influence of heat treatment condition on the high velocity impact response of aluminium alloy 7075 targets have been determined. Both experimental and numerical studies were conducted using a 7.62 mm hard steel core projectile. The numerical simulation used a 7.62 mm Ogival nose shaped projectile with a target thickness ranging from 20 to 26 mm. High velocity impact experiments on T651 and solution treated targets, with rolled plate thicknesses ranging from 21 to 25 mm were carried out to validate the numerical findings. The microhardness of the targets was measured using Vicker's microhardness tester and fractographs were examined using a scanning electron microscope. The projectile penetrated regions were analyzed using light microscopy. A good correlation between the numerical and experimental ballistic behaviour of aluminium alloy 7075 targets was observed and an optimum target thickness of 21 and 24 mm was observed for the T651 and solution treated targets to prevent the projectile's penetration. It was also noted that, after the projectile's impact, solution treated targets had higher microhardness compared to T651 condition targets. This is due to higher work hardening of solution treated targets near the penetration channel. Even though T651 targets have a lower depth of penetration compared to solution treated targets, ‘splintering’ failure of the T651 targets is observed. In contrast, ‘petalling’ and ‘plugging’ kinds of failures were noticed on the solution treated targets. Thus, solution treatment of ballistic targets may enhance the ballistic limit of armoured vehicles.

Research on the Impact-Induced Deflagration Behavior by Aluminum/Teflon Projectile

Although the ignition-and-growth model can simulate the ignition and detonation behavior of traditional energy materials well, it seems insufficient to simulate the impact-induced deflagration behavior of reactive materials (RMs) using current finite element codes due to their more complicated ignition threshold and lower reaction rates. Therefore, a simulation method for the impact-induced deflagration behavior of a reactive materials projectile (RMP) is developed by introducing tunable ignition threshold conditions for RMs, and a user-defined subroutine is formed by the secondary development on the equation of state (EOS). High-velocity impact experiments were performed to prove the validity of simulations. The results show that the user-defined subroutine for RMs is competent in simulating the ignition and deflagration behavior under impact conditions, because the reaction ratio, morphology and temperature distribution of RMP fragments are all well consistent with experiments, theory, and current reports from other researchers. In this way, the quantitative study on the deflagration reaction of RMs can be implemented and relevant mechanisms are revealed more clearly.

Preparation and High-Velocity Impact Experiment for Three-Dimensional-Printed Concrete

Preparation and High-Velocity Impact Experiment for Three-Dimensional-Printed Concrete

In-situ thermal analysis of intermetallic and thermite projectiles in high velocity impact experiments

Particle fragmentation influences thermochemical energy conversion processes in different ways and is of significance in energy generation technologies. Different reactive material formulations trigger varied thermal response in extreme environments such as high velocity impact. This study investigated optical thermal response of powder gun launched intermetallic (Al:Zr) and thermite (Al:MoO3) projectiles using pyrometry and thermography. Projectiles were launched at 1250 m/s into an air-filled chamber and impacted a steel witness plate to create a dust explosion. The pyrometer was configured to measure temperatures directly at the point of impact, while the thermographic system measured temperatures throughout the explosion chamber. Results show that impact temperatures ranged between 3500 and 4000 K, but that the dynamics of energy conversion were different for the intermetallic and thermite projectiles. The intermetallic exhibited secondary reactions due to fragmented debris impacting the walls of the chamber. The thermite exhibited greater gas generation, propelling the debris field, and producing a more stochastic response with faster spreading and dissipation of thermal energy. Unique features such as microexplosions within fragmented particles were also analyzed. While both reactive materials produce similar temperatures, their mechanisms of energy conversion and release are different, indicating the potential of these materials for different ballistic applications.

Dispersion and shattering strength of rocky and frozen planetesimals studied by laboratory experiments and numerical simulations

We have developed a method to investigate the whole mass–velocity distribution of impact fragments generated by catastrophic disruption of simulated planetesimals. Flash X-ray radiography including 12 iron particles for tracers was used to visualize the interior of the target, and the velocity distribution of the whole target was estimated by using the velocities of the tracers measured by X-ray images. High-velocity impact experiments in the laboratory and numerical simulations were conducted for four types of targets simulating rocky and frozen planetesimals at various specific energies, Q. These targets consisted of frozen clays with three different water contents ranging from 25 to 45 wt% and porous gypsum with a porosity of 51%. The shattering strength, QS*, and the mass–velocity distribution (MVD) were studied for these targets. The QS* of the frozen clays varied by a factor of 3–4 times, depending on the water content, and the QS* for porous gypsum was almost the same as that for the frozen clays with lower water contents. The numerical impact simulations led to slightly different QS* and MVD values for the frozen clay targets, possibly because of the partly ductile behavior of these samples. The MVDs resulting from the porous gypsum targets were well reproduced in the simulations. The cumulative mass of fragments with an ejection velocity slower than a specific velocity was examined to introduce a median velocity, v⁎, charactering the mass–velocity distribution. The v⁎ is defined as the velocity at which the cumulative mass corresponds to a half of the original target mass in the distribution. The v⁎ values of the frozen clays were described by the empirical equation v∗ = εQγ with almost the same ε and γ, irrespective of the water content, but the v⁎ of porous gypsum was about 1/3 that of the frozen clays. These experimental results were well reproduced by the numerical simulations for both frozen clays and porous gypsum targets. The dispersion strength, QD*, could be derived by comparing v⁎ with the escape velocity, vesc, of a target body with an effective mass, M, and radius, R. From this, a semi-theoretical equation showing the dispersion strength was derived: QD∗=1ε2GMR1/21/γ. Numerical simulations of catastrophic disruptions including self-gravity were conducted to directly determine QD* at large scale. These calculations showed that the effective mass of the target body, which is used in the computation of vesc = v⁎, should be a half of the original target mass, M = Mtarget /2. Our results suggest that this approach for computing the semi-theoretical dispersion strength is suitable for bodies larger than ~10 km.

High-velocity impact response of fiber metal laminates: Experimental investigation of projectile's deformability

The aim of this research is to investigate the influence of projectile's deformability on ballistic impact response of fiber metal laminates. High-velocity impact experiments have been carried out via a light gas gun setup using rigid, semi-rigid and deformable projectiles with the same diameter, nose shape and mass. Fiber metal laminates have been made of two identical aluminum facing plates and different number of glass/epoxy composite plies in the middle. Several local and global mechanisms for kinetic energy absorption of projectiles have been detailed and ballistic limit velocity, as well as specific perforating energy for all cases have been determined. The results indicated that by increasing the deformability of the projectile, the amount of local and global wasting energy mechanisms for dissipating the velocity of projectiles have been increased. Furthermore, the interaction between non-rigid projectiles and fiber metal laminate targets as well as permanent deformation of non-rigid projectiles, had important effects on preventing the projectile penetration. By increasing the deformability of projectiles and/or increasing the number of composite plies, permanent deformation of facing plates, fiber breakage, crushing as well as delamination and debonding have been increased and local damage modes in facing plates changed from petalling to plugging. Besides, rigid projectiles possessed less specific perforating energy compared with deformable projectiles and required minimum initial velocity for full penetration.

The behaviour of thermoplastic and thermoset carbon fibre composites subjected to low-velocity and high-velocity impact

The present paper describes the results from experimental and theoretical modelling studies on the behaviour of continuous carbon fibre/polymer matrix composites subjected to a relatively low-velocity or high-velocity impact, using a rigid, metallic impactor. Drop-weight and gas-gun tests are employed to conduct the low-velocity and high-velocity impact experiments, respectively. The carbon fibre composites are based upon a thermoplastic poly(ether–ether ketone) matrix (termed CF/PEEK) or a thermoset toughened epoxy matrix (termed CF/Epoxy), which has the same fibre architecture of a cross-ply [03/903]2s lay-up. The studies clearly reveal that the CF/PEEK composites exhibit the better impact performance. Also, at the same impact energy of 10.5 ± 0.3 J, the relatively high-velocity test at 54.4 ± 1.0 m s−1 leads to more damage in both types of composite than observed from the low-velocity test where the impactor struck the composites at 2.56 m s−1. The computationally efficient, two-dimensional, elastic, finite element model that has been developed is generally successful in capturing the essential details of the impact test and the impact damage in the composites, and has been used to predict the loading response of the composites under impact loading.

High-velocity impact onto a high-frictional fabric treated with adhesive spray coating and shear thickening fluid impregnation

The ballistic performance of a bullet-proof fabric can be increased by an increment in the friction between fibres. For enhancement of this performance, numerous studies on the shear thickening fluid (STF)-impregnated fabric have been conducted. The STF as a fluid, however, has inherent shortcomings. Our research aim is to understand and compare experimentally two different bullet-proof fabrics treated with a simple spray coating and STF impregnation. In this study, 71 single yarn pull-out and 90 high-velocity impact experiments were carried out. It was remarkable that the newly proposed Heracron fabric coated with a commercial coating spray increased by more than 90% the energy absorption before penetration, with only less than 15% of add-on weight. It was found that the polymeric anchors created on the fibre produce an exceptionally high level of friction between fibres, according to a microscopic morphological analysis and the single-yarn pull-out experiment. This study revealed the physical explanation of this coating method, showed its feasibility, and considered its effectiveness with excellent results.