Predictive models and experiments for high-velocity and high-temperature impacts in Inconel-alloy panels.

performedusingacustom-madetwo-stagelight-gasgunrig,withthespecimensbeingsubjectedtohightemper- atures(upto1007°C).Thepanelshavebeenimpactedusingsphericalprojectileswithvelocitiesrangingfrom0.5 to 2.2 km/s. During the experiments the failure of the targets has been evaluated by varying parameters like the projectilediameter,itsdensityandtheobliqueimpactangle.Ananalyticalmodeltoestimatetheresidualvelocity and theballisticlimit equations hasbeenestablished.Finite element models(FEM) combined with phenomeno- logical analytical models have been also developed to validate the predictive results obtained by the analytical model. The simulations from the FEM and the analytical models provide a good match with the experimental data. For the two typical cases (normal impact and oblique impact), the shapes and sizes of the damaged holes havebeen also well predictedby the numericalmodel.Equivalent diameters of the impacts have also been iden- ti ﬁ ed as functions of the velocity, diameter of the projectile and panel thickness.


Introduction
Inconel superalloys have been successfully used in the aeronautical [1][2][3], aerospace [4,5] and nuclear industry [6,7] due to their outstanding mechanic properties and corrosion resistance at elevated temperatures. The engineering applications in which Inconel superalloys structures are in general used involve the existence of a fracture or perforation threat and a strong thermally induced degradation [4,8,9].
A significant body of work concerning experimental and numerical analyses has been carried out to investigate the mechanical behavior and the dynamic failure mode of Inconel. Kajberg et al. [10] have developed three different modified fracture criteria to characterize and evaluate the mechanical behavior of Inconel 718 subjected to high strain rates (1000s −1 ) and high temperature (650°C) loadings. The criteria were verified with calibration experiments and the failure predictions were consistent with the real ones observed in the specimens. The effects of different strain rates on the performance of Inconel in hot environments have been evaluated by Lin [11], with a resulting modified constitutive model developed to characterize the hot deformation behavior of the 718 Alloy. The constitutive models of Inconel alloys are strain-rate dependent, and various experimental tests have also shown that the temperature is a non-negligible factor [12][13][14]. Split Hopkinson Pressure Bar (SHPB) tests have been used to investigate the failure and mechanical properties at high strain rates [15,16]. Lee and his team [17] have proposed an approach to evaluate the dynamic shear response and shear localization characteristics of Inconel 718 alloy at temperatures ranging from −150°C to 550°C. The microstructural evolution of the Inconel 718 subjected to high temperatures (950°C to 1100°C) and high strain rates (from 0.01 s −1 to 1 s −1 ) have been also studied [18].
Several research teams have also focused on the ballistic impact response and failure mechanisms of metallic structures. Erice et al. [19] have performed a series of high-temperature ballistic impact experiments to obtain the mechanical behavior of Inconel 718. Mohotti [20] has investigated the ballistic limit curve for aluminum-polyurea composites subjected to relatively low velocity (945 m/s) impact loading, and an analytical model has also been developed to predict the residual velocity of the projectiles. A novel configuration for orbital debris shielding has been proposed by Huang [21], with a series of impact experiments also being conducted to evaluate the protection efficiency. A new metallic energy-absorbing bumper for vehicles has been successfully designed by Peng [22], and the crashworthiness of the structure has also been tested using both numerical and experimental techniques. The peak impact force and the penetration characteristics of Inconel 718 at high velocity impacts and an empirical ballistic limit curve have been derived by Di Sciuva et al. [23]. The impact response and the dynamic perforation mechanism of honeycomb sandwich panels have been extensively investigated by Sun [24]. The effects of the environmental temperature, impact velocity and their associated energy on the damage resistance of honeycomb sandwich and carbon carbon composites subjected to impacts have been studied systematically by Xie et al. [25,26].
Because the debris and dust does not always impact the shields along a perpendicular (normal) direction, the effect of the incident impact angle has also been systematically evaluated for space engineering [27,28]. Masahiro [29] have studied the size distribution of fragments in oblique impacts, and the results have revealed that size distributions and affected regions are strongly correlated to the strike angle. Tore et al. [30] have performed numerous normal and oblique impacts and found that 20 mm AA6082-T4 aluminum plates could not be perforated by the projectile when the incident angle exceeds 60°. Zhang et al. [31] have also studied the effects of impact angles and velocities on the perforation behavior of carbon fiber reinforced plastics, and the fracture patterns due to delamination and perforation have also been investigated.
This paper presents an experimental and analytical study of the effects of high velocity impacts (554 m/s to 2200 m/s) on Inconel718 and Inconel617 panels at temperatures of 25°C, 450°C, 700°C and 1000°C/1007°C. The experimental tests were performed using a custom-made facility. An analytical model that describes the impact on the plates is developed. The model allows predicting the residual velocity and the ballistic limit equations for the impact case. Impact responses have also been numerically investigated with an ABAQUS/ Explicit Finite Element model. The performance of the plates under oblique impacts is also investigated to consider some realistic loading situations, like space debris impact. To the best of the Authors' knowledge there is significant scarcity of data and models available in open literature about the performance of Inconel alloy panels under oblique impacts, in particular when performed at high velocities and high temperatures above 1000°C. The objective of this paper is to provide some general design guidelines for metallic thermal protection shields with the proposed models and experimental data.

Specimen preparation
The experimental specimens used in this paper have been made from Inconel alloys (Inconel718 and Inconel617 - Fig. 1). The diameters of the spherical projectiles were measured before the tests, with a maximum deviation between their values less than 0.1 mm. The dimensions of panels were determined to ensure a reliable connection with the customized test rig and enough room for the high-velocity oblique impact.
The geometric and material parameters considered in the experiments are illustrated in Tables

High temperature impact facilities set-up and test procedure
The impact facilities consist in a two-stage light-gas gun equipped with a fast electric heating system (Figs. 2 and 3). A custom-designed fast electric heating system is installed in the impact chamber to heat and also measure the temperatures of the specimens. To heat the samples, two ends of the specimens are first connected to a pair of copper electrodes that are then fixed to a supporting back plate ( Fig. 2(b)). Voltage between 1 V and 4 V is applied at the two ends of the specimen via a transformer. Current between 10 A and 5000A is controlled, with the transient of the current causing a rapid temperature rising. A multi-wavelength pyrometer for a temperature higher than 299°C (up to 3000°C) has been used to measure and monitor the temperature of the specimens except for the ones subjected to room temperature (RT). The pressure of the chamber is kept at atmospheric levels during the tests.
The ballistic performance of the specimens is evaluated through normal and oblique impacts with velocities from 554 m/s to 2200 m/s. Fig. 4 shows a general sketch of the impact test performed. The projectiles are made of stainless steel, ZrO 2 and Si 3 N 4 because of the outstanding hardness and toughness of those materials. Spherical projectiles with different diameters have been accelerated to the pre-determined velocity to impact the center of the targets with four incident angels (0°, 15°, 30°a nd 45°). The temperatures during the impact tests were kept under control at about 25°C (RT), 450°C, 700°C and 1000°C/1007°C.

Impact test results
Eighteen high-velocity impact experiments have been performed. Only two plates have been completely destroyed, and no geometric deformation of the projectiles has also been observed at the same time. Circular holes were presented after the normal impact tests, while the plates subjected to oblique impact have shown holes with elliptical shapes (Fig. 13). The topologies of the holes have been evaluated by measuring the size of the damage holes. Tables 1 and 2 present a summary of the two test cases considered in this work. The thickness of the high-velocity impacts targets is relative small; that leads to the presence of holes with similar dimensions between the front and the back surfaces, with a mean deviation lower than 5%. The data contained in   Tables 1 and 2 represent the average between the front and back surfaces.
Inconel718 panels with thickness of 1.8 mm have been used as target in ten oblique impact experiments. The impact energy of the INC-1 sample (about 5.4 J) was almost completely absorbed by the panel, and no perforation was observed on its back side. The impact energy carried by the projectile increases with the increase of its diameter and the initial velocity. As a consequence, the INC-7 sample with a projectile of velocity of 1.47 km/s and a diameter of 5 mm showed the largest damage area. Although the diameter of the projectile of the INC-3 test was smaller than the one related to the INC-6 impact, the INC-3 plate still exhibited a relatively large perforated hole area because of the higher impact velocity. For a constant projectile diameter, the tangential component of the velocity plays a significant role in the oblique impact tests, therefore so the values of the longest and shortest ellipse axis of the holes were different for the various impacts. The INC-9 and INC-10 tests were carried out in the same conditions (temperature, impact angle and diameter), however a larger damage area was observed in the INC-10 plate. The lower the velocity of the projectile, the rougher the edge around the hole would appear. An expanding shape was also observed in the back side of the INC-10 target.
The normal impact experiments have been performed with the 1 mm-thick Inconel617 panels. During two experiments (G3 and G4) the specimens have been hit by projectiles with diameter of 5 mm at constant impact velocity (about 1.7 km/s). The strength of the specimens at high temperature has shown a dramatic reduction compared to the room temperature case; the G3 sample therefore featured a larger circular damage hole at over 1000°C, in comparison with the G4 specimen.
In summary, a multiple parameters test campaign has been used during the experimental investigations. The impact energy carried by the projectile has affected the dimensions of the damage section. No obvious wrinkles and deformations in the area surrounding the perforation have been observed. The holes featured the same shape on the front and back sides of the plates.

Analytical model
High velocity impacts can be divided into three different categories: within the ballistic, the shattered and vaporized ranges [32]. In this paper the metal panels experienced ballistic range impacts. Studies concerning the perforation modes of metal specimens within the ballistic range impact have been described in a very limited number of papers so far [32,33]. In those works the three velocity impact regimes have been differentiated by observing the features of the damaged targets. At low velocities impact (ballistic regime) the projectile tends to hit the target and bounces off leaving a local dent on the front side of the panels. The shattered regime has been characterized by the state of the back surface, with a perforation that tends to become dominated by an out-diffusion shape. The third regime (vaporized range) is characterized by a compression/shear failure of the target, and the type of perforation mode turns into a plug-shaped formation. The Inconel alloys plates tested at high velocity and temperature in this work feature perforations dominated by the formation of shaped plugs. The inside section around the holes of the perforated plates in this work appear  smooth, and therefore one could conclude that the portion of the specimen perforated is sheared by the projectile. The projectiles were also intact after the tests. The residual velocity and the ballistic limit equations are important metrics and tools to design metallic thermal protection systems; the residual velocity is indicative of the protective capacity of the system, while the ballistic limit equations provide useful guidelines at the initial design stage.
The analytical model is based on the presence of an ideal spherical projectile that carries kinetic energy and hits the specimen at an impact angle. The perforated section of the target is removed by the shear force generated along the incident direction. The overall impact process assumes that the local energy dissipation is neglected, and the projectile plus the specimen debris travel with the same velocity after the impact. The equation that governs the conservation of energy can be formulated as: As a simplification one can assume that the resistance acting on the projectile and the plug when they move forward relative to the surrounding plate material is mainly constituted by shearing forces [34]. The work W s has therefore the following expression: The term W f can be estimated by momentum and energy considerations along the normal direction [35], i.e. W f = m p m b V p 2 /2(m p + m b ). One then obtains: The residual velocity V f can therefore be derived as: The ballistic limit state can be defined as the zero residual velocity (V f = 0). The ballistic limit equation is therefore: Common integral formulas can be applied to deduct the terms m p = πd p 3 ρ p /6 and m w = πd h 2 t w ρ w /4 used in this paper. Taking the two expressions into Eqs. (4) and (5), the residual velocity and the ballistic limit equation can then be simplified as follows: The analytical model is valid for thin target panels of isotropic materials and for cases in which the deflection of the velocity caused by the thin panel can be ignored.

Finite element modeling
The explicit Finite Element code ABAQUS (version 6.13) has been used for the numerical analysis. The FE model of the Inconel plates is shown in Fig. 5. The temperature-dependent mechanical and the material properties of the materials used in the simulation (Inconel alloys, steel, Si 3 N 4 and ZrO 2 ) are described in Table 3.
The mesh density around the contact region and within a radius of ten millimeters has been increased to provide a more accurate prediction of the impact response close to the target. Before carrying the explicit analysis, mesh size and density, maximum time increment and element type of the FE model have been evaluated (see Table 4 and Fig. 6). Since the spherical projectiles used during the tests showed no visible deformation, the projectile has been modelled here as a rigid body.
The general contact algorithm [36] has been adopted to model the surface erosion on the target during the high-velocity impact, with the self-contact algorithm of the target being activated during the simula-  tion. Normal and tangential contact behavior has also been included. The hard contact model has been employed to define the normal behavior in all the cases, while for the oblique impact cases the static-kinetic exponential decay algorithm has been adopted to define the tangential behavior (static and kinetic coefficients of 0.27 and 0.16 [24]). The projectile had a predefined velocity field at the initial step of the simulation. The fixtures present in the tests have been represented by full clamps (zeroing all the nodal DOFs) at the two sides of the target. The high strain-rate behavior of the plastic metal has been represented by the Johnson-Cook (J-C) model [14,37,38]. The constitutive laws can be defined as a function of the yield stress and the effects of the strain rate, strain hardening and thermal softening [38,39]: Equations [14,40,41] contain J-C parameters identified experimentally. To this end, the data from reference [42] have been used in this paper. Tables 5 and 6 list the J-C constitutive relation and the J-C failure criteria input parameters for the Inconel alloys. All the simulations have been implemented by the ABAQUS/Explicit solver which was installed on the workstation with 64GB RAM.

Validation of the FE model
Experimental results from open literature related to light gas gun tests [19] have been used first to verify the validity of the proposed numerical model. Erice et al. [19] have performed high velocity impacts on Inconel718 samples within a temperature range between 25 and 700°C. The numerical solutions provided by the presently developed model are compared against the experimental results in [19] (Figs. 7 and 8). The FE model established in this paper provides an accurate prediction of the residual velocities and shape of the panels. The maximum deviation of the residual velocity from the experimental data does not exceed 11.2%. The proposed FE model has been also validated by comparing the numerical predictions against the experimental results carried out in the present work. As listed in Table 7, the relative error of the damage area ranged from~0% to 17.4%.
Figs. 9 and 10 show the general failure mechanism of the metallic specimens subjected to normal and oblique impact loading. The von-Mises stress distributions of the target at the moment of the impact are illustrated in Figs. 9(a) and 10(a). As the impact progresses on, the local stresses around the impacted section exceed the ultimate strength of the alloys; the material yields first and then cracks. Finally, the eroded elements are removed (Figs. 9-10(b), (c) and (d)). As the applied force is perpendicular to the target, the transient stress distribution is almost symmetrical during the normal impact. During oblique impacts, however, the transverse impact component tends to produce an additional stress field and a transient stress distribution combined with the one induced by the normal impact. The effect of the lateral velocity of the projectile modifies the contact region and creates an ellipse-shaped damage zone.
The impact responses predicted by the numerical results have been compared with the experimental results (Figs. [11][12][13]. Shapes and sizes of the damaged zones described by the FE model appear to be quite consistent with the experimental data. The scale bars in the Figs. 11-13 are displayed in millimeters. Plastic deformation will occur when the ductile panels are subjected to low strike velocity (Fig. 8). No apparent failure is observed after the impacts, and the projectile tends to rebound. When the impact velocity increases a local crater is left on the front side of the panels (Fig. 11). The plug-shaped deformation caused by the compression/shear failure in the panels will occur when the impact energy exceeds the strain energy associated to the resistance of the panel. Also, the higher impact energy  a Parameter A (initial yield stress at different temperatures) were listed in Table 3. Table 6 Failure criteria. the projectile carries, the smoother the perforation edge results (Figs. 12  and 13). The deformation in the damaged zone tends to be highly localized when the impact energy is increased [43,44].

Predictions and tests
The residual velocities and ballistic limit curves reflect the impact protection performance of metallic thermal protection shields (MTPS). This paragraph is dedicated to correlate those parameters to numerical and experimental results.

Residual velocity predictions and numerical simulations
The diameter of the perforation hole d h is an essential parameter for the analytical expressions derived in Section 3. The validated FE model is applied to estimate an expression for d h . Forty different numerical simulations have been carried out related to the two types of impact tests. The two cases have included normal velocities ranging from 200 m/s to 2000 m/s, and panel thickness varying between 0.5 mm and 2 mm. The environmental temperatures ranged from 25°C (room Fig. 8. Comparisons of the shape of non-perforated panels at room temperature provided by the current model and the experimental results in Ref. [19].
In the equations, c w = 5699.76 m/s is the speed of sound in Inconel alloys [45]. The predictions related to the residual velocity show a general good agreement with the simulation results. For the particular conditions considered, the effect of shattered and scattered metallic debris may not be ignored. This is particularly true when the impact velocity exceeds 1 km/s and the residual energy cannot be completely absorbed by all the shattered debris, something that has been also observed during other experiments [46]. In addition, data related to the effective yield shear strength of the alloy during the dynamic loading are very limited in open literatures, therefore the quasi-static shear strength at room temperature is used here to calculate energy lost W s during the penetration. This provides some justifications for the   difference in velocities between the numerical predictions and the theoretical results.

Ballistic limit curve prediction for the experimental tests
The diameter of the projectile diameter is here chosen as the critical parameter. Ballistic limit impact velocities lower than 3 km/s have been calculated by introducing Eqs. (10) and (11) into Eq. (7), and verified with the experimental results (Fig. 15). For the oblique impact case the impact velocity V p cosθ is replaced with V pθ in Eq. (7). Fig. 15 shows the ballistic limit predictions for the four combinations of target and projectile considered in this work, with the points representing the experimental data. Single data located above the curve indicate that the target will be definitely perforated. The closer the point approaches to the curve, the lower the kinetic energy is after the impact. Data below the curve like in Fig. 15(a) indicate that no perforation will occur. All the experimental data obtained in this work (see Table 1) confirm the validity of the ballistic curves developed and their applicability to predict the general impact performance of Inconel alloy panels.

Conclusions
The behavior of Inconel plates under high-temperature high velocity impacts at elevated temperatures have been investigated in this paper. By using numerical and experimental methods, the impact resistance capacity of metallic panels and the ballistic limits performances have been evaluated. Experimental tests have been carried out in a custom two-stage light-gas gun rig, and an analytical model combined with a FE approach have also been established. Multivariate parameters such as temperature, impact velocity, impact angle, panel thickness and projectile diameter have been considered in these impact tests. The residual velocity and the ballistic limit equations for the different test cases have been identified. The main conclusions of the work are as follows: Both normal and oblique impact cases showed one dominating perforation mode, i.e. the one related to combined compression and shear failure. The analytical model developed is applicable to the plugged perforation mode. A phenomenological method was adopted to validate the FE model. The shape and geometry of the area of the holes obtained by the numerical model agrees well with tests results.
The residual velocity has been calculated using the analytical and numerical approaches. The results were in general good agreement, except for some particular cases. The ballistic limit curve developed to predict the impact resistance of the Inconel alloy plates has provided good results, with all the experimental data correctly predicted.
The proposed models and the experimental results can provide useful guidelines to design airframe and spaceframe MTPS that consider the effects of temperature, panel thickness, impact velocity, impact angle and projectile diameter on the performance of the target panels.