Tuning microstructures of TC4 ELI to improve explosion resistance

Chnl Zhn , Ynwi Wn ,b, Lin Wn ,b,c,*, Zixun Nin , Guoju Li ,Donpin Chn , Zhi-Wi Yn , Yuchn Son , Xuci Wn

a School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China

b National Key Laboratory of Science and Technology on Materials under Shock and Impact, Beijing 100081, China

c State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China

d Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China

e School of Aeronautical Engineering, Zhengzhou University of Aeronautics, Henan Province, Zhengzhou 450046, China

f Shanxi Jiangyang Chemical Co., Ltd., Shanxi Province, Taiyuan 030041, China

g Shandong Institute of Non-metallic Materials, Shandong Province, Jinan 250031, China

Keywords:Microstructure Finite element modelling Parameter optimization Failure characteristics Explosion resistance

ABSTRACT A reasonable heat treatment process for TC4 ELI titanium alloy is crucial to tune microstructures to improve its explosion resistance.However, there is limited investigation on tuning microstructures of TC4 ELI to improve explosion resistance.Moreover, the current challenge is quantifying microstructural changes’ effects on explosion resistance and incorporating microstructural changes into finite element models.This work aims to tune microstructures to improve explosion resistance and elucidate their antiexplosion mechanism, and find a suitable method to incorporate microstructural changes into finite element models.In this work,we systematically study the deformation and failure characteristics of TC4 ELI plates with varying microstructures using an air explosion test and LS-DYNA finite element modeling.The Johnson-Cook (JC) constitutive parameters are used to quantify the effects of microstructural changes on explosion resistance and incorporate microstructural changes into finite element models.Because of the heat treatment, one plate has equiaxed microstructure and the other has bimodal microstructure.The convex of the plate after the explosion has a quadratic relationship with the charge mass,and the simulation results demonstrate high reliability,with the error less than 17.5%.Therefore,it is feasible to obtain corresponding JC constitutive parameters based on the differences in microstructures and mechanical properties and characterize the effects of microstructural changes on explosion resistance.The bimodal target exhibits excellent deformation resistance.The response of bimodal microstructure to the shock wave may be more intense under explosive loading.The well-coordinated structure of the bimodal target enhances its resistance to deformation.

1.Introduction

High-performance titanium alloy plates are increasingly used in vehicle protection as they are lighter and have higher specific strength than steel [1-5].The TC4 ELI alloy is a medium-strength titanium alloy obtained by reducing the interstitial elements in the conventional TC4 alloy[6],and its mechanical properties can be adjusted and optimized through heat treatment [7].For example,heat treatment can elevate the primary α phase in the two-phase region of the TC4 ELI alloy to increase the strength, although it decreases the ductility [8].

Wang et al.[9] found that the microstructure and mechanical properties of TC4 ELI plates subjected to annealing treatment and solution treatment above the β transition temperature (Tβ) were relatively uniform, with higher resistance to fatigue cracking and fracture toughness.Lei et al.[8] found that as the solution temperature increases, the primary α phase decreases, the strength increases, and the ductility decreases in the two-phase region of TC4 ELI titanium alloy.TC4 ELI titanium alloy can achieve good mechanical properties with the heat treatment process of 955°C/(1 h)air-cooling(AC) +550°C/(8 h)AC.El-Hadad et al.[10]found that the hardness of Ti-6Al-4V alloy increased from 380 to 575 and 656 HV respectively when the alloy was water quenched in the β and α/β phase regions after aging for 6 h at 550°C,and there was no significant change after aging.The hot tensile strength of the forged specimen increased from 671 MPa to 756 MPa after water quenching in the β or α/β phase region, while the tensile strength decreased to 644 MPa after air cooling in the β phase region.The fracture mode of the tensile specimen after solution treatment was more ductile than that of the forged specimen.Therefore, it is crucial to develop a reasonable heat treatment process for TC4 ELI titanium alloy to obtain excellent mechanical properties.

The explosion resistance of titanium alloy plates, especially those of the TC4 ELI plate with high toughness and plasticity,is less well studied than that of steel plates[11-13],aluminum alloy plates[14-16],and sandwich structures[17-19].Fu et al.[11]found that global plastic deformation is the primary damage mode of strain rate-sensitive armor steel subjected to close blast loading.Bassiri et al.[16]discovered that under short-range explosion loads,as the impulse increases, 2024-T3’s damage shifts from overall deformation to local fracture.Dolce et al.[10]observed that fiber composite type significantly influences the explosion resistance of fiber composites.Fiber composites absorb explosion impact energy mainly through progressive failure mechanisms such as compression, shear and failure.With the increase of explosive mass, the overall deformation of fiber composite plate changes into serious local damage.Bassiri et al.[20,21] discovered that delamination and fiber fracture are the main forms of damage to composite materials under the action of explosion.The explosion energy is mainly dissipated through different damage mechanisms such as fiber fracture, fiber stretching, and plastic deformation, while the dissipation effect of debonding on the explosion energy is not significant.The damage modes of fiber metal laminates subjected to close-range explosion are mainly fiber fracture, debonding, and overall deformation.As the explosion impulse increases, the damage mode shifts from global deformation to highly localized perforation.Moreover, disc-shaped explosives cause greater local damage than spherical explosives.Fan et al.[22]found that the TC4 alloy cylinder treated with a double annealing process will not quickly develop an adiabatic shear failure during blasting and thus has excellent anti-explosion performance.Zhang et al.[23]tested a 1.6 mm TC4 alloy plate subjected to explosive loading and found that the tensile stress is mainly responsible for the target’s failure,but they did not provide an in-depth analysis of the target’s deformation mechanism.Ning et al.[3] compared a 12 mm equiaxed Ti6321 alloy plate and a 12 mm Weissmann Ti6321 plate and found that the former has a higher deformation resistance while the latter has a higher spalling resistance and a lower thickness thinning rate.However, this study does not analyze the deformation and failure process of the target.More research is needed to determine the structural features that contribute to strong antiexplosion performance as well as the underlying mechanisms.

Banded shear deformation localization is a common phenomenon in titanium alloys during high strain rate loading [24,25].Xu et al.[24] discovered that, during the explosive loading process,deformation twins emerged in TC4 titanium alloy,followed by the evolution of local shear bands and the formation of dynamic recrystallization grains without distortion in the shear bands.Similarly, Fan and Kong et al.[26] observed that the thermal conductivity of TC4 titanium alloy is minimal, and the heat generated by large plastic deformation could raise the grain to or near its melting point temperature,leading to thermal softening and shear band formation.Zheng et al.[4]found that the microstructure was the main factor leading to the change of failure mechanism in Ti-6Al-4V target when subjected to 12.7 mm armor-piercing(AP)threat.In the equiaxed targets, the regularly spaced propagating characteristics of adiabatic shear bands (ASBs), together with the ASBs induced cracks led to the formation of delamination and fragmentation, which promoted the failure mechanism of ductile hole enlargement.In the lamellar targets, the net-like expansion features of ASBs and the ASBs induced cracks resulted in plugging and star fragments, which were favorable for the failure mechanism of brittle fracture.Therefore,we should not underestimate the impact of thermal softening and the formation of shear bands due to significant plastic deformation on the explosion resistance of titanium alloys during explosive loading.

The Johnson-Cook(JC)constitutive model,which describes the relationship between the flow stress and the effective plastic strain,strain rate, and temperature during the plastic deformation and failure of materials, is suitable for characterizing the dynamic mechanical response of TC4 ELI plates under high strain rate conditions.Common fitting methods for the JC model, including the traditional uncoupling method [27], the clustering global optimization method[28],etc.,tend to be complicated and do not always give consistent results.They often require many model parameters(e.g., data under different temperatures and strain rates).But they still didn’t consider mesh size adaptability, and the obtained material constitutive parameters cannot always be accurately used in finite element modeling.An ideal method needs to not only quickly and efficiently fit the JC constitutive model but also consider the influence of the finite element model.

This work aims to find a suitable heat treatment process to make TC4 ELI plates with moderate strength,good plasticity and fracture toughness,and excellent explosion resistance.Two 12 mm TC4 ELI plates with different microstructures were designed and their explosion resistance was studied by explosion test and numerical simulation.We determined the optimal material parameters by combining the LS-OPT parameter identification with automatic optimization to adjust the model parameters iteratively, which significantly reduces the time and cost of fitting the JC constitutive model,thus addressing the low efficiency from manual comparison between simulation and test curves.We then revealed the explosion resistance mechanism through finite element simulation and microstructure analysis.The results provide a valuable reference for the performance optimization and engineering practice of TC4 ELI plates.

2.Materials and methods

This paper tuned the microstructure of TC4 ELI target by changing the heat treatment process.Two sets of solution treatment temperatures were set below the (α+β)/β phase transition point,and the same holding time and cooling method were used to obtain two different heat treatment processes.

2.1.The flowchart of the research

Fig.1.The flowchart of the research.

The flowchart of the research is shown in Fig.1.This paper is mainly divided into two parts:experiment and simulation,and the two parts complement each other.The experiment includes four parts: heat treatment, mechanical performance testing, explosion testing, and microstructure observation.Microstructure observation is carried out after heat treatment and explosion testing,respectively.The simulation includes two parts: SHPB simulation and explosion testing simulation.The SHPB simulation is conducted after SHPB testing, but the explosion testing simulation is conducted before the explosion testing.In the experiment section,two kinds of TC4 ELI targets with different microstructures were obtained by changing the heat treatment process.Subsequently,microstructure observations,mechanical performance testing,and explosion testing were carried out on the targets.The basic mechanical performance data such as tensile strength and compressive strength of TC4 ELI targets with different microstructures were obtained through mechanical performance testing,which provided support for SHPB simulation optimization and obtaining appropriate JC constitutive parameters.Grid independent verification is required before explosion testing simulation.First,the grid convergence analysis of the air domain grid is carried out.Then,the convergence analysis of the target grid is carried out using the converged air domain grid and the JC constitutive parameters optimized from SHPB simulation.The main evaluation indexes of the target’s anti-explosion performance, such as peak deformation displacement, convex, energy consumption, failure mode, and stress and strain distribution during the deformation process, are obtained through explosion simulation.Finally, the reliability of the explosion testing simulation is verified through explosion testing,and the damage characteristics of the target after the explosion test are observed microscopically, and the failure mechanism is analyzed.

2.2.Heat treatment and microstructure observation

The hot-rolled annealed TC4 ELI plates(195 mm×195 mm×12 mm) were manufactured according to ASTM B265 and ASTM B898 by the Luoyang Ship Materials Research Institute.The surface density is 53.52 kg/m2.The chemical composition is given in Table 1.The(α+β)/β transition temperature is 970°C according to differential scanning calorimetry [25].The plates were treated at below the phase transition temperature(holding for 1 h at 800°C or 960°C and then air-cooling to ambient temperature, Fig.2) to obtain the solution treated TC4 ELI plates(referred to as I800and T960respectively) with good strength and toughness [29].

Table 1 Chemical composition of the pristine TC4 ELI plate (wt%) [25].

To characterize the microstructure,the surface of the plates was ground and polished, corroded for 10-15 s with a mixture of hydrofluoric acid, nitric acid, and deionized water (1:5:44 v/v), and then examined by optical microscopy (OM) and scanning electron microscopy (SEM).

2.3.Parameter identification of the JC constitutive model

The strength equation of the JC constitutive model is shown in Eq.(1) [23].

where σ is the equivalent stress,εpeis the equivalent plastic strain,˙ε*is the relative equivalent plastic strain rate (˙ε*= ˙εpe/˙ε0, ˙ε0=1.0 s-1), T* = (T - Tr)/(Tm- Tr) is the dimensionless temperature,Tmis the melting point of the material,Tris room temperature,and A, B, n, C, and m are material constants.The basic JC constitutive parameters of the TC4 alloy are in Refs.[23,30].

Fig.2.The heat treatment process of the plate.

The mechanical behavior of I800and T960at high strain rates was examined by the split Hopkinson pressure bar (SHPB) test.The impact rod,incident rod,and transmission rod are made of stainless steel and have a diameter of 16 mm, and their length is 20 cm,100 cm, and 100 cm, respectively.The compression tests were carried out at a strain rate of 103s-1, and the sample size is φ = 5 mm × 5 mm.The experimental SHPB results are used to optimize and obtain the JC parameters through LS-OPT parameter identification with automatic optimization.Specifically, the JC parameters are used to calculate, by finite element modeling, the contact force between the input rod and the plate and the corresponding displacement difference between the two nodes in SHPB(thus simulating the SHPB) [31] until the deviation between the experimental and the simulated SHPB is less than 0.01(Fig.3).The SHPB simulation results are automatically extracted from LS-DYNA by LS-OPT based on the continuous response surface algorithm to iteratively optimize the JC parameters.The reference data of the LSOPT optimization are obtained by numerical simulation.Four variables(b,n,c,and d1)are created through global sensitivity analysis for LS-OPT, and their optimization intervals are given in Table 2.

2.4.Explosion test

Fig.3.The 1/4 finite element simulation model of the SHPB test.

Table 2 Optimization interval of main optimization variables [23,30,32].

The explosion test uses two sensors to measure the shock wave overpressure at 2 m away from the charge column (Fig.4(a)) (see Table 3).The target plate(195 mm×195 mm)is fixed by C-shaped clamps on the target frame, and the deformation area is 170 mm × 170 mm (Fig.4(b)).The cylindrical charge (45 mm in diameter) inside a paper shell is placed at the corresponding blast height on top of a triangular support made of cardboard paper,which in turn sits at the center of the plate.The height of the cylinder corresponds to the amount of TNT (1.61 g/m3) used, and the two sensors are level with the center of the charge column(Fig.4(c)).The standoff distance,i.e.,the vertical distance between the bottom surface of the cylindrical charge and the top surface of the plate (thus also the height of the triangular cardboard paper support), is 40 mm.The charge is initiated at the center of the top surface of the charge column.After the detonation,the two sensors record the change of the shock wave overpressure with time [33].The convex of the plate(the height of the bulge at the center of the plate)is measured at the end.

2.5.Numerical simulation of the explosion test

Fig.5 shows the finite element model of the simplified experimental apparatus, which includes the explosive (blue), the air domain (brown), the target plate (red), the target frame (green),and the clamps (eight colored blocks).Here, the explosive and air use Euler mesh, and the target, target frame, and clamps use Lagrange mesh.The modelling methods and material parameters are set according to Ref.[23].The structured arbitrary Lagrange-Euler (S-ALE) method is used to study the effect of the grid size of the air domain on the peak overpressure in an explosion.The overpressure of the air grid next to the center of the target(i.e., at 40 mm from the bottom of the cylindrical charge) is the incident pressure (PI).The deformation of the plate during the simulation is defined as the vertical displacement(Dc)at the center of the bottom face of the plate from its original position.

Different microstructures in the FE model by different JC constitutive parameters are considered.According to the mechanical properties of TC4 ELI plates with different microstructures,different JC constitutive parameters (from subsection 3.2) are assigned to model different microstructures in FEM.

3.Results and discussion

3.1.Effect of heat treatment on microstructure and mechanical properties

On the OM images(see Fig.6), the I800and T960plates show equiaxed and bimodal structures respectively.The I800plate has equal amounts of equiaxed α phase and β phase,but there is more α phase than the β transition structure in the T960plate.Table 3 shows the mechanical properties of the heat-treated TC4 ELI plates.The match between strength and plasticity is better for T960than for I800.The T960plate has 3.1% higher elongation and 1.5% higher tensile strength, as well as a stronger strain rate effect, but it has lower compressive strength at high strain rate.The I800plate has 4%higher yield strength at 0.001 s-1and 11.7% higher impact toughness, respectively.

3.2.The SHPB results and the JC model

The JC parameters are calculated as described based on the experimental SHPB results in Fig.7.Table 4 gives the SHPB test results with the strain at 0.1.Table 5 lists the optimized JCconstitutive parameters of the I800and T960plates.The numerical and the measured SHPB results are highly consistent(Fig.8).It can also be seen from Fig.8 that the I800and T960plates have similar dynamic compressive strength (see Table 6).

Table 3 The mechanical properties of the heat-treated TC4 ELI plates.

Fig.4.Schematic diagram of the explosion impact test device[18]:(a)The components of the test setup;(b)The size of the target plate and the deformation area;(c)The positions of the sensor and the target; (d) Picture of the explosion test setup.

Fig.5.Finite element model showing (a) the partial air domain; (b) the explosive; (c) the full air domain; (d) Simulation of the incident pressure in the air domain and the displacement at the center of the bottom face of the target.

3.3.Simulation of the detonation test

3.3.1.Charge and overpressure

For a spherical charge, the theoretical peak overpressure in the air domain can be calculated by Henrich’s empirical formula as follows [34]:a Strain = 0.1.

Fig.6.Optical microscopy images of the (a) I800 and (b) T960 TC4 ELI plates.

Fig.7.The compressive strength of the (a) I800 and (b) T960 TC4 ELI plates at different strain rates from SHPB.

Table 4 Simulated and measured compressive strength of the TC4 ELI alloy plates.

Table 5 Optimized JC constitutive model parameters of the TC4 ELI plates.

Table 6 Air domain overpressure at 2 m away from the center of the charge column.

where R is the distance from the explosion center to the point of interest (m), W is the TNT equivalent of the charge (kg), Z is the specific distance, and Pmaxis the peak overpressure (MPa).

A cylindrical charge can be converted to an equivalent spherical charge with the equal radius conversion:

where r’ is the radius of the equivalent spherical charge, r is the radius of the top surface of the cylindrical charge, and h is the height of the cylindrical charge.Likewise, the TNT amount of the equivalent spherical charge can be calculated as:

where w is the actual TNT amount of the cylindrical charge.Eq.(4)applies only when the propagation distance of the shock wave is less than h.Thus, for a cylindrical charge with a length-diameter ratio (L/D) greater than 1, the theoretical peak overpressure (see Table 6) in the air domain can be obtained by combining Eqs.(2)-(5).

Fig.8.Comparison between simulation and test results of true stress-true strain curves.

Fig.9.Incident pressure with varying air domain grid size.

3.3.2.Grid size of the air domain

The effect of grid size can be illustrated with the explosion of 200 g TNT.The incident overpressure begins to stabilize when the grid size is decreased to 3 mm × 3 mm × 1 mm (Fig.9, Table 7).

According to Table 7, the numerical and the theoretical peak incident overpressure match the best when the grid size of the air domain is 1 mm × 1 mm × 1 mm.Simulations also show that the convex of the target plate is not sensitive to the grid size of the target.The grid size of the air domain and the target is selected as 1 mm × 1 mm × 1 mm to improve the convergence of the target deformation [34], and because large grids cause excessive relative distortion and introduce significant simulation error.

3.3.3.Calculation capacity

As too many grids in the S-ALE method increases the demand on the computing ability, we first checked if the calculation for the 200 mm × 200 mm × 210 mm whole air domain (Fig.10) can be simplified with the calculation from a partial air domain [23,35].Fig.10 shows for both the I800and T960plates in an explosion with 100 g TNT,the time course of the displacement calculated using the whole air domain agrees well with the result of the partial air domain (100 mm × 100 mm × 210 mm).In addition, the deformation results provided in Figs.10, 11 and 13 are a grid in the initiation direction at the center point of the back explosion surface of the plate.The sketch map is shown in Fig.5(d).Therefore,in all subsequent simulations,the partial air domain is used to reduce the demand on the computation capacity.

3.3.4.Grid size of the target

The effect of grid size of the target can be illustrated under the partial air domain(100 mm×100 mm×210 mm).Fig.11 shows for the T960plate in an explosion with 100 g TNT,the time course of the displacement calculated using varying target grid size agrees well with each other.According to Table 8, simulations also show that the peak displacement and convex of the target is not sensitive to the grid size of the target.Therefore,in all subsequent simulations,given the compatibility between the target grid size and the air domain grid, the target grid size is selected as 1 mm × 1 mm × 1 mm.

3.3.5.Evolution of the shock wave

Fig.12 shows the propagation of the explosive shock wave in air from the explosion of 200 g TNT.After the explosion, the shock wave travels radially and axially,creating an inverted cone shape in Fig.12(b).The velocity is much higher in the axial direction than in the radial direction, and the charge below the initiation point is sequentially detonated during the blast process.Due to the superposition of shock waves,energy is constantly supplemented behind the wavefront.In contrast, the overpressure attenuates rapidly at the front of the shock wave because energy is not effectively supplemented.The maximum pressure inside the entire shock wave area,referred to as the detonation pressure,reaches 7.4 GPa at 2 μs(Fig.12(b)) and increases to 14.26 GPa at 8 μs (Fig.12(f)).Afterwards, the region of maximum overpressure gradually shifts from the front edge to the central region of the shock wave,mainly due to the high aspect ratio(L/D=1.736)of the cylindrical charge.

Table 7 Peak incident overpressure with varying air domain grid size.

Fig.10.Equivalence of calculation using the whole and partial air domains for the (a) I800 and (b) T960 TC4 ELI plates.

Fig.11.Equivalence of calculation using the partial air domains for the T960 TC4 ELI plate with varying target grid size.

3.3.6.Target failure process

For both the I800and T960plates, after the detonation, their deformation firstly peaks and then decreases gradually to converge to a specific value(Fig.13),presumably because of the inertia of the plate.Additional simulation for the T960plate shows that the convex would increase very little when the charge is more than 300 g (Table 9), likely due to the larger L/D ratio of the cylindrical charge.The relationship can be summarized as follows:

where R is the rebound of the plate,Rmis the rebound rate,Pdis the peak deformation, and Pcis the plate convex.

The von Mises Stress,an equivalent stress that combines normal and shear stresses,can describe the state of the material under the combined action of multiple stresses.Figs.14-16 illustrate the stress development for the I800plate under 100 g TNT.The target is subjected to the shock wave at 20 μs, and the contact stress is distributed along the radial direction (Fig.14(a)).The stress gradually decreases along the radius.In Fig.12, the pressure from the shock wave weakens from the center to the periphery, which matches well the spread of the stress wave in Fig.14(a) on the target plate from the center towards to boundary.The stress wave propagates at a consistent circumferential speed.The stress distribution has a similar radial propagation direction as the shock wave.The equivalent stress in the central area of the plate(970 MPa,Figs.14(a)and 14(b)) quickly exceeds the yield strength of the alloy (829 MPa).Hence, the central area of the plate first enters the yield state and then undergoes plastic deformation.The interaction between the shock wave and the plate continues as time elapses.The stress gradually concentrates in the area near the clamps in a symmetric pattern because the clamps can induce and attract the propagation of stress waves through the plate.The stress is mainly distributed along the dotted lines in Figs.14(d)and 14(e).On the bottom face of the target plate at 160 us,the apparent tensile stress (1087 MPa) is lower than the plate’s tensile strength(1350.1 MPa), and the shear stress is 580 MPa near the junction zone of the clamping area (Figs.15 and 16).As a result, the plate only experiences plastic deformation without fracture or any cracks on the bottom face.The plastic deformation of the plate emerges in the late stage of explosion loading (Figs.13,15 and 16).The localization of plastic strain occurs both at the boundary and in the central region of the plate,and the maximum plastic strain appears in the central region and clamping area.The intensity of the shock wave decreases rapidly after 23 us,which quickly reduces the force of the shock wave on the plate.However,the strain generated in the plate remains due to inertia, which causes durable plastic deformation in the plate.

Figs.17 and 18 illustrate the stress and strain patterns of the I800plate under 300 g TNT loading.The crack source appears at the center of the plate at 120 μs(Fig.17(f)).The plate cracks or fractures to absorb the energy released by the blast wave when the stress exceeds its tensile strength.There is obvious stress concentration at the crack tip at 150 μs, which initiates the fracture of the plate(Fig.17(g)).Subsequently, stress is gradually released at the crack area,and the extreme stress is shifted from the center of the plate to its boundary and to the areas near the clamp.The plate exhibits a tensile fracture because the maximum tensile stress (1757 MPa)exceeds its tensile strength (1350.1 MPa).Compared with the situation of 100 g TNT loading,the propagation characteristics of the stress waves are similar in the initial stage, and the impact of the blast wave and the explosive product on the plate has a longer duration.The plate likely experiences more apparent thermal softening and uniform stress distribution, greater explosive impulse, and higher tensile stress.As a result,the plate has a weaker bearing capacity, and there is more significant plastic deformation and tensile fracture.

Fig.12.Propagation of the shock wave at(a)0 μs;(b)2 μs;(c)5 μs;(d)8 μs;(e)12 μs;(f)13 μs;(g)14 μs;(h)15 μs;(i)17 μs;(j)18 μs;(k)19 μs;(l)23 μs after the explosion of 200 g TNT.

Fig.13.Development of plate deformation under different explosive loads.

Table 8 Peak displacement and convex with varying target grid size.

Table 9 Simulated peak deformation and plate convex.

Fig.19 illustrates the stress and strain patterns of the T960plate under 100 g TNT loading.Before 50 μs,the stress wave propagation characteristics resembles that of the I800plate under 100 g TNT loading.Compared with the I800plate,the T960plate has a smaller peak deformation and a smaller convex(Table 9),although it has a larger equivalent stress on the top face at the instant of maximum displacement(975.7 MPa at 160 μs for I800,1060 MPa at 185 μs for T960), possibly because of the microstructural response characteristics of the titanium alloy plates under the explosion load.

Figs.20 and 21 illustrates the stress and strain patterns of the T960plate under 300 g TNT loading.No cracks appear on the top face,but there are cross cracks in the central area of the bottom face where considerable plastic strain exists.The concentration of stress is subsequently transferred to the area near the clamps, and the stress in the crack area is released at 185 μs, when the maximum tensile stress in the plate (1424 MPa) exceeds the plate’s tensile strength(1359.8 MPa).The effective stress in the central area of the T960plate does not show a sudden increase before cracks appear on the top face of the plate(Fig.20(d)),which is unlike the situation of the I800plate(Fig.17(f)),possibly because there are more abundant interfaces between the grain phase in the bimodal T960titanium alloy that can consume energy during the deformation.In addition,as the microstructure of the T960plate can respond to deformation in a more coordinated manner,a smaller area is affected by cracks on the bottom of the T960plate, there is less plastic deformation,and the plate still maintains a strong impact resistance.It can be seen from Figs.14-21 that, for both the I800and T960plates, the clamping area and the plate center are the most vulnerable.

Fig.22 shows that the simulated maximum deformation of the target is positively correlated with the charge mass, because a higher charge mass creates more explosive energy, stronger shock wave,and greater stress.The target has more deformation when it needs to withstand greater blast wave impulse and explosion impact.However,the charge mass has little effect on the rebound of the plate,which stays at approximately 4.6 mm (Table 9).

The energy of the shock wave can be dissipated by the compression and deformation of the plate, the formation and propagation of cracks,and fractures.The plastic deformation of the plate is the primary venue of energy consumption.Table 10 illustrates the energy consumption of the plates under different explosion loads.Both the convex and the energy consumption increase with rising charge mass.The two different plates show nearly identical capacity for energy dissipation through plastic deformation when the explosive load is the same.The I800plate shows better anti-explosion performance when the charge is 200 g TNT, with a smaller convex and a greater energy consumption.Under 300 g TNT load, I800consumes energy through crack propagation and fracture (Figs.17(g)-17(l) and Fig.18), and T960consumes energy through crack propagation(Fig.21).Nevertheless,it is not possible to extract and separate the energy consumption of crack propagation and target rupture through simulation.The energy consumption capacity is thus likely underestimated for the plates under 300 g TNT load, especially for I800.

3.4.The explosion test

Fig.23 and Table 11 summarize the results of the explosion test.The target hit by the shock wave mainly suffers tensile, compression,and shear failures due to the changes in the wave propagation characteristics[36].The measured convex of the I800and T960plates(Table 10)follows a quadratic function relationship with the charge mass:

For the I800plate:

where y is the convex of the target plate(mm) and x is the charge mass (kg).

Fig.14.The von Mises stress patterns on the top face of the I800 plate under 100 g TNT loading at (a) 20 μs.; (b) 30 μs; (c) 50 μs; (d) 100 μs; (e) 160 μs; (f) 500 μs.

Fig.15.Stress and strain patterns of the top face of the I800 plate under 100 g TNT loading at maximum deformation:(a)Maximum principal stress;(b)Maximum shear stress;(c)Effective plastic strain.

Fig.16.Stress and strain patterns of the bottom face of the I800 plate under 100 g TNT loading at maximum deformation:(a)Maximum principal stress;(b)Maximum shear stress;(c) Effective plastic strain.

Fig.17.The von Mises stress patterns on the top face of the I800 plate under 300 g TNT loading at(a)25 μs;(b)40 μs;(c)50 μs;(d)95 μs;(e)100 μs;(f)120 μs;(g)150 μs;(h)210 μs;(i) 300 μs; (j) 400 μs; (k) 500 μs; (l) 1638 μs.

Fig.18.Stress and strain patterns of the bottom face of the I800 plate under 300 g TNT loading at maximum deformation:(a)Maximum principal stress;(b)Maximum shear stress;(c) Effective plastic strain.

Fig.19.The von Mises stress patterns on the top face of the T960 plate under 100 g TNT loading at (a) 30 μs; (b) 50 μs; (c) 70 μs; (d) 185 μs; (e) 500 μs; (f) 2830 μs.

The plate is more severely damaged when the charge mass is greater, although the convex of the T960plate grows by only 0.47 mm when the charge is increased from 200 g TNT to 300 g TNT.For the I800plate,only local deformation occurs when the charge is 100 g TNT or 200 g TNT, but there are “branch” shaped fractures,tensile tears,and transverse shear failures in the central area of the plate when the charge is 300 g TNT.The T960plate experiences local deformations when the charge is 100 g TNT, but it gives “river pattern” cracks that bifurcate and spread into various directions without fractures when the charge is 200 g TNT or 300 g TNT.Because the I800plate contains many layered equiaxed crystals,has a large crack plastic zone with a bent crack growth path, and has good impact toughness(Fig.6),it does not easily form cracks when the plastic deformation is small.The T960plate is less prone to fracture when subjected to large plastic deformation because it has both the equiaxed α phase and the lamellar β transition structure,allowing its microstructure to respond to deformation in a coordinated manner.There are triangular melting marks (pits) on the top face of the plates, which can be related to the local high temperature because the triangular cardboard support under the charge gathers energy [23].

The experimental observations are consistent with the simulation results,with the error of the convex less than 17.5%(Table 10).The simulated convex is slightly smaller since the simulation does not consider the geometric defects in the plate, or the contact between the detonation wave and the plate due to the narrowing of the air domain [35].

3.5.Response and microstructure analysis of the target after blast loading

Three rectangular pieces were cut off from the I800and T960plates that underwent the explosion test with 200 g TNT (Fig.24)and examined by OM and SEM to study the microstructure evolution at different positions on the plate.The sides of each piece are referred to as the thickness section and denoted by their dimension, as the plate is 12 mm thick.

Fig.20.The von Mises stress patterns on the top face of the T960 plate under 300 g TNT loading at(a)25 μs;(b)30 μs;(c)35 μs;(d)40 μs;(e)60 μs;(f)80 μs;(g)100 μs;(h)150 μs;(i) 175 μs; (j) 185 μs; (k) 500 μs; (l) 2160 μs.

Table 10 Energy consumption of the I800 and T960 plates under different explosion loads.

Figs.25 and 26 give the OM and SEM images of the corner of plates(i.e.,Piece 1).The I800plate contains many layered equiaxed α phases that are around 8 μm in diameter, while the T960plate has equiaxed α phases arranged disorderly and scattered near the β grain boundary of the β transition structure (Fig.25).A regular arrangement of the equiaxed α phase in the structure improves the ductility of the alloy[37].As seen in Figs.26(a)-26(h),the β phase in the I800structure becomes more discontinuous after the explosion,likely because the shock wave loading damages the structural continuity.For the T960plate, with reference to Fig.6, the α/α+β ratio decreases from around 70%-25%after the explosion,because the high temperature and high pressure of the shock wave and explosion products transform part of the equiaxed α phase into the lamellar α+β structure.Numerous fine secondary acicular α phases exist inside in the coarse β phase but not in the acicular β phase.The acicular α phases are arranged regularly, and the angle between two α phases is about 60°.Figs.26(g) and 26(h)shows the SEM of Piece 2 from the I800plate after the explosion test.The microstructure is uneven on the top face,and there are ordered equiaxed crystals with a smaller size on the thickness section.The layered and the nearly circular equiaxed crystals are staggered.The observations can be related to the significant impact and thermal effects brought by the shock wave to the top face of the plate.Figs.26(h)-26(k) shows the SEM of Piece 2 from the T960plate after the explosion test.On the top face,the content of the equiaxed α phase is relatively high (about 50%), and the equiaxed α phase and the β transition structure alternate.The two thickness sections are similar, with the β transition structure being dominant and much less (＜5%) equiaxed α phase, forming a basket-like structure.The angle is mainly 90°-120°in acicular α phase clusters.Due to the lower content of fine equiaxed α phase in all thickness sections,cracks are more likely to initiate in the thickness section under blast loading.

Fig.23.Pictures of the TC4 ELI plates after the explosion test.

For the Piece 3 from the I800plate,after the explosion,there are melting marks on the surface,and the microstructure is otherwise similar to Piece 2 and Piece 1.For the Piece 3 from the T960plate,there are oxygen-rich α layers (about 60 μm thick) in the 20 mm × 12 mm thickness section, and a basket-like structureexists below the α layer (Fig.27(b)).The α layer is enriched in oxygen, nitrogen, and carbon possibly because of the high temperature generated by the explosion,as the high temperature improves the oxidation efficiency and the diffusion activation energy of the material, which can promote the migration of atoms within the alloy.When the plate is exposed to the high temperature generated by the explosion, oxygen atoms can diffuse to the surface of the structure and thus stabilize the α phase.As a result,the α phase on the surface of the plate does not transform into the β phase but generates many α layers that are coarse, hard, and brittle.These layers differ from the α phase in the bulk of the plate,as can be seen by comparing the top and bottom halves of Fig.27(b).The initiation and expansion of cracks on the plate surface will be accelerated when the surface is enriched with oxygen, nitrogen, and carbon atoms,as they reduce the plasticity of the surface structure and the strain before cracking occurs.The continuing deformation due to stress consequently creates a roughened and embrittled surface,and generates cracks on the surface,lowering the impact toughness of the T960plate.The weak ability for the α phase and the β phase to have coordinated deformation also lowers the impact toughness Fig.28.

Table 11 The measured convex of the TC4 ELI plates and the sensed overpressure.

Fig.24.Sampling from the I800 and T960 plates after detonation test with 200 g TNT.

Fig.28 shows the SEM and energy-dispersive X-ray spectroscopy(EDX)images of the 20 mm×12 mm thickness section at the center(Piece 3) of the T960plate.Taken together(Figs.25-28), for the I800plate after explosion impact with 200 g TNT,the content of the equiaxed α phase in the structure decreases from the corner to the center of the plate.The distribution of the equiaxed α phase becomes less ordered,and the microstructure becomes less capable of coordinated deformation.On the T960plate,after the explosion of 200 g TNT, there is an increase in both the content and the size of the equiaxed α phase in the microstructure from the corner to the center, which deteriorates the material properties.All these changes can be attributed to the temperature effect of the shock wave.The structural change is more evident at the center of the plates because the concentration of temperature is more significant at the center of the plate than on the boundary.

Fig.25.OM of the corner (Piece 1) of the (a) I800 and (b) T960 plates.

Fig.26.SEM of the corner of the(a-f)Piece 1 and(g-k)Piece 2.(a,c-f)Top face of the I800 plate;(b)Top face of the T960 plate;(g)Top face of the I800 plate;(h)Thickness section(30 mm × 12 mm) of the I800 plate; (i) 15 mm × 12 mm thickness section of the T960 plate; (j) Top face of the T960 plate; (k) 30 mm × 12 mm thickness section of the T960 plate.

Fig.27.OM of the 20 mm × 12 mm thickness section at the center (Piece 3) of the (a) I800 and (b) T960 plates.

Fig.28.SEM and energy-dispersive X-ray spectroscopy (EDX) images of the 20 mm × 12 mm thickness section at the center (Piece 3) of the T960 plate.

Fig.29.OM of the crack growth path on the bottom face of the T960 plate after the explosion of 200 g TNT.

Fig.30.The adiabatic shear band-induced failure characteristics of the T960 plate at high strain rates caused by the shock wave from 200 g TNT.

Fig.29 shows the crack propagation path contour and the microstructure near the crack on the bottom face of the T960plate.The crack propagation path has the shape of a tortuous river with bifurcations.The crack gradually narrows.The curvy path of crack propagation can effectively dissipate the impact energy.According to the local magnification image of the region near the crack tip,the cracks propagate in the β transition structure, some acicular α phases near the cracks are cut off,and some equiaxed α phases are penetrated,all of which effectively release the stress concentration at the crack tip.The α-cluster boundaries with various orientations are more likely to prevent crack propagation and deflect cracks,prompting the cracks to terminate at the α-cluster boundaries.Furthermore, under the action of high strain rate loading by the explosive shock, the degree of strain hardening varies in different regions of the plate, and the temperature in the local region rises.Obviously, adiabatic shear localization, manifesting as adiabatic shear bands (ASBs), can generate cracks.Fig.30 shows the characteristics of the ASB-induced failure caused by the shock wave on the T960plate at high strain rates.The ASBs exhibit a combination of ablative melting and deformation bands.

4.Conclusions

In this work, we investigated the interaction between TC4 ELI plates with different microstructures and the blast shock wave with various loads, and analyzed the failure modes and the damage mechanisms of the plates.

(1) The I800and T960plates show equiaxed and bimodal structures respectively.T960shows high tensile strength and elongation,and the match between strength and plasticity is better for T960than for I800.The numerical and the measured SHPB results are highly consistent, and the I800and T960plates have similar dynamic compressive strength.

(2) There is a good agreement between the simulated and the experimental convex for the studied plates,with the error of the convex less than 17.5%.The simulated convex is slightly smaller since the simulation does not consider the geometric defects in the plate.The failure modes of the plates are mainly dome-shaped local plastic deformation,cracks on the bottom surface, and central fracture.

(3) The target has more deformation when it needs to withstand greater blast wave impulse and explosion impact.However,the charge mass has little effect on the rebound of the plate,which stays at approximately 4.6 mm.

(4) The bimodal TC4 ELI plate, referred to as T960, has excellent explosive resistance under the threat of 100 g TNT and 300 g TNT but exhibits larger plastic deformation under the threat of 200 g TNT.The equiaxed TC4 ELI plate,referred to as I800,is more sensitive to the explosion load.It only experiences local plastic deformation failure under the threat of 100 g TNT and 200 g TNT but develops fracture failure in the central area under the threat of 300 g TNT.

(5) For the I800plate, the failure mechanism is mainly ductile fracture, and the microstructure has poorer ability to have coordinated deformation.Its equiaxed grains loses the orderly distribution after the explosion.For the I960plate,the failure mechanism is mainly the formation of an extended crack.Its equiaxed α crystals are coarse,and hard and brittle oxygen-rich α layers are formed near the crack region.Furthermore,under the action of high strain rate loading by the explosive shock, there is obvious adiabatic shear localization, manifesting as adiabatic shear bands (ASBs),that can generate cracks.

Declaration of competing interest

The authors declare no conflicts of interest.

Acknowledgements

The authors would like to acknowledge National Key Laboratory of Science and Technology on Materials under Shock and Impact(Grant No.WDZC2022-4) to provide fund for conducting experiments.