Dynamic mechanical behaviors and failure thresholds ...

Materials Science & Engineering A 719 (2018) 178–191

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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

Dynamic mechanical behaviors and failure thresholds of ultra-high strength low-alloy steel under strain rate 0.001/s to 106/s

T

⁎

Jie Rena, Yuxin Xua, , Xiaoxu Zhaoa,b, Pengduo Zhaoc a

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, PR China College of Information Engineering, Capital Normal University, Beijing 100048, PR China c Naval Academy of Armament, Beijing 100161, PR China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Ballistic impact Dynamic mechanical behaviors Failure thresholds Reversible α→ε phase transformation Ultra-high strength low-alloy martensite steel

In this study, the dynamic mechanical behaviors of the typical ultra-high strength low-alloy martensite steel 35CrMnSiA under strain rate 0.001/s～106/s were studied through quasi-static compressive tests (0.001/s), SHPB tests (2000/s～5000/s) and planar plate impact tests together with DISAR tests (105/s～106/s). The XRD analysis and metallographic observation were conducted to investigate the microstructure evolutions and failure mechanism of 35CrMnSiA under different stress states. Under uniaxial stress state, the adiabatic shear failure occurs as long as the rise rate of plastic strain energy density reaches 10.58× 106 J·m−3 µ s−1 and the plastic strain energy density is above 4.51× 108 J·m−3. For 35CrMnSiA samples under uniaxial strain state, the critical pressure for reversible phase transformation (α → ε , BCC→HCP) falls in the range of 17.57–19.19 GPa. Characterized by prominent temperature rise and volume shrinkage, the α → ε phase transformation induced by continuous dynamic recrystallization contributed to increasing the strength but weakening the ductility of 35CrMnSiA. In addition, the Hugoniot coefficients for 35CrMnSiA under a wide range of pressures have been determined. Moreover, the failure thresholds for 35CrMnSiA were obtained by dynamic fracture experiments and high velocity impact experiments: 35CrMnSiA projectiles fractured over impact pressure of 2.59 GPa, and when the impact pressure exceeded 21.25 GPa above which 35CrMnSiA suffered phase transformation, the projectiles had severe mass abrasion.

1. Introduction As one of the most fundamental materials used in construction of national economy and defense industry, alloy steel first appeared in the second half of the 19th century. With the increasing demand of high strength and great ductility, ultra-high strength low-alloy steel was developed and widely used in production and life. Fe–C–Ni–Si–Cr–Co, Fe–C–Cr–Mn/Ni, Fe–C–Si–Cu–Cr–Ni–V have been developed through alloy design and microstructural design to get the satisfying mechanical property [1]. Wang and Voisin [2] reported the hierarchical austenitic 316 L stainless steels with high strength and ductility, which are additively manufactured by laser powder-bed-fusion technique. Tomita [3] modified the heat treatment process of ultra-high strength 4340 steel (Fe-0.40C-1.79Ni-0.80Cr-0.80Mn-0.23Si-0.23Mo) to improve the fracture toughness under lower temperature. Using the heat treatment of designated quenching–partitioning–tempering (Q–P–T), Wang [4] has increased the tensile strength of Fe–0.485C–1.195Mn–1.185Si–0.98Ni–0.21Nb steel up to 2000 MPa with the elongation over 10%. But the dynamic mechanical behaviors of newly-modified ultra-high strength ⁎

alloy steel, especially under high pressure and high strain rate, are seldom found in public literature. Ultra-high strength low-alloy steel is often selected as the material for the shell of armor-piercing warhead, pipeline of oil and gas, pressure vessel, landing gear, load-bearing part of bridge and large buildings. They must withstand and survive harsh environments like extreme dynamic loads (such as impact and explosion). Therefore, it is necessary to understand the dynamic mechanical behaviors of materials subjected to a wide range of strain rates and different stress states. Many researchers have discussed the competition between the effect of strain hardening and thermal softening of high strength steels in plastic flow stage: Hu [5] compared the yield strength, hardening module and failure strain of ultra-high strength alloy steel AerMet 100 subjected to quasi-static and dynamic compressive loading within strain rate 560/s ～2500/s. Singh [6] conducted the SHPB tests to investigate the strain rate sensitivity of mild steel under strain rate 125/s～2350/s and determined the parameters for Cowper-Symonds and Johnson-Cook models. Lu [7] studied the compressive behaviors of hypo-eutectoid steel 42CrMo within strain rate 10−3/s～4500/s, and proposed a

Corresponding author. E-mail address: [email protected] (Y. Xu).

https://doi.org/10.1016/j.msea.2018.02.019 Received 20 November 2017; Received in revised form 3 February 2018; Accepted 5 February 2018 Available online 11 February 2018 0921-5093/ © 2018 Elsevier B.V. All rights reserved.


J. Ren et al.

Nomenclature TRIP νεp σflow εp εp* DISAR Cp Tt te tp Ce ρ0 D u Up

U0 t0 σHEL Ue σs υ C0, λ η ν σ E h BCC FCC HCP

transformation-induced plasticity plastic strain energy density flow stress plastic strain maximum/failure plastic strain displacement interferometer system for any reflector velocity of plastic wave target thickness arrival time of elastic wave arrival time of plastic wave longitudinal sound velocity under uniaxial strain state density shock wave velocity particle velocity free surface particle velocity after plastic wave loading

original free surface particle velocity before velocity jump time for velocity jump Hugoniot elastic limit free surface particle velocity after elastic wave loading equivalent yield strength Poisson's ratio Hugoniot coefficients volumetric strain specific volume normal stress internal energy Lagrangian position Body-Centered Cubic Face-Centered Cubic Hexagonal-Closed Packed

martensite transformation pressure is about 13 GPa. Sadjadpour and Rittle [21,22] demonstrated that the α → ε phase transformation can occur at extremely low levels of stress (of the order of a GPa) in comparison to transformation stress of 13 GPa under shock loading conditions of uniaxial strain and presented a model coupling plasticity and phase transformation with application to dynamic shear deformation of iron. Due to the addition of various alloying elements to improve the performance of iron, the critical pressure for phase transformation would also change [23]. The acquisition of phase transformation threshold for typical ultra-high strength low-alloy steel would provide guidance for the selection of accurate coefficients for equation of state in the design of engineering structures. As for the fracture characteristics of ultra-high strength steel, existing investigations are mainly about the low velocity impact. Rakvag [24,25] studied the deformation and fracture modes of high strength steel projectiles by Taylor bar impact experiments and numerical simulation with the impact velocity ranging from 100 m/s～350 m/s. Xiao [26] investigated the effect of projectile hardness on the deformation and fracture behavior of high strength steel 38CrSi projectile under the impact velocity 200 m/s～600 m/s. Paris [27] conducted the oblique ballistic experiments to study the effect of obliquity angle and the thickness of armor steel plate on shattering behavior of the 14.5 mm armor piercing steel projectiles with the impact velocity of 930 ± 1 m/s. Kenkmann [28] carried out the hypervelocity (2500 m/s～5300 m/s) cratering experiments with steel projectiles and sandstone targets to investigate the deformation and melting of steel projectiles. The fracture behavior of ultra-high strength low-alloy steel projectile under the impact velocity 1000 m/s～2500 m/s which covers the phase transformation velocity thresholds for ultra-high strength low-alloy steel are seldom founded in open literature, neither the reveal of mass abrasion nor the effect of phase transformation to the fracture of ultra-high strength low-alloy steel. It is noticed that although these efforts revealed the dynamic mechanical behaviors of various steels under different strain rates, the experiments on ultra-high strength low-alloy steel with the strain rate over 106/s are rarely reported. In the circumstances of ultra-high velocity impact, the strain rate usually exceeds 106/s and the material is partially characterized as fluid. The effect of phase transformation and the change of failure modes should be considered in the engineering

constitutive model based on crystal plasticity theory. Niu [8] investigated the dynamic compressive mechanical properties of 30CrMnSiNi2A steel by SHPB tests at 30 °C～700 °C and 3000/s～ 10000/s. Weston [9] investigated the compressive plastic flow characteristics of shock-hardened Remco iron over strain rate 0.001/s～ 9000/s and attributed the sharp increase in flow stress at 0.05% strain to the pressure-induced polymorphic phase change. Rahmaan [10] investigated the effect of strain rate on flow stress and anisotropy characteristics of DP600, TRIP780 and AA5182-O at strain rates 10/s, 100/s and 1000/s. Nahme [11] studied the dynamic compressive behaviors (10−3/s < dε / dt < 106/s) of three kinds of high strength armor steel: Mars 190, Mars 240 and Mars 300 by quasi-static compression, SHPB, Taylor impact and planar plate impact tests and analyzed the shear and spalling failure properties under different strain rates. Li [12] carried out planar plate impact tests to study the effect of structural anisotropy on Hugoniot elastic limit, spall strength, deformation and damage of 2205 duplex (austenite-ferrite) stainless steel under high strain rate loading. The studies mentioned above have analyzed the strain rate sensitivity and failure behaviors of various kinds of steel within strain rate 0.001/s～106/s, but there is seldom description of the connection between low pressure high strain rate state (SHPB tests) and high pressure high strain rate state (Planar plate impact tests), which would provide guidance for the selection of the proper strength and failure models together with coefficients for materials subjected to different stress states and loading forms. Strain-induced martensite transformation has been researched by many scholars. Talonen [13] and Rodríguez-Martínez [14] studied the effect of strain rate on strain-induced γ → α′ martensite transformation and mechanical behaviors of austenitic stainless steel AISI 304 at strain rates 10−5/s～102/s. Peng [15] further proposed a kinetic model based on Olson-Cohen model [16] to describe the martensitic transformation of stainless steel 304 occurred in tensile tests at room temperature. Taking into account the transformation of retained austenite into martensite, Gronostajski [17] investigated the microstructural changes and flow stress of advanced high-strength steels (AHSS) TRIP690 and DP600 subject to deformation at strain rates 0.001/s～2500/s. Chen [18] investigated the deformation mechanisms of 304 stainless steel subjected to surface impacts within strain rates 10/s～105/s, and concluded that the deformation mechanisms have transformed from dislocation-mediated mechanism (10/s～103/s) to twinning-mediated mechanism (104/s～105/s). Sugimoto [19] investigated the influence of forming temperature and strain rate on the ductility and strain-induced transformation behavior of high-strength transformation-induced plasticity-aided dual-phase steel. Giles [20] used an opposed-anvil x-ray diffraction apparatus and high-pressure light metallography to study the high-pressure transformation in iron, and concluded that the

Table 1 Main chemical compositions of 35CrMnSiA.

179

C(%)

Si(%)

Mn(%)

Cr(%)

Ni(%)

Cu(%)

0.36

1.22

0.90

1.20

0.04

0.08


J. Ren et al.

improve the strength and ductility of 35CrMnSiA and avoid the unexpected brittle fracture, the heat treatment process of 970 ℃ quenching for 25 min + 890 ℃ quenching for 17 min + 200 ℃ tempering for 90 min was adopted for 35CrMnSiA [34]. As shown in Fig. 1, 35CrMnSiA is composed of fine lath martensites after heat treatment. The quasi-static tensile and compressive mechanical properties are displayed in Table 2. With great ductility, 35CrMnSiA samples did not break subjected to quasi-static compressive loading with strain rate 0.001/s. 2.2. Apparatus for SHPB tests SHPB (Split Hopkinson Pressure Bar) tests were conducted to characterize the dynamic compressive behaviors of 35CrMnSiA under strain rates 2000/s～5000/s. In SHPB tests, cylindrical 35CrMnSiA samples were subjected to uniaxial stress state. The parameters of Split Hopkinson Pressure Bar are listed in Table 3. The projectile was propelled by compressed N2. The samples for SHPB tests were machined into Φ5 mm× 5 mm. In order to protect the bar from damage of ultrahigh strength steel sample and further reduce the friction between the sample and the bar, two gaskets with lubricant were placed at the end of incident bar and transmission bar.

Fig. 1. Microstructure of 35CrMnSiA after heat treatment.

Table 2 Quasi-static mechanical properties of 35CrMnSiA at room temperature. Tensile yield strength (MPa)

Tensile strength (MPa)

Tensile modulus (GPa)

Broken elongation (%)

Compressive yield strengtha(MPa)

Hardness (HRC)

1366

1716

194

10

1675

49.3

a

2.3. Apparatus for planar plate impact tests Proof stress of material at 0.2% permanent strain.

In order to investigate the dynamic response of 35CrMnSiA under higher strain rates (105～106/s) loading, the planar plate impact tests were conducted with the impact velocities from 300 m/s to 1700 m/s. In the planar plate impact tests, the 35CrMnSiA samples were subjected to uniaxial strain state. For the tests with the impact velocities ranging from 300 m/s to 900 m/s, the shock wave velocity and stress-time response was measured by manganin pressure sensors. But as the impact velocity exceeded 900 m/s, due to the mechanical strength inadequacy of manganin pressure sensor, the shock wave velocity and the velocity history of free surface particle was measured by optical probes and DISAR (Displacement Interferometer System for Any Reflector) probe.

analysis. The acquisition of the dynamic mechanical properties, microstructure evolutions and failure thresholds for ultra-high strength low-alloy steel under a wide range of strain rate 0.001/s～106/s can guide researchers and engineers to choose the proper models and parameters in the design and analysis of materials and structures. In this work, the quasi-static compressive tests, SHPB tests and planar plate impact tests were carried out to study the dynamic mechanical behaviors of ultra-high strength low-alloy martensite steel 35CrMnSiA under strain rate 0.001/s to 106/s. In addition, combined with XRD analysis and metallographic observation of original and postimpact microstructures, microstructure evolutions and failure mechanisms of 35CrMnSiA under different stress states were discussed. The prominent factors and thresholds for adiabatic shear failure and reversible α → ε (BCC → HCP) phase transformation have been analyzed. Furthermore, the critical fracture velocity and pressure thresholds for 35CrMnSiA projectile were obtained by dynamic fracture experiments and high velocity impact experiments, and the damage evolution law for 35CrMnSiA projectile was quantified.

2.3.1. Tests with manganin pressure sensors As shown in Fig. 2(a), two manganin pressure sensors were embedded into three target plates by PE adhesive, which has satisfying fluidity and bonding strength. The dimension of the flying disk is Φ 24 mm × 2.5 mm. With the diameter of 30 mm, each target plate is 2.5 mm in thickness. The thickness of adhesive layer between two target plates is about 0.1 mm and the interfacial effect and weakening effect on shock wave can be neglected. The flying disk supported by sabot was propelled by one stage light gas gun. The impact velocity of flying disk was measured by electromagnetic velocity-testing coil and the shock wave velocity could be calculated according to the initial response time of two sensors.

2. Materials and methods 2.1. Materials As a typical ultra-high strength low-alloy steel, 35CrMnSiA displays its prominent superiority in high strength, great ductility, easy access, low price and facile heat treatment process. It can serve as the equivalent material for the shell of blast and fragmentation warhead [29,30]. Consequently, it is widely used as the material for high velocity penetrators in many investigations [31–33]. The main chemical compositions of 35CrMnSiA are listed in Table 1. The main alloying elements included in 35CrMnSiA are Si, Cr and Mn which contribute to increasing the strength and hardness of steel. In order to further

2.3.2. Tests with optical probes and DISAR As shown in Fig. 2(b), the shock wave velocity was measured by optical probes (four were positioned coplanar with the front surface of the target plate, one was placed perpendicular to the back surface of the target plate) which were pre-sheltered by aluminum foils and would shine when subjected to high impact pressure. The arrival and departure time of the shock wave in target can be detected by the change of light intensity of light probes. In order to reduce the noncoplanar

Table 3 Parameters of Split Hopkinson Pressure Bar. Diameter of the bar (mm)

Diameter of the projectile (mm)

Length of the projectile (mm)

Material

Density (g/cm3)

Elastic modulus (GPa)

Velocity of elastic longitudinal wave (m/s)

14.5

14.5

200

maraging steel

7.85

197

5000

180


J. Ren et al.

Support frame 35CrMnSiA target

Optical Probes

Holes for Optical Probes Fig. 2. Sketches of the planar plate impact tests set up. (a) the shock wave velocity is measured by manganin pressure sensors; (b) the shock wave velocity is measured by optical probes. 2600

2600

(a)

2400

Stress Collapse

2200

2000

2000

1800

35CrMnSiA steel

1600

Compression test

True Stress (MPa)

True Stress (MPa)

(b)

2400

2200

Temperature:298K

1400

0.001/s 2400/s 2800/s 3300/s 4100/s 4200/s 4550/s

1200 1000 800 600 400 200 0 0.00

1800 1600

2400/s 2800/s 3300/s 4100/s 4200/s 4550/s

1400 1200 1000 800 600 400 200 0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0

10

20

30

40

50

60

70

80

90

Time (μs)

True Strain

Fig. 3. Dynamic compressive response of 35CrMnSiA samples in SHPB tests. (a) stress-strain curves at evaluated strain rates; (b) stress-time curves at evaluated strain rates.

original 24000/s 2800/s 3300/s 4100/ss 4200/s

origin nal

2400/s

2800/s

3300/s

4100/s

42 200/s

error caused by the light probe and target plane, the arrival time of the shock wave was taken as the average of the four mutually orthogonal light probes’ testing values. Meanwhile, the DISAR (Displacement Interferometer System for Any Reflector) probe was placed perpendicular to the back surface of the target. It could record the velocity history of free surface particle. For the tests with the impact velocity below 1300 m/s, the flying disk (Φ 30 mm × 2.5 mm) was propelled by onestage light gas gun, and the dimension of target plate is Φ 24 mm × 2.5 mm; for the tests with the impact velocity over 1300 m/s, the flying disk (Φ 24 mm × 2.5 mm) was propelled by two-stage light gas gun, and the dimension of target plate is Φ 19 mm × 2.5 mm. In order to simplify the calculation and analysis, the material for flying disk was kept the same as the target. In order to assure the planeness of impact, the surfaces of the flying disk and target were polished by fine sandpaper and cleaned by alcohol. To avoid the

4550/s

45550/s

Fig. 4. The original and retrieved 35CrMnSiA samples subjected to uniaxial stress state.

181


J. Ren et al. 2400

As displayed in Fig. 3(a), in dynamic compressive tests, especially for ultra-high strength steel, there is no obvious yield point. Therefore, as shown in Fig. 5, we use the intersection of bilinear fitting curves of elastic stage and the initial plastic flow stage (with true strain between 0.05 and 0.10) as the yield point. The experimental results are listed in Table 4. As shown in Table 4, the yield strength and maximum/compressive strength approximately increased with the increase of strain rate. The yield strength of 35CrMnSiA under quasi-static loading is 1675 MPa, while it increases to 1855 MPa under strain rate 2400/s and to 2172 MPa under strain rate 4550/s, with an increment of 10.75% and 29.67% respectively. 35CrMnSiA exhibited strong strain rate hardening effect at the initial plastic yielding stage. Since the strain hardening effect of high strength steel is not as strong as that of highductility steel [36], and the strain hardening module of high strength steel in dynamic compressive tests is less than the value in quasi-static compressive tests due to thermal softening [5], it is noticed that at strain 0.02 the quasi-static flow stress is higher than the dynamic flow stresses under strain rate 2400/s～4100/s.

3300/s

2200 2000

True Stress (MPa)

1800 1600 1400 1200 1000 800 600 400 200 0 0.00

0.04

0.08

0.12

0.16

0.20

0.24

0.28

True Strain Fig. 5. Determination of the yield point for 35CrMnSiA in SHPB tests.

Table 4 Dynamic compressive properties of 35CrMnSiA subjected to uniaxial stress state at room temperature. Loading Pressure of compressed N2 (atm)

Strain rate(/s)

Yield strength (MPa)

Maximum/Compressive strength (MPa)

5 6 7 9 9 9.5

2400 2800 3300 4100 4200 4550

1855 1980 1950 1934 2004 2172

2191(Maximum stress) 2212(Maximum stress) 2245(Maximum stress) 2194(Maximum stress) 2457(Compressive stress) 2348(Compressive stress)

3.2. Results for planar plate impact tests Table 5 presents the results of the planar plate impact tests. The particle velocity equals to one-half of the impact velocity under symmetrical impact. The retrieved flying disks and targets are shown in Fig. 6. From Fig. 6, it is observed that there was no macroscopic cracking or large plastic deformation except for slight buckling both for flying disks and targets below impact velocity of 1240 m/s. However, it was a pity that we did not find the retrieved flying disk and target subjected to the impact velocity of 1733 m/s, so we could not make the conclusion that whether the target fractured over impact velocity of 1240 m/s. The test results of the free surface particle velocity history are shown in Fig. 7. The arrival time of each wave can be identified by the saltation of the velocity of free surface particle. Under impact velocity of 607 m/s, 35CrMnSiA transformed from the purely elastic state into the elastic-plastic state (Hugoniot state) above HEL (Hugoniot elastic limit, the axial yield strength of material subjected to uniaxial strain state). When the impact velocity increased to 1240 m/s, the plastic wave spilt into the 1st plastic wave P1 and the phase transformation wave P2. It is interesting that the phase transformation wave could not be observed at the higher impact velocity of 1733 m/s. Barker [37] has pointed out that the three-wave (Elastic precursor E-The 1st plastic wave P1-The Phase transformation wave P2) structure could not be observed if the impact pressure is above the critical pressure. The Phase transformation wave P2 caught up with the 1st plastic wave P1 and a shock wave with higher velocity emerged following the elastic precursor E. And it is sure that the phase transformation occurred at the impact velocity of 1733 m/s. As given in Table 7, the dynamic response parameters for 35CrMnSiA under uniaxial strain state were calculated based on the material parameters in Table 6. According to the Rankin-

unloading of the crossrange and reflected rarefaction wave to the loading compression wave, the ratio of target thickness to flying disk thickness should be less than 4 and the ratio of target diameter to target thickness should be greater than 2 [35]. 3. Results 3.1. Results for SHPB tests Under different loading pressures, averages from three identical tests were used for quantitative analysis. Fig. 3(a) displays the compressive stress-strain curves of 35CrMnSiA under strain rates 0.001/s～ 4550/s. The original and retrieved samples are shown in Fig. 4. It shows that the tested samples had homogeneous heading deformation below strain rate 4100/s, but had adiabatic shear fracture along 45-degree over strain rate 4200/s. 35CrMnSiA sample had critical fracture subjected to loading pressure of 9 atm, corresponding to the strain rate 4100/s～4200/s. The failure strain over strain rate 4200/s is about 0.23. Table 5 The results of planar plate impact tests. No.

1 2 3 4 5 6a 7a 8a a

Flying disk diameter (mm)

24 24 24 24 24 30 30 24

Flying disk thickness (mm)

2.477 2.474 2.481 2.469 2.497 2.468 2.484 2.474

Target diameter (mm)

30 30 30 30 30 24 24 19

Target thickness (mm) 1st plate

2nd plate

3rd plate

2.485 2.480 2.494 2.478 2.491 2.486 2.468 2.478

2.490 2.477 2.482 2.470 2.514

2.486 2.446 2.490 2.476 2.504

The shock wave velocity was measured by optical probes.

182

Impact velocity (m/s)

Particle velocity (m/s)

Shock wave velocity (m/s)

325 607 623 906 984 607 1240 1733

162 304 312 453 492 304 620 866

4336 4698 4401 4881 4549 4797 3942 4678


J. Ren et al.

(a) flying

1st plate

2nd plate 3rd plate

(b) flying disk 1st plate

(c) flying disk

target

disk

Fig. 6. The retrieved flying disks and targets of 35CrMnSiA in planar plate impact tests. (a) impact velocity: 325 m/s; (b) impact velocity: 623 m/s; (c) impact velocity: 1240 m/s.

1800

(a)

Free Surface Particle Velocity (m/s)

Free Surface Particle Velocity (m/s)

1400 1200 1000 800 600

Hugoniot State

Phase Transformation Wave P2

400 200

Plastic Wave P1

HEL

Elastic Precursor E Impact Velocity:1240m/s

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

(b)

1600 1400 1200 1000 800 600 400

Impact Velocity:607m/s Impact Velocity:1240m/s Impact Velocity:1733m/s

200 0 0.0

1.4

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Time (μs)

Time (μs)

Fig. 7. The free surface particle velocity profiles of 35CrMnSiA samples. (a) structure of the free surface particle velocity profile; (b) free surface particle velocity profiles at evaluated impact velocities.

Table 6 Material parameters for 35CrMnSiA.

Table 8 Hugoniot coefficients for 35CrMnSiA.

ρ0 /(g / cm3)

E (GPa)

Ce (m/ s )

ν

Impact Pressure(GPa)

C0 (m/s)

λ

7.85

194

5768

0.3

< 17.57 > 19.19

4393 2091

0.519 2.986

Table 7 The dynamic response parameters for 35CrMnSiA under uniaxial strain state. Impact velocity (m/s)

Velocity of plastic wave(m/s)

Impact pressure (GPa)

Strain rate (× 106/s)

HEL(MPa)

607 1240 1733

5103 5160 5286

11.43 19.19 31.82

1.01 2.30 4.07

2625 2772 3043

Hugoniot jump conditions [38], the plastic wave velocity can be calculated by:

Equivalent yield strength (MPa)

Cp =

1500 1584 1739

P = ρ0 Du

4800


+ (tp − te )

(1)

Where Cp is the velocity of plastic wave, Tt is target thickness, te is the arrival time of elastic wave, tp is the arrival time of plastic wave, Ce is the longitudinal sound velocity under uniaxial strain state. The impact pressure can be calculated by

5000

(2)

where D is shock wave velocity, u is particle velocity. The increase in particle velocity is induced by both elastic and plastic wave. In consideration that the strength of elastic wave is far less than that of plastic wave, and the velocity of elastic wave is only approximately 25% higher than the value of plastic wave under uniaxial strain state [39], we neglect the effect of elastic wave and calculate the average strain rate by

4600 4400 4200 4000 3800 3600

Experimental Data D = 4393 + 0.519u D = 2091 + 2.986u

3400 3200 3000 100

Tt Tt Ce

200

300

400

500

600

700

800

ε̇ =

1 Up − U0 2Cp tp − t0

(3)

Where Up is the free surface particle velocity after plastic wave loading, U0 is the original free surface particle velocity before velocity jump, t0 is the time for velocity jump. The HEL (Hugoniot elastic limit) can be calculated by

900

Particle velocity (m/s) Fig. 8. The fitted shock wave velocity-particle velocity curves of 35CrMnSiA.

σHEL = 183

1 ρ Ce Ue 2 0

(4)


J. Ren et al. 35

50

35CrMnSiA Steel

35CrMnSiA Steel 45

Experimental Point Calculated by P =ρ Du

40

Calculated by P =ρ C (1-v/v )/[1-λ(1-v/v )]

Calculated by P =ρ C η /[1-λη]

25

Pressure P /GPa

Pressure P /GPa

35

Experimental Point Calculated by P =ρ Du

30

30 25 20 15

20

15

10

10

5

5 0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

0.02

0.04

0.06

V/V

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Volumetric Strain η Fig. 9. PH – V and PH –η Hugoniot curves of 35CrMnSiA. 2200

3200

(a)

2800

Equivalent Yield Strength (MPa)

Axial Yield Strength (MPa)

(b) 2100

Quasi-static One-dimensional stress state One-dimensional strain state

3000

2600 2400 2200 2000 1800 1600 -10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

2000 1900 1800 1700 1600 1500 1400 -10

16

Quasi-static One-dimensional stress state One-dimensional strain state

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

Logarithm of Strain Rate

Logarithm of Strain Rate

Fig. 10. The relations between yield strength and the logarithm of strain rate at different stress states. (a) Axial yield strength versus Logarithm of strain rate; (b) Equivalent yield strength versus Logarithm of strain rate. 12 11 10

11 10

7 6 5 4

8 7 6 5 4

3

3

2

2

1

1

0 0.00

0.01

0.02

(b)

Impact velocity:325m/s Impact velocity:607m/s Impact velocity:623m/s

9

8

Stress (GPa)

Stress (GPa)

9

12

(a)

Impact velocity: 607m/s sensor 1# sensor 2#

0.03

0.04

0.05

0.06

0.07

0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Strain

Strain

Fig. 11. The stress-strain curves of 35CrMnSiA under uniaxial strain state. (a) the stress-strain curves measured by sensor 1# and sensor 2#; (b) the stress-strain curves of 35CrMnSiA under evaluated impact velocities.

19.19 GPa. Detailed description about phase transformation will be given in Section 4.2. Many experimental investigations have revealed that the shock wave velocities are linear with the particle velocities in a wide range of pressures without phase transformation [38]. On account of the phase transformation observed in Fig. 7(b), the coefficients for D-u relation are obtained by piecewise linear fitting with the least square method (as shown in Fig. 8).

Where Ue is the free surface particle velocity after elastic wave loading. The equivalent yield strength under uniaxial strain state can be calculated by the following formula [40]:

σs =

1 − 2υ σHEL 1−υ

(5)

Where σs is equivalent yield strength, υ is Poisson's ratio, σHEL is Hugoniot elastic limit. From Table 7, it is concluded that the critical phase transformation pressure for 35CrMnSiA is between 11.43 GPa and

D = C0 + λu 184

(6)


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The impact temperature rise in planar plate impact tests is calculated according to the following formula [42]:

Table 9 The calculation of characteristic parameters for 35CrMnSiA under uniaxial strain state. No.

1 2 3 4 5 6 7 8




Volumetric strain (× 10−2)

Impact temperature rise (K)

325 607 607 623 906 984 1240 1733

4336 4698 4797 4401 4881 4549 3942 4678

5.53 11.19 11.43 10.76 17.36 17.57 19.19 31.82

3.75 6.46 6.33 7.08 9.28 10.82 15.73 18.52

0.81 2.81 2.67 3.56 7.45 11.55 476.87 863.32

ΔTH = T0 e γ0 ηH +

ηH

η2 ⎡ e−γ0 η ⎤ dη − T0 ⎢ ⎥ (1 λη)3 − ⎣ ⎦

(8)

4. Discussions 4.1. Adiabatic shear failure In order to analyze the microstructure evolutions of ultra-high strength low-alloy martensite steel under uniaxial stress state, the metallographic observation by optical microscope was performed to investigate the shear failure characteristics of 35CrMnSiA. Fig. 12 displays the microstructures of the post-impact 35CrMnSiA samples under critical fracture strain rate 4100/s ~ 4200/s. Compared with the original microstructure of 35CrMnSiA (as shown in Fig. 1), the orientation of lath martensites after impact became slightly disordered and there was no significant plastic deformation, as given in Fig. 12(a). Under strain rate 4200/s, the adiabatic shear band and crack are observed in Fig. 12(b1). The width of the observed shear band which is 364.31 μ m in length varies from 1.54 μ m to 4.04 μ m. By split and fracture, the adiabatic shear band completely developed into crack. The branch of shear band is also observed in Fig. 12(b1). As displayed in Fig. 12(b2), grain refinement is noticed at the tip of the crack. Furthermore, the white oxide inclusion which is the product of adiabatic temperature rise is observed in the crack (Fig. 12(b3)). As shown in Fig. 3(a), 35CrMnSiA was characterized by strain hardening under strain rate 2400/s. But with the increase of strain rate, microstructure softening and thermal softening had gradually become the prominent factors for material behavior [44]. Above strain rate 4200/s, 35CrMnSiA samples had highly localized plastic deformation in an extremely short time, which could be approximated as the quasiadiabatic process. The plastic strain energy density of 35CrMnSiA samples in SHPB tests can be calculated by formula [45]:

1 ⎛ ∂u ⎞ = 0 (mass) ρ0 ⎝ ∂h ⎠t 1 ⎛ ∂σ ⎞ = 0 (momentum) ρ0 ⎝ ∂h ⎠t

⎛ ∂E ⎞ + σ ⎛ ∂u ⎞ = 0 (energy) ρ0 ⎝ ∂h ⎠t ⎝ ∂t ⎠h

∫0

where T0 is room temperature, C0 and λ are Hugoniot coefficients, γ0 is calculated by equation λ = (γ0 + 1)/2 [43], cp is the specific heat at constant pressure, η is volumetric strain calculated by η = u/ D . As shown in Table 9, the impact temperature rise is less than 15 K below the impact velocity of 1240 m/s. There are remarkable rises of 476.87 K and 863.32 K under impact velocity of 1240 m/s and 1733 m/s respectively, which proves that the phase transformation of 35CrMnSiA under uniaxial strain state is characterized by prominent temperature rise. Compared with uniaxial stress state, the higher temperature rise and less loading time in uniaxial strain state did not result in adiabatic shear failure, because 35CrMnSiA is no longer sensitive to shear strength in Hugoniot state. From the discussions above, it can be concluded that impact pressure and temperature rise are the decisive factors for the phase transformation of 35CrMnSiA under uniaxial strain state. As shown in Fig. 9 and Table 9, the phase transformation is characterized by significant volume shrinkage as well.

where C0 and λ are Hugoniot coefficients. According to the distribution of all (D, u) points in Fig. 8, it is concluded that there was no phase change in 35CrMnSiA target plate under impact velocity of 984 m/s, corresponding to the impact pressure of 17.57 GPa. The fitting results are listed in Table 8. Furthermore, the piecewise expressed relationships of impact pressure versus specific volume ratio and volumetric strain are shown in Fig. 9. Fig. 9 indicates that the experimental results are in good agreement with the theoretical calculations, which proves the veracity of the fitted Hugoniot coefficients. The relations of yield strength versus the logarithm of strain rate are shown in Fig. 10. Fig. 10(a) shows that the axial yield strength increases with the increasing strain rate. Compared to uniaxial stress state, the axial yield strength of 35CrMnSiA under uniaxial strain state has increased significantly. However, as shown in Fig. 10(b), the equivalent yield strengths under uniaxial strain state are less than the value under strain rate 2400/s in uniaxial stress state, which indicates that there is no definite rule between equivalent yield strength and strain rate. It is noted that the equivalent yield strength under strain rate 1.01 × 106/s and 2.30 × 106/s are even less than the quasi-static yield strength. To better investigate the dynamic mechanical behavior of 35CrMnSiA under uniaxial strain state, the Lagrangian analysis [41] was carried out to compute the spatial and temporal distribution of internal energy, specific volume, strain and particle velocity of 35CrMnSiA samples, and the derived stress-strain curves are shown in Fig. 11. All computations are based on the conservation equations expressed in Lagrangian coordinate:

⎛ ∂ν ⎞ − ⎝ ∂t ⎠h ⎛ ∂u ⎞ + ⎝ ∂t ⎠h

λC02 γ η e0 H• cP

(7)

Where ρ0 is initial density, u is particle velocity, ν is specific volume, σ is normal stress, E is internal energy, t is time and h is Lagrangian position coordinate. Fig. 11(a) shows that the result of sensor 1# is in good agreement with that of sensor 2#. The peak stress of sensor 2# is slightly lower than that of sensor 1# because the wave is attenuating during the propagation. Consequently, the result of sensor 1# is used for further analysis. When comparing Fig. 11(b) with Fig. 3(a), it can be seen that 35CrMnSiA samples are characterized by high stress but small strain under uniaxial strain state, and characterized by low stress but large strain under uniaxial stress state. The loading time was below 1 μs in planar plate impact tests, which was far less than that in SHPB tests. In planar plate impact tests, the strength of elastic wave was far less than that of plastic wave and could be reasonably neglected. Therefore, the yield point (HEL point) is not obvious in Fig. 11, above which 35CrMnSiA lost much of its shear strength and started behaving like fluid. And the material is characterized by noticeable strain softening after peak stress.

νεp =

∫0

εp*

σflow dεp

(9)

where νεp is plastic strain energy density, εp is plastic strain, σflow is flow stress. For unbroken samples, εp* equals to maximum plastic strain; and for broken samples, εp* equals to failure plastic strain where the stress collapses. As shown in Table 10, the plastic strain energy density of 35CrMnSiA sample reaches the maximum value at the critical failure strain rate 4100/s. In order to further analyze the strain rate effect, the rise rate of plastic strain energy density is calculated by differential. As shown in Fig. 13, the adiabatic shear failure occurs when the rise rate of plastic strain energy density of 35CrMnSiA sample reaches 10.58 × 106 J·m−3 ∙μ s−1 and the plastic strain energy density is more than 4.51 × 108 J·m−3. For ultra-high strength low-alloy steel which is characterized by adiabatic shear failure under uniaxial stress state, the rise rate 185


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(a)

(b2))

(b3)

(b11)

Fig. 12. Optical micrographs of post-impact 35CrMnSiA samples under uniaxial stress state. (a) the microstructure of 35CrMnSiA sample under strain rate 4100/s; (b1) adiabatic shear band and crack in 35CrMnSiA sample under strain rate 4200/s; (b2) grain refinement in 35CrMnSiA sample under strain rate 4200/s; (b3) white oxide inclusion in 35CrMnSiA sample under strain rate 4200/s.

4.2. Reversible α → ε (BCC →

of plastic strain energy density and plastic strain energy density which take the strain energy, stress-strain history and rate effect into account could be used as failure criterion.

HCP) phase transformation

In order to further investigate the phase transformation of 35CrMnSiA subjected to high impact pressure and the effect of phase transformation on the mechanical performance of 35CrMnSiA, the XRD and metallographic analysis on original and post-impact samples were 186


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performance of 35CrMnSiA. With scan velocity of 2.25°/s, the X-ray (from Cu target) scan results are shown in Fig. 14. The intensity-2θ spectra of original sample and post-impact sample subjected to the impact pressure of 11.43 GPa are almost the same, both with three characteristic peaks at 44.5°, 64.7° and 82°, corresponding to the crystallographic direction (110)α , (200)α and (211)α , respectively. As the impact pressure increases to 19.19 GPa, the intensity of all peaks sharply decreases so that the (200)α , (211)α peaks are too small to be observed. The crystallite size estimated from FWHM value reduces from 172 A(0 GPa), 185 A(11.43 GPa) to 139 A(19.19 GPa). The drop in diffracted intensity could be attributed to the decreased crystallite size and increased internal stress. In addition, it is observed in Fig. 14 that the (110)α peak has a slight right shift under the impact pressure of 19.19 GPa, which results from the lattice contraction induced by residual compressive stress. In planar plate impact tests, the micrographs of post-impact samples of 35CrMnSiA under different impact velocities are shown in Fig. 15. There are no obvious differences between the original microstructure (as shown in Fig. 1) and microstructures under the impact velocities of 325 m/s and 623 m/s (Fig. 15(a1), (a2), (b1) and (b2)). As shown in Fig. 15(c1) and (c2), the grain refinement is clearly observed as the impact velocity increases to 1240 m/s. HCP ε -phase iron which is much denser than BCC α -phase iron at the phase boundary is stable only at extremely high pressure. The continuous dynamic recrystallization took place during the thermal deformation process when the dislocation density was consumed by the transformation from low-angle grain boundary to high-angle grain boundary. Finally, the sub-grains grew into the grains and the grain refinement is observed. SEM observation was conducted to better analyze the evolution of martensites under high velocity impact. Compared with the microstructures below the impact velocity of 1200 m/s (as shown in Fig. 16(a), (b) and (c)), some microvoids are observed in the sample under the impact velocity of 1240 m/s (as shown in Fig. 16(d)), which are believed to be the product of heat and volume shrinkage. From the discussions above, we can conclude that the ultrafine grains contribute to improving the strength of 35CrMnSiA and reducing the ductility of material. If the high pressure is continuously applied to the sample, the microvoids would develop into crack and fracture.

Table 10 The calculation results of SHPB tests by energy method. Maximum/Failure strain

Plastic strain energy density (× 108 J·m−3)

Loading time of plastic wave ( μ s)

2400 2800 3300 4100 4200 4550

0.19(Maximum strain) 0.23(Maximum strain) 0.27(Maximum strain) 0.36(Maximum strain) 0.23(Failure strain) 0.24(Failure strain)

3.06 4.09 5.02 6.70 4.51 4.64

62 63 65 65 44 42

se rate of plastic strain energy density (x10 6 J m-3

s-1)

Strain rate (/s)

12

4550/s

11 10

4100/s

9

4200/s

8

3300/s

7

2800/s

6

2400/s

5 4 3 0

5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Time (μs)

Fig. 13. The relationship of rise rate of plastic strain energy density versus time.

44.5 (110)

Intensity (a.u.)

82

64.7 (200)

(211)

5. Validation

0GPa

The dynamic fracture experiments and high velocity impact experiments were performed to further investigate the relationship between dynamic mechanical behaviors and fracture thresholds of ultrahigh strength low-alloy steel projectiles subjected to ballistic impact loading. In dynamic fracture experiments, the blunt-nosed 35CrMnSiA projectiles were machined into Φ11.2 mm × 40 mm with the nominal mass of 30 g. The ultra-high strength low-alloy steel (tensile strength:1579 MPa) plate which is 15.30 mm in thickness acted as the rigid target. As shown in Fig. 17, the 35CrMnSiA projectiles had shear fracture along 45-degree at the head with the impact velocity of 149.1 m/s and 164.4 m/s，but had tension-shear mixed fracture over impact velocity 263.7 m/s. Table 11 reveals that the critical fracture velocity for 35CrMnSiA projectile is near 149.1 m/s, corresponding to the impact pressure of 2.59 GPa, which is close to the compressive strength of 35CrMnSiA under critical fracture strain rate 4200/s (compressive strength: 2457 MPa) in SHPB tests. Moreover, as shown in Fig. 18, the ratio of residual length to original length of projectile quadratically decreases with the increasing impact pressure. When impacting the steel target with the thickness of 35 mm, the 30 g projectile totally fragmented and could not pass through the target with the velocity as high as 2010 m/s (as shown in Fig. 19(a1) and (a2)). Consequently, in order to improve the perforating capacity of the ultra-high strength low-alloy steel projectile, we increase the mass of projectile from 30 g to 40 g to further investigate the fracture behavior

11.429GPa 19.186GPa 10

20

30

40

50

60

70

80

90

2θ (deg) Fig. 14. Intensity-2θ spectra of 35CrMnSiA samples subjected to different impact pressures.

conducted. There are three kinds of crystal structures of solid steel: BCC (Body-Centered Cubic), FCC (Face-Centered Cubic) and HCP (Hexagonal-Closed Packed). Bargen and Boehler [46] pointed out that subjected to quasi-hydrostatic pressure, phase transformation of iron from BCC α -phase to HCP ε -phase happens at 15.3 GPa. On account that HCP ε -phase of iron is only stable at extremely high pressure (above 13 GPa) [47], the reverse ε → α transition which leaves no ε -phase behind happens when the shock wave unloads [48]. Consequently, it is difficult to detect the ε -phase that has ever transitorily existed by XRD or direct microstructure observation. But in this research, what we concern is the effect of phase transformation on the mechanical 187


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(a1)

(a2)

(b1)

(b2)

(c1)

(c2)

Fig. 15. Optical micrographs of post-impact 35CrMnSiA samples under uniaxial strain state. (a1) impact velocity: 325 m/s, magnification: 200 × ; (a2) impact velocity: 325 m/s, magnification: 500 × ; (b1) impact velocity: 623 m/s, magnification: 200 × ; (b2) impact velocity: 623 m/s, magnification: 500 × ; (c1) impact velocity: 1240 m/s, magnification: 200 × ; (c2) impact velocity: 1240 m/s, magnification: 500 × .

From Table 9, it is observed that there is a significant increase in impact temperature rise from 11.55 K to 476.87 K above the critical phase transformation pressure 17.57 GPa. And some blue areas observed in Fig. 20 are also the product of impact temperature rise, which proves that the reversible α → ε phase transformation characterized by prominent impact temperature rise results in the noticeable mass abrasion. Based on the ballistic impact experiment results listed in Tables 11 and 12, for the blunt-nosed cylindrical ultra-high strength low-alloy steel projectiles with the mass ranging from 30 g to 40 g, the relationship between residual mass/original mass of projectile and impact pressure could be quantified as

of ultra-high strength low-alloy steel projectile subjected to high velocity impact loading. High velocity impact experiments were carried out to study the failure modes and threshold of 35CrMnSiA projectiles subjected to high velocity impact loading. The nominal mass of the blunt-nosed cylindrical projectile with the dimension of Φ12.8 mm × 40 mm is 40 g. Propelled by Φ14.5 mm ballistic gun and two-stage light gas gun, the impact velocity of the projectiles varies from 500 m/s～1800 m/s. With the nominal thickness of 15 mm, 20 mm, 25 mm and 35 mm, all targets are manufactured from high strength steel (tensile strength:787 MPa), and the experimental results are shown in Table 12. According to onedimensional impact theory [39] and Hugoniot coefficients for high strength steel target (C0 = 4381 m/s, λ = 0.717) obtained from planar plate impact tests, the calculated impact pressures are shown in Table 12. From Table 12, it is observed that the ratio of residual mass to original mass of 35CrMnSiA projectiles are around 62% below impact velocity 1283 m/s. It is noticeable that there is sharp decline in this ratio from 59.82% to 30.06% above impact velocity 1283 m/s, corresponding to the impact pressure of 21.25 GPa. Fig. 19(b1) and Fig. 20 reveal that the 35CrMnSiA projectiles had severe fractures and mass abrasion over impact velocity 1283 m/s, and it totally fragmented with the impact velocity of 1760 m/s.

Residual mass/original mass of projectile(%) 100 0GPa < p < 2.59GPa ⎧ ⎪ 0.51p2 − 12.29p + 128.90 2.59GPa ≤ p < 8.91GPa ⎪ 61.5 8.91GPa ≤ p < 21.25GPa = ⎨ 2 ⎪ 0.21p − 16.29p + 312.41 21.25GPa ≤ p < 33.08GPa ⎪ 0 p ≥ 33.08GPa ⎩

(10)

where p is impact pressure. As shown in Fig. 21, it is concluded that the projectile has no fracture below impact pressure 2.59 GPa, and the 188


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(a)

(b)

(c)

(d)

Microvoid

original

149.1m/s

164.4m/s

263.7m/s

Residual length/Original length of projectile (%)

Fig. 16. SEM micrographs of original and post-impact 35CrMnSiA samples under uniaxial strain state. (a) original microstructure; (b) impact velocity: 325 m/s; (c) impact velocity: 623 m/s; (d) impact velocity: 1240 m/s.

362.5m/s 501.8m/s

Fig. 17. The original and retrieved projectiles of 35CrMnSiA in dynamic fracture experiments.

100

Experimental data Fitting curve

95 90 85 80 75 70 65 60 2

3

4

5

6

7

8

9

Impact pressure (GPa) Fig. 18. The relationship between the ratio of residual length to original length of projectile and impact pressure.

Table 11 The results of dynamic fracture experiments. Impact velocity(m/s)

Impact pressure(GPa)

Residual length/ original length of projectile (%)

Residual mass/original mass of projectile (%)

149.1 164.4 263.7 362.5 501.8

2.59 2.86 4.62 6.38 8.91

100 100 88.75 73.75 67.5

99.57 98.65 83.99 70.37 60.33

Consequently, for high velocity (impact pressure < 21.25 GPa) impact, the perforating capacity of projectile could be improved by increasing the impact velocity; but for ultra-high velocity (impact pressure > 21.25 GPa) impact, due to the severe mass abrasion resulted from phase transformation, the projectile mass should also be increased to improve the perforating capacity of projectile. 6. Conclusions

residual mass/original mass decreases quadratically with the increasing impact pressure within impact pressure 2.59 GPa～8.91 GPa; when the impact pressure lies between 8.91 GPa and 21.25 GPa, the residual mass/original mass is stable at about 61.5%; then when the impact pressure ranges from 21.25 GPa to 33.08 GPa, the projectile has severe mass abrasion and the residual mass/original mass decreases dramatically with the impact pressure in the quadratic form; and when the impact pressure is above 33.08 GPa, the projectile fragments totally.

This paper focused on the dynamic mechanical behaviors and failure thresholds of typical ultra-high strength low-alloy martensite steel 35CrMnSiA under strain rate 0.001/s～106/s. There are four main parts in this study. First, the SHPB tests with the strain rate ranging from 2000/s～5000/s have been done to investigate the dynamic compressive behavior of 35CrMnSiA under uniaxial stress state. In the second part, the planar plate impact tests within the strain rate 105/s～ 189


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(a1)

(b1)

(b2)

(b3)

Target thickness (mm)


Ballistic performance


Residual mass/ original mass of projectile (%)

15

751.1 856.7 986.2 1034.1 1283 1464.3 1481.9 1760.0

penetrated perforated perforated perforated perforated perforated perforated perforated

13.56 15.58 16.55 17.49 21.25 25.48 25.92 33.08

61.50 60.98 63.06 63.54 59.82 30.06 30.84 totally fractured

25 35

Residual mass/original mass of projectile (%)

Table 12 The results of high velocity impact experiments.

20

100

Experimental data Fitting curve

90 80 70 60 50 40 30 20 10 0 0

106/s were conducted to investigate the dynamic response of 35CrMnSiA under uniaxial strain state. In the third part, combined with XRD and metallographic observation, the microstructure evolutions and failure mechanism of 35CrMnSiA under different stress states have been discussed. In the last part, the dynamic fracture experiments and high

751.1m/s

856.7m/s

986.2m/s

1034.1m/s 1283m/s

fractured projectile

(c)

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 34

Fig. 21. Relationship between residual mass/original mass of projectile and impact pressure.

1464.3m/s 1481.9m/s

Blue area

(b)

2

Impact Pressure (GPa)

(a) original

Fig. 19. The damage instances of 30 g and 40 g 35CrMnSiA projectiles and 35 mm high strength steel targets. (a1) the fractured 30 g projectile; (a2) the impact side of high strength steel target under the impact of 30 g projectile (impact velocity: 2010 m/s); (b1) the fragmented 40 g projectile; (b2) the impact side of high strength steel target under the impact of 40 g projectile (impact velocity: 1760 m/s); (b3) the rear side of high strength steel target under the impact of 40 g projectile.

residual projectile

(a2)

fractured projectile

190

Fig. 20. The original and retrieved projectiles of 35CrMnSiA in high velocity impact experiments. (a) the original and retrieved projectiles of 35CrMnSiA below impact velocity 1760 m/s; (b) the fractured projectile found in the shot hole (target thickness: 25 mm, impact velocity:1159.1 m/s); (c) the fractured projectile found in the shot hole (target thickness: 35 mm, impact velocity:1413.8 m/s).


J. Ren et al.

velocity impact experiments were carried out to study the failure thresholds of ultra-high strength low-alloy steel projectiles. Some main conclusions from this study are listed as following:

•

•

•

•

[11] [12]

Subjected to uniaxial stress state, 35CrMnSiA sample would have adiabatic shear failure as long as the rise rate of plastic strain energy density reaches 10.58 × 106 J·m−3µ s−1 and the plastic strain energy density is above 4.51 × 108 J·m−3. For ultra-high strength lowalloy steel which is characterized by adiabatic shear failure under uniaxial stress state, the rise rate of plastic strain energy density and plastic strain energy density could be used to estimate the failure of material. The planar plate impact tests results showed that impact pressure and temperature rise are the decisive factors for the phase transformation of ultra-high strength low-alloy martensite steel subjected to uniaxial strain state. For 35CrMnSiA, reversible α → ε (BCC → HCP) phase transformation with the significant effect of heat and volume shrinkage occurs within the impact pressure of 17.57 GPa～ 19.19 GPa. The continuous dynamic recrystallization-induced grain refinement in 35CrMnSiA contributes to the increase in strength but decrease in ductility. And the Hugoniot coefficients for 35CrMnSiA under a wide range of pressures have been fitted piecewise. The 35CrMnSiA projectiles fractured over impact velocity of 149.1 m/s, corresponding to the impact pressure of 2.59 GPa; and when the impact velocity exceeded 1283 m/s, corresponding to the impact pressure of 21.25 GPa, the projectiles suffered severe mass abrasion due to the reversible α → ε phase transformation which is characterized by great impact temperature rise. The damage evolution law for 35CrMnSiA projectile is quantified. For high velocity (impact pressure < 21.25 GPa) impact, the perforating capacity of projectile could be improved by increasing the impact velocity; but for ultra-high velocity (impact pressure > 21.25 GPa) impact during which the material suffers severe mass abrasion due to the phase transformation, the projectile mass should also be increased to improve the perforating capacity of projectile.

[13]

[14]

[15]

[16] [17]

[18]

[19]

[20] [21]

[22] [23] [24] [25]

[26] [27] [28]

[29]

Acknowledgement

[30] [31]

This work was supported by the Natural Science Foundation of China (No.11402027). Laboratory of High Pressure Physics in Southwest Jiaotong University and China State Key Laboratory of Explosion Science and Technology are acknowledged.

[32]

[33] [34]

References

[35] [36]

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