Strain rate, temperature and structure effects on the flow and fracture stresses of metals and alloys under shockwave

Transcription

1 International Symposium on Current Problems in Solid Mechanics in honor of Professor R. J. Clifton Brown University Greek island of Symi, June 24-29, 212 Strain rate, temperature and structure effects on the flow and fracture stresses of metals and alloys under shockwave loading G.I. Kanel, S.V. Razorenov, E.B. Zaretsky and S.I. Ashitkov Joint Institute for High Temperatures of Russian Academy of Sciences, Moscow; Institute of Problems of Chemical Physics of Russian Academy of Sciences, Chernogolovka, Department of Mechanical Engineering, Ben Gurion University, Beer Sheva, Israel

2 Motivation The need of the basis for developing the models and constitutive relationships which would be workable over wide range of strain rates, stresses and temperatures. The need of new information about basic mechanisms of plastic deformation and fracture at high strain rate. Approaching the ultimate values of the shear strength and tensile strength. Coupling with atomistic simulations.

3 Strain rate and temperature effects in general Ideal shear strength Phonon drag controlled flow Frenkel s estimation of the ideal shear strength: τ c G/2π (1926) Flow Stress Thermally activated flow T 1 T 2 > T 1 Quasistatic, Hopkinson bars Shock Waves Strain Rate For low loading rates, plastic deformation is aided by thermal fluctuations. Dislocation motion is impeded at barriers and a combination of thermal agitation and applied stress is required to activate dislocations over the obstacles. In order to provide high rate of deformation one should apply so high stresses that are enough to overcome the usual dislocation barriers without any aid from thermal fluctuations. Under the high-rate conditions, viscous phonon drag becomes dominant in resistance to motion of dislocations. Since the phonon drag is proportional to the temperature, an increase of the flow stress with increasing temperature should occur at the highest strain rates.

4 APPEARANCE OF MATERIAL PROPERTIES IN A FREE SURFACE VELOCITY HISTORY Flyer plate Sample VISAR u fs (t) Available loading conditions: Peak stresses:.1 1 GPa Load durations: 1 ns 1 µs Time resolution of the measurements: 1 ns Free Surface Velocity, km/s 1.2 Steel 4Kh.8.4. Polymorphous transformation Hugoniot elastic limit (HEL) Time (µsec) u fs Spall signal Hugoniot elastic limit: HEL = ρ c l u fs HEL /2 Yield stress: Spall strength: Phase transition pressure: Y = HEL (1-2ν)/(1-ν) σ sp = ρ c b ( u fs + δ)/2 p α ε = ρ D 1 u fs1 /2

5 Femtosecond interferometric microscopy for study laser-driven shock waves Ti:S laser: τ L =15 fs, λ=8 nm Initial before pump pulse Transient 1 ns delay after pump Attenuators Probe: 4nm, 15 fs Interferometer CCD Target Delay line Pump: 8nm, 15 fs SHG Displacement z, nm 8 Al nm 76 nm 12 nm Temporal resolution: 1-13 s Spatial resolution: 2 µm Phase measurement accuracy: ~ π/2 (1nm) Time t, ps Free surface displacement histories

6 Free Surface Velocity, km/s σ HEL Development of Elastic Precursor Waves in Relaxing Materials.25 mm 1.5 mm.44 mm 5 1 HEL Time, ns 5 mm mm Mg - 4.5% Al alloy dσ x dh du dt HEL HEL u = ρ t V = ρ t 1 + c dσ x dh 1 + c l l u t σ x t 2 2 ( & σ + c V& ) dσ 1 2 = ρ dh c HEL HEL = 4 3 l G & γ c l p l x G.E. Duvall. In: Stress Waves in Inelastic Solids, edited by H. Kolsky and W. Prager, 1964 Ahrens T.J. and Duvall G.E. J. Geophys. Res., 71(18), (1966). J. R. Asay, G. R. Fowles, and Y. Gupta, J. Appl. Phys. 43, 744 (1972).

7 Decay of elastic precursor wave in aluminum Atomistic Simulations: HEL up to 15-2 GPa (G /G)σ HEL, GPa Ashitkov et al, 211 Ashitkov et al, 21 Whitley et al, 211 σ HEL =.16/X.63 Winey et al, 29 Gupta et al, 29 Al Garkushin et al, 21 } } Experiments with Femtosecond Laser Pulses Plate impact Arvidsson et al, Distance, mm The data are well described by empirical relationship σ HEL = S h h ) ( α h = 1 mm, S =.16 GPa, α =.63 dσ dh HEL = 4 3 G & γ c l p γ& p = 3 4 Sαc ( l h h h G ) ( α + 1) & γ p = α τ E α Sαcl 4 SG hg

8 Relationship between the plastic strain rate and the shear stress at HEL Plastic strain rate γ', s Al 1 mm 1 µm γ '= 9.1 x 1 7 τ 2.59 τ, MPa Al τ HEL at 5-1 mm τ HEL = (γ '/9.1x1 7 ).39 τ = lg(γ ') (G /G)τ HEL, GPa Plastic strain rate γ ', s -1 At ~(2-5) 1 3 s -1 the Hopkinson bar tests show sharp increase of sensitivity of the flow stress to strain rate (see K. Sakino. J. Phys. IV France, 1, Pr , 2, as an example). Decay of HEL sharply decelerates at the distance of 5-1 mm (~1 3 s-1 strain rate)

9 Strain rate and stress in plastic shock wave Free Surface Velocity, km/s Mg-4.5%Al, 1.8 mm du fs /dt = (.8-1.2)x1 8 km/s 2 dε x /dt = (du fs /dt )/2U S = (.8-1.2)x1 7 s -1 dγ max /dt = (dε x /dt )/2 = (.4-.6)x1 7 s -1 Pressure, Stress Hugoniot σ x (v) Hydrostat p(v) Rayleigh line (4/3)τ (2/3)Y HEL Time, ns Specific Volume Total strain rate in steady wave: & ε = u& Shear strain rate at 1-D compression: Plastic shear strain rate: & γ p x & ε x = 2 p & γ = U & τ 2G & S ε x 2 σ x - p, MPa 2 τ h = 3/4 (σ -p) = MPa max x 15 1 L.C.Chhabildas, and J.R. Asay. J. Appl. Phys., 5(4), (1979) J.W. Swegle and D.E. Grady. J. Appl. Phys. 58, 692 (1985) D. E. Grady. Structured shock waves and the fourth-power law. J. Appl. Phys. 17, 1356 (21) V/V

10 Accelerated relaxation in plastic shock wave 3 Mg-4.5%Al mm τ, MPa 2 15 At HEL τ = 11γ '.24 In plastic shock at 5-1 mm γ ' ~ τ mm γ' p, s -1 The strain rate in plastic shock wave is faster that at the HEL by an order of magnitude. Acceleration of plastic deformation is associated with multiplication of dislocations.

11 Temperature effects

12 SHOCK-WAVE LOADING OF ALUMINUM SINGLE CRYSTALS AT ELEVATED TEMPERATURES 7 8 Free Surface Velocity, m/s o C 47 o C 2 o C Sample thickness 2.85 mm. Free Surface Velocity, m/s µm, 622 o C 425 µm, 2 o C Time, µs Time, ns The Hugoniot elastic limit and the rise time of plastic shock wave unexpectedly grow with increasing the temperature; A strong rate sensitivity results in a strong decay of the elastic precursor wave.

13 Behavior of AD1 aluminum at ~6 C Free Surface Velocity, m/s AD mm 65 o C 5.37 mm 2 o C Time, ns Increase in the HEL and rise time of plastic shock wave as compared to the room temperature data. Free Surface Velocity, m/s mm, 592 o C mm, 619 o C mm, 65 o C mm, 612 o C Time, ns

14 Initial flow stress at high strain rates and elevated temperatures 4 σ HEL, GPa o C Al AD1 6 o C σ HEL =.625 / x.362 Shear stress, MPa Al AD1 6 o C 2 o C Distance, mm Plastic strain rate, s -1 Ultimate shear strength ( ideal strength ) should decrease with increasing the temperature.

15 Strain rate and temperature effects in aluminum 4 Flow Stress Thermally activated flow T 1 Quasistatic, Hopkinson bars Phonon drag controlled flow T 2 > T 1 Shock Waves Shear stress, MPa Al AD1 6 o C 2 o C Strain Rate Plastic strain rate, s -1 The shock-wave tests confirm general view on strain rate and temperature effects: The transitions in rate controlling mechanism occur at ~3 1 3 s -1 when the temperature is 2 C and at smaller strain rate ~1 2 s -1 at 6 C; Anomalous thermal hardening takes place in the high rate sensitivity region.

16 Strain rate and temperature effects in pure aluminum Shear stress, MPa Al 99.99% Linear 2 mm τ HEL α α +1 = A & γ 932 K τ = lg(γ ').1 mm 932 K 8 K 5 K 3 K Plastic shock wave 3 K Shear Stress, MPa s s s Plastic strain rate, s -1 Temperature, K The linear dependences τ (T ) at fixed strain rates are in agreement with the mechanism of control of the dislocations motion by phonon friction.

17 Plastic strain rate, s Relationship between the plastic strain rate and the shear stress at HEL & γ = Bτ β 2.7 < β < 4 2 mm Al 99.99%.1 mm 3 K 5 K 8 K 932 K Velocity as a function of the applied shear stress for an edge dislocation in aluminum Shear stress, MPa D.L. Olmsted,.G. Hecto, W.A. Curtin and R.J. Clifton. Modelling Simul. Mater. Sci. Eng. 13, 371 (25) The motion of dislocations sharply decelerates at ~1 MPa of the shear stress that is not compatible with the observed strong dependence γ (τ). The dislocation density of 1 15 m -2 is required to provide 1 9 s -1 strain rate with a sound-speed dislocation motion. Probably the process is mainly controlled by the rate of nucleation of dislocations (or shear bands).

18 Comparison of shock response of Al single crystal, polycrystalline Al and commercial aluminum AD1 Free Surface Velocity, m/s Al Single crystal 622 o C 2.97 mm AD1 2 mm, 619 o C Polycrystalline Al o C 2. mm HEL, GPa 1.1 Al 661 Pure Al 851 K Al, average Time, µs.1 1 Distance, mm The spike-like shape of the elastic precursor wave is an evidence of accelerating stress relaxation as a result of multiplication of dislocations behind the precursor front. In the alloys the large plastic strain rate immediately behind the elastic precursor front is provided by an abundance of the dislocation nucleation sites without essential contribution of the multiplication processes. It may be supposed that increase of the temperature does not ease the nucleation and multiplication processes.

19 D16 aluminum alloy (Al 224) Free Surface Velocity, m/s D16 (Al 224).5 mm 5 mm (G /G)σ HEL, GPa Ashitkov et al, 211 Ashitkov et al, 21 Whitley et al, 211 Gupta et al, 29 σ HEL =.16/X.63 Winey et al, 29 Arvidsson et al, 1975 Al D16 (Al 224) Garkushin et al, Time, ns Distance, mm Weak precursor decay The HEL of the alloy exceeds that of aluminum at the propagation distances more than.1 mm

20 Shock behavior of iron at normal and elevated temperatures 3 2. Hugoniot Elastic Limit, GPa HEL R.F. Smith et al, 211 Yield Stress, GPa HEL Y Distance, mm Temperature, o C Weak precursor decay The yield stress decreases monotonously with heating

21 YIELD STRENGTH OF TITANIUMS AT ELEVATED TEMPERATURES Yield Stress, GPa Commercial Ti Ti 99.99% Ti S Yield Stress, Y.2, GPa Uniaxial stress 1-D strain (Shock) Ti S Temperature, o C Strain Rate, s -1 The flow stress in the pure metal is small and comparable with the phonon friction forces. Therefore the growth of the latter contributes essentially into the drag of the dislocations. Alloys contain numerous obstacles that have been created specifically to increase the yield strength. The stress needed to overcome these obstacles far exceeds the forces of phonon drag.

22 Temperature effect at large strain Shear stress, MPa Al 99.99% Linear 2 mm τ HEL α = A & γ α K τ = lg(γ ').1 mm 932 K 8 K 5 K 3 K Plastic shock wave 3 K Plastic strain rate, s -1 S. E. Grunschel, R. J. Clifton, and T. Jiao. In: Shock compression of Condense Matter 211, p.1335 Data for plastic strain γ p = at the HEL and γ p.1 in plastic shock wave The work hardening may cause larger effect than the phonon friction

23 Grain size effects

24 Armco iron 6 5 µm Free Surface Velocity, m/s Armco, as-received Armco, forged Iron.2 mm thick µm Free Surface Velocity, m/s Forged Armco iron, 2.7 mm As received Time, ns Time, ns Refinement of the grain structure results in twofold increase of and some smaller increase of the dynamic yield strength.

25 Coarse-grained and ultrafine-grained tantalum Free surface velocity, m/s CG, HR = 77 UFG, HR = HEL, GPa CG 3. UFG Sample Thickness, mm Time, µs In spite of larger hardness, ultrafine-grained tantalum demonstrates lower HEL and faster plastic compression. Obviously, in the UFG material the elastic precursor wave decays faster. Grain boundaries are the dislocation sources. HEL Distance

26 Conclusions for development of material models Flow Stress Hardened High Temperature Strain Rate Anomalous thermal hardening occurs in the domain of high rate sensitivity of the flow stress; Mechanical hardening of a material shifts the transition towards higher strain rates; Hardened material may demonstrate less flow stress at high strain rate. Both the work hardening and the work softening may accompany the high-rate deformation

27 Spall fracture

28 SPALL PHENOMENA UNDER SHOCK LOADING Spalling is the process of internal rupture of a body due to tensile stresses generated as a result of a compression pulse reflected from the free surface. σ x Free surface x σ x Free surface x

29 The wave dynamics at reflection of a shock pulse from the free surface t C_ p Spall Hugoniot K C + Riemann's Isentropes C + u fs C + Shock front Free surface x Spall Strength u m u K C - (tail) u u u fs u f The peak tensile stress just before the fracture corresponds to the intersection point K of the Riemann s isentropes u m Acoustic approach: σ sp = 1 2 ρ o c u o fs t

30 SPALL STRENGTH OF ALUMINUMS OF DIFFERENT PURITY Free Surface Velocity, m/s Al single crystal Commercial aluminum AD1 (99.3% purity) Al % ( u δu) 1 σ sp = ρcb pb Time, µs Single crystals always exhibit highest dynamic tensile strength. Pure metals often show higher spall strength than harder alloys.

31 APPROACHING THE IDEAL STRENGTH Pressure, GPa -2-4 Water PMMA Al Cu Fe Mo σ sp / σ id PMMA Epoxy Mo Water Cu Al Fe Tension Compression.6-6,6,8 1, 1,2 ρ/ρ.4. V/V, s As much as 3 % of ideal strength is reached at load duration of a nanosecond range.

32 Equations of State in the Negative Pressure Domain Matter Estimated σ id, GPa σ id ab initio, GPa σ id at 3 K from EOS or MD, GPa Aluminum (Sin ko and Smirnov, 22) 12.2 EOS (Faizullin and Skripov, 27) Copper (Černý and Pokluda, 27) 21. EOS (Faizullin and Skripov, 27) Molybdenum (Joshi and Gupta, 27) 42.9 (Černý and Pokluda, 27) Iron (Friakyz et al, 23) 27.7 (Černý and Pokluda, 27) 13.4 (Sin ko and Smirnov, 24) 13.5 EOS (Faizullin and Skripov, 27) PMMA 1.39 Epoxy 1.34 Water EOS (Speedy, 1982).22 MD (Netz et al, 21)

33 APPROACHING THE IDEAL STRENGTH 2 Spall strength, GPa Al σ spall = (ε' /1 8 ).2 Single Crystals AD1 Plate impacts Ideal strength Al 99.99% MD Ashitkov et al, 21 Foils Moshe, Eliezer, 2 Laser & particle beams Strain rate, s -1 At least 6 % of ideal strength is reached at load duration of a picosecond range.

34 Intragranular and intergranular fracture of Cu +.1%Si

35 Grain size effect on the spall strength. Armco iron and tantalum. Free Surface Velocity, m/s Free Surface Velocity, m/s Fe single crystal σ sp =6.8 GPa Sp.thick. 43 µm Armco, as-received σ sp = 3.62 GPa Sp.thick. 33 µm Armco, forged σ sp = 5.25 GPa Sp.thick. 4 µm Iron.2 mm thick Time, ns Forged σ sp = 3.3 GPa Armco iron, 2.7 mm Single crystal, σ sp = 4 GPa Time, ns As received, σ sp = 2.1 GPa Free surface velocity, m/s Refinement of the grain structure results in increase of the spall strength. The spall strength does not correlate with the HEL. Ta CG, HR = 77 UFG, HR = 14 Time, µs Ta

36 Influence of a heat treatment and polymorphic transformation on the spall behavior of steel Free Surface Velocity, km/sec Chromium-doped structural steel. Chemical composition: C.4 wt%, Si.3 wt%, Mn.6 wt%, Cr 1 wt% Quenched As received Time, µsec State of material As received Quenched As received Quenched As received Quenched Peak Stress, GPa * 2 ~75 ~8 Spall Strength, GPa * Spall fracture occurred at the boundary between the initial and transformed matter in this shot Refinement of the grain size as a result of reversible α-ε transformation increases the spall strength value

37 SPALL STRENGTH OF SINGLE CRYSTALS AND POLYCRYSTALLINE METALS AT MELTING 4 1, s -1 Spall Strength, GPa s -1 Al Zn (1) Temperature, o C Spall Strength, GPa 1,,5, - Aluminum AD1 - Magnesium Mg95 Mg Al,4,6,8 1, Homologous Temperature T/T m The strength of polycrystalline metals drops when the material begins to melt whereas single crystals maintain a high resistance to spall fracture when melting should start; In polycrystalline solids melting may start along grain boundaries at temperatures below the melting temperature of the crystal: pre-melting phenomenon; Superheated solid states were realized in the crystals under tension

38 Thank you for your attention!