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[Андрей Пряхни]

Dislocation pinning effects induced by nano-precipitates during warm laser shock peening: Dislocation dynamic simulation and experiments

Yiliang Liao,1 Chang Ye,1 Huang Gao,1 Bong-Joong Kim,2 Sergey Suslov,2 Eric A. Stach,2,3 and Gary J. Cheng1,3,a)
1School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47906, USA
2School of Materials Science, Purdue University, West Lafayette, Indiana 47906, USA
3Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47906, USA

(Received 17 April 2011; accepted 8 June 2011; published online 26 July 2011)

Warm laser shock peening (WLSP) is a new high strain rate surface strengthening process that has been demonstrated to significantly improve the fatigue performance of metallic components. This improvement is mainly due to the interaction of dislocations with highly dense nanoscale precipitates, which are generated by dynamic precipitation during the WLSP process. In this paper, the dislocation pinning effects induced by the nanoscale precipitates during WLSP are systematically studied. Aluminum alloy 6061 and AISI 4140 steel are selected as the materials with which to conduct WLSP experiments. Multiscale discrete dislocation dynamics (MDDD) simulation is conducted in order to investigate the interaction of dislocations and precipitates during the shock wave propagation. The evolution of dislocation structures during the shock wave propagation is studied. The dislocation structures after WLSP are characterized via transmission electron microscopy and are compared with the results of the MDDD simulation. The results show that nano-precipitates facilitate the generation of highly dense and uniformly distributed dislocation structures. The dislocation pinning effect is strongly affected by the density,

size, and space distribution of nano-precipitates. [doi:10.1063/1.3609072]

I. INTRODUCTION

Warm laser shock peening (WLSP) is an innovative thermo-mechanical processing technique that has great poten-tial for improving the mechanical properties of metallic mate-rials, including surface hardening and fatigue life.1–3 One of the most promising characteristics of WLSP is that highly dense and uniformly distributed dislocation structures can be formed due to the interaction between gliding dislocation structures and dense nanoscale precipitates generated during WLSP by dynamic precipitation (DP). The pinning effect of nano-precipitates on the dislocation motion provides the key contribution to mechanical improvements such as enhancing surface hardness, stabilizing residual stress, and preventing crack initiation, thus improving fatigue life and strength. Therefore, it is worthwhile to study the interaction of disloca-tion and nano-precipitates during the shock wave propagation and its effects on the dislocation evolution and mechanical enhancement.

There have been lots of efforts at investigating the pin-ning effects on dislocation evolution. It is generally accepted that dislocation structures overcome obstacles with a small characteristic radius and a low volume density via the shear-ing mechanism, whereas the dislocation motion in the matrix containing unshearable obstacles is governed by the Orowan process, which leaves the obstacles surrounded by pinned dislocation loops. In addition, the strengthening effect of

a)Author to whom correspondence should be addressed. Electronic mail: [e-mail].

0021-8979/2011/110(2)/023518/8/$30.00 110, 023518-1 V 2011 American Institute of Physics
C

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023518-2 Liao et al.

dislocation behaviors at the matrix–precipitate interface by proposing a back force model associated with the anti-phase boundary energy. Khraishi et al.23,25 reported a fundamental understanding of the particle strengthening in metal-matrix composites with a particle size of around 1000b and the hardening effect of a spatial distribution of defect clusters with a radius of 2b to 10b. However, the dislocation evolu-tion and strengthening effect predicted by these studies have not been compared with experimental results.

In this study, aluminum alloy 6061 (AA6061) and AISI 4140 steel are chosen for use in the WLSP experiments. The dislocation structures after WLSP processing are character-ized using TEM and are compared with the results of MDDD simulation. The strengthening effect due to the dislo-cation pinning is investigated by the hardness test after WLSP experiments and stress/strain curves during the shock loading by MDDD simulation. The effects of the density, size, and space distribution of nano-precipitates are studied.

II. EXPERIMENT AND SIMULATION

A. WLSP experiment and characterization

The materials used in this study are AA6061 (with the following chemical compositions in wt.%: Mg-0.92, Si-0.76, Fe-0.28, Cu-0.22, Ti-0.10, Cr-0.07, Zn-0.06, Mn-0.04, Be-0.003, V-0.01, and Al-balance) and AISI 4140 steel (with the following chemical compositions in wt.%: C-0.41, Si-0.21, Mn-0.83, P-0.025, S-0.027, Cr-0.91, Mo-0.18, and Fe-bal-ance). Before laser shock peening, AA6061 samples are sol-utionized at 550 C for 3 h and subsequently quenched in water, and AISI 4140 steel samples are austenitized for 20 min at 850 C and oil quenched down to room temperature. This is done to isolate the microstructures generated by WLSP. Aluminum foil with a uniform thickness of 30 microns and BK7 glass with a high laser transmission coeffi-cient are selected as the ablative coating material and the confining media, respectively. The elevated warm tempera-ture in WLSP is manipulated by a hot plate placed below the sample fixture. The temperature is monitored with a digital scientific thermometer. A Q-switched ND-YAG laser (Sure-lite III from Continuum, Inc.), operating at a wavelength of 1064 nm with a pulse width (full width at half maximum [FWHM]) of 5 nss is used to deliver the pulsed laser. An op-tical power meter (Newport, type 1916c) is used to measure the pulse laser energy. The laser beam diameter is calibrated using a photosensitive paper (Kodak Linagraph, type 1895). The laser power intensity I0 is adjusted by the Q-switched delay time and is calculated as I0 ¼ 0:1E=½pðd=2Þ2t&, where E is the pulse laser energy, d is the laser beam diameter, and t is the pulse width. The laser power intensity is one of the most important laser parameters in this study, because it determines the peak pressure of the laser-induced plasma (as discussed in Sec. II C). The experimental conditions are shown in Table I.

Transmission electron microscopes (FEI-Tecnai TEM and FEI-Titan TEM operated at 200 kV and 300 kV, respec-tively) are used to characterize the microstructures after WLSP. To prepare the TEM sample, a thin layer of the sam-ple surface after peening is sectioned by a diamond saw. The

J. Appl. Phys. 110, 023518 (2011)
TABLE I. Experimental conditions of WLSP.

Laser wavelength 1064 nm
Laser beam overlap 75%
Sample thickness 2.38 mm
WLSP temperature for steel 4140 250 C
Laser beam diameter 2 mm
Pulse duration 5 ns
WLSP temperature for AA6061 160 C

sample is then polished to a thickness of 30 microns. The final thinning is carried out via the H-Bar method using a focused ion beam (Nova-200). Before TEM observations, the samples are cleaned with acetone in order to get a better image quality. In addition, the FWHM value of the 2h angle as measured via x-ray diffraction (Bruker D8-Discover XRD) is utilized to compare the relative defect density after processing. Furthermore, the surface hardness after WLSP is measured by the micro-hardness tester with a 25 g load and a 10 s holding time.

B. Background on MDDD simulation theory

The mechanical properties of metallic materials are gov-erned by the dislocations’ collective motion and their inter-actions among themselves and with other crystal defects. Based on the fundamental physics theories of dislocation motion and interaction, the multiscale discrete dislocation dynamics model has been developed by Zbib and co-workers.26,27 MDDD merges two length scales: the nano-micro scale for the plasticity, and the continuum scale for the energy transport. This hybrid elasto-viscoplastic simulation model couples DD with finite element analysis to predict both the microstructure evolution and macro-mechanical behaviors.

At the nano-micro level, the dislocation loops with arbi-trary shapes in DD are discretized into short segments (bounded by nodes j and j þ 1), and their dynamics are ruled by the local stress distribution arising from the interactions within themselves and with other crystal defects, such as point and cluster defects, microcracks, microvoids, etc. The velocity and motion of a dislocation node is traced by solv-ing a “Newtonian” equation consisting of an inertia term, a drag term, and a driving force vector [Eqs. (1) and (2)]:

mivi þ 1 vi ¼ Fi; mi ¼ 1 dW ; (1)

MiðT; PÞ vi dv
X ! bi vi þ Fiself ;
Fi ¼ N 1 rjs;jþ1 þ rother (2)
j¼ 1

where mi is the effective dislocation segment mass density, Mi is the dislocation mobility determined by temperature T and pressure P, W is the total energy per unit length of a moving dislocation, vi is the dislocation velocity, and b is the Burgers vector. Fi is the Peach-Kohler force on a dislocation node i, which is governed by three components: the stress
from all dislocation loops and curves N 1 rs , the self-
force Fi self , and the term r other j¼1 j;jþ1
representing the combined
P

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where li, vgi, ni, V, and N are the dislocation segment length, the glide velocity, a unit normal to the slip plane, the volume of the representative volume element, and the total number of dislocation segments, respectively.
In the present work, the highly diffused nano-precipi-tates generated by WLSP are considered by mapping into the MDDD computational cells a spatial distribution of Frank sessile loops. These loops serve as internal stress sources that interact elastically with the nearby moving dislocation segments. This elastic interaction leads to a distortion in the strain field, resulting in a pinning behavior of the dislocation motion and a hardening behavior of the stress-strain curve.
In MDDD, the contributions of all of the Frank sessile loops are added up and substituted into the rother term in Eq. (2). A
closed form expression of the stress field of one such Frank sessile loop is shown as Eqs. (5) and (6). It is obtained by integrating the Peach-Koehler (PK) equation for the self stresses of any curved closed dislocation loop.29

effects of the internal lattice friction, external applied stresses, and stresses due to other crystal defects such as the stacking-fault tetrahedral and Frank sessile loops.
At the macro level, the macroscopic plastic strain rate ep and the plastic spin Wp are related to and determined by the motion of each dislocation segment:

023518-3 Liao et al.

ep ¼ XN livgi ðni bi þ bi niÞ; i¼1 2V

Wp ¼ XN livgi ð ni bi bi niÞ; i¼1 2V

J. Appl. Phys. 110, 023518 (2011)

C. LSP loading

The laser shock peening (LSP) model proposed by Fab-bro et al.32 is widely used to predict the shock pressure dur-ing LSP. It assumes that the shock propagation in the confining medium and the target could be simplified as a one-dimensional problem and that the laser irradiation is uni-form. This assumption is appropriate when the laser beam

(3) size is relatively large (millimeter scale). This model is fur-ther extended by Peyre et al.33 to analyze the plastically affected depth and superficial residual stresses.

(4) The relationship between the laser intensity I0 and the peak pressure P can be expressed as in Eq. (7):

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P ¼ 0:01 a Z I0 ; (7)
2a þ 3

where a is the efficiency of the interaction. Z is the combined shock impedance, defined as Z ¼ 2/(1/Z1 þ 1/Z2), where Z1 and Z2 are the shock impedance of the material and the con-fining media, respectively. It is found that the peak shock pressure is proportional to the square root of the laser inten-sity and could be solved numerically by giving initial values of the interaction efficiency (normally 0.2 to 0.5) and the laser intensity. Therefore, the effect of the laser intensity on the pinning effect could be considered during MDDD simu-lation by adjusting the applied strain rate in a reasonable range (105 to 107/s). It is worth mentioning that the shock pressure decay as a function of time and distance to the top surface are considered by MDDD codes, which makes MDDD more practical for simulating the LSP process.34

x D. Simulation setup and parameters
rxz ¼ C0 ½D1EðkÞ þ D2KðkÞ&;
In this work, AA6061 is utilized as an example for
q
rzz ¼ C0½D3EðkÞ þ D4KðkÞ&; MDDD simulation. The simulated aluminum matrix has a
face-centered-cubic single crystal structure in which the
rxy ¼ xy C D E k D K k C0 D E k D K k ; magnitude of the Burgers vector is 0.286 nm, the lattice pa-
f ½ 5 ð Þ þ 6 ð Þ& þ ½ 7 ð Þ þ 8 ð Þ&g
q2 rameter is 0.405 nm, and the computational cell size is
rxx ¼ C ½ D9EðkÞ þ D10KðkÞ& þ C0½D11EðkÞ þ D12KðkÞ&; 1600b*1600b*4000b in volume. In the simulations, several
Frank-Read dislocation sources 200b to 400b in length are
(5) initialized in the cells on {111} glide planes to provide an

where the coefficients D1 through D16, used to simplify the initial dislocation density on the order of 1012 m 2. The con-
tinuity of the dislocation curves and the conservation of dis-
stress expressions, are functions of spatial coordinates
location flux across the boundaries are ensured by applying
including the loop radius R, the cylindrical coordinates q and
the periodic boundary condition. The following material pa-
2 2 ) 1/2 . The
z, and the position vector of a field point r ¼ (q þ z 3
detailed expressions of D1 to D16 can be found in the litera- rameters of AA6061 are utilized: density q ¼ 2850 kg/m ,
ture. 25,30
K(k) and E(k) are the complete elliptic integrals of Poisson ratio v ¼ 0.33, dislocation mobility M ¼ 30000/pa s,
10
the first and second kind from the PK equation, and k is the Burgers vector b ¼ 2.86 10 m, shear modulus at room
modulus of these integrals. The parameters C, C0, a, b, and k temperature G RT ¼ 26.7 GPa, and shear modulus at 160 C
35,36

are defined as G160 C ¼ 26.1 GPa.
In order to simulate the WLSP process, the simulations
Gbz Gbz are designed to have uniaxial strain loading along the z
C ; C0 ; a r2 R2; b 2 R; direction with a high strain rate of 105 to 107/s. The four lat-
¼ p 1=2 ¼ 2pð1 vÞ ¼ þ ¼ q (6) eral sides of the cells are confined so as to move only in the
k ¼ 2b loading direction, and the bottom surface is rigidly fixed.
;
The time step in our simulations is 10 11 s, which is suitable
a þ b
for laser based experiments with a short laser pulse duration
where bz is the elastic constant and G and v are the shear time (nanoseconds) and an ultra-high strain rate. As men-
modulus and Poisson’s ratio, respectively.30,31 tioned before, Frank sessile loops serving as local barriers

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023518-4 Liao et al. J. Appl. Phys. 110, 023518 (2011)

for the dislocation motion are initially distributed into the cells. The radius R of these loops is set within an interval of 10b to 40b in order to match the size of nano-precipitates generated by WLSP, which is 3 to 12 nm in radius as observed by TEM. The pinning effects of nano-precipitates on the dislocation evolution and mechanical hardening are systematically studied by adjusting the number and radius of the Frank sessile loops.

III. RESULTS AND DISCUSSION

A. Effects of dislocation pinning on dislocation structures

1. Microstructures characterized by TEM after WLSP experiments

The TEM images in Fig. 1 present the microstructures in AA6061 and steel 4140 processed by WLSP. The process-ing temperatures for these two materials are 160 C and 250 C, respectively, which are the optimized temperatures for mechanical properties as reported in our previous study.1,3 The experiments are carried out with a laser intensity of 2 GW/cm2 for AA6061 and 4 GW/cm2 for steel 4140, which generate a shock wave with a peak pressure of around 3 to 4 GPa and a plastic strain rate of over 106/s (as calculated by Fabbro’s model32). As shown in Figs. 1(a) and 1(b), the highly dense spherical nano-precipitates with diameters of around 6 to 10 nm are generated after processing (pointed out by arrows). The nucleation taking place during WLSP can be explained by the dynamic precipitation effect due to the thermal energy supplied by the warm temperature and by the high strain rate plastic deformation provided by the laser

shock pressure. As the high strain rate plastic deformation occurs, the highly dense dislocations are generated. The dis-locations interact and tangle with each other to form disloca-tion cores, which are considered as the potential nucleation sites for precipitation. The warm processing temperature pro-vides sufficient thermal energy to assist the migration of sol-ute atoms (Mg and Si in aluminum alloy and carbon in steel) and the growth of precipitates. These precipitates could hinder dislocation motion via the pinning effect. In order to continue the plastic deformation, the generation of more new mobile dislocations is necessary. Consequently, the presence of nano-precipitates results in the formation of highly dense and uniformly distributed dislocations due to the particle– dislocation interaction [see Figs. 1(c) and 1(d)].

For comparison, the TEM images in Fig. 2 show micro-structures after LSP at room temperature. As shown in Fig. 2(a), very few precipitates are observed. This is benefi-cial for the formation of the pile-up of localized dislocations and lamellar dislocation boundaries. This dislocation pile-up is also called dislocation walls or slip bands (under certain slip planes) and results from the high strain rate plastic defor-mation.37–39 As observed in Figs. 2(b)–2(d), dislocation pile-ups with a high dislocation density are generated by room temperature LSP (pointed out by arrows). The regions with a relatively much lower dislocation density, known as the dis-location free zone, are also identified.

One can clearly deduce from Figs. 1 and 2 that the exis-tence of highly diffused spherical nano-precipitates domi-nates the arrangement of dislocation structures during shock wave propagation. As a dislocation moves, the nano-precipi-tates acting as obstacles interact elastically with the nearby

FIG. 1. (Color online) TEM images showing microstructures after WLSP: highly dense spherical nano-precipitates (pointed out by red arrows) are gen-erated in AA6061, and highly dense and uniformly distributed dislocations are entangled with nano-precipitates in (c) AA6061 and (d) steel 4140.

FIG. 2. (Color online) TEM images showing microstructures after LSP at room temperature. (a) Nano-precipitates are hardly observed in AA6061. Dislocation pile-ups (pointed out by red arrows) are formed in (b) AA6061 and (c),(d) steel 4140.

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023518-5 Liao et al. J. Appl. Phys. 110, 023518 (2011)

dislocations and hinder dislocation slips via the pinning effect. Without these obstacles, the dislocation motion is not resisted and takes the lowest energy consuming direction, which in turn causes the formation of dislocation pile-ups and a free zone. Therefore, WLSP creates uniformly distrib-uted dislocation structures with a high density due to the high nucleation rate during processing. The more detailed precipitate–dislocation interaction and the resulting disloca-tion structures will be addressed later based on MDDD simulation.

2. Effect of nano-precipitates on dislocation structures—MDDD simulation

Figure 3 shows the dislocation multiplication and propa-gation during WLSP as predicted by MDDD simulation. It is observed that the uniformly distributed dislocations are formed in the computational cells with highly dense nano-precipitates [Fig. 3(a)]. This predicted dislocation arrange-ment is similar to the arrangement of the microstructures af-ter WLSP observed in Figs. 1(c) and 1(d). As dislocations move, they encounter the second phase precipitates, which serve as local barriers to impede the dislocation motion due to the pinning effect. In order to propagate further, disloca-tions have to overcome and bypass these obstacles via the cross-slip mechanism, resulting in the formation of disloca-tion jog and dipole structures, which could change the slip planes and reduce the activation energy for cross-slip. The jog and dipole structures observed in the MDDD simulation are illustrated in Fig. 4(a). The dislocation jog can be described as two dislocation segments lying on two parallel slip planes with a distance of one or a few atomic distances and connected by another dislocation segment with a differ-ent orientation. When the jog is large enough, the two dislo-

FIG. 3. (Color online) The dislocation multiplication and propagations in DD cells (a) with highly dense and diffused nano-precipitates (Frank sessile loops are not visible in the figure) and (b) without nano-precipitates.

FIG. 4. (Color online) Schematic view of dislocation motion mechanisms:

(a) jog and dipole structures; (b) dislocation slip bands.

cation segments on the parallel planes grow independently; in contrast, if the distance between two parallel planes is suf-ficiently small, a dislocation dipole consisting of two parallel edge dislocations with opposite Burgers vectors is formed. However, in the computational cells with no or few nano-precipitates, it is much easier for dislocation slip bands to form than it is for jog and dipole structures because there are fewer local obstacles. As a consequence, the relatively inho-mogeneously distributed dislocation structures are formed as illustrated in Fig. 3(b), presenting as the dislocation slip bands with a higher density and the dislocation free zone with a lower density [see Fig. 4(b)]. This inhomogeneous dislocation arrangement is similar to that observed in Figs. 2(b)–2(d). Furthermore, as observed in Fig. 3, the propaga-tion and multiplication of dislocations in MDDD cells with highly dense obstacles are faster than those in MDDD cells with few obstacles. During shock wave propagation, the obstacles serve as local barriers to dislocation motion via the pinning effect. In order to continue the plastic deformation, the generation of new mobile dislocations is necessary, which induces the multiplication of dislocations for a high density.

Both the TEM study and the MDDD simulation confirm that uniformly distributed dislocations with a high volume density are generated after WLSP. The interaction between nanoscale precipitates and dislocation structures plays an im-portant role in the formation of this unique microstructure. This dislocation arrangement and nano-precipitate–disloca-tion interaction provide a great potential for enhancing me-tallic materials’ mechanical properties, such as increasing the surface strength, stabilizing residual stress, and prevent-ing crack initiation and propagation, thus enhancing the fa-tigue life and strength.1,3

B. Effects of nano-precipitates on dislocation pinning

As reported in our previous study,2 the precipitation dur-ing WLSP is strongly affected by the warm processing tem-perature and the applied laser intensity. The elevated temperature has a favorable influence on the nucleation rate by decreasing the chemical driving force of the precipitation; however, the higher dislocation density introduced by the stronger laser intensity could assist and accelerate the nuclea-tion growth due to the lower volume strain energy and the higher dislocation core energy. Therefore, the higher process-ing temperature and stronger laser power result in a greater volume density of nano-precipitates (103 to 104/lm3). Further-more, the size of the nano-precipitate is governed by the

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023518-6 Liao et al. J. Appl. Phys. 110, 023518 (2011)

FIG. 5. (Color online) The effects of processing temperature and laser power intensity on (a) surface hardness and (b) the FWHM of 2h.

processing (aging) time. For example, the spherical precipi-tates in AA6061 with a diameter of 10 nm are generated by dynamic precipitation with an aging time on the nanosecond level, whereas the rod-shaped precipitates 100 nm in length exist in the T6 condition sample due to the longer duration of static aging (8 h). In addition, a lower precipitate density is normally induced with the growth of the precipitate size, because the nucleation growth is mainly caused by the migra-tion of nearby nucleation atoms. Thus, it is worthwhile to fur-ther investigate the dislocation pinning effect affected by the density, size, and space distribution of nano-precipitates.

1. Effect of volume density of nano-precipitate

The surface hardnesses of AA6061 after LSP and WLSP with various processing temperatures and laser intensities are compared in Fig. 5(a). It can be seen that both the ele-vated temperature and the enhanced laser intensity could result in a greater surface hardness. For instance, with the same laser intensity of 1.6 GW/cm2, the surface hardness af-ter WLSP at 160 C is 40.4% higher than that after LSP, increased from 94 to 132 VHN (VHN denotes the Vickers hardness number); with the same WLSP temperature of 160 C, the surface hardness shows an 8% increase, from 125 to 135 VHN, when the laser intensity is increased from 0.8 to 2.4 GW/cm2. The same phenomenon in steel 4140 was reported in our previous study.3 Although both LSP and WLSP benefit from the strain hardening introduced by the plastic deformation, only WLSP can generate the highly dense nano-precipitates through dynamic precipitation. Therefore, this hardening effect is mainly caused by the dislocation pinning effect of nano-precipitates, and the hardening ratio

affected by the temperature and laser intensity can be explained as due to the fact that the higher temperature and stronger laser power can dramatically increase the volume density of nano-precipitates by providing more thermal energy and a greater number of nucleation sites for the pre-cipitation.2 In addition, the value of the FWHM of 2h as measured by XRD is used to compare the relative defect den-sity [see Fig. 5(b)]. It is found that both the elevated process-ing temperature and the enhanced laser intensity could cause a greater value of the FWHM, representing a higher defect density. The results agree with the surface hardness test and confirm that the enhanced pinning effect caused by a higher volume density of nano-precipitates is responsible for the temperature and laser intensity effects on the hardening ratio.

In order to verify the hardening effect caused by the pin-ning effect, MDDD simulation is carried out by initially inserting various volume densities of nano-precipitates into computational cells. The resulting stress/strain curves and the time evolutions of the dislocation density are shown in Fig. 6. It can be seen that the flow stress is enhanced by an increasing number of nano-precipitates [see Fig. 6(a)]. For instance, when the number of nano-precipitates is increased from 0 to 100, the yield stress at 0.2% strain is enhanced by 27.9% from 301 to 385 MPa. This demonstrates that the gen-eration of nano-precipitates has a great potential to harden metallic materials due to the dislocation pinning effect. The greater number of internal obstacles could induce a stronger pinning effect, resulting in a greater hardening behavior. Additionally, a relatively greater dislocation multiplication rate and a faster multiplication speed are observed in the MDDD cells with highly dense nano-precipitates [see Fig.

FIG. 6. (Color online) The effect of the volume density of nano-precipitates on

(a) the stress/strain curve and (b) dislo-cation multiplication.

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023518-7 Liao et al. J. Appl. Phys. 110, 023518 (2011)

FIG. 7. (Color online) Stress/strain curves from MDDD simulations show-ing (a) the size effect and (b) the space distribution effect of nano-precipitates on hardening.

6(b)]. As the shock wave propagates in the material, interac-tion between dislocations and precipitates takes place, lead-ing to the generation of dislocation loops surrounding obstacles through the Orowan mechanism. Thus, the increase of the dislocation multiplication with nano-precipitates can be attributed to the pinning effect as well. This confirms the hardening behavior during WLSP observed via the hardness test (Fig. 5) and stress/strain curves [Fig. 6(a)], because the plastic stress in solids is believed to occur as a result of the generation and transport of dislocations. In addition, the increase in dislocation multiplication by nano-precipitates agrees well with the dislocation morphologies observed via TEM (Fig. 1) and MDDD simulation (Fig. 3), which have a higher density and a uniformly distributed arrangement.

2. Effect of size and space distribution of nano-precipitate

In order to gain better sight into the dislocation pinning effect, the size and space distribution effects of nano-precipi-tates have been considered via MDDD simulation as shown in Fig. 7. The space distribution refers to how the particles distribute in the computational cells. With the same volume fraction of particles, a smaller size but greater density of par-ticles results in a denser space distribution, which also implies a shorter inter-particle distance. It can be seen that with the same density, the precipitates with a larger size could induce a stronger hardening behavior [Fig. 7(a)]. For example, the yield stress at 0.2% strain is increased by 15.7% from 362 to 419 MPa when the precipitate size is changed from 10b to 40b in radius. This size effect is mainly due to the stronger pinning effect of larger obstacles. The gliding dislocations shear through the smaller obstacles by the shearing-through mechanism and bypass the larger, unshearable obstacles. This bypassing mechanism requires a greater external stress and energy to bow out dislocation seg-ments and leave a dislocation loop surrounding obstacles af-ter crossing. In addition, it also can be found that with the same volume fraction of precipitates, the pinning effect on hardening is more significant in MDDD cells with precipi-tates having a smaller size but a greater density—the so-called space distribution effect. As illustrated in Fig. 7(b), with the same volume fraction (0.04%), the yield stress in the MDDD cell having 36 precipitates with a shorter radius (14b) is 17.1% higher than that in the cell having 12 precipi-

tates with a longer radius (20b). This is because the higher obstacle density provides more potential positions for the dislocation–obstacle interaction, and the contributions of all of these interactions add up to govern the dislocation motion. Consequently, stabilized dislocation structures with a uni-formly distributed arrangement could form, and this is re-sponsible for the hardening. This phenomenon has also been reported in the literature. For instance, to quantitatively investigate the size and space distribution effect, Nembach8 and Mohles7 analyze the critical resolved shear stress (CRSS) as a function of the precipitate size and volume frac-tion, where CRSS is defined as the minimum external applied stress needed to overcome the interaction force between dislocations and precipitates. This model illustrates that with the same volume fraction, the precipitates with a smaller size but a greater density require a greater value of CRSS. This agrees well with the MDDD simulation results as observed in Fig. 7. The pinning effect affect by the size and space distribution of nano-precipitates brings us another interesting research topic for future work based on WLSP experiments by manipulating the dynamic precipitation time.

IV. CONCLUSIONS

In this study, the dislocation pinning effects of highly dense and diffused nanoscale precipitates generated by WLSP have been investigated. The dislocation evolution affected by the pinning effect is characterized via TEM and compared with a MDDD simulation. The pinning effect on hardening is studied by means of the surface hardness test and the stress/strain curves predicted by MDDD. The effects of the volume density, size, and distribution of nano-precipi-tates on the pinning behavior are considered. The results indicate the following:

(1) the uniformly distributed dislocations with a high density are formed after WLSP due to the interaction between the gliding dislocations and the highly dense nano-precipitates;

(2) the processing temperature and the laser intensity of WLSP govern the volume density of nano-precipitates, and thus the pinning effect; and

(3) the dislocation pinning effect is influenced by the vol-ume density, size, and space distribution of nano-precipitates.

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023518-8 Liao et al.

ACKNOWLEDGMENTS

The authors appreciate the support from a NSF grant (CMMI 0900327) and the Office of Naval Research (ONR) through the Young Investigator Program.

1C. Ye, Y. L. Liao, and G. J. Cheng, Adv. Eng. Mater. 12(4), 291 (2010). 2Y. Liao, C. Ye, B. Kim, S. Suslov, E. A. Stach, and G. J. Cheng, J. Appl. Phys. 108, 063518 (2010).

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[lokijagida]

Мне отчего-то кажется, что здесь вы вряд ли найдете настолько радикальных альтруистов...

[Linch]

Нужно было подсчитать количество знаков и назвать тематику текста. Затем спросить, кто может перевести. Начать договариваться.
Не выставлять текст полностью. Вы заняли много места, сделали чтение неудобным. Людям, которые не менее заняты, чем Вы. Вы хотите, чтобы только Вам было удобно?
Вспоминается Володька Пряхин из фильма "Самая обаятельная и привлекательная". Вы из той же фамилии?
Вы думали что ли, что это машина переводит? Есть определённые нормы общения. Или нет определённых норм ? Для научных.

[Chuk]

Выслал свое предложение на Ваш e-mail.

[Linch]

Вы понимаете, что такое время. Что прежде, чем Вы найдёте переводчика, может уйти целый день? Вы понимаете, что такое время?

Я просто попытался открыть обратившемуся глаза на то, что такое Интернет и какое для него нужно время. Обратившийся может рассмотреть возможность пойти в бюро переводов своего города.

Тот, кто зарегистрирован как Linch, не берётся за научные переводы.

Чук, время!

[Linch]

Последнее моё сообщение было для спрашивавшего.