Dislocation Pinning Effects Induced by Nano-Precipitates During Warm Laser Shock Peening: Dislocation Dynamic Simulation and Experiments" (2011)

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7-15-2011 Dislocation pinning effects induced by nano- precipitates during warm laser shock peening: Dislocation dynamic simulation and experiments Yiliang Liao Purdue University, [email protected]

Chang Ye Purdue University, [email protected]

Huang Gao Purdue University, [email protected]

Bong-Joong Kim Purdue University

Sergey Suslov Birck Nanotechnology Center, Purdue University, [email protected]

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Liao, Yiliang; Ye, Chang; Gao, Huang; Kim, Bong-Joong; Suslov, Sergey; Stach, Eric A.; and Cheng, Gary J., "Dislocation pinning effects induced by nano-precipitates during warm laser shock peening: Dislocation dynamic simulation and experiments" (2011). Birck and NCN Publications. Paper 975. http://dx.doi.org/10.1063/1.3609072

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Authors Yiliang Liao, Chang Ye, Huang Gao, Bong-Joong Kim, Sergey Suslov, Eric A. Stach, and Gary J. Cheng

This article is available at Purdue e-Pubs: http://docs.lib.purdue.edu/nanopub/975 Dislocation pinning effects induced by nano-precipitates during warm laser shock peening: Dislocation dynamic simulation and experiments Yiliang Liao, Chang Ye, Huang Gao, Bong-Joong Kim, Sergey Suslov et al.

Citation: J. Appl. Phys. 110, 023518 (2011); doi: 10.1063/1.3609072 View online: http://dx.doi.org/10.1063/1.3609072 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v110/i2 Published by the AIP Publishing LLC.

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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. VC 2011 American Institute of Physics. [doi:10.1063/1.3609072]

I. INTRODUCTION precipitates also attracts great interest and has been quantitatively studied using several proposed models.4–11 It is found Warm laser shock peening (WLSP) is an innovative that the strengthening effect greatly depends on the morphol- thermo-mechanical processing technique that has great poten- ogy and dispersion of precipitates. Nonetheless, none of this tial for improving the mechanical properties of metallic mate- research takes into account the ultra-highly diffused nano- rials, including surface hardening and fatigue life.1–3 One of scale precipitate cluster (5 nm to 10 nm in radius and 103 to the most promising characteristics of WLSP is that highly 104/lm3 in volume density) generated by DP, although most dense and uniformly distributed dislocation structures can be of them consider precipitates introduced by static aging with formed due to the interaction between gliding dislocation a much larger size and lower volume density. The disloca- structures and dense nanoscale precipitates generated during tion pinning effects and the resulting dislocation structures WLSP by dynamic precipitation (DP). The pinning effect of under extremely high strain rate processing (>106/s) have nano-precipitates on the dislocation motion provides the key been seldom studied experimentally. contribution to mechanical improvements such as enhancing To investigate the interaction of dislocation and precipi- surface hardness, stabilizing residual stress, and preventing tatation, not only transmission electron microscopy12–15 crack initiation, thus improving fatigue life and strength. (TEM) but also several simulation methods have been uti- Therefore, it is worthwhile to study the interaction of disloca- lized, such as molecular dynamic (MD) simulation,16–20 tion and nano-precipitates during the shock wave propagation Monte Carlo (MC) simulation,21,22 and dislocation dynamic and its effects on the dislocation evolution and mechanical (DD) simulation.9,23–25 Both MD and MC simulations are enhancement. usually restricted by the limited size (nanoscale) and the There have been lots of efforts at investigating the pin- short duration (picoseconds) due to the prohibitive computa- ning effects on dislocation evolution. It is generally accepted tional cost, whereas DD simulation can be applied for much that dislocation structures overcome obstacles with a small larger sizes (more than 10000b, with b being the Burgers characteristic radius and a low volume density via the shear- vector) and longer times (more than 100 ns). Therefore, DD ing mechanism, whereas the dislocation motion in the matrix simulation is more suitable for investigating the effects of containing unshearable obstacles is governed by the Orowan the highly diffused nanoscale precipitate cluster on disloca- process, which leaves the obstacles surrounded by pinned tion behaviors. Multiscale discrete dislocation dynamics dislocation loops. In addition, the strengthening effect of (MDDD), proposed by Zbib et al.,26,27 is one of the most advanced DD models, particularly for studying the dis- a)Author to whom correspondence should be addressed. Electronic mail: location evolution, dislocation/particle interaction, and parti- 28 [email protected]. cle strengthening. For instance, Yashiro et al. studied

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

Downloaded 23 Jul 2013 to 128.46.221.64. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions 023518-2 Liao et al. J. Appl. Phys. 110, 023518 (2011) dislocation behaviors at the matrix–precipitate interface by TABLE I. Experimental conditions of WLSP. proposing a back force model associated with the anti-phase boundary energy. Khraishi et al.23,25 reported a fundamental Laser wavelength 1064 nm Laser beam overlap 75% understanding of the particle strengthening in metal-matrix Sample thickness 2.38 mm composites with a particle size of around 1000b and the WLSP temperature for steel 4140 250 C hardening effect of a spatial distribution of defect clusters Laser beam diameter 2 mm with a radius of 2b to 10b. However, the dislocation evolu- Pulse duration 5 ns tion and strengthening effect predicted by these studies have WLSP temperature for AA6061 160 C 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 sample is then polished to a thickness of 30 microns. The dislocation structures after WLSP processing are character- final thinning is carried out via the H-Bar method using a ized using TEM and are compared with the results of focused ion beam (Nova-200). Before TEM observations, MDDD simulation. The strengthening effect due to the dislo- the samples are cleaned with acetone in order to get a better cation pinning is investigated by the hardness test after image quality. In addition, the FWHM value of the 2h angle WLSP experiments and stress/strain curves during the shock as measured via x-ray diffraction (Bruker D8-Discover loading by MDDD simulation. The effects of the density, XRD) is utilized to compare the relative defect density after size, and space distribution of nano-precipitates are studied. processing. Furthermore, the surface hardness after WLSP is measured by the micro-hardness tester with a 25 g load and a II. EXPERIMENT AND SIMULATION 10 s holding time. A. WLSP experiment and characterization The materials used in this study are AA6061 (with the B. Background on MDDD simulation theory following chemical compositions in wt.%: Mg-0.92, Si-0.76, The mechanical properties of metallic materials are gov- Fe-0.28, Cu-0.22, Ti-0.10, Cr-0.07, Zn-0.06, Mn-0.04, Be- erned by the dislocations’ collective motion and their inter- 0.003, V-0.01, and Al-balance) and AISI 4140 steel (with the actions among themselves and with other crystal defects. following chemical compositions in wt.%: C-0.41, Si-0.21, Based on the fundamental physics theories of dislocation Mn-0.83, P-0.025, S-0.027, Cr-0.91, Mo-0.18, and Fe-bal- motion and interaction, the multiscale discrete dislocation ance). Before laser shock peening, AA6061 samples are sol- dynamics model has been developed by Zbib and co- utionized at 550 C for 3 h and subsequently quenched in workers.26,27 MDDD merges two length scales: the nano- water, and AISI 4140 steel samples are austenitized for 20 micro scale for the plasticity, and the continuum scale for the min at 850 C and oil quenched down to room temperature. energy transport. This hybrid elasto-viscoplastic simulation This is done to isolate the microstructures generated by model couples DD with finite element analysis to predict WLSP. Aluminum foil with a uniform thickness of 30 both the microstructure evolution and macro-mechanical microns and BK7 glass with a high laser transmission coeffi- behaviors. cient are selected as the ablative coating material and the At the nano-micro level, the dislocation loops with arbi- confining media, respectively. The elevated warm tempera- trary shapes in DD are discretized into short segments ture in WLSP is manipulated by a hot plate placed below the (bounded by nodes j and j þ 1), and their dynamics are ruled sample fixture. The temperature is monitored with a digital by the local stress distribution arising from the interactions scientific thermometer. A Q-switched ND-YAG laser (Sure- within themselves and with other crystal defects, such as lite III from Continuum, Inc.), operating at a wavelength of point and cluster defects, microcracks, microvoids, etc. The 1064 nm with a pulse width (full width at half maximum velocity and motion of a dislocation node is traced by solv- [FWHM]) of 5 nss is used to deliver the pulsed laser. An op- ing a “Newtonian” equation consisting of an inertia term, a tical power meter (Newport, type 1916c) is used to measure drag term, and a driving force vector [Eqs. (1) and (2)]: the pulse laser energy. The laser beam diameter is calibrated using a photosensitive paper (Kodak Linagraph, type 1895). 1 1 dW miv_i þ vi ¼ Fi; mi ¼ ; (1) The laser power intensity I0 is adjusted by the Q-switched MiðT; PÞ vi dv delay time and is calculated as I ¼ 0:1E=½pðd=2Þ2t, where ! 0 XN1 E is the pulse laser energy, d is the laser beam diameter, and s other self Fi ¼ rj;jþ1 þ r bi vi þ Fi ; (2) t is the pulse width. The laser power intensity is one of the j¼1 most important laser parameters in this study, because it determines the peak pressure of the laser-induced plasma (as where mi is the effective dislocation segment mass density, discussed in Sec. II C). The experimental conditions are Mi is the dislocation mobility determined by temperature T shown in Table I. and pressure P, W is the total energy per unit length of a Transmission electron microscopes (FEI-Tecnai TEM moving dislocation, vi is the dislocation velocity, and b is the and FEI-Titan TEM operated at 200 kV and 300 kV, respec- Burgers vector. Fi is the Peach-Kohler force on a dislocation tively) are used to characterize the microstructures after node i, which is governed by three components:P the stress N1 s WLSP. To prepare the TEM sample, a thin layer of the sam- from all dislocation loops and curves j¼1 rj;jþ1, the self- self other ple surface after peening is sectioned by a diamond saw. The force Fi , and the term r representing the combined

Downloaded 23 Jul 2013 to 128.46.221.64. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jap.aip.org/about/rights_and_permissions 023518-3 Liao et al. J. Appl. Phys. 110, 023518 (2011) effects of the internal lattice friction, external applied C. LSP loading stresses, and stresses due to other crystal defects such as the The laser shock peening (LSP) model proposed by Fab- stacking-fault tetrahedral and Frank sessile loops. bro et al.32 is widely used to predict the shock pressure dur- At the macro level, the macroscopic plastic strain rate e_p ing LSP. It assumes that the shock propagation in the and the plastic spin Wp are related to and determined by the confining medium and the target could be simplified as a motion of each dislocation segment: one-dimensional problem and that the laser irradiation is uni- XN form. This assumption is appropriate when the laser beam p livgi e_ ¼ ðÞni bi þ bi ni ; (3) size is relatively large (millimeter scale). This model is fur- 2V 33 i¼1 ther extended by Peyre et al. to analyze the plastically XN affected depth and superficial residual stresses. p livgi W ¼ ðÞn b b n ; (4) The relationship between the laser intensity I0 and the 2V i i i i i¼1 peak pressure P can be expressed as in Eq. (7): rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where li, vgi, ni, V, and N are the dislocation segment length, a P ¼ 0:01 Z I ; (7) the glide velocity, a unit normal to the slip plane, the volume 2a þ 3 0 of the representative volume element, and the total number of dislocation segments, respectively. where a is the efficiency of the interaction. Z is the combined In the present work, the highly diffused nano-precipi- shock impedance, defined as Z ¼ 2/(1/Z1 þ 1/Z2), where Z1 tates generated by WLSP are considered by mapping into the and Z2 are the shock impedance of the material and the con- MDDD computational cells a spatial distribution of Frank fining media, respectively. It is found that the peak shock sessile loops. These loops serve as internal stress sources pressure is proportional to the square root of the laser inten- that interact elastically with the nearby moving dislocation sity and could be solved numerically by giving initial values segments. This elastic interaction leads to a distortion in the of the interaction efficiency (normally 0.2 to 0.5) and the strain field, resulting in a pinning behavior of the dislocation laser intensity. Therefore, the effect of the laser intensity on motion and a hardening behavior of the stress-strain curve. the pinning effect could be considered during MDDD simu- In MDDD, the contributions of all of the Frank sessile loops lation by adjusting the applied strain rate in a reasonable are added up and substituted into the rother term in Eq. (2).A range (105 to 107/s). It is worth mentioning that the shock closed form expression of the stress field of one such Frank pressure decay as a function of time and distance to the top sessile loop is shown as Eqs. (5) and (6). It is obtained by surface are considered by MDDD codes, which makes integrating the Peach-Koehler (PK) equation for the self MDDD more practical for simulating the LSP process.34 stresses of any curved closed dislocation loop.29 D. Simulation setup and parameters x r ¼ C0 ½D EðkÞþD KðkÞ ; xz q 1 2 In this work, AA6061 is utilized as an example for MDDD simulation. The simulated aluminum matrix has a r ¼ C0½D EðkÞþD KðkÞ ; zz 3 4 face-centered-cubic single crystal structure in which the xy 0 magnitude of the Burgers vector is 0.286 nm, the lattice pa- rxy ¼ fgCD½þ5EðkÞþD6KðkÞ C ½D7EðkÞþD8KðkÞ ; q2 rameter is 0.405 nm, and the computational cell size is 0 1600b*1600b*4000b in volume. In the simulations, several rxx ¼ CD½þ9EðkÞþD10KðkÞ C ½D11EðkÞþD12KðkÞ ; Frank-Read dislocation sources 200b to 400b in length are (5) initialized in the cells on {111} glide planes to provide an initial dislocation density on the order of 1012 m2. The con- where the coefficients D1 through D16, used to simplify the stress expressions, are functions of spatial coordinates tinuity of the dislocation curves and the conservation of dis- including the loop radius R, the cylindrical coordinates q and location flux across the boundaries are ensured by applying z, and the position vector of a field point r ¼ (q2 þ z2)1/2. The the periodic boundary condition. The following material parameters of AA6061 are utilized: density q ¼ 2850 kg/m3, detailed expressions of D1 to D16 can be found in the literature.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, Burgers vector b ¼ 2.86 1010 m, shear modulus at room the first and second kind from the PK equation, and k is the 0 temperature GRT ¼ 26.7 GPa, and shear modulus at 160 C modulus of these integrals. The parameters C, C , a, b, and k 35,36 are defined as G160 C ¼ 26.1 GPa. In order to simulate the WLSP process, the simulations are designed to have uniaxial strain loading along the z Gb Gb C ¼ z ; C0 ¼ z ; a ¼ r2 þR2; b ¼ 2qR; direction with a high strain rate of 105 to 107/s. The four lat- p 2pð1vÞ (6) eral sides of the cells are confined so as to move only in the 2b 1=2 loading direction, and the bottom surface is rigidly fixed. k ¼ ; 11 aþb The time step in our simulations is 10 s, which is suitable 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

FIG. 1. (Color online) TEM images showing microstructures after WLSP: FIG. 2. (Color online) TEM images showing microstructures after LSP at highly dense spherical nano-precipitates (pointed out by red arrows) are gen- room temperature. (a) Nano-precipitates are hardly observed in AA6061. erated in AA6061, and highly dense and uniformly distributed dislocations Dislocation pile-ups (pointed out by red arrows) are formed in (b) AA6061 are entangled with nano-precipitates in (c) AA6061 and (d) steel 4140. and (c),(d) steel 4140.

2. Effect of nano-precipitates on dislocation cation segments on the parallel planes grow independently; structures—MDDD simulation in contrast, if the distance between two parallel planes is suf- ﬁciently small, a dislocation dipole consisting of two parallel Figure 3 shows the dislocation multiplication and propa- edge dislocations with opposite Burgers vectors is formed. gation during WLSP as predicted by MDDD simulation. It is However, in the computational cells with no or few nano- observed that the uniformly distributed dislocations are precipitates, it is much easier for dislocation slip bands to formed in the computational cells with highly dense nano- form than it is for jog and dipole structures because there are precipitates [Fig. 3(a)]. This predicted dislocation arrange- fewer local obstacles. As a consequence, the relatively inho- ment is similar to the arrangement of the microstructures af- mogeneously distributed dislocation structures are formed as ter WLSP observed in Figs. 1(c) and 1(d). As dislocations illustrated in Fig. 3(b), presenting as the dislocation slip move, they encounter the second phase precipitates, which bands with a higher density and the dislocation free zone serve as local barriers to impede the dislocation motion due with a lower density [see Fig. 4(b)]. This inhomogeneous to the pinning effect. In order to propagate further, disloca- dislocation arrangement is similar to that observed in Figs. tions have to overcome and bypass these obstacles via the 2(b)–2(d). Furthermore, as observed in Fig. 3, the propaga- cross-slip mechanism, resulting in the formation of dislocation and multiplication of dislocations in MDDD cells with tion jog and dipole structures, which could change the slip highly dense obstacles are faster than those in MDDD cells planes and reduce the activation energy for cross-slip. The with few obstacles. During shock wave propagation, the jog and dipole structures observed in the MDDD simulation obstacles serve as local barriers to dislocation motion via the are illustrated in Fig. 4(a). The dislocation jog can be pinning effect. In order to continue the plastic deformation, described as two dislocation segments lying on two parallel the generation of new mobile dislocations is necessary, slip planes with a distance of one or a few atomic distances which induces the multiplication of dislocations for a high and connected by another dislocation segment with a differ- density. ent orientation. When the jog is large enough, the two dislo- 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 important role in the formation of this unique microstructure. This dislocation arrangement and nano-precipitate–dislocation interaction provide a great potential for enhancing metallic materials’ mechanical properties, such as increasing the surface strength, stabilizing residual stress, and preventing crack initiation and propagation, thus enhancing the fatigue life and strength.1,3

B. Effects of nano-precipitates on dislocation pinning As reported in our previous study,2 the precipitation during WLSP is strongly affected by the warm processing temperature 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 nucleation growth due to the lower volume strain energy and the higher dislocation core energy. Therefore, the higher processing temperature and stronger laser power result in a greater FIG. 3. (Color online) The dislocation multiplication and propagations in 3 4 3 DD cells (a) with highly dense and diffused nano-precipitates (Frank sessile volume density of nano-precipitates (10 to 10 /lm ). Further- loops are not visible in the ﬁgure) and (b) without nano-precipitates. more, the size of the nano-precipitate is governed by the

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- affected by the temperature and laser intensity can be tates in AA6061 with a diameter of 10 nm are generated by explained as due to the fact that the higher temperature and dynamic precipitation with an aging time on the nanosecond stronger laser power can dramatically increase the volume level, whereas the rod-shaped precipitates 100 nm in length density of nano-precipitates by providing more thermal exist in the T6 condition sample due to the longer duration of energy and a greater number of nucleation sites for the pre- static aging (8 h). In addition, a lower precipitate density is cipitation.2 In addition, the value of the FWHM of 2h as normally induced with the growth of the precipitate size, measured by XRD is used to compare the relative defect den- because the nucleation growth is mainly caused by the migra- sity [see Fig. 5(b)]. It is found that both the elevated process- tion of nearby nucleation atoms. Thus, it is worthwhile to fur- ing temperature and the enhanced laser intensity could cause ther investigate the dislocation pinning effect affected by the a greater value of the FWHM, representing a higher defect density, size, and space distribution of nano-precipitates. 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 1. Effect of volume density of nano-precipitate temperature and laser intensity effects on the hardening The surface hardnesses of AA6061 after LSP and WLSP ratio. with various processing temperatures and laser intensities In order to verify the hardening effect caused by the pin- are compared in Fig. 5(a). It can be seen that both the ele- ning effect, MDDD simulation is carried out by initially vated temperature and the enhanced laser intensity could inserting various volume densities of nano-precipitates into result in a greater surface hardness. For instance, with the computational cells. The resulting stress/strain curves and same laser intensity of 1.6 GW/cm2, the surface hardness af- the time evolutions of the dislocation density are shown in ter WLSP at 160 C is 40.4% higher than that after LSP, Fig. 6. It can be seen that the flow stress is enhanced by an increased from 94 to 132 VHN (VHN denotes the Vickers increasing number of nano-precipitates [see Fig. 6(a)]. For hardness number); with the same WLSP temperature of 160 C, instance, when the number of nano-precipitates is increased the surface hardness shows an 8% increase, from 125 to 135 from 0 to 100, the yield stress at 0.2% strain is enhanced by VHN, when the laser intensity is increased from 0.8 to 2.4 27.9% from 301 to 385 MPa. This demonstrates that the gen- GW/cm2. The same phenomenon in steel 4140 was reported eration of nano-precipitates has a great potential to harden in our previous study.3 Although both LSP and WLSP metallic materials due to the dislocation pinning effect. The benefit from the strain hardening introduced by the plastic greater number of internal obstacles could induce a stronger deformation, only WLSP can generate the highly dense pinning effect, resulting in a greater hardening behavior. nano-precipitates through dynamic precipitation. Therefore, Additionally, a relatively greater dislocation multiplication this hardening effect is mainly caused by the dislocation rate and a faster multiplication speed are observed in the pinning effect of nano-precipitates, and the hardening ratio 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) dislocation multiplication.

FIG. 7. (Color online) Stress/strain curves from MDDD simulations showing (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- tates with a longer radius (20b). This is because the higher tion between dislocations and precipitates takes place, lead- obstacle density provides more potential positions for the ing to the generation of dislocation loops surrounding dislocation–obstacle interaction, and the contributions of all obstacles through the Orowan mechanism. Thus, the increase of these interactions add up to govern the dislocation motion. of the dislocation multiplication with nano-precipitates can Consequently, stabilized dislocation structures with a uni- be attributed to the pinning effect as well. This confirms the formly distributed arrangement could form, and this is re- hardening behavior during WLSP observed via the hardness sponsible for the hardening. This phenomenon has also been test (Fig. 5) and stress/strain curves [Fig. 6(a)], because the reported in the literature. For instance, to quantitatively plastic stress in solids is believed to occur as a result of investigate the size and space distribution effect, Nembach8 the generation and transport of dislocations. In addition, the and Mohles7 analyze the critical resolved shear stress increase in dislocation multiplication by nano-precipitates (CRSS) as a function of the precipitate size and volume frac- agrees well with the dislocation morphologies observed via tion, where CRSS is defined as the minimum external TEM (Fig. 1) and MDDD simulation (Fig. 3), which have a applied stress needed to overcome the interaction force higher density and a uniformly distributed arrangement. between dislocations and precipitates. This model illustrates that with the same volume fraction, the precipitates with a 2. Effect of size and space distribution of nano- smaller size but a greater density require a greater value of precipitate CRSS. This agrees well with the MDDD simulation results In order to gain better sight into the dislocation pinning as observed in Fig. 7. The pinning effect affect by the size effect, the size and space distribution effects of nano-precipi- and space distribution of nano-precipitates brings us another tates have been considered via MDDD simulation as shown interesting research topic for future work based on WLSP in Fig. 7. The space distribution refers to how the particles experiments by manipulating the dynamic precipitation time. distribute in the computational cells. With the same volume fraction of particles, a smaller size but greater density of par- IV. CONCLUSIONS ticles results in a denser space distribution, which also In this study, the dislocation pinning effects of highly implies a shorter inter-particle distance. It can be seen that dense and diffused nanoscale precipitates generated by with the same density, the precipitates with a larger size WLSP have been investigated. The dislocation evolution could induce a stronger hardening behavior [Fig. 7(a)]. For affected by the pinning effect is characterized via TEM and example, the yield stress at 0.2% strain is increased by compared with a MDDD simulation. The pinning effect on 15.7% from 362 to 419 MPa when the precipitate size is hardening is studied by means of the surface hardness test changed from 10b to 40b in radius. This size effect is mainly and the stress/strain curves predicted by MDDD. The effects due to the stronger pinning effect of larger obstacles. The of the volume density, size, and distribution of nano-precipi- gliding dislocations shear through the smaller obstacles by tates on the pinning behavior are considered. The results the shearing-through mechanism and bypass the larger, indicate the following: unshearable obstacles. This bypassing mechanism requires a greater external stress and energy to bow out dislocation seg- (1) the uniformly distributed dislocations with a high density ments and leave a dislocation loop surrounding obstacles af- are formed after WLSP due to the interaction between ter crossing. In addition, it also can be found that with the the gliding dislocations and the highly dense nano- same volume fraction of precipitates, the pinning effect on precipitates; hardening is more significant in MDDD cells with precipi- (2) the processing temperature and the laser intensity of tates having a smaller size but a greater density—the so- WLSP govern the volume density of nano-precipitates, called space distribution effect. As illustrated in Fig. 7(b), and thus the pinning effect; and with the same volume fraction (0.04%), the yield stress in (3) the dislocation pinning effect is influenced by the vol- the MDDD cell having 36 precipitates with a shorter radius ume density, size, and space distribution of nano- (14b) is 17.1% higher than that in the cell having 12 precipi- precipitates.

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