Prismatic Loops Research Articles

Comparative analysis of mechanical properties for mono and poly-crystalline copper under nanoindentation – Insights from molecular dynamics simulations

Crystallographic orientation and grain size for monocrystalline and polycrystalline materials respectively play a critical role in defining their mechanical behaviour under nanoindentation. To understand their effects on mechanical properties, molecular dynamics (MD) simulations help in revealing the underlying physical phenomena governing the nanoindentation behaviour. This paper attempts to comparatively analyse and study the effects of crystallographic orientations of monocrystalline copper {(100), (110) and (111)} and critical grain size of polycrystalline copper on the nanoindentation response using MD simulations. The results obtained for indentation load vs. depth curve, hardness, dislocations, and elastic recovery were analysed for comparison. Cu(111) exhibited an average hardness of 12.62 GPa, which is 18.27% more than that of Cupoly. The pile-ups of 8 Å size were observed in Cupoly; and this was higher than any of copper system studied here. The dislocation extraction algorithm (DXA) analysis revealed that the total dislocations in Cu(111) was 34.23% and 153.8% lower than that of Cu(110) and Cupoly, respectively. Cu(111) comprised of highest Stair-rod dislocation along with LC and Hirth locks. Furthermore, a prismatic loop comprised of sessile dislocations also appeared in Cu(111). The elastic depth recovery rate for Cu(100) was 52.75%, 41.60% and 40.66% higher than that of Cu(110), Cu(111) and Cupoly, respectively. This study revealed that the nanoindentation based mechanical performances of monocrystalline copper systems, specifically Cu(111) were superior to any other copper systems.

Punching of arbitrary face prismatic loops from hydrogen nanobubbles in copper

When a metal surface is exposed to prolonged irradiation with energetic H−, the ions are expected to penetrate into bulk and dissolve in the matrix. However, the irradiated surfaces exhibit dramatic morphological changes in the form of “blisters” covering the surface exposed to irradiation. Blistering is usually explained by accumulation of implanted gas in the bubbles near surface. However, the exact mechanism of continuous growth of a bubble after it reaches the measurable size is still not fully clear. Commonly such growth is related to prismatic loop punching, which is a short time scale process not easily accessible by experimental techniques. Even atomistic modelling of loop punching in FCC metals is somewhat cumbersome. Since the void surfaces in these metals yield easily through shear loops, these were debatably suggested to explain the plastic growth of a bubble in copper, without demonstrating the detachment of these loops from the void.We address the mechanisms of fast bubble growth in Cu which is associated with blistering of Cu surface exposed to H− irradiation. We observe the emission of a complete prismatic loop enclosed within the number of shear loops with the Burgers vectors aligned with the gliding direction of the prismatic loop. We show that the prismatic loops punched from the bubble surface do not need to be smaller than the bubble cross-section. These simulations capture the general trend of dislocation emission in the condition of hydrostatic pressure exerted by the accumulated gas on the wall of the bubble.

Orientation Dependent Mechanical Responses and Plastic Deformation Mechanisms of ZnSe Nano Films under Nanoindentation.

Although ZnSe has been widely studied due to its attractive electronic and optoelectronic properties, limited data on its plastic deformations are available. Through molecular dynamics simulations, we have investigated the indentations on the (001), (110), and (111) planes of ZnSe nano films. Our results indicate that the elastic modulus, incipient plasticity, elastic recovery ratio, and the structural evolutions during the indenting process of ZnSe nano films show obvious anisotropy. To analyze the correlation of structural evolution and mechanical responses, the atomic displacement vectors, atomic arrangements, and the dislocations of the indented samples are analyzed. Our simulations revealed that the plastic deformations of the indented ZnSe nano films are dominated by the nucleation and propagation of 1/2<110> type dislocations, and the symmetrically distributed prismatic loops emitted during the indenting process are closely related with the mechanical properties. By studying the evolutions of microstructures, the formation process of the dislocations, as well as the formation mechanisms of the emitted prismatic loops under the indented crystalline planes are discussed. The results presented in this work not only provide an answer for the questions about indentation responses of ZnSe nano films, but also offer insight into its plastic deformation mechanisms.

Dislocation Topological Evolution and Energy Analysis in Misfit Hardening of Spherical Precipitate by the Parametric Dislocation Dynamics Simulation.

Interaction of a single dislocation line and a misfit spherical precipitate has been simulated by the Parametric Dislocation Dynamics (PDD) method in this research. The internal stress inside the precipitate is deduced from Eshelby’s inclusion theory, the stress of the dislocation line and outside the precipitate is calculated by Green’s function. The influence of different relative heights of the primary slip plane on dislocation evolution is investigated, while the cross-slip mechanism and annihilation reaction are considered. The simulation results show three kinds of dislocation topological evolution: loop-forming (Orowan loop or prismatic loop), helix-forming, and gradual unpinning. The dislocation nodal force and the velocity vectors are visualized to study dislocation motion tendency. According to the stress–strain curve and the energy curves associated with the dislocation motion, the pinning stress level is strongly influenced by the topological change of dislocation as well as the relative heights of the primary slip plane.

Advanced method for structure-strength-ductility assessment of dispersion-strengthened FCC metals using activation work, mean slip distance and constitutive relation analyses: Decoding the Haasen plot

The role of cross-slip activation on controlling dislocation mechanisms and deformation debris creation in a dispersion-strengthened matrix (DSM) face-centred cubic metal, GlidCop®, has been elucidated using experimental measurement of the strain rate sensitivity, S, the mean slip distance, λ, and constitutive relation analyses (CRA) from 78 to 473 K. If the stress for cross-slip activation is larger than that of DSM yield stress, geometrically necessary prismatic loops (GNPL) are generated, but the rate controlling kinetics is that of vacancy-drag for cube-textured copper wire-specimens. With increasing temperature, percolation continues to occur by Orowan looping. However, upon yielding, GNPL formation is replaced by various types of dipole loop creation due to dislocation intersections from multiple slip. Loops that convert to stacking fault tetrahedra are measurable, but opposite sign dipoles are dynamically annihilated by pipe diffusion reducing debris retention. The rate controlling mechanisms are identified in the temperature range in which S is constant and the activation energy to overcome the obstacle becomes identical to the measurable activation work. This study shows that cross-slip activation stress determined by CRA, when superposed on the yield stress versus temperature plot of DSM alloys, can identify the mechanism-change temperatures. Subsequent S versus temperature profiles, determined from a new method of Haasen plot analysis of up- and down-strain-rate change tests, can delineate the prime rate-controlling mechanisms, characterize the stored debris and determine whether non-shearing or shearing of particles had occurred. Hence, an advanced method to characterize plastic behavior of DSM alloys has been developed.

Dissociated prismatic loop punching by bubble growth in FCC metals.

Materials performance can be significantly degraded due to bubble generation. In this work, the bubble growth process is elaborated in Cu by atomistic modeling to bridge the gap of experimental observations. Upon continuous He implantation, bubble growth is accommodated first by nucleation of dislocation network from bubble surface, then formation of dissociated prismatic dislocation loop (DPDL), and final DPDL emission in langle 110rangle directions. As the DPDL is found capable of collecting He atoms, this process is likely to assist the formation of self-organized bubble superlattice, which has been reported from experiments. Moreover, the pressurized bubble in solid state manifests the shape of an imperfect octahedron, built by Cu {111} surfaces, consistent with experiments. These atomistic details integrating experimental work fill the gap of mechanistic understanding of athermal bubble growth in Cu. Importantly, by associating with nanoindentation testings, DPDL punching by bubble growth arguably applies to various FCC (face-centered cubic) metals such as Au, Ag, Ni, and Al.

3D discrete dislocation dynamic investigations of persistent slip band formation in FCC metals under cyclical deformation

The formation of persistent slip bands (PSBs) at early stages of fatigue plays an important role in fatigue damage. In order to get a better understanding of the physics involved at the dislocation scale, 3D discrete dislocation dynamic simulations are set up in the case of an isolated surface grain of Cu cyclically loaded in single slip. Simulations reveal the complex transformation process of the dislocation microstructure from a homogeneous distribution into an organized microstructure made of slip bands mainly composed of dislocation dipoles and prismatic loops. These slip bands are the embryo of the PSBs observed for large number of cycles. The localization mechanism evidenced by the simulations is well explained from a stress field analysis which highlights the role of cross-slip. A saturation regime is reached after a few cycles during which dislocation microstructure, dislocation densities and height of extrusions/intrusions remain unchanged. Furthermore, the linear relationship between the volume fraction of slip bands and the imposed plastic strain amplitude is retrieved by the simulations and the stability of the slip bands is verified by decreasing the plastic strain amplitude after the saturation regime is reached. Finally, when compared to AISI 316L stainless steel, Cu shows a tendency to build more bands with relatively larger thicknesses which is attributed to the differences in the cross-slip probability.

Phase field model for self-climb of prismatic dislocation loops by vacancy pipe diffusion

In this paper, we present a phase field model for the self-climb motion of prismatic dislocation loops via vacancy pipe diffusion driven by elastic interactions. This conserved dynamics model is developed under the framework of the Cahn-Hilliard equation with incorporation of the climb force on dislocations, and is based on the dislocation self-climb velocity formulation established in Ref. (Niu et al., 2017). The phase field model has the advantage of being able to handle the topological and geometrical changes automatically during the simulations. Asymptotic analysis shows that the proposed phase field model gives the dislocation self-climb velocity accurately in the sharp interface limit. Numerical simulations of evolution, translation, coalescence and repelling of prismatic loops by self-climb show excellent agreement with discrete dislocation dynamics simulation results and the experimental observation.

Effect of Si content on the uniaxial tensile behavior of Mo-Si solid solution alloys

Recrystallized binary Mo-0.2 wt.% Si (Mo-0.68 at.% Si) and Mo-0.3 wt.% Si (Mo-1.0 at.% Si) alloys and a ternary Mo-0.75 wt.% Si-0.14 wt.% B (Mo-2.5 at.% Si-1.2 at.% B) alloy were tested in uniaxial tension as a function of temperature in vacuum and the results are compared to previous results on recrystallized commercial purity (CP) Mo and a binary Mo-0.1 wt.% Si (Mo-0.34 at.% Si) solid solution alloy. Yield strength increases with increasing Si content at all temperatures examined except at room temperature where the 0.1 wt.% Si alloy demonstrates softening; atomistic simulation confirms this behavior to be associated with Si segregation to the core and the associated ease of kink nucleation. Tensile ductility at room temperature rapidly deteriorates with increasing Si content in solid solution but in the Mo-0.3 wt.% Si solid solution alloy, tensile ductility of ~10% was measured at 300°C and thereafter, it increases rapidly at higher temperatures. Serrated flow occurs in the temperature range 600°C~800°C with the serration amplitude increasing with increasing Si content; atomistic simulation illustrates O trapping by Si in solid solution and subsequent de-trapping/release at higher temperatures that can account for the onset temperature delay of serrated flow in these Mo-Si solid solution alloys relative to commercial purity Mo. The serrated flow phenomenon is accompanied by significant work hardening; the presence of dislocation tangles, dipoles and prismatic loops in specimens fractured above ≥ 700°C accounts for the observed work hardening.

Plastic Deformation and Hardening Mechanisms of a Nano-twinned Cubic Boron Nitride Ceramic.

A very interesting experimental finding shows that a nano-twinned cubic boron nitride (NT-cBN) ceramic has size-dependent hardness. In order to reveal the hardening mechanism of NT-cBN, the plastic deformation mechanism of single-crystalline cubic boron nitride (SC-cBN) under nano-indentation is first studied, and then that of NT-cBN is further investigated using atomistic simulations with a parameter-modified Tersoff potential. It is found that the plastic deformation of SC-cBN under nano-indentation is mainly attributed to serial dislocation behaviors, such as the formation of dislocation embryos, shear loops, and prismatic loops. In comparison, for NT-cBN, the plastic behavior is much more complex, which is influenced by a dislocation blockage, absorption, dissociation, and re-nucleation due to the interaction between dislocations and twin boundaries (TBs). From the plastic deformation mechanism of NT-cBN, it is found that the size-dependent hardening behavior of NT-cBN is a competitive result between the hardening sources, including slip transfer, dislocation accumulation, and suppression of dislocation nucleation, and the softening sources, including TBs being destroyed, parallel slips of dislocations, and the formation of new sites for dislocation nucleation. The smaller the distance between the adjacent TBs, the more dominant the role of hardening sources is, resulting in the high size-dependent hardness of NT-cBN. The results in this paper should be helpful for the optimized design of high strength and toughness of nano-structured cBN ceramics.

Validation of Novel Geometrically Necessary Dislocations Calculation Model Using Nanoindentation of the Metal Matrix Nanocomposite

The present work aims to develop a geometrically necessary dislocations (GNDs) generation model to accommodate the mismatch of the coefficient of thermal expansion (CTE) and elastic modulus between the matrix and reinforcement. Interstitial prismatic loops have been punched in the spherical ceramic reinforced matrix. The developed model is verified using nanoindentation experimentation into the metal matrix nanocomposite (MMnC). The nanoreinforcements are in-situ developed into the Mg matrix. As per hypothesis, Taylor strengthening dominates the Orowan and Hall–Petch strengthening. The experimentally obtained yield strength is very close to the theoretically estimated one.

Formation of prismatic dislocation loops during unloading in nanoindentation

The formation of prismatic dislocation loops during nanoindentation of bcc iron is simulated with discrete dislocation plasticity. Interestingly, it is not the loading phase, but the unloading phase of the test which is found to be crucial for prismatic loop formation when indenting a (001) crystal surface. In this case, prismatic loops do not form during loading, but develop as the indenter is removed, in contrast to (111) indentation where prismatic loops are nucleated almost immediately upon loading.

Dissociated prismatic loop punching by bubble growth in Cu

Dissociated prismatic loop punching by bubble growth in Cu

Contact formation mechanism between squeezed crystalline solids

The mechanism was proposed and experimentally approved for the final stage of the high temperature contact formation after generation of closed pores in the contact plane. The mechanism is that the pores being healed by the dislocation-diffusion mechanism form assemblages of vacancy type prismatic dislocation loops which alternate with clusters of previously formed interstitial prismatic loops. Between the vacancy-type loops and interstitial ones the diffusion interaction is established resulting in recombination of defects with different signs, the contact formation, pore healing, and decreasing stress and dislocation density in the contact area.

The influence of hydrogen on plasticity in pure iron\u2014theory and experiment

Tensile stress relaxation is combined with transmission electron microscopy to reveal dramatic changes in dislocation structure and sub structure in pure α-Fe as a result of the effects of dissolved hydrogen. We find that hydrogen charged specimens after plastic deformation display a very characteristic pattern of trailing dipoles and prismatic loops which are absent in uncharged pure metal. We explain these observations by use of a new self consistent kinetic Monte Carlo model, which in fact was initially used to predict the now observed microstructure. The results of this combined theory and experimental study is to shed light on the fundamental mechanism of hydrogen enhanced localised plasticity.

An improved method to model dislocation self-climb

Dislocations can provide short circuit diffusion paths for atoms resulting in a dislocation climb motion referred to as self-climb. A variational principle is presented for the analysis of problems in which fast dislocation core diffusion is the dominant mechanism for material redistribution. The linear element based self-climb model, developed in our previous work [1] Liu, Cocks and Tarleton (2020 J. Mech. Phys. Solids 135 103783), is significantly accelerated here, by employing a new finite element discretisation method. The speed-up in computation enables us to use the self-climb model as an effective numerical technique to simulate emergent dislocation behaviour involving both self-climb and glide. The formation of prismatic loops from the break-up of different types of edge dislocation dipoles are investigated based on this new method. We demonstrate that edge dipoles sequentially pinch-off prismatic loops, rather than spontaneously breaking-up into a string of loops, to rapidly decrease the total dislocation energy.

Growth mechanism of subsurface hydrogen cavities in tungsten exposed to low-energy high-flux hydrogen plasma

Due to a lack of direct experimental results, the detailed mechanisms that govern the blistering behavior of tungsten (W) exposed to ITER-relevant condition in nuclear fusion remain unclear. The growth mechanism of hydrogen (H) blisters is one example. In this work, recrystallized W was exposed to H plasma at 50 eV, 1.5×1026m−2, and 573 K. Transmission electron microscopy (TEM) samples were prepared using plasma-focused ion beam (FIB) followed by flash-polishing to effectively remove surface damages induced by FIB. The TEM images revealed that the general blisters observed on the exposed surface are associated with underlying cavities. A considerable amount of dislocations were found in the vicinity of the cavities. Prismatic dislocation loop arrays were observed, including small size 'coffee-bean' prismatic loops and large size prismatic loops. Near the tip of surfaces cavities, evidences for the emission of shear loops were also found. Based on the experimental findings, a multi-stage growth mechanism of H cavities was proposed. The loop-punching mechanism is operative for both very small cavities and cavities with sizes larger than several hundreds of nanometers. Whereas at intermediate sizes, cavities grow by emitting shear loops from the cavity tip.

Effect of Tip Roundness on the Nanoindentation of Fe Crystals

Indentation tips are never atomically sharp, but rounded at their end. We use atomistic simulation to study the effect of tip roundness for the particular case of a cube-corner pyramidal indenter by comparing the results of a spherical, a sharp cube-corner, and a rounded cube-corner tip during indention into bcc Fe. We find that as soon as the tip has indented so deeply that the spherical geometry does not hold any longer, strong deviations between the dislocation plasticity behavior show up. The rounded cube-corner tip produces less dislocations and a smaller plastic zone than the spherical indenter, when indented to the same depth. The results are better comparable, however, when the same displaced volume is considered. Finally, the dislocation nucleation mode is affected by the geometry, changing from homogeneous to heterogeneous nucleation as the tip changes from rounded to sharp. The cube-corner tips are found to produce more twinning and delay the formation of prismatic loops. For a penetration depth beyond the radius of the rounded cube-corner tip, atomic sharp pyramidal tips produce similar quantitative (hardness, dislocation density) and qualitative (pileup, dislocation arrangement) results compared to its rounded counterpart. Our results will prove important for understanding the differences between spherical indenter tips, as they are often used in simulation, and pyramidal tips, as they are used in experiment.

Energy analysis of misfit hardening by parametric dislocation dynamics simulation

The interaction between dislocation and misfitting precipitate has been investigated by the parametric dislocation dynamics (PDD) based on Green's function method. The present research is aimed at quantitative analysis of the effect of the key parameters (geometry of precipitate, existence of cross-slip, radius of precipitate and dislocation source length) on the precipitation and dislocation hardening. Simulation results revealed that the dislocation bypassing process is varied depending on the geometry of the precipitate and slip plane, where dislocation is cutting through or leaving the Orowan loop and prismatic loop behind the precipitate. Furthermore, the cross-slip accompanied with the jog formation contributes to the dislocation strengthening because of self-energy of dislocation. The interaction energy analysis revealed that misfit hardening can be remarkably increased by the smaller radius of precipitate and also the smaller length of dislocation source. Hence simultaneous hardening by dislocation strengthening and misfit hardening is suggested by the present study.

Strain Recovery and Defect Characterization in Mg‐Implanted Homoepitaxial GaN on High‐Quality GaN Substrates

The evolution of defects due to high‐pressure annealing of magnesium ion‐implanted epitaxial GaN grown on high‐quality GaN substrates is investigated. Changes in the implant‐induced strain are quantified as a function of annealing temperature and time. After annealing at 1300 °C for 10 min, the implant‐induced strain is fully relieved and accompanied by the presence of extended defects such as basal plane stacking faults and prismatic loops. Approximately one‐third of the original implant‐induced strain remains after annealing at 700 °C, and 5% of the original strain remains at 1000 °C for 100 min. In all cases, nearly all of the recovered strain occurs within first few minutes of annealing. A prominent increase in the asymmetric (104) triple axis X‐ray rocking curve full width at 0.01 maximum (FW0.01M) is observed after annealing at 1300 °C for 10 min. After annealing at 1300 °C for 100 min, a subsequent decrease in FW0.01M is correlated with a reduction of the extended defect density from 4 × 108 to 3 × 107 cm−2, determined through transmission electron microscope (TEM) measurements. Further reduction in the density of the extended defects by optimizing annealing temperature and time is expected to improve the performance of GaN‐based vertical power devices.