Geometrically Necessary Dislocation Density Research Articles

Crystal plasticity finite element simulation of NiTi shape memory alloy under canning compression based on constitutive model containing dislocation density

Crystal plasticity finite element (CPFE) simulation is employed for revealing plastic deformation mechanism of NiTi shape memory alloy (SMA) under canning compression at 400 °C, where only B2 austenite phase exists and it presents plastic deformation by dislocation slip without stress-induced martensite phase transformation and deformation twinning. Statistically stored dislocation (SSD) and geometrically necessary dislocation (GND) densities are incorporated into crystal plasticity constitutive model for strain gradient. Texture evolution, stress and strain fields, SSD and GND densities are obtained on the basis of CPFE simulation. With progression of plastic deformation, γ-fiber (<111>) texture is gradually strengthened, which is further validated by the experimental data. Heterogeneous plastic deformation of NiTi polycrystalline cylinder model subjected to canning compression is illustrated by distribution of stress and strain based on all the slip systems, where stress concentration mainly emerges near the grain boundaries and large strain appears in the core location of NiTi polycrystalline cylinder. SSD density and GND density exhibit a heterogeneous distribution in the similar manner. Both SSDs and GNDs aggregate near the grain boundaries. SSD density increases with increasing plastic strain, whereas GND density decreases with increasing plastic strain. In addition, the total dislocation density increases with the increase of plastic strain. The developed CPFE model is an effective tool for simulating plastic deformation of NiTi SMA in the appropriate temperature range where dislocation slip is responsible for plastic deformation and work hardening is dominant during plastic deformation.

A non-local methodology for geometrically necessary dislocations and application to crack tips

A non-local method for the establishment of geometrically necessary dislocation (GND) based on a non-local domain integral has been developed and incorporated into crystal plasticity finite element (CPFE) formulations. The proposed non-local GND method has been validated through a four-point bending case, where the mesh sensitivity of the traditional GND method has been substantially diminished by virtue of the applied non-local domain integral. A comprehensive parametric study has been conducted to investigate the non-local domain effect on the GND calculation. The application of the non-local GND method has resembled the experimental observation of the GND density distribution near a crack tip, and improved the stress field compared to the local method. The improvement on the accuracy of predicting a microstructural driving force at crack tips reveals the necessity of applying the non-local GND method in predicting material fatigue life.

In Situ TEM Observation of Cooperative Grain Rotations and the Bauschinger Effect in Nanocrystalline Palladium.

We report on cooperative grain rotation accompanied by a strong Bauschinger effect in nanocrystalline (nc) palladium thin film. A thin film of nc Pd was subjected to cyclic loading–unloading using in situ TEM nanomechanics, and the evolving microstructural characteristics were investigated with ADF-STEM imaging and quantitative ACOM-STEM analysis. ADF-STEM imaging revealed a partially reversible rotation of nanosized grains with a strong out-of-plane component during cyclic loading–unloading experiments. Sets of neighboring grains were shown to rotate cooperatively, one after the other, with increasing/decreasing strain. ACOM-STEM in conjunction with these experiments provided information on the crystallographic orientation of the rotating grains at different strain levels. Local Nye tensor analysis showed significantly different geometrically necessary dislocation (GND) density evolution within grains in close proximity, confirming a locally heterogeneous deformation response. The GND density analysis revealed the formation of dislocation pile-ups at grain boundaries (GBs), indicating the generation of back stresses during unloading. A statistical analysis of the orientation changes of individual grains showed the rotation of most grains without global texture development, which fits to both dislocation- and GB sliding-based mechanisms. Overall, our quantitative in situ experimental approach explores the roles of these different deformation mechanisms operating in nanocrystalline metals during cyclic loading.

Experimental and numerical analysis on bulge forming process of GH4738 thick-walled ring

Ring rolling technology is widely used in the production of GH4738 aerospace rings, but the ring produced by ring rolling often has the phenomenon of uneven stress and unqualified strength. To solve these problems, the thick-walled ring bulge forming technology was proposed. In this paper, a 3D-coupled thermo-mechanical FE model of the GH4738 rectangular ring bulging process was developed, which is verified to be in good agreement with the experimental process. Based on this model, the thermal parameter distribution and evolution of GH4738 rectangular ring during the bulging process were investigated systematically. Then, the evolution of the minimum bulging displacement (BD) required for rings with the change of ring size was obtained by comparing the stress distribution of rings during the bulging process in seven cases. All these provide a theoretical basis for the selection of optimal BD in practical production. Finally, the influence of the bulging process on the microstructure and mechanical properties of GH4738 alloy ring was analyzed by experimental means, and it was verified that the bulging process can play a good role in improving the strength of the ring from the perspective of the average geometrically necessary dislocation (GND) density. The experimental results indicate that with the increase of BD, the grain size of the ring does not change that much, but the average GND density increases gradually, and the yield strength and tensile strength of the ring increase significantly.

Effects of precipitate on the slip activity and plastic heterogeneity of Mg-11Y-5Gd-2Zn-0.5Zr (wt. %) during room temperature compression

To understand the effects of precipitate on the deformation mechanisms and plastic heterogeneity of a cast Mg–11Y-5Gd-2Zn-0.5Zr (wt.%) alloy, quantitative comparison studies were performed on the solid solution (T4) and peak-aged (T6) samples during room temperature compression based on slip trace analysis and electron backscatter diffraction (EBSD) analysis. At 10% plastic strain: no twins were observed in both T4 and T6 samples; the dominant slip mode transitioned from 2 nd order pyramidal <c+a> slip (34.1%) to basal <a> slip (50.5%) after the T6 treatment, which indicated that the precipitate-hardening effect for pyramidal slip was stronger than that for basal slip. Substantial active slip systems (up to 40%) exhibited low normalized Schmid factors (<0.1), implying that local stress deviated from the globally applied stress. Compared to the T4 sample, a larger magnitude of geometrically necessary dislocation (GND) density was found in the T6 sample, which indicated that the precipitates enhanced the plastic heterogeneity in terms of GND density. Most of the high GND density areas were near grain boundaries (GBs), but they also appeared in grain interiors. Almost every near-GB area with larger GND density tended to follow the conditions: (1) large orientation discrepancy between neighborhood grains; (2) at least one grain exhibiting slip traces; (3) the GB with the X phase. The GBs where slip transfer occurs tended to exhibit a homogeneous GND density distribution.

Evolution of geometrically necessary dislocation at the γ-γ′ interface and its effect on tensile deformation behaviour of disk super alloy

Abstract The evolution of geometrically necessary dislocation density (GND) at the γ and primary γ′ interface during tensile deformation of turbine disk alloy was studied. Extensive electron microscopy analysis (i.e. EBSD and TEM) was carried out to explore the structure and GND evolution at the γ-γ′ interfaces. It is found that GND value is highest for tensile test specimens at 800 °C, whereas the lowest for tensile specimen tested at 350 °C, and this is attributed to γ/γ′ misfit (δ) value. At high-temperature tensile deformation (i.e. at 720 and 800 °C) specimen starts necking just after the yield point, compared to RT, 350 and 650 °C tensile tested specimens. It is evidenced from GND values and grain interior distortion that localized plastic deformation in γ-matrix near to γ-γ′ interfaces is the primary reason for necking just after yielding of material. Higher GND values and grain interior distortion are caused by the greater value of δ at high test temperature due to difference in thermal expansion between γ and γ′.

Indentation size effect, geometrically necessary dislocations and pile-up effects in hardness testing of irradiated nickel

The indentation size effect response, based on dislocation density, of commercially pure Ni irradiated at 120°C with 6MeV protons to 0.1dpa, was compared with non-irradiated Ni. Irradiation-induced defects were characterised by TEM. Nano-scale and micro-scale indentation tests were carried out. The Nix-Gao (NG) model was applied to determine the increase in the bulk yield strength arising from irradiation induced defects, which agreed well with the predicted increase in yield strength from the Bacon-Kocks-Scattergood (BKS) obstacle hardening model, using a superposition of SFT, glissile perfect loops and sessile Frank loops. A bi-linear trend was observed in the NG model in both the non-irradiated and irradiated material, indicating a transition in deformation mechanisms for indents in the ‘nano-scale’ regime. The extent of the bi-linear trend was minimized if indentation pile-up was measured and accounted for. It is shown that, in this material, care must be taken when interpreting measurements of the increase in hardness due to irradiation induced defects when measurements are made from depths shallower than ̴500nm. It is experimentally shown using both strain gradient plasticity modelling and independent SEM/EBSD analysis that there is a higher density of geometrically necessary dislocations (GNDs) present in the deformation volume under an indent in the irradiated material when compared to the analogous indent in the non-irradiated material; this results from a more confined plastic deformation volume under the indent in the irradiated material. It is proposed that sessile Frank loops inhibit plastic deformation by acting as obstacles to dislocation motion which results in deformation under the indenter tip being more localised. The result is a larger difference in hardness between the irradiated and non-irradiated material when measured using nanoindentation compared to bulk hardness testing. The increase in GND density in nanoindentation of irradiated material can be accounted for by correcting for indentation pile-up.

Revealing the hardening mechanisms of ion-irradiated nanostructured multilayers/substrate systems: A theoretical model

In this work, a mechanistic model is proposed for modeling the depth-dependent hardness of ion-irradiated nanostructured multilayers/substrate systems. Four dominant hardening mechanisms during the whole nanoindentation process are systematically analyzed, which include the indentation size effect (ISE) induced by geometrically necessary dislocations (GNDs), irradiation hardening determined by irradiation-induced defects, substrate effect and interface hardening existing within the multilayers. Thereinto, the former three are determined by the average density of dislocations and defects within the plasticity affected region (PAR), and are noticed to be affected by both the indentation depth and existing interface between the film and substrate layer. By considering the interface effect on both the geometrical shape and expansion ability of the PAR, the hardness-depth relation of ion-irradiated nanostructured multilayers/substrate systems is explicitly deduced at four different stages. Based on this model, the evolution of related microstructures in the film and substrate can be quantitatively analyzed, which involves the PAR, and average density of irradiation-induced defects and GNDs. The rationality and accuracy of the proposed model are validated by comparing the theoretical results with the experimental data, including two types of unirradiated systems (the YSZ/Al2O3 multilayers/Si substrate and W/Si system) and an ion-irradiated YSZ/Al2O3 multilayers/Si substrate system. The proposed model offers a promising way to qualitatively analyze other mechanical properties of ion-irradiated nanostructured multilayers/substrate systems.

Mechanisms Controlling Ductility Loss from Abrupt Strain Path Changes in a Low Carbon Steel

The effect of Strain Path Changes (SPCs) on the mechanical properties and crystal-level features of deformation for a single phase, ferritic steel has been investigated. SPCs were applied via a two-step deformation process, which included pre-straining via cold rolling, followed by uniaxial tension. The pre-strain magnitude and direction, as well as the tensile direction, varied between the specimens. The role of texture and micromechanics were examined in-situ, via Synchrotron X-Ray Diffraction (SXRD), and ex-situ, via Electron Backscatter Diffraction (EBSD). Abrupt strain paths (i.e. strain paths where the pre-strain and the subsequent loading directions differ; here they are orthogonal) result in a significant ductility reduction, becoming more prevalent for high pre-strain magnitudes. The macroscopic response, as well as the texture configuration were greatly dependent on the pre-strain direction but were insensitive to the direction of uniaxial tension. Increasing pre-strain magnitudes resulted in a stagnation of lattice strain hardening rates in all macroscopic directions and in a significant increase in the Geometrically Necessary Dislocation (GND) densities. This was vastly increased for specimens rolled perpendicular to the as-received prior rolling direction. No correlation was found between the GND density and the grain orientation, eliminating this as a controlling ductility factor for BCC ferrite. Instead, the initial texture, the texture developed in a subsequent pre-strain influences the density of dislocations accumulated in all grains, and ultimately determines ductility.

Nonlinear ultrasonic technique for the characterization of microstructure in additive materials.

This study employs nonlinear ultrasonic techniques to track microstructural changes in additively manufactured metals. The second harmonic generation technique based on the transmission of Rayleigh surface waves is used to measure the acoustic nonlinearity parameter, β. Stainless steel specimens are made through three procedures: traditional wrought manufacturing, laser-powder bed fusion, and laser engineered net shaping. The β parameter is measured through successive steps of an annealing heat treatment intended to decrease dislocation density. Dislocation density is known to be sensitive to manufacturing variables. In agreement with fundamental material models for the dislocation-acoustic nonlinearity relationship in the second harmonic generation, β drops in each specimen throughout the heat treatment before recrystallization. Geometrically necessary dislocations (GNDs) are measured from electron back-scatter diffraction as a quantitative indicator of dislocations; average GND density and β are found to have a statistical correlation coefficient of 0.852 showing the sensitivity of β to dislocations in additively manufactured metals. Moreover, β shows an excellent correlation with hardness, which is a measure of the macroscopic effect of dislocations.

Investigation of the evolution of Geometrically Necessary Dislocation (GND) tensor in a type 316 steel by using in-situ EBSD technique

This paper reports the evolution of GND tensor in 316 austenitic steel at the plastic stage. A significant increase of five GND tensors can be observed. The variations of average values of both positive and negative GND tensors were very symmetric. The largest rise of GND tensor happened at the early plastic stage, while the biggest increase of zero-value point occurred at the later. This result indicates that the rapid accumulation of GND density is a precursor to the defects formation or other material degradation behaviors. Thus, the GND tensors can also be utilized for the degradation analysis of 316 steel.

Revealing relationships between microstructure and hardening nature of additively manufactured 316L stainless steel

Relationships between microstructures and hardening nature of laser powder bed fused (L-PBF) 316 L stainless steel have been studied. Using integrated experimental efforts and calculations, the evolution of microstructure entities such as dislocation density, organization, cellular structure and recrystallization behaviors were characterized as a function of heat treatments. Furthermore, the evolution of dislocation-type, namely the geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs), and their impacts on the hardness variation during annealing treatments for L-PBF alloy were experimentally investigated. The GND and SSD densities were statistically measured utilizing the Hough-based EBSD method and Taylor's hardening model. With the progress of recovery, the GNDs migrate from cellular walls to more energetically-favourable regions, resulting in the higher concentration of GNDs along subgrain boundaries. The SSD density decreases faster than the GND density during heat treatments, because the SSD density is more sensitive to the release of thermal distortions formed in printing. In all annealing conditions, the dislocations contribute to more than 50% of the hardness, and over 85.8% of the total dislocations are GNDs, while changes of other strengthening mechanism contributions are negligible, which draws a conclusion that the hardness of the present L-PBF alloy is governed predominantly by GNDs.

Ductility and plasticity of ferritic-pearlitic steel after severe plastic deformation

A ferritic-pearlitic steel was subjected to severe plastic deformation (SPD) through Equal Channel Angular Pressing (ECAP) at room temperature, obtaining strengths greater than 1 GPa. Steel constituents were identified by light microscopy displaying similar grain sizes around 14 μm for the pearlite, and 13 μm and 18 μm for the ferrite before and after heat treatment, respectively. Texture changed from a rolling type to a simple shear texture with higher intensity after 4 ECAP passes. After different severe plastic deformation magnitudes, an ultra-fine grain structure was obtained with grain sizes between 0.9 μm-0.36 μm. The substantial grain size reduction was related to heterogeneous Geometrically Necessary Dislocations (GNDs) distribution in the as-received material with pearlite showing higher GNDs densities than ferrite. The remarkable strength increase after ECAP processing was found to be dependent on both small grain sizes and high dislocation densities. On the other hand, the low ductility of the ultrafine-grained (UFG) material was associated with a high annihilation rate of mobile dislocations at deformations greater than 0.39. Additionally, excellent plasticity properties were associated with a high density of immobile dislocations as well as high GND densities inside the deformed grains.

Selective laser melting of high-strength, low-modulus Ti–35Nb–7Zr–5Ta alloy

The state-of-the-art alloys for load-bearing implant applications lack the necessary functional attributes and are largely a compromise between biocompatibility and mechanical properties. While commercial alloys pose long-term toxicity and detrimental stress shielding effects, the newly developed alloys are closing in on the gaps, however, falling short of the desired elastic modulus necessary to rule out stress shielding. In this work, we report the fabrication of a low modulus β-Ti alloy, Ti–35Nb–7Zr–5Ta (TNZT), by selective laser melting (SLM) with optimized laser parameters. The as-prepared SLM TNZT shows a high ultimate tensile strength (~630 MPa), excellent ductility (~15%) and a lower elastic modulus (~81 GPa) when compared to the state-of-the-art cp-Ti and Ti-based alloys. The mechanical performance of the as-printed TNZT alloy has been examined and is correlated to the microstructure (grain structure, phase constitution and dislocation density). It is proposed that a high density of GND (geometrically necessary dislocations), resulting from rapid cooling, in the as-prepared condition strengthens the alloy, whereas the single phase β-bcc crystal structure results in lowering the elastic modulus. High grain boundary area and a preferred crystal orientation of {200} planes within the bcc crystal lattices contribute to an additional drop in the elastic modulus of the alloy. It is shown that the TNZT alloy, processed by SLM, demonstrates the best combination of strength and modulus, illustrating its potential as a promising biomaterial of the future.

A predictive strain-gradient model with no undetermined constants or length scales

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

Influence of microstructural heterogeneity and plastic strain on geometrically necessary dislocation structure evolution in single-phase and two-phase alloys

Deformation of single phase and two phase materials can be heterogeneous depending on the grain size distribution, orientation of the grains, amount and arrangement of the second phase and phase transformation during plastic deformation and twins. The deformation heterogeneity requires generation of geometrically necessary dislocations (GND) to maintain contact of the deforming grains and phases. Depending on the amount and character of deformation at the microscopic length scale, the evolution of the GND density changes. The present paper discusses the buildup of the GND density in different microstructural configurations using, single phase ferritic interstitial free (IF) steel, dual phase (DP) steel containing ferrite and martensite and austenitic stainless steel prone to deformation induced martensitic transformation and twining and whether GND density can be used as a descriptor of the deformation characteristics of the materials. The estimation of GND content using electron backscatter diffraction (EBSD) is recognized. The application potential of the present study is in understanding the in-grain deformation behavior of single phase IF steel, two phase DP steel, transformation induced plasticity assisted austenitic stainless steel to assess the forming of the steels for automobile applications. It should also facilitate the validation of strain gradient plasticity dependent damage model.

Effect of an improved pin design on weld formability and mechanical properties of adjustable-gap bobbin-tool friction stir welded Al-Cu aluminum alloy joints

An improved tool was designed to enhance weld formation for adjustable-gap bobbin-tool friction stir welding. No macro defects are observed as the welding speed increases from 120 to 240 mm/min. Microstructure analysis shows the maximum density of geometrically-necessary dislocations reaches 2.52 ×1013m-2 presenting at the stir zone (SZ). The Guinier-Preston-Bagaryatsky zones in heat affected zone (HAZ) and SZ are partially dissolved, and the relative volume fraction of S and θ phases in SZ is larger than that in HAZ. The hardness of the joints exhibits a W-shaped distribution. The minimum hardness is obtained at the HAZ. As the welding speed increases, the tensile strength initially increases up to 400 MPa at 180 mm/min, and then decreases. Poor mechanical properties at 60 mm/min and 300 mm/min are related to void defect.

Effects of temperature and load on fretting fatigue induced geometrically necessary dislocation distribution in titanium alloy

The effects of temperature and load on fretting fatigue induced geometrically necessary dislocation (GND) distribution in titanium alloy are studied by electron back-scattered diffraction (EBSD) in this paper. Fretting fatigue experiments under different temperature and load in TC11 titanium alloy are carried out and samples with small cracks are obtained. With Hough-based EBSD, the misorientation and GND densities induced by fretting fatigue are analyzed in both crack formation zone and crack tip. The results show that in the crack formation zone and crack tip, both temperature and load have obvious effects on the GND densities. With the increase of temperature and load, the GND densities rise significantly, which agrees with the decreasing tendency of fretting fatigue lives. The peak positions of GND density agree well with the crack formation locations, indicating the close relation between GND concentration and fretting fatigue crack formation. The relationship between GND density and distance from the crack path is studied. The results of individual GND densities on each slip system show that ‘Pyramidal<c+a>' and ‘Screw<a>' dislocations compose a majority of total GND density.

Deformation mechanism of bimodal microstructure in Ti-6Al-4V alloy: The effects of intercritical annealing temperature and constituent hardness

The so-called bimodal microstructure of Ti-6Al-4V alloy, composed of primary α grains (αp) and transformed β areas (βtrans), can be regarded as a “dual-phase” structure to some extent, the mechanical properties of which are closely related to the sizes, volume fractions, distributions as well as nano-hardness of the two constituents. In this study, the volume fractions of primary α grains (vol.%(αp)) were systematically modified in three series of bimodal microstructures with fixed primary α grain sizes (0.8 μm, 2.4 μm and 5.0 μm), by changing the intercritical annealing temperature (Tint). By evaluating the tensile properties at room temperature, it was found that with increasing Tint (decreasing vol.%(αp)), the yield strength of bimodal microstructures monotonically increased, while the uniform elongation firstly increased with Tint until 910 °C and then drastically decreased afterwards, thereby dividing the Tint into two regions, namely region I (830−910 °C) and region II (910−970 °C). The detailed deformation behaviors within the two regions were studied and compared, from the perspectives of strain distribution analysis, slip system analysis as well as dislocation analysis. For bimodal microstructures in region I, due to the much lower nano-hardness of βtrans than αp, there was a clear strain partitioning between the two constituents as well as a strain gradient from the αp/βtrans interface to the grain interior of αp. This activated a large number of geometrically necessary dislocations (GNDs) near the interface, mostly with <c+a> components, which contributed greatly to the extraordinary work-hardening abilities of bimodal microstructures in region I. With increasing Tint, the αp/βtrans interface length density gradually increased and so was the density of GNDs with <c+a> components, which explained the continuous increase of uniform elongation with Tint in this region. For bimodal microstructures in region II, where the nano-hardness of βtrans and αp were comparable, neither a clear strain-partitioning tendency nor a strain gradient across the αp/βtrans interface was observed. Consequently, only statistically stored dislocations (SSDs) with <a> component were activated inside αp. The absence of <c+a> dislocations together with a decreased volume fraction of αp resulted into a dramatic loss of uniform elongation for bimodal microstructures in region II.

3D HR-EBSD Characterization of the plastic zone around crack tips in tungsten single crystals at the micron scale

High angular resolution electron backscatter diffraction (HR-EBSD) was coupled with focused ion beam (FIB) slicing to characterize the shape of the plastic zone in terms of geometrically necessary dislocations (GNDs) in W single crystal in 3 dimensions. Cantilevers of similar size with a notch were fabricated by FIB and were deformed inside a scanning electron microscope at different temperatures (21 ∘C, 100 ∘C and 200 ∘C) just above the micro-scale brittle-to-ductile transition (BDT). J-integral testing was performed to analyse crack growth and determine the fracture toughness. At all three temperatures the plastic zone was found to be larger close to the free surface than inside the specimen, similar to macro-scale tension tests. However, at higher temperature, the 3D shape of the plastic zone changes from being localized in front of the crack tip to a butterfly-like distribution, shielding more efficiently the crack tip and inhibiting crack propagation. A comparison was made between two identically deformed samples, which were FIB-sliced from two different directions, to evaluate the reliability of the GND density estimation by HR-EBSD. The analysis of the distribution of the Nye tensor components was used to differentiate between the types of GNDs nucleated in the sample. The role of different types of dislocations in the plastic zone is discussed and we confirm earlier findings that the micro-scale BDT of W is mainly controlled by the nucleation of screw dislocations in front of the crack tip.