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Author: Hing-Shun Leung
Publisher:
ISBN: 9781361035603
Category :
Languages : en
Pages :
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Book Description
This dissertation, "Dislocation-density-function Dynamics Simulation for Crystal Plasticity: a Full-dynamics, All-dislocation Approach" by Hing-shun, Leung, 梁慶淳, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today''s computing power. Dislocation-density based approaches are a way forward but a critical issue to address is a realistic description of the interactions between dislocations. In this thesis, a new scheme for computational dynamics of dislocation-density functions is proposed, which takes full consideration of the mutual elastic interactions between dislocations based on the Hirth-Lothe formulation. Other features considered include (i) continuity nature of the movements of dislocation densities, (ii) forest hardening, (iii) generation according to high spatial gradients in dislocation densities, and (iv) annihilation. Numerical implementation by the finite-volume method, which is well suited for flow problems with high gradients, is discussed. Numerical examples performed for a single-crystal aluminium model show typical strength anisotropy behaviour comparable to experimental observations. Furthermore, this approach has been applied to three engineering problems and discussed in detail: (i) Application on small-scale crystal plasticity successfully captures a number of key experimental features, including power-law relation between strength and size, low dislocation storage and jerky deformation. (ii) Crystal softening and enhanced cell formation are predicted by applying oscillatory loads. The simulations reveal the main mechanism for subcell formation under oscillatory loadings to be the enhanced elimination of statistically stored dislocations by the oscillatory stress, leaving behind geometrically necessary dislocations with low Schmid factors which then form the subgrain walls. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings. (iii) Tensile deformation of tri-crystals with grain size ranging from 200 to 500 can be divided into three stages. The results indicate different controlling mechanisms of the flow stress at different stages of deformation and grain sizes. Changing the middle grain tilt angle with respect to the outer grains is found to affect the stress-strain relationship and the distribution of plastic strain in the three grains. A refined meso-scale scheme based on the full dynamics of dislocation-density functions is also proposed aiming to bridge across the meso scale. In this scheme, the evolution of the dislocation-density functions is derived from a coarse-graining procedure which clearly defines the relationship between the discrete-line and density representations of the dislocation microstructure. Full dynamics of the dislocation-density functions are considered based on an "all-dislocation" concept in which statistically stored dislocations are preserved and treated in the same way as geometrically necessary dislocations. Elastic interactions between dislocations are treated in accordance with Mura''s formula for eigen-stress. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity, and a special scheme is devised for this purpose. The model is applied to simulate a number of intensive microstructures involving discrete dislocation events, including loop expansion and shrinkage under applied and self-stress, dipole annihilation, and Orowan
Author: Hing-Shun Leung
Publisher:
ISBN: 9781361035603
Category :
Languages : en
Pages :
Get Book Here
Book Description
This dissertation, "Dislocation-density-function Dynamics Simulation for Crystal Plasticity: a Full-dynamics, All-dislocation Approach" by Hing-shun, Leung, 梁慶淳, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today''s computing power. Dislocation-density based approaches are a way forward but a critical issue to address is a realistic description of the interactions between dislocations. In this thesis, a new scheme for computational dynamics of dislocation-density functions is proposed, which takes full consideration of the mutual elastic interactions between dislocations based on the Hirth-Lothe formulation. Other features considered include (i) continuity nature of the movements of dislocation densities, (ii) forest hardening, (iii) generation according to high spatial gradients in dislocation densities, and (iv) annihilation. Numerical implementation by the finite-volume method, which is well suited for flow problems with high gradients, is discussed. Numerical examples performed for a single-crystal aluminium model show typical strength anisotropy behaviour comparable to experimental observations. Furthermore, this approach has been applied to three engineering problems and discussed in detail: (i) Application on small-scale crystal plasticity successfully captures a number of key experimental features, including power-law relation between strength and size, low dislocation storage and jerky deformation. (ii) Crystal softening and enhanced cell formation are predicted by applying oscillatory loads. The simulations reveal the main mechanism for subcell formation under oscillatory loadings to be the enhanced elimination of statistically stored dislocations by the oscillatory stress, leaving behind geometrically necessary dislocations with low Schmid factors which then form the subgrain walls. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings. (iii) Tensile deformation of tri-crystals with grain size ranging from 200 to 500 can be divided into three stages. The results indicate different controlling mechanisms of the flow stress at different stages of deformation and grain sizes. Changing the middle grain tilt angle with respect to the outer grains is found to affect the stress-strain relationship and the distribution of plastic strain in the three grains. A refined meso-scale scheme based on the full dynamics of dislocation-density functions is also proposed aiming to bridge across the meso scale. In this scheme, the evolution of the dislocation-density functions is derived from a coarse-graining procedure which clearly defines the relationship between the discrete-line and density representations of the dislocation microstructure. Full dynamics of the dislocation-density functions are considered based on an "all-dislocation" concept in which statistically stored dislocations are preserved and treated in the same way as geometrically necessary dislocations. Elastic interactions between dislocations are treated in accordance with Mura''s formula for eigen-stress. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity, and a special scheme is devised for this purpose. The model is applied to simulate a number of intensive microstructures involving discrete dislocation events, including loop expansion and shrinkage under applied and self-stress, dipole annihilation, and Orowan
Author: Hing-Shun Leung
Publisher: Open Dissertation Press
ISBN: 9781361035580
Category : Technology & Engineering
Languages : en
Pages : 198
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Book Description
This dissertation, "Dislocation-density-function Dynamics Simulation for Crystal Plasticity: a Full-dynamics, All-dislocation Approach" by Hing-shun, Leung, 梁慶淳, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today's computing power. Dislocation-density based approaches are a way forward but a critical issue to address is a realistic description of the interactions between dislocations. In this thesis, a new scheme for computational dynamics of dislocation-density functions is proposed, which takes full consideration of the mutual elastic interactions between dislocations based on the Hirth-Lothe formulation. Other features considered include (i) continuity nature of the movements of dislocation densities, (ii) forest hardening, (iii) generation according to high spatial gradients in dislocation densities, and (iv) annihilation. Numerical implementation by the finite-volume method, which is well suited for flow problems with high gradients, is discussed. Numerical examples performed for a single-crystal aluminium model show typical strength anisotropy behaviour comparable to experimental observations. Furthermore, this approach has been applied to three engineering problems and discussed in detail: (i) Application on small-scale crystal plasticity successfully captures a number of key experimental features, including power-law relation between strength and size, low dislocation storage and jerky deformation. (ii) Crystal softening and enhanced cell formation are predicted by applying oscillatory loads. The simulations reveal the main mechanism for subcell formation under oscillatory loadings to be the enhanced elimination of statistically stored dislocations by the oscillatory stress, leaving behind geometrically necessary dislocations with low Schmid factors which then form the subgrain walls. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings. (iii) Tensile deformation of tri-crystals with grain size ranging from 200 to 500 can be divided into three stages. The results indicate different controlling mechanisms of the flow stress at different stages of deformation and grain sizes. Changing the middle grain tilt angle with respect to the outer grains is found to affect the stress-strain relationship and the distribution of plastic strain in the three grains. A refined meso-scale scheme based on the full dynamics of dislocation-density functions is also proposed aiming to bridge across the meso scale. In this scheme, the evolution of the dislocation-density functions is derived from a coarse-graining procedure which clearly defines the relationship between the discrete-line and density representations of the dislocation microstructure. Full dynamics of the dislocation-density functions are considered based on an "all-dislocation" concept in which statistically stored dislocations are preserved and treated in the same way as geometrically necessary dislocations. Elastic interactions between dislocations are treated in accordance with Mura's formula for eigen-stress. Dislocation generation is considered as a consequence of dislocations to maintain their connectivity, and a special scheme is devised for this purpose. The model is applied to simulate a number of intensive microstructures involving discrete dislocation events, including loop expansion and shrinkage under applied and self-stress, dipole annihilation, and Orowan
Author: Franz Roters
Publisher: John Wiley & Sons
ISBN: 3527642099
Category : Technology & Engineering
Languages : en
Pages : 188
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Book Description
Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.
Author: Peter Gumbsch
Publisher: Springer Science & Business Media
ISBN: 3709102839
Category : Technology & Engineering
Languages : en
Pages : 401
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Book Description
The latest state of simulation techniques to model plasticity and fracture in crystalline materials on the nano- and microscale is presented. Discrete dislocation mechanics and the neighbouring fields molecular dynamics and crystal plasticity are central parts. The physical phenomena, the theoretical basics, their mathematical description and the simulation techniques are introduced and important problems from the formation of dislocation structures to fatigue and fracture from the nano- to microscale as well as it’s impact on the macro behaviour are considered.
Author: Shamseddin Akhondzadeh
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Most metals are crystalline materials that can undergo significant plastic (permanent) deformation when subjected to applied loading. Plastic deformation is usually accompanied by an increase in the flow stress of the material. This phenomenon is called strain hardening and is of vital importance in many engineering applications, including aerospace, automotive, and power generation industries. Developing accurate material models to predict the plastic response and hardening behavior of metals during deformation is a prerequisite to the engineering design processes, which requires a physical understanding of the underlying deformation mechanisms. In single crystals, plastic deformation of the crystal is governed by the evolution of dislocations--line defects inside the crystalline materials which marks the boundary between the slipped and unslipped regions--moving and interacting in response to the applied loading. Dislocation dynamics (DD) simulations, which track the time-space trajectories of individual dislocation lines, provide a promising tool to establish a physical link between the dislocation microstructure evolution and the strain hardening phenomenon. However, the high computational cost of DD simulations renders the accessible length and time scales to well below those which are relevant to most engineering applications. Due to this challenge, instead of directly using DD simulations for engineering applications, we have utilized DD simulations to delineate how constitutive relations of crystal plasticity (CP) can be constructed for FCC copper, based on coarse-graining of high-throughput DD simulations. This thesis consists of three main components, and we show how they fit together into a complete, physical model like three pieces of a puzzle. The first piece is a massive DD simulation database that we were able to generate thanks to recent computational advances in DD, including the subcycling time-integration algorithm and its implementation on Graphics Processing Units (GPUs). By systematically coarse-graining the database we present a strain hardening model which consists of two components: 1) a dislocation multiplication model, which accounts for slip-free multiplication, and 2) an exponential flow-rule connecting slip system shear rate to the resolved shear stress through an exponential function. These components can be thought of as the second and third puzzle pieces. By analyzing the data, it was discovered that dislocation multiplication frequently occurs on slip systems which experience zero applied shear stress (i.e., zero Schmid factor) and have a plastic strain rate of zero; we termed such multiplication slip-free multiplication and it serves as the second puzzle piece. This finding questions the assumption of the existing phenomenological expression that multiplication is proportional to the shear rate. We propose to add a correction term to the generalized Kocks-Mecking expression to account for slip-free multiplication, whose mechanistic explanation is provided. A major finding of this thesis is that DD results suggest an exponential flow-rule, in contrast to the commonly used power-law flow-rule, even in the cases where thermal fluctuations are not present. The exponential flow-rule is the third piece in the puzzle of the presented strain hardening model. We demonstrate that the observed exponential flow-rule, despite the common notion that thermal fluctuations are the responsible mechanism, can be explained by statistical properties of the dislocation links. Hence, by statistically analyzing the number density and plastic activity of links in terms of their length, we formulate a physically justified link length based flow rule which can numerically capture the exponential dependence of shear rate on shear stress. The proposed link length based flow-rule has two key components: 1) the number density of links on each slip system, which was observed to follow the sum of two exponentials distribution, and 2) an average velocity of links as a function of resolved shear stress and link length, whose fitting coefficients are independent of the loading orientation. The exponential dependence of on resolved shear stress is traced to the spatial fluctuation of the internal stress field, which can be approximated by a Laplace distribution. The proposed average velocity function incorporates the Laplace distribution in its form. This thesis shows that discrete dislocation dynamics simulations can be used to inform higher length scale models of non-phenomenological constitutive relations. The presented model captures the strain hardening as a result of slip system interactions in FCC single crystals. It works as an example for developing similar coarse-grained models based on DDD which includes additional strain hardening mechanisms such as cross-slip, or precipitate hardening. We hope that the present thesis motivates more researchers to use DDD simulations for constructing constitutive relations.
Author: Taira Suzuki
Publisher: Springer Science & Business Media
ISBN: 364275774X
Category : Science
Languages : en
Pages : 237
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Book Description
In the 1950s the direct observation of dislocations became possible, stimulat ing the interest of many research workers in the dynamics of dislocations. This led to major contributions to the understanding of the plasticity of various crys talline materials. During this time the study of metals and alloys of fcc and hcp structures developed remarkably. In particular, the discovery of the so-called in ertial effect caused by the electron and phonon frictional forces greatly influenced the quantitative understanding of the strength of these metallic materials. Statis tical studies of dislocations moving through random arrays of point obstacles played an important role in the above advances. These topics are described in Chaps. 2-4. Metals and alloys with bcc structure have large Peierls forces compared to those with fcc structure. The reasons for the delay in studying substances with bcc structure were mostly difficulties connected with the purification techniques and with microscopic studies of the dislocation core. In the 1970s, these difficulties were largely overcome by developments in experimental techniques and computer physics. Studies of dislocations in ionic and covalent bonding materials with large Peierls forces provided infonnation about the core structures of dislocations and their electronic interactions with charged particles. These are the main subjects in Chaps. 5-7.
Author: Eric Bayerschen
Publisher: KIT Scientific Publishing
ISBN: 3731506068
Category : Technology (General)
Languages : en
Pages : 278
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Book Description
In experiments on metallic microwires, size effects occur as a result of the interaction of dislocations with, e.g., grain boundaries. In continuum theories this behavior can be approximated using gradient plasticity. A numerically efficient geometrically linear gradient plasticity theory is developed considering the grain boundaries and implemented with finite elements. Simulations are performed for several metals in comparison to experiments and discrete dislocation dynamics simulations.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
Accurate simulation of the plastic deformation of ductile metals is important to the design of structures and components to performance and failure criteria. Many techniques exist that address the length scales relevant to deformation processes, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dislocations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focused at the global material response that use DD-generated information to enhance the fidelity of CP models. To ascertain to what degree the predictions of CP are consistent with those of DD, we compare their global and microstructural response in a number of deformation modes. After using nominally homogeneous compression and shear deformation dislocation dynamics simulations to calibrate crystal plasticity ow rule parameters, we compare not only the system-level stress-strain response of prismatic wires in torsion but also the resulting geometrically necessary dislocation density fields. To establish a connection between explicit description of dislocations and the continuum assumed with crystal plasticity simulations we ascertain the minimum length-scale at which meaningful dislocation density fields appear. Furthermore, our results show that, for the case of torsion, that the two material models can produce comparable spatial dislocation density distributions.
Author: Zhuo Zhuang
Publisher: Academic Press
ISBN: 0128145927
Category : Technology & Engineering
Languages : en
Pages : 450
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Book Description
Dislocation Based Crystal Plasticity: Theory and Computation at Micron and Submicron Scale provides a comprehensive introduction to the continuum and discreteness dislocation mechanism-based theories and computational methods of crystal plasticity at the micron and submicron scale. Sections cover the fundamental concept of conventional crystal plasticity theory at the macro-scale without size effect, strain gradient crystal plasticity theory based on Taylar law dislocation, mechanism at the mesoscale, phase-field theory of crystal plasticity, computation at the submicron scale, including single crystal plasticity theory, and the discrete-continuous model of crystal plasticity with three-dimensional discrete dislocation dynamics coupling finite element method (DDD-FEM). Three kinds of plastic deformation mechanisms for submicron pillars are systematically presented. Further sections discuss dislocation nucleation and starvation at high strain rate and temperature effect for dislocation annihilation mechanism. Covers dislocation mechanism-based crystal plasticity theory and computation at the micron and submicron scale Presents crystal plasticity theory without size effect Deals with the 3D discrete-continuous (3D DCM) theoretic and computational model of crystal plasticity with 3D discrete dislocation dynamics (3D DDD) coupling finite element method (FEM) Includes discrete dislocation mechanism-based theory and computation at the submicron scale with single arm source, coating micropillar, lower cyclic loading pillars, and dislocation starvation at the submicron scale
Author: Alan R. Rosenfield
Publisher:
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 808
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Book Description
