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Huajian Gao - One of the best experts on this subject based on the ideXlab platform.
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determination of the microscale stress Strain curve and Strain Gradient Effect from the micro bend of ultra thin beams
International Journal of Plasticity, 2008Co-Authors: Zhaofeng Shi, Bin Huang, Henry Tan, Yonggang Huang, Tongyi Zhang, K C Hwang, Huajian GaoAbstract:Abstract A simple method is established to determine the microscale uniaxial stress–Strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–Strain curve, together with the cantilever beam experiments, is used to determine the Strain Gradient Effect in Au thin beams. The Effect of finite rotation is also discussed.
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A conventional theory of mechanism-based Strain Gradient plasticity
International Journal of Plasticity, 2003Co-Authors: Yonggang Huang, Huajian GaoAbstract:Abstract There exist two frameworks of Strain Gradient plasticity theories to model size Effects observed at the micron and sub-micron scales in experiments. The first framework involves the higher-order stress and therefore requires extra boundary conditions, such as the theory of mechanism-based Strain Gradient (MSG) plasticity [J Mech Phys Solids 47 (1999) 1239; J Mech Phys Solids 48 (2000) 99; J Mater Res 15 (2000) 1786] established from the Taylor dislocation model. The other framework does not involve the higher-order stress, and the Strain Gradient Effect come into play via the incremental plastic moduli. A conventional theory of mechanism-based Strain Gradient plasticity is established in this paper. It is also based on the Taylor dislocation model, but it does not involve the higher-order stress and therefore falls into the second Strain Gradient plasticity framework that preserves the structure of conventional plasticity theories. The plastic Strain Gradient appears only in the constitutive model, and the equilibrium equations and boundary conditions are the same as the conventional continuum theories. It is shown that the difference between this theory and the higher-order MSG plasticity theory based on the same dislocation model is only significant within a thin boundary layer of the solid.
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the flow theory of mechanism based Strain Gradient plasticity
Mechanics of Materials, 2003Co-Authors: Xinming Qiu, Yueguang Wei, Yonggang Huang, Huajian Gao, Keh Chih HwangAbstract:The flow theory of mechanism-based Strain Gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to Strain Gradient Effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].
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Effect of intrinsic lattice resistance in Strain Gradient plasticity
Acta Materialia, 2001Co-Authors: Xinming Qiu, William D. Nix, Yonggang Huang, K C Hwang, Huajian GaoAbstract:The theory of mechanism-based Strain Gradient (MSG) plasticity is generalized in this paper in order to account for the Effect of intrinsic lattice resistance in the Taylor dislocation model. A multiscale, hierarchical framework is adopted to link the Strain Gradient plasticity theory on the mesoscale to the Taylor dislocation model on the microscale. It is established that the interaction between the Strain Gradient Effect and the friction stress (intrinsic lattice resistance) is weak. The hardness increase due to intrinsic lattice resistance is nearly independent of the Strain Gradient Effect. The linear relation between the square of micro-indentation hardness and reciprocal of indentation depth established by Nix and Gao has been extended to explain experimental data for bcc tungsten where the Effect of intrinsic lattice resistance plays a significant role.
J Li - One of the best experts on this subject based on the ideXlab platform.
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a micromechanics based Strain Gradient damage model for fracture prediction of brittle materials part ii damage modeling and numerical simulations
International Journal of Solids and Structures, 2011Co-Authors: J Li, T Pham, Radhi Abdelmoula, F Song, C P JiangAbstract:In this paper, we established a Strain-Gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the Strain-Gradient Effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the Strain-Gradient constitutive law established in the first part of this work (Li, 2011), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the Strain Gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size Effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications.
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a micromechanics based Strain Gradient damage model for fracture prediction of brittle materials part i homogenization methodology and constitutive relations
International Journal of Solids and Structures, 2011Co-Authors: J LiAbstract:Abstract In this paper, we first describe a homogenization methodology with the aim of establishing Strain Gradient constitutive relations for heterogeneous materials. The methodology presented in this work includes two main steps. The first one is the construction of the average Strain-energy density for a well-chosen RVE by using a homogenization technique. The second one is the transformation of the obtained average Strain-energy density to that for the continuum. An important characteristic of this method is its self-consistency with respect to the choice of the RVE: the Strain Gradient constitutive law built by using the present method is independent of the size and the form of the RVE. In the frame of this homogenization procedure, we have constructed a Strain Gradient constitutive relation for a two-dimensional elastic material with many microcracks by adopting the self-consistent scheme. It was shown that the Effective behavior of cracked solids depends not only on the crack density but also on the average crack size with which the Strain Gradient is associated. The proposed constitutive relation provides a starting point for the development of an evolution law of damage including Strain Gradient Effect, which will be presented in the second part of this work.
Yueguang Wei - One of the best experts on this subject based on the ideXlab platform.
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trans scale characterization of interface fracture in peel test for metal film ceramic substrate systems
Engineering Fracture Mechanics, 2019Co-Authors: Jingru Song, Yueguang WeiAbstract:Abstract In order to describe the interfacial fracture behaviors of the metal thin film with nano- or microscale thickness peeled on the ceramic substrate, a trans-scale mechanics model has been adopted. In the trans-scale mechanics model, both the Strain Gradient Effect and surface/interface Effect are considered. In addition, two fracture process models are used in present study, which are the cohesive zone model and the virtual internal bond model. Using the trans-scale mechanics theory and the interface models, the size Effect of the interfacial separation strength between the metal thin films and the ceramic substrates is analyzed systematically by using the peel test. The results show that the fracture process zone size could be taken as the indicator of the trans-scale interface fracture characterization. The interface Effect should be considered when the fracture process zone size is at the nanoscale, and the obtained interfacial separation strength is much higher than the conventional separation strength. The material length scale parameters of the metal films are determined by comparing the interfacial energy release rate predicted by the scale theories with the experimental results, which shows that the material length scale parameter could be regarded as the size of active plastic zone in the small scale yielding case during the peeling process.
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the flow theory of mechanism based Strain Gradient plasticity
Mechanics of Materials, 2003Co-Authors: Xinming Qiu, Yueguang Wei, Yonggang Huang, Huajian Gao, Keh Chih HwangAbstract:The flow theory of mechanism-based Strain Gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to Strain Gradient Effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].
Jianzhong Zhao - One of the best experts on this subject based on the ideXlab platform.
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a unified size dependent plate model based on nonlocal Strain Gradient theory including surface Effects
Applied Mathematical Modelling, 2019Co-Authors: Xingming Guo, Jianzhong ZhaoAbstract:Abstract Based on the nonlocal Strain Gradient theory and surface elasticity theory, a unified size-dependent plate model is developed for buckling analysis of rectangular nanoplates. The developed model is capable of capturing nonlocal Effect, Strain Gradient Effect as well as surface energy Effects simultaneously. Moreover, by selecting appropriate shape function, the present model can be reduced to not only Kirchhoff and Mindlin plate models but also various higher-order shear deformation plate models. The non-classical governing equations and associated boundary conditions are established by using the principle of minimum potential energy. Analytical solutions for critical buckling load of rectangular nanoplates under various boundary conditions are obtained. Verification of the proposed model is carried out by comparing the degenerated results with those reported in open literature. The Effects of nonlocal parameter, material length scale parameter, geometric parameters, shear deformation and surface energy on the buckling behavior of rectangular nanoplates under different boundary conditions are discussed in detail. The numerical results show that the critical buckling load evaluated by nonlocal Strain Gradient theory is lower than that predicted by classical continuum theory when the nonlocal parameter is larger than the material length scale parameter, and is higher than that evaluated by classical continuum theory when the nonlocal parameter is smaller than the material length scale parameter. However, when taking surface Effects into account, the critical buckling load is mainly affected by surface Effects at large length-to-thickness ratio, and depends on the combined Effects of nonlocality, Strain Gradient and surface energy at small length-to-thickness ratio.
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a unified nonlocal Strain Gradient model for nanobeams and the importance of higher order terms
International Journal of Engineering Science, 2017Co-Authors: Xingming Guo, Jianzhong ZhaoAbstract:Abstract In present paper, a unified size-dependent high-order beam model which contains various higher-order shear deformation beam models as well as Euler–Bernoulli and Timoshenko beam models is developed to study the simultaneous Effects of nonlocal stress and Strain Gradient on the bending and buckling behaviors of nanobeams by using the nonlocal Strain Gradient theory. For this objective, a nonlocal parameter is introduced to capture the nonlocal Effect and a material length scale parameter is involved to evaluate the Strain Gradient Effect. The governing equations and the associated boundary conditions are formulated by using Hamilton's principle. Navier's method is utilized to obtain the analytical solutions for bending and buckling of a simply supported nanobeam. The present model is validated by comparing the obtained results with those available in literature. The influences of nonlocal parameter, material length scale parameter, slenderness ratio and shear deformation on the bending and buckling behaviors of the nanobeam are examined in detail. Results reveal that within the framework of nonlocal Strain Gradient theory, results predicted by Timoshenko beam model and various higher-order beam models are almost same with some negligible differences. Moreover, it is found that the nanobeam could exhibit either stiffness-softening Effect or stiffness-hardening Effect, which depends on the relative magnitude of the nonlocal parameter and the material length scale parameter.
C P Jiang - One of the best experts on this subject based on the ideXlab platform.
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a micromechanics based Strain Gradient damage model for fracture prediction of brittle materials part ii damage modeling and numerical simulations
International Journal of Solids and Structures, 2011Co-Authors: J Li, T Pham, Radhi Abdelmoula, F Song, C P JiangAbstract:In this paper, we established a Strain-Gradient damage model based on microcrack analysis for brittle materials. In order to construct a damage-evolution law including the Strain-Gradient Effect, we proposed a resistance curve for microcrack growth before damage localization. By introducing this resistance curve into the Strain-Gradient constitutive law established in the first part of this work (Li, 2011), we obtained an energy potential that is capable to describe the evolution of damage during the loading. This damage model was furthermore implemented into a finite element code. By using this numerical tool, we carried out detailed numerical simulations on different specimens in order to assess the fracture process in brittle materials. The numerical results were compared with previous experimental results. From these studies, we can conclude that the Strain Gradient plays an important role in predicting fractures due to singular or non-singular stress concentrations and in assessing the size Effect observed in experimental studies. Moreover, the self-regularization characteristic of the present damage model makes the numerical simulations insensitive to finite-element meshing. We believe that it can be utilized in fracture predictions for brittle or quasi-brittle materials in engineering applications.