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Yonggang Huang - One of the best experts on this subject based on the ideXlab platform.
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A dislocation density based Strain Gradient model
International Journal of Plasticity, 2006Co-Authors: Steffen Brinckmann, Thomas Siegmund, Yonggang HuangAbstract:Abstract Strain Gradients play a vital role in the prediction of size-effects in the deformation behavior of metals at the micrometer scale. At this scale the behavior of metals strongly depends on the dislocation distribution. In this paper, a dislocation density based Strain Gradient model is developed aiming at predictions of size-effects for structural components at this scale. For this model, the characteristic length is identified as the average distance of dislocation motion, which is deformation dependant and can be determined experimentally. The response of the model is compared to the Strain Gradient plasticity model of Huang et al. [Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., 2004. A conventional theory of mechanism-based Strain Gradient plasticity. Int. J. Plasticity 20, 753–782]. It is shown that the present Strain Gradient model, which only requires a physically measurable length-scale, can successfully predict size effects for a bar with an applied body force and for void growth.
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mechanism based Strain Gradient crystal plasticity i theory
Journal of The Mechanics and Physics of Solids, 2005Co-Authors: Yonggang HuangAbstract:Abstract We have been developing the theory of mechanism-based Strain Gradient plasticity (MSG) to model size-dependent plastic deformation at micron and submicron length scales. The core idea has been to incorporate the concept of geometrically necessary dislocations into the continuum plastic constitutive laws via the Taylor hardening relation. Here we extend this effort to develop a mechanism-based Strain Gradient theory of crystal plasticity. In this theory, an effective density of geometrically necessary dislocations for a specific slip plane is introduced via a continuum analog of the Peach–Koehler force in dislocation theory and is incorporated into the plastic constitutive laws via the Taylor relation.
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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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A study of microbend test by Strain Gradient plasticity
International Journal of Plasticity, 2003Co-Authors: W. Wang, Yonggang Huang, K.j. Hsia, A. ChandraAbstract:Abstract Metallic materials display strong size effect when the characteristic length associated with plastic deformation is on the order of microns. This size effect cannot be explained by classical plasticity theories since their constitutive relations do not have an intrinsic material length. Strain Gradient plasticity has been developed to extend continuum plasticity to the micron or submicron regime. One major issue in Strain Gradient plasticity is the determination of the intrinsic material length that scales with Strain Gradients, and several microbend test specimens have been designed for this purpose. We have studied different microbend test specimens using the theory of Strain Gradient plasticity. The pure bending specimen, cantilever beam, and the microbend test specimen developed by Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale Acta Mater. 46, 5109–5115) are found suitable for the determination of intrinsic material length in Strain Gradient plasticity. However, the double cantilever beam (both ends clamped) is unsuitable since its deformation is dominated by axial stretching. The Strain Gradient effects significantly increase the bending stiffness of a microbend test specimen. The deflection of a 10-μm thick beam is only a few percent of that estimated by classical plasticity.
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The Strain Gradient effect in microelectromechanical systems (MEMS)
Journal of Microelectromechanical Systems, 2002Co-Authors: Zhenyu Xue, M T A Saif, Yonggang HuangAbstract:Metallic materials display strong size effect when the characteristic length of deformation is of the order of microns. The theory of mechanism-based Strain Gradient (MSG) plasticity established from the Taylor dislocation model has captured this size dependence of material behavior at the micron scale very well. The Strain Gradient effect in microelectromechanical systems (MEMS) is investigated in this paper via the MSG plasticity theory since the typical size of MEMS is of the order of microns (comparable to the internal material length in MSG plasticity). Through an example of a digital micromirror device (DMD), it is shown that the Strain Gradient effect significantly increases the mechanical Strain energy in the DMD, and reduces the rotation time of the micromirror. However, the Strain Gradient has no effect on the critical bias voltage governing the fast rotation of the micromirror.
J W Hutchinson - One of the best experts on this subject based on the ideXlab platform.
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Strain Gradient plasticity under non proportional loading
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2014Co-Authors: N A Fleck, J W Hutchinson, J R WillisAbstract:A critical examination is made of two classes of Strain Gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quant...
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On lower order Strain Gradient plasticity theories
European Journal of Mechanics - A Solids, 2003Co-Authors: Christian Frithiof Niordson, J W HutchinsonAbstract:By way of numerical examples, this paper explores the nature of solutions to a class of Strain Gradient plasticity theories that employ conventional stresses, equilibrium equations and boundary conditions. Strain Gradients come into play in these modified conventional theories only to alter the tangent moduli governing increments of stress and Strain. It is shown that the modification is far from benign from a mathematical standpoint, changing the qualitative character of solutions and leading to a new type of localization that is at odds with what is expected from a Strain Gradient theory. The findings raise questions about the physical acceptability of this class of Strain Gradient theories.
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Mechanism-based Strain Gradient plasticity—II. Analysis
Journal of the Mechanics and Physics of Solids, 2000Co-Authors: Yonggang Huang, Huajian Gao, William D. Nix, J W HutchinsonAbstract:Abstract A mechanism-based theory of Strain Gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic Strain and Strain Gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on Strain Gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based Strain Gradient plasticity, and kinematic relations among Strains, Strain Gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic Strain Gradients. In bending of thin beams and torsion of thin wires, mechanism-based Strain Gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to Strain Gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that Strain Gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.
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mechanism based Strain Gradient plasticity ii analysis
Journal of The Mechanics and Physics of Solids, 2000Co-Authors: Yonggang Huang, Huajian Gao, W D Nix, J W HutchinsonAbstract:Abstract A mechanism-based theory of Strain Gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic Strain and Strain Gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on Strain Gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based Strain Gradient plasticity, and kinematic relations among Strains, Strain Gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic Strain Gradients. In bending of thin beams and torsion of thin wires, mechanism-based Strain Gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to Strain Gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that Strain Gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.
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mechanism based Strain Gradient plasticity i theory
Journal of The Mechanics and Physics of Solids, 1999Co-Authors: Yonggang Huang, J W HutchinsonAbstract:Abstract A mechanism-based theory of Strain Gradient plasticity (MSG) is proposed based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic Strain and Strain Gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on Strain Gradient. While such linear dependence is predicted by the Taylor hardening model relating the flow stress to dislocation density, existing theories of Strain Gradient plasticity have failed to explain such behavior. We believe that a mesoscale theory of plasticity should not only be based on stress–Strain behavior obtained from macroscopic mechanical tests, but should also draw information from micromechanical, Gradient-dominant tests such as micro-indentation or nano-indentation. According to this viewpoint, we explore an alternative formulation of Strain Gradient plasticity in which the Taylor model is adopted as a founding principle. We distinguish the microscale at which dislocation interaction is considered from the mesoscale at which the plasticity theory is formulated. On the microscale, we assume that higher order stresses do not exist, that the square of flow stress increases linearly with the density of geometrically necessary dislocations, strictly following the Taylor model, and that the plastic flow retains the associative structure of conventional plasticity. On the mesoscale, the constitutive equations are constructed by averaging microscale plasticity laws over a representative cell. An expression for the effective Strain Gradient is obtained by considering models of geometrically necessary dislocations associated with bending, torsion and 2-D axisymmetric void growth. The new theory differs from all existing phenomenological theories in its mechanism-based guiding principles, although the mathematical structure is quite similar to the theory proposed by Fleck and Hutchinson. A detailed analysis of the new theory is presented in Part II of this paper.
Huajian Gao - One of the best experts on this subject based on the ideXlab platform.
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Mechanism-based Strain Gradient crystal plasticity—II. Analysis
Journal of the Mechanics and Physics of Solids, 2005Co-Authors: Chung-souk Han, Huajian Gao, William D. NixAbstract:Abstract In part I of this series (Mechanism-based Strain Gradient crystal plasticity—I. Theory. J. Mech. Phys. Sol. (2005), accepted for publication), we have proposed a theory of mechanism-based Strain Gradient crystal plasticity (MSG-CP) to model the effect of inherent anisotropy of a crystal lattice on size-dependent non-uniform plastic deformation at micron and submicron length scales. In the present paper, several example problems are investigated to show how crystal anisotropy is reflected by the MSG-CP theory.
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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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A finite deformation theory of Strain Gradient plasticity
Journal of the Mechanics and Physics of Solids, 2002Co-Authors: K. C. Hwang, Yonggang Huang, Hanqing Jiang, Huajian GaoAbstract:Abstract Plastic deformation exhibits strong size dependence at the micron scale, as observed in micro-torsion, bending, and indentation experiments. Classical plasticity theories, which possess no internal material lengths, cannot explain this size dependence. Based on dislocation mechanics, Strain Gradient plasticity theories have been developed for micron-scale applications. These theories, however, have been limited to infinitesimal deformation, even though the micro-scale experiments involve rather large Strains and rotations. In this paper, we propose a finite deformation theory of Strain Gradient plasticity. The kinematics relations (including Strain Gradients), equilibrium equations, and constitutive laws are expressed in the reference configuration. The finite deformation Strain Gradient theory is used to model micro-indentation with results agreeing very well with the experimental data. We show that the finite deformation effect is not very significant for modeling micro-indentation experiments.
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Effect of intrinsic lattice resistance in Strain Gradient plasticity
Acta Materialia, 2001Co-Authors: Xinming Qiu, Yonggang Huang, William D. Nix, 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.
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Mechanism-based Strain Gradient plasticity—II. Analysis
Journal of the Mechanics and Physics of Solids, 2000Co-Authors: Yonggang Huang, Huajian Gao, William D. Nix, J W HutchinsonAbstract:Abstract A mechanism-based theory of Strain Gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic Strain and Strain Gradient. This theory is motivated by our recent analysis of indentation experiments which strongly suggest a linear dependence of the square of plastic flow stress on Strain Gradient. Such a linear dependence is consistent with the Taylor plastic work hardening model relating the flow stress to dislocation density. This part of this paper provides a detailed analysis of the new theory, including equilibrium equations and boundary conditions, constitutive equations for the mechanism-based Strain Gradient plasticity, and kinematic relations among Strains, Strain Gradients and displacements. The theory is used to investigate several phenomena that are influenced by plastic Strain Gradients. In bending of thin beams and torsion of thin wires, mechanism-based Strain Gradient plasticity gives a significant increase in scaled bending moment and scaled torque due to Strain Gradient effects. For the growth of microvoids and cavitation instabilities, however, it is found that Strain Gradients have little effect on micron-sized voids, but submicron-sized voids can have a larger resistance against void growth. Finally, it is shown from the study of bimaterials in shear that the mesoscale cell size has little effect on global physical quantities (e.g. applied stresses), but may affect the local deformation field significantly.
N A Fleck - One of the best experts on this subject based on the ideXlab platform.
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Strain Gradient plasticity under non proportional loading
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2014Co-Authors: N A Fleck, J W Hutchinson, J R WillisAbstract:A critical examination is made of two classes of Strain Gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quant...
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Strain Gradient effects in surface roughening
Modelling and Simulation in Materials Science and Engineering, 2006Co-Authors: Ulrik Borg, N A FleckAbstract:A thin aluminium sheet comprising of large polycrystals is pulled in uniaxial tension and the resulting surface profile is measured in a scanning electron microscope. The surface profile near the grain boundaries reveals a local deformation pattern of width of a few micrometres and is strong evidence for Strain Gradient effects. Numerical analyses of a bicrystal undergoing in-plane tensile deformation are also studied using a Strain Gradient crystal plasticity theory and also by using a Strain Gradient plasticity theory for an isotropic solid. Both theories include an internal material length scale. An interfacial potential that penalizes the dislocations in crossing the grain boundary is included in the analysis. The results indicate that the surface profile is strongly dependent upon the choice of this potential and on the material length scale.
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Strain Gradient plasticity theory and experiment
Acta Metallurgica Et Materialia, 1994Co-Authors: N A Fleck, G M Muller, M F Ashby, J W HutchinsonAbstract:Abstract Dislocation theory is used to invoke a Strain Gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocation. The density of the geometrically necessary dislocations scales with the Gradient of plastic Strain. A deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of Strain hardening and Strain Gradient hardening. The theory is a non-linear generalization of Cosserat couple stress theory. Tension and torsion experiments on thin copper wires confirm the presence of Strain Gradient hardening. The experiments are interpreted in the light of the new theory.
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a phenomenological theory for Strain Gradient effects in plasticity
Journal of The Mechanics and Physics of Solids, 1993Co-Authors: N A Fleck, J W HutchinsonAbstract:Abstract A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The Strain Gradient theory fits within the general framework of couple stress theory and involves a single material length scale l. Minimum principles are developed for both deformation and flow theory versions of the theory which in the limit of vanishing l, reduce to their conventional counterparts: J2 deformation and J2 flow theory. The Strain Gradient theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.
Arthur C.m. Chong - One of the best experts on this subject based on the ideXlab platform.
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experiments and theory in Strain Gradient elasticity
Journal of The Mechanics and Physics of Solids, 2003Co-Authors: Arthur C.m. Chong, Fan Yang, Jianxun Wang, Pin TongAbstract:Abstract Conventional Strain-based mechanics theory does not account for contributions from Strain Gradients. Failure to include Strain Gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize Strain Gradient behaviors. This set enables the application of the higher-order equilibrium conditions to Strain Gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new Strain Gradient theory, a Strain Gradient elastic bending theory for plane-Strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the Strain Gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic Strain Gradient effect is significant in elastic deformation of small-scale structures.
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Model and experiments on Strain Gradient hardening in metallic glass
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2001Co-Authors: David C C Lam, Arthur C.m. ChongAbstract:Hardnesses of polycrystalline metals at shallow indent depth have been observed to increase because of Strain Gradients. Dislocation-based Strain Gradient plasticity models were proposed and good agreements were obtained. Metallic glasses have been observed to exhibit shear localization behaviour similar to metals. Nanoindentation have been conducted on Vitreloy metallic glasses in this study to determine the hardness variation as a function of the indent depth. Hardnesses at shallow indent depth were observed to increase significantly and comparison of the dislocation-based Strain Gradient indentation model indicated disagreement. An alternate Strain Gradient plasticity indentation model based on cluster theory of yield for glassy metal was developed and good agreement with data was obtained. The implication of the results and analysis on Strain Gradient behaviour is discussed.
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Characterization and Modeling of Specific Strain Gradient Modulus of Epoxy
Journal of Materials Research, 2001Co-Authors: David C C Lam, Arthur C.m. ChongAbstract:Microscale sensing and actuating components are prevalent in microelectromechanical systems. Deformations of microscale components are dependent not only on the Strains in the body, but also on the Strain Gradients. The contribution of Strain Gradients to plastic hardening is characterized by the specific Strain Gradient modulus of the material. The specific Strain Gradient modulus has been predicted to vary with the plastic Strain. The moduli of plastically preStrained epoxy specimens were experimentally characterized in this investigation using nanoindentation. PreStraining induced softening and an energy model are developed to separate the effect of preStrain softening from the effect of Strain Gradient. The results indicated that the contribution of Strain Gradient to hardening was initially large but diminished with increased plastic deformation. A model was developed for power law material and was shown to compare well with the experimental results.
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Strain Gradient plasticity effect in indentation hardness of polymers
Journal of Materials Research, 1999Co-Authors: Arthur C.m. Chong, David C C LamAbstract:Plasticity in material is typically described as a function of Strain, but recent observations from torsion and indentation experiments in metals suggested that plasticity is also dependent on Strain Gradient. The effects of Strain Gradient on plastic deformation in thermosetting epoxy and polycarbonate thermoplastic were experimentally investigated by nanoindentation and atomic force microscopy in this study. Both thermosetting and thermoplastic polymers exhibited hardening as a result of imposed Strain Gradients. Strain Gradient plasticity theory developed on the basis of a molecular kinking mechanism has predicted Strain Gradient hardening in polymers. Comparisons made between indentation data and theoretical predictions correlated well. This suggests that Strain Gradient plasticity in glassy polymers is determined by molecular kinking mechanisms.
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INDENTATION MODEL AND Strain Gradient PLASTICITY LAW FOR GLASSY POLYMERS
Journal of Materials Research, 1999Co-Authors: Arthur C.m. ChongAbstract:Plastic deformation of metals is generally a function of the Strain. Recently, both phenomenological and dislocation-based Strain Gradient plasticity laws were proposed after Strain Gradients were experimentally found to affect the plastic deformation of the metal. A Strain Gradient plasticity law is developed on the basis of molecular theory of yield for glassy polymers. A Strain Gradient plasticity modulus with temperature and molecular dependence is proposed and related to indentation hardness. The physics of the Strain Gradient plasticity in glassy polymer is then discussed in relation to the modulus.
