• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.87-97
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• 2004

In gradient-dependent plasticity theory, the yield strength depends on the Laplacian of an equivalent plastic strain measure (hardening parameter), and the consistency condition results in a differential equation with respect to the plastic multiplier. The plastic multiplier is then discretized in addition to the usual discretization of the displacements, and the consistency condition is solved simultaneously with the equilibrium equations. The disadvantage is that the plastic multiplier requires a Hermitian interpolation that has four degrees of freedom at each node. Instead of using a Hermitian interpolation, in this article, a 3-node incompatible (trigonometric) interpolation is proposed for the plastic multiplier. This incompatible interpolation uses only the function values of each node, but it is continuous across element boundaries and its second-order derivatives exist within the elements. It greatly reduces the degrees of freedom for a problem, and is shown through a numerical example on localization to yield good results.

• Transactions of Materials Processing
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• v.3 no.2
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• pp.229-242
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• 1994

An approximate procedure based on a combination micro-macroscopic theories of plasticity for predicting the crystallographic texture during the plane strain forming of fcc metals has been developed. This procedure is divided into two steps. Firstly, we extract the history of the deformation gradient at all deformed elements with a elasto-plastic finite element method using isotropic plasticity model. Secondly, we use this deformation gradient history to predict the crystallographic deformation texture based on the Bishop-Hill theory. Renouard and Wintenberger' method is chosen for selecting the active slip systems. The predicted results have been compared with reported experimental results. The calculated results are in good agreement with their results.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.05a
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• pp.205-208
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• 2001

Localized shear band is investigated through the analysis of one-dimensional model for simple shearing deformation of thermally rate dependent material. Generally mesh size or interval of nodes play an important role in determining the overall flow behavior of the material. In order to observe these size effects we adapted non-local theory by including higher order strain gradients of the equivalent strain into the constitutive equation for the flow stress. for the ease of convergence and numerical stability the inplicit finite difference scheme is employed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1994.06a
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• pp.1-9
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• 1994

Three recent developments made at Rensselaer in sheet material forming processes are briefly reviewed in this paper. These advances represent three broad disciplines of Process Simulation, Forming Processes, and Computer-Aided Measurement Methods. The first development deals with simple and quick computer simulation of 2D sheet forming process without depending on popular finite element analysis methods. An analytical method based on a thin shell theory accounts for bending and unbending effects, and is capable of simulating practical sheet metal forming processes under the plane strain condition. The second area is concerned with innovative methods to improve formability of sheet materials by temperature gradient forming. The drawing limit is increased by such an improved temperature gradient forming process. The third and final area deals with a totally new experimental technique to capture 3D geometry data and measure strain distributions of sheet metal parts using a digital 35mm SLR camera.

• Transactions of Materials Processing
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• v.15 no.8 s.89
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• pp.591-596
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• 2006

Torsion testing was employed to investigate the deformation and recrystallization behavior of coarse-grained Alloy 718, and the results are compared with the compression testing results. Mechanical testing was conducted on bulk Alloy718 samples within the temperature ranges, $1000^{\circ}C{\sim}1100^{\circ}C$. The strain gradient formed in the torsion specimens resulted in a recrystallization behavior which varied along the radial direction from the center to the surface. The flow curves based on effective stress and effective strain as obtained by Fields and Backofen's isotropic deformation theory and the dynamic recrystallization within the compression tested samples and torsion tested samples are different. The different deformation and recrystallization behavior can be rationalized by the fact that the deformation in the coarse-grained torsion specimens is not uniform and thus the strain gradient within the specimens cannot be analytically predicted by FE simulation. Thus, the extent of recrystallization cannot be properly predicted by the established recrystallization equations based on compression tests.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.10
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• pp.1229-1237
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• 2013

In this study, the theory of spherical indentation based on incremental plasticity is extended to an indentation method for evaluating creep properties. Through finite element analysis (FEA), the point where the elastic strain effect is negligible and the creep strain gradient constant is taken as the optimum point for obtaining the equivalent strain rate and stress. Based on FE results for spherical indentation with various values of creep exponent and creep coefficient, we derive by regression an equation to calculate creep properties using two normalized variables. Finally a program is generated to calculate creep exponent and creep coefficient. With this method, we obtain from the load-depth curve creep exponents with an average error of less than 1.5 % and creep coefficients with an average error of less than 1.0 %.