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Andreas Mortensen - One of the best experts on this subject based on the ideXlab platform.
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tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain Rate Hardening matrix
Acta Materialia, 2014Co-Authors: Amael Cohades, Andreas MortensenAbstract:We use the long-wavelength model of Hutchinson and Neale (1977) and Ghosh (1977) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to two-parameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, and to estimate the influence of matrix strain and strain-Rate Hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-Rate Hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle-phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best stRategy is to aim for small layer thicknesses. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-Rate Hardening matrix
Acta Materialia, 2014Co-Authors: Amael Cohades, Andreas MortensenAbstract:We use the long-wavelength model of Hutchinson and Neale (1977) and Ghosh (1977) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to two-parameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, and to estimate the influence of matrix strain and strain-Rate Hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-Rate Hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle-phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best stRategy is to aim for small layer thicknesses. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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An analysis of the tensile elongation to failure of laminated metal composites in the presence of strain-Rate Hardening
Acta Materialia, 2012Co-Authors: Arda Çetin, Cécile Bernardi, Andreas MortensenAbstract:We extend the analysis of Hutchinson and Neale (Hutchinson JW, Neale KW. Acta Metall 1977;25:839) and Ghosh (Ghosh AK. Acta Metall 1977;25:1413) predicting the tensile elongation to failure of strain-Rate-dependent plastic materials to two-phase composites deforming quasistatically according to the equistrain rule of mixtures. The analysis incorpoRates the influence of work Hardening and strain-Rate Hardening in both composite constituent phases. It is shown that the problem can be formulated in a manner that condenses the seven underlying material parameters into four dimensionless numbers for composites of power-law Hardening phases, the number of parameters falling to two for linear Hardening. It then emerges that the stabilizing influence of both work Hardening and strain-Rate Hardening is, within assumptions of the model, always predominantly exerted by the phase that carries the greater share of the composite stress. It is also shown that the prediction can be simplified so as to enable an approximate but convenient direct graphical deduction of the tensile elongation of ductile laminated metal composites (LMCs), knowing the work Hardening and strain-Rate Hardening characteristics of the two phases making the composite. The utility of this graphical scheme is illustRated with two examples, namely LMCs containing one phase of (modeRately ductile) aluminium alloy or of a (low-ductility) nanocrystalline metal. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Hoon Huh - One of the best experts on this subject based on the ideXlab platform.
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Correlation of microscopic structures to the strain Rate Hardening of SPCC steel
International Journal of Mechanical Sciences, 2010Co-Authors: Hoon Huh, C.g. Park, J.s. Kang, M.y. Huh, Jonghun Yoon, H.g. KangAbstract:Abstract The high strain Rate properties of steel have been studied for accuRate crashworthiness of vehicles. The mechanical properties at high strain Rates show different characteristics from those at the quasi-static state. In order to seek for the physical phenomenon of the strain Rate Hardening, a microscopic investigation has been conducted for the texture evolution and dislocation behavior of steel. Tensile tests were performed at strain Rates ranged from 0.001/s to 100/s, which is the common range in practical vehicle crashes to investigate the microstructural variation and dislocation behavior. According to experimental results of the EBSD and TEM experiment, the texture evolution does not develop remarkably with the variation in strain Rates, while dislocation structure and behavior investigated by TEM experiments show significant difference with the variation in strain Rates. The change in the dislocation structure, behavior, and density with the variation of strain Rates clearly explains the mechanism of the strain Rate Hardening showing that round half-loop dislocations are replaced by straight and crossing dislocations and then by cell structured dislocations.
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Microscopic Investigation of the Strain Rate Hardening for Polycrystalline Metals
Transactions of Materials Processing, 2008Co-Authors: J.h. Yoon, C.g. Park, J.s. Kang, J.h. Suh, M.y. Huh, H.g. Kang, Hoon HuhAbstract:Polycrystalline materials such as steels(BCC) and aluminum alloys(FCC) show the strain Hardening and the strain Rate Hardening during the plastic deformation. The strain Hardening is induced by deformation resistance of dislocation glide on some crystallographic systems and increase of the dislocation density on grain boundaries or inner grain. However, the phenomenon of the strain Rate Hardening is not demonstRated distinctly in the rage of to strain Rate. In this paper, tensile tests for various strain Rates are performed in the rage of to then, specimens are extracted on the same strain position to investigate the microscopic behavior of deformed materials. The extracted specimens are investigated by using the electron backscattered diffraction(EBSD) and transmission electron microscopy(TEM) results which show the effect of texture orientation, grain size and dislocation behavior on the strain Rate Hardening.
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Dynamic limit analysis formulation for impact simulation of structural members
International Journal of Solids and Structures, 2006Co-Authors: Kee Poong Kim, Hoon HuhAbstract:Abstract This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-Rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain Hardening, strain-Rate Hardening and thermal softening. The time dependent term in the governing equation is integRated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-Rate Hardening and thermal softening as well as strain Hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstRates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the Rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.
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Crash Analysis of Auto-body Structures Considering the Strain-Rate Hardening Effect
International Journal of Automotive Technology, 2000Co-Authors: Woo Jong Kang, Hoon HuhAbstract:The crashworthiness of vehicles with finite element methods depends on the geometry modeling and the material properties. The vehicle body structures arc generally composed of various members such as frames. stamped panels and deep-drawn parts from sheet metals. In order to ensure the impact characteristics of auto-body structures. the dynamic behavior of sheet metals must be examined to provide the appropriate constitutive relation. In this paper, high strain-Rate tensile tests have been carried out with a tension type split Hopkinson bar apparatus specially designed for sheet metals. Experimental results from both static and dynamic tests with the tension split Hopkinson bar apparatus arc interpolated to construct the Johnson-Cook and a modified Johnson-Cook equation as the constitutive relation. that should be applied to simulation of the dynamic behavior of auto-body structures. Simulation of auto-body structures has been carried out with an elasto-plastic finite clement method with explicit time integration. The stress integration scheme with the plastic predictor-elastic corrector method is adopted in order to accuRately keep track of the stress-strain relation for the Rate-dependent model accuRately. The crashworthiness of the structure with quasi-static constitutive relation is compared to the one with the Rate-dependent constitutive model. Numerical simulation has been carried out for frontal frames and a hood of an automobile. Deformed shapes and the impact energy absorption of the structure are investigated with the variation of the strain Rate.
Romesh C. Batra - One of the best experts on this subject based on the ideXlab platform.
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Instability strain and shear band spacing in simple tensile/compressive deformations of thermoviscoplastic materials
International Journal of Impact Engineering, 2007Co-Authors: Romesh C. Batra, Z.g. WeiAbstract:Abstract We analyze the stability of homogeneous simple tensile/compressive deformations of an isotropic heat-conducting thermoviscoplastic bar by studying the growth of infinitesimal perturbations superimposed upon a homogeneous deformation. The smallest axial strain at which the superimposed perturbation has a positive initial growth Rate is called the instability strain. Two criteria are used to determine the shear band spacing; (i) the wave number, ξ m , of the perturbation that has the maximum initial growth Rate gives the spacing, L s = 2 π / ξ m , between adjacent shear bands, and (ii) L s = inf t 0 ⩾ 0 2 π / ξ m ( t 0 ) where t 0 is the time when the homogeneous solution is perturbed. It is found that the geometric softening/Hardening significantly affects the instability strain and the value of L s . The effect of varying the thermal conductivity, the strain-Rate Hardening exponent and the average axial strain Rate on L s has been delineated. It is found that L s ∝ ( nominal axial strain Rate ) - 0.757 . However, for L s ∝ ( thermal conductivity ) χ ¯ , the value of χ ¯ strongly depends upon the strain Rate Hardening exponent m . No scaling law is found between L s and the Taylor–Quinney parameter. For L s ∝ ( specific heat ) χ , the value of χ depends upon the strain-Rate Hardening exponent m and increases monotonically with an increase in the value of m .
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Shear band spacing in thermoviscoplastic materials
International Journal of Impact Engineering, 2006Co-Authors: Romesh C. Batra, Z.g. WeiAbstract:Abstract A closed-form expression for shear band spacing in strain-Hardening, strain-Rate-Hardening and thermally softening thermoviscoplastic materials is derived by studying the stability of a homogeneous solution of equations governing its simple shearing deformations. The wavelength of the perturbation that maximizes its initial growth Rate is assumed to determine the shear band spacing, L s . The dependence of L s upon various material parameters and the nominal strain Rate, ɛ ˙ , is delineated. When written as L s = A 1 k χ 1 or A 2 ɛ ˙ χ 2 where A 1 and A 2 are parameters and k is the thermal conductivity, it is found that χ 2 ≃ - 0.787 and χ 1 depends upon the strain-Rate Hardening exponent m ; χ 1 ≃ 0.5 for m ≃ 10 - 6 and n ≃ 0.011 , decreases rapidly to 0.21 for m ≃ 10 - 4 and n ≃ 0.011 , and then increases slowly to 0.25 for m ≃ 0.05 and n ≃ 0.011 . However, for m = 0 and n ≠ 0 , χ 1 = 1 .
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Effect of material parameters on shear band spacing in work-Hardening gradient dependent thermoviscoplastic materials
International Journal of Plasticity, 1999Co-Authors: L. Chen, Romesh C. BatraAbstract:We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The eAect of material elasticity is neglected but that of work Hardening, strain-Rate Hardening, thermal softening, and strain-Rate gradients is considered. The consideration of strain-Rate gradients introduces a material characteristic length into the problem. A homogeneous solution of the governing equations is perturbed at diAerent values t0 of time t, and the growth Rate at time t0 of perturbations of diAerent wavelengths is computed. Following Wright and Ockendon’s postulate that the wavelength of the dominant instability mode with the maximum growth Rate at time t0 determines the minimum spacing between shear bands, the shear band spacing is computed. It is found that for the shear band spacing to be positive, either the thermal conductivity or the material characteristic length must be positive. Approximate analytical expressions for locally adiabatic deformations of dipolar (strain-Rate gradientdependent) materials indicate that the shear band spacing is proportional to the square-root of the material chaRateristic length, and the fourth root of the strain-Rate Hardening exponent. The shear band spacing increases with an increase in the strain Hardening exponent and the thermal conductivity of the material. # 1999 Elsevier Science Ltd. All rights reserved.
Amael Cohades - One of the best experts on this subject based on the ideXlab platform.
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tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain Rate Hardening matrix
Acta Materialia, 2014Co-Authors: Amael Cohades, Andreas MortensenAbstract:We use the long-wavelength model of Hutchinson and Neale (1977) and Ghosh (1977) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to two-parameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, and to estimate the influence of matrix strain and strain-Rate Hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-Rate Hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle-phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best stRategy is to aim for small layer thicknesses. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
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Tensile elongation of unidirectional or laminated composites combining a brittle reinforcement with a ductile strain and strain-Rate Hardening matrix
Acta Materialia, 2014Co-Authors: Amael Cohades, Andreas MortensenAbstract:We use the long-wavelength model of Hutchinson and Neale (1977) and Ghosh (1977) to estimate the uniform tensile elongation of two-phase composites deforming quasistatically according to the equistrain rule of mixtures, in which one phase is ductile while the other fractures progressively according to two-parameter Weibull statistics. We use shear-lag models in the literature to quantify load transfer from the ductile phase to the fractured brittle phase, and to estimate the influence of matrix strain and strain-Rate Hardening, of brittle phase fracture characteristics, and of phase volume and strength ratios, on the composite strain to failure as dictated by the onset of unstable necking. Calculations show that strain and strain-Rate Hardening of the ductile phase do relatively little to increase the ductility of the composite. Two parameters play a dominant role, namely the brittle-phase Weibull modulus and a dimensionless parameter describing load transfer across the two phases. The main practical implication of this analysis is that, to produce reasonably ductile two-phase composites, the best stRategy is to aim for small layer thicknesses. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Z.g. Wei - One of the best experts on this subject based on the ideXlab platform.
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Instability strain and shear band spacing in simple tensile/compressive deformations of thermoviscoplastic materials
International Journal of Impact Engineering, 2007Co-Authors: Romesh C. Batra, Z.g. WeiAbstract:Abstract We analyze the stability of homogeneous simple tensile/compressive deformations of an isotropic heat-conducting thermoviscoplastic bar by studying the growth of infinitesimal perturbations superimposed upon a homogeneous deformation. The smallest axial strain at which the superimposed perturbation has a positive initial growth Rate is called the instability strain. Two criteria are used to determine the shear band spacing; (i) the wave number, ξ m , of the perturbation that has the maximum initial growth Rate gives the spacing, L s = 2 π / ξ m , between adjacent shear bands, and (ii) L s = inf t 0 ⩾ 0 2 π / ξ m ( t 0 ) where t 0 is the time when the homogeneous solution is perturbed. It is found that the geometric softening/Hardening significantly affects the instability strain and the value of L s . The effect of varying the thermal conductivity, the strain-Rate Hardening exponent and the average axial strain Rate on L s has been delineated. It is found that L s ∝ ( nominal axial strain Rate ) - 0.757 . However, for L s ∝ ( thermal conductivity ) χ ¯ , the value of χ ¯ strongly depends upon the strain Rate Hardening exponent m . No scaling law is found between L s and the Taylor–Quinney parameter. For L s ∝ ( specific heat ) χ , the value of χ depends upon the strain-Rate Hardening exponent m and increases monotonically with an increase in the value of m .
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Shear band spacing in thermoviscoplastic materials
International Journal of Impact Engineering, 2006Co-Authors: Romesh C. Batra, Z.g. WeiAbstract:Abstract A closed-form expression for shear band spacing in strain-Hardening, strain-Rate-Hardening and thermally softening thermoviscoplastic materials is derived by studying the stability of a homogeneous solution of equations governing its simple shearing deformations. The wavelength of the perturbation that maximizes its initial growth Rate is assumed to determine the shear band spacing, L s . The dependence of L s upon various material parameters and the nominal strain Rate, ɛ ˙ , is delineated. When written as L s = A 1 k χ 1 or A 2 ɛ ˙ χ 2 where A 1 and A 2 are parameters and k is the thermal conductivity, it is found that χ 2 ≃ - 0.787 and χ 1 depends upon the strain-Rate Hardening exponent m ; χ 1 ≃ 0.5 for m ≃ 10 - 6 and n ≃ 0.011 , decreases rapidly to 0.21 for m ≃ 10 - 4 and n ≃ 0.011 , and then increases slowly to 0.25 for m ≃ 0.05 and n ≃ 0.011 . However, for m = 0 and n ≠ 0 , χ 1 = 1 .
