Numerical Modeling for Strain Hardening of Two-phase Alloys with Dispersion of Hard Fine Spherical Particles

Abstract

Synopsis :Plasticdeformationanddislocationaccumulationindispersionhardeningalloysarenumericallyanalyzedbyacrystalplasticityfiniteelement technique and work hardening characteristics are discussed. The critical resolved shear stress for slip system is given by the extended expression of the Bailey-Hirsch type model which include the Orowan stress as size effect of microstructure. Work hardening of slip system is estimated by statistically stored dislocation (SSD) density. Increment of the SSD density is evaluated by slip strain and the mean free path of dislocations (the Kocks-Mecking model). The mean free path depends on the average spacing of dispersed particles, which is also used to estimate the Orowan stress. The average spacing of dispersed particles is calculated from the volume fraction and average diameter of dispersed particles.Asaresult,flowstresslevelattheinitialstageofdeformationagreedverywellwithexperimentalresultbutworkhardeningrate was higher than that of experiment. From this fact, it is considered that the mean free path and the average spacing of dispersed particles are different spacing factors. When we assume that the mean free path is two to three times larger than the average spacing of dispersed particles, numerical result of the strain hardening agrees very well with experimental one.

Crystal Plasticity Analysis of Microscopic Deformation Mechanisms and GN Dislocation Accumulation Depending on Vanadium Content in β Phase of Two-Phase Ti Alloy

“…The clp, that is a code for three-dimensional CPFE analysis developed by Ohashi, 10,2023) is employed in this study. The clp was employed for the analysis of the deformation of materials with face-centered cubic structures, 2327) bcc structures, 28,29) and hcp structures. 30,31) The constitutive equations employed in this study are shown below.…”

Crystal Plasticity Analyses of Scale Dependent Mechanical Properties of Ferrite/Cementite Lamellar Structure Model in Pearlite Steel Wire with Bagaryatsky or Pitsch-Petch Orientation Relationship

“…Details of this effect were discussed elsewhere for single phase material 19) and applied also to two-phase microstructure. 20) In this paper, the length scale d is assumed to be equal to lamellar thickness 1,2) when we evaluate the CRSS of the ferrite layer. For the evaluation of CRSS of cementite layers, on the other hand, the Orowan stress is not included because dislocations are supplied from ferrite layers 7) before dislocation sources inside the cementite layers are activated and the curvature radius of the dislocation transferred from the ferrite layer is assumed to be sufficiently large compared to the lamellar thickness, that is, d→∞.…”

“…It was used to clarify scale dependent mechanical properties of single-phase polycrystalline model 19) and two-phase material model with precipitate. 20) In this paper, we examine mechanical properties of simplified models of the pearlite steel wire by the crystal plasticity analysis. Models are composed of three-layers; a ferrite lamella is sandwiched by two cementite lamellae.…”

A Unified Model for Plasticity in Ferritic, Martensitic and Dual-Phase Steels

“…The technique often employed is to just use the mean free path of a pure and single-crystal material and introduce a proportionality constant that expresses the reduction of the mean free path by other kinds of obstacles, Λ = DΛ pm , where Λ pm is the mean free path of pure single-crystal material and D is a constant, which decreases with increasing number and strength of obstacles; however, it usually becomes just a fitting parameter without any physical meaning [37]. Okuyama and Yasuda suggested to apply the shortest Λ of obstacles when several obstacles are present [38,39], but that idea makes the value of Λ homogeneous, although it should vary depending on the position of dislocations and obstacles in actual steels.…”