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.
Image-based deformation simulation of microstructures in metals is attracting attention; however, the data conversion processes from the images of microstructures into the geometric models for the deformation simulation are now inconvenient, and there is a possibility that it prevents diffusion of the image-based simulation. In order to solve the problem, we developed an interface geometric models for Crystal Plasticity Finite Element (CPFE) analysis. The interface incorporates several functions for data cleaning and coarse graining of the microstructures: functions to narrow down the limits of Eulerian angles presenting crystal orientations, integrate crystal grains with similar crystal orientations, eliminate small crystal grains, select representative crystal orientation in each crystal grain, and so on. The interface was applied to an orientation map of polycrystal microstructure in pure titanium, and the course-grained geometric models were successfully obtained. Image-based CPFE analysis was conducted using the geometric models with different number of finite elements. The numbers of crystal grains were assumed to be around 50 in any geometric models. A dislocation density dependent constitutive equation was employed and uniaxial tensile loading was applied to the geometric models by the forced displacement. The results showed that spatial distributions of stress, strain, and dislocation density were good agreement among geometric models with different number of elements in both elastic and plastic ranges while values of the strain and dislocation density showed quantitatively dependency of the number of elements on their distributions in the plastic ranges. These features indicate that the qualitatively similar results can be obtained using the developed interface on the condition that coarse graining of the microstructures does not occur even though the number of elements is changed.
Macroscopic mechanical responses of alloy steels dispersed with fine vanadium carbide particles [1] were analyzed by crystal plasticity finite element method. Average distance of dispersed particles was used as a microscopic length scale and introduced to the models of the critical resolved shear stress and the mean free path of dislocations. Numerical result of yield stress agreed well with that of experimental result [1], but that of the work hardening rate was slightly higher than that of experimental one. When the dislocation mean free path was set to be 2 to 3 times the average spacing of dispersed particles, the work hardening rate fit better with the experimental one.
The relationship between yield stress and the distribution of microscopic plastic deformation was numerically investigated by using a crystal plasticity finite element method (CP-FEM) in the model where particles were randomly distributed. It was in order to reveal which particle spacing. i.e., the maximum, minimum or average particle spacing, can be taken as the representative length which controls yielding. The critical resolved shear stress for the onset of the slip deformation in any element was defined under the extended equation in the Bailey-Hirsch type model. The model includes the term of the Orowan stress obtained from the local values of the representative length. Each particle spacing was distributed with a standard deviation of approximately 2 to 3 times larger than the average particle spacing. The macroscopic mechanical properties obtained with CP-FEM were in good agreement with those experimentally obtained. The onset of microscopic slip deformation depended on the particle distribution. Plastic deformations started first in the area where the particle size is larger, then the plastic region grows in the areas where the particle spacing is smaller. Slip deformation had occurred in 90% of the matrix phase by the macroscopic yield point. The length factor in the Orowan equation was the average spacing of the particles in the model, which is in good agreement with Foreman and Makin. The CP-FEM indicated that in dispersed hardened alloys, microscopic load transfer occurred between the areas where the large particles spacing and the small one at the yielding.
Inhomogeneous deformation of a single ¡-¢ colony in a Ti6Al4V alloy under uniaxial tensile conditions was numerically simulated using a crystal plasticity finite element (CPFE) method, and we predicted density changes in geometrically necessary dislocations (GNDs) depending on the vanadium concentration in the ¢ phase (V ¢ ). The geometric model for the CPFE analysis was obtained by converting data from electron back-scatter diffraction patterns into data for the geometric model for CPFE analysis, using a data conversion procedure previously developed by the authors. The results of the image-based crystal plasticity analysis indicated that smaller V ¢ induced greater stress in the ¡ phase and smaller stress in the ¢ phase close to the ¡-¢ interfaces in the initial stages of deformation because of the elastically softer ¢ phase with lower V ¢ . This resulted in greater strain gradients and greater GND density close to the interfaces in the initial stages of deformation within the single ¡-¢ colony when the ¢ phase plastically does not deform. [
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