Session: 03-20-02: Space Manufacturing II

Paper Number: 166569

Predicting the Strain-Gradient Effect During Deformation of Precipitation Hardened Ti-6Al-4V Alloy Using a Mean-Filed Polycrystal Plasticity Material Model 

In this work, a mean-field strain gradient (SG) plasticity model is developed using viscoplastic selfconsistent (VPSC) polycrystal plasticity model which accounts for grain size effect during deformation, the model is termed as SG-VPSC. Many materials exhibit different mechanical properties like elastic or plastic response while tested on large or small (micron) samples. This is evident from the experiments, for example: indentation hardness of metals and ceramics increases as the indenter size decreases and precipitation hardened aluminum alloys show increased strength. These size effects are attributed to the length scales associated with microstructure which cannot be simulated by classical constitutive models where stress depends locally on dimensionless strains. The constitutive model relies on the inclusion of higher strain gradients (SG) which introduces length scale in constitutive modeling. SG is developed due to accumulation of geometrically necessary dislocations (GNDs) and its calculation inside a grain is the preliminary stage of SG plasticity model development. In recent years, several full-field models have been developed to incorporate SG effects by numerically calculating GNDs inside grains using finite element analysis (FEA) framework but very few literatures exist for mean-field material modeling framework. The main advantage of a mean-field SG plasticity model is that it will enable multi-level modeling of metal samples incorporating large number of grains compared to few grains in a full-field SG model. In this paper, SG formulation in a mean-field model is implemented by numerically calculating GNDs and its associated back-stress inside grains. The strain gradient effect is captured by the evolution of GNDs during the deformation process. Recent development in mean-field polycrystal plasticity models by the incorporation of field fluctuations (second order) formulation is utilized for this purpose. Second order formulations of stress, lattice spin enables the calculation of intragranular misorientation and lattice rotation spreads. The lattice rotation spreads are then sampled in a fixed spatial coordinate systems inside a grain to obtain a spatial distribution of lattice rotations. The GND density calculation used in this study is based on finite deformation theory that takes the ‘curl’ of spatial distribution of lattice rotations and calculate the Nye’s dislocation tensor which is based on finite deformation definition of Nye tensor. The model can be applied to model precipitation hardened metals and alloys used in aerospace industry. Titanium (Ti) alloy Ti-6Al-4V (Ti64) is a widely used material in space industry for manufacturing of aircraft parts due to its high strength, stiffness to weight ratio, fatigue resistance, toughness and corrosion resistance. Ti64 is sometimes precipitation hardened to increase its yield strength. The validation of our SG plasticity model is done by simulating the grain size effect of precipitation hardened Ti64 under uniaxial tension. The accurate prediction of texture, mechanical response and twin volume fraction validates the capability of the model. The future research will be directed to link the SG-VPSC model in FE framework using commercial software package Abaqus through user material (UMAT) subroutine to enable modeling of multi- level of deformation using different geometries of samples which can be used for metal forming process in industries and many material experiments.

Presenting Author: Iftekhar Riyad University of New Hampshire

Presenting Author Biography: Iftekhar Riyad is a PhD candidate in Mechanical Engineering department of University of New Hampshire. His research is focused on computational solid mechanics, crystal plasticity and experimental material characterization.

Authors:

Iftekhar Riyad University of New Hampshire
M Shafiqur Rahman Louisiana Tech University