The article presents a microstructure-based mechanical model of hexagonal close-packed (hcp) α-titanium representative of the mesoscale and analyzes the contribution of a pyramidal slip to plastic deformation. We discuss the size of a representative volume element (RVE) enabling mesoscale phenomena to be correctly reproduced, focusing on deformation-induced surface roughening (DISR) and plastic strain localization. It is shown that the ignorance of a pyramidal slip in simulations leads to overestimated stress values in an hcp material. A polycrystalline model is capable of reproducing the mesoscale phenomena until plastic strain begins to localize at the length scale comparable to the model size.

The phenomenon of mesoscale deformation-induced surface roughening in titanium polycrystals is examined experimentally and numerically. The evolution of the surface morphology under uniaxial tension is analyzed in terms of the standard and ad hoc roughness parameters and the fractal dimension. The statistical estimates are compared to the grain-scale stress-strain fields in order to reveal an interrelation between the in-plane plastic strains and out-of-plane surface displacements. A strong correlation with a determination coefficient of 0.99 is revealed between the dimensionless roughness parameter R_d and the corresponding in-plane plastic strain. The standard roughness parameters R_a and R_RMS are shown to correlate linearly with the in-plane strains, but only for moderate tensile deformation, which is due to filtering out low-frequency components in the surface profiles. The fractal dimension D_F changes with the subsection strains in a sawtooth fashion, with an abrupt drop in the neck region. The descent portions of the D_F dependences are supposedly related to the appearance of low-frequency components in the structure of the surface profiles.

A crystal plasticity finite element model is developed and implemented to numerically study the deformation behavior of hexagonal close-packed metals using α-titanium as an example. The model takes into account micromechanical deformation mechanisms through dislocation slip along prismatic, basal, and first-order <c+a> pyramidal systems, as well as tensile twinning. Twin initiation follows a two-conditional criterion requiring that both the resolved shear stress in a twin system and the accumulated pyramidal slip simultaneously reach their critical values. Three-dimensional polycrystalline models are generated using the step-by-step packing method. The crystal plasticity constitutive model describing the deformation behavior of grains is integrated into the boundary-value problem of continuum mechanics, including dynamic governing equations. The three-dimensional problem is solved numerically using the finite element method. The micromechanical model is tested for an α-titanium single crystal along the [0001] direction and a polycrystal consisting of 50 grains. The numerical results reveal that twin propagation is controlled by the critical value of accumulated pyramidal slip, emphasizing the need for experimental calibration. The agreement between numerical and experimental results provides the model validation at the meso- and macroscales.

Crystal plasticity models combined with an explicit consideration of a polycrystalline structure are an effective tool for studying the deformation phenomena throughout length scales. A numerical solution to the boundary-value problems with an explicit account for misrostructural features requires extensive computational resources. The use of explicit time integration schemes effectively reduces computational costs yet providing a qua-sistatic solution with a high degree of accuracy. In this paper, we discuss the numerical aspects of crystal plasticity finite element simulations of quasistatic deformation phe-nomena in terms of explicit dynamics. The equations for plastic strain rate are formulated in a way to minimize strain rate sensitivity, which is the necessary condition for simulat-ing quasistatic deformation at artificially high strain rates. The problems of model verifi-cation and testing at the micro, meso, and macroscales are discussed using the example of aluminum single- and polycrystals.

Deformation-induced surface roughness in commercially pure titanium under uniaxial tension is studied experimentally. Stop-and-study experimental technique is used to obtain roughness profiles at different deformation stages. Various statistical characteristics including fractal dimension, R_RMS, R_a and a dimensionless roughness parameter are used to quantify surface morphology. Fractal dimension calculation procedure and its improvement are discussed. A dependence of the statistical parameters on local strain was revealed.