The effects of surface-layer grain size and texture on deformation-induced surface roughening in polycrystalline titanium hardened by ultrasonic impact treatment

Abstract

The ultrasonic impact treatment (UIT) of titanium specimens leads to the grain refinement and formation of a strong basal texture in the surface layer, affecting the mechanical properties of the UIT titanium parts. In this paper, we aim at investigating numerically the effects which the UIT-modified microstructure has on the micro- and mesoscale deformation behavior of titanium specimens subjected to uniaxial tension. For this purpose, three-dimensional polycrystalline models taking an explicit account of the grain morphology and crystallographic orientations of the base material and UIT modified surface layer are generated by the method of step-by-step packing and implemented in the finite-element calculations. The constitutive models describing the nonlinear behavior of individual grains are implemented in terms of anisotropic elasticity and crystal plasticity theories. The boundary value problem is solved within a dynamic approach using the ABAQUS/Explicit package. This study allows distinguishing between the grain size and texture effects and drawing conclusions on their roles in the stress-strain evolution, plastic strain localization and deformation-induced surface roughening in UIT titanium specimens under loading.

Introduction

Surface modification of metallic materials results in the formation of specific material properties defined by the surface treatment method, base material and surface layer compositions, geometry of the interface between the surface layer and base material [[1], [2], [3], [4], [5], [6], [7], [8], [9]]. To date, a number of studies have demonstrated that surface treatments by coating deposition or surface hardening have a pronounced effect on the processes developing on the surface of a loaded part, including deformation-induced surface roughening (see, e.g. Refs. [[5], [6], [7], [8], [9], [10]]). Since surface roughening is an intrinsic defect, in polycrystalline materials it is closely associated with their microstructure, including crystal lattice structure, grain size, shape and spatial arrangement, crystallographic texture, precipitates, interfaces between microstructural elements (e.g., grain boundaries, substrate-coating interface, etc.) [[10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]]. In the general case, surface roughness in loaded materials evolves at different spatial scales, evident as the orange peel pattern at the grain scale [[8], [9], [10], [11], [12]], banding, roping or ridging at the mesoscale [9,10,[14], [15], [16], [17], [18], [19], [20]], and macroscopic waviness at the specimen length scale [21,22].

We have recently shown [23] that deformation-induced roughening would provide valuable information for evaluating material strain state on the micro- and mesoscales though it is commonly treated as an unwanted phenomenon which deteriorates the surface quality and mechanical properties of materials. In contrast to experimental estimations of stresses or plastic strains mainly involving indirect methods (e.g., measurements of dislocation density, calculations based on the X-ray diffraction), the out-of-plane surface displacements are measurable quantities which can be compared with the simulation data both qualitatively and quantitatively.

While a large body of experimental and numerical data on deformation-induced roughening are available at present, only a few studies have systematically investigated this phenomenon in surface-modified materials. Previous research findings (see, e.g. Ref. [[6], [7], [8], [9], [10]]) are contradictory because the conclusions are drawn on the basis of experiments on different materials and surface treatment techniques. Compared to as-received materials, the deformation-induced roughness in surface-hardened specimens is reported to be smoother in some cases and more pronounced in the others. Mizuno and Mulki [6] have considered commercial low carbon killed steel with five different zinc and zinc alloy coatings under tensile, Erichsen and bending loadings to reveal the changes in surface roughness with the coating type, strain degree, and deformation mode. The coated specimens, both with hard and soft coatings, were characterized by similar roughening as the uncoated ones. The authors attributed the difference in roughness between the specimens under study to the mean width of the cracks developing in coatings. Analyzing the effects of coatings with different mechanical properties on the roughening phenomenon, Sachtleber et al. [10] have observed the same tendencies in the grain-scale roughness behavior in both uncoated and coated aluminum alloy specimens and revealed the differences in surface waviness. The strongest waviness and smoothest orange peel pattern were observed in the material with a hard coating, while the aluminum specimen with a soft coating demonstrated the largest grain-scale roughness.

Little attention has been paid so far to theoretical studies of strain-induced surface roughening and accompanying stress and strain localization in surface-treated materials. For estimation of surface roughness, Lytvynenko et al. [25] have proposed a mathematical approach based on expansion coefficients of statistical estimates (expectation estimates) and have demonstrated the approach efficiency on the nanostructured titanium specimens subjected to laser shock-wave treatment. Some experimental studies [9,26] reported that ultrasonic impact treatment (UIT) had resulted in the grain refinement and formation of a strong basal texture in the surface layer of titanium specimens. It was shown that both factors notably affected surface roughening and plastic strain localization. However, the individual contributions of these factors failed to be evaluated by the experimental techniques. This kind of data can be obtained numerically within the micromechanical approach [27]. In recent studies [27,28], we have numerically analyzed certain aspects of surface roughening and plastic strain localization in surface-treated steel and titanium specimens. The grain boundaries in the bulk of the materials were shown to cause stresses acting perpendicular to the loading axis, which gave rise to out-of-plane surface displacements forming ridges and valleys. The surface-hardened layer was shown to delay the surface roughness development. Since the mechanisms of dislocation glide are blocked in the nanostructured surface layer, it was treated as an amorphous layer. Using this idealized model, we have concluded that the nanostructured surface layer smoothes surface roughening by suppressing low-scale displacements.

This paper continues numerical investigations along these lines. A step forward in this direction is the development of three-dimensional microstructural models taking into explicit account the microstructural features of UIT-modified surface layers in a realistic way. In this contribution the deformation behavior of UIT-hardened commercially pure titanium under uniaxial tension is studied numerically using three-dimensional polycrystalline models with explicit consideration of the surface layer grain structure and texture. This research is aimed at gaining a better understanding of the individual and combined effects that the grain size and texture have on the micro- and mesoscale deformation-induced roughness, stress-strain evolution, and plastic strain localization under loading.