Deformation-induced Surface Roughening Research Articles

Experimental and Numerical Investigation of Mesoscale Deformation-Induced Surface Roughening in Polycrystalline Metals and Alloys (Review)

Experimental and Numerical Investigation of Mesoscale Deformation-Induced Surface Roughening in Polycrystalline Metals and Alloys (Review)

Deformation-Induced Surface Roughening of an Aluminum-Magnesium Alloy: Experimental Characterization and Crystal Plasticity Modeling.

The deformation-induced surface roughening of an Al-Mg alloy is analyzed using a combination of experiments and modeling. A mesoscale oligocrystal of AA5052-O, obtained by recrystallization annealing and subsequent thickness reduction by machining, that contains approx. 40 grains is subjected to uniaxial tension. The specimen contains one layer of grains through the thickness. A laser confocal microscope is used to measure the surface topography of the deformed specimen. A finite element model with realistic (non-columnar) shapes of the grains based on a pair of Electron Back-Scatter Diffraction (EBSD) scans of a given specimen is constructed using a custom-developed shape interpolation procedure. A Crystal Plasticity Finite Element (CPFE) framework is then applied to the voxel model of the tension test of the oligocrystal. The unknown material parameters are determined inversely using an efficient, custom-built optimizer. Predictions of the deformed shape of the specimen, surface topography, evolution of the average roughness with straining and texture evolution are compared to experiments. The model reproduces the averaged features of the problem, while missing some local details. As an additional verification of the CPFE model, the statistics of surface roughening are analyzed by simulating uniaxial tension of an AA5052-O polycrystal and comparing it to experiments. The averaged predictions are found to be in good agreement with the experimentally observed trends. Finally, using the same polycrystalline specimen, texture-morphology relations are discovered, using a symbolic Monte Carlo approach. Simple relations between the Schmid factor and roughness can be inferred purely from the experiments. Novelties of this work include: realistic 3D shapes of the grains; efficient and accurate identification of material parameters instead of manual tuning; a fully analytical Jacobian for the crystal plasticity model with quadratic convergence; novel texture-morphology relations for polycrystal.

Quantification of Mesoscale Deformation-Induced Surface Roughness in α-Titanium

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 Rd and the corresponding in-plane plastic strain. The standard roughness parameters Ra and RRMS 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 DF changes with the subsection strains in a sawtooth fashion, with an abrupt drop in the neck region. The descent portions of the DF dependences are supposedly related to the appearance of low-frequency components in the structure of the surface profiles.

The relationship between mesoscale deformation-induced surface roughness, in-plane plastic strain and texture sharpness in an aluminum alloy

Experimental and numerical studies are performed to reveal an interrelation between mesoscale deformation-induced surface roughening and in-plane plastic strain in an aluminum alloy. Experimentally, roughness evolution in selected subsections of a uniaxially loaded specimen is examined using a stop-and-study technique. The experimental analysis is complemented by the micromechanical simulations for deformation-induced surface roughening in model polycrystals, with special attention being given to the texture effect on roughness characteristics. The experimental and numerical roughness patterns are analyzed in terms of a relative roughness parameter calculated as a ratio of the rough profile length to the profile evaluation length. This parameter is found to correlate exponentially with in-plane plastic strain with the coefficient of determination 0.99, which implies a strong interrelation between the two quantities. The results prove the assumption that in-plane plastic strains accumulated in a loaded material can be evaluated from the estimations of mesoscale surface roughness.

A Correlation between Deformation-Induced Surface Roughness and In-Plane Plastic Strain in an Aluminum Alloy at the Mesoscale

Experimental and numerical studies on deformation-induced surface roughening in a commercial purity aluminum alloy are presented and discussed. Mesoscale surface profiles evolving in the experimental and numerical specimens in the course of tension are processed to reveal a correlation between roughness characteristics and in-plane plastic strains at the mesoscale. A dimensionless parameter calculated as a ratio of the rough profile length to the profile evaluation length has been used for quantitative estimations of the mesoscale roughness patterns. The dimensionless roughness parameter is shown to depend exponentially on the in-plane plastic strains at the mesoscale. The results support an early assumption that in-plane plastic strains accumulated in a loaded material can be evaluated from the estimations of mesoscale surface roughness.

The effect of texture sharpness on deformation-induced surface roughening in α-titanium

The deformation behavior of hexagonal metals is known to be strongly affected by a material texture. This paper aims at understanding the effect of a basal texture on the deformation-induced surface roughness in α-titanium. The effect of the basal texture severity on the deformation behavior is estimated for polycrystals characterized by the same grain geometry and different crystallographic orientations. For this purpose, three-dimensional polycrystalline models with the grain morphology and crystallographic orientations integrated explicitly are constructed using the step-by-step packing method. The texture severity is shown to strongly affect mesoscale roughness patterns. A more pronounced basal texture leads to suppression of the microscale surface roughness formed by displacements of individual grains perpendicular to the free surface (the orange peel pattern) and mesoscopic surface roughness formed by the displacements of grain groups. The basal texture reduces the material ability to deform perpendicular to the loading axis, while the prismatic slip gives rise to in-plane shear banding.

A microstructure-based mechanical model of deformation-induced surface roughening in polycrystalline α-titanium at the mesoscale

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.

MESOSCALE DEFORMATION-INDUCED SURFACE PHENOMENA IN LOADED POLYCRYSTALS

The paper reviews the results of numerical analyses for the micro-and mesoscale deformation-induced surface phenomena in three-dimensional polycrystals with the explicit account for the grain structure. The role of the free surface and grain boundaries in the appearance of the grain-scale stress concentrations and plastic strain nucleation is illustrated on the examples of aluminum polycrystals. Special attention is paid to the discussion of mesoscale deformation-induced surface roughening under uniaxial tension.

On the definition of RVE size in simulations of mesoscale deformation-induced surface roughening in polycrystals

The mesoscale deformation-induced surface roughening is formed by grain clusters involved in collective out-of-plane displacements. In order to reproduce these processes in simulations by the crystal plasticity finite element method, a polycrystalline structure is introduced into consideration explicitly. A topical issue related to this kind of simulations is how many grains the model should contain to be a representative of the mesoscale. In this study, four polycrystalline models with different sizes and a number of grains are examined to determine the representative volume element capable of reproducing mesoscale deformation-related phenomena. It is shown that the range of plastic deformation where the model is applicable directly correlates with its size and a number of grains. The more grains are arranged along the axis of tension, the larger plastic strain the model is able to accommodate.

Mechanical Aspects of Deformation-Induced Surface Roughening in the Presence of Inclusions in a Subsurface Layer. Numerical Modeling

The mechanical aspects of deformation-induced surface roughening inherent in microstructural inhomogeneity are studied numerically using single inclusion models. Three-dimensional finite-element calculations of uniaxial tension are performed for a set of single inclusion models where a cubic-shaped inclusion is embedded into a homogeneous matrix. The inclusion-to-surface distance, tilt angle about the axis of tension, and the ratio between the matrix and inclusion elastic-plastic properties are varied in different combinations to study the effects which these parameters have on the development of out-of-plane surface displacements under uniaxial tension. It has been shown that all stress and strain tensor components in the vicinity of inclusions take on nonzero values, including those directed across the load axis. Thus, the free surface becomes rough under the action of internal forces originated from the inhomogeneous stress-strain fields. Some illustrative examples of surface roughening under uniaxial tension are shown for multiple ellipsoidal inclusions periodically arranged in a subsurface layer of an elastic-plastic material.

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

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.

Numerical study of the texture effect on deformation-induced surface roughening in titanium polycrystals

The influence of a texture on the mesoscale deformation-induced surface roughening in titanium polycrystals is studied using direct microstructure-based simulations. Relying on the experimental data for commercial purity titanium, equiaxed grain conglomerates are generated by the method of step-by-step packing. The grain constitutive behavior is described in terms of crystal plasticity, with the grain orientations being assigned randomly or representing a basal texture. The micro- and mesoscale roughness evolution in the model polycrystals under uniaxial tension is calculated using ABAQUS/Explicit. In order to quantify mesoscale roughening, a dimensionless roughness parameter is calculated for a set of experimental and numerical roughness profiles evolving in the course of tension. The mesoscale roughness parameter is shown to grow nonlinearly with the plastic strain of the evaluated mesoscale regions. Particularly, it begins increasing rapidly in the region of neck formation well before necking becomes macroscopically evident. The basal texture is shown to significantly affect the plastic strain localization and roughness patterns. The mesoscale roughness, strongly pronounced in the untextured polycrystal, is mostly suppressed in the presence of texture. A set of in-plane shear bands are formed in the textured polycrystal at an angle of 45° to the tensile axis much like those observed experimentally.

Plastic strain localization in surface-hardened titanium polycrystals

In this paper, features of plastic strain localization in commercial purity titanium surface-hardened by ultrasonic impact treatment (UIT) are numerically investigated. Three- dimensional polycrystalline structures inherent in unhardened and UIT surface-hardened titanium specimens are generated by a step-by-step packing method. For taking into account the deformation mechanisms at the micro- and mesoscales, constitutive equations describing a nonlinear behavior of individual grains are constructed using crystal plasticity theory. Quasi-static boundary value problems are solved in a dynamic statement using ABAQUS\\Explicit finite-element package to simulate uniaxial tension of the model polycrystalline specimens. Based on the calculation results, conclusions are drawn on the effect of the UIT surface- hardened layer on the plastic strain localization and deformation-induced surface roughening in model polycrystals.

Early prediction of macroscale plastic strain localization in titanium from observation of mesoscale surface roughening

The numerical and experimental investigations have been performed to establish a correlation between local strains and mesoscale deformation-induced surface roughening in commercial purity titanium specimens. The evolution of surface profiles in selected regions of the specimens is examined in the course of uniaxial tension. Complementing the experimental studies, crystal plasticity finite-element simulations of deformation-induced surface roughening are performed for a model polycrystal. It has been shown that a series of out-of-plane surface displacements characterized by different amplitudes and frequencies are formed in the experimental and computational specimens under tension. Roughening intensifies on a larger scale when smaller length scale deformation mechanisms are exhausted. In order to quantify the multiscale surface patterns a dimensionless roughness parameter has been proposed. Unlike the traditional methods of roughness assessment, unfiltered profiles are analyzed to take into account the deformation mechanisms that are at work at different length scales. The dimensionless roughness parameter is shown to be sensitive to and well correlated with the local plastic strains. In the region of macroscopic necking, the mesoscale roughness begins to increase nonlinearly well ahead of the visible evidence of the macroscale strain localization, while in the other regions it ceases to increase at all. The results support the assumption that the plastic strain localization and fracture can be predicted early from estimations of mesoscale surface roughness.

Improving Hydro-formability of a Ferritic Stainless Steel Tube Through Severe Plastic Deformation

The aim of this work is to improve the hydro-formability of a 409L ferritic stainless tube through a treatment involving severe plastic deformation followed by annealing. For this purpose, the variation in hydro-formability is determined in terms of parameters like the circumferential R-value and the circumferential elongation after application of the abovementioned treatment. In addition, the deformation-induced surface roughening of the tube, called ridging, is measured through tension tests before and after the treatment. Moreover, the evolution in tube texture caused by the treatment is studied to reveal the relationship between the hydro-formability parameters and the texture. The results show that the treatment dramatically improves the hydro-formability through a marked modification in texture. For example, the emergence of the {110}〈100〉 texture component through the present treatment causes a noticeable increase in the circumferential elongation and the circumferential R-value of the tube while decreasing the degree of ridging.

Deformation-induced surface roughening of an Al-Mg alloy

We analyze the deformation-induced surface roughening of an Al-Mg alloy. One aspect of our work is an effort to model the exact roughening behavior of a mesoscale-size specimen that contains a small number of grains. Such a specimen is obtained using prestrain, recrystallization annealing and subsequent machining. It contains one layer of grains through the thickness and is tested under uniaxial tension. A laser confocal microscope is then used in order to measure the surface profile of a deformed specimen. We apply crystal plasticity finite element method to a voxel model of a given specimen. The exact arrangement of grains in the voxel model is reconstructed from a pair of electron backscatter diffraction (EBSD) scans using a custom-developed shape interpolation procedure. The material properties of the Al-Mg alloy are found using an efficient black-box optimizer. The exact shape of the deformed specimen wasn’t fully captured, however results on average surface roughness show good matching between model and experiment.

Micromechanical model of deformation-induced surface roughening in polycrystalline materials

A micromechanical model has been developed to describe deformation-induced surface roughening in polycrystalline materials. The three-dimensional polycrystalline structure is taken into account in an explicit form with regard to the crystallographic orientation of grains to simulate the micro- and mesoscale deformation processes. Constitutive relations for describing the grain response are derived on the basis of crystal plasticity theory that accounts for the anisotropy of elastic-plastic properties governed by the crystal lattice structure. The micromechanical model is used to numerically study surface roughening in microvolumes of polycrystalline aluminum and titanium under uniaxial tensile deformation. Two characteristic roughness scales are distinguished in the both cases. At the microscale, normal displacements relative to the free surface are caused by the formation of dislocation steps in grains emerging on the surface and by the displacement of neighboring grains relative to each other. Microscale roughness is more pronounced in titanium, which is due to the high level of elastic-plastic anisotropy typical of hcp crystals. The mesoscale roughness includes undulations and cluster structures formed with the involvement of groups of grains. The roughness is quantitatively evaluated using a dimensionless parameter, called the degree of roughness, which reflects the degree of surface shape deviation from a plane. An exponential dependence of the roughness degree on the strain degree is obtained.

Micro- and mesomechanical aspects of deformation-induced surface roughening in polycrystalline titanium

This article addresses the problem of multiscale surface roughening in commercial purity titanium subjected to uniaxial tension. In situ investigations of the evolution of grain- and mesoscale roughness in selected regions of titanium specimens were performed. Based on the experimental data obtained, 3D polycrystalline models with explicit consideration of grain structure were generated and implemented in finite-element calculations. Constitutive models of grains were constructed, using crystal plasticity theory to take into account the elastic-plastic anisotropy on the grain scale. The experimental and numerical results obtained have shown that a series of multiscale surface undulations are formed on the free surface of the specimen subjected to tension. The smallest out-of-plane surface displacements are attributed to intragrain dislocation glide. Larger displacements are associated with relative grain motion. The latter give rise to the formation of an orange peel pattern. The displacements of the two types are a microscale phenomenon. The largest surface displacements formed by the grain groups involved in out-of-plane and in-plane cooperative motion are referred to as the mesoscale roughness. The latter is found to correlate well with local strains of the specimen regions under examination. The main conclusion drawn from the experimental and numerical results is that it is the mesoscale that will furnish a clue to prediction of plastic strain localization and fracture of materials far in advance of the macroscale manifestation of these processes.

A micromechanical analysis of deformation-induced surface roughening in surface-modified polycrystalline materials

The effect of surface layer modification on the deformation-induced surface roughening in polycrystalline materials is investigated numerically. Three-dimensional constitutive models of as-received and surface-hardened polycrystals are constructed and implemented in finite-difference calculations. The free surface is shown to undergo out-of-plane displacements due to microscale stresses developing in the subsurface layer and acting across the free surface. The surface-hardened layer as thin as half the grain diameter efficiently suppresses grain-scale surface displacements. The thicker is the hardened layer, the smoother is the surface of the material.

Quantification of Three-Dimensional Surface Deformation using Global Digital Image Correlation

A novel method is presented to experimentally quantify evolving surface profiles. The evolution of a surface profile is quantified in terms of in-plane and out-of-plane surface displacements, using a Finite Element based Global Digital Image Correlation procedure. The presented method is applied to a case study, i.e. deformation-induced surface roughening during metal sheet stretching. The surface roughness was captured in-situ using a confocal optical profiler. The Global Digital Image Correlation method with linear triangular finite elements is applied to track the three-dimensional material movement from the measured height profiles. The extracted displacement fields reveal the full-field kinematics accompanying the roughening mechanism. Local deviations from the (average) global displacements are the result of the formation, growth, and stretching of hills and valleys on the surface. The presented method enables a full-field quantitative study of the surface height evolution, i.e. in terms of tracked surface displacements rather than average height values such as Root-Mean-Square or height-height correlation techniques. However, the technique does require that an initial surface profile, i.e. contrast, is present and that the contrast change between two measurements is minimal.