Using matrix methods to characterise the evolution of deformation induced surface roughness in aluminium sheet

Abstract

The deformation induced surface roughness of polycrystalline AA6022-T4 aluminium was evaluated with two different analysis protocols. The first determined the rms roughness R q with linear roughness profiles to be consistent with literature practice. When plotted against strain, the correlation coefficient indicated an excellent linear fit; however, further analysis revealed the roughening behaviour did not support the literature consensus of a linear relationship between plastic strain and R q . The second determined R q by matrix methods. This evaluation demonstrates that when R q data are acquired via linear profiles, they are strongly influenced by correlations. Conversely, matrix based methods sample all of the data and are unaffected by the presence of correlations. Eliminating the correlations in the profile data produced the same R q behaviour obtained with the matrix methods. An R q behaviour that exhibits saturation is more representative of the complexities observed in the plastic deformation process of a polycrystal.

A Study of the Fundamental Relationships between Deformation-Induced Surface Roughness and Strain Localization in AA5754

“…When the tensile axis of rolled sheet specimens lies in the transverse orientation to the RD, the evolved surface roughness tends to be slightly more severe than when the tensile axis is parallel to the RD. [17] Therefore, the scope of this study focused on samples deformed in the transverse direction.…”

“…The resulting matrix was then trimmed to a square 512 9 512-pixel (800 9 800-lm) 262,144-element array, to facilitate the matrix-based mathematical operations. [17] After conversion, the extreme values (taken to be values in the height data greater than ±6r, where r is the standard deviation for all the heights in that matrix) were filtered from the data sets. This step was necessary because some of the statistical parameters used to interpret the surface data are highly sensitive to outlier data points.…”

“…The statistical uncertainty associated with profilebased analysis can be minimized by extending the Rt parameter to a matrix form. [17] This is accomplished by creating a Euclidean distance matrix. [35] The construction of this matrix required subdividing a 512-row 9 512-column source matrix into smaller matrices consisting of 64 element cells (8 pixels/row 9 8 pixels/column).…”

“…[16] The results of a recent evaluation of deformationinduced surface roughness with plastic strain plainly demonstrated that the linear relationship between the surface root-mean-squared (RMS) roughness (Sq) and the plastic strain reported in the literature is a statistical artifact resulting from inadequate sampling. [17] That is, such a simple expression relating strain and deformation-induced surface roughness does not accurately reflect the true deformation behavior of the free surface of a polycrystalline material. The findings of this study [17] also reveal that the linear relationship between surface roughness and strain is a consequence of the methods used to acquire and analyze the roughness data.…”

“…[17] That is, such a simple expression relating strain and deformation-induced surface roughness does not accurately reflect the true deformation behavior of the free surface of a polycrystalline material. The findings of this study [17] also reveal that the linear relationship between surface roughness and strain is a consequence of the methods used to acquire and analyze the roughness data. The assessments of the roughening behavior in the literature are largely derived from sets of linear profiles; they express the surface roughness as the simple average of a single scalar roughness parameter that describes the dispersion of heights within the profiles about the mean (e.g., Ra, the arithmetic average roughness, or Rq, the RMS average roughness).…”