Quantitative Characterization of Boundary Roughness in Metals

The boundary migration during recrystallization is by nature a heterogeneous process and local structural variations form on recrystallization boundaries, as revealed from modern techniques such as synchrotron X-rays and advanced electron microscopy. The local structural variations, in the form of protrusions and retrusions, can provide a dragging/driving force due to the local boundary curvature and affect the further migration of recrystallization boundaries through the deformed matrix. In order to develop new understandings and models for boundary migration that take the heterogeneous local structural aspects into account, a detailed characterization is essential of partly recrystallized microstructures focusing on the local shapes of the boundaries, in particular on whether protrusions and retrusions are formed or not. Quantification of the “amount” of boundary roughness in the form of protrusions and retrusions is of importance for statistical investigations into the factors that potentially influence the recrystallization boundary roughening. A method is developed for quantitative characterization of 2-D line features. The area integral invariant (AII) is employed as a morphological variable to obtain information of local structural variations such as protrusions and retrusions formed on recrystallization boundaries. The AII value is directionindependent allowing unbiased characterization of morphological irregularities with both closed and non-closed boundary profiles. The length scale at which the rough features are characterized is determined by a parameter termed sampling radius used to measure the AII values. A number of roughness parameters are developed based on the AII dataset for a boundary or boundary segment, whose local morphological characteristics are represented by individual AII value acquired along the boundary or boundary segment. With the quantified boundary roughness at two length scales: 1 μm and 3 μm, the roughening behaviors of a large number of recrystallization boundaries are statistically analyzed and the effects of several parameters: materials purity, deformation strain, annealing temperature and boundary alignment direction, are evaluated. It is revealed that recrystallization boundaries in general are rough and the roughening behaviors of recrystallization boundaries are affected by the investigated parameters, more significantly at the length scale of 1 μm. It is found that the higher roughness is often associated with the higher migrating rates of recrystallization boundaries. A new method is presented to quantitatively characterize the morphology of graphite nodules in cast iron, as an extended application of the AII method to characterize the 2-D line features. This method develops a morphological variable “dispersion” to obtain information about local morphological characteristics that is subsequently merged into a parameter termed dispersion index, to represent the nodule’s morphology as a whole. The potential of the method is validated by quantifying the morphology of graphite nodules with complicated shape and by measuring the nodularity of an image with many graphite nodules. Project period: 2013.09-2016.08 Education: Doctor of Philosophy

[1]  R. Dauskardt,et al.  On the interpretation of the fractal character of fracture surfaces , 1990 .

[2]  Knut Conradsen,et al.  Boundary Fractal Analysis of Two Cube-oriented Grains in Partly Recrystallized Copper , 2015 .

[3]  F. J. Humphreys.  The nucleation of recrystallization at second phase particles in deformed aluminium , 1977 .

[4]  S. Schmidt,et al.  Watching the Growth of Bulk Grains During Recrystallization of Deformed Metals , 2004, Science.

[5]  S. Pizer,et al.  The Image Processing Handbook , 1994 .

[6]  B. Nowicki.  Multiparameter representation of surface roughness , 1985 .

[7]  Q. Liu,et al.  Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminium , 1998 .

[8]  Michael Kraus,et al.  Koch Snowflake , 2009, Encyclopedia of Database Systems.

[9]  N. Hansen,et al.  Microstructure and strength of nickel at large strains , 2000 .

[10]  D. J. Jensen,et al.  Through-thickness texture gradients in cold-rolled aluminum , 2000 .

[11]  N. Hansen,et al.  Initial stages of recrystallization in aluminium containing both large and small particles , 1981 .

[12]  B. H. Kaye.  Applied fractal geometry and powder technology , 1995 .

[13]  Daniel Cremers,et al.  Integral Invariants for Shape Matching , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  C. Labrecque,et al.  Review ductile iron: fifty years of continuous development , 1998 .

[15]  M. Avrami.  Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei , 1940 .

[16]  N. Costa,et al.  Influence of Graphite Nodules Geometrical Features on Fatigue Life of High-Strength Nodular Cast Iron , 2008 .

[17]  Manabu Tanaka,et al.  Fracture toughness and crack morphology in indentation fracture of brittle materials , 1996, Journal of Materials Science.

[18]  B. Mandelbrot,et al.  Fractal character of fracture surfaces of metals , 1984, Nature.

[19]  Sven Loncaric,et al.  A survey of shape analysis techniques , 1998, Pattern Recognit..

[20]  D. Juul Jensen,et al.  In-Situ Investigation of Local Boundary Migration During Recrystallization , 2014, Metallurgical and Materials Transactions A.

[21]  Wei Liu,et al.  Analysis of the growth of individual grains during recrystallization in pure nickel , 2009 .

[22]  D. Juul Jensen,et al.  Evolution of Microstructure and Texture during Annealing of Aluminum AA1050 Cold Rolled to High and Ultrahigh Strains , 2010 .

[23]  D. J. Jensen,et al.  Boundary migration during recrystallization: experimental observations , 2015 .

[24]  Guilin Wu,et al.  Automatic determination of recrystallization parameters based on EBSD mapping , 2008 .

[25]  K. Lücke,et al.  Orientation of recrystallized grains in strained aluminum single crystals , 1959 .

[26]  A. F. Padilha,et al.  Observations of grain boundary protrusions in static recrystallization of high-purity bcc metals , 2007 .

[27]  Niels Skat Tiedje,et al.  Graphite nodule count and size distribution in thin-walled ductile cast iron , 2008 .

[28]  W. B. Whalley,et al.  Three implementations of fractal analysis of particle outlines , 1989 .

[29]  John W. Cahn,et al.  The Impurity-Drag Effect in Grain Boundary Motion , 2013 .

[30]  A. F. Padilha,et al.  The growth of protrusions at the boundary of a recrystallized grain , 2006 .

[31]  R. Vandermeer,et al.  On the estimation of cahn-hagel interface migration rates , 1994 .

[32]  C. Maurice,et al.  Grain boundary mobilities during recrystallization of Al–Mn alloys as measured by in situ annealing experiments , 2005 .

[33]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[34]  W. Ludwig,et al.  Direct observation of grain boundary migration during recrystallization within the bulk of a moderately deformed aluminium single crystal , 2014 .

[35]  N. Hansen,et al.  Microstructural evolution in nickel during rolling from intermediate to large strains , 1993, Metallurgical and Materials Transactions A.

[36]  D. Kuhlmann-wilsdorf,et al.  Microstructural evolution in rolled aluminium , 1992 .

[37]  Yonghao Zhang,et al.  Three-dimensional investigation of recrystallization nucleation in a particle-containing Al alloy , 2012 .

[38]  E. Lauridsen,et al.  Recrystallization kinetics of individual bulk grains in 90% cold-rolled aluminium , 2003 .

[39]  D. Jensen.  Growth of nuclei with different crystallographic orientations during recrystallization , 1992 .

[40]  H. Poulsen,et al.  The three dimensional X-ray diffraction technique , 2012 .

[41]  E. Holm,et al.  Grain boundary interface roughening transition and its effect on grain boundary mobility for non-faceting boundaries , 2007 .

[42]  Satoru Yamamoto,et al.  On the Solidification Process of Nodular Cast Iron , 1977 .

[43]  Martin Allen,et al.  Measurement of boundary fractal dimensions: review of current techniques , 1995 .

[44]  D. Juul Jensen,et al.  Molecular dynamics simulations of grain boundary migration during recrystallization employing tilt and twist dislocation boundaries to provide the driving pressure , 2008 .

[45]  D. Stefanescu,et al.  Graphite shape characterisation in cast iron—from visual estimation to fractal dimension , 2002 .

[46]  L. Ryde,et al.  On the kinetics of recrystallisation in cold worked metals , 1989 .

[47]  A. Lyckegaard,et al.  In situ measurements of growth rates and grain-averaged activation energies of individual grains during recrystallization of 50% cold-rolled aluminium , 2011 .

[48]  Weilie Zhou,et al.  Scanning Microscopy for Nanotechnology: Techniques and Applications , 2007 .

[49]  N. Hansen,et al.  Recrystallisation of channel die deformed single crystals of typical rolling orientations , 2001 .

[50]  Sidnei Paciornik,et al.  Automatic Classification of Graphite in Cast Iron , 2005, Microscopy and Microanalysis.

[51]  P. Beck,et al.  Strain Induced Grain Boundary Migration in High Purity Aluminum , 1950 .

[52]  Brian Klinkenberg,et al.  A review of methods used to determine the fractal dimension of linear features , 1994 .

[53]  N. Moelans,et al.  Phase-field simulation study of the migration of recrystallization boundaries , 2013 .

[54]  M. E. Kassner,et al.  Current issues in recrystallization: a review , 1997 .

[55]  Michael L. V. Pitteway.  Algorithm for drawing ellipses or hyperbolae with a digital plotter , 1967, Comput. J..

[56]  M. Avrami.  Kinetics of Phase Change. I General Theory , 1939 .

[57]  S. Zucker,et al.  Evaluating the fractal dimension of profiles. , 1989, Physical review. A, General physics.

[58]  N. Moelans,et al.  A phase-field simulation study of irregular grain boundary migration during recrystallization , 2015 .

[59]  E. Holm,et al.  How Grain Growth Stops: A Mechanism for Grain-Growth Stagnation in Pure Materials , 2010, Science.

[60]  D. Kuhlmann-wilsdorf,et al.  Overview no. 96: Evolution of F.C.C. deformation structures in polyslip , 1992 .

[61]  D. Kuhlmann-wilsdorf,et al.  Low energy dislocation structures due to unidirectional deformation at low temperatures , 1986 .

[62]  G. Winther,et al.  Dislocation structures. Part I. Grain orientation dependence , 2007 .

[63]  Importance of Local Structural Variations on Recrystallization , 2013 .

[64]  D. Bérubé,et al.  High precision boundary fractal analysis for shape characterization , 1999 .

[65]  Joseph R. Davis,et al.  Properties and selection : irons, steels, and high-performance alloys , 1995 .

[66]  S. Dutch,et al.  Linear Richardson plots from non-fractal data sets , 1993 .

[67]  L. M. Alves.  Foundations of measurement fractal theory for the fracture mechanics , 2012 .

[68]  Q. Liu,et al.  Stored energy and structure in top-down processed nanostructured metals , 2009 .

[69]  F. Haessner.  Recrystallization of metallic materials , 1978 .

[70]  Johannes Wallner,et al.  Integral invariants for robust geometry processing , 2009, Comput. Aided Geom. Des..

[71]  S. Schmidt,et al.  Simulations of boundary migration during recrystallization using molecular dynamics , 2007 .

[72]  D. J. Jensen,et al.  Local boundary migration during recrystallization in pure aluminium , 2011 .

[73]  Hsun Hu,et al.  The Orientation Dependence of the Rate of Grain Boundary Migration , 1950 .

[74]  Roberto Enrique Boeri,et al.  Shape and Count of Free Graphite Particles in Thin Wall Ductile Iron Castings , 2002 .

[75]  D. Juul Jensen,et al.  Deformed metals – structure, recrystallisation and strength , 2011 .

[76]  D. J. Jensen,et al.  Growth rates and misorientation relationships between growing nuclei/grains and the surrounding deformed matrix during recrystallization , 1995 .

[77]  Yuichi Tanaka,et al.  Evaluation of Fatigue Limit of Spheroidal Graphite Cast Iron , 1995 .

[78]  Harumi Kosuge.  High purity aluminum. , 1988 .

[79]  Nacim Betrouni,et al.  Fractal and multifractal analysis: A review , 2009, Medical Image Anal..

[80]  K. Lücke,et al.  A quantitative theory of grain-boundary motion and recrystallization in metals in the presence of impurities , 1957 .

[81]  The fractal dimension of grain-boundary fracture in high-temperature creep of heat-resistant alloys , 1993, Journal of Materials Science.

[82]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[83]  D. J. Jensen,et al.  Grain boundary mobility during recrystallization of copper , 1997 .

[84]  D. Juul Jensen,et al.  Microstructural-Based Measurement of Local Stored Energy Variations in Deformed Metals , 2007 .