Dislocation pileups in small grains

While the grain size effect (GSE) is universally observed in polycrystalline metals and alloys, extended dislocation pileups (DPUs) at grain boundaries (GBs) are rarely observed. Although this discrepancy was noticed over 50 years ago, DPUs are still widely accepted as the explanation for the GSE, often expressed as the Hall-Petch (HP) relationship. To provide a quantitative assessment of the pileup hypothesis, four classical pileup models were compared to three sets of numerical calculations, spanning a grain size range from 25 nm to 25mm. To do so, the stress field and Peach-Köhler force for short dislocation segments and circular dislocation loops were calculated as closed-form expressions and simplified to the case of pileups. Published values for the Hall-Petch constant provide the reference for estimating the critical tip stress for transmission of plastic strain from one grain to its neighbour. The results are compared in terms of consistency between models and between models and experiments. Different assumptions on the pileup geometry induce important variations in the results. Tendencies found in the numerical models resemble the trends marked in compilations of experimental results; predicted values for dislocation density and plastic shear upon yielding disagree with commonly accepted values. Added to the scarceness of experimental observation, the analysis indicates that DPUs play a role in polycrystal plasticity but do not consistently explain the GSE.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Maria Santofimia Navarr

Optimization of crystallographic texture for sheet-forming applications using Taylor-based Models

Plastic deformation of metallic materials is an inherently anisotropic process as a result of the presence of preferential orientations in their crystallographic texture. Crystal plasticity modeling, which allows simulating the response of polycrystal aggregates taking into account their texture and other microstructural parameters, has been extensively used to predict this behavior. In this work, crystal plasticity models are used to deal with the opposite problem: given a desired behavior, determine how to modify a texture to approximate this behavior in the most efficient way. This goal can be expressed as an optimization problem, in which the objective is to find the texture with the best formability properties among all the possible ones. An incremental optimization method, based on the gradient descent algorithm, has been developed and applied to different initial textures corresponding to typical steel and aluminum sheet products. According to expectations, the textures found present a stronger γ fiber component. Moreover, the method sets the basis for the development of more complicated optimization schemes directed toward optimizing specific materials and forming processes.(OLD) MSE-

Grain boundary character distribution derived from three-dimensional microstructure reconstruction

Manual serial sectioning which includes consecutive steps of sample preparation and Electron Back Scattering Diffraction (EBSD) measurement was employed to extract the twodimensional (2D) sections of a pure nickel sample and to reconstruct the three-dimensional (3D) microstructure. A general alignment algorithm based on the minimization of misorientation between two adjacent sections has been developed to accurately align the sections. By employing this alignment algorithm, any in-plane (translational) and rotational misalignment as well as the planparallelity can be corrected. Surface triangulation technique was used to reconstruct the grain boundary surfaces. The Grain Boundary Character Distribution (GBCD) was derived from reconstructed grain boundaries. The results show that a smoother grain boundary plane can be obtained after precise translational and rotational alignment and correction of planparallelity. The relative grain boundary energy was computed as a function of the five grain boundary parameters based on equilibrium at triple lines. The results show that the grain boundary planes carrying a ?3 type misorientation are dominantly parallel to the {111} crystal plane, which indicates the presence of coherent twin boundaries. It was observed that coherent ?3 type boundaries exhibit the minimum relative grain boundary energy, which is approximately 57% smaller than the average of all ?3 boundaries, including also incoherent twin boundaries.Materials Science and EngineeringMechanical, Maritime and Materials Engineerin

A multivariate grain size and orientation distribution function: Derivation from electron backscatter diffraction data and applications

Two of the microstructural parameters most influential in the properties of polycrystalline materials are grain size and crystallographic texture. Although both properties have been extensively studied and there are a wide range of analysis tools available, they are generally considered independently, without taking into account the possible correlations between them. However, there are reasons to assume that grain size and orientation are correlated microstructural state variables, as they are the result of single microstructural formation mechanisms occurring during material processing. In this work, the grain size distribution and orientation distribution functions are combined in a single multivariate grain size orientation distribution function (GSODF). In addition to the derivation of the function, several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, as well as in the generation of representative volume elements for full-field models and as input in simulations using mean-field methods.Team Erik OffermanTeam Jilt Sietsm

Fully automated orientation relationship calculation and prior austenite reconstruction by random walk clustering

Two new methods, one for determining the experimentally observed Orientation Relationship (OR) and another for reconstructing prior austenite phase, are proposed. Both methods are based on the angular deviation of the OR at the grain boundaries. The first algorithm identifies the optimum OR using the misorientation distribution of the entire scan i.e. without manual selection of parent grains. The second algorithm reconstructs the parent phase using a random walk clustering technique that identifies groups of closely related grains based on their angular deviation of the OR.Materials Science and EngineeringMechanical, Maritime and Materials Engineerin

Measuring plasticity with orientation contrast microscopy in aluminium 6061-T4

Orientation contrast microscopy (i.e., electron backscattered diffraction, EBSD) was employed to monitor the plastic strain in loaded tensile samples of aluminium alloy Al6061 in T4 condition. The kernel average misorientation (KAM) is known to be an appropriate parameter in orientation contrast microscopy which has the potential to characterise the plastic strain by monitoring the local misorientations. This technique was applied here to gauge the extent of the plastic zone around a fatigue crack. To establish the magnitude of strain (which can be identified by the KAM parameter), a series of tensile samples were strained in the range of 1% to 25%. KAM maps were compared, and the average misorientations were related to the tensile strain values. The KAM distribution functions for all the strained samples were derived from a large scanned area. In addition, Vickers microhardness tests were conducted for these series of samples. This allowed the comparison of the mesoscopic plastic strain measured by Vickers microhardness with the micro plastic strain locally obtained by KAM. Noise was observed in the average KAM values up to a plastic strain of 1.5%. For the plastic strain exceeding 1.5%, noise no longer dominates the KAM map, and a positive—though not linear—correspondence between plastic strain and KAM was observed. The observed plastic zone at the tip of the fatigue crack by micro-Vickers hardness measurements was about an order of magnitude higher than the plastic zone observed on the KAM maps. In view of the calibration of KAM values on the tensile samples, it could be concluded that in the larger area of the plastic zone, the strain did not exceed the critical value of 1.5%(OLD) MSE-1(OLD) MSE-

The Role of Parent Phase Topology in Double Young–Kurdjumow–Sachs Variant Selection during Phase Transformation in Low-Carbon Steels

The present paper investigates the role of parent phase topology on a crystallographic variant selection rule. This rule assumes that product phase nuclei appear at certain grain boundaries in the parent structure, such that a specific crystallographic orientation relationship is observed with both parent grains at either side of the grain boundary. The specific crystallographic orientation correspondence considered here is the Young–Kurdjumow–Sachs (YKS) orientation relationship <112>90◦ (which exhibits 24 symmetrical equivalents). The aforementioned relationship is characteristic of phase transformations in low-carbon steel grades. It is shown that, for different parent phase textures, ~20% of the grain boundaries comply with the double YKS condition allowing for a tolerance of 5◦, ignoring the presence of topology in the parent phase microstructure. The presented model allows for connecting the presence of a specific parent phase topology with the condition of the double YKS variant selection rule in a number of practical cases: (i) for hot rolled Ti–Interstitial Free (IF) steel with and without Mn addition, (ii) for cold rolled IF steel exhibiting very strong texture memory after forward and reverse α ⇋ γ phase transformation and (iii) for a martensitic transformation in a Fe–8.5% Cr steel. It is shown that the double YKS variant selection criterion may explain several specific features of the observed transformation textures, while assuming a non-correlated arbitrary pair topology of the parent austenite structure (implying that for N parent orientations N/2 pairs are selected in an arbitrary manner).Team Jilt Sietsm

A New Electron Backscatter Diffraction-Based Method to Study the Role of Crystallographic Orientation in Ductile Damage Initiation

The third generation of advanced high strength steels shows promising properties for automotive applications. The macroscopic mechanical response of this generation can be further improved by a better understanding of failure mechanisms on the microstructural level and micro-mechanical behavior under various loading conditions. In the current study, the microstructure of a multiphase low silicon bainitic steel is characterized with a scanning electron microscope (SEM) equipped with an electron backscatter diffraction detector. A uniaxial tensile test is carried out on the bainitic steel with martensite and carbides as second phase constituents. An extensive image processing on SEM micrographs is conducted in order to quantify the void evolution during plastic deformation. Later, a new post-mortem electron backscatter diffraction-based method is introduced to address the correlation between crystallographic orientation and damage initiation. In this multiphase steel, particular crystallographic orientation components were observed to be highly susceptible to micro-void formation. It is shown that stress concentration around voids is rather relaxed by void growth than local plasticity. Therefore, this post-mortem method can be used as a validation tool together with a crystal plasticity-based hardening model in order to predict the susceptible crystallographic orientations to damage nucleation.(OLD) MSE-3(OLD) MSE-

Quantitative correlation between slip patterning and microstructure during tensile elongation in 6xxx series aluminum alloy

To the purpose of evaluating the effect of deformation on the microstructure, aluminum structures were analyzed on tensile strained samples extended to 25% elongation. In the substructure of these deformed samples linear slip patterns were observed, generally confined to the bulk of the grain. In order to study the crystallographic aspect of these slip patterns, two methods were applied based on orientation contrast microscopy (EBSD). The first method is the statistical analysis of stereological nature, which allows us to determine the incidence of certain crystallographic planes with the slip patterns. In other to corroborate the statistical method, also a 3D analysis was carried out on two perpendicular planes of observation (TD and ND sections). The results of both methods were in a very good agreement. It was found that the linear features are predominantly parallel to the {111} crystal planes, although the frequency of {111} planes was not exclusive; also other crystal planes such as {112} and {110} are involved. These observations give a stronger statistical basis for similar observations earlier made by TEM on much smaller fields of observation.Materials Science and EngineeringMechanical, Maritime and Materials Engineerin

Thermo-mechanical fatigue lifetime assessment of spheroidal cast I\iron at different thermal constraint levels

In previous work on the thermo-mechanical fatigue (TMF) of compacted graphite iron (CGI), lifetimes measured under total constraint were confirmed analytically by numerical integration of Paris’ crack-growth law. In current work, the results for CGI are further validated for spheroidal cast iron (SGI), while TMF tests at different constraint levels were additionally performed. The Paris crack-growth law is found to require a different CParis parameter value per distinct constraint level, indicating that Paris’ law does not capture all physical backgrounds of TMF crack growth, such as the effect of constraint level. An adapted version of Paris’ law is developed, designated as the local strain model. The new model considers cyclic plastic strains at the crack tip to control crack growth and is found to predict TMF lifetimes of SGI very well for all constraint levels with a single set of parameters. This includes not only full constraint but also over and partial constraint conditions, as encountered in diesel engine service conditions. The local strain model considers the crack tip to experience a distinct sharpening and blunting stage during each TMF cycle, with separate contributions to crack-tip plasticity, originating from cyclic bulk stresses in the sharpening stage and cyclic plastic bulk strains in the blunting stage.Emerging Materials(OLD) MSE-3(OLD) MSE-