Geometric Compatibilities Research Articles

Effects of γ/γ lamellar interfaces on interlamellar crack propagation behaviors of TiAl alloys

Interlamellar fracture is one of the failure modes of fully lamellar (FL) TiAl alloys. Here, the effects of three types of γ/γ lamellar interfaces, which are termed true twin (TT), 120° rotational order fault (ROF), and pseudo-twin (PT), subjected to uniaxial tensile loading on the interlamellar crack propagation behaviors of an FL γ-TiAl alloy have been investigated by molecular dynamics method. The results show that the introduction of the PT and ROF interface weakens the tensile strength of single crystal TiAl, while the introduction of the TT interface can effectively improve the tensile strength of the material. Moreover, the cracks in the three interfaces exhibit different propagation behaviors and propagation rates. Specifically, the ROF and PT interfaces exhibit the most desirable and least desirable crack resistances, respectively, which are related to the geometric compatibilities of the interfaces and plastic deformation of crack tips. We also found that the sequence of fracture toughness (ROF > TT > PT) is consistent with that of the flow stresses (ROF > TT > PT). In addition, in the early stage of crack propagation, deformation twins serve as a toughening mechanism that reduces crack tip stress and retards crack extension.

Estimating of Bending Force and Curvature of the Bending Plate in a Three-Roller Bending System Using Finite Element Simulation and Analytical Modeling.

Many industries such as shipbuilding require steel bending plates in a wide range of radii, thus bending machines are often designed and produced on a custom basis in shipyards. From a design perspective, however, the bending force and the radius of the bending plate as a function of vertical displacement of the upper roller must be known. In this paper, a hybrid numerical–analytical approach is proposed to investigate the three-roller bending process for two plates of steel used in the naval industry. Firstly, the bending process is modeled using the finite element (FE) method and regression models for the bending force as a function of plate thickness and vertical displacement of the upper roller were constructed. Then, based on the findings from FE analysis, using the bent bar theory, two analytical expressions for the bending force were derived. Using geometric and deformation compatibilities, analytical expressions for the vertical displacement of the upper roller as a function of the curvature of the bending plate were also developed. The FE results suggest that the cross section of the plate is practically a plastic hinge in the tangent area of the upper roller and that the deformation compatibilities must be considered in order to estimate the curvature radius of the bending plate using analytical formulations. These results are of practical importance in designing rolling machines to estimate the setting parameters.

A Combined Cold Extrusion for a Drive Shaft: A Parametric Study on Tool Geometry.

Parametric investigations related to shoulder angle on tool geometry for a combined cold extrusion of a drive shaft, which consisted of spur gear and internal spline structures, were conducted through three-dimensional FE (finite element) simulations. The drive shaft was required to be about 92.00 mm for the face width of the top land on the spur gear part and roughly 22.70 mm for the groove depth of the internal spline section. AISI 1035 carbon steel material with a diameter of 50.00 mm and a length of 121.00 mm was spheroidized and annealed, then used as the initial billet material. A preform as an intermediate workpiece was adopted to avoid the excessive accumulation of plastic deformation during the combined cold extrusion. Accordingly, the cold forging process involves two extrusion operations such as a forward extrusion and a combined extrusion for the preform and the drive shaft. As the main geometric parameters influencing the dimensional quality and the deformed configuration of the final product, the two shoulder angles of θ1 and θ2 for the preform forging and the combined extrusion were both considered to be appropriate at 30°, 45°, and 60°, respectively. Using nine geometric parameter combinations, three-dimensional finite element simulations were performed, and these were used to evaluate the deformed features and the geometric compatibilities on the spur gear structure and the internal spline feature. Based on these comparative evaluations using the numerically simulated results, it is shown that the dimensional requirements of the target shape can be satisfied with the shoulder angle combination of (45°, 45°) for (θ1, θ2).

Evolutionary Hough Games for coherent object detection

In this paper we propose a novel, game-theoretic approach for finding multiple instances of an object category as sets of mutually coherent votes in a generalized Hough space. Existing Hough-voting based detection systems have to inherently apply parameter-sensitive non-maxima suppression (NMS) or mode detection techniques for finding object center hypotheses. Moreover, the voting origins contributing to a particular maximum are lost and hence mostly bounding boxes are drawn to indicate the object hypotheses. To overcome these problems, we introduce a two-stage method, applicable on top of any Hough-voting based detection framework. First, we define a Hough environment, where the geometric compatibilities of the voting elements are captured in a pairwise fashion. Then we analyze this environment within a game-theoretic setting, where we model the competition between voting elements as a Darwinian process, driven by their mutual geometric compatibilities. In order to find multiple and possibly overlapping objects, we introduce a new enumeration method inspired by tabu search. As a result, we obtain locations and voting element compositions of each object instance while bypassing the task of NMS. We demonstrate the broad applicability of our method on challenging datasets like the extended TUD pedestrian crossing scene.

Austenite–martensite interface in shape memory alloys

A two-scale phase field simulation is developed for austenite–martensite interface to understand the effects of crystalline symmetry and geometric compatibilities on the reversibility of structural phase transformations in shape memory alloys. It is observed that when the middle eigenvalue of martensite transformation strain is equal to zero, an exact austenite–martensite interface is formed with negligible elastic energy. On the other hand, when the middle eigenvalue is different from 0, an inexact interface between austenite and martensitic twin is formed, and the corresponding elastic energy increases with the increased magnitude of the middle eigenvalue, resulting in substantially higher energy barrier for austenite–martensite transformation, and thus higher thermal hysteresis in shape memory alloys.

Combinatorial search of thermoelastic shape-memory alloys with extremely small hysteresis width

Reversibility of structural phase transformations has profound technological implications in a wide range of applications from fatigue life in shape-memory alloys (SMAs) to magnetism in multiferroic oxides. The geometric nonlinear theory of martensite universally applicable to all structural transitions has been developed. It predicts the reversibility of the transitions as manifested in the hysteresis behaviour based solely on crystal symmetry and geometric compatibilities between phases. In this article, we report on the verification of the theory using the high-throughput approach. The thin-film composition-spread technique was devised to rapidly map the lattice parameters and the thermal hysteresis of ternary alloy systems. A clear relationship between the hysteresis and the middle eigenvalue of the transformation stretch tensor as predicted by the theory was observed for the first time. We have also identified a new composition region of titanium-rich SMAs with potential for improved control of SMA properties.

Perceptual organization with image formation compatibilities

The work presents a methodology contributing to boundary extraction in images of approximate polyhedral objects. We make extensive use of basic principles underlying the process of image formation and thus reduce the role of object-specific knowledge. Simple configurations of line segments are extracted subject to geometric–photometric compatibilities. The perceptual organization into polygonal arrangements is based on geometric regularity compatibilities under projective transformation. The combination of several types of compatibilities yields a saliency function for extracting a list of most salient structures. Based on systematic measurements during an experimentation phase the adequacy and degrees of compatibilities are determined. The methodology is demonstrated for objects of various shapes located in cluttered scenes.

A discrete element model for vibration analysis of mixed edge plates

In this paper, the free vibration analysis of plates with mixed edge boundaries is presented. A discrete element model is developed for the present study. In the solution process, the original domain is discretised into small subdomains with the admissible functions of each subdomain represented by sets of orthogonal polynomials. Higher-order polynomials in the set are generated using the Gram-Schmidt recurrence process. Continuity matrices derived from the geometric compatibilities between subdomains are used to couple the eigenvectors of adjacent subdomains. The global stiffness and mass matrices are considered to be the sum of the stiffness and mass matrices of the constitutive subdomains after pre- and post-multiplied by the respective continuity matrices. Convergence and comparison studies were carried out to demonstrate the accuracy and efficiency of the proposed method in solving this class of problems.

On The Use Of The Domain Decomposition Method For Vibration Of Symmetric Laminates Having Discontinuities At The Same Edge

A free vibration analysis of symmetrically laminated plates with mixed edge boundary conditions is presented. A highly efficient and accurate domain decomposition method is employed. To establish the model, the original domain is first assumed to be an assemblage of small subdomains, with the admissible functions of each subdomain represented by sets of orthogonal polynomials. These polynomials are generated by using the Gram-Schmidt procedure. The continuity matrices resulting from the geometric compatibilities between the subdomains are used to couple the eigenvectors of adjacent subdomains. The stiffness and mass matrices of each subdomain, after pre- and post-multiplying by the respective continuity matrices, are assembled to form the global stiffness and mass matrices. To demonstrate this method, the free vibrations of symmetrically laminated plates of various types of mixed edge boundaries are calculated.

The Lega Dembi gold mine: an example of shear zone-hosted mineralization in the Adola greenstone belt, Southern Ethiopia

In the Adola Gold District of Southern Ethiopia the outline of the contacts that separate the greenstone belt and the gneissic terrain defines regional scale ductile to brittle-ductile shear zones. Possibly economic mineralization is found to be controlled by these major shear zones. Mapping out and documenting the movement senses of these major shear zones in detail, therefore, was vital for the prediction of the nature and orientation of the minor structures that are likely to host gold deposits. Structural information combined with identification and mapping of suitable host rocks such as the Lega Dembi schists, can provide a powerful tool in exploration for gold in the Adola area. Such techniques are not only important in mineralized areas such as the Lega Dembi Gold Mine, where some, but not all, mineralized structures have been discovered, but also in unexplored terrains. Mapping at a scale of 1:25,000 resulted in detection of several superposed shearing events with both sinistral and dextral senses of displacement. These shear zones are expressed as ductile, brittle-ductile and brittle types. Study of geometric compatibilities between the structural elements viz., shear zones, tectonic lineations and folds helped in locating the Lega Dembi Gold Mine within a grossly N-S trending major ductile transcurrent sinistral shear zone. This has subsequently been reactivated and overlapped by N-S trending mesoscale shear zones with similar trend but of opposed sense of displacement. The formation of the later dextral shear zones took place under similar ductile conditions within a single but extended phase of deformation, D 2, that generated the reversed motion. Generally D 3 E-W wrench faults with minor WNW-ESE/WSW-ENE trending conjugate pairs and mesoscale D 4N-S/NE-SW trending conjugate systems of brittle to brittle-ductile shear zones have been recognized. Mineralization is hosted by quartz veinlets and stringers that propagated along mesoscale D 2 ductile to brittle-ductile shear zones.