Direction Of Plastic Flow Research Articles

Crack Tip Profiles Generated by Anisotropic Damage

A variety of crack tip profiles could appear under the fracture processes controlled by anisotropic damage laws. The modelling on damage generated crack tip pro files plays a significant role in the design of fracture resistant materials. An anisotropic damage evolution law is proposed herein which takes into account the deterioration effects on polymers by plastic flow, stress triaxiality and mitial draw direction. When combined with a hyperelastic and viscoplastic constitutive framework at finite deformation, the pres ent damage theory enables us to simulate numerically the crack tip profiles for both plane strain small scale yield (SSY) and single edge cracked panel (SECP) geometries. Five typ ical crack tip profiles are generated by different settings of anisotropic damage parameters. They are featured by: crack tip superblunting, branching or spearhead profile, trident shape damage channeling, sharp notch and blunted notch with possible material detach ment.

Symmetry‐preserving return mapping algorithms and incrementally extremal paths: A unification of concepts

AbstractIn this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo‐internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.

An Isotropic Hardening Elastoplastic Model for Sand Considering the Stress Path Dependency in Three-Dimensional Stresses

ABSTRACT An isotropic hardening elastoplastic constitutive model for sand is developed by extending the model for clay proposed before. This model for sand (named tij-sand model) can precisely take into consideration the influence of intermediate principal stress on the deformation and strength characteristics by using the concept of the mechanical quantity tij and the influence of stress path on the direction of plastic flow by dividing the plastic strain increment into two components, in the same way as the previous model for clay (tij -clay model). In the present paper, a new “plastic work based on tij” W*p is defined, and it is experimentally shown that W*p is proper as the quantity of state for sand. Then, the model for sand is formulated by employing W*p as the strain hardening parameter, in place of the plastic volumetric strain ɛvp in the model for clay. The validities of the model are confirmed by various shear and consolidation tests under triaxial compression, triaxial extension and three different principal stresse conditions and stress probe tests under triaxial compression and extension conditions. All of the soil parameters of the model can be determined by a conventional triaxial compression test after loading-unloading-reloading isotropic consolidation.

Neodymium—iron—boron permanent magnets prepared by rapid solidification

The preparation of Nd-Fe-B permanent magnets by rapid solidification processing is described. The initial rapid quench is typically carried out by melt spinning; magnetic hardening can be achieved either by quenching directly from the melt or by annealing an overquenched precursor. In both instances, optimum permanent magnet properties are associated with the formation of a uniform, finely crystalline (<100 nm diam) microstructure consisting primarily of the Nd2Fe14B phase. Consolidation of the rapidly solidified material into isotropic magnets can be achieved by conventional cold compaction of the powder with a resin binder or by hot pressing to full density. Owing to the extremely fine grain size, orientation of the isotropic ribbons by grinding followed by magnetization would be extremely difficult. Crystallographic anisotropy can be achieved, however, by hot deformation. Alignment occurs entirely by thermomechanical means with rotation of the easy crystallographic direction normal to the direction of plastic flow. Energy products to 40 MGOe have been achieved by this technique. Properties of the various types of magnets prepared from this rapidly solidified material are presented as is microstructural data for the material at key points in the manufacturing process.

A critical assessment of methods of correcting for drift from the yield surface in elasto‐plastic finite element analysis

AbstractThe analysis of elasto‐plastic boundary value problems using the finite element method involves many discretizations. These lead to the problem of yield surface drift in which the stress state predicted at the end of an elasto‐plastic increment of loading does not lie on the current yield surface. As such discrepancies are comulative it is important to ensure that the stresses are corrected back to the yield surface during each increment of loading.In this paper five methods of accounting for this drift are examined. These involve correcting the stresses by projecting back along the plastic flow, the total strain increment and the accumulated effective stress direction. In addition a ‘correct’, method which accounts for the changes in elastic strains which accompany any stress correction is considered. This method is theoretically more sound than the other approximate approaches. All five methods have been used in finite element analyses of the stress changes that occur adjacent to a single pile installed in a uniform deposit of soil on pile loading. The soil was assumed to be normally consolidated and was modelled using a form of modified Cam Clay. Comparison of these results with an analysis, in which yield surface drift was negligible indicated that only the ‘correct’ method and the method involving projecting back along the plastic flow direction give accurate predictions. Substantiai errors occur if the other methods of correcting for yield surface drift are employed. It is recommended that the ‘correct’ method be adopted for finite element calculations.

Geological aspects of deformation in continental shear zones

Abstract A method of kinematic analysis of structures, microstructuresand mineral preferred orientations, initially devised in the study of peridotites, has been applied to crustal rocks bearing evidence of large strains produced in metamorphic environments. Three tectonic lineaments (Angers-Lanvaux, Montagne Noire and Maydan) were selected. They illustrate a general situation arising in continental crusts when they are deformed by ductile transcurrent fault systems. The Angers-Lanvaux structure is bilaterally symmetric; its dominant feature is the horizontal stretching lineation which is parallel to the fold axes. The foliation and slaty cleavage in the most surficial formations wrap around the axis of the whole structure. The folds in the slates away from the axis also exhibit axes parallel to the general trend, but no stretching lineations. These folds are attributed to crustal shortening in a direction normal to the ductile fault. In the Montagne Noire recumbent folds are thrusted away from the axis of the structure over at least 25 km. The metamorphism is also centered on the structure and symmetrically reduced away from it. The core of the structure is occupied by a strongly lineated orthogneiss, cut by a late intrusive granite. The Maydan axial zone displays clear evidence of partial melting at various scales within the deformed gneisses: (1) in gashes perpendicular to the stretching lineation which in these anatectic formations tends to plunge at more than 45°; (2) in bands of deformed pegmatites; and (3) possibly in granites which on the one hand intrude the surrounding formations and on the other converge with increasing deformation on the fault zone. The quartz preferred orientations and microstructures in quartzite layers from Angers indicate that the plastic flow plane and direction lie, respectively, close to the foliation and lineation, the slight departure is ascribed to a flow with a rotational shear component. All this suggests a general model for the origin of such ductile zones. The horizontal relative displacement of crustal blocks along a ductile band is responsible for its overall steeply dipping foliation and horizontal lineations. Viscous heating progressively tends to concentrate the plastic flow along its axis. It is also responsible for the development of metamorphism and of anatexis at depth; the partially melted rocks tend to rise, building at shallower depth the arched structure in the axis of the ductile zone, with a continuing flowage parallel to this axis probably now in the solid state; they can also intrude the surrounding terrain as undeformed batholiths. The folds parallel to the stretching lineation in the axial zone are explained by the fact that, due to the escape of anatectic melts, the formations at depth flow in a narrowing channel. The upwelling of the axial structure induces a compression with folding in the surrounding sedimentary formations and gravity nappe sliding away from the axis.

The effects of crack tip plastic flow directions upon microscopic dimple shapes

Precision matching of fracture surfaces formed by microvoid coalescence has shown that mating dimples seldom have identical shapes. The differences in shapes has been used to indicate the differences in plastic flow on either side of the crack tip during crack growth, and this in turn has been used to give preliminary indications of the stress directions and relative magnitudes at the crack tip. The differences in dimple shapes caused by fracture Modes I, IIand combinations of these are discussed. Eight modes of microvoid coalescence have been found. Two new modes are introduced. Six more are predicted.

Plastic Flow in Piercing Process

Plastic flow of metals was measured from the beginning to the end of piercing process. On the steady of plastic flow, the material, located farther than a distance equal to half the diameter of the die from the punch, was not in the state of plastic deformation, and the dead metal under the punch was not found when the area reduction was more than 50%. At the beginning and the end of piercing process, plastic flow directions and strains were determined during small stepwise deformation process from distorted grid lines on the cross section, and especially the forming process of the dead metal was studied.