Strain Localized Regions Research Articles

Dislocation structures in the strain localized region in fatigued 70/30 brass and the interaction with grain boundary

Long-term fatigue tests of polycrystalline 70/30 brass were carried out under low strain amplitudes in vacuum, and dislocation structures of the strain localized regions developed were examined by means of transmission electron microscopy In the planar dislocation structures, the strain localized regions (SLRs) bounded by a pair of parallel active glide layers were frequently observed in favorably oriented grains. Where the SLRs impinge on grain boundaries (GBs), extrusion-type deformations were sometimes formed notwithstanding the restraints of the neighboring grains. On the basis of observations, the mechanism of crack initiation at the GB is discussed.

Dislocation structure of strain localized region and fatigue crack initiation in 70/30 brass, 85/15 brass and pure copper.

Although a number of models for the formation of extrusions and intrusions have been proposed, most of them are not considered to be sufficient. It is not yet clear whether or not the same mechanism may be responsible for the formation of extrusions in 70/30 brass, 85/15 brass and pure copper with different capability of cross slip. In this paper, investigations on dislocation structures of strain localized regions and fatigue crack initiation in these metals subjected to a long term stress cycling in vacuum were carried out by means of transmission electron microscopy. The strain localized regions bounded by two adjacent active glide layers were observed in the favorably oriented grains. Such strain localized regions were in close association with the formation of extrusion and transcrystalline cracking. At the intersections of the strain localized regions and the grain boundaries, extrusion-type deformations were sometimes formed due to the restraints of slip motions by the neighbouring grains.

Stability against localization of softening into ellipsoids and bands: Parameter study

Strain-localization instabilities due to strain-softening which result from distributed damage such as cracking in heterogeneous brittle materials are analysed. Attention is restricted to the stability problem of equilibrium states. This problem is not equivalent to bifurcation of the equilibrium path, which may occur before stability of equilibrium is lost. The continuum is local but is enhanced by the localization limiter used in the crack band model, consisting of a lower bound on the minimum dimension of the strain-localization region, which is regarded as a material property. Presented are derivations of the critical state conditions for localization of initially uniform strain into ellipsoidal domains within an infinite continuum and into a planar band within a layer of finite thickness. These derivations are simpler than the previous Bažant's derivations of the general stability conditions for these localizations. A numerical parameter study of the critical states is made for a broad range of material properties as well as various initial stress states and relative sizes of the strain-softening region. The material is described by Drucker-Pragcr plasticity with strain-softening that is caused by yield limit degradation. The Hatter the ellipsoidal domain, or the larger the size of the body (layer thickness), the smaller is found to be the strain-softening slope magnitude at which the critical state is reached. A softening Drucker-Prager material is found to be stable against planar-band localizations in infinite continuum for a certain range of softening material parameters.

Dislocation structures in the strain localized region in fatigued 85/15 brass

The correlation between the formation of extrusions and the dislocation structures in polycrystalline 85/15 brass subjected to a long term stress cycling with a low strain amplitude in vacuum was examined by means of transmission electron microscopy. The overall dislocation structures consisted of two types of structures,i.e., copper-type and 70/30 brass-type. Within them the strain localized regions bounded by two closely located active slip layers were frequently observed. In these boundary layers appeared a fringe pattern which was suggestive of intensive slip. Extrusions were formed in close association with the two closely located layers, and the initiation and growth of fatigue cracks occurred along one of them. On the basis of these observations, the mechanism of extrusion formation and of fatigue crack initiation are discussed.

Strain analysis in machining using metallographic methods

Strain patterns in 4340 steel chips created during turning at speeds between 36 and 440 m/min (119 and 1442 sfpm) are examined metallographically. A new method, based on the grain elongation orientation in the chip, is developed for quantification of local strains created during plane strain deformation in the primary and secondary deformation zones. This method is applied to both continuous and to sawtooth type chips. Strains determined by this method compare well with strains computed from chip thickness measurements, but there appear to be systematic differences. Strain localization is evident in chips formed at the higher cutting speeds. This strain localization does not appear to extend to the rake face side of the chip. The shear angle calculated from the strain in the strain-localized regions compares favorably with the orientation of these regions.

A finite element analysis of the punch stretching of elastic-plastic circular discs.

The Stretching of peripherally clamped, thin, circular discs over rigid, cyrindrical punches is studied by means of an Updated Lagrangian type finite element method. The analysis is based on the elastic-plastic membrane theory ; it accounts for finite strain and displacement and embodies the classical J 2 flow law and the J 2 deformation theory. The geometry of the punch face varied between a hemispherical and a relatively shallow spherical (flat-bottomed) cap. Three models were employed to account for friction at the interface of the punch and disk. These were a no-friction, a full sticking condition and Coulomb friction hypothesis. The disk fails by excessive thinning. The region of strain localization and the rate at which the local neck grows are influenced by the punch geometry and the interfacial frictional conditions. The Coulomb friction and full-sticking models promote the formation of a local neck, and this is further accelerated the flatter the base of the punch. The material property n-value also affects the local neck. The calculations support the hypothesis that the higher the n-value, the better the material distributes the strain. It is also demonstrated that the result is not much affected by the different material models (J 2 F and J 2 D).

Strain localisation in biaxially stretched sheets containing compact defects—I: Experimental investigation

The influence of void formation at inclusion particles on strain localisation in biaxial stretching was explored in two different grades of low-carbon steel sheets. In a rimmed steel containing many inclusions with thicknesses in the range 10–20 μm, localisation was initiated by cavitation at the larger particles and its development usually involved shear-linking of two or more cavities at different levels in the sheet thickness direction. In an aluminium-killed steel containing few inclusions with thicknesses > 10μ m , the contribution of void formation to the initiation of strain localisation was less clear but, as with the rimmed steel, biaxial extension was terminated by ductile fracture involving growth and coalescence of cavities in inclusion-rich regions. With both steels, the regions of strain localisation were of small aspect-ratio in the sheet-plane when first detected. For this reason it appeared doubtful if the long-groove model proposed by Marciniak and Kuczynski can give a realistic representation of the strain-localisation process. Experiments made with sheets containing regular arrays of axisymmetric indentations have clarified some of the influences of the aspect ratio of the defects and of the manner in which interaction and coalescence of the strain fields associated with closely spaced compact defects can lead to groove-like behaviour in the later stages of stretching.

Strain localisation in biaxially stretched sheets containing compact defects—II: Analysis using a finite element model

The development of strain localisation in a biaxially stretched sheet of work hardening material which contains a regular array of axisymmetric defects has been analysed by the finite element method. The defects were circular regions of reduced initial thickness and their spacing was close enough to permit interaction of the individual fields of strain concentration, leading to the formation of coherent regions of strain localisation across the sheet. Numerical results for the effects of defect severity on limit strains given by the new model are compared with those given by Marciniak and Kuczynski's long groove model. When failure is assumed to coincide with completed localisation, the forms of the relationships between limit strains and the applied strain state predicted by the two models are closely similar but, in order to give similar magnitudes of the limit strains, the defect severities and the defect strains required in the axisymmetric defect model are much larger than those in the long groove model. For this reason, when defect strains are limited by fracture, the strain state dependencies predicted by the two models can be distinctly different. For the case of a typical drawing quality low-carbon steel, the predictions of the axisymmetric defect model are in much closer accord with experimental values than are those of the long groove model.