Geometrical Hardening Research Articles

Analogous mechanical behaviors in and directions of Cu nanowires under tension and compression at a high strain rate

This study analyzes the plastic deformation on the atomic scale of Cu nanowires (NWs)with and orientations during uniaxial tension and compression, using a molecular dynamicsimulation. The maximum local stress (MLS) method is employed to evaluate mechanicalbehavior during deformation. Following yielding, the flow stress strongly depends on thevariation in the degree of orientation caused by twinning. Both the tension of the NW and the compression of the NW cause twin deformation and consequent geometrical softening. In contrast, thecompression of the NW and the tension of the NW form twin bands and cause geometrical hardening. These behaviors result inthe stress–strain curves that reveal the pseudo-skew-symmetry characteristic.With respect to the difference between the critical resolved shear stress(τc) associated with thedistinct orientations, τc depends strongly on the surface critical resolved stress(τsc). Undertension, τsc depends on the degree of lattice distortion. A larger lattice distortion (pre-tensile stress) corresponds tohigher τsc. However, under compression, a geometrical factor can be used to describe the difference inτsc between the different orientations. A larger geometrical factor corresponds to a largerτsc.

The Effect of Strain Path Change on Texture Evolution at Finite Strain of Multiphase Steel: Numerical and Experimental Investigations

Two-stage sequences of simple shear and/or uniaxial tensile tests conducted on TRIP800 steel sheet and supplemented by texture measurements are reported. The purpose is a better understanding of the macroscopic work-hardening behaviour and its microstructural origin. According to the previously published work on single phase ferrite steel; the peculiar macroscopic transient effect in flow stress was mainly associated to the microstructural destabilization (e.g. reinforcement, dissolution or rearrangement of the previously formed dislocation walls). In addition, the macroscopic work-softening observed at the beginning of the second stage of cross-loading was attributed to the micro-band occurrence. Considering the actual multiphase steel, the main difference lies in the absence of the peculiar transient effect in flow stress upon cross-loading (where no macroscopic work-softening is observed) and the associated microstructural mechanisms (no formation of micro-bands). Besides, the initial texture for the actual multiphase steel is in some extent different to the previously investigated single phase steel mainly made up of the γ-fibre. Therefore, a detailed analysis of the measured deformed textures is carried out in order to investigate the contribution of the texture evolution on the macroscopic work-hardening. The computations of the orientation stability map as well as the predicted texture evolutions using the classical full constraint Taylor- Bishop-Hill (TBH) model are performed for a better understanding of the observed texture development. The influence of the texture evolution on the shape of the stress-strain curves, as well as on the remaining symmetries of the material, is also discussed. Explicitly, we show that despite the presence of a well developed texture in the as-received and deformed material, the contribution of the geometrical hardening (i.e. textural evolution) on the macroscopic behaviour remains small compared to the microstructural one.

Plastic instability and Lüders bands in the tensile test: the role of crystal orientation

Considère's plastic stability criterion in tensile testing is rewritten by separating the effects of intrinsic and geometrical hardening for single and polycrystals deforming by slip. The Taylor factor is employed to describe the effect of orientation change in the stability of plastic deformation for which a new instability parameter has been defined. Analytical results are presented for single slip in f.c.c. and h.c.p. crystals, while numerical simulations were done for the polycrystal case using the Taylor model. Localization may lead to the formation of Lüders bands if the strains are limited either by intrinsic hardening or by geometric hardening (discussed on the example of a zinc single crystal).

Poroplastic properties of calcium-leached cement-based materials

Asymptotic calcium leaching of cement-based materials produces a new material composed of C–S–H with low C/ S ratio on the order of 1 and a high porosity generated by the dissolution of Portlandite (CH) crystals, which creates a new pore-size family in the micrometer range. This paper investigates the role of these two phenomena in the multiaxial inelastic and hardening deformation behavior, in compression, of calcium-leached cement pastes and mortars. From triaxial tests and SEM microscopy, it is shown that the low C/ S C–S–H matrix is highly plastically deformable, which is consistent with the high degree of polymerization and the effect of the C/ S ratio on the intrinsic cohesion of C–S–H. The validity of the effective stress concept is experimentally proven for calcium-leached cement paste and mortar and provides evidence that the low C/ S C–S–H solid phase of the cement paste is a pure cohesive incompressible material. In turn, the large pores created by the CH dissolution provides expansion space for the incompressible solid during compressive loading. Once this porosity is filled, the volume deformability is exhausted, and the material dilates to failure. In a similar way, the early tendency of mortars to dilate is found to be a consequence of a competition between plastic material behavior of the matrix (plastic hardening) and porosity-controlled structural deformation (geometrical hardening) triggered by frictional dilation mechanisms in the Interfacial Transition Zone (ITZ).

Phase-field modelling of the thermo-mechanical properties of carbon steels

The high temperature stress model for continuously cast steels has been developed. The effect of dendritic morphology on the mechanical strength of carbon steels has been investigated for the first time with a thermodynamically based calculation of dendritic morphology by a phase-field model. The characteristic solid fraction at the liquid impenetrable temperature (LIT) was evaluated as 0.9 by investigating the contact behavior of secondary arms during unidirectional solidification of δ and γ phases. Geometrical hardening of the mushy zone due to the contact and combining of dendrite arms has been evaluated using a geometrical hardening parameter defined as the contact ratio between adjacent secondary arms in the transverse cross section of primary arms. The critical solid fraction at zero strength temperature (ZST) was evaluated as 0.65 from the minimum non-zero contact ratio. The calculated critical fracture strength with the stress model for steels in a mushy zone describes the measured tensile strength well.

A plasticity model for metal powder forming processes

Abstract In this paper, a double-surface plasticity model, based on a combination of a convex yield surface consisting of a failure envelope, such as a Mohr–Coulomb yield surface and, a hardening cap model, is developed for the nonlinear behaviour of powder materials in the concept of a generalized plasticity formulation for the description of cyclic loading. This model reflects the yielding, frictional and densification characteristics of powder along with strain and geometrical hardening which occur during the compaction process. The solution yields details on the powder displacement from which it is possible to establish the stress state in the powder and the densification is derived from consideration of the elemental volumetric strain. A hardening rule is used to define the dependence of the yield surface on the degree of plastic straining. Finally, an adaptive finite element model (FEM) analysis is employed by the updated Lagrangian formulation to simulate the compaction of a set of complex powder forming processes.

Finite element analysis of deformation behaviour in ductile matrix containing hard particles

Three-dimensional finite element analyses were carried out to study the deformation behaviour in ductile matrix-hard particle composite systems. Models with transversely aligned and staggered particle distributions were used. The deformation constraints in the models were investigated and the development of triaxial stress states in the models was studied. It was determined that the strengthening behaviour arises as a result of geometrical hardening in the early stage of composite deformation. Special deformation stages in the overall stress-strain behaviour of the composite microstructures such as initiation of microyielding, expansion of the plastically deformed region, and spread of plastic flow were determined by following the development of plasticity.

Orientation of nucleating faults in anisotropic media: insights from three-dimensional deformation experiments

Physical experiments have been undertaken to investigate the influence of planar rheological anisotropy on the orientation of fault structures in three-dimensional flow associated with layer-normal shortening. The experimental results indicate that plane strain is a special case, characterised by the lowest angle between the faults and the principal extension direction for any combination of rheology and flow type during progressive pure shear. A model is proposed wherein the role of the anisotropy appears to be two-fold. First, it determines that shear bands operate internally by a mechanism involving rotating slip surfaces during fault nucleation. The initial orientation of the faults is determined by the optimisation of the driving processes in the propagating shear bands as a partial function of the angle they make with the external anisotropy. Second, it induces directionally dependent variation in the resistance to flow, which manifests itself differently according to the symmetry of the strain ellipsoid in three dimensions ( X ≥ Y ≠ 1 ≥ Z). In flattening flow, it is proposed that anisotropy-induced geometrical hardening leads to an increase in the angles made by the shear bands with the principal extension directions of the deformation. In constriction, the same effect is seen in XZ sections, but in YZ sections it is suggested that the wide range of fault orientations observed is due to anisotropy-induced geometrical softening. It is possible that the low angle of dip of crustal-scale extensional detachment faults may reflect anisotropic behaviour of the lower continental crust.

Continuum aspects of directionally dependent cracking of an interface between copper and alumina crystals

Abstract Directionally dependent cracking along the interface of a Cu/Al2O3 bicrystal has been analyzed using continuum mechanics. This work extends previous analyses by considering the elastic anisotropy and plastic deformation of copper. The goals of the analysis are: (1) To provide a possible continuum explanation of the experimentally observed directionally dependent cracking, and (2) to understand the effect of continuum deformation on the competition between dislocation nucleation at a crack tip (i.e., tip blunting and alleviation of the stress concentration) and cleavage. First, the mode mixity of the elastic fields at the crack tip is calculated by considering the traction vector on the interface as derived from anisotropic elasticity. This is compared to the results from isotropic elasticity. The effects of anisotropy, as pertaining to dislocation nucleation and cleavage, are discussed. Elastic-plastic FEM analyses within both the `small strain' and finite deformation formulations have been performed for the two crack directions in. Furthermore, a variety of hardening laws, including ideal plasticity, were used to investigate the robustness of the solutions. Comparisons between the FEM analyses show that the general sectorial nature of the crack tip stress fields isthe same for all hardening laws chosen. The effects of geometrical hardening and softening are pronounced in a finite deformation, ideal plasticity analysis. However, even moderate hardening greatly diminishes these effects. If the hardening law saturates, the resulting near tip fields are similar to those of an ideally plastic material. The two crack tip orientations affect the nature of the localization of the plastic deformation. These effects are discussed in the context of different hardening laws. In addition, the interface traction phase angle is changed significantly by the plastic deformation with consequences regarding dislocation nucleation and cleavage. Overall, no clear continuum-based explanation of directionally dependent fracture was found, but it is clear that elastic anisotropy and plastic deformation should, in general, be taken into account. Finally, critical problems encountered in this type of analysis are identified and some directions for future research are suggested.

Numerical and experimental analysis of load capacity of pressure vessels for large deformations

A method of theoretical and experimental investigations of large deformations and load capacity of pressure vessels has been proposed. Algorithms and programs for numerical analysis (with the finite element method) of spatial stress and strain state and load capacity have been worked out according to the Prandtl-Reuss theory of plastic flow. Loading in the vessel was realized in an incremental way. The loading process was continued up to the moment when the maximum loading was obtained (i.e. the moment when state of equilibrium of the vessel was not possible). It has been found that in thin-walled circular vessels with rigid bottoms, when a ratio of length to their diameter is less than three, the effect of geometrical hardening can be observed because a shape of the vessel approaches a more resistant spherical one.

Plastic anisotropy and geometrical hardening in quartzites : Takeshita, T; Wenk, H R TectonophysicsV149, N3/4, June 1988, P345–361

Plastic anisotropy and geometrical hardening in quartzites : Takeshita, T; Wenk, H R TectonophysicsV149, N3/4, June 1988, P345–361

Plastic anisotropy and geometrical hardening in quartzites

Lattice rotation in crystals which creates a characteristic preferred orientation in deformed tectonites takes place whenever slip (dislocation glide) is involved in the deformation process. The crystal lattice either rotates to an orientation favorable for further slip or to one that is unfavorable, resulting in an overall hardening or softening of the polycrystal during deformation. This effect of plastic anisotropy which arises due to changes in the crystal orientation distribution is analyzed quantitatively for quartz polycrystals using the Taylor model. The results indicate that in easy {basal}〈a〉 slip region (low temperature), quartzites become softer in flattening with increasing strain, whereas in easy {prism} 〈a〉 slip region (high temperature), quartzites become softer in elongation with increasing strain. Accordingly, deformation is facilitated by flattening at low temperature and by elongation at high temperature if it can be heterogeneous to a certain degree. This is borne out by geological observations, which indicate that at low metamorphic grade flattening to plane strain is the most frequently observed strain mode (e.g., Moine thrust), whereas at high metamorphic grade constriction is favored (e.g., Sambagawa belt). The strain distribution in a large geological body may depend on internal anisotropic plastic properties such as preferred slip systems as well as imposed external boundary conditions. Heterogeneities are also observed on the hand specimen scale. Grains in orientations where easier slip systems are difficult to activate remain relatively undeformed in a ductile matrix consisting of grains in which strain is accommodated mostly by easier slip systems. Some aspects of the Taylor model for creep rate sensitivity are discussed.

A new yield function for compressible [formula omitted] materials

A new yield function for compressible P M materials has been derived based upon a yield criterion postulated by the authors. This function was experimentally verified for the uniaxial state of compressive stress using the P M aluminum alloy X7091 as a model material, and excellent agreement was found between theoretical and experimental results for the density dependence of the yield and geometrical hardening. Yield surfaces for various density levels have been generated in a three-dimensional principal-stress space using computer graphics.

A phenomenological model of thermalization in cluster fuel elements

A simplified model to evaluate the neutron spectrum in cluster fuel elements, which was previously concerned with ‘thermal’ effects, has been extended to take into account the epithermal ones. This has been done on the basis of a simple separation of the ‘homogeneous’ spectrum effects, which have been evaluated by means of a preliminary homogenization of the cell. On the basic homogeneous spectrum obtained in this way the heterogeneity effects characteristic of the fuel element (rethermalization and geometrical hardening)-separately evaluated- have been applied. The difficulties connected with the introduction in this simple framework of the interference effects between hardening and rethermalization are discussed and a comparison with the reaction-rate ratios measured at Chalk River is presented.