Anisotropic Plastic Deformation Research Articles

Analytical solution of anisotropic plastic deformation induced by micro-scale laser shock peening

Laser shock peening (LSP) is a process to improve material fatigue life by introducing compressive residual surface stress in a target. The residual stresses are introduced when a high-intensity laser impinges on an ablative layer deposited on the surface of the target material. The interaction between laser and the ablative layer creates a high pressure plasma that leads to plastic deformation. If the laser spot size is of the order of a few micrometers, the potential exists to use this process to enhance the fatigue life of micro-scale components or to selectively treat highly localized regions of macroscale components. However, for such micro-scale laser shock peening (μLSP), the laser spot size is likely to be of the order of the material grain size. Therefore the material properties must be treated as anisotropic and heterogeneous rather than isotropic and homogeneous. In the present work, anisotropic slip line theory is employed to derive the stress and deformation fields caused by μLSP on single crystal aluminum which is oriented so that plane strain conditions are admitted. The predicted size of the deformed region is compared with deformation measurement by atomic force microscopy (AFM) and with lattice rotation measurement by electron backscatter diffraction (EBSD). In addition, single crystal plasticity finite element simulations are performed for the process. The results suggest that the analytical solution captures the salient features of the deformation state and is able to predict the size of the resulting plastically deformed region.

On stress rate and plasticity constitutive equations referred to a body-fixed coordinate system

Investigators have viewed the stress rate in two different ways: the material (body-fixed) point of view and the Eulerian point of view. We discuss the Zaremba–Jaumann rate and Oldroyd’s rate from the material viewpoint and apply them to the material formulation of a theory of plasticity for materials undergoing anisotropic plastic deformation. Significant advantages of the material formulation are that the derivation of equations is straight forward, the distortion of yield surface can be easily accounted for, and the issue of self-consistent elastic equation does not arise. A convected (body-fixed) coordinate system that is imbedded in the material element is used to define a convected material element. Constitutive equations in a theory of plasticity are written with respect to this element referred to the body-fixed coordinate system. A material type yield function is a function of stress components and it is invariant under either a superimposed rigid rotation of the body or an arbitrary change of observer. The kinematic hardening evolves by the co-rotational rate and it is disassociated from the general kinematic of deformation. The latter evolves by the convected rate.

Size-dependent ion-beam-induced anisotropic plastic deformation at the nanoscale by nonhydrostatic capillary stresses

We develop a phenomenological model for size-dependent anisotropic plastic deformation of colloidal nanoparticles under ion irradiation. We show that, at the nanoscale, nonhydrostatic capillary stresses drive radiation-induced Newtonian viscous flow, counteracting the stress state that initiates the anisotropic viscous strains in the high-temperature thermal spike region around the ion track. We present experimental data using colloidal silica nanoparticles in the $10--100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ size range that show that the deformation is indeed strongly size dependent, in excellent agreement with the model. This work allows for the prediction of the ion-beam-induced shape modification of a whole range of nanostructures.

Development of Intergranular Stresses in Zirconium Alloy Cladding Tubes: Experimental and Numerical Studies

Complementary methods have been used to analyse residual stresses in zirconium alloy tubes which were manufactured by cold rolling : X-ray diffraction and scale transition model. A modified elasto-plastic self-consistent model (EPSC) has been used to simulate the experiments and exhibits agreement with experimental data. X-ray diffraction analysis in rolling direction shows opposite stress values for {10 14 } and { 2022} planes respectively. The measured strains were generated by an anisotropic plastic deformation. Plastic incompatibility stress on X-ray measurements should be taken into account so as to make a correct interpretation of the experimental data.

Prediction of intragranular strains in metallic polycrystals with a two‐level homogenisation approach: Influence of dislocation microstructure on the mechanical behaviour

AbstractA two‐level homogenisation approach is applied to the micro‐mechanical modelling of the elasto‐plasticity of polycrystalline materials during various strain‐path changes. The model is tested by simulating the development of intragranular strains during different complex loads. Mechanical tests measurements are used as a reference in order to validate the model. The anisotropy of plastic deformation in relation to the evolution of the dislocation structure is analysed. The results demonstrate the relevance of this approach for FCC polycrystals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

High Speed Skating Rinks using Oriented Ice Crystals

Frictional anisotropy is observed with crystallographic planes and sliding orientations of ice. Availing this phenomenon, a high speed skating rink was made by use of a large-single crystal ice and its lowest frictional plane. Moreover, new rinks will be made using anisotropy in plastic deformation of ice. The lower friction of curling rinks and oriented snow grains at surface came in sight. These high speed rinks were derived from the basis adhesion theory, and self-inconsistency in frictional melting theory as classical frictional mechanism was revealed.

Self-organised nano-structuring of thin oxide-films under swift heavy ion bombardment

Surface instabilities and the resulting self-organisation processes play an important role in nano-technology since they allow for large-array nano-structuring. We have recently found that the occurrence of such instabilities in thin film systems can be triggered by energetic ion bombardment and the subsequent self-assembly of the surface can be nicely controlled by fine-tuning of the irradiation conditions. The role of the ion in such processes is of double nature: If the instability is latently present already in the virgin sample, but self-assembly cannot take place because of kinetic barriers, the ion impact may just supply the necessary atomic mobility. On the other hand, the surface may become instable due to the ion beam induced material modifications and further irradiation then results in its reorganisation. In the present paper, we will review recently observed nano-scale self-organisation processes in thin oxide-films induced by the irradiation with swift heavy ions (SHI) at some MeV/amu energies. The first example is about SHI induced dewetting, which is driven by capillary forces already present in the as-deposited samples. The achieved dewetting pattern show an amazing similarity to those observed for liquid polymer films on Si, although in the present case the samples were kept at 80K and hence have never reached their melting point. The second example is about self-organised lamellae formation driven by planar stresses, which are induced by SHI bombardment under grazing incidence and result in a surface instability and anisotropic plastic deformation (hammering effect). Taking advantage of these effects and modifying the irradiation procedure, we were able to generate more complex structures like NiO-“nano-towers” of 2μm height and 200nm in diameter.

Anisotropic deformation of metallo-dielectric core–shell colloids under MeV ion irradiation

We have studied the deformation of metallo-dielectric core–shell colloids under 4MeV Xe, 6 and 16MeV Au, 30MeV Si and 30MeV Cu ion irradiation. Colloids of silica surrounded by a gold shell, with a typical diameter of 400nm, show anisotropic plastic deformation under MeV ion irradiation, with the metal flowing conform the anisotropically deforming silica core. The 20nm thick metal shell imposes a mechanical constraint on the deforming silica core, reducing the net deformation strain rate compared to that of pure silica. In colloids consisting of a Au core and a silica shell, the silica expands perpendicular to the ion beam, while the metal core shows a large elongation along the ion beam direction, provided the silica shell is thick enough (>40nm). A minimum electronic energy loss of 3.3keV/nm is required for shape transformation of the metal core. Silver cores embedded in a silica shell show no elongation, but rather disintegrate. Also in planar SiO2 films, Au and Ag colloids show entirely different behavior under MeV irradiation. We conclude that the deformation model of core–shell colloids must include ion-induced particle disintegration in combination with thermodynamical effects, possibly in combination with mechanical effects driven by stresses around the ion tracks.

Yield and Plastic Deformation of Mg-Alloy AZ31 at Elevated Temperatures

The yield and plastic deformation behaviour of wrought Mg-alloy AZ31 sheets were investigated at elevated temperatures from ambient to 300°C. It is found that the 0.2% proof stress and ultimate strength decrease linearly with increasing temperature, and the Young’s modulus goes down in the same way. Whereas the ductility, expressed by elongation, increases with temperature, in contrast to the decrease in uniform elongation. The plastic deformation anisotropy, represented by the ratio of transverse and thickness strain of the plate sample, decreases as the temperature increases, and at about 225°C, coincidentally, reaches to unity. The activation volumes for yield stress and ultimate strength are discussed with a thermal activation law-Arrhenius Equation.

Cylindrical void in a rigid-ideally plastic single crystal II: Experiments and simulations

Experimental results and finite element simulations of plastic deformation around a cylindrical void in single crystals are presented to compare with the analytical solutions in a companion paper: Cylindrical void in a rigid-ideally plastic single crystal I: Anisotropic slip line theory solution for face-centered cubic crystals [Kysar, J.W., Gan, Y.X., Mendez-Arzuza, G., 2005. Cylindrical void in a rigid-ideally plastic single crystal I: Anisotropic slip line theory solution for face-centered cubic crystals, International Journal of Plasticity, 21, 1481–1520]. In the first part of the present paper, the theoretical predictions of the stress and deformation field around a cylindrical void in face-centered cubic (FCC) single crystals are briefly reviewed. Secondly, electron backscatter diffraction results are presented to show the lattice rotation discontinuities at boundaries between regions of single slip around the void as predicted in the companion paper. In the third part of the paper, the finite element method has been employed to simulate the anisotropic plastic deformation behavior of FCC single crystals which contain cylindrical voids under plane strain condition. The results of the simulation are in good agreement with the prediction by the anisotropic slip line theory.

Anisotropic plastic deformation by viscous flow in ion tracks

A model describing the origin of ion beam-induced anisotropic plastic deformation is derived and discussed. It is based on a viscoelastic thermal spike model for viscous flow in single ion tracks derived by Trinkaus and Ryazanov. Deviatoric (shear) stresses, brought about by the rapid thermal expansion of the thermal spike, relax at ion track temperatures beyond a certain flow temperature. Shear stress relaxation is accompanied by the generation of viscous strains. The model introduces differential equations describing the time evolution of the radial and axial stresses, enabling an exact derivation of the viscous strains for any ion track temperature history $T(t)$. It is shown that the viscous strains effectively freeze in for large track cooling rates, whereas reverse viscous flow reduces the net viscous strains in the ion track for smaller cooling rates. The model is extended to include finite-size effects that occur for ion tracks close to the sample edge, enabling a comparison with experimental results for systems with small size. The ``effective flow temperature approach'' that was earlier introduced by Trinkaus and Ryazanov by making use of Eshelby's theory of elastic inclusions, follows directly from the viscoelastic model as a limiting case. We show that the viscous strains in single ion tracks are the origin of the macroscopic anisotropic deformation process. The macroscopic deformation rate can be directly found by superposing the effects of single ion impacts. By taking realistic materials parameters, model calculations are performed for experimentally studied cases. Qualitative agreement is observed.

Modeling of fatigue crack growth threshold development for a microstructurally small crack

A method for predicting the fatigue crack growth threshold using finite element analysis is investigated. The proposed method consists of monitoring the plastic strain hysteresis energy dissipation in the crack tip plastic zone, with the threshold being defined in terms of a critical value of this dissipated energy. Two-dimensional plane-strain elastic–plastic finite element analyses are conducted to model fatigue crack growth in a middle-crack tension M(T) specimen. A single-crystal constitutive relationship is employed to simulate the anisotropic plastic deformation near the tip of a microstructurally small crack without grain boundary interactions. Variable amplitude loading with a continual load reduction is used to generate the load history associated with fatigue crack growth threshold measurement. Load reductions with both constant load ratio R and constant maximum stress intensity K max are simulated. In comparison with a fixed K max load reduction, a fixed R load reduction is predicted to generate a 35% to 110% larger fatigue crack growth threshold value.

Mesoscopic residual stresses of plastic origin in zirconium: interpretation of X-ray diffraction results

Complementary methods have been used to analyse residual stresses in a heat-treated Zr702 sheet which had undergone uniaxial plastic deformation: X-ray diffraction and self-consistent models. The elastoplastic self-consistent model has been used to simulate the experiments and exhibits agreement with experimental data. X-ray diffraction analysis in the rolling direction shows opposite stress values for {10\bar{1}4} and {20\bar{2}2} planes, respectively. The measured strains were generated by an anisotropic plastic deformation. The comparison between ∊ϕψversussin2ψ and simulations confirms that prismatic slip is the main active deformation mode. Plastic incompatibility stress in X-ray measurements should be taken into account in order to make a correct interpretation of the experimental data.

Shear localization-martensitic transformation interactions in Fe-Cr-Ni monocrystal

A Fe-15 wt pet Cr-15 wt pet Ni alloy monocrystal was deformed dynamically (strain rate similar to10(4) s(-1)) by the collapse of an explosively driven thick-walled cylinder under prescribed initial temperature and strain conditions. The experiments were carried out under the following conditions: (a) alloy in austenitic state, temperature above transformation temperature; (b) alloy in transformed state; and (c) alloy at temperature slightly above g,, propitiating concurrent shear-band propagation and martensitic transformation. The alloy exhibited profuse shear-band formation, which was a sensitive function of the deformation condition. Stress-assisted and strain-induced martensitic transformation competes with shear localization. The alloy deformed at a temperature slightly above g, shows a significantly reduced number of shear bands. The anisotropy of plastic deformation determines the evolution of strains and distribution of shear bands. The different conditions showed significant differences that are interpreted in terms of the microstructural anisotropy. Calculated shear-band spacings based on the Grady-Kipp (GK) and Wright-Ockendon (WO) theories are compared with the observed values. The microstructure within the shear bands was characterized by transmission electron microscopy. Regions of sub-micron grain sizes exhibiting evidence of recrystallization were observed, as well as amorphous regions possibly resulting from melting and rapid resolidification.

Anisotropy of plastic deformation in rolled aluminum

Tensile properties were investigated along different directions in rolled sheets of recrystallized commercial purity aluminum. The dependence of the flow stress anisotropy on the prestrain level was analyzed in relation to the evolution of the dislocation structure during rolling. The anisotropy of the stress–strain behavior at a prestrain of 0.17 was studied. It is found that the directionality of the planar dislocation boundaries formed during prestraining gives a major contribution to the anisotropic plastic behavior. The magnitude of this contribution depends on the prestrain, which controls the boundary spacing and misorientation.

A statistical TEM investigation of dislocation channeling mechanism in neutron irradiated zirconium alloys

Plastic deformation in irradiated zirconium alloys occurs in a very heterogeneous manner at the grain scale by the clearing up of radiation-induced prismatic loops by gliding dislocations and the channeling of these dislocations inside narrow bands of the grain. A statistical TEM investigation of this mechanism has been performed on neutron irradiated recrystallized Zr alloys tested at 350 °C. Due to the strong anisotropy of plastic deformation, different loading conditions have been investigated. It is shown that for transverse tensile tests and closed end burst tests, only basal channels are observed, whereas for axial tensile tests, prismatic and pyramidal channels are observed. This phenomenon can be understood in terms of texture and interactions between dislocations and irradiation induced loops. From Schmid factor calculations, we have also been able to prove that irradiation leads to a higher increase of critical resolved shear stresses for prismatic and pyramidal slip systems than for basal slip system.

Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure

The anisotropic plastic deformation behavior of extruded 5000 series aluminum alloy tubes, A5154-H112, of 76 mm outer diameter and 3.9 mm wall thickness is investigated, using a servo-controlled tension-internal pressure testing machine. This machine is capable of applying arbitrary stress or strain paths to a tubular specimen using an electrical, closed-loop control system. Detailed measurements were made of the initial yield locus, contours of plastic work for different levels of work-hardening, and the directions of the incremental plastic strain vectors for both linear and combined stress paths. It is found that the measured work contours constructed in the principal stress space are similar in shape, and that the directions of the incremental plastic strain vectors remain almost constant at constant stress ratios. The work-hardening behavior predicted using Hosford's or the Yld2000-2d yield functions under the assumption of isotropic hardening agrees closely with the observations for both linear and combined stress paths. The material is thus found to work-harden almost isotropically. Both yield functions are effective phenomenological plasticity models for predicting the anisotropic plastic deformation behavior of the material.

Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure

Anisotropic plastic deformation of extruded aluminum alloy tube under axial forces and internal pressure

Ion beam-induced anisotropic plastic deformation of silicon microstructures

Amorphous silicon micropillars show anisotropic plastic shape changes upon irradiation with 30 MeV Cu ions. The transverse plastic strain rate is (2.5±0.2)×10−17 cm2/ion at 77 K, which is about one order of magnitude less than that of silica glass. In contrast, crystalline silicon pillars, irradiated under the same conditions, do not exhibit anisotropic deformation. A viscoelastic and free volume model is used to qualitatively describe the data. By irradiating partially amorphous structures a variety of silicon microshapes can be fabricated.

Ion beam-induced anisotropic plastic deformation at 300 keV

Contrary to earlier predictions, ion irradiation at energies as low as 300 keV causes dramatic anisotropic plastic deformation of silica glass. Spherical colloidal silica particles with diameters of 125, 305, and 1030 nm were irradiated with Xe ions at energies in the range 0.3–4.0 MeV at temperatures between 85 and 380 K. Irradiation-induced anisotropic plastic deformation changes the colloid shape from spherical into oblate ellipsoidal at a rate that strongly increases with ion energy. At a fixed fluence, the transverse diameter increases with electronic energy loss. Even at an energy as low as 300 keV large particle anisotropy was found (size aspect ratio of 1.43 at 1×1015 cm−2). The transverse plastic strain gradually decreases with increasing irradiation temperature: it decreases by a factor 4.5 between 85 and 380 K. The data are in agreement with a viscoelastic thermal spike model for anisotropic deformation.