Strain gradient plasticity modelling of high-pressure torsion

Gradient plasticity modelling combining a micro-structure-related constitutive description of the local material behaviour with a particular gradient plasticity frame is presented. The constitutive formulation is based on a phase mixture model in which the dislocation cell walls and the cell interiors are considered as separate 'phases', the respective dislocation densities entering as internal variables. Two distinct physical mechanisms, which give rise to gradient plasticity, are considered. The first one is associated with the occurrence of geometrically necessary dislocations leading to first-order strain gradients; the second one is associated with the reaction stresses due to plastic strain incompatibilities between neighbouring grains, which lead to second-order strain gradients. These two separate variants of gradient plasticity were applied to the case of high-pressure torsion: a process known to result in a fairly uniform, ultrafine grained structure of metals. It is shown that the two complementary variants of gradient plasticity can both account for the experimental results, thus resolving a controversial issue of the occurrence of a uniform micro-structure as a result of an inherently non-uniform process. © 2007 Elsevier Ltd. All rights reserved.

Strain gradients in Cu-Fe thin films and multilayers during micropillar compression

Plastic strain gradients can influence the work-hardening behaviour of metals due to the accumulation of geometrically necessary discolations at the micron/submicron scale. A finite element model based on the conventional theory of mechanism-based strain-gradient plasticity has been developed to simulate the micropillar compression of Cu–Fe thin films and multilayers. The modelling results show that the geometric constraints lead to inhomogeneous deformation in the Cu layers, which agrees well with the bulging of Cu layers observed experimentally. Plastic strain gradients develop inside the individual layers, leading to extra work-hardening due to the accumulation of geometrically necessary dislocations. In the multilayer specimens, the Cu layers deform more severely than the Fe layers, resulting in the development of tensile stresses in the Fe layers. It is proposed that these tensile stresses are responsible for the development of micro-cracks in the Fe layers.

Strain localisation patterns under equal-channel angular pressing

Instabilities of plastic flow in the form of localised shear bands were experimentally observed to result from equal-channel angular pressing (ECAP) of magnesium alloy AZ31. The appearance of shear bands and their spacing were dependent on velocity of the pressing and applied back-pressure. A generic gradient plasticity theory involving second-order strain gradient terms in a constitutive model was applied to the case of AZ31 deformed by ECAP. Linear stability analysis was applied to the set of equations describing the deformation behaviour in the process zone idealised as a planar shear zone. A full analytical solution providing a dispersion relation between the rate of growth of a perturbation and the wave number was obtained. It was shown that the pattern of incipient localised shear bands exhibits a spectrum of characteristic lengths corresponding to admissible wave numbers. The interval of the spectrum of wave numbers of viable, i.e. growing, perturbations predicted by linear stability analysis was shown to be in good agreement with the experimentally observed spectrum. The effect of back-pressure applied during ECAP was also considered. The predicted displacement of the shear band spectrum towards lower wave numbers, shown to be a result of the decreased shear strain rate in the shear zone, was consistent with the experimentally observed increase of the band spacing with increased back-pressure. A good predictive capability of the general modelling frame used in conjunction with linear stability analysis was thus demonstrated in the instance of the particular alloy system and the specific processing conditions considered.

Effect of microstructure on the stability of retained austenite in transformation-induced-plasticity steels

Two Fe-0.2C-1.55Mn-1.5Si (in wt pet) steels, with and without the addition of 0.039Nb (in wt pet), were studied using laboratory rolling-mill simulations of controlled thermomechanical processing. The microstructures of all samples were characterized by optical metallography, X-ray diffraction (XRD), and transmission electron microscopy (TEM). The microstructural behavior of phases under applied strain was studied using a heat-tinting technique. Despite the similarity in the microstructures of the two steels (equal amounts of polygonal ferrite, carbide-free bainite, and retained austenite), the mechanical properties were different. The mechanical properties of these transformation-induced-plasticity (TRIP) steels depended not only on the individual behavior of all these phases, but also on the interaction between the phases during deformation. The polygonal ferrite and bainite of the C-Mn-Si steel contributed to the elongation more than these phases in the C-Mn-Si-Nb-steel. The stability of retained austenite depends on its location within the microstructure, the morphology of the bainite, and its interaction with other phases during straining. Granular bainite was the bainite morphology that provided the optimum stability of the retained austenite.

Transmission electron microscopy characterization of the bake-hardening behavior of transformation-induced plasticity and dual-phase steels

The effect of prestraining (PS) and bake hardening (BH) on the microstructures and mechanical properties has been studied in transformation-induced plasticity (TRIP) and dual-phase (DP) steels after intercritical annealing. The DP steel showed an increase in the yield strength and the appearance of the upper and lower yield points after a single BH treatment as compared with the as-received condition, whereas the mechanical properties of the TRIP steel remained unchanged. This difference appears to be because of the formation of plastic deformation zones with high dislocation density around the “as-quenched” martensite in the DP steel, which allowed carbon to pin these dislocations, which, in turn, increased the yield strength. It was found for both steels that the BH behavior depends on the dislocation rearrangement in ferrite with the formation of cell, microbands, and shear band structures after PS. The strain-induced transformation of retained austenite to martensite in the TRIP steel contributes to the formation of a complex dislocation structure.

Application of radial return mapping algorithm for finite strain elastoplasticity in a hybrid finite element and particle-in-cell model

The radial return mapping algorithm within the computational context of a hybrid Finite Element and Particle-In-Cell (FE/PIC) method is constructed to allow a fluid flow FE/PIC code to be applied solid mechanic problems with large displacements and large deformations. The FE/PIC method retains the robustness of an Eulerian mesh and enables tracking of material deformation by a set of Lagrangian particles or material points. In the FE/PIC approach the particle velocities are interpolated from nodal velocities and then the particle position is updated using a suitable integration scheme, such as the 4th order Runge-Kutta scheme[1]. The strain increments are obtained from gradients of the nodal velocities at the material point positions, which are then used to evaluate the stress increment and update history variables. To obtain the stress increment from the strain increment, the nonlinear constitutive equations are solved in an incremental iterative integration scheme based on a radial return mapping algorithm[2]. A plane stress extension of a rectangular shape J2 elastoplastic material with isotropic, kinematic and combined hardening is performed as an example and for validation of the enhanced FE/PIC method. It is shown that the method is suitable for analysis of problems in crystal plasticity and metal forming. The method is specifically suitable for simulation of neighbouring microstructural phases with different constitutive equations in a multiscale material modelling framework.

Investigation of deformation mechanisms involved in the plasticity of AZ31 Mg alloy: in situ neutron diffraction and EPSC modelling

In situ neutron diffraction and Elasto-Plastic Self-Consistent (EPSC) polycrystal modelling have been employed to investigate which deformation mechanisms are involved in the plasticity of extruded AZ31 Mg alloy during the tensile loading along the extrusion direction. On the basis of this study we were able to determine the relative activity of the slip and twinning deformation modes. By tuning the parameters of the EPSC model (i.e. the critical resolved shear strengths and hardening parameters), excellent agreement with the experimental data has been achieved. It is shown that the strain in the crystallographic ⟨c ⟩direction is accommodated mainly by ⟨c + a ⟩ dislocation slip on second-order pyramidal planes. The results further indicate that either slip of ⟨a ⟩dislocations occurs on {10.1} pyramidal planes or cross-slip from basal and prismatic planes takes place.

Nanoparticle enhanced conductivity in organic ionic plastic crystals : space charge versus strain induced defect mechanism

High conductivity in solid-state electrolytes is a critical requirement for many advanced energy and other electrochemical applications. Plastic crystalline materials have shown promise in this regard, and the inclusion of nanosized inorganic particles in both amorphous and crystalline materials has indicated order of magnitude enhancements in ion transport induced by space charge or other defect enhancement. In this paper we present conductivity enhancements in the plastic crystal N,N‘-ethylmethylpyrrolidinium bis(trifluoromethanesulfonyl)amide ([C₂mpyr][NTf₂]) induced by nanosized SiO₂ particles. The addition of the nanoparticles dramatically increases plasticity and ion mobility. Positron annihilation lifetime spectroscopy (PALS) measurements indicate an increase in mean defect size and defect concentration as a result of nanoparticle inclusion. The scaling of the conductivity with size suggests that a “trivial space charge” effect is operable, although a strain induced enhancement of defects (in particular extended defects) is also likely given the observed increase in plasticity.

Comparison of mechanical behaviour of thin film simulated by discrete dislocation dynamics and continuum crystal plasticity

3D finite element simulations of 9-grain multicrystalline aggregates are performed within the framework of the classical continuum crystal plasticity and discrete dislocation dynamics. The results are processed in a statistical way by ensemble averaging. The comparison is made at three levels: macroscopic stress–strain curves, average stress values per grain, local values of stress and plastic strain. The comparison shows that some similarities are observed in the stress and strain distributions in both simulations approaches. But there are also large discrepancies caused by the discrete nature of plasticity in DDD. The DDD simulations provide higher stress levels in the aggregate due to the small number of dislocation sources and to the stress field induced by individual dislocations.

Microstructure-property relationship of the high strength low alloy steels during tensile testing at high strain rates

Positive The influence of strain-rate on the room temperature mechanical properties of the Dual-Phase and Transformation Induced Plasticity (TRIP) steels was investigated.The results showed that both the plastic strain, and strength properties increased with increasing strain rates at high strain rates.At strain rates lower than approximateil 1s ~ (-1) the properties no longer have an advantageous proportionality to strain rate and remain strain rate neutral.Possible explanations are offered for trends exhibited, in terms of thermal and athermal considerations, in relation to the respective microstructures of the two steels

Strain hardening behavior of high performance FBDP, TRIP and TWIP steels

Based on n-value differential equation and microstructural observation, strain hardening behaviors of FBDP, TRIP, and TWIP steels during uniaxial tension were investigated. TRIP steel exhibits both superior strength and ductility than FBDP steel, and TWIP steel displays much higher total and uniform elongations in comparison to FBDP and TRIP steels. The instantaneous n values of FBDP and TRIP steels increase at small strains, reach a maximum value, smoothly decrease at higher strains, and then rapidly drop up to the specimen rupture. The strain hardening of TRIP steel persists at higher strains where that of FBDP steel begins to diminish. TWIP steel exhibits gradually increased instantaneous n values over the whole uniform plastic deformation, implying that TWIP steel shows a much larger strain hardening capability than FBDP and TRIP steels.

Asymmetric rolling of interstitial-free steel using differential roll diameters. Part I : mechanical properties and deformation textures

IF steel sheets were processed by conventional symmetric and asymmetric rolling (ASR) at ambient temperature. The asymmetry was introduced in a geometric way using differential roll diameters with a number of different ratios. The material strength was measured by tensile testing and the microstructure was analyzed by optical and transmission electron microscopy as well as electron backscatter diffraction (EBSD) analysis. Texture was also successfully measured by EBSD using large surface areas. Finite element (FE) simulations were carried out for multiple passes to obtain the strain distribution after rolling. From the FE results, the velocity gradient along selected flow lines was extracted and the evolution of the texture was simulated using polycrystal plasticity modeling. The best mechanical properties were obtained after ASR using a roll diameter ratio of 2. The textures appeared to be tilted up to 12 deg around the transverse direction, which were simulated with the FE-combined polycrystal plasticity modeling in good agreement with measurements. The simulation work revealed that the shear component introduced by ASR was about the same magnitude as the normal component of the rolling strain tensor.

On the low temperature strain aging of bainite in the TRIP steel

The aging behavior of a thermomechanically processed Mo-Al-Nb transformation-induced plasticity steel with ultrafine microstructure was investigated using transmission electron microscopy and atom probe tomography (APT). Strain aging at 73 K (200 °C) for 1800 seconds led to a significant bake-hardening response (up to 222 MPa). Moreover, aging for 1800 seconds at room temperature after 4 pct pre-strain also revealed a bake-hardening response (~60 MPa). The experimental results showed the formation of carbon Cottrell atmospheres around dislocations and the formation of carbon clusters/fine carbides in the bainitic ferrite during aging. It is proposed that this is associated with the high dislocation density of bainitic ferrite with formation of a complex dislocation substructure after pre-straining and its high average carbon content (~0.35 at. pct). The segregation of carbon and substitutional elements such as Mn and Mo to the retained austenite/bainitic ferrite interface during aging was observed by APT. This segregation is likely to be the preliminary stage for Mo-C particles’ formation. The aging after pre-straining also induced the decomposition of retained austenite with formation of ferrite and carbides.

Job strain — attributable depression in a sample of working Australians: assessing the contribution to health inequalities

Background The broad aim of this study was to assess the contribution of job strain to mental health inequalities by (a) estimating the proportion of depression attributable to job strain (low control and high demand jobs), (b) assessing variation in attributable risk by occupational skill level, and (c) comparing numbers of job strain–attributable depression cases to numbers of compensated 'mental stress' claims. Methods Standard population attributable risk (PAR) methods were used to estimate the proportion of depression attributable to job strain. An adjusted Odds Ratio (OR) of 1.82 for job strain in relation to depression was obtained from a recently published meta-analysis and combined with exposure prevalence data from the Australian state of Victoria. Job strain exposure prevalence was determined from a 2003 population-based telephone survey of working Victorians (n = 1101, 66% response rate) using validated measures of job control (9 items, Cronbach's alpha = 0.80) and psychological demands (3 items, Cronbach's alpha = 0.66). Estimates of absolute numbers of prevalent cases of depression and successful stress-related workers' compensation claims were obtained from publicly available Australian government sources. Results Overall job strain-population attributable risk (PAR) for depression was 13.2% for males [95% CI 1.1, 28.1] and 17.2% [95% CI 1.5, 34.9] for females. There was a clear gradient of increasing PAR with decreasing occupational skill level. Estimation of job strain–attributable cases (21,437) versus "mental stress" compensation claims (696) suggest that claims statistics underestimate job strain–attributable depression by roughly 30-fold. Conclusion Job strain and associated depression risks represent a substantial, preventable, and inequitably distributed public health problem. The social patterning of job strain-attributable depression parallels the social patterning of mental illness, suggesting that job strain is an important contributor to mental health inequalities. The numbers of compensated 'mental stress' claims compared to job strain-attributable depression cases suggest that there is substantial under-recognition and under-compensation of job strain-attributable depression. Primary, secondary, and tertiary intervention efforts should be substantially expanded, with intervention priorities based on hazard and associated health outcome data as an essential complement to claims statistics.