Elastic-plastic Transition Research Articles

Development of a laboratory-based transmission diffraction technique forin situdeformation studies of Mg alloys

A laboratory-based transmission X-ray diffraction technique was developed to measure elastic lattice strains parallel to the loading direction duringin situtensile deformation. High-quality transmission X-ray diffraction data were acquired in a time frame suitable forin situloading experiments by application of a polycapillary X-ray optic with a conventional laboratory Cu X-ray source. Based on the measurement of two standard reference materials [lanthanum hexaboride (NIST SRM 660b) and silicon (NIST SRM 640c)], precise instrumental alignment and calibration of the transmission diffraction geometry were realized. These results were also confirmed by the equivalent data acquired using the standard Bragg–Brentano measurement geometry. An empirical Caglioti function was employed to describe the instrumental broadening, while an axis of rotation correction was used to measure and correct the specimen displacement from the centre of the goniometer axis. For precise Bragg peak position andhkilintensity information, a line profile fitting methodology was implemented, with Pawley refinement used to measure the sample reference lattice spacings (do(hkil)). It is shown that the relatively large X-ray probe size available (7 × 7 mm) provides a relatively straightforward approach for improving the grain statistics for the study of metal alloys, where grain sizes in excess of 1 µm can become problematic for synchrotron-based measurements. This new laboratory-based capability was applied to study the lattice strain evolution during the elastic–plastic transition in extruded and rolled magnesium alloys. A strain resolution of 2 × 10−4at relatively low 2θ angles (20–65° 2θ) was achieved for thein situtensile deformation studies.In situmeasurement of the elastic lattice strain accommodation with applied stress in the magnesium alloys indicated the activation of dislocation slip and twin deformation mechanisms. Furthermore, measurement of the relative change in the intensity of 0002 and 10\overline 13 was used to quantify {10\overline 12}〈\overline 1011〉 tensile twin onset and growth with applied load.

Effect of silicon on the elastic–plastic transition of GaAs crystal

Effect of silicon doping on the elastic–plastic transition of GaAs crystal is demonstrated by results of nanoindentations and ab initio simulations. The experiments show that an increase of silicon concentration causes a decrease of the contact pressure at the onset of permanent deformation of GaAs nanovolume. We found the substitutional Si point defects to decrease the pressure of GaAs-I → GaAs-II phase transformation, which proves the elastic–plastic transition of Si-doped GaAs crystal is a phase-change-driven phenomenon.

Molecular dynamics simulation of incipient plasticity of nickel substrates of different surface orientations during nanoindentation

The present study aims to elucidate the anisotropic characteristics in material responses for crystallographic nickel substrates with (001), (011) and (111) surface orientations during nanoindentation. Molecular dynamic simulation is applied to compensate for the experimental limitation of nanoindentation, particularly for pure nickel substrates. Defect nucleation and evolution in Ni single crystal of these three crystal orientations was examined. Hardness and Young’s modulus are also extracted in different orientations. The Young’s modulus of (111) crystallographic orientation is the largest, while that of (001) surface is the smallest. The sensitivity of the yield point for face centred cubic crystals depends on the crystallographic orientation. The (001) crystallographic orientation reaches the yield point first, while the (111) crystallographic orientation is the most difficult in which to achieve yield. Using a visualisation method of centrosymmetry parameter, the homogeneous nucleation and early evolution of dislocations were investigated, deepening understanding of incipient plasticity at the atomic scale. The present results suggest that defect nucleation and evolution are the root of curve jitter. The indentation depth of the elastic–plastic transition point varies in the different crystallographic orientation models, and appears latest in the (111) model. The strain energy of the substrate exerted by the tip is stored by the formation of homogeneous nucleation and is dissipated by the dislocation slide in the {111} glide plane. The three nickel substrates with different crystallographic orientations exhibit different forms of dislocation propagation.

Elastic-Plastic Transition Problems

The concept of generalized strain measure has been useful for study of elastic plastic transitions. According to classical theory, the elastic-plastic transitions are linear in nature but this theory does not tell about non-linearity in elastic-plastic transitions. It was B.R Seth who explained the non-linear nature of transition state. The elastic-plastic transition problems are helpful to calculate stresses for initial yielding and for fully plastic state. The concept of elastic-plastic transition has been elaborated by discussing various elastic-plastic problems.

Molecular dynamics simulations of shock initiation of hexanitrohexaazaisowurtzitane/trinitrotoluene cocrystal

Multiscale shock technique (MSST) has been shown to accurately reproduce the thermodynamic and chemical reaction paths throughout the shock wave fronts and reaction zone of shock initiation of energetic materials. A 1:1 cocrystal of hexanitrohexaazaisowurtzitane/trinitrotoluene (CL20/TNT) is shocked along the 110 orientations under the conditions of shock velocities lying in the range 610 kms-1 in ReaxFF molecular dynamics simulations. Products recognition analysis leads to reactions occurring with shock velocities of 7 kms-1 or stronger, and the shock initiation pressure is 24.56 GPa obtained from the conservation of Rankine-Hugoniot relation. Comparisons of the relationships are carried out between shock velocity and particle velocity, shock velocities and elastic-plastic transition. During shock initiation with the shock velocities lying in the range 78 kms-1, the shocked systems correspond to an elastic-plastic deformation, primary chemical reactions, and secondary chemical reactions. And the elastic-plastic transition coincides with the chemical reaction at higher shock velocity (9 kms-1), the cocrystal material response is over-driven, and all the thermodynamic properties show steep gradients, the compressed material by the shock wave steps into the plastic region, and a large number of carbon atoms appear in the early stage of over-driven shock initiation.

In situ atomic scale mechanical microscopy discovering the atomistic mechanisms of plasticity in nano-single crystals and grain rotation in polycrystalline metals

In this review, we briefly introduce our in situ atomic-scale mechanical experimental technique (ASMET) for transmission electron microscopy (TEM), which can observe the atomic-scale deformation dynamics of materials. This in situ mechanical testing technique allows the deformation of TEM samples through a simultaneous double-tilt function, making atomic-scale mechanical microscopy feasible. This methodology is generally applicable to thin films, nanowires (NWs), tubes and regular TEM samples to allow investigation of the dynamics of mechanically stressed samples at the atomic scale. We show several examples of this technique applied to Pt and Cu single/polycrystalline specimens. The in situ atomic-scale observation revealed that when the feature size of these materials approaches the nano-scale, they often exhibit “unusual” deformation behaviours compared to their bulk counterparts. For example, in Cu single-crystalline NWs, the elastic–plastic transition is size-dependent. An ultra-large elastic strain of 7.2%, which approaches the theoretical elasticity limit, can be achieved as the diameter of the NWs decreases to ∼6nm. The crossover plasticity transition from full dislocations to partial dislocations and twins was also discovered as the diameter of the single-crystalline Cu NWs decreased. For Pt nanocrystals (NC), the long-standing uncertainties of atomic-scale plastic deformation mechanisms in NC materials (grain size G less than 15nm) were clarified. For larger grains with G<∼10nm, we frequently observed movements and interactions of cross-grain full dislocations. For G between 6 and 10nm, stacking faults resulting from partial dislocations become more frequent. For G<∼6nm, the plasticity mechanism transforms from a mode of cross-grain dislocation to a collective grain rotation mechanism. This grain rotation process is mediated by grain boundary (GB) dislocations with the assistance of GB diffusion and shuffling. These in situ atomic-scale images provide a direct demonstration that grain rotation, through the evolution of the misorientation angle between neighbouring grains, can be quantitatively assessed by the dislocation content within the grain boundaries. In combination with the revolutionary Cs-corrected sub-angstrom imaging technologies developed by Urban et al., the opportunities for experimental mechanics at the atomic scale are emerging.

Research on Elastic-Plastic Transition and Hardening Effect for Monocrystalline Silicon Surfaces

Based on molecular dynamics method, a nanoindentation simulation of the silicon crystal is built and the load-displacement curve is drawn. According to the load-displacement curve, the elastic-plastic transition of silicon crystal is analyzed. The results show that the critical point in the elastic-plastic transition is between 15 and 20 angstroms. In addition, different crystal planes of silicon crystal are loaded for five cycles respectively; the nanohardness is calculated and the nanohardness curve is obtained. The results show that after the first plastic deformation of the silicon crystal surface is occurred, the surface will have a higher hardness and a higher elasticity. Therefore, in the ultra precision machining, in order to reduce the occurrence of damage, the depth of the processing should be controlled in the range of elasticity. Moreover, the method of small quantities in high frequency can increase mechanical properties on the surface.

Thermo elastic-plastic transition of transversely isotropic thick-walled circular cylinder under internal and external pressure

Purpose – The purpose of this paper is to provide the guidance on a design and integrity evaluation of a cylinder under pressure, for which stress analysis has been done for transversely isotropic thick-walled circular cylinder under internal and external pressure with thermal effects. Design/methodology/approach – Transition theory has been used to evaluate plastic stresses based on the concept of generalized principal Lebesgue strain measure which simplifies the constitutive equations and helps to achieve better agreement between the theoretical and experimental results. Findings – It can be concluded that circular cylinder with thermal effects under internal and external pressure made of isotropic material (steel) is on the safer side of the design as compared to the cylinder made of transversely isotropic material (i.e. magnesium and beryl) because percentage increase in effective pressure required for initial yielding to become fully plastic is high for isotropic material (steel) as compared to transversely isotropic material (i.e. magnesium and beryl). It can also be concluded that out of two transversely isotropic materials, beryl is better choice for design of cylinder as compared to magnesium material because percentage increase in effective pressure required for initial yielding to become fully plastic is high for beryl as compared to magnesium. Originality/value – A detailed investigation of thermal transversely isotropic thick-walled circular cylinder under internal and external pressure has been done which leads to the idea of “stress saving” that minimizes the possibility of fracture of cylinder.

Onset of plasticity of helium-implanted ferritic/martensitic steels during nanoindentation

The onset of plasticity during nanoindentation is a new method to investigate the irradiation damage of structural materials in fission and fusion reactors. In this paper, nanoindentation experiment was carried out to helium implanted F82H-IEA and nano-sized oxide dispersion strengthened F82H-ODS steels for studying the elastic-plastic transition at a constant loading rate. The onset of plasticity shifted after helium implantation. By a statistical thermal activation model, activation volume was extracted to discuss the strength of barrier for dislocation motion. The results reveal an increase in the pinning force and number density of effective obstacles for dislocation motion in He-implanted F82H-IEA, and a decrease in the local pinning force without changing the density of effective obstacles in He-implanted F82H-ODS.

The interaction of precipitation and deformation in a binary Mg–Ca alloy at elevated temperatures

The effect of pre-deformation on precipitation hardening response as well as the work-hardening behavior of a binary Mg–Ca alloy are investigated. Our results show that application of 5% pre-deformation increases the precipitation hardening response of the material and decreases the annealing time by 50%. The dislocations introduced during the pre-deformation process act as predominant nucleation sites and result in a higher number of precipitates of smaller size. During the thermomechanical treatments, the work hardening behavior is altered by the state of the precipitates, namely, under-aged, peak-aged and over-aged. After the elastic–plastic transition, under-aged and peak-aged materials show a continuously decreasing work-hardening rate, while the over-aged material has an initial constant work-hardening rate. The absolute values of the work hardening rate are far less sensitive to the precipitation stage compared to aluminum alloys; a fact that explains the low work hardening capacity of magnesium compared to aluminum.

A Comprehensive Elastic-Plastic Single-Asperity Contact Model

Generally, the contact of rough surfaces is modeled and analyzed through statistical approaches, including microgeometrical measurements and description of the asperities in contact (shape, size, spacing, and asperity height), developing theoretical expressions to describe the mechanical behavior of the asperities in contact, and finally extending it to the whole surface contacts. In some of the main contact models like the Kogut-Etsion model (KE model), Jackson-Green model (JG model), and Shankar-Mayuram model (SM model), an axisymmetrical hemispherical asperity in contact with a rigid flat surface is modeled and analyzed using finite element concepts and the resultant contact parameter relations are extended to rough surface contacts. The present work addresses the complete effect of Poisson's ratio and its influence in sub surface yielding, elastic-plastic transition and inception of fully plastic contact by accounting realistic material behavior which are not covered by the above models. A unified single-asperity model is proposed and, based on the results, empirical relations are developed to predict the contact parameters (dimensionless contact load and contact area), which are then extended to statistical rough surface contacts.

Extension of subloading surface model for accurate prediction of elastoplastic deformation behavior of metals with cyclic softening

The subloading surface model has been formulated and applied to the prediction of cyclic loading behavior of metals. However, the existing formulation of this model is limited to metals exhibiting only the cyclic hardening. In the present paper, the material functions prescribing the elastic-plastic transition are extended so as to describe the inverse and reloading behavior and the strain accumulation in cyclic loading more accurately for metals exhibiting not only the cyclic hardening but also the cyclic softening behavior. The experiments on the uniaxial cyclic loading of the seamless steel pipe P110 which exhibits the cyclic softening are performed for the mechanical ratcheting and the constant strain amplitudes. The simulations to the test data are performed by using the same set of material constants. Then, the validity of the extended model for the description of cyclic loading behavior of the seamless steel pipe is verified by comparisons with the test data.

Anomalous elastic–plastic transition of MgO under shock compression

The particle velocity profiles of an MgO single crystal under shock compression were measured up to a pressure of 35 GPa by a velocity interferometer system for any reflector using a LiF window combined with a powder gun. The Hugoniot-elastic limit (HEL) of MgO along the ⟨100⟩ direction was 2.9–4.3 GPa and the initial elastic waves contain some oscillations. Along the ⟨110⟩ direction, the HEL was higher than along the ⟨100⟩ direction and anomalous, two-step-structure elastic waves were observed. These characteristics are discussed based on the slip system of the MgO crystal.

Fractal Shear Bands at Elastic-Plastic Transitions in Random Mohr-Coulomb Materials

This paper studies fractal patterns forming at elastic-plastic transitions in soil- and rock-like materials. Taking either friction or cohesion as nonfractal vector random fields with weak noise-to-signal ratios, it is found that the evolving set of plastic grains (i.e., a shear-band system) is always a monotonically growing fractal under increasing macroscopic load in plane strain. Statistical analysis is used to assess the anisotropy of those shear bands. All the macroscopic responses display smooth transitions, but as the randomness vanishes, they turn into a sharp response of an idealized homogeneous material. Parametric study shows that increasing hardening or friction makes the transition more rapid. In addition, randomness in cohesion has a stronger effect than randomness in friction, whereas dilatation has practically no influence. Adapting the concept of scaling functions, the authors find the elastic-plastic transitions in random Mohr-Coulomb media to be similar to phase transitions in condensed-matter physics: the fully plastic state is a critical point, and with three order parameters (reduced Mohr-Coulomb stress, reduced plastic volume fraction, and reduced fractal dimension), three scaling functions are introduced to unify the responses of different materials. The critical exponents are demonstrated to be universal regardless of the randomness in various constitutive properties and their random noise levels.

Microstructure effects on shock response of Cu nanofoams

Microstructure effects on shock response of Cu nanofoams are investigated with molecular dynamics simulations, including elastic-plastic deformation, Hugoniot states, void collapse, nanojetting, and vaporization. The microstructure features examined include pore shape, arrangement and size, as well as grain boundaries. The elastic-plastic transition, void collapse, and jetting including vaporization, are dependent on the microstructure, although to different extents. The void arrangement and aspect ratio play an important role. The effects of grain boundaries and void size are less pronounced. Considering the measurement scatter inherent for porous materials, the high pressure Hugoniot states are not sensitive to microstructure. Jetting during void collapse is due to tensorial velocity gradients (direction and amplitude), and a combined result of forward, divergent, and convergent flows with varying contributions; this mechanism and related processes are common for different microstructures. Free surface jetting involves necking and cavitation. Elliptical voids with large aspect ratios, and with their centers aligned linearly with the shock direction, are particularly efficient in inducing high speed jetting and vaporization.

Elastic-Plastic Transition under Uniaxial Stress BCC Tantalum

Classical molecular dynamics and lattice dynamics were utilized to study the elastic-plastic transition underuniaxial stress in defect free body center cubic (BCC) Tantalum crystals. We demonstrate that the nucleation of defects at the time scales of molecular dynamics in tantalum is due to dynamical instabilities (soft-phonons). Uniaxial compressions test were simulated along the crystallographic directions (100), (110) and (111). The results show that the nucleation of defeccts in the direction (110) is due to crystal twinning.

Modeling of Strain Hardening in the Aluminum Alloy AA6061

In this paper, the evolution of work-hardening and dynamic recovery rates vs the flow stress increase (σ − σy) in Al-Mg-Si alloys is presented. The experimental data have been extracted from stress–strain curves. All curves show an initial very rapid decrease in slope of the σ–e curve, which is associated with the elastic–plastic transition. After the elastic–plastic transition, there are typically two distinctive behaviors. For underaged alloys, there is an approximately linear decrease of work-hardening rate as (σ − σy) increases. However, for overaged alloys after elastic–plastic transition, there is a plateau in the work-hardening rate followed by an almost linear decrease. The maximum work-hardening and dynamic recovery rates are found to be dependent on the aging state. In order to investigate these phenomena, a model has been employed to simulate the work-hardening behavior of Al-Mg-Si alloys. The model is based on a modified version of Kocks–Mecking–Estrin (KME) model, in which there are three main components: (1) hardening due to forest dislocations, grain boundaries, and sub-grains; (2) hardening due to the precipitates; and (3) dynamic recovery. The modeling results are discussed and compared with the experimental data.

Removal of plastic instabilities by reversal of the applied stress

This paper presents experiments showing that the inversion of the sense of the applied stress on a specimen deformed in tension (respectively compression) results in the removal of mechanical instabilities such as the yield point and the Lüders band in a ferritic steel or serrations in an Al–Mg alloy. We show that this behaviour is connected neither to the mechanical set-up (tension, torsion, …) , nor to the crystal geometry, but to the development of antagonist internal stresses during plastic flow. We develop a multi-domain analysis of the effect of these stresses and emphasize the importance of the analysis of the elastic–plastic transition.

The dynamic effect on mechanical contacts between nanoparticles

The rich behaviors of high-speed mechanical contacts at the nanoscale have been studied. The seldom observed elastic-plastic transition governed by Hertz and Thornton models has been clearly unveiled, the origins of the hardening effect and the deformation mechanism of nanoscale plasticity have been discussed in terms of structural changes after compression and a series of physical quantities are measured including contact forces, contact radius, contact stress, coefficient of restitution and total impact time. Our simulation results closely resemble experiments and/or theoretical predictions: (i) when impact speed v is higher than Y/ρc0, the elastic-plastic deformation transition occurs, (ii) the yielded apparent elastic modulus and hardness are larger than those of the bulk, (iii) the initiating yield stress Y and hardness P0 still satisfy P0 ≈ 1.6Y, (iv) particle's volume decreases during compression, (v) contact radius a follows a [proportionality] v(2/5), (vi) at v ≥ 2000 m s(-1), the coefficient of restitution follows e [proportionality] v(-1/4) and (vii) the total time of impact follows Tc [proportionality] v(-1/5). However, there also exist many quantitative differences. The contact radius and final contact radius are underestimated by the continuum predictions while the total impact time is overestimated, but all of them reasonably agree with theoretical predictions with an increase of contact area and impact speed. The theoretical equation is adapted to predict the final contact radius during normal impact, in which the contact radius at zero load is also formulated.

A continuous Masing approach for a physically motivated formulation of temperature and strain-rate dependent plasticity

This study proposes a physically motivated continuous Masing-type model able to accurately describe the temperature and strain-rate dependent elastic–plastic behaviour of a low alloy steel. A modified Cauchy formulation for the element yield strain distribution function is presented that describes a continuous elastic–plastic transition on the basis of four physically interpretable and easily determinable parameters. The performance of the model is compared to conventional strain-hardening models as well as to monotonic and loading–unloading experiments. Furthermore, the description of monotonic temperature and strain-rate dependent constitutive behaviour of a bainitic 2CrMoNiWV steam turbine rotor steel is evaluated on the basis of experimental data. The proposed model represents very well the elastic–plastic constitutive behaviour of 2CrMoNiWV and allows for an adequate extrapolation from a restricted experimentally covered regime. It is believed to form a promising basis for the development of plasticity model formulations.