Generalizing J_2 flow theory: Fundamental issues in strain gradient plasticity

It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed： one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhans and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.

A phenomenological model for plastic flow behavior of rotating band material with a large temperature range

The plastic flow behavior of the rotating band material is investigated in this paper. The rotating band material is processed from H96 brass alloy, which is hardened to a much higher yield strength compared to the annealed one. The dynamically uniaxial compression behavior of the material is tested using the split Hopkinson pressure bar(SHPB) with temperature and strain rate ranging from 297 to 1073 K and500 to 3000 s^(-1), respectively, and a phenomenological plastic flow stress model is developed to describe the mechanical behavior of the material. The material is found to present noticeable temperature sensitivity and weak strain-rate sensitivity. The construction of the plastic flow stress model has two steps. Firstly, three univariate stress functions, taking plastic strain, plastic strain rate and temperature as independent variable, respectively, are proposed by fixing the other two variables. Then, as the three univariate functions describe the special cases of flow stress behavior under various conditions, the principle of stress compatibility is adopted to obtain the complete flow stress function. The numerical results show that the proposed plastic flow stress model is more suitable for the rotating band material than the existing well-known models.

STUDY ON FLOW STRESS OF 7022 ALUMINUM ALLOY SHEET UNDER DIFFERENT TEMPERATURES AND STRAIN RATES

Warm tensile tests for aluminum alloy 7022 sheet are held at different temperatures and strain rates. The range of temperature is 293-773 K and that of the strain rate is 0. 001-0.1 s^-1. The warm tensile properties,relations among temperature,strain rate,and the flow stress are discussed. Constitutive equations under the warm tension are obtained based on revised Hooke law and Grosman equation. It is concluded that flow stress declines with the increase of the temperature and the decrease of the strain rates. The elongation percentage increases with the increase of the temperature and the decrease of strain rate.

Multi-layer Tectonic Model for Intraplate Deformation and Plastic-Flow Network in the Asian Continental Lithosphere

In a large area of the east—central Asian continent there is a unified seismic network system composed of two families of large—seismic belts that intersect conjugately. Such a seismic network in the middle—upper crust is actually a response to the plastic flow network in the lower lithosphere including the lower crust and lithospheric mantle. The existence of the unified plastic flow system confirms that the driving force for intraplate tectonic deformation results mainly from the compression of the India plate, while the long-range transmission of the force is carried out chiefly by means of plastic flow. The plastic flow network has a control over the intraplate tectonic deformation.

Homogeneous Plastic Flow of Fully Amorphous and Partially Crystallized Zr_(41.2)Ti_(13.8)Cu_(12.5)Ni_(10)Be_(22.5) Bulk Metallic Glass

The homogeneous plastic flow of fully amorphous and partially crystallized Zr(41.2)Ti(13.8)Cu(12.5)Ni(10)Be(22.5) bulk metallic glass (Vitl) has been investigated by compression tests at high temperatures in supercooled liquid region. Experimental results show that at sufficiently low strain rates, the supercooled liquid of the fully amorphous alloy reveals Newtonian flow with a linear relationship between the flow stress and strain rate. As the strain rate is increased, a transition from linear Newtonian to nonlinear flow is detected, which can be explained by the transition state theory. Over the entire strain rate interval investigated, however, only nonlinear flow is present in the partially crystallized alloy, and the flow stress for each strain rate is much higher. It is found that the strain rate-stress relationship for the partially crystaltized alloy at the given temperature of 646 K also obeys the sinh law derived from the transition state theory, similar to that of the initial homogeneous amorphous alloy. Thus, it is proposed that the flow behavior of the nanocrystalline/amorphous composite at 646 K is mainly controlled by the viscous flow of the remaining supercooled liquid.

THE VOID-SIZE EFFECT ON PLASTIC FLOW LOCALIZATION IN THE GURSON MODEL

Recent studies have shown that the size of microvoids has a significant effect on the void growth rate.The purpose of this paper is to explore whether the void size effect can influence the plastic flow localization in ductile materials.We have used the extended Gurson's dilatational plasticity theory,which accounts for the void size effect,to study the plastic flow localization in porous solids with long cylindrical voids.The localization model of Rice is adopted,in which the material inside the band may display a different response from that outside the band at the incipient plastic flow localization.The present study shows that it has little effect on the shear band angle.

STUDY OF TRANSFORMATION PLASTICITY IN TETRAGONAL ZIRCONIA POLYCRYSTALS BY MOIRE INTERFEROMETRY

Transformation plasticity in ceria-stabilized tetragonal zirconia poly- crystals due to the stress-induced tetragonal-to-monoclinic martensitic transforma- tion under tension and bending is studied by moire interferometry. The whole fringe patterns including u fields and v fields are acquired. According to these patterns, the distributions of transformation plasticity in transformation zones are obtained, and the phenomenon of plastic flow localization for transformation is revealed. The above work provides a significant experimental foundation for establishing transformation constitutive relations

The hot compressive deformation behavior of cast Mg-Gd-Y-Zn-Zr alloys with and without LPSO phase in their initial microstructures

Samples of Mg-8.2Gd-3.8Y-1.1Zn-0.4Zr alloy with and without an intragranular lamellae-shaped long period stacking ordered(LPSO)phase were prepared through heat treatment and a series of hot compression tests on these materials were conducted to examine and evaluate the influence of LPSO on the hot compressive deformation behavior and deformation mechanisms at a given alloy composition.The values of activation energy for plastic flow(Qc)of the solution treated(without LPSO phase)and annealed alloys(with intragranular LPSO phase)were larger than that for pure Mg,indicating that the presence of a high amount of rare earth(RE)elements and LPSO in the Mg matrix significantly increases Qc.The Qcvalue of the annealed alloy was larger than that of the solution treated alloy at all the strain levels(223.3 vs.195.5 k J/mol in average)and the largest difference in Qcbetween the two alloys was recorded at the smallest strain of 0.1 where precipitation of LPSO during deformation was limited in the solution treated alloy.These observations imply that the formation of LPSO phase out of the RE-rich solid solution matrix during deformation increases Qc,but the increment is not so large.Analysis of the hot compressive data of the alloys with LPSO phase and the alloys with RE-rich solid solution matrix in literatures indicates the similarity of the effect of the LPSO and RE-rich solid solution matrix phases on Qcand high-temperature strength.

Stress-drop effect on brittleness evaluation of rock materials

Uniaxial or triaxial compression test of cylindrical rock specimens using rock mechanics testing machine is a basic experimental method to study the strength and deformation characteristics of rock and the development process of rock fracture. Extensive literature review has been conducted on this issue;meanwhile, experimental and numerical studies have been conducted on the stress-drop effect on the brittleness of rock materials. A plastic flow factor of λ is proposed to describe the stress-drop effect. Evaluation methods of the factor λ corresponding to the four yield criteria of rock mass are proposed. Those four yield criteria are Tresca criterion, von-Mises criterion, Mohr-Coulomb criterion and Drucker-Prager criterion. For simplicity purposes, an engineering approximation approach has been proposed to evaluate the stress-drop with a non-zero strain increment. Numerical simulation results validated the effectiveness of the plastic flow factors λ as well as the engineering approximation approach. Based on the results in this study, finite element code can be programmed for brittle materials with stress-drop, which has the potential to be readily incorporated in finite element codes.

ON NONPROPORTIONAL CYCLIC PLASTIC BEHAVIOR OF STEEL 40

An experimental investigation was carried out on the flow characteristic and hardening of steel 40 subjected to complex combined axial-torsional cyclic straining. For a specific cyclic strain path, the steel has mainly cyclic softening behavior when the strain amplitude is small. While with an increase of the effective strain amplitude, the softening becomes small, but there is the cyclic softening even though the steel is subjected to the cyclic loading by a square strain path. However, the steel has cyclic additional hardening by a nonproportional path, compared with the proportional cycling. Generally, the additional hardening is small and its historical effect is not obvious at small strain amplitude. The additional hardening is remarkable by a cross-triangular strain path of large strain amplitude. The memory of the history of nonproportional cyclic loading, the direction of plastic flow and the plastic modulus of the steel were also studied.

INSTANTANEOUS THERMAL EXPANSION BEHAVIOR OF HETEROGENEOUS MATERIALS WITH A WORK-HARDENING ELASTOPLASTIC MATRIX AND ELASTIC SPHEROIDAL INHOMOGENEITIES

The instantaneous thermal expansion behavior of-two-phase heterogeneous materials subjected to a uniform temperature change is explored in the present study. The matrix phase is assumed to be a work-hardening ductile metal and the dispersive phase is assumed to consist of either aligned or randomly-oriented, elastic,, spheroidal inhomogeneities. The plastic flow and decreasing stiffness of the matrix during Eshelby's transformation strain of the equivalent inclusions are accounted for by using the deformation theory of plasticity. The explicit results of the instantaneous overall thermal expansion coefficients and the critical inelastic temperature changes are presented for aligned disc- and fiber-inclusions. For the spherical and randomly-oriented spheroidal inclusion, the present study demonstrates that when the yielding of the composites is governed by the average matrix stress, the overall response is always elastic in spite of the temperature change.

Thermal shock of subsurface material with plastic flow during scuffing

The thermal shock of subsurface material with shear instability and severe plastic flow during scuffing was investigated.The scuffing damage of M50 steel was tested using a high-speed rolling-sliding contact test rig,and the transient temperature during scuffing was calculated using the Fourier transform method considering the effects of both frictional heat and plastic work.The results show that a thermal shock with a rapid rise and subsequent rapid decrease in the contact temperature is generated in the subsurface layers.The frictional power intensity generates a high temperature rise,leading to the austenitization of the subsurface material.Consequently,the plastic flow is generated in the subsurface layer under the high shear stress,and the resulting plastic strain energy generates a further temperature increase.Subsequently,a rapid decrease in the contact temperature quenches the material,resulting in clear shear slip bands and retained austenite in the subsurface layers of the M50 steel.

Magnetic resonance imaging and cell-based neurorestorative therapy after brain injury

Restorative cell-based therapies for experimental brain injury, such as stroke and traumatic brain injury,substantially improve functional outcome. We discuss and review state of the art magnetic resonance imaging methodologies and their applications related to cell-based treatment after brain injury. We focus on the potential of magnetic resonance imaging technique and its associated challenges to obtain useful new information related to cell migration, distribution, and quantitation, as well as vascular and neuronal remodeling in response to cell-based therapy after brain injury. The noninvasive nature of imaging might more readily help with translation of cell-based therapy from the laboratory to the clinic.

Numerical simulation for the comparison of thermal and plastic material flow behavior between symmetrical and asymmetrical boundary conditions during friction stir welding

An accurate description of the contact condition between the tool and the workpiece material is one of the most important issues for expounding the underlying multi-physics coupled mechanism during friction stir welding(FSW)process.In the present study,a novel asymmetrical boundary condition around the tool-workpiece contact interface is proposed for the FSW of AA2024-T4 alloy.A three-dimensional computational fluid dynamics model is employed for the comparison of the coupled thermal and plastic material flow behavior between asymmetrical and symmetrical boundary conditions.Numerical results of heat generation,temperature distribution,tunnel defect formation and material flow streamline during the welding process are quantitatively analyzed.Besides,various experimental measuring methods are utilized to obtain information about temperature,thermal cycle,tool torque and horizontal cross-section around the exiting keyhole.It is revealed that the modeling results of heat flux density and temperature distribution around the pin,as well as material flow characteristics all change significantly for the two models with different boundary conditions.Particularly,the asymmetrical boundary condition is more capable of predicting temperature fluctuation,plastic material flow along the vertical direction,as well as tunnel defect formation during FSW.Therefore,the superiority of the model with asymmetrical boundary condition over the symmetrical one during the numerical simulation of FSW is elucidated.

Recent progress in studies of experimental rock mechanics and tectonophysics in China

This paper reviews the recent progress in the studies of experimental rock mechanics and tectonophysics concerning seismology and physics of the Earths interior in China. The progress is presented in the following aspects: a) A lot of results of experiment and numerical simulation enrich our knowledge of the brittle fracturing process under the condition with heterogeneity in material and structure; b) Some new results on frictional behavior of non-homogeneous faults reveal the complexity of faulting behavior; c) Some new results on the brittle-plastic transition and plastic flow are obtained; especially the important progress is obtained on rheological properties of rocks in the lower crust and the upper mantle; d) A lot of experimental results are obtained on rock physics at high temperature and pressure and have been used in study of material composition and state. These results provide useful information for understanding the physical properties and deformation mechanisms of material of the Earths interior and earthquake physics.

Depinning Dynamics of Fluid Monolayer on a Quenched Substrate

Langevin simulations are preformed on the depinning dynamics of fluid monolayer on a quenched substrate. With increase in the strength of the substrate, we find for the first time a crossover from elastic crystal to smectic flows as well as a crossover from smectic to plastic flows above the depinning. A power-law scaling relationship can be derived between the drift velocity and the driving force for both the elastic crystal and smectic flows, but fails to be obtained for the plastic flow. The power-law exponents are found to be no larger than 1 for the elastic crystal flow and larger than 1 for the smeetic flow. The critical driving force and the averaged intensity of Bragg peaks remain invariant basically in the regime of smectic flow. A sudden increase in the critical driving force is observed within the crossover from the smeetic to plastic flows, and the averaged intensity of Bragg peaks shows sudden decreases within the crossovers both from the elastic crystal to smectic flows and from the smectic to plastic flows. The results are helpful for understanding the slip dynamics of fluids on a molecular level.

PREDICTION OF PATH-DEPENDENT FAILURE IN ALUMINUM SHEET METALS UNDER FORMING OPERATIONS

An approximate macroscopic yield criterion for anisotropic porous sheet metals is adopted in a failure prediction methodology that can be used to investigate the failure of sheet metals under forming operations. This failure prediction methodology is developed based on the Marciniak-Kuczynski approach by assuming a slightly higher void volume fraction inside randomly oriented imperfecte analysis. Here, a nonproportional deformation history including relative rotation of principal stretch directions is identified in a selected critical element of an aluminum sheet from a FEM fender forming simulation. Based on the failure prediction methodology, the failure of the critical sheet element is investigated under the non-proportional deformation history. The results show that thiven non-proportional deformation history.

THE VARIATIONAL PRINCIPLES AND APPLICATION OF NONLINEAR NUMERICAL MANIFOLD METHOD

The physical-cover-oriented variational principle of nonlinear numerical manifold method (NNMM) for the analysis of plastical problems is put forward according to the displacement model and the characters of numerical manifold method (NMM). The theoretical calculating formulations and the controlling equation of NNMM are derived. As an example, the plate with a hole in the center is calculated and the results show that the solution precision and efficiency of NNMM are agreeable.

Static and dynamical cavitation for incompressible hyperelastic-plastic material

Bifurcation problems both for static and dynamical cavitation in a solid sphere composed of the incompressible hyperelasticplastic material, under uniformly distributed tensile boundary dead load were studied. For each problem, cavity forms at the center of the sphere when the tensile load is larger than its critical value. Bifurcation curves and the growth curves for the plastic deformation region were given. For static cavitation, the deformation displays three stages, namely, fully elastic, elasto-plastic and fully plastic stages. For dynamical cavitation, the cavity grows without bound and the sphere displays plastic flow.

Evaluation of embankment foundation creep in conditions of deep bedding of roof in permafrost soils

Railroad operating experience in permafrost conditions has shown that deformations of embankments on thawing foun- dations last for a long time. After an initial period of heat settlement due to permafrost degradation, the determining factor is the plastic flow of seasonal thawed soils of the foundation upper layer under the embankment. This paper provides a method to evaluate these deformations, and calculation examples using data from line sections of the Chum-Labytnangi Railway in northwestern Russia. It also discusses several methods of embankment stabilization, including the use of ver- tical thermosiphons.