Showing papers on "Viscoplasticity published in 2007"

Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet

Abstract: Uniaxial compression test data were obtained from magnesium alloy AZ31B sheet material tested along three sample directions (rolling, transverse and normal direction) over the temperature range T = 22–250 ◦ C. The yield point during in-plane compression is insensitive to temperature, up to 200 ◦ C, suggesting that athermal mechanisms are responsible for yielding. The in-plane compression samples exhibit very low r-values, which provides another signature of significant twinning activity in magnesium sheet, in addition to the characteristic sigmoidal strain hardening curve. By varying the critical resolved shear strengths (CRSS) and hardening behaviors of the deformation mechanisms, it is possible to model the changes in the flow stress profile, the strain anisotropy, and texture evolution using a viscoplastic self-consistent polycrystal model. Notably, the CRSS values for basal slip were observed to be constant, while that of twinning increased slightly, and the CRSS values of thermally activated slip

Plasticity and geophysical flows: A review

Abstract: The objective of this review is to examine how the concept of plasticity is used in geophysical fluid dynamics. Rapid mass movements such as snow avalanches or debris flows involve slurries of solid particles (ice, boulder, clay, etc.) within an interstitial fluid (air, water). The bulk behavior of these materials has often been modeled as plastic materials, i.e., a plastic material yields and starts to flow once its stress state has significantly departed from equilibrium. Two plastic theories are of common use in fluid dynamics: Coulomb plasticity and viscoplasticity. These theories have little in common, since ideal Coulomb materials are two-phase materials for which pore pressure and friction play the key role in the bulk dynamics, whereas viscoplastic materials (e.g., Bingham fluids) typically behave as single-phase fluids on the macroscopic scale and exhibit a viscous behavior after yielding. Determining the rheological behavior of geophysical materials remains difficult because they encompass coarse, irregular particles over a very wide range of size. Consequently, the true nature of plastic behavior for geophysical flows is still vigorously debated. In this review, we first set out the continuum-mechanics principles used for describing plastic behavior. The notion of yield surface rather than yield stress is emphasized in order to better understand how tensorial constitutive equations can be derived from experimental data. The notion of single-phase or two-phase behaviors on the macroscopic scale is then examined using a microstructural analysis on idealized suspensions of spheres within a Newtonian fluid; for these suspensions, the single-phase approximation is valid only at very high or low Stokes numbers. Within this framework, the bulk stress tensor can also be constructed, which makes it possible to give a physical interpretation to yield stress. Most of the time, depending on the bulk properties (especially, particle size) and flow features, bulk behavior is either Coulomb-like or viscoplastic in simple-shear experiments. The consequences of the rheological properties on the flow features are also examined. Some remarkable properties of the governing equations describing thin layers flowing down inclined surfaces are discussed. Finally, the question of parameter fitting is tackled: since rheological properties cannot be measured directly in most cases, they must be evaluated from field data. As an example, we show that the Coulomb model successfully captures the main traits of avalanche motion, but statistical analysis demonstrates that the probability distribution of the friction coefficient is not universal.

A new constitutive equation for elastoviscoplastic fluid flows

Abstract: From a thermodynamic theory, a new model for elastoviscoplastic fluid flow is presented It extends the Bingham viscoplastic model and the Oldroyd viscoelastic model Fundamental flows are studied: simple shear flow, uniaxial elongation and large amplitude oscillatory shear The complex moduli (G',G'') are founded to be in qualitative agreement with experimental data for materials that present microscopic network structures and large scale rearrangements Various fluids of practical interest, such as liquid foams, droplet emulsions or blood, present such elastoviscoplastic behavior: at low stress, the material behaves as a viscoelastic solid, whereas at stresses above a yield stress, the material behaves as a fluid

Gradient single-crystal plasticity with free energy dependent on dislocation densities

Abstract: This study develops a small-deformation theory of strain-gradient plasticity for single crystals. The theory is based on: (i) a kinematical notion of a continuous distribution of edge and screw dislocations; (ii) a system of microscopic stresses consistent with a system of microscopic force balances, one balance for each slip system; (iii) a mechanical version of the second law that includes, via the microscopic stresses, work performed during viscoplastic flow; and (iv) a constitutive theory that allows: • the free energy to depend on densities of edge and screw dislocations and hence on gradients of (plastic) slip; • the microscopic stresses to depend on slip-rate gradients. The microscopic force balances when augmented by constitutive relations for the microscopic stresses results in a system of nonlocal flow rules in the form of second-order partial differential equations for the slips. When the free energy depends on the dislocation densities the microscopic stresses are partially energetic, and this, in turn, leads to backstresses in the flow rules; on the other hand, a dependence of these stresses on slip-rate gradients leads to a strengthening. The flow rules, being nonlocal, require microscopic boundary conditions; as an aid to numerical solutions a weak (virtual power) formulation of the flow rule is derived.

Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations

Abstract: The higher-order stress work-conjugate to slip gradient in single crystals at small strains is derived based on the self-energy of geometrically necessary dislocations (GNDs). It is shown that this higher-order stress changes stepwise as a function of in-plane slip gradient and therefore significantly influences the onset of initial yielding in polycrystals. The higher-order stress based on the self-energy of GNDs is then incorporated into the strain gradient plasticity theory of Gurtin [2002. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5–32] and applied to single-slip-oriented 2D and 3D model crystal grains of size D. It is thus found that the self-energy of GNDs gives a D - 1 -dependent term for the averaged resolved shear stress in such a model grain under yielding. Using published experimental data for several polycrystalline metals, it is demonstrated that the D - 1 -dependent term successfully explains the grain size dependence of initial yield stress and the dislocation cell size dependence of flow stress in the submicron to several-micron range of grain and cell sizes.

Flows of viscoplastic materials: models and computations

Abstract: Viscoplasticity is characterized by a yield stress, below which the materials will not deform, and above which they will deform and flow according to different constitutive relations. Viscoplastic models include the Bingham plastic, the HerschelBulkley model, and the Casson model. All of these ideal models are discontinuous. Analytical solutions exist for such models in simple flows. For general flow fields, it is necessary to develop numerical techniques to track down yielded/unyielded regions. This can be avoided by introducing into the models a continuation parameter, which facilitates the solution process and produces virtually the same results as the ideal models by the right choice of its value. This work reviews several benchmark problems of viscoplastic flows, such as entry and exit flows from dies, flows around a sphere and a cylinder, and squeeze flows. Examples are also given for typical processing flows of viscoplastic materials, where the extent and shape of the yielded/unyielded regions are clearly shown.

A finite element method for animating large viscoplastic flow

Abstract: We present an extension to Lagrangian finite element methods to allow for large plastic deformations of solid materials. These behaviors are seen in such everyday materials as shampoo, dough, and clay as well as in fantastic gooey and blobby creatures in special effects scenes. To account for plastic deformation, we explicitly update the linear basis functions defined over the finite elements during each simulation step. When these updates cause the basis functions to become ill-conditioned, we remesh the simulation domain to produce a new high-quality finite-element mesh, taking care to preserve the original boundary. We also introduce an enhanced plasticity model that preserves volume and includes creep and work hardening/softening. We demonstrate our approach with simulations of synthetic objects that squish, dent, and flow. To validate our methods, we compare simulation results to videos of real materials.

Rheology of concentrated carbon nanotube suspensions

Abstract: The rheological properties of non-Brownian carbon nanotube suspensions are measured over a range of nanotube volume fractions spanning the transition from semidilute to concentrated. The polymer-stabilized nanotubes are “sticky” and form a quiescent elastic network with a well-defined shear modulus and yield stress that both depend strongly on nanotube volume fraction with different but related critical exponents. We compare controlled-strain-rate and controlled-stress measurements of yielding in shear flow, and we study the effect of slow periodic stress reversal on yielding and the arrest of flow. Our measurements support a universal scaling of both the linear viscoelastic and steady-shear viscometric response. The former allows us to extract the elastic shear modulus of semidilute nanotube networks for values that are near or below the resolution limit of the rheometers used, while the latter provides a similar extrapolation of the yield stress. A simple scaling argument is used to model the dependence...

Deformation of (Mg,Fe)SiO3 post-perovskite and D'' anisotropy.

Abstract: Polycrystalline (Mg0.9,Fe0.1)SiO3 post-perovskite was plastically deformed in the diamond anvil cell between 145 and 157 gigapascals. The lattice-preferred orientations obtained in the sample suggest that slip on planes near (100) and (110) dominate plastic deformation under these conditions. Assuming similar behavior at lower mantle conditions, we simulated plastic strains and the contribution of post-perovskite to anisotropy in the D″ region at the Earth core-mantle boundary using numerical convection and viscoplastic polycrystal plasticity models. We find a significant depth dependence of the anisotropy that only develops near and beyond the turning point of a downwelling slab. Our calculated anisotropies are strongly dependent on the choice of elastic moduli and remain hard to reconcile with seismic observations.

Optional Strain-Rate Forms for the Johnson Cook Constitutive Model and the Role of the Parameter

Abstract: Summary: A brief review of the standard Johnson-Cook model is presented. Three optional strain-rate forms are introduced and calibrated to laboratory data for A36 steel. Next a brief description of the LS-DYNA implementation of the new strain-rate forms within the existing viscoplastic formulation of the JohnsonCook model is presented. Finally, all four calibrated strain-rate forms are exercised in single element uniaxial stress test simulations, and the results are compared with the A36 steel effective stress versus effective plastic strain data at three different strain rates. The comparison of the calibrated model response to the quasi-static A36 steel data is used to illustrate the role of the Johnson-Cook parameter 0 e& .

An elasto-viscoplastic interface model for investigating the constitutive behavior of nacre

Abstract: In order to better understand the strengthening mechanism observed in nacre, we have developed an interface computational model to simulate the behavior of the organic present at the interface between aragonite tablets. In the model, the single polymer-chain behavior is characterized by the worm-like-chain (WLC) model, which is in turn incorporated into the eight-chain cell model developed by Arruda and Boyce [Arruda, E.M., Boyce, M.C., 1993a. A three-dimensional constitutive model for the large stretches, with application to polymeric glasses. Int. J. Solids Struct. 40, 389–412] to achieve a continuum interface constitutive description. The interface model is formulated within a finite-deformation framework. A fully implicit time-integration algorithm is used for solving the discretized governing equations. Finite element simulations were performed on a representative volume element (RVE) to investigate the tensile response of nacre. The staggered arrangement of tablets and interface waviness obtained experimentally by Barthelat et al. [Barthelat, F., Tang, H., Zavattieri, P.D., Li, C.-M., Espinosa, H.D., 2007. On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J. Mech. Phys. Solids 55 (2), 306–337] was included in the RVE simulations. The simulations showed that both the rate-dependence of the tensile response and hysteresis loops during loading, unloading and reloading cycles were captured by the model. Through a parametric study, the effect of the polymer constitutive response during tablet-climbing and its relation to interface hardening was investigated. It is shown that stiffening of the organic material is not required to achieve the experimentally observed strain hardening of nacre during tension. In fact, when ratios of contour length/persistent length experimentally identified are employed in the simulations, the predicted stress–strain behavior exhibits a deformation hardening consistent with the one measured experimentally and also captured by the phenomenological cohesive model used in the study carried out by Barthelat et al. [Barthelat, F., Tang, H., Zavattieri, P.D., Li, C.-M., Espinosa, H.D., 2007. On the mechanics of mother-of-pearl: a key feature in the material hierarchical structure. J. Mech. Phys. Solids 55 (2), 306–337]. The simulation results also reveal that the bulk modulus of the polymer controls the rate of hardening, feature not captured by more simple cohesive laws.

Coupled thermo-mechanical modelling of bulk-metallic glasses: Theory, finite-element simulations and experimental verification

Abstract: A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989–1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress–strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni–Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429–3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress–strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress–strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82–87].