Showing papers on "Viscoplasticity published in 2014"

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Abstract: The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Experimental signatures of a nonequilibrium phase transition governing the yielding of a soft glass.

Abstract: We present direct experimental signatures of a nonequilibrium phase transition associated with the yield point of a prototypical soft solid-a binary colloidal glass. By simultaneously quantifying single-particle dynamics and bulk mechanical response, we identified the threshold for the onset of irreversibility with the yield strain. We extracted the relaxation time from the transient behavior of the loss modulus and found that it diverges in the vicinity of the yield strain. This critical slowing down is accompanied by a growing correlation length associated with the size of regions of high Debye-Waller factor, which are precursors to yield events in glasses. Our results affirm that the paradigm of nonequilibrium critical phenomena is instrumental in achieving a holistic understanding of yielding in soft solids.

The development of continuum damage mechanics-based theories for predicting forming limit diagrams for hot stamping applications:

Abstract: This paper presents a novel plane-stress continuum damage mechanics (CDM) model for the prediction of the different shapes of forming limit diagrams (FLCs) for aluminium alloys under hot stamping conditions. Firstly, a set of uniaxial viscoplastic damage constitutive equations is determined from tensile experimental data of AA5754 at a temperature range of 350–550℃ and strain rates of 0.1, 1.0 and 10 s−1. The tests were carried out on Gleeble materials simulator (3800). Based on the analysis of features of FLCs for different materials forming at different temperatures, a plane-stress damage equation is proposed to take account the failure of materials at different stress-state sheet metal forming conditions. In this way, a set of multiaxial viscoplastic damage constitutive equations is formulated. The model is calibrated from the FLC data at temperature of 350℃ and strain rate of 1.0 s−1 for AA5754. A good agreement has been achieved between the experimental and numerical data. The effect of the maximum p...

Microscale plastic strain heterogeneity in slip dominated deformation of magnesium alloy containing rare earth

Abstract: The propensity for the magnesium alloy ZEK100 to develop large microscale plastic strain heterogeneity has been quantified and correlated to microstructure using a combination of experiments and simulations. Conditions were specifically selected where deformation is dominated by slip rather than twinning. Digital image correlation measurements of intragranular plastic strain heterogeneity have revealed plastic strains as large as 5 times the macroscopic tensile strain. This strain amplification was found to be neither spatially correlated nor correlated with crystal orientation. Large local strains were, however, found to be statistically linked to proximity to grain boundaries. This suggests the importance of interactions between neighboring grains. To investigate this further full-field viscoplastic Fast Fourier Transform (VPFFT) crystal plasticity simulations were performed on synthetic microstructures representative of the material studied experimentally. It was found that both the macroscopic stress–strain response as well as the local plastic strain distribution could be well reproduced when the anisotropy in ‘hardness’ of the basal and non-basal slip systems was sufficiently high. Strain amplification was found to occur, in this case, to slip in regions of high basal slip activity adjacent to regions of high non-basal slip activity.

Plane wave simulation of elastic-viscoplastic single crystals

Abstract: Despite the large amount of research that has been performed to quantify the high strain rate response of Aluminum, few studies have addressed effects of crystal orientation and subsequent crystal-level microstructure evolution on its high strain rate response. To study orientation effects in single crystal Al, both a constitutive model and novel numerical method have been developed. A plane wave formulation is developed so that materials undergoing anisotropic viscoplastic deformation can be modeled in a thermodynamically consistent framework. Then, a recently developed high strain rate viscoplastic model is extended to include single crystal effects by incorporating higher order crystal-based thermoelasticity, anisotropic plasticity kinetics, and distinguishing influences of forest and parallel dislocation densities. Steady propagating shock waves are simulated for [100], [110], and [111] oriented single crystals and compared to existing experimental wave profile and strength measurements. Finally, influences of initial orientation and peak pressure ranging from 0 to 30 GPa are quantified. Results indicate that orientation plays a significant role in dictating the high rate response of both the wave profile and the resultant microstructure evolution of Al. The plane wave formulation can be used to evaluate microstructure-sensitive constitutive relations in a computationally efficient framework.

Two-temperature continuum thermomechanics of deforming amorphous solids

Abstract: There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material – the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations – are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables, that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.

Thermomechanical constitutive modelling of shape memory polymer including continuum functional and mechanical damage effects

Abstract: A multi-mechanism-based phenomenological model is developed within the finite deformation kinematics framework for capturing the thermomechanical behaviour of shape memory polymers (SMPs) both during programming and in service. Particularly, the damage mechanisms in SMPs are studied within the continuum damage mechanics (CDMs) framework in which they are classified into mechanical or physical damage, induced during service condition, e.g. fatigue and functional damage induced during thermomechanical cycles, e.g. shape recovery loss. Statistical mechanics is incorporated to describe the initiation and saturation of these deformation mechanisms. The main advantage of the presented viscoplastic model, comparing to the existing counterparts, is its simplicity by minimizing the need for curve fitting, and capability in simulating the nonlinear stress–strain behaviour of amorphous, crystalline or semicrystalline SMPs. The developed viscoplastic CDM model takes into account several distinctive deformation mechanisms involved in the thermomechanical cycle of SMPs, including glass transition loss events, temperature-dependent material properties, stress relaxation, shape recovery transient events and damage effects. The established model correlates well with the experimental results and its computational capabilities provide material designers with a powerful design tool for future SMP applications.

Modeling of flow behavior of Ti–6Al–4V alloy at elevated temperatures

Abstract: Titanium alloy grade Ti–6Al–4V has been widely used for many applications such as aircraft structural component, machine parts and especially parts for medical equipment. To better understand the deformation behavior and microstructure evolution of the material under the hot working process is significant for achieving desired dimension and final mechanical properties of a product. In this study, stress–strain responses of the Ti–6Al–4V alloy were investigated using compression tests at different elevated temperatures and strain rates. The determined flow behaviors of the alloy were subsequently calculated according to the constitutive models based on the hyperbolic sine equation, the Cingara equation, and the Shafiei and Ebrahimi equation. Influences of both work hardening and dynamic recrystallization on the hot deformation behavior of the material were described. Then, the predicted flow curves were compared with experimental results and obtained discrepancies were characterized. Accurate modeling of flow curves can considerably assist in design of the forming process.

Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading

Abstract: A very soft clay layer is highly compressible and exhibits significant creep under loading. The classical linearly elastic constitutive relationship and small-strain assumption are not suitable for...

Echoes in x-ray speckles track nanometer-scale plastic events in colloidal gels under shear

Abstract: We report x-ray photon correlation spectroscopy experiments on a concentrated nanocolloidal gel subject to in situ oscillatory shear strain. The strain causes periodic echoes in the speckle pattern that lead to peaks in the intensity autocorrelation function. Above a threshold strain that is near the first yield point of the gel, the peak amplitude decays exponentially with the number of shear cycles, signaling irreversible particle rearrangements. The wave-vector dependence of the decay rate reveals a power-law distribution in the size of regions undergoing shear-induced rearrangement. The gel also displays strain softening well below the threshold, indicating a range of strains at which the rheology is nonlinear but the microscopic deformations are reversible.

A photoviscoplastic model for photoactivated covalent adaptive networks

Abstract: Light activated polymers (LAPs) are a class of contemporary materials that when irradiated with light respond with mechanical deformation. Among the different molecular mechanisms of photoactuation, here we study radical induced bond exchange reactions (BERs) that alter macromolecular chains through an addition-fragmentation process where a free chain whose active end group attaches then breaks a network chain. Thus the BER yields a polymer with a covalently adaptable network. When a LAP sample is loaded, the macroscopic consequence of BERs is stress relaxation and plastic deformation. Furthermore, if light penetration through the sample is nonuniform, resulting in nonuniform stress relaxation, the sample will deform after unloading in order to achieve equilibrium. In the past, this light activation mechanism was modeled as a phase evolution process where chain addition-fragmentation process was considered as a phase transformation between stressed phases and newly-born phases that are undeformed and stress free at birth. Such a modeling scheme describes the underlying physics with reasonable fidelity but is computationally expensive. In this paper, we propose a new approach where the BER induced macromolecular network alteration is modeled as a viscoplastic deformation process, based on the observation that stress relaxation due to light irradiation is a time-dependent process similar to that in viscoelastic solids with an irrecoverable deformation after light irradiation. This modeling concept is further translated into a finite deformation photomechanical constitutive model. The rheological representation of this model is a photoviscoplastic element placed in series with a standard linear solid model in viscoelasticity. A two-step iterative implicit scheme is developed for time integration of the two time-dependent elements. We carry out a series of experiments to determine material parameters in our model as well as to validate the performance of the model in complex geometrical and loading configurations. The comparison between the finite element simulations and experiments shows that the model can accurately capture the response of the LAP under a wide range of coupled photo-mechanical loading conditions, such as light induced stress relaxation, creep in tension, and bending. Furthermore, we demonstrate the versatility of the model by simulating a series of examples that exhibit complex three-dimensional, time-dependent photodeformation, including photoorigami, photoforming, and photobulge tests.

2D viscoplastic finite element modelling of slow landslides: the Portalet case study (Spain)

Abstract: This paper proposes a hydro-geomechanical finite element model to reproduce the kinematic behaviour of large slow landslides. The interaction between solid skeleton and pore fluids is modelled with a time dependent u–pw formulation and a groundwater model that takes into account recorded daily rainfall intensity. A viscoplastic constitutive model based on Perzyna’s theory is applied to reproduce soil viscous behaviour and the delayed creep deformation. The proposed model is applied to Portalet landslide (Central Spanish Pyrenees). This is an active paleo-landslide that has been reactivated by the construction of a parking area at the toe of the slope. The stability analysis reveals that, after the constructive solutions were undertaken, the slope is in a limit equilibrium situation. Nevertheless, time-dependent analysis reproduces the nearly constant strain rate (secondary creep) and the acceleration/deceleration of the moving mass due to hydrological changes. Overall, the model reproduces a 2-m displacement in the past 8 years that coincides with in situ monitoring data. The proposed model is useful for short- and mid-term predictions of secondary creep. However, long-time predictions remain uncertain, stability depends strongly on the position of the water table depth and new failures during tertiary creep due to soil temporal microstructural degradation are difficult to calibrate.