Viscoplastic Effects Research Articles

A Modeling Framework for the Thermoforming of Carbon Fiber Reinforced Thermoplastic Composites.

A comprehensive modeling framework for the thermoforming of polymer matrix woven laminate composite was developed. Two numerical indicators, the slip path length and traction magnitude, have been identified to be positively correlated to matrix smearing and wrinkling defects. The material model has been calibrated with picture-frame experimental results, and the prediction accuracy for intra-ply shear and thickness distribution was examined with measurements of the physically formed parts. Specifically, thickness prediction for most locations on the formed parts was accurate within an 11.6% error margin. However, at two points with significant intra-ply shear, the prediction errors increased to around 20%. Finally, a parametric study was conducted to determine the relationship between various process parameters and the quality of the formed part. For the trapezoidal part, orienting the laminate at 45 degrees to the mold axis reduces the likelihood of matrix smear and wrinkling defects. Although this laminate orientation yielded a greater spatial variation in part thickness, the thickness deviation is lower than that for the 0-degree orientation case. Two forming analyses were conducted with ramp rates of 25 mm/s and 80 mm/s to match the equipment's operational limits. It was observed that higher forming rates led to a greater likelihood of defects, as evidenced by a 15% and 10% increase in the formed part areas with longer slip paths and higher traction magnitudes, respectively. It was discovered that shallower molds benefit from faster ramp rates, while deeper molds require slower rates to manage extensive shearing, stretching and bending. Faster forming rates lead to smaller thickness increases at high intra-ply shear regions, indicating a shift from intra-ply shear to out-of-plane bending due to the visco-plastic effect of the molten laminate and can negatively impact part quality. Lastly, it was shown that a well-conceived strategy using darts could improve the part quality by reducing the magnitude of the defect indicators.

Development and experimental characterization of the thermomechanical behavior of a scaled steel ladle

AbstractA steel ladle usually employs mortarless refractory masonry in the innermost layer in direct contact with molten steel. The behavior of such masonry under high thermal loading is complex and essential for designing such installation. A large‐scale experimental campaign was carried out focusing on a simplified, laboratory‐scaled, pilot steel ladle built with multiple refractory linings as in an industrial ladle. Tests were performed under transient thermal loading up to 1400°C with new and used working linings. The results showed that the distribution of temperatures between the refractory linings was similar for all specimens and confirmed the importance of the selection of the refractory materials in the distinct linings of the ladle to limit heat losses. The heterogeneity in the distribution of dry joints and the effect of the dry joint thickness were also measured using strain gauges. The measurements indicate the effect of viscoplasticity in the working lining on the steel shell, which shows a progressive reduction in the strain starting at 1200°C. The tests performed on the working linings show lower strain built‐up due to large viscoplastic deformation and increased joint thickness.

Slot coating of viscoplastic materials: A computational study of the effects of viscoplasticity on the flow dynamics and low-flow limit

Yield-stress materials such as structurally complex formulations of paints, slurries, and waxes have been long ubiquitous in the coating industry, though the practice of coating engineering remains largely empirical as the fundamental role of viscoplasticity due to the yield stress of the coating material in most coating applications is still unclear. Here, we couple a recent harmonic mean viscosity regularization for the Bingham model with a well-established finite element/elliptic mesh generation method for free surface flows to present a detailed computational study of slot coating applications of viscoplastic materials. By neglecting inertia and focusing on the downstream section of a slot coater, we introduce suitable dimensionless parameters to discuss a comprehensive set of results that unravels a striking impact of viscoplasticity on the flow dynamics and low-flow limit. We show that viscoplastic effects have major implications to the velocity field and recirculation pattern in the coating bead as well as to the development length and free surface in the film formation region. Most importantly, we find that viscoplastic effects markedly widen the operating window of the process, delaying the onset of the low-flow limit and thereby suggesting that structurally complex yield-stress materials may be used to coat thinner films and/or at higher speeds than predicted by the standards far established for simple Newtonian liquids.

Viscoplastic elliptical objects impacting a solid surface

This theoretical and numerical study focuses on the physical mechanism driving the spreading of viscoplastic elliptical millimetric/centimetric objects after they impact a solid surface under no-slip conditions. The two-dimensional impacting objects are described as Bingham fluids. The two-dimensional numerical simulations are based on a variational multi-scale approach devoted to multiphase non-Newtonian fluid flows. The obtained results are analyzed considering the spreading dynamics, energy budgets and scaling laws. They show that, under negligible capillary effects, the impacting kinetic energy of the elliptical objects is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: inertio-viscous, inertio-plastic, and mixed inertio-visco-plastic. These regimes are strongly affected by the initial aspect ratio of the impacting objects, which reveals the possibility of using morphology to control spreading. Finally, the results are summarized in a diagram linking the object's maximum spreading and spreading time with different spreading regimes through a single dimensionless parameter called impact number.

Closure to “Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts”

Closure to “Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts”

Discussion of “Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts”

Discussion of “Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts”

Monitoring early age concrete hydration through time-dependent wave dispersion

This paper explores into the intricate realm of wave dispersion behavior within the early stages of fresh concrete, with a specific focus on the dynamic interplay between micro-structure evolution and rheological properties in the quasi-solid state. Based on the characteristic of wave dispersion is factored by impulse frequency, the range used for the experiment is from 40 kHz to 100 kHz, where the wavelength is enough to be influenced by the medium. The time-dependent analytical solution and FE simulation show more linear changes in phase velocity at different times during the quasi-solid state. On the other hand, experimental data exhibits more dispersion behavior, likely due to the effect of viscoplasticity. To simulate the viscoplasticity effect, the FE simulation is compared between cases with applied viscoplasticity and without viscoplasticity. The phase velocity in the viscoplasticity case decreases by approximately 30% compared to the non-viscoplasticity case. This demonstrates that the effect of viscoplasticity cannot be overlooked in the quasi-solid state of concrete. The wave dispersion behavior in the early stages is predominantly influenced by particles and viscoplasticity, causing changes in phase velocity over time and impulse frequency. The highest phase velocity is observed between 50 kHz to 60 kHz. As the concrete undergoes hydration and hardening, both group velocity and phase velocity generally increase with the same frequency impulse. This study aims to unravel the complexities inherent in these phenomena, shedding light on the fundamental mechanisms governing wave dispersion in quasi-solid materials.

The role of viscoplastic drop shape in impact

The impact of fluid drops on solid substrates is a cardinal fluid dynamics phenomenon intrinsically related to many fields. Although these impacting objects are very often non-spherical and non-Newtonian, previous studies have mainly focused on spherical Newtonian drops. As a result, both shape and rheological effects on the drop-spreading dynamics remain largely unexplored. In the present work we use a mixed approach combining experiments with multiphase three-dimensional numerical simulations to extend the work reported by Luu & Forterre (J. Fluid Mech., vol. 632, 2009, pp. 301–327) by highlighting the fundamental role of shape in the normal impact of viscoplastic drops. Such complex fluids are highly common in various industrial domains and ideally behave either like a rigid body or a shear-rate-dependent liquid, according to the stress solicitation. Spherical, prolate, cylindrical and prismatic drops are considered. The results show that, under negligible capillary effects, the impacting kinetic energy of the drop is dissipated through viscoplastic effects during the spreading process, giving rise to three flow regimes: (i) inertio-viscous, (ii) inertio-plastic, and (iii) mixed inertio-visco-plastic. These regimes are deeply affected by the drop initial aspect ratio, which in turn reveals the possibility of using drop shape to control spreading. The physical mechanisms driving the considered phenomenon are underlined by energy budget analyses and scaling laws. The results are summarised in a two-dimensional diagram linking the drop maximum spreading, minimum height and final shape with different spreading regimes through a single dimensionless parameter, here called the impact number.

A Review of Delamination Damage of Composite Materials

The theoretical and practical achievements in the field of the theory of strength and reliability of composite materials are discussed in a review conducted on the scientific research conducted on the effect of delamination on the reliability and quality of composites. The methodological aspects of the stability of the mechanical characteristics of composite materials under the combined action of cyclic and impact loads are examined, as are the manufacturing and processing technologies. The reasons for delamination, such as technological, manufacturing and application, free edge, joints and loads, are revealed. The influence of delamination on the bearing capacity of structural elements made of composite materials is analyzed. The mechanism of delamination growth is outlined, and the criteria and processes are defined, such as the growth of delamination cracks in a multidirectional laminated plate from a straight edge, edge delamination during plate bending, delamination in plates in the field of residual stresses, etc. The importance of taking into account the visco-plastic effect at the top of the edge crack of delamination of composite materials is emphasized. The concept of critical delamination behavior is characterized, and the issues of delamination stability are described.

A Variational Beam Model for Failure of Cellular and Truss‐Based Architected Materials

A variational formulation of a beam model is presented for predicting the inelastic and geometrically nonlinear mechanical behavior of cellular and truss‐based architected materials. Emphasis is placed on the constitutive description of base materials commonly used in additive manufacturing, including polymers and metals, and the derivation of effective incremental potentials incorporating the effects of damage and viscoplasticity. The model is demonstrated in a variety of problems including the fracture of polymeric honeycombs, the tightening of woven architected materials, as well as the compression of metallic foams. The model's easy calibration–on the basis of single‐strut tests–and its successful validation—through experiments of additively manufactured specimens–indicate its promise as an efficient design tool for architected materials within a wide range of engineering applications.

A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics

We present a generalized constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a generalized constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. We present several side-by-side comparisons with physics simulations for specific constitutive models to show that our generalized model produces visually similar results. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations. We present several 3D simulations to highlight the robustness of our method, even with multiple different materials. To the best of our knowledge, our approach is the first to recover the knowledge of unknown material properties without making explicit assumptions about the data.

An isotropic viscoelastic phase field fracture model for flexural loading of freshwater columnar ice

This work presents the development and implementation of a coupled isotropic phase field fracture and viscoelastic computational model to simulate the fracture of freshwater columnar ice undergoing flexural stresses. An existing incremental constitutive model is extended to capture ice behavior up to and just after material fracture occurs. Crack initiation and propagation is modeled through a Griffith’s energy-based phase field formulation that includes contributions from viscous energy dissipation. The variational formulation and implementation of the material model in the open-source platform Dolfinx is discussed. We present 3-point flexural bending experimental data of freshwater columnar ice grown in controlled conditions which are used to inform the model’s mechanical properties. We find that the coupled model captures the creep and fracture behavior of ice specimens well for strain rates on the order of 10−5s−1 at −10 °C. Finally we show that although our model includes viscoplastic effects, freshwater ice under these conditions develops little viscous energy and therefore instantaneous mechanisms dominate its fracture behavior.

Effect of Viscoplasticity on Localization in Saturated Clays and Plastic Silts

A numerical study is presented of the effects of viscoplasticity on localization processes in sensitive, saturated clays and plastic silts. Numerical simulations of laboratory specimens of sensitive, viscoplastic soil subjected to monotonic, undrained, direct simple shear loading were performed using a viscoplastic constitutive model. Parametric analyses evaluated the effects of soil sensitivity, postpeak strain-softening rate, and strain rate dependency, as well as specimen size, mesh discretization, and loading rate. The numerical results showed that the global strain at which a localization forms primarily depends on the strain rate dependency of the soil’s shearing resistance relative to its rate of postpeak strain softening. A regression model is subsequently presented that relates the global strain at the onset of localization to the soil’s strain rate dependency and postpeak strain-softening rate. The results indicate that the inclusion of reasonable levels of viscoplasticity significantly increases the strain that can develop before a localization develops in clays and plastic silts with modest strain-softening rates. The consistency of the numerical results with available laboratory observations is discussed. Implications for practice and future research needs are discussed.

Viscoplastic effects of Newtonian fluids in nanopores: a molecular dynamics study

Understanding the influence of fluid–solid interactions on low-velocity non-Darcy flow in ultra-low permeability reservoirs is essential for enhanced oil recovery. The Poiseuille flows of C12H26 and argon under different pressure gradients in a nanopore are simulated using the molecular dynamics method. The results demonstrate that the confined fluids behave as elastic solids under lower pressure gradient but as viscous fluids under higher pressure gradient in the simulation. With increase of the external pressure gradient, the generated shear stress exceeds the yield stress related to the fluid-solid interaction and leads to a transition. This phenomenon indicates that the confined fluids in the nanopore exhibit apparent viscoplasticity. According to the viscoplastic hypothesis, the confined fluid can be divided into elastic and viscous layers, depending on the competition between the shear and yield stresses. The simulation results also indicate the yield stress increases near the wall. Assuming that the yield stress is inversely proportional to the distance from the wall, a non-Darcy flow model is proposed to calculate the flow rate by pressure gradient. The predictions of the model are consistent with the simulations for both C12H26 and argon, indicating the similarity of viscoplastic effects on the seepage of both fluid-nanopore systems.

Numerical modelling of the KOBO extrusion process using the Bodner–Partom material model

Numerical simulations of the extrusion process assisted by die cyclic oscillations (KOBO extrusion) is presented in this paper. This is highly non-linear coupled thermo-mechanical problem. The elastic-viscoplastic Bodner–Partom-Partom material model, assuming plastic and viscoplastic effects in a wide range of strain rates and temperatures, has been applied. In order to perform simulations, the user material procedure for B–P material has been written and implemented in the commercial FEM software. The coupled Eulerian–Lagrangian method has been used in numerical computations. In CEL method, explicit integration of the constitutive equations is required and remeshing is not necessary even for large displacements and large strains analyses. The results of numerical simulations show the heterogeneous distribution of stress and strain inside container and the non-uniform distribution of strain in the extruded material. The increase of material temperature has been noted. The results obtained (stress, temperature, location of plastic zones) qualitatively confirm the results of experimental investigations. The application of the user material procedure allows accessing all material state variables (current yield stress, hardening parameters, etc.), and therefore it gives detailed information about phenomena occurring in extruded material inside recipient. This information is useful for a proper selection of parameters of the KOBO extrusion process e.g. synchronization of the punch displacement with the die oscillations frequency to avoid the saturation of material isotropic hardening, which blocks the progress of extrusion.

Sensitivity of the slip condition and viscoplastic effect of the micropolar-Casson fluid during a non-isothermal blade coating process

Blade coating is a technique where blade operates as a typical smoothening tool to coat a fluid layer on the moving substrate. This study presents the heat transfer impact on the blade coating process by employing the micropolar-Casson fluid with slip condition and viscous dissipation. The non-dimensional expressions are simplified by operating the Lubrication Approximation Theory (LAT). Analytical solution of the velocity, temperature, and pressure gradient are obtained while numerical (root finding algorithm) used to acquire the pressure and other mechanical quantities. Impacts of coupling number, slip parameter, Brinkman number, microrotation, and Casson parameter on the various mechanical and flow characteristics are inspected through graphs and in tabular form. Micropolar effects decrease the coating thickness and increase the blade load, whereas viscoplastic effect results give the opposite effect. Hence, these factors may help in an efficient coating process and improve the substrate life.

Investigating the relationship of hardness and flow stress in metal forming

Hardness is routinely utilised to link the bulk material properties to surface contact mechanics. Besides possible differences in the material properties between bulk and surface, there is no established relation between hardness and the thermo-viscoplastic flow stress of materials used in the context of metal forming processes. The purpose of this study is to investigate such relationship using 6061 and 6016 aluminium alloys manufactured by hot rolling. Optical microscopy and Vickers hardness tests at different loads and temperatures ranging from 22°C up to 450°C were carried out. A time-dependent Finite Element model of an indentation using thermo-viscoplastic material model based on bulk samples was developed and compared with experiments. Overall, no significant difference between bulk and surface for neither alloy was experimentally identified. The hardness decrease with temperature of the alloys is quantified and ready-to-use constraint factor maps associating the thermo-viscoplastic flow stress with hardness of the materials are presented. The numerical model allowed visualisation of viscoplastic effects, whereas comparisons to the experiments in terms of hardness and topography validated the model and constitutive equations. Constitutive equations derived from compression tests of bulk samples can confidently describe deformation at the surface level and so, be used to develop a contact model in the tribological context of metal forming.

Modeling diffusive phase transformation and fracture in viscoplastic materials

In recent years, the phase-field method has attracted a lot of attention and has emerged as one of the most efficient tools for modeling fracture and phase transformation. The phase-field method is based on the regularization of discontinuities which allows the resolution of complex problems using classical numerical methods. A multiphase-field model which is essential for describing crack propagation in non-static heterogeneous materials is still missing. In this work, we fill this gap by combining the fracture phase-field approach based on Griffith’s theory with the phase-field approach for diffusive phase transformation in viscoplastic materials. Several benchmark examples of increasing complexity demonstrate, the effect of viscoplasticity and diffusive phase transformation on fracture behavior based on the critical loading, energy density until failure and crack topology. We show that viscoplastic activity at the crack tip mitigates the effect of pre-existing defects on mechanical strength. In a heterogeneous case, it is shown that viscoplastic activity introduces an intermediate fracture response between the reference behavior, which does not take into consideration the phase transformation-induced residual stresses, and the elastic behavior, which integrates these residual stresses by taking into account only the elasticity. The interaction between the heterogeneities and the crack topology is also highlighted.

Non-Newtonian and viscoplastic models of a vertically aligned thick liquid film draining due to gravity

We consider theoretically the two-dimensional flow in a vertically aligned thick liquid film supported at the top and bottom by wire frames. The film gradually thins as the liquid drains due to gravity. We focus on investigating the influence of non-Newtonian and viscoplastic effects, such as shear thinning and yield stress, on the draining and thinning of the liquid film, important in metallic and polymeric melt films. Lubrication theory is employed to derive coupled equations for a generalized Newtonian liquid describing the evolution of the film's thickness and the extensional flow speed. We use the non-Newtonian (power-law and Carreau) and viscoplastic (Bingham and Herschel–Bulkley) constitutive laws to describe the flow rheology. Numerical solutions combined with asymptotic solutions predict the late-time power-law thinning rate of the middle section of the film. For a Newtonian liquid, a new power law thinning rate of t−2.25 is identified. This is in comparison with a thinning rate of t−2 predicted for a thin Newtonian liquid film neglecting gravity, suggesting a weak dependence on gravity for the drainage of thicker films. For a non-Newtonian and viscoplastic liquid, varying the power law index and the yield stress influences the timescale of the thinning, but has weak dependence on the late-time thinning rate relative to the Newtonian thinning rate. The shortcomings of the power-law model are exposed when the shear rate is low and these are resolved using the Carreau model.

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.