Viscoplastic Effects Research Articles

Implementation of a viscoplastic substrate creep model in the thermomechanical simulation of the WAAM process

This research work focusses on the implementation of a viscoplastic creep model in the thermomechanical simulation of the wire arc additive manufacturing (WAAM) process for Ti-6Al-4 V structures. Due to the characteristic layer by layer manufacturing within the WAAM process, viscoplastic material effects occur, which can be covered by implementing a creep model in the thermomechanical simulation. Experimental creep tests with a wide temperature, load and time range were carried out to examine short-term creep behaviour in particular. A Norton-Bailey creep law is used to accurately fit the experimental data and describe the base material’s creep behaviour. Subsequently, the fitted Norton-Bailey creep law was implemented in the thermomechanical simulation of the WAAM process. Finally, to determine the effect of creep on global distortion and local residual stress state in the substrate, simulations of a simplified linear, three-layer WAAM structure, with and without applying the implemented creep law, were carried out and compared to experimental data. The thermomechanical simulation with implemented creep model reveals a significant improvement in the numerical estimation of distortion and residual stress state in the substrate. The maximum distortion is reduced by about 13% and respectively the mean absolute percentage error between simulation and experiment decreases by about 34%. Additionally, the estimation accuracy with respect to the local residual stress state in the substrate improved by about 10%.

An invariant-based elasto-visco-plastic model for unidirectional polymer composites at finite strains

An invariant-based constitutive model for unidirectional composites, including viscous effects in the elastic and plastic regimes at finite strains, is proposed. The model is based on the multiplicative decomposition of the deformation gradient, using an isoclinic configuration to avoid the non-uniqueness of intermediate configurations. The visco-elastic behaviour is represented by the generalised Maxwell model, combined with a transversely isotropic yield function and a non-associative plastic potential. Visco-plastic effects are introduced through the Perzyna overstress function. The theoretical basis of the material model and the computational treatment within the finite element solution procedure are presented in detail. Two algorithms are proposed for an implicit integration of the evolution equations: (i) a semi-implicit stress update, and (ii) a fixed-point iterative fully implicit stress update. A comparison of their performance reveals that the former becomes faster, even though the latter guarantees the quadratic convergence rate in the Newton–Raphson scheme. The predicted stress–strain response for different fibre orientation angles is in close agreement with experimental data obtained under quasi-static and dynamic loading. The model can also capture the important re-orientation of the fibres due to external loading.

A time‐based arc‐length like method to remove step size effects during fracture propagation

AbstractAn arc‐length like method is presented which alters the size of the time increment when simulating crack propagation problems. By allowing the time increment to change during the time step a constraint can be imposed, which is used to enforce the fracture to propagate a single element length per time step. This removes the effect of the (interface) element size on propagating fractures, and therefore allows smooth fracture propagation during the simulation. The benefits of the scheme are demonstrated for three cases: mode‐I crack propagation in a double cantilever beam, a shear fracture including inertial and viscoplastic effects in the surrounding material, and a pressurized fracture inside a poroelastic material. These cases highlight the ability of this scheme to obtain more accurate and nonoscillatory results for the force–displacement relation, to remove numerically induced stepwise fracture propagation, and to allow for arbitrary propagation velocities. An added benefit is that plastic strains surrounding a fracture are no longer affected by the (interface) element size.

Phase transformation and viscoplasticity coupling in polycrystalline nickel-titanium-hafnium high-temperature shape memory alloys

The objective of this study was to investigate the interactions between phase transformation and viscoplasticity during uniaxial constant force thermal cycling (UCFTC) of a Ti-rich Ni-Ti-20Hf (at.%) high-temperature shape memory alloy (HTSMA). These tests were conducted (up till failure) at 1, 10 and 50 ∘C/min, to vary the duration of exposure to high temperatures, viz. the amount of viscoplasticity, and to examine the rate-dependency of actuation. The macroscopic results from the tests were used to investigate the evolution of transformation temperatures, hysteresis, transformation and irrecoverable strains for the cycles in which the effect of potential damage mechanisms could be assumed to be negligible. The phenomena that affected the behavior were: viscoplasticity at 1 ∘C/min, transformation-induced plasticity (TRIP) at 10 and 50 ∘C/min, and accumulation of retained martensite at all the three rates. More interestingly, the response at 1∘C/min indicated a unique interplay between the effect of viscoplasticity over phase transformation and static recovery. The retained martensite was identified through a series of DSC and XRD analyses, and its contribution to TRIP strain was quantified through a UCFTC test. Furthermore, a test involving alternating isothermal creep and UCFTC at 10 ∘C/min was conducted to investigate an effect of viscoplasticity produced by creep on the behavior, while reducing the viscoplasticity during thermal cycling. The alternating test revealed an effect of phase transformation over the viscoplastic strain rate. The experimental investigations demonstrated a rate-dependent phase transformation behavior, and a two-way coupling between phase transformation and viscoplasticity, bringing out the importance of understanding viscoplastic deformations in phase-transforming materials.

Modeling Lithospheric Deformation Using a Compressible Visco‐Elasto‐Viscoplastic Rheology and the Effective Viscosity Approach

AbstractDeformations of the colder regions of the lithosphere mainly occur in the frictional regime. In geodynamic models, frictional plastic deformations are often highly localized (shear bands) and are used as proxies for faults. However, capturing the generation and evolution of shear bands in geodynamic models is troublesome. Indeed, mesh dependency and lack of convergence affect, to some extent, the results of geodynamic models. Here we extend the most common plasticity implementation used in geodynamic codes (effective viscosity approach [EVA]) to include the combined effects of elastic compressibility, plastic dilatancy, strain softening, and viscoplasticity. The latter acts as a regularization that cures most of the known issues of geodynamic models related to frictional plasticity. Using regularized models based on the M2Di MATLAB routines, we show that volumetric elasto‐plastic deformations can significantly impact crustal‐scale shear banding. We also show that the artificial overstress caused by viscoplasticity can be mitigated by employing power‐law models. Furthermore, we demonstrate that plasticity algorithms common in geodynamics (based on the EVA) can be as accurate as those obtained with algorithms typically used in engineering (return mapping with a consistent tangent operator). Finally, we show examples of long‐term tectonic deformations using the state‐of‐the art geodynamic code MDoodz. They indicate that viscoplastic regularization can be used efficiently to obtain reliable simulations in geodynamics.

Viscoplastic flow in a pipe of complex cross section with stick–slip at the wall

The Poiseuille flow of a Bingham fluid with the yield slip condition at the wall is examined. The governing equations are solved employing the accelerated augmented Lagrangian method for both the viscoplastic model and the yield slip equation. We solve numerically the flow in pipes with different cross sections: equilateral and isosceles triangles, L-shape, and hourglass-shape. The combined effects of viscoplasticity and slip on the flow have been investigated. The evolution of the unyielded regions has been studied. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are identified in ducts of various cross sections.

Numerical study of non-isothermal analysis of exiting sheet thickness in the calendering of micropolar-Casson fluid

This theoretical analysis reports on the non-isothermal calendering process of micropolar-Casson fluid and studies the viscoplastic and microrotation effects by utilizing the lubrication approximation (LAT). Exact dimensionless velocity and pressure gradient solutions are achieved. Then a numerical integration technique determined other mechanical quantities. Implementing the finite difference approximations resolved the energy expression. Graphs show how material parameters influence the pressure, pressure gradient, leave-off distance, temperature distribution, force, and power function. Temperature distribution increases with increased coupling number N and decreased Casson parameter [Formula: see text]. Force and power function increase with increased coupling number and decreased Casson parameter. Both Casson and coupling number control the pressure distribution and exiting sheet thickness.

The role of micro-inertia on the shock structure in porous metals

The behavior of porous materials under shock loading is a multi-scale problem bridging orders of magnitude across the macroscale geometry and the microscale pores. Under static loading, this problem is well understood, relating mechanisms of pore closure and crushing to the equivalent macroscale models. The dynamic response of porous solids under shock loading is related to the effects of viscoplasticity and micro-acceleration fields around the void boundaries. The significance of the micro-inertia effects in modeling the dynamic behavior of porous materials remains an open question. In this work, an experimental investigation on closed-cell porous aluminum with small porosity provides the evidence for the first time of micro-inertia's fundamental role in describing the shock structure in these materials. Materials with different levels of porosity were manufactured using a modified process of additive manufacturing to achieve a mean pore size below 50μm. Plate impact experiments on porous aluminum samples were conducted at pressures in the range of 2 to 11 GPa. The structure of the steady shock was characterized as a function of porosity and shown to validate behavior revealed by an analytical approach (Czarnota et al. [J. Mech. Phys. Solids 107 (2017)]), highlighting the fundamental role of micro-inertia effects in such cases.

The converging flow of viscoplastic fluid in a wedge or cone

Abstract

Microscale diffusion-mechanics model for a polymer-based solid-state battery cathode

A non-linear microscale diffusion-mechanics model combining mass transport and linear momentum balance equations, with elasto-viscoplastic polymer constitutive law and interfacial traction-separation law is proposed to provide a new insight into the effects of viscoplasticity and interfacial damage on the in situ diffusive-mechanical behaviour of a polymer-based cathode for a solid-state battery (SSB). Diffusion and mechanics are coupled through two mechanisms: (1) active particle (AP) volumetric change dependence on Li concentration, and (2) interfacial flux dependence on mechanical opening. The model is resolved for a simple cathode microstructure using an axisymmetric unit cell concept, and integrated with the non-linear finite-element solver ABAQUS with the help of its user subroutines (UMAT and UINTER). Finite-element simulations reveal that plastic deformations of the polymer due to volumetric changes of the AP reduce the value of the interfacial opening displacement, which is desirable for maintaining interfacial flux. The results also demonstrate that slower battery charging rates may lead to a softer polymer response, and thus a smaller interfacial gap. Moreover, a comparison between the linear elastic and current elasto-viscoplastic models for the polymer electrolyte shows that even 5% volumetric shrinkage of the AP leads to an overprediction of the interfacial opening with the linear elastic material law, which limits its validity in modelling polymer-based SSBs.

Computational Approach of the Cortical Bone Mechanical Behavior Based on an Elastic Viscoplastic Damageable Constitutive Model

Bone mechanical behavior varies according to the mechanical loading to which it is subjected, and its response effectiveness mainly depends on its quality. Thus, measuring the indicators controlling the bone quality is required to assess its strength. Indeed, the Finite Element Method (FEM) provides a non-invasive tool to interpret bone quality. Therefore, this work coupled the FEM with a micromechanical law, aiming to provide an exhaustive description of the human bone mechanical behavior. Anisotropy, viscoplasticity and damage were introduced in the material behavior law and the damage evolution was plotted based on the applied loading. Then a sensitivity study was conducted to evaluate the effects of viscoplasticity and damage parameters on bone behavior. The obtained numerical results were in a good agreement with the previously reported experimental data and allowed to distinguish key parameters from non-significant ones. This new computational model provided a better understanding of the main parameters affecting bone behavior.

Experimental insights into consolidation rates during one-dimensional loading with special reference to excess pore water pressure

Consolidation rate has significant influence on the settlement of structures founded on soft fine-grained soil. This paper presents the results of a series of small-scale and large-scale Rowe cell consolidation tests with pore water pressure measurements to investigate the factors affecting the consolidation process. Permeability and creep/resistance structure factors were considered as the governing factors. Intact and reconstituted marine clay from the Polish Carpathian Foredeep basin as well as clay–sand mixtures was examined in the present study. The fundamental relationship correlating consolidation degrees based on compression and pore water pressure was assessed to indicate the nonlinear soil behaviour. It was observed that the instantaneous consolidation parameters vary as the process progresses. The instantaneous coefficient of consolidation first drastically increases or decreases with increase in the degree of consolidation and stabilises in the middle stage of the consolidation; it then decreases significantly due to viscoplastic effects occurring in the soil structure. Based on the characteristics of the relationship between coefficient of consolidation and degree of dissipation at the base, the consolidation range that complies with theoretical assumptions was established. Furthermore, the influence of coarser fraction in clay–sand mixtures in controlling the consolidation rates is discussed.

Viscoplastic effects on plane strain fracture of FCC and BCC single crystals

In the present work, simulations of mode I crack growth and plastic yielding at a crack tip in a plane strain crystal are considered. The theory of crystal plasticity is used and the analyses are made for small strains and rotations. The crack tip is considered as if it is inserted in a metallic grain (single crystal). Two types of crystals are simulated: face-centered cubic (FCC) and body-centered cubic (BCC). The crack growth zone is modeled by cohesive interfaces whose separation process is described by a cohesive zone model. The material and the cohesive surfaces have independent constitutive relations and fracture is an outcome of the deformation process. The cohesive tractions are implemented within the finite element method model through the principle of virtual work. A finite element mesh with rectangular bilinear elements is combined with cohesive elements to model the structure. BCC structures showed a greater toughness than FCC structures in the orientation tested, considering all other properties the same. Viscous properties influence on fracture—crack growth characteristics such as crack extension and time for the beginning of the growth process—were also explored and direct comparisons between the two types of crystal were made. In these cases, FCC crystals showed a greater rate dependency than BCC.

Integration of viscoplastic effects in a one-dimensional constitutive model for ground response analysis

During an earthquake, strain-rate effects affect both the stiffness and damping behaviour of soils, yet existing constitutive models for ground response analysis are typically formulated within a rate-independent framework. In this paper, a one-dimensional (1D) viscoplastic stress–strain model is presented to introduce strain rate effects in ground response analysis. Its constitutive equations are based on a model that uses a cubic spline fit of the modulus reduction curve and a coordinate transformation technique to match any input modulus reduction and damping curve. A viscous stress component is added to model the effect of strain rate on the mechanical behaviour of soils using a single input parameter. The model is able to reproduce the linear increase in shear strength with the logarithm of shear strain rate and allows the introduction of viscous effects in 1D ground response analysis with control over damping and modulus reduction behaviour. The model is implemented in a software for ground response analysis and used to predict the results of a centrifuge test modeling 1D wave propagation. The results show that the model accurately predicts the amplification and attenuation of shear waves, in a context where strain rates impact the response of the model significantly.

On failure mode transition: a phase field assisted non-equilibrium thermodynamics model for ductile and brittle fracture at finite strain

A non-equilibrium thermodynamics model of viscoplasticity coupled with damage is presented. Keeping in view the experimentally observed failure mode transitions, e.g. brittle to ductile, under dynamic loading condition, the emphasis of the present work has been to endow the formulation with capability of modelling such transitions in a physically consistent manner. Within a framework of internal variables, the current formulation tracks the effect of isotropic viscoplasticity with accumulated plastic strain, and a scalar phase field variable traces the degradation of the material caused by either tensile cracking or shear induced failure. An explicit-implicit strategy is adopted for numerical implementation of the nonlinear formulation. A series of numerical simulations has been carried out on notched metallic specimen to demonstrate the predictive ability of the proposed model and to investigate the influence of several parameters in governing failure mode transition.

Elasto-Viscoplastic Material Model of a Directly-Cast Low-Carbon Steel at High Temperatures.

A model-based process control of material production processes demands realistic material models describing the local evolution of the thermal and mechanical state variables, i.e., temperature, stress, strain, or plastic strain, for the relevant microstructure state. In the present work, a material model for the specific microstructure in a continuously cast strand shell, viable for reproducing cyclic viscoplastic effects, was developed for a 0.17 wt.% C steel. Experimental data was generated using directly-cast samples and a well-controllable testing facility to apply representative loading conditions. Displacement- and force-controlled experiments in the temperature range of 700–1100 °C were conducted, with a special focus on the relevant strain rates documented for the straightening operation. A temperature-dependent constitutive material model combining elastic, plastic, and viscoplastic effects was parameterized to fit the whole set of experimentally-determined material response curves. In order to account for the cyclic plastic material response, a combination of isotropic and kinematic hardening was considered. The material model sets a new standard for the material description of a continuously cast strand shell, and it can be applied in elaborate continuous casting simulations.

Multiphysics Coupling Method to Simulate the Friction Stir Welding Process

In In this work the methods are developed to perform simulations of the friction stir welding process using the ANSYS software working scheme, developing multiphysics couplings between computational fluid dynamics tools to Model the viscoplastic effect of the fluidity of the material when it is stirred by means of a solid tool modeled in the Transient Structure application that allows calculating the thermo-mechanical effects of the study process. The results show the validations corresponding to the modeled and experimentally performed analysis showing a lot of reliability in the proposed method. The torque reached in the process is maintained in the ranges of 14 Nm, the maximum temperature reached in the process was 540°C, this being 78.3% of the melting temperature of the material studied, having an adequate range for these studies.

Thermo-viscoplastic numerical modeling of metal forging process by Pseudo Inverse Approach

Constant demands of light-weighting have forced many industries to resort to manufacturing practices that promise a component with a higher strength-to-weight ratio. Hot forging is one such method used to produce parts using difficult-to-form materials as well as to achieve complex geometries. Although numerical methods provide an efficient means to predict the material yield and the stress/strain states of the product at different stages of forming and classical methods are accurate enough to provide a suitable representation of the process, they tend to be computationally expensive. This limits their use in process optimization studies. The Pseudo Inverse Approach (PIA) developed in the context of 2D axisymmetric cold forming, provides a quick and fairly accurate estimate of the stress and strain fields in the final product for a given initial shape. In this work, the PIA is extended to include the thermal and viscoplastic effects associated with the hot forging process. The results are compared with commercially available software based on the classical approaches to show the efficiency and the limitations of PIA.

Numerical simulation of the dynamics of a reinforced concrete slab under an air shock wave

Deformation and fracture of a reinforced concrete slab under the effect of an air shock wave are considered. The research involves data from the public experiment "Blind Blast Test". The slab is loaded by an air shock wave resulting from high explosive detonation in a shock tube. The results of calculations and experiments are compared quantitatively and qualitatively. Quantitative comparison is made for the history of movement of the reinforced concrete slab key points during the process of deformation. Qualitative comparison is made for photographs of the destruction of a real reinforced concrete slab and distribution of the damage fields obtained by calculation. The numerical simulation is carried out in the LS-DYNA code, and the finite element method with an explicit time integration scheme is used. The CSCM (Continuous Surface Cap Model) model is used to model the concrete material. This model is an isotropic constitutive model with three-variant surface of ductility; the strength characteristics of the material depend on the rate of loading, and its damage is considered separately for compressive and tensile loads, which allows taking into account the partial recovery of compressive strength. The mathematical description of the model is given as part of the paper. Steel reinforcement of the concrete slab is modeled explicitly with beam finite elements. Finite element meshes of the concrete volume and reinforcing elements are coupled by means of the kinematic automatically calculated equations. The properties of the reinforcement are set within the classical theory of elastic-plastic strengthening material flow with the criterion of limiting states in the form of Huber-Mizes and taking into account visco-plastic effects. The influence of boundary conditions, practical mesh convergence, and capability of the mathematical model to predict the location of zones of material failure, displacement, and deformation of the structure are studied.

Grain Shape Effect and the Viscoplastic Parameter on the Evolution of Isotropic and Kinematic Hardening of Metallic Materials under Cyclic Loading

The main objective of this work is to study the grain shape effect (aspect ratio α = a / b) and the viscoplastic parameter γ on the evolution of the kinematic and isotropic hardening of FCC type metallic materials, under uniaxial cyclic Tension-Compression ‘‘TC’ and to interpret these results. These parameters of shape and viscoplastic were developed and introduced by Abdul-Latif and Radi, indeed in this study we use their model. Expressed within the framework of a self-consistent approach, the rate-dependent inelastic strain is examined at the crystallographic slip system level describing a constitutive model for FCC metallic polycrystals, whereas the elastic strain is determined at the granular level. Based on the Eshelby’s tensor, the elastic behavior is assumed to be compressible. For a polycrystalline structure, the grains deform plastically by crystallographic slip located at the most favorably oriented systems supporting a high resolved shear stress . The approach considers that the inclusion (grain) form is ellipsoidal of half axes defining by a, b and c such as a ≠b= c. Several numerical tests are carried out highlighting the role of shape and viscoplastic parameter on the evolution of kinematic and isotropic hardening. A general comparison between the and effect on the overall hardening of the polycrystal shows that this work hardening is more sensitive to the parameter (for given ) compared to (for given). Keywords: Grain shape effect, Ellipsoidal inclusion, Viscoplastic parameter effect, Kinematic and isotropic hardening, Uniaxial cyclic ‘‘TC‘‘, Self-consistent model.