Viscoplastic Dissipation Research Articles

Elasto-viscoplastic model for rayon yarns

AbstractIn this paper we develop a new model for the simulation of the mechanical behavior of rayon twisted yarns, at macroscopic level. A yarn with its continuous filaments is represented by an equivalent three-dimensional solid of cylindrical shape, discretized by finite elements, with properly defined local anisotropic material properties. The new constitutive model, inspired by experimental results on rayon untwisted yarns, is formulated in the framework of the thermodynamics of irreversible processes and includes visco-elastic and visco-plastic dissipation mechanisms. The effect of twist is taken into account by including the direction of the fibers in the free energy definition. The overall model is validated comparing numerical and experimental results on twisted rayon yarns.

Interfacial Crack Growth-Based Fatigue Lifetime Prediction of Thermoelectric Modules under Thermal Cycling.

As a result of the complexity and difficulty of the lifetime assessment of the thermoelectric (TE) module, the related research is still immature. In this work, to predict the lifetime of the Bi2Te3-based TE module from the perspective of cyclic thermal stress leading to interface cracking, the viscoplastic behavior of the solder layer is first described by the Anand material ontology model, and then the sprouting and expansion of interface cracking of the module are simulated by combining the Darveaux model and the viscoplastic dissipation energy accumulated during the thermal stress cyclic loading. After that, the complete lifetime prediction model of the TE module is established on the basis of the thermal cycling experiments and the finite element simulation calculation data, which can simply and efficiently predict the cycle number of the module resistance rise and its rise rate. The prediction deviations are 6.1 and 6.7%, respectively, verifying the feasibility of the model. The work in this paper can provide a reference for the life evaluation of TE modules.

A viscoelastic-viscoplastic constitutive model for nanoparticle-reinforced epoxy composites: Particle, temperature, and strain rate effects

The mechanical behavior of nanoparticle-reinforced epoxy (NP/epoxy) exhibits highly nonlinear characteristics accompanied by particle, temperature, and strain rate effects, which are of great significance in the study of composites. This study presents a viscoelastic-viscoplastic (VE-VP) constitutive model applied to rigid silica and soft rubber nanoparticle reinforced epoxies (SNP/epoxy and RNP/epoxy), which are subjected to a wide strain rates and temperatures. The proposed constitutive model is based on the decomposition of the Helmholtz free energy into equilibrium and non-equilibrium parts. The equilibrium part employs the hyperelastic strain energy density function to capture the rubbery state property. The non-equilibrium part is decomposed into viscoelastic strain energy density functions and viscoplastic dissipation potential to capture the glassy state behavior. Temperature- and particle- dependent models were introduced into the proposed VE-VP model. To validate the effectiveness of the VE-VP model, the uniaxial compressive responses of the SNP/epoxy and RNP/epoxy were systematically tested. The results demonstrate that the VE-VP constitutive model can capture the nonlinear compressive behaviors of SNP/epoxy and RNP/epoxy over a strain-rate range of 10 − 2 s − 1 to 10 3 s − 1 and a temperature range of − 80 ℃ to 80 ℃ . Finally, the analysis of the model parameters indicates that the strain softening and hardening are strongly affected by the temperature and strain rate. • Two typical nanoparticles (rigid silica and soft rubber) are utilized to reinforced epoxy. • A viscoelastic-viscoplastic constitutive model for nanoparticles reinforced epoxy incorporating the particle, temperature and strain rate effects is proposed. • The compressive behaviors over wide range of temperature and strain rate are experimentally investigated and well predicted by proposed model. • The activation energy and hyperelastic coefficient in proposed model are strongly affected by temperature and strain rate.

Computational Study of Tear Testing of a Single Weld Formed by Fused Filament Fabrication

Abstract The tear test is widely used to measure the fracture toughness of thin rubber sheets and polymer films. More recently, the tear test has been applied to polymer materials produced by melt extrusion additive manufacturing to measure the fracture toughness of a single weld between two printed (extruded) filaments. This paper presents a finite element modeling study of the tearing of a weld between two printed filaments to investigate the mechanics of the tear test and the effects of geometry and material properties on the measured tear energy. The mechanical behavior of the printed filaments was described by a viscoplastic model for glassy polymers and the weld was represented using cohesive surface elements and the Xu–Needleman traction–separation relationship. The geometric model and the material parameters were chosen based on experimental measurements. The tear energy varied with the specimen dimensions, the curvature of the printed filaments, the yield stress relative to the cohesive strength of the weld, and the post-yield stress drop. The effects of the hardening modulus were small. These factors altered the viscoplastic dissipation in the material ahead of the propagating crack tip. The results showed that viscoplastic dissipation could constitute a large fraction of the tear energy and is strongly affected by the specimen dimensions and the geometry and material properties of the printed filament. There was also considerable mode mixty in the tear energy. The findings can be used to design tear tests to measure the intrinsic fracture toughness of the weld.

Phase Contrast X‐Ray Imaging of the Collapse of an Engineered Void in Single‐Crystal HMX

AbstractImaging the collapse of a single void that creates a hot spot initiation site in an otherwise defect‐free explosive is challenging given the spatial and temporal scales involved in explosive systems. This work presents our attempt to examine a single hot spot mode (void collapse) in single‐crystal octahydro‐l,3,5,7‐tetranitro‐l,3,5,7‐tetrazocine (HMX) embedded in Sylgard. The hot spot heating mechanisms involved with pore collapse include adiabatic heating, jetting, and viscoplastic dissipation. Quantifying the dynamics of a pore collapse is a crucial step to understanding which mechanisms dominate during ignition events. Our experiments were conducted with a single‐stage, light‐gas gun at Argonne National Laboratory's Advanced Photon Source, applying the phase contrast imaging technique while collecting high‐speed video. The details of HMX single crystal production, defect (pore) engineering, and sample construction, along with experimental results are presented here. These results demonstrate that detailed collapse dynamics can be obtained from homogeneous, single‐crystal explosives with this approach. Qualitative comparisons are made with simulation data which show good agreement in the transition between a quasi‐symmetric pore collapse and an asymmetric collapse with jetting across the pore as measured with normalized pore area and pore circularity.

Thermomechanical fatigue life prediction of metallic materials by a gradient‐enhanced viscoplastic damage approach

AbstractFatigue failure plays an important role in engineering applications, especially when structural components experience significant cyclic thermal loading and complex force loading simultaneously. During the last decades, several post‐processing techniques have been developed based on empirical investigations of experimental evidence to predict the fatigue life of materials. The work at hand postulates a conventional continuum damage theory for thermomechanical fatigue failure modeling. In particular, an implicit gradient‐enhanced approach is employed to address the ill‐posedness of the partial differential equation system when the damage onsets. An internal fatigue variable is phenomenologically defined based on the accumulation of viscoplasticity. In the sequel, a regularized fatigue variable is obtained to further yield the damage softening function, which straightforwardly applies to the stress, material tangent, and viscoplastic dissipation. A multi‐field problem, consisting of the strain field, the temperature, and the non‐local variable, is taken into consideration, leading to a fully coupled system. This numerical methodology is consistently derived and implemented into the context of the finite element method. Several representative and demonstrative examples are performed, which yield good numerical stability and agreement with experimental data. Conclusive findings and further perspectives close this article.

Thermodynamically consistent nonlinear viscoplastic formulation with exact solution for the linear case and well-conditioned recovery of the inviscid one

In this work, a consistent viscoplasticity formulation is derived from thermodynamical principles and employing the concept of continuum elastic corrector rate. The proposed model is developed based on the principle of maximum viscoplastic dissipation for determining the flow direction. The model uses both the equivalent viscoplastic strain and its rate as state variables. Power balance and energy balance give, respectively, separate evolution equations for the equivalent viscoplastic strain rate and the viscoplastic strain, the former written in terms of inviscid rates. Several key points distinguish our formulation from other proposals. First, the viscoplastic strain rate (instead of a yield function) consistently distinguishes conservative from dissipative behaviours during reverse loading; and the discrete implicit integration algorithm is an immediate discretization of the continuum theory based on the mentioned principles considered as separate equations. Second, the inviscid solution is recovered in a well-conditioned manner by simply setting the viscosity to zero. Indeed, inviscid plasticity, viscoelasticity and viscoplasticity are particular cases of our formulation and integration algorithm, and are recovered just by setting the corresponding parameters to zero (viscosity or yield stress). Third, the linear viscoplasticity solution is obtained in an exact manner for proportional loading cases, independently of the time step employed. Four, general nonlinear models (Perzyna, Norton, etc) may be immediately incorporated as particular cases both in the theory and the computational implementation.

A variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers

This study presents a variationally consistent formulation of the thermo-mechanically coupled problem with non-associative viscoplasticity for glassy amorphous polymers. First, the decomposition of the equivalent plastic strain is carried out to derive the variational consistent evolution law of the shear yield strength with reference to the analogous approach taken for formulating the Armstrong-Frederick model. Second, an alternative form of the dual viscoplastic dissipation potential is proposed to recast the principle of maximum plastic dissipation for viscoplasticity to be of the same form of rate-independent plasticity with the introduction of the extended yield function. Third, we address the optimization problem relevant to the thermo-mechanically coupled behavior of glassy amorphous polymers within the incremental variational framework with the help of the parameterization of flow rules. Thanks to the achieved variational consistency, the mathematical model derived by the proposed formulation can enjoy several benefits for ensuring the stability of the strongly coupled discretized equations in the monolithic method under the condition that the material behavior is stable. In addition, since the present formulation does not require the time derivative of the shear yield strength, the resulting evolution equation accommodates the time variations of temperature in terms of its material properties, implying that it is amenable to various thermal processes other than isothermal ones. Numerical examples are presented to demonstrate the capability of the proposed formulation in simulating actual compression tests conducted on a PMMA specimen that exhibits complex thermo-mechanically coupled phenomena.

Porous polycrystal plasticity modeling of neutron-irradiated austenitic stainless steels

A micromechanical model for quantifying the simultaneous influence of irradiation hardening and swelling on the mechanical stiffness and strength of neutron-irradiated austenitic stainless steels is proposed. The material is regarded as an aggregate of equiaxed crystalline grains containing a random dispersion of pores (large voids due to large irradiation levels) and exhibiting elastic isotropy but viscoplastic anisotropy. The overall properties are obtained via a judicious combination of various bounds and estimates for the elastic energy and viscoplastic dissipation of voided crystals and polycrystals. Reference results are generated with full-field numerical simulations for dense and voided polycrystals with periodic microstructures and crystal plasticity laws accounting for the evolution of dislocation and Frank loop densities. These results are calibrated with experimental data available from the literature and are employed to assess the capabilities of the proposed model to describe the evolution of mechanical properties of highly irradiated Solution Annealed 304L steels at 330oC. The agreement between model predictions and simulations is seen to be quite satisfactory over the entire range of porosities and loadings investigated. The expected decrease of overall elastic properties and strength for porosities observed at large irradiation levels is reported. The mathematical simplicity of the proposed model makes it particularly apt for implementation into finite-element codes for structural safety analyses.

Current density dependent shear performance and fracture behavior of micro-scale BGA structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under coupled electromechanical loads

The shear performance and fracture behavior of micro-scale ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under coupled electromechanical loads with the increasing current density (from 6 × 103 to 1.1 × 104 A/cm2) were investigated systematically. Severe Joule heating and current crowding effects on actual temperature, shear strength, damage and fracture behavior of the joints under coupled electromechanical loads were studied by theoretical formulation and experimental characterization, as well as finite element simulation. Results demonstrate that severe Joule heating and current crowding effects lead to significantly increased temperature in the joints, which is much higher than the ambient temperature. The shear strength of joints under coupled electromechanical loads shows strong dependence on current density, in terms of a relatively rapid monotonic decrease with the increasing current density. Moreover, a fully coupled finite element model was developed to characterize the degree of damage of joints under coupled electro-mechanical loads. The results show that electric current leads to aggravated damage in the joints, and damage occurs and accumulates much more easily in joints subjected to high density current stressing. The maximum viscoplastic dissipation energy density increases monotonically with current density. With increasing current density, there is a transition in fracture position (path) from the solder matrix to the solder/IMC interface of the joints, which corresponds to a shift in fracture mode from ductile fracture to brittle fracture.

The effect of interface shock viscosity on the strain rate induced temperature rise in an energetic material analyzed using the cohesive finite element method

In this work, shock induced failure and local temperature rise behavior of a hydroxyl-terminated polybutadiene (HTPB)—ammonium perchlorate (AP) energetic material is modeled using the cohesive finite element method (CFEM). Thermomechanical properties used in the model were obtained from four different experiments: (1) dynamic impact experimental measurements for fitting a viscoplastic constitutive model, (2) in situ mechanical Raman spectroscopy (MRS) measurements of the separation properties for fitting a cohesive zone model, (3) a pulse laser induced particle impact experiment combined with the MRS for measurement of the interface shock viscosity, and (4) Raman thermometry experiments for measurement of HTPB, AP, and HTPB-AP interface thermal conductivity. HTPB-AP interface regions with high density of particles were found to be more susceptible to local temperature rise due to the presence of viscoplastic dissipation as well as frictional heating. The increase in the interface shock viscosity lead to a decrease in both the viscoplastic and frictional dissipation. This resulted in a decrease in the maximum temperature and the density of local regions with a maximum temperature rise within the HTPB-AP microstructure. A power law relation for the decrease in viscoplastic energy dissipation, temperature rise and the density of the local temperature rise with the interface shock viscosity was obtained.

Damage and fracture characterization of asphalt concrete mixtures using the equivalent micro-crack stress approach

In this paper, a new parameter termed “equivalent micro-crack stress” (σmc) is proposed for the evaluation of the cracking performance of asphalt mixtures with respect to their resistance to the initiation of micro-crack. The “equivalent micro-crack stress” (σmc) is a function of the material stiffness and the “micro-crack initiation threshold” (MCIT). The MCIT is a critical strain energy density at the instance of initiation of micro-crack. Experimental testing is carried out for the evaluation of the cracking performance of unmodified and wax modified asphalt mixtures using the Superpave IDT tests at −20°C, −10°C and 0°C. The low temperature range is used in the study to minimize the effect of viscoplastic dissipation on the material cracking behaviour. The result shows that the “equivalent micro-crack stress” (σmc) gives a good indication of the material cracking performance of the unmodified and wax modified mixtures. A Finite Element Analysis is performed to assess the validity of the proposed approach under cyclic loading condition in the controlled-stress mode. The result shows that there is a good agreement between the material cracking performance in both monotonic and cyclic loading conditions using the proposed approach. The higher the “effective micro-crack stress” (σmc) , the better the fracture performance of the mixture.

Finite stopping times for freely oscillating drop of a yield stress fluid

The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variational inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. The free surface is assumed to evolve with a normal velocity of the flow. We also consider capillary forces acting along the free surface. Based on the variational inequality formulation an energy equality is obtained, where kinetic and free energy rate of change is in a balance with the internal energy viscoplastic dissipation and the work of external forces. Further, the paper considers free small-amplitude oscillations of a droplet of Herschel-Bulkley fluid under the action of surface tension forces. Under certain assumptions it is shown that the finite stopping time Tf of oscillations exists once the yield stress parameter is positive and the flow index α satisfies α ≥ 1. Results of several numerical experiments illustrate the analysis, reveal the dependence of Tf on problem parameters and suggest an instantaneous transition of the whole drop from yielding state to the rigid one.

Calorimetric consequences of thermal softening in Johnson–Cook’s model

At high loading rates, the development of adiabatic shear bands in metals is conventionally attributed to the strong interactions induced by viscoplastic dissipation within the bands and thermal softening effects. The rheological equation proposed by Johnson and Cook takes both viscoplastic hardening and thermal softening into account. The present paper reviews and includes this equation into a thermodynamic framework in order to analyse the energy impacts of thermal softening. Indeed this latter implies the existence of a thermomechanical coupling source, probably non-negligible and which must be considered when estimating temperature variations induced by shear band development.

Constitutive modeling of the rate-dependent resilient and dissipative large deformation behavior of a segmented copolymer polyurea

Phase-separated segmented copolymers comprised of hard and soft segments can be tailored to offer hybrid mechanical performance including a highly dissipative yet resilient large strain behavior. The phase-separated morphology provides multiple relaxation processes which lead to a rate-dependent stress–strain behavior with a transition in rate sensitivity. In addition to the viscoelastic–viscoplastic dissipation pathways, stretch-induced softening due to microstructural breakdown provides a significant source of dissipation as evident in the hysteresis observed during cyclic loading. Extensive shape recovery is observed upon unloading, showing a highly resilient behavior in tandem with extensive dissipation. Here a microstructurally informed three-dimensional constitutive model is developed to capture the remarkable features of the large strain behavior of the segmented copolymers. The model employs multiple micro-rheological mechanisms to capture the time-dependent nonlinear constitutive responses of both hard and soft domains as well as the stretch-induced softening of the hard domains. In direct comparison to experimental data, the model is found to successfully capture the behavior of an exemplar polyurea copolymer over least six orders of magnitude in strain rate (10−3 to 103 s−1) including a transition in rate sensitivity at 1 s−1. The model is also shown to be predictive of the highly dissipative yet resilient stress–strain behavior under a variety of cyclic loading conditions. The microstructurally informed nature of the model provides insights into tailoring copolymeric microstructures to provide tunable energy storage and dissipation mechanisms in this important class of material.

Numerical modeling of friction stir welding processes

This work describes the formulation adopted for the numerical simulation of the friction stir welding (FSW) process. FSW is a solid-state joining process (the metal is not melted during the process) devised for applications where the original metallurgical characteristics must be retained. This process is primarily used on aluminum alloys, and most often on large pieces which cannot be easily heat treated to recover temper characteristics.Heat is either induced by the friction between the tool shoulder and the work pieces or generated by the mechanical mixing (stirring and forging) process without reaching the melting point (solid-state process).To simulate this kind of welding process, a fully coupled thermo-mechanical solution is adopted. A sliding mesh, rotating together with the pin (ALE formulation), is used to avoid the extremely large distortions of the mesh around the tool in the so called stirring zone while the rest of the mesh of the sheet is fixed (Eulerian formulation).The orthogonal subgrid scale (OSS) technique is used to stabilize the mixed velocity–pressure formulation adopted to solve the Stokes problem. This stabilized formulation can deal with the incompressible behavior of the material allowing for equal linear interpolation for both the velocity and the pressure fields.The material behavior is characterized either by Norton–Hoff or Sheppard–Wright rigid thermo-visco-plastic constitutive models.Both the frictional heating due to the contact interaction between the surface of the tool and the sheet, and the heat induced by the visco-plastic dissipation of the stirring material have been taken into account. Heat convection and heat radiation models are used to dissipate the heat through the boundaries.Both the streamline-upwind/Petrov–Galerkin (SUPG) formulation and the OSS stabilization technique have been implemented to stabilize the convective term in the balance of energy equation.The numerical simulations presented are intended to show the accuracy of the proposed methodology and its capability to study real FSW processes where a non-circular pin is often used.

Viscoplastic analysis for direct impact of sports balls

A coefficient of restitution (COR) is used to represent viscoplastic dissipation of energy in the contact region of colliding bodies [6]. A model has been developed that distinguishes between rate-independent plastic and rate-dependent viscous energy dissipation during impact. A nondimensional contact force shape factor for compression α is introduced which can be measured experimentally. The measured α and COR are used to separate the energy dissipated during collision into part due to plastic deformation and another part due to viscous dissipation. In comparison to the viscoelastic compliance model, the viscoplastic compliance model approximates the force profile accurately, especially in terms of the maximum force that occurs during impact.

Investigation of damage evolution in short glass fibers reinforced polyamide 6,6 under tensile loading using infrared thermography

Mechanical properties of polymers are very sensitive to environmental conditions in particular temperature. In the case of mechanical testing, thermomechanical coupling induce heat sources to be activated during the deformation and damage processes so that the temperature of the specimen may vary during testing. Depending on the characteristic temporal and spacial scales of the deformation and damage processes involved by the loading this temperature increase might be uniform or highly localized. The aim of the study is to investigate the temperature field evolution of glass fibers reinforced polyamide 6,6 with 0% (PA66GF00), 10% (PA66GF10), 20% (PA66GF20) and 30% (PA66GF30) glass fiber. In addition to infrared thermography, digital image correlation (DIC) was used to quantify deformation localization zones and correlate them to identified heat dissipation sources. Until necking, the heat distribution was found to be nearly homogeneous on PA66GF00 with a well marked thermoelastic region, succeeded by an homogeneous heat increase due to viscoplastic dissipation. Necking is associated to strong heat increase that is localized on the the necking area. The thermal response of short fiber reinforced materials was found to differ markedly from the uncharged one. Strong heterogeneity of the thermal was observed and was associated to localisation processes at different scales (investigated by DIC). The effect of the applied strain rate on the observed thermal heterogenities was investigated. In addition to DIC, the volume damage evolution was monitored using X-ray computed microtomography in particular region.

Fracture and Energy Partitioning in Uncooked and Cooked Noodles

ABSTRACTHumans perform fascinating science experiments at home on a daily basis when they undertake the modification of natural and naturally-derived materials by a cooking process prior to consumption. The material properties of such foods are of interest to food scientists (texture is often fundamental to food acceptability), oral biologists (foods modulate feeding behavior), anthropologists (cooking is probably as old as the genus Homo and distinguishes us from all other creatures) and dentists (foods interact with tooth and tooth replacement materials). Material scientists may be interested in the drastic changes in food properties observed over relatively short cooking times. In the current study, the mechanical properties of one of the most common (and oldest at 4,000+ years) foods on earth, the noodle, were examined as a function of cooking time. Two types of noodles, each made from natural materials (wheat flour, salt, alkali and water) by kneading dough and passing them through a pasta-making machine. These were boiled for between 2–14 min and tested at regular intervals from raw to an overcooked state. Cyclic tensile tests at small strain levels were used to examine energy dissipation characteristics. Energy dissipation was >50% per cycle in uncooked noodles, but decreased by an order of magnitude with cooking. Fractional dissipation values remained approximately constant at cooking times greater than 7 min. Overall, a greater effect of cooking was on viscoplastic dissipation characteristics rather than fracture resistance. The results of the current study plot the evolution of a viscoplastic mixture into an essentially elastic material in the space of 7 minutes and have broad implications for understanding what cooking does to food materials. In particular, they suggest that textural assessments by consumers of the optimally cooked state of food has a definite physical definition.

The Effect of Self-Assembled Monolayers on Interfacial Fracture

This paper describes a series of experiments and analyses that were used to examine crack growth near sapphire/epoxy interfaces. Adhesion of the epoxy to the sapphire was enhanced by coating the sapphire with mixtures of two silane coupling agents that form self-assembled monolayers. A new biaxial loading device was used to conduct a series of mixed-mode fracture experiments. Crack opening interferometry, atomic force microscopy, and angle-resolved X-ray photoelectron spectroscopy allowed cohesive zone sizes, fracture surface topographies, and loci of fracture to be established. The experiments were complemented by finite element analyses that accounted for the rate- and pressure-dependent yielding of the epoxy. The analyses also made use of traction-separation laws to represent the various interphases that were produced by the mixed monolayers. The intrinsic toughness (defined as the area underneath the traction-separation curve) of the bare sapphire interfaces was independent of mode-mix and lower than values from previous experiments with glass/epoxy and quartz/epoxy specimens. The increase in overall toughness with mode-mix was completely accounted for by viscoplastic dissipation in the epoxy outside the cohesive zone. The minimum toughness of the coated sapphire interfaces was about five times higher than the mode-mix independent intrinsic toughness of the uncoated specimens. The increase in overall toughness with mode-mix was almost completely accounted for by increases in the intrinsic toughness as the traction-separation law varied with mode-mix. As a result, viscoplastic dissipation outside the cohesive zone was minimal. Atomic force fractography and X-ray photoelectron spectroscopy indicated that the crack growth mechanisms and the loci of fracture in the coated and uncoated specimens were quite different.