Viscoplastic Model Research Articles

Viscoplastic photoalignment modeling of asymmetric surface restructuring in azopolymer films by elliptically polarized light

This study aims to test and validate the modern orientation approach of Saphiannikova & co. within the context of viscoplastic photoalignment (VPA) modeling. We focus on the formation of topographical...

Refined model of leather

The structure of finished leather and semi-finished products differ in physical and mechanical parameters. To obtain the properties of elasticity, pliability, and viscosity required in leather production, it is necessary to ensure their values that guarantee the high quality of the resulting product. In this article, a model for finished leather is obtained based on combining the viscoelastic Kelvin model with the deformationinert Khusanov model and the Bingham–Shvedov viscoplastic model. This model makes it possible to improve the elastic-viscous plastic deformation of a fibrous material (leather). The possibility of clarifying the pattern of change in the deformation curve depending on the time the fibrous material is loaded by a certain force was explored. The aim of refining the deformation curve is that in known models, at the initial moment of loading, deformation occurs instantly up to a certain value, which does not fully describe the real physical process of deformation of the material. Consequently, in the proposed refined model, the deformation is fixedat zero value, which provides a real physical pattern of deformation of the fibrous material. The refined model will serve designers of technological machines to develop parameters of deformation during the mechanical processing of elastic-viscous plastic materials.

Study of high-temperature uniaxial low cyclic fatigue and creep–fatigue behavior of P92 steel using a unified viscoplastic constitutive model

Study of high-temperature uniaxial low cyclic fatigue and creep–fatigue behavior of P92 steel using a unified viscoplastic constitutive model

Comparison of thermal-fatigue lives of conventional and hybrid solder joints: Experiment and FE analysis

This paper presents experimental and numerical results of thermal-fatigue lives of conventional and hybrid solder joints of memory module. Thermal fatigue test is performed for three loading cases having different the maximum temperature and temperature range, from which crack initiation cycles and crack propagation rates are measured. It shows that measured crack initiation cycles are similar and much smaller than failure cycles for all cases. Measured crack propagation rates, however, vary significantly depending on the conditions. Measured crack propagation rates for the hybrid solder joints are more than twice, compared to that of conventional solder joints. For analysis, elastic-visco-plastic FE analysis using the Anand unified visco-plastic model combining plasticity and creep is performed, from which the volume-average value of inelastic dissipation energy density per cycle is calculated at the crack initiation location. To quantify thermal-fatigue lives of conventional and hybrid solder joints, four parameters in the energy-based Darveaux model are determined for conventional and hybrid solder joints from present experimental and FE analysis results.

Identification of thermo-viscoplastic behavior for AA6061 under in-plane biaxial loadings

This work aims to investigate the thermo-visco-plastic behavior of an aluminum alloy (AA6061) sheet metal submitted to in-plane biaxial loadings under warm conditions. Biaxial tensile tests are performed in a temperature range from room temperature to 160 °C, and in a strain rate range from quasi-static to the so-called “intermediate” strain rate (up to few s−1). The specimen shape used in this study has been previously defined and validated by the authors to identify the viscoplastic hardening models of metallic alloys at large strains. A specific device leading to a uniform temperature in the sample is associated with a dynamic biaxial traction bench to carry out the temperature and strain rate dependent characterizations. From these experiments, both the experimental forces measured on each axis of the in-plane biaxial specimen and the principal strains at the center of the specimen are obtained. These experimental data are then used in an inverse analysis loop, based on a finite element model of the biaxial test, to calibrate the parameters of a thermo-viscoplastic strain hardening model by minimizing the difference between the experimental and numerical principal strains at the center point of the specimen. Finally, it is shown that the identified hardening model well predicts the flow stress of AA6061 under different temperatures and strain rates for a strain level of up to 40%.

Study on the reliability of nano-silver-coated tin solder joints for flip chips

Abstract The nano-silver-coated tin (Sn@Ag) paste was modeled using the method of the Anand unified viscoplastic constitutive model and elastic model. After thermal cyclic loading, the plastic strain of the solder joints increased cumulatively, while the maximum equivalent stress remained basically stable. The simulation results show that the maximum displacement occurs at the solder joint at the farthest end from the center of the chip, which is a dangerous solder joint. Using the finite element method and EPRI (the American Electric Power Research Institute) estimation method, the fatigue life of the nano-silver-coated tin solder joint is predicted to be 616 weeks, which is significantly higher than that of the nano-silver solder joint. It is indicated that adding a certain amount of nano-tin to the nano-silver paste to form a core–shell structure can improve the shear strength of the solder joint and reduce the plastic strain, thereby significantly improving the reliability of the solder joint. It is proved by experiments that the nano-silver paste is feasible for flip–chip interconnection. The research on this topic provides experimental reference and theoretical basis for the application of a new generation of interconnection materials in power devices and promotes the development and application of microelectronic packaging technology.

Creep-fatigue life prediction of notched structure after an advanced surface strengthening treatment in a nickel-based superalloy at 650°C

The elucidation of creep-fatigue damage mechanisms is still controversial for high-temperature structures after surface strengthening treatments, which serves as a critical foundation for the development of an accurate life prediction method. In this work, a numerical procedure is constructed for the prediction of creep-fatigue life improvement, where a dual-scale modeling approach is proposed to integrate important strengthening factors and microstructure features. The macro-scale finite element (FE) simulation aims to investigate the cyclic deformation behavior in a notched structure by using a viscoplastic constitutive model. The initial stress field is predetermined based on the experimental residual stress. The micro-scale FE analysis is employed to investigate the local damage evolution occurring at the notched root by combining size-dependent crystal plasticity with grain boundary cavity model. The cycle-by-cycle deformation histories are extracted from the macro-scale FE model and subsequently are utilized as boundary conditions in the micro-scale FE one. From the experimental perspective, the submerged micro-abrasive waterjet peening (SMA-WJP) process is carried out for creep-fatigue life improvement of the notched structure. Results shows that the notched structure treated by the SMA-WJP process forms an obvious plastic layer with the depth of 20 μm and residual stress with the maximum value of -926 MPa. The predicted numbers of cycles to crack initiation agree with the creep-fatigue experimental ones before and after SMA-WJP. In detail, the surface residual stress and plastic layer are unable to suppress the cavity nucleation on the grain boundaries of internal material. As a consequence, the creep-fatigue life improvement is diminished as the hold time increases, which can be accurately predicted by the developed numerical procedure.

Implementation of a modified Graham-Walles viscosity function within a Chaboche viscoplastic constitutive model

This work provides a numerical framework for the accurate prediction of operational life of metallic components exhibiting a non-classical creep behavior under constant loadings and very high temperature. A modified Graham-Walles type analytical viscoplastic function is implemented into a Chaboche unified viscoplastic constitutive model. The numerical model is integrated into the finite element software Lagamine following a fully-implicit two-step radial return mapping algorithm. The non-linear system of equations is solved using a robust Newton-Raphson method. The computational efficiency of the model is enhanced by implementing a sub-step routine, thereby decreasing the average number of iterations of the finite element software. The validation of the model is performed using experimental data available in the literature on the non-classical creep behavior of Incoloy 800H, a Ni-superalloy exhibiting a two-step creep strain rate minima attributed to multiple complex dislocation-precipitate interactions.

Fractional order viscoplastic modeling of anisotropically overconsolidated clays with modified isotach viscosity

Current overstress typed elastic viscoplastic models fall short in describing some time-dependent mechanical behaviors of anisotropically overconsolidated clays comprehensively. This paper presents a rigorous fractional order anisotropic elastic viscoplastic two-surface model for such clays, based on the principles of fractional consistency viscoplasticity and bounding or subloading surface theory. First, a three-dimensional formulation of isotach viscosity is proposed and integrated into two rate-dependent surfaces, i.e., the loading surface and yield surface. Then, by incorporating the stress-fractional operator of the rate-dependent loading surface into isotropic, progressive, and rotational hardening rules, the incremental form of stress-strain-time model with a fractional order viscoplastic flow rule is developed by meeting the consistency condition on the loading surface. Accordingly, the proposed model cannot only maintain the predictive capabilities of a classic bounding surface model but also describe the general features of the time-dependent behavior under various stress conditions. Validation and versatility of the proposed fractional order elastic viscoplastic model are successfully evaluated against constant strain-rate and stress relaxation tests on anisotropically overconsolidated resedimented Boston Blue clay.

Multidisciplinary approach for the prediction of cement paste rheological properties: physical analysis, experimental rheology and microstructural modelling

AbstractIn this contribution, an interdisciplinary approach was employed to investigate and describe the fresh rheology of cementitious pastes, using analytical techniques, microstructural modelling, and experimental rheometry. The pastes, based on Ordinary Portland Cement and Limestone Calcined Clay Cement at a solid volume fraction of Φ = 0.45, were subjected to various analyses. Physical and chemical analyses were conducted including laser granulometry and isothermal heat flow calorimetry. Dynamic rotational rheometry and static oscillatory rheometry, along with viscoplastic and viscoelastic rheological modelling were used to support the characterization of the pastes. A physics‐based Monte‐Carlo algorithm was developed to numerically describe rheological properties such as structural buildup and yield stress. The results showed that as the physical properties of the pastes became more complex, the correlation of several analysis methods went more challenging. However, the combination of analytical, experimental, and phenomenological rheology allowed for a more distinct characterization of the cement paste. These findings can serve as a basis for further multidisciplinary rheological characterization of cementitious building materials.

Viscoplastic simple shear at finite strains

The equations governing the simple shear deformation of an incompressible inelastic material undergoing finite strain are derived in this paper. The constitutive assumptions are kept in their most general form to allow the incorporation of widely used viscoplastic or viscoelastic models from the literature. It is shown that, while for a hyperelastic material the simple shear problem is completely determined by a single parameter, the amount of shear, in the viscoplastic case, the elastic deformation is the superposition of a triaxial stretch and a simple shear, whose determination requires the solution of three coupled nonlinear evolution equations. We evaluate such a solution for different material models and compare it with three-dimensional finite element simulations to assess its accuracy. We further assess the performance of these models using experimental data from filled rubber, focusing on their ability to capture the observed behaviour, such as the well-known Payne effect. Additionally, we extend our simple shear solution to address torsion and the extension of thin-walled cylinders. These derivations and analyses offer valuable insights for experimentalists engaged in the mechanical characterization of soft materials.

Deformation mechanism of high ductility Mg-Gd-Mn alloy during tensile process

In this research, a high ductility Mg-Gd-Mn magnesium alloy was designed and developed, with an elongation capability surpassing 50%. To gain insights into the underlying mechanism behind the high ductility of the Mg-2Gd-0.5Mn alloy, quasi-in-situ electron backscattered diffraction and two-beam diffraction were conducted. The results reveal that the Mg-Gd-Mn alloy exhibits a distinct rare-earth texture, and the activation of non-basal slip systems is evident from the clear observation of non-basal slip traces during the later stages of deformation. However, the primary deformation mechanisms in Mg-Gd-Mn alloy remain basal <a> slip and {10–12} tensile twinning, and the remarkable ductility observed in Mg-Gd-Mn alloys can be attributed to the softening of non-basal slip modes, which leads to a coordinated deformation between various modes of deformation. To further validate this conclusion, an analysis was conducted using a visco-plastic self-consistent (VPSC) model to investigate the relative activity of basal and non-basal slip in Mg-Gd-Mn alloys. The obtained results align well with experimental observations, providing additional support for the hypothesis.

A macroscopic viscoelastic viscoplastic constitutive model for porous polymers under multiaxial loading conditions

A macroscopic constitutive model, the Porous Eindhoven Glass Polymer (Porous EGP) model, is presented to describe the deformation behavior of cavitated rubber toughened polymers under multiaxial loading conditions. It is shown that the proposed macroscopic constitutive model is able to describe the non-linear pre-yield regime, strain rate dependence, post-yield behavior (strain softening and hardening) and void evolution for loading conditions ranging from shear to equi-triaxial (pure triaxial) tension and compression. The Porous EGP model is a combination of a well established non-linear viscoelastic viscoplastic model, the Eindhoven Glassy Polymer (EGP) model, and the modified Gurson model. The Gurson model is adopted to determine the equivalent stress and plastic rate of deformation tensor making it depending on the void volume fraction, deviatoric and hydrostatic stress. The macroscopic constitutive model is developed based on the response of realistic 3D representative volume elements (RVEs) containing randomly positioned mono-disperse inclusions. The constitutive behavior of the matrix phase in this full-field model is described by the EGP model, and the cavitated inclusions are idealized as voids. Their response is studied for a range of void volume fractions, multiaxial loading conditions, strain rates and thermodynamic states. The yield behavior of the heterogeneous material depends non-linearly on the macroscopic hydrostatic stress. This response is well captured with the proposed macroscopic constitutive model.

Thermomechanical behavior and microstructural characteristics of 7055 aluminum alloy during friction stirring welding

This study employed a viscoplastic finite element model and re-meshing technique to investigate the thermomechanical response of 7055 aluminum alloy during friction stir welding (FSW). The stirring pin rotates at 800–1200 rpm and moves at 80–120 mm/min (i.e., welding speed) during the FSW process. The temperature field and viscoplastic flow were mathematically modeled based on a computational solid mechanics method and predicted by a three-dimensional coupled thermomechanical numerical simulation. To validate the simulation results, real-time temperature measurements at the welded joint were acquired via thermocouples embedded in the plate prior to the welding process. Additionally, optical microscopy and electron backscatter diffraction techniques were used to examine the metallographic structure and grain orientation of the welds, respectively. The results revealed a temperature difference of 5–10 ℃ between the advancing and retreating sides of the plate. The material on the advancing side was extruded upward in a circular motion and eventually reached the surface. Meanwhile, the material on the retreating side moved half a revolution around the pin and remained at the original depth of the plate. Complete dynamic recrystallization occurred in the weld nugget, resulting in the formation of fine equiaxed grains with random orientation. In the thermomechanically affected zone, the proximity to the weld nugget was associated with an increased proportion of high-angle grain boundaries and recrystallized structures. Simultaneously, the intensity of the deformation texture decreased, while the recrystallized texture showed an initial strengthening followed by a subsequent weakening. This comprehensive investigation contributes to a deeper understanding of the thermomechanical behavior and metallographic characterization of 7055 aluminum alloy during the FSW process.

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

The application of a novel variable-order fractional calculus on rheological model for viscoelastic materials

Viscoelastic materials have become popular for novel multifunctional materials in emerging modern technologies, which have complex elastic-viscous-plastic behaviors. The variable-order fractional derivative has been gradually applied to characterize such variable memory effects of complex physical systems, while existing definitions are somewhat controversial. The new Scarpi’s variable-order fractional calculus has rigorous mathematical logic compared with the existed definitions. However, its practicality and feasibility in engineering are ambiguous due to the fewer applications up to now. In this paper, we aimed at introducing the Scarpi’s variable-order fractional derivative into the rheological applications of viscoelastic materials. Based on the Scarpi’s variable-order fractional derivative, the fractional Zener model and fractional viscoelastic-visoplastic models are established, and the parameters sensitivity on stress-strain relation is discussed. Then, the proposed models are then applied to depict different rheological behaviors of polymers at various temperatures and strain rates, and the results show that they have excellent agreement for experimental data compared to the reference model. It is observed that the order increases linearly with strain of the viscoelastic model and decreases exponentially with strain of the viscoplastic model. Furthermore, the physical significance of the corresponding fractional order parameters is investigated. It is found that they have the variation relation with temperatures and strain rates. It reveals that the variable fractional order can be regarded as an index to characterize the evolution of mechanical behaviors of polymers.

The gravitational signature of the dynamics of oceanization in the Gulf of Aden

We perform a new gravity analysis in the Gulf of Aden with the aim of finding new constraints on the geodynamic evolution of the area. Our analysis is developed within the frame of the recent GO_CONS_GCF_2_TIM_R6 global gravity model solution (Brockmann et al., 2021) that reflects the Earth's static gravity field as observed by GOCE (Gravity field and steady-state Ocean Circulation Explorer). We analyzed the solution at different harmonic degrees, to account for different depths and dimensions of the sources. Terrain correction has been performed by means of a spherical tesseroidal methodology (Marotta and Barzaghi, 2017) and the obtained corrected Geodetic Residual Gravitation has been compared to the Model Residual Gravitation predicted by means of a 2D visco-plastic finite element thermo-mechanic model that simulates the dynamics of the Gulf of Aden, from rifting to oceanization. In order to perform the comparison between observed and predicted gravitational features, data have been extracted along five profiles crossing the Gulf of Aden at different sectors, from the south-east to the north west. Via the Model Residual Gravitation we reproduce its geodetic counterpart, obtaining a characteristic hat-shaped pattern, with a central plateau portraying the highest values, flanked by two regions where the residual gravitation diminishes, finally reaching the lowest values at the far continental domains. The maximum variations of the residual gravitation values, from ridge to continental domain, range between 280 and 420 mGal and the steepest decrease occurs over distances of 200 km for the thick crust model and of 100–150 km for the thin crust model. Finally, the comparison between Geodetic and Model Residual Gravitation allows to further constrain the dynamics of the Gulf of Aden oceanization occurring by a slow passive rift of a hot 150 km thick lithosphere characterized by an initial 40 km thick crust.

Compression Behavior and Textures of Ti57-Nb43 Alloy at High Temperatures.

The mechanical behavior, microstructures, as well as the crystallographic textures of the Ti57-Nb43 alloy were investigated on cylindrical specimens compressed at high temperatures, in the range of 700-1000 °C, and strain rates between 0.001 and 1.0 s-1. Hardening, followed by softening behaviors, were observed as a function of strain due to the occurrence of dynamic recrystallization/recovery in hot deformation. The modified five-parameter Voce-type equation described well the stress-strain curves, but, for the present alloy, it was also possible with only four parameters. A new two-variables polynomial function was employed on the four parameters that described well the flow curves as a direct function of temperature and strain rate. It permitted the reduction in the number of parameters and had the predictive capacity for the flow stress at any temperature, strain, and strain rate in the investigated range. The crystallographic textures were similar at all temperatures, with an increase in intensity from 900 °C. The textures could be characterized by a double <100> and <111> fiber and a unique component of (001) <110>, the latter inherited from the initial hot-rolling texture. Viscoplastic polycrystal self-consistent deformation modeling reproduced the measured textures showing that dynamic recrystallization did not alter the development of the deformation texture, only increased its intensity.

Leadfree SnAgCu Solder Materials Characterization at High Strain Rates at Low Test Temperatures and Drop and Shock Simulation Using Input-G Method

Abstract Electronics will experience high and low working temperatures during operations, handling, and storage in severe environments applications such as download drilling, aircraft, and transportation. Temperatures in the vehicle underhood applications can range from −65 °C to +200 °C. Lead-free solder materials continue to evolve under varying thermal workloads. Material characteristics may deteriorate if operating conditions are harsh or heavy. Nonetheless, lead-free solders are susceptible to high strains, which can lead to electronic device failure. A better understanding of solder alloys is needed to ensure reliable operation in harsh environments. New doped solder alloys have recently been created by adding Ni, Co, Au, P, Ga, Cu, and Sb to SnAgCu (SAC) solder alloys to improve mechanical, thermal, and other qualities. SAC-Q has recently been made using Sn–Ag–Cu and the addition of Bi (SAC+Bi). It was discovered that adding dopants to SAC alloys may enhance mechanical characteristics and reduce aging damage. There is no published data on SAC solder alloys after prolonged storage at high strain rates and low functioning temperatures. The materials characterization of SAC (SAC105 and SAC-Q) solder after extended storage at low working temperatures (−65 °C–0 °C) and high strain rates (10–75 per sec) is investigated in this article. To characterize the material constitutive behavior, the Anand viscoplastic model was utilized to derive nine Anand parameters from recorded Tensile data. The generated nine Anand parameters were used to validate the Anand model's reliability. A strong correlation was established between experimental data and Anand's predicted data. The Anand parameters were used in a finite element framework to simulate drop events for a ball-grid array package on printed circuit board assembly to calculate hysteresis loop and plastic work density. The plastic work per shock event measures the damage progression of the solder interconnects. Thermal aging effects have been studied in terms of the hysteresis loop and the evolution of PWD.

A viscoplastic constitutive model for unsaturated soils based on nonstationary flow surface theory

AbstractA viscoplastic constitutive model is developed to describe the viscoplastic behavior of unsaturated soils. The proposed model accounts for the stain‐rate and suction effects on yield by adopting an unsaturated isotach concept. The nonstationary flow surface theory (NSFS) is applied for modeling the viscoplastic behavior, with the yield surface which can evolve with the viscoplastic strain, viscoplastic strain rate and suction. Meanwhile, the progressively hardening concept is adopted for reproducing the viscoplastic behavior of soil at an over‐consolidated state. For the validation, a series of loading conditions are considered based on the data from the literature. Results show that the proposed model is able to reproduce the main viscoplastic behaviors of unsaturated highly compacted Gaomiaozi (GMZ) bentonite, Glenroy silt and Qianjiangping landslide (QL) soil, including CRS compression tests, rate‐dependent triaxial shear tests, and triaxial creep tests.