Viscoplastic Model Research Articles

Effect of loading modes on uniaxial creep-fatigue deformation: A dislocation based viscoplastic constitutive model

A comprehensive investigation was conducted on the stress-strain responses and microstructural evolutions of 9Cr3Co3WCu martensitic steel at 650 ℃ subjected to low cycle fatigue tests, strain-controlled creep-fatigue tests (SNCFTs), and hybrid stress-strain-controlled creep-fatigue tests (HSSCFTs). The creep strain accumulation per cycle in HSSCFTs exhibited three stages: an initial decrease in the early cycles, followed by a prolonged period of steady increase, culminating in a rapid increase prior to fracture. In contrast, the creep strain accumulation in SNCFTs showed a consistent decreasing trend throughout the test. Through the employment of advanced characterization techniques, the evolution of dislocation density exhibited a decreasing rate in all cases, and a fracture morphology characterized by a large size of creep voids was observed in HSSCFTs. Consequently, a dislocation-based viscoplastic constitutive model was developed, incorporating a relaxation parameter, a slip deformation resistance model and a dislocation density evolution model interacting with the grain boundary. The proposed model demonstrated excellent congruences under fatigue, creep, creep-fatigue, and multi-step creep- fatigue tests between experimental and simulated results, thereby confirming its capability to comprehensively capture cyclic deformation under various loading modes.

Double-peak strain hardening behavior of Mg–1.2 wt.%Y alloy

In this study, the mechanical behavior and deformation mechanism of an extruded Mg–1.2 wt.%Y rod under tension and compression along the extrusion direction (ED) were systematically investigated through experiments and crystal plasticity simulations. A double-peak strain hardening behavior comprising five distinct stages was observed under compression along the ED. The five stages are as follows: a fast drop in the strain hardening rate (stage I), steady increase in the strain hardening rate (stage II), gradual decrease in the hardening rate (stage III), second increase in the strain hardening rate (stage IV), and rapid decrease in the strain hardening rate (stage V). This unique strain hardening behavior led to an ultimate compressive strength of up to 539 MPa at a high strain of 0.4. Crystal plastic simulations using an elastic viscoplastic self-consistent model revealed a high activity and a long process of {101¯2} twinning in a strain range of 0–0.35 under compression along the ED. The twinning behavior examined via electron backscattering diffraction indicated that the {101¯2} twinning was activated in both grains with relatively high and very low Schmid factors. Subsequently, the mechanism for the presence of this double-peak strain hardening was established and, finally, the significance of this double-peak strain hardening for strengthening Mg alloys was discussed.

Effects of cellulose nanofibrils on rheological and mechanical properties of 3D printable cement composites

This study explores the effects of cellulose nanofibrils (CNF), a relatively new type of nanocellulose material, on the rheological and printability characteristics of cementitious mixtures, and the mechanical properties of 3D printed specimens. The rheology of the mortar mixtures with varying ratios of CNF is thoroughly assessed first. Two testing protocols, stress growth test and ramp test, are followed for rotational measurements using a shear rheometer with a building cell and vane motor. Stress growth tests are carried out to quantify the static yield stress of the cementitious mixtures. Ramp tests are conducted to determine dynamic yield stress and plastic viscosity of the mixes using the Bingham visco-plastic material model. As oscillatory measurements, amplitude sweep tests are carried out to determine the viscoelastic properties of the mortar mixes, including storage modulus and critical strain that are found to be essential for buildability. Thermogravimetric analysis (TGA) is conducted to assess the effects of CNF on the hydration characteristics of the mixtures. The printability and the buildability of the mortar mixtures incorporating CNF are assessed using a 3D concrete printer equipped with a 10 mm diameter nozzle and screw pump mechanism. Tensile, flexural, and compressive strength tests are conducted to determine the mechanical properties of 3D printed specimens with varying ratios of CNFs. Scanning electron microscopy (SEM) is used to conduct the microstructural analysis on fractured surfaces of the mechanically tested specimens. Results indicate that adding CNF at least 0.3 wt% of cement has a favorable effect on the rheological properties of cement composites.

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory. The shear modulus model for the ambient β phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the β phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress–strain response of tin was measured at strain rates of 10−3 to 3×103s−1 and temperatures ranging from 87 to 373 K. The Preston–Tonks–Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to 105s−1. The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid–liquid but never a fully liquid state, never fully lost strength, stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

Investigation of in-plane visco-deformation in PMMA indentation via TLV model calibrated with tensile specimens

Time-dependent in-plane deformation in PMMA indentation is investigated via two-layer visco-plasticity model (TLV). The parameters of TLV model for PMMA were calibrated for tensile specimens using finite element analysis (FEA) and an optimization approach. The TLV model with the calibrated parameters was then employed to simulate nano- and micro-indentation behaviors including creep, relaxation, and other responses under various test conditions. Comparisons of experimental and FEA indentation load-depth curves showed agreement except the last unloading segment. This discrepancy was attributed to the inability of TLV model in replicating the delayed elastic recovery. In addition, deformation recovery with in-plane displacement (ui) was observed over a few days after indentation load removal. The characteristics of ui recovery and the factors influencing its magnitude are discussed. The proportionality of relative ui recovery rate prominently featured in the viscoelastic properties of PMMA, regardless of indentation history.

Prediction of Short- to Long-Term Cyclic Deformation Behavior and Fatigue Life of Polymers.

The prediction of mechanical behavior and fatigue life is of major importance for design and for replacing costly and time-consuming tests. The proposed approach for polymers is a combination of a fatigue model and a governing constitutive model, which is formulated using the Haward-Thackray viscoplastic model (1968) and is capable of capturing large deformations. The fatigue model integrates high- and low-cycle fatigue and is based on the concept of damage evolution and a moving endurance surface in the stress space, therefore memorizing the load history without requesting vague cycle-counting approaches. The proposed approach is applicable for materials in which the fatigue development is ductile, i.e., damage during the formation of microcracks controls most of the fatigue life (up to 90%). Moreover, damage evolution shows a certain asymptote at the ultimate of the low-cycle fatigue, a second asymptote at the ultimate of the high-cycle fatigue (which is near zero), and a curvature of how rapidly the transition between the asymptotes is reached. An interesting matter is that similar to metals, many polymers satisfy these constraints. Therefore, all the model parameters for fatigue can be given in terms of the Basquin and Coffin-Manson model parameters, i.e., satisfying well-defined parameters.

Modeling of Texture Development during Metal Forming Using Finite Element Visco-Plastic Self-Consistent Model

In directional forming processes, such as rolling and extrusion, the grains can develop preferred crystal orientations. These preferred orientations—the texture—are the main cause for material anisotropy. This anisotropy leads to phenomena such as earing, which occur during further forming processes, e.g., during the deep drawing of sheet metal. Considering anisotropic properties in numerical simulations allows us to investigate the effects of texture-dependent defects in forming processes and the development of possible solutions. Purely phenomenological models for modeling anisotropy work by fitting material parameters or applying measured anisotropy properties to all elements of the part, which remain constant over the duration of the simulation. In contrast, crystal plasticity methods, such as the visco-plastic self-consistent (VPSC) model, provide a deeper insight into the development of the material microstructure. By experimentally measuring the initial texture and using it as an initial condition for the simulations, it is possible to predict the evolution of the microstructure and the resulting effect on the mechanical properties during forming operations. The results of the simulations with the VPSC model show a good agreement with corresponding compression tests and the earing phenomenon, which is typical for cup deep drawing.

A three-dimensional viscoelastic–viscoplastic and viscodamage constitutive model for unidirectional fibre-reinforced polymer laminates

A novel 3D viscoelastic–viscoplastic and viscodamage constitutive model is proposed to predict the viscous effects due to dynamic loading conditions of unidirectional carbon fibre-reinforced polymer laminates at the meso-scale level. The present model is developed under continuum damage mechanics and the thermodynamics of irreversible processes framework. The viscoelastic response is modelled using the generalised Maxwell model, while an overstress model is employed to address the viscoplastic strain. The onset of the viscodamage mechanisms is based on experimental expressions, and their propagation is defined as a function of the corresponding fracture toughness. The mechanical response of the present constitutive model under pure longitudinal shear loading conditions at different strain rates is presented. The higher the strain rate is, the stiffer the responses in the viscoelastic and viscoplastic regions are. Additionally, the onset of viscodamage increases with higher strain rates. Off-axis compressive experimental data at two different strain rates are employed to demonstrate the capabilities of the present model with good predictions being obtained.

Evaluation of warm mix effect in laboratory using a self-developed WMA additive Alube

In response to the problems of high mixing temperatures and energy consumption of polymer-modified asphalt mixtures in road construction, a surfactant-based warm mix additive ‘Alube’ was developed. The warm mix SBS-modified asphalt and its mixture were prepared. Their rheological performance and chemical structure were analysed by the rheological and microscopic tests. The active mixing power (P) of asphalt mixtures were examined by the variable speed mixing (VSM) test. The mixing flowability model was then established to evaluate the warm mix effect. The results indicated that the mixing flowability of asphalt mixtures obeyed the linear Bingham visco-plastic model, and the slope and intercept of the flow straight characterised the mixing viscosity and plastic limit. It is evaluated that 0.7% Alube1 and Evotherm reduced the mixing temperature of SBS-modified asphalt mixture by 14°C and 12°C, respectively. Moreover, Alube1 is suitable for a wide range of applications through warm mix asphalt technology.

Numerical Simulation of Mold Filling of Polymeric Materials with Friction Effect during Hot Embossing Process at Micro Scale.

The filling efficiency during the hot embossing process at micro scale is essential for micro-component replication. The presence of the unfilled area is often due to the inadequate behavior law applied to the embossed materials. This research consists of the identification of viscoplastic law (two-layer viscoplastic model) of polymers and the optimization of processing parameters. Mechanical tests have been performed for two polymers at 20 °C and 30 °C above their glass transition temperature. The viscoplastic parameters are characterized based on stress-strain curves from the compression tests. The influences of imposed displacement, temperature, and friction on mold filling are investigated. The processing parameters are optimized to achieving the complete filling of micro cavities. The replication of a micro-structured cavity has been effectuated using this process and the experimental observations validate the results in the simulation, which confirms the efficiency of the proposed numerical approach.

Compaction localization in geomaterials: A mechanically consistent failure criterion

Compaction bands play a key role in the deformation processes of porous rocks and explain different aspects of physical processes in geological formations. The state-of-the-art description of the localized strains that lead to compaction banding has limitations from the mechanical point of view. Thus, we describe the phenomenon using a consistent axiomatic formulation. We build a viscoplastic model using minimal assumptions; we base our model on six principles to study compaction band strain localization triggered by viscous effects. We analyze different stress states to determine the conditions that trigger compaction bands. Laboratory experiments show that a material undergoes different strain localizations depending on the confinement pressure; thus, we perform a series of numerical experiments that reproduce these phenomena under varying triaxial compression conditions. These simulations use a simple viscoplastic constitutive model for creep based on Perzyna’s viscoplasticity and show how confinement changes the strain localization type for different triaxial tests.

Critical solder joint in insulated gate bipolar transistors (IGBT) power module for improved mechanical reliability

This investigation identifies the critical solder joint in a typical Insulated Gate Bipolar Transistor (IGBT) module and provided new knowledge on how operating thermal loads degrade IGBT-attach, Diode-attach, and Substrate solder joints in the device. SolidWorks software is used to create three realistic 3-D Finite Element (FE) models of the typical IGBT module used in this investigation. In-service operating power and IEC 60068–2-14 thermal cycles are implemented in ANSYS mechanical package to simulate the response of the three solder joints in the FE models to the load cycles. The solder in the joints is lead-free alloy of 96.5% tin, 3% silver, and 0.5% copper (SAC305) composition. The SAC305 material properties are modelled as time and temperature dependent with Anand's visco-plastic model employed as the constitutive model. Results show that the key degradation mechanism of solder joints in IGBT module are stress, plastic strain, and strain energy magnitudes. Accumulated plastic strain in the joints is found the predominant damage factor. Critical solder joint in the module depends on the load cycle the device experiences. IGBT-attach solder joint is critical in active power load cycle. Substrate solder joint degraded most in passive thermal cum combined passive thermal and active power load cycles.

Prediction of mechanical properties and fatigue life of nanosilver slurry in chip interconnection

This article investigates the failure mode and mechanism of copper pillar solder joints in temperature cycling experiments, focusing on a Cu/nano Ag/Cu solder joint structure. The hot pressing bonding condition at 300 °C with insulation for 10 s is chosen for the experiments. Based on the life test results, the thermal cycling fatigue life of the nanosilver solder joint is determined to be 2050 cycles. To gain further insights, finite element software ANSYS is employed to simulate nanosilver solder joints in flip chips, revealing the stress–strain distribution within the solder joints. The simulation utilizes the Anand viscoplastic constitutive model for the solder joint, providing a reasonable representation of the stress–strain behavior under thermal cycling load. Notably, the simulation highlights that the maximum stress and strain occur in the contact area between the solder joint and the copper column. To enhance accuracy, the calculation equation is refined using relevant experience, resulting in a prediction of the thermal fatigue life of nanosilver solder joints. This prediction aligns closely with the experimental results. The research outcomes not only contribute valuable insights into the behavior of nanosilver solder but also serve as a reference for its application in electronic packaging.

Simulation of cold-rolled 2024 Al alloy thick plate based on visco-plastic self-consistent model

2024 Al has been used in various fields. However, most cold-rolled Al has poor strength and plasticity, so it needs a solution and aging treatment. The rolled reduction has an important influence on microstructure. For different rolled reductions, microstructure has different evolution rules even under the same solution and aging treatment. Therefore, different rolled reduction has a great influence on the subsequent treatment. In this paper, deform simulation analysis technique was used to study the changes of strain of 2024 Al alloy during rolling deformation, and visco-plastic self-consistent was used to study the texture evolution of 2024 Al alloy, which provided a new method for the study of deformation behavior and anisotropy during rolling.

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics, but also significant time-dependent characteristics under high in-situ stress, which is attributed to the time-dependent fracture of thin-layered rocks. This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics. The anisotropic long-term strength, creep fracturing process, and fracture orientation characteristics of thin-layered rocks under different loading angles (β, ω) and intermediate principal stress were summarized. A three-dimensional (3D) non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior. The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method. By constructing the plastic potential function and overstress index related to loading angles and stress state, the anisotropic time-dependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded. The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.

A new hybrid local radial basis function collocation method for 2.5D thermo-mechanical modelling of continuous casting of steel

This study presents a new strong-form meshless method to solve the thermo-mechanical problem of the solidification process in the continuous casting of steel. A two-dimensional slice that travels in the casting direction is modelled in the Lagrangian system. The newly developed mechanical model is one-way coupled to the thermal model, where the heat flux due to the mould, sprays, rolls and radiation are imposed to solve heat transfer in the strand. The resulting temperature and metallostatic pressure govern the Norton-Hoff visco-plastic model used for computing shrinkage of the solid shell and induced residual stresses. The results are used to estimate critical areas susceptible to hot-tearing formation. The mechanical model uses a generalised plane strain assumption that includes linear strains perpendicular to the slice and enables the computation of the straightening of the strand. The thermo-mechanical model is spatially discretised with a local radial basis function collocation method (LRBFCM). The mechanical part includes a new hybrid method that combines LRBFCM with finite differences for increased stability. The presented work shows how the developed model is used to assess the impact of casting velocity on the solid shell shrinkage and the probability of hot-tearing occurrence in the continuous casting of square billets.

Ductile Fracture of Titanium Alloys in the Dynamic Punch Test

Estimates of physical and mechanical characteristics of materials at high strain rates play a key role in enhancing the accuracy of prediction of the stress–strain state of structures operating in extreme conditions. This article presents the results of a combined experimental–numerical study on the mechanical response of a thin-sheet rolled Ti-5Al-2.5Sn alloy to dynamic penetration. A specimen of a titanium alloy plate underwent punching with a hemispherical indenter at loading rates of 10, 5, 1, and 0.5 m/s. The evolution of the rear surface of specimens and crack configuration during deformation were observed by means of high-speed photography. Numerical simulations were performed to evaluate stress distribution in a titanium plate under specified loading conditions. To describe the constitutive behavior and fracture of the Ti-5Al-2.5Sn alloy at moderate strain rates, a physical-based viscoplastic material model and damage nucleation and growth relations were adopted in the computational model. The results of simulations confirm a biaxial stress state in the center of specimens prior to fracture initiation. The crack shapes and plate deflections obtained in the calculations are similar to those observed in experiments during dynamic punching.

Thermal fatigue life prediction of Ag-2.5Sn solder joint in flip chip

The heat dissipation needs of high-power devices cannot now be met by traditional packing solders due to the fast development of microelectronics interconnect technology. In addition to having outstanding thermal and electrical conductivity, nano-silver-tin paste better satisfies the needs of electronic devices. Studying the thermal reliability of solder joints is extremely important, this article investigates the fatigue life of the nano-silver-tin solder joints in temperature cycling experiments. Based on the life test results, the thermal cycling fatigue life of the nano-silver-tin solder joint is determined to be 2880 cycles. Finite element software was used to replicate the chip’s bonding process and assess the solder joint stress and strain distribution. The stress and strain of nano-silver-tin solder connections under thermal cycling load are accurately modeled using the Anand viscoplastic model and elastic model. The findings indicate that the contact region between the solder connections and copper columns is where the chip generates the most stress and strain. The fatigue life of the solder joint is estimated by using the Coffin–Manson modified equation, and this prediction aligns closely with the experimental results.

Predicting Mechanical Properties of Polymer Materials Using Rate-Dependent Material Models: Finite Element Analysis of Bespoke Upper Limb Orthoses.

Three-dimensional printing-especially with fused deposition modeling (FDM)-is widely used in the medical field as it enables customization. FDM is versatile owing to the availability of various materials, but selecting the appropriate material for a certain application can be challenging. Understanding materials' mechanical behaviors, particularly those of polymeric materials, is vital to determining their suitability for a given application. Physical testing with universal testing machines is the most used method for determining the mechanical behaviors of polymers. This method is resource-intensive and requires cylinders for compression testing and unique dumbbell-shaped specimens for tensile testing. Thus, a specialized fixture must be designed to conduct mechanical testing for the customized orthosis, which is costly and time-consuming. Finite element (FE) analysis using an appropriate material model must be performed to identify the mechanical behaviors of a customized shape (e.g., an orthosis). This study analyzed three material models, namely the Bergström-Boyce (BB), three-network (TN), and three-network viscoplastic (TNV) models, to determine the mechanical behaviors of polymer materials for personalized upper limb orthoses and examined three polymer materials: PLA, ABS, and PETG. The models were first calibrated for each material using experimental data. Once the models were calibrated and found to fit the data appropriately, they were employed to examine the customized orthosis's mechanical behaviors through FE analysis. This approach is innovative in that it predicts the mechanical characteristics of a personalized orthosis by combining theoretical and experimental investigations.

Localized plastic strain accumulation in shape memory ceramics under cyclic loading

The premature failure of shape memory ceramics (SMC)s under cyclic loading is a critical issue limiting their applications as actuators and thermal protection layers. Martensitic phase transformation (MPT), essential for superelasticity and shape memory functionalities in SMCs, induces localized plastic deformations due to phase expansion. In polycrystalline materials, the accumulation of localized plastic strain serves as the primary mechanism for fatigue crack initiation under cyclic loading. In this research, a phase-field (PF) phase transformation model coupled with a viscoplasticity model is presented to study the effects of microstructural features, engineered pores, and sample size on plastic strain accumulation (PSA) during cyclic loading of SMCs. Our findings highlight that the grain boundaries (GB)s are critical regions with high PSA, with noticeable reductions observed by decreasing the grain boundary density (GBD). Additionally, we found that engineered pores effectively reduced cyclic PSA, however, we identified a threshold on the volume fraction of pores. Also, textured microstructures with certain characteristics demonstrate significant influence on PSA. A cross-correlation data analysis approach is employed to study the relationship between the studied microstructural features and PSA to facilitate the identification of the most important factors controlling the irreversible PSA during compressive cyclic loading. By mitigating the rate of PSA, significant enhancements in cyclic life before fatigue crack initiation can be achieved, enabling superior performance in practical applications.