Flow Stress Evolution Research Articles

A finite volume–based thermo-fluid-mechanical model of the LPBF process

The multi-physics coupling feature of the laser powder bed fusion (LPBF) process poses great challenges to numerical models regarding computational fidelity and efficiency. This paper proposed a finite volume–based model for predicting integrated thermo-fluid-mechanical behaviors of the LPBF process. The model directly unifies the heat transfer, fluid flow and solid mechanics simulations within a predefined mesh, enabling simultaneous solutions for the fluid domain under Eulerian description and the solid domain under Lagrangian description. Three benchmark tests accounting for individual problems were conducted to validate the model's accuracy and effectiveness. Track-scale LPBF simulations were performed to unravel the intricate interplay between thermal, fluid and mechanical behaviors. The numerical predictions of surface morphologies, molten pool dynamics and melt track dimensions aligned well with the experimental observations. The spatiotemporal evolution of transient thermal stress was accurately captured and the predicted residual stress field showed consistency with nanoindentation measurements. The proposed model was found robust in simultaneously predicting the temperature distribution, melt flow and residual stress evolutions of the LPBF process, and showed strong potential for addressing other similar multi-physics coupling problems.

Micromechanism insights and constitutive modeling for deformation in a novel high manganese austenitic steel

We explore the mechanical behavior and microstructural evolution of a novel high manganese austenitic steel (HMAS), extensively applied in underground engineering and structural construction. Our investigation focuses on two variants of HMAS, namely HMAS-1.9 and HMAS-10, which exhibit distinct yield strengths and elongation behaviors. Electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and X-ray diffraction (XRD) were employed to elucidate the evolution of microstructures during plastic deformation. Based on these experimental results, we developed a new phenomenological multiscale constitutive model that captures the mechanical behavior of HMAS, integrating micromechanisms and microstructural evolutions. Optimized with the MATLAB genetic algorithm toolbox, this model was successfully implemented in a uniaxial tensile finite element model (FEM) within ABAQUS, proving its efficacy in predicting both macroscopic flow stress and microstructural evolutions. Our findings highlight the important roles of initial grain size, dislocation density, and twin fraction in determining the mechanical properties of HMAS. Throughout the deformation process, both HMAS variants demonstrate similar plastic deformation behaviors, characterized by comparable rates of increase in dislocation density and twinning fraction, accompanied by a consistent trend of grain refinement. These findings not only deepen our understanding of the complex relationship between microstructure and mechanical properties of the HMAS steel, but also provide an effective multiscale constitutive modeling approach for predicting its deformation behavior.

Effects of multiple relaxation times in the annular flow of pulsatile electro-osmotic flow of a complex biological fluid: blood with low and high cholesterol

This study investigates the electro-osmotic flow of a biological fluid (blood with varying cholesterol levels) in annular flow to simulate a first approximation to arterial occlusion. The fluid´s rheology is characterized by a multi-modal convected Maxwell model equation. The charge density follows the Boltzmann distribution, governing the electrical field. Mathematically, this scenario can be modeled by the Poisson–Boltzmann partial differential equation. Assuming a small zeta potential (less than 25 mV) using the Debye–Huckel approximation and considering a pulsatile electrical field, analytical solutions are derived using the Fourier transform formalism. These solutions, expressed in terms of the modified Bessel function, provide transfer functions for axial velocity and volumetric flow as functions of material parameters represented by characteristic dimensionless numbers. This study further analyzes thermal, electric, inertial, viscoelastic, and various interactions within the plasma, hematocrit, hematocrit–cholesterol, and cholesterol–cholesterol as well as weight concentration through numerical simulations. Finally, the flow and rheology predictions are validated using experimental data on human blood with varying cholesterol levels. The obtained transfer functions reveal that the electric–thermal–viscoelastic effects and the multiple geometric relationships contribute to the dynamic response of the interactions between the input electrical field and output volumetric flow and shear stress functions, leading to and evolution of resonance curves. It is noteworthy that electro-osmotic flow in blood with pathologies associated with low and high cholesterol has been scarcely reported in the literature on rheology. Thus, this work represents a significant contribution to the field.

Numerical and experimental investigation of the dynamic mechanical behavior of precipitation-strengthed NiCoCrSi0.3C0.048 medium-entropy alloy

An extended crystal plasticity model and an optimized neural network are established to investigate the mechanical behavior of CoCrNiSi0.3C0.048 Medium entropy alloy (MEA) with a three-level hierarchical precipitation structure under dynamic compressive deformation at a variety of ranges of strain rates. The interaction between the matrix and first-level precipitates is described by a presented hybrid representative volume element RVE model, involving the effects of volume fraction (Vf), radius and geometric distribution on heterogeneous deformation. Effects of second- and third-level precipitates are realized through the extended crystal plasticity constitutive model, reflecting the motion mechanism of dislocations near the precipitates in the form of initial slip resistance. Meanwhile, this study investigates the influence of the presence of primary precipitates on the initiation of slip systems within special grains with Goss or S orientations in the matrix. Additionally, it provides a more in-depth explanation of the underlying principles behind the suppression of Goss texture formation by the precipitates from the perspective of slip systems analysis. The changing of volume fractions affects flow stress evolution. Avoiding suffering from expensive computational consumption by the crystal plasticity finite element method, an artificial neural network model optimized through a genetic algorithm, is presented to predict stress-strain responses and texture evolution results under varying compression strain rates. A reliable dataset derived from crystal plasticity finite element models and experimental results is utilized to train, test, and validate the genetic algorithm-based artificial neural network model. This model demonstrates good prediction capability in dynamic mechanical behavior and texture evolution, showcasing the feasibility and efficacy of the proposed neural network model. Compared to the CPFEM method, neural network models can greatly improve computational efficiency.

The dynamic evolution of powder flow and wall normal stress in different flow pattern silos

Major safety accidents involving silos in industrial processes are closely associated with abnormal wall stresses. The effects of different flow patterns and particle velocity distribution on wall stresses are investigated during silo discharge. The existence of particle velocity retardation layer near the wall boundary in the mass flow was observed by tracer particles and high-speed camera. The silo discharge undergoes a transformation from funnel flow to mass flow at a hopper half angle of 30°. As the outlet diameter increases, the time point of the flow pattern transformation becomes more and more later. The evolution of particle velocity in the central of the funnel flow is related to the outlet velocity wave propagation and the V-shaped surface expansion. The relationship between stress fluctuations and velocity characteristics is established. The flow channel simultaneously expands upwards as the velocity wave propagates and generates a periodic fan-shaped velocity wave at the top. The formation of stress concentration zone at the bin/hopper transition was observed.

Deformation-induced HCP phase transformation of CrCoNiSi0.3 medium-entropy alloy under high strain rate tension

The yield strength of a CrCoNiSi0.3 medium-entropy alloy is significantly increased from 450 MPa (quasi-static, 0.001 s−1) to 1600 MPa (at a strain rate of 5000 s−1) under dynamic tension, with a considerable ductility of 60%. The high strain-rate sensitivity (SRS) of strength and work hardening is obtained, and the strength SRS reaches 0.408. The dominant deformation mechanisms are abundant multiple-twinning, increasing fractions of deformation twins and phase transformation from face-centered-cubic to hexagonal-close-packed (HCP) phases with a strain rate. A universal dislocation-hardened constitutive model considering the evolution of the twin and HCP transformation is established to predict the flow stress and microstructure evolution.

Investigation of size effect on flow stress of Cu-3wt.%Ag-0.5 wt%Zr thin sheets at room and cryogenic temperature based on geometrically necessary dislocation evolution behavior

The influence of the grain sizes ranging from 23.4 to 69.2 μm on mechanical properties of Cu-3wt.%Ag-0.5 wt%Zr thin sheets was investigated by conducting uniaxial tensile experiments at room temperature (RT 298 K) and cryogenic temperature (CT 77 K). At RT, the strength and ductility of the sheet decreased as the grain size increased, and the size effect on flow stress was observed when the ratio of thickness to grain size (t/d) was less than 4.5. At CT, the sheet exhibited excellent strength and ducility, accompanied by a reduction in the size effect on flow stress. GND distribution maps showed that the average GND density of grains in the sample surface (surface grains) was lower than that of grains in the core of the sample (core grains). As the distance from the grain boundary increased, the GND density decreased. A constitutive model was developed for Cu-3wt.%Ag-0.5 wt%Zr thin sheets based on the dislocation accumulation and recovery process, which was able to predict the effects of grain size and deformation temperature on the flow stress and GND evolution in Cu-3wt.%Ag-0.5 wt%Zr thin sheets. This constitutive model indicated that CT not only inhibited the GND recovery process but likewise promoted the GND accumulation process. The established constitutive model revealed that the ratio of SSD density to GND density increased with increasing strain. The total dislocation density and GND density of samples deformed at CT was higher than those of samples deformed at RT.

Thermal Deformation Behavior and Microstructural Evolution of Multicomponent Mg-Li-Zn-Al-Y Alloys under Hot Compression.

High-temperature compression tests on Mg-11.5Li-2.5Zn-0.35Al-0.3Y (in wt.%) were carried out on a Gleeble-3500 thermal simulator. Flow stress and microstructural evolution were analyzed at different temperatures (T = 473 K, 523 K, 573 K, and 623 K) and strain rates (ε˙ = 1 s-1, 0.1 s-1, 0.01 s-1, and 0.001 s-1). On this basis, the constitutive model of the alloy was established using the Arrhenius-type constitutive model, and the thermal processing map of the alloy was drawn based on the DMM (dynamic material modeling) theory. The experimental results show that the flow stress of the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy decreases with an increase in temperature and a decrease in strain rate. The grain size increases uniformly with the increase in temperature, while a sudden increase occurs with the decrease in strain rate. The predicted value of the model is compared with the experimental value to verify the correctness of the model, and the correlation coefficient, R = 0.9690, was calculated, which further proves the applicability of the model to the Mg-11.5Li-2.5Zn-0.35Al-0.3Y alloy. This alloy can be safely plastic-deformed 473 K~623 K and 0.001 s-1~1 s-1.

A lode-dependent plasticity model for high-strength structural steel

In this study, a new plasticity model was developed to characterize the mechanical behavior of high-strength structural steel under multiaxial stress states. This model utilizes a Lode-dependent yield criterion in conjunction with a non-associated flow rule and isotropic hardening law to determine the evolution of the plastic flow stress. Further, a detailed numerical implementation algorithm for this plasticity model is presented, including the integration algorithm of the constitutive equations using an implicit elastic predictor-return mapping method and formulation of the consistent tangent modulus. To validate the proposed plasticity model, six types of Q690 high-strength steel specimens were tested under monotonic loading. These specimens can be used to obtain the elastoplastic response of the material under uniaxial tension, compression, pure shear, tensile shear, and plane strain state, respectively. Corresponding numerical simulations were performed for each specimen using ABAQUS/Standard with the proposed model being introduced into the analysis via the UMAT user subroutine. Then, the prediction performance of the proposed plasticity model was investigated by comparing the load-displacement curves of each test specimen obtained from both experiments and numerical simulations. It is shown that the proposed plasticity model can accurately predict the mechanical response of the high-strength steel under different stress states and enables to visualize the key stress state parameters and material strength variation at the failure region of each specimen, which confirms the promising prospect of this new model in practical applications.

A multi-physics material point method for thermo-fluid-solid coupling problems in metal additive manufacturing processes

The metal additive manufacturing (AM) process involves complex multi-physics coupling phenomena associated with the heat transfer, fluid flow, and solid mechanics that bring challenge to the current numerical methods. In this study, a multi-physics material point method is proposed for solving thermo-fluid–solid coupling problems in metal additive manufacturing processes. In this method, the material domain is discretized by a structured grid and a set of particles with corresponding variants for the heat transfer, fluid flow, and thermal stress evolution, under both Eulerian and Lagrangian descriptions. The interaction between these fields is naturally handled by the same structured grid and particles. Moreover, a semi-implicit local iteration technique is proposed to efficiently solve heat transfer with solid–liquid phase change, an improved Chorin’s projection method is introduced to handle Darcy’s damping, and a staggered derivation scheme with a sub-cell occupation technique is proposed to solve surface tension and Marangoni forces. A set of numerical examples, including the benchmark problems and the selective laser melting AM problems, is presented to validate the proposed method, where good agreements have been achieved with the analytical, numerical, and experimental data available in the literature. It is demonstrated that the proposed method is a powerful tool for thermo-fluid–solid coupling problems in metal additive manufacturing and other multi-physics problems.

Twinning, dynamic recrystallization, and texture evolution in as-solution AZ80 Mg alloy during hot compression

The characteristics of twins, dynamic recrystallization (DRX), and texture evolution of as-solution AZ80 Mg alloy at different strains, strain rates and temperatures during hot deformation were investigated by EBSD analysis systematically. The activation of twin variants, their interactions, and their role in microstructure and mechanical response are emphasized. The results show that: a large number of {10–12} tension twins and a twin “cross” structure containing three types of twin-twin boundaries (TTBs) were formed at a strain of 0.10, a strain rate of 0.1 s−1, and a temperature of 300 °C. Meanwhile, the original grain is subdivided by high-angle boundaries (HAGBs) converted from twin boundaries (TBs), and the flow stress curve exhibits a feature of concave curvature at a higher strain rate and a lower temperature. As the strain increases, the dominant DRX mechanism is converted from continuous DRX (CDRX) to discontinuous DRX (DDRX) after peak stress, while particle stimulation nucleation (PSN) occurs throughout the process. The strong base texture is weakened by twinning and DRX, where twinning deviates from the parent grain by 86° and DDRX grains deviate from the parent grain by 5°–20°. The diagram of relationships between flow stress and microstructure evolution and texture is established.

Influence of pre-precipitation on the multi-stage hot deformation behavior of an Al-Cu-Mg-Zr alloy: Experiments and integrated modeling

Most industrial hot working operations of heat treatable Al alloys are frequently comprised of several successive deformation stages, and therefore the in-depth understanding and better prediction of flow stress evolution during multi-stage thermomechanical processing are required in modern aluminum industries. In this work, the effects of pre-precipitation microstructures on the complicated flow stress behaviors of an Al-Cu-Mg-Zr alloy during multi-stage hot deformation were first investigated. Further, a new integrated model was developed to predict the multi-stage flow stress behaviors. Concretely, by considering dynamic microstructural evolution, a microstructure-based constitutive KM + Avrami model in which the parameters could be well described by the empirical relationship with the Zener-Hollomon parameter was developed to predict the whole flow stress evolutions of single-stage deformation. Then, a novel approach was proposed to describe the whole flow behaviors during multi-stage hot deformation by integrating the microstructure-based constitutive approaches and a physically-based recovery model for static softening. A good modeling capability and agreement between the modeled and experimental flow stress results was found for the studied alloy with three types of pre-precipitation microstructures. In addition, the in-depth dynamic and static softening mechanisms with the influences of pre-precipitation were also discussed based on modeling analysis and microstructural observations.

Incorporating dynamic recrystallization into a crystal plasticity model for high-temperature deformation of Ti-6Al-4V

During hot deformation of (α+β) titanium alloys, the simultaneous action of strain and temperature in the (α+β) regime facilitates dynamic recovery, dynamic recrystallization (DRX), and phase transformations via non-equilibrium paths. DRX is manifested in the form of fine recrystallized α or β grains. In the present study, a two-phase crystal plasticity finite element framework (CP-DRX) has been developed which incorporates DRX kinetics into the crystal plasticity (CP) model to predict the flow characteristics of Ti-6Al-4V alloys during thermo-mechanical processing. The CP slip system parameters, as well as elastic properties from both α and β phases of Ti, are calibrated for different strain rate conditions. An EBSD-informed two-phase microstructure representation has been utilized in the CP-DRX framework to explore the time-dependent evolution of DRX microstructure and crystal orientation for different strain rate conditions. The proposed CP-DRX can capture the evolution of crystal orientation and plastic flow stress–strain response of polycrystalline Ti-6Al-4V during the deformation process. Furthermore, the proposed model is able to capture the softening behavior, observed in average stress–strain response from experiments performed using a Gleeble thermomechanical simulator and predict the recrystallization texture.

High Cycle Fatigue Behaviour of 316L Stainless Steel Produced via Selective Laser Melting Method and Post Processed by Hot Rotary Swaging.

This paper deals with a study of additively manufactured (by the Selective Laser Melting, SLM, method) and conventionally produced AISI 316L stainless steel and their comparison. With the intention to enhance the performance of the workpieces, each material was post-processed via hot rotary swaging under a temperature of 900 °C. The samples of each particular material were analysed regarding porosity, microhardness, high cycle fatigue, and microstructure. The obtained data has shown a significant reduction in the residual porosity and the microhardness increase to 310 HV in the sample after the hot rotary swaging. Based on the acquired data, the sample produced via SLM and post-processed by hot rotary swaging featured higher fatigue resistance compared to conventionally produced samples where the stress was set to 540 MPa. The structure of the printed samples changed from the characteristic melting pools to a structure with a lower average grain size accompanied by a decrease of a high fraction of high-angle grain boundaries and higher geometrically necessary dislocation density. Specifically, the grain size decreased from the average diameters of more than 20 µm to 3.9 µm and 4.1 µm for the SLM and conventionally prepared samples, respectively. In addition, the presented research has brought in the material constants of the Hensel-Spittel formula adapted to predict the hot flow stress evolution of the studied steel with respect to its 3D printed state.

Correlated structure viscoplastic self-consistent polycrystal plasticity: Application to modeling strain rate sensitive deformation of Ti-6Al-4 V

This paper presents a multi-level viscoplastic self-consistent (VPSC) model for correlated structures (CS-VPSC). A polycrystalline aggregate response is homogenized over inclusions, which are linearized using the generalized affine scheme. Response of the inclusions is that of either a single grain or a correlated structure of multiple single crystals. The single crystal response is a strain rate adjusted power-law viscoplastic formulation, which considers not only the driving force in the glide direction but also the two orthogonal shear and three normal components of the driving force. The resistance to slip is grain size sensitive and based on the evolution of dislocation density. Furthermore, the resistances of prismatic and basal slip systems are adjusted based on the geometry of slip transfer between adjacent correlated structures. The overall model linking the single crystal micro-scale to a correlated structure meso‑scale to an aggregate macro-scale response is also coupled with the implicit finite elements (FE-CS-VPSC). The model is used for modeling strain rate sensitive mechanical response and microstructural evolution of additively manufactured Ti-6Al-4 V (Ti64) alloy in two conditions. As-built and stress-relived (SR) microstructure consisted of correlated α-lath/lamellar structures, while thermo-hydrogen refined microstructure (THRM) consisted primarily of α- and β-globular structures and some correlated α-lath/lamellar structures. Electron backscatter diffraction data, neutron diffraction data, and mechanical data were used to initialize, calibrate, and validate the model. To this end, the flow stress and texture evolution of the materials in tension and compression under quasi-static and high strain rate deformations were predicted using CS-VPSC, while the texture evolution during rolling and impact was simulated using FE-CS-VPSC. Good predictions of the texture evolution and mechanical response including the tension/compression asymmetry allowed us to discuss the roles of correlated structures, slip system activation stresses, size effects, strain partitioning between phases, and slip activities in such predictions.

Research on hot deformation behaviour of as-cast W12Cr4V5Co5 steel

ABSTRACT Hot working response of as-cast W12Cr4V5Co5 steel was investigated by isothermal compression testing in the temperature range of 1000-1150°C and strain rate range of 0.01-10 s−1. Experimental results showed that the flow stress and microstructure evolution were susceptible to the hot deformation parameters. Work hardening first occurred at a small strain, followed by softening, and finally, an approximate dynamic equilibrium was achieved between work hardening and softening. The activation energy of deformation was calculated to be 557.33 kJ mol−1, and constitutive equations compensated with strain were proposed to describe the flow stress as a function of deformation parameters. Microstructure analysis indicated that the average grain size decreased with the increase in strain rate and the decrease in deformation temperature. Additionally, the simulation of hot deformation via Deform-3D software revealed the sample's inhomogeneous deformation during hot compression. This study may provide guidance for hot working of as-cast W12Cr4V5Co5 steel.

Anisotropy in dynamic recrystallization behavior of AZ31 magnesium alloy

Deformation behavior as well as microstructural evolutions of a rolled AZ31 magnesium alloy with and without pre-existing extension twins were studied using compression tests which performed along different orientations at a temperature range of 25–350 °C. The results implied that the initial texture not only influence the evolution of flow stress, but also change the size and fraction of recrystallized grains. In contrast to samples parallel to rolling and transverse directions, compression along normal direction resulted in a respectful softening at 150 °C. The largest size and fraction of new grains at 250 °C were recorded after deformation along rolling direction, while the maximum flow softening was observed during deformation along normal direction. The anisotropy in microstructural evolutions was still retained at 350 °C. Pre-existing twins could reduce the anisotropy of material in respect of flow stress as well as DRX progression, where TD sample showed the lowest DRX fraction at 250 °C. Quaternion misorientation data obtained from EBSD analysis of pretwinned material implied that initial texture could not significantly influence final texture. A different misorientation distribution was realized after deformation of pretwinned material along ND and RD directions.

Temperature-Dependent Material Property Databases for Marine Steels—Part 3: HSLA-80

Integrated Computational Materials Engineering (ICME)-based tools and techniques have been identified as the best path forward for distortion mitigation in thin-plate steel construction at shipyards. ICME tools require temperature-dependent material properties—including specific heat, thermal conductivity, coefficient of thermal expansion, elastic modulus, yield strength, flow stress, and microstructural evolution—to achieve accurate computational results for distortion and residual stress. However, the required temperature-dependent material property databases of US Navy-relevant steels are not available in the literature. Therefore, a comprehensive testing plan for some of the most common marine steels used in the construction of US Naval vessels was completed. This testing plan included DH36, HSLA-65, HSLA-80, HSLA-100, HY-80, and HY-100 steel with a nominal thickness of 4.76 mm (3/16-in.). This report is the second part of a seven-part series detailing the pedigreed steel data. The first six reports will report the material properties for each of the individual steel grades, whereas the final report will compare and contrast the measured steel properties across all six steels. This report will focus specifically on the data associated with HSLA-80 steel.

Role of temperature and strain rate on evolution of microstructure, flow stress and constitutive equation in hot deformation of AZ80A Mg alloy

Role of temperature and strain rate on evolution of microstructure, flow stress and constitutive equation in hot deformation of AZ80A Mg alloy

Accuracy of Variational Formulation to Model the Thermomechanical Problem and to Predict Failure in Metallic Materials

The main purpose of this study is to develop a variational formulation for predicting structure behavior and accounting for damage mechanics in metallic materials. Mechanical and coupled thermomechanical models are used to predict failure in manufacturing processes. Ductile failure is accompanied by a significant amount of plastic deformation in metallic structural components. Finite element simulation of damage evolution in ductile solids is presented in this paper. Uncoupled models are implemented in a finite element model simulating deep drawing as well as cutting processes. Based on the Johnson–Cook model, the effect of deformation on the evolution of flow stress is described. The combined effect of strain, strain rate, and temperature on plasticity and damage behavior in cutting processes is considered. The accuracy of these models is verified when predicting ductile damage in forming and cutting processes.