Grain statistics effect on deformation behavior in asymmetric rolling of pure copper foil by crystal plasticity finite element model

The grain statistics effect was investigated through asymmetric rolling of pure copper foil by a realistic polycrystalline aggregates model and crystal plasticity element finite model.A polycrystalline aggregate model was generated and a crystal plasticity-based finite element model was developed for each grain and the specimen as a whole.The crystal plasticity model itself is rate dependent and accounts for local dissipative hardening effects and the original orientation of each grain was generated based on the orientation distribution function（ODF）.The deformation behaviors,including inhomogeneous material flow,decrease of contact press and roll force with the increase of grain size for the constant size of specimens,were studied.It is revealed that when the specimens are composed of only a few grains across thickness,the grains with different sizes,shapes and orientations are unevenly distributed in the specimen and each grain plays a significant role in micro-scale plastic deformation and leads to inhomogeneous deformation and the scatter of experimental and simulation results.The slip system activity was examined and the predicted results are consistent with the surface layer model.The slip band is strictly influenced by the misorientation of neighbor grain with consideration of slip system activity.Furthermore,it is found that the decrease of roll force and the most active of slip system in surface grains are caused by the increase of free surface grain effect when the grain size is increased.The results of the physical experiment and simulation provide a basic understanding of micro-scaled plastic deformation behavior in asymmetric foil rolling.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

Prediction of grain scale plasticity of NiTi shape memory alloy based on crystal plasticity finite element method

Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.

Texture evolution and inhomogeneous deformation of polycrystalline Cu based on crystal plasticity finite element method and particle swarm optimization algorithm

Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method(CPFEM) with particle swarm optimization(PSO) algorithm. The texture-based representative volume element(TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function(ODF) based on electron backscattered diffraction(EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method(FEM) software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function(ODF). The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain—stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.

Crystal plasticity model to predict fatigue crack nucleation based on the phase transformation theory

A crystal plasticity model is developed to predict the fatigue crack nucleation of polycrystalline materials,in which the accumulated dislocation dipoles are considered to be the origin of damage.To describe the overall softening behavior under cyclic loading,a slip system-level dislocation density-related damage model is proposed and implemented in the finite element analysis with Voronoi tessellation.The numerical model is applied to calibrate the stress-strain relationship at different cycles before fatigue crack nucleation.The parameters determined from the numerical analysis are substituted into a modified phase transformation model to predict the critical fatigue crack nucleation cycle.Comparing with the experimental results of Sn-3.0Ag-0.5Cu(SAC305)alloy and P91 steel,the proposed method can describe the constitutive behavior and predict the fatigue crack nucleation accurately.

Thermo-kinetic characteristics on stabilizing hetero-phase interface of metal matrix composites by crystal plasticity finite element method

Using dislocation-based constitutive modeling in three-dimension crystal plasticity finite element(3D CPFE)simulations,co-deformation and instability of hetero-phase interface in different material systems were herein studied for polycrystalline metal matrix composites(MMCs).Local stress and strain fields in two types of 3layer MMCs such as fcc/fcc Cu-Ag and fcc/bcc Cu-Nb have been predicted under simple compressive deformations.Accordingly,more severe strain-induced interface instability can be observed in the fcc/bcc systems than in the fcc/fcc systems upon refining to metallic nanolayered composites(MNCs).By detailed analysis of stress and strain localization,it has been demonstrated that the interface instability is always accompanied by high-stress concentration,i.e.,thermodynamic characteristics,or high strain prevention i.e.,kinetic characteristics,at the hetero-phase interface.It then follows that the thermodynamic driving forceG and the kinetic energy barrier Q during dislocation and shear banding can be adopted to classify the deformation modes,following the so-called thermo-kinetic correlation.Then by inserting a high density of high-energy interfaces into the Cu-Nb composites,such thermo-kinetic integration at the hetero-phase interface allows a successful establishment of MMCs with the high△G-high Q deformation mode,which ensures high hardening and uniform strain distri-bution,thus efficiently suppressing the shear band,stabilizing the hetero-phase interface,and obtaining an exceptional combination in strength and ductility.Such hetero-phase interface chosen by a couple of thermodynamics and kinetics can be defined as breaking the thermo-kinetic correlation and has been proposed for artificially designing MNCs.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed.The model was implemented in elastic-plastic self-consistent(EPSC)and crystal plasticity finite element(CPFE)frameworks for grain-scale simulations.A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy,ZEK100.The constitutive parameters were thereafter refined using the CPFE.The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200℃.In particular,the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction,for the first time.The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy.Finally,this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Mechanical Anisotropy of Selective Laser Melted Ti-6Al-4V Using a Reduced-order Crystal Plasticity Finite Element Model

In this study,a reduced-order crystal plasticity finite element(CPFE)model was developed to study the effects of the microstructural morphology and crystallographic texture on the mechanical anisotropy of selective laser melted(SLMed)Ti-6Al-4V.First,both hierarchical and equiaxed microstructures in columnar prior grains were modeled to examine the influence of the microstructural morphology on mechanical anisotropy.Second,the effects of crystallographic anisotropy and textural variability on mechanical anisotropy were investigated at the granular and representative volume element(RVE)scales,respectively.The results show that hierarchical and equiaxed CPFE models with the same crystallographic texture exhibit the same mechanical anisotropy.At the granular scale,the significance of crystallographic anisotropy varies with different crystal orientations.This indicates that the present SLMed Ti-6Al-4V sample with weak mechanical anisotropy resulted from the synthetic effect of crystallographic anisotropies at the granular scale.Therefore,combinations of various crystallographic textures were applied to the reduced-order CPFE model to design SLMed Ti-6Al-4V with different mechanical anisotropies.Thus,the crystallographic texture is considered the main controlling variable for the mechanical anisotropy of SLMed Ti-6Al-4V in this study.

Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model(ΔEVPSC) with the predominant twinning reorientation(PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.

Analysis of the mechanism of orientations evolution during hot rolling and mechanical properties of TiBw/TA15 composites based on crystal plasticity finite element model

An in-depth understanding of the crystal orientation evolution during hot rolling of TiB whisker(TiBw)/TA15 composites and the anisotropy of the as-rolled plates can help fully utilize the material proper-ties.In this paper,the crystal plasticity finite element models of high-temperature(HT)β-phase and room-temperature(RT)α-phase were constructed from electron backscattering diffraction data.Based on this,the orientation evolution during hot rolling in the single-phase region and the effects of the matrix texture on the mechanical properties of the as-rolled plates were analyzed.The effect of TiBw on the anisotropy was studied by the composites finite element model.Results showed that theα-fiber texture of theβ-phase was formed during HT rolling.This texture was converted to the T-texture of theα-phase at RT during cooling according to the Burgers orientation relationships.The TiBw had little effect on the matrix texture composition.The TiBw and matrix texture caused the matrix to have higher strength along the rolling direction and the transverse direction,respectively.The matrix texture dominated the difference in mechanical properties because its effect exceeded that of TiBw.The effect of the matrix on the mechanical properties was caused by the Schmid factors(SFs)and the critical resolved shear stress(CRSS)of the slip system together.The slip mode was influenced by SFs determined by the angular rela-tionship between the crystal orientation and the loading direction.The CRSS of the activated slip system determined the yield strength.

Finite element simulation of influences of grain interaction on rolling textures of fcc metals

A rate dependent crystal plasticity constitutive model considering self and latent hardening in finite element analysis was developed to simulate rolling textures of pure aluminum. By changing the assignment of orientations to finite elements, i.e. assigning the same set of orientations to all elements or different orientations to different elements, the influences of grain interaction on the formation of rolling textures were numerically simulated with this kind of crystal plasticity finite element model. The simulation results reveal that the grains without considering grain interaction rotate faster than those considering grain interaction, and the rotation of grain boundary is slowed down due to the grain interaction. For a good simulation more elements should be assigned to one grain, in which the effects of both the boundary and interior parts of grain contribute to the formation of rolling textures.

A novel method of rapidly modeling optical properties of actual photonic crystal fibres

The flexible structure of photonic crystal fibre not only offers novel optical properties but also brings some difficulties in keeping the fibre structure in the fabrication process which inevitably cause the optical properties of the resulting fibre to deviate from the designed properties. Therefore, a method of evaluating the optical properties of the actual fibre is necessary for the purpose of application. Up to now, the methods employed to measure the properties of the actual photonic crystal fibre often require long fibre samples or complex expensive equipments. To our knowledge, there are few studies of modeling an actual photonic crystal fibre and evaluating its properties rapidly. In this paper, a novel method, based on the combination model of digital image processing and the finite element method, is proposed to rapidly model the optical properties of the actual photonic crystal fibre. Two kinds of photonic crystal fibres made by Crystal Fiber A/S are modeled. It is confirmed from numerical results that the proposed method is simple, rapid and accurate for evaluating the optical properties of the actual photonic crystal fibre without requiring complex equipment.

Fatigue Analysis of Steel Catenary Risers Based on a Plasticity Model

The most critical issue in the steel catenary riser design is to evaluate the fatigue damage in the touchdown zone accurately. Appropriate modeling of the riser-soil resistance in the touchdown zone can lead to significant cost reduction by optimizing design. This paper presents a plasticity model that can be applied to numerically simulate riser-soil interaction and evaluate dynamic responses and the fatigue damage of a steel catenary riser in the touchdown zone. Utilizing the model, numerous riser-soil elements are attached to the steel catenary riser finite elements, in which each simulates local foundation restraint along the riser touchdown zone. The riser-soil interaction plasticity model accounts for the behavior within an allowable combined loading surface. The model will be represented in this paper, allowing simple numerical implementation. More importantly, it can be incorporated within the structural analysis of a steel catenary riser with the finite element method. The applicability of the model is interpreted theoretically and the results are shown through application to an offshore 8.625 steel catenary riser example. The fatigue analysis results of the liner elastic riser-soil model are also shown. According to the comparison results of the two models, the fatigue life analysis results of the plasticity framework are reasonable and the horizontal effects of the riser-soil interaction can be included.

Stress distributions on crown-luting cement-substrate system with finite element method

The aim of this work is to analyze the stress distributions on a crown-luting cement-substrate system with a finite-element method in order to predict the likelihood of interfacial micro cracks, radial or circumferential cracks, delamination, fracture and delamination with torsion. The contact and layer interface stresses in elastic layered half-space indented by an elastic sphere were examined using finite element method. The model consists of crown, luting cement and substrate. The solutions were carried out for three different elastic moduli of luting cement. It was placed between the cement and the substrate as a middle layer and its elastic module was chosen lower than the elastic module of crown and higher than the elastic module of dentin. An axisymmetric finite element mesh was set up for the stress analysis. Stress distributions on the contact surface and the interfaces of crown-luting cement and luting cement-dentin have been investigated for three different values of luting cement by using ANSYS. The effects of the luting cement which has three different elastic moduli on the pressure distribution and the location of interfacial stresses of the multi-layer model have been examined. The mechanism of crack initiation in the interfaces and interracial delamination was also studied quantitatively. For each luting cement, the pressure distribution is similar at the contact zone. Stress discontinuities occur at the perfect bonding interfaces of the crown-luting cement and the substrate-luting cement. The maximum stress jumps are obtained for the highest and the lowest elastic module of the luting cement. In the crown-luting cement-substrate system, failures may initiate at crown-luting cement region for luting cement with the lowest elastic module value. In addition, failures at luting cement-substrate region may occur for luting cement with the highest elastic module. In the luting cement, the medium elastic module value is more suitable for stress distribution in crown-luting cement-substrate interfaces.

Two-dimensional simulation on the rolling process of semi-solid 60Si2Mn by finite element method

The effect of various process variables on the law of metal flow for semi-solid rolling 60Si2Mn was studied by finite element method. Semi-solid 60Si2Mn can be described as compressible rigid visco-plastic porous material saturated with liquid. In terms of ther-mo-mechanical coupling condition, the distributions of stress, velocity and temperature were studied using software MARC. The simulation results show that the rigid visco-plastic model can accurately describe the semi-solid 60Si2Mn rolling process. The great deformation can achieve completely in view of low flow stress of semi-solid slurry.

An elasto-visco-plastic constitutive model of polypropylene incorporating craze damage behavior and its validation

An elasto-visco-plastic constitutive model incorporating the craze damage behavior was developed for the polypropylene(PP), by using the plastic failure model applied for the concrete, to capture the craze yielding and stress-whitening phenomena. In addition, the developed constitutive model was implemented into finite element codes in Abaqus to simulate the tensile deformation. The standard uniaxial tensile tests were carried out. The stress-strain curves from the uniaxial tensile tests show that the stress keeps decreasing after yielding and the yield stress rises with the increasing of the strain rate. It is worth noting that the craze damage is more visible with higher strain rate. The stress-whitening can be seen clearly around the fracture. The uniaxial tensile tests using specially designed specimen with circular holes weakening were performed for the validation of the developed model. The simulation results of the tensile deformation of the hole-weakened specimen suggest that the stress-whitening could be attributed to the equivalent visco-plastic strain. By comparing between the simulation analysis and the experimental results, the proposed model can describe the stress whitening phenomenon with good accuracy.

Damage Detection in Reinforced Concrete Berthing Jetty Using a Plasticity Model Approach

A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately.In this research,the concrete damage plasticity constitutive model is used to develop the numerical model of a deck beam on a berthing jetty in the Abaqus finite element package.The model constitutes a solid section of 3D hexahedral brick elements for concrete material embedded with 2D quadrilateral surface elements as reinforcements.The model was validated against experimental results of a beam of comparable dimensions in a cited literature.The validated beam model is then used in a three-point load test configuration to demonstrate its applicability for preliminary numerical evaluation of damage detection strategy in marine concrete structural health monitoring.The natural frequency was identified to detect the presence of damage and mode shape curvature was found sensitive to the location of damage.

Fifty years of finite elements——a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.

Development of Integrated Computational Materials Engineering(ICME)Model for Mg Alloy Design and Process Optimization

Integrated computational materials engineering(ICME)has emerged to be one of the most powerful materials genome engineering(MGE)approaches in designing new materials and manufacturing processes in recent years.It has successfully deployed many new products for the electronic,automotive,and aerospace industries.This paper reviews the current status of research on first principles in the design of high-strength Mg alloys,discusses the application of crystal plasticity finite element models to the microscale slip,twinning,microstructure morphology,texture evolution,and macroscopic forming of Mg alloys,and introduces the research progress of crystal plasticity finite element models and phase field models,meta cellular automata models and first principles coupled models respectively,around the need for multi-scale coupled simulations of Mg alloys.The key technology obstacles of integrating the first principles,crystal plasticity finite element,and microstructure models for Mg alloys have been solved.This paper can provide a reference for the design of new Mg alloy compositions and the development of high-performance Mg alloys.