Crystal Plasticity Constitutive Model Research Articles

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.

A dislocation density-based crystal plasticity constitutive model: comparison of VPSC effective medium predictions with ρ-CP finite element predictions

This work presents a dislocation density-based crystal plasticity constitutive model for glide kinetics, strengthening and dislocation density evolution, implemented in the effective medium-based visco-plastic self consistent (VPSC) framework and the spatially resolved, ρ-CP crystal plasticity finite element framework. Additionally, a distribution of intragranular stresses is introduced in the VPSC framework, instead of the conventionally used mean value of grain stress for effective medium calculations. The ρ-CP model is first calibrated to predict the mechanical response of a bcc ferritic steel with an initial rolled texture. The same set of constitutive model parameters are then used in VPSC to predict the aggregate stress–strain response and total dislocation densities. For these VPSC simulations, the interaction parameter governing the interaction between the grain and the effective medium in the Eshelby inclusion formalism, and a scalar parameter representative of the distribution of intragranular stresses within a grain, are used to calibrate the VPSC predictions in order to match the predictions of the ρ-CP model. A parametric study is performed to understand the effect of these two parameters on the VPSC predictions. Further, simulations are also performed for a random untextured polycrystal to identify the corresponding VPSC simulation parameters for predicting a similar response as the ρ-CP model. The novelty of the work is in the same set of constitutive models and associated parameters have been implemented in VPSC and ρ-CP to predict similar aggregate stress–strain response and total dislocation densities. This finite element-calibrated effective medium crystal plasticity approach reduces the computational time by at least two orders of magnitude and represents an advance towards the development of multiscale crystal plasticity modeling tools.

Microscopic mechanism of plastic heterogeneous deformation of columnar-grained polycrystalline ice

Studying ice deformation starting from crystal scale can provide insight into the microscopic mechanisms of ice deformation. In this paper, a crystal plasticity constitutive model of ice considering the dislocation slip mechanism and grain-size dependence was implemented within the finite element framework, and a modeling approach starting from ice single crystals based on the crystal plasticity finite element method (CPFEM) was proposed to study the elastic-viscoplastic deformation of polycrystalline ice samples. Finite element models of ice single crystals and columnar-grained polycrystalline ice characterizing the microstructure were established successively, and the proposed method was validated by comparing the uniaxial compression prediction results of ice single crystals and columnar-grained polycrystalline ice with the existing experimental data. Finally, the microscopic mechanism of plastic heterogeneous deformation of columnar-grained polycrystalline ice under constant strain rate compression conditions was analyzed. The results indicate that the modeling approach from ice single crystals to polycrystalline ice samples based on CPFEM can reasonably describe the mechanical properties of ice deformation. The deformation of columnar-grained polycrystalline ice globally exhibits apparent slip bands around 30° - 60° relative to the loading direction and locally presents intragranular localization bands parallel or perpendicular to the C-axis. This plastic heterogeneous deformation phenomenon is related to the elastic-viscoplastic anisotropy of ice single crystals and the interaction of neighboring grains at grain boundaries (GBs).

Microstructural size effect on the notch fatigue behavior of a Ni-based superalloy using crystal plasticity modelling approach

Fatigue performances of critical structures are strongly affected by the microstructural (e.g. grain, defect, inclusion, etc.) size effect, and it is thus important to quantify their detrimental effect. In this work, a numerical procedure is constructed to quantify the influence of microstructure on the mechanical and fatigue behaviors of Ni-based superalloy GH4169. Specifically, by combining sub-modelling approach with crystal plasticity constitutive model, a dual-scale modelling approach is developed for studying grain-level mechanical behavior of Ni-based superalloy GH4169 notched components. In addition, the dislocation-based Tanaka-Mura-Wu model is applied for fatigue crack initiation life prediction. The Paris law is then utilized for fatigue crack propagation analysis based on the simulated short crack. To study the microstructural size effect on fatigue crack initiation and propagation behaviors, sub-models containing various grain orientation, grain size, defect size/shape are built and analysed. Finally, a series of fatigue tests on notched specimens of Ni-based superalloy GH4169 were carried out for method validation. Results indicate that the established dual-scale modelling approach and fatigue life prediction framework yields good agreement with experimental results.

The anisotropic grain size effect on the mechanical response of polycrystals: The role of columnar grain morphology in additively manufactured metals

Additively manufactured (AM) metals exhibit highly complex microstructures, particularly in terms of grain morphology which typically features heterogeneous grain size distribution, irregular and anisotropic grain shapes, and the so-called columnar grains. The conventional morphological descriptors based on grain shape idealization are generally inadequate for representing complex and anisotropic grain morphology of AM microstructures. The primary aspect of microstructural grain morphology is the state of grain boundary spacing or grain size whose effect on the mechanical response is known to be crucial. In this paper, we formally introduce the notion of axial grain size from which we derive mean axial grain size, effective grain size, and grain size anisotropy as robust morphological descriptors capable of effectively representing highly complex grain morphologies. We instantiated a discrete sample of polycrystalline aggregate as a representative volume element (RVE) featuring random crystallographic orientation and misorientation distributions. However, the instantiated RVE incorporates the typical morphological features of AM microstructures including distinctive grain size heterogeneity and anisotropic grain size owing to its pronounced columnar grain morphology. We ensured that any anisotropy observed in the macroscopic mechanical response of the instantiated sample primarily originates from its underlying anisotropic grain size. The RVE was then employed for mesoscale full-field crystal plasticity simulations corresponding to uniaxial tensile deformation along various axes via a spectral solver and a physics-based crystal plasticity constitutive model which was developed, calibrated, and validated in earlier studies. Through the numerical analyses, we isolated the contribution of anisotropic grain size to the anisotropy in the mechanical response of polycrystalline aggregates, particularly those with the characteristic complex grain morphology of AM metals. This contribution can be described by an inverse square relation.

Unveiling orientation dependence of anisotropic plasticity in polycrystalline copper by nanoindentation.

The mechanical properties of crystalline materials are influenced by their deformation behavior, which is associated with their microstructural characteristics. Specifically, crystallographic orientation greatly affects the microscale plastic deformation of individual grains. In this study, experiments and finite element simulations of Berkovich nanoindentations are conducted to investigate the impact of crystallographic orientation in polycrystalline copper. A crystal plasticity constitutive model is developed for copper materials, which accurately captures their indentation mechanical response. The results showed that the indentation behavior of polycrystalline copper exhibits a high degree of anisotropy due to significant variation in slip systems for different crystallographic orientations. This results in different mechanical responses of individual grains and distinct material pileup morphologies on the indented surface. Additionally, the study revealed that crystallographic orientation plays a critical role in determining the indentation size effect. These findings have important implications for the design of materials where plasticity is a crucial factor.

Crystal plasticity constitutive model and thermodynamics informed creep-fatigue life prediction model for Ni-based single crystal superalloy

Ni-based single crystal superalloys are the main constituent materials for aeroengine turbine blades. They are subjected to extensive in-service plastic deformation and creep-fatigue interaction, which can cause damage and failure and hence limit the turbine blade durability. In this study, a novel crystal plasticity-based constitutive model is proposed to predict the cyclic inelastic deformation of Ni-based single crystal superalloy under creep-fatigue loads, and the key aspects examined include cyclic strain hardening, ratcheting and stress relaxation behavior. The novelty of the model lies in the introduction of a dislocation density parameter in the kinematic hardening rule to describe the evolutionary characteristics of hysteresis loops. The constitutive model is implemented via the crystal plasticity finite element method and the predictions are in good agreement with experimental results. Furthermore, thermodynamic entropy generation is innovatively adopted as an indicator parameter for analysis of Ni-based single crystal creep-fatigue failure, and the corresponding creep and fatigue damage models are developed to evaluate the degree of damage. The half-life concept associated with the steady-state hysteresis loop is employed in the failure model to predict the creep-fatigue life without being limited by the computational efficiency of the crystal plasticity finite element method. The proposed model can well capture the characteristics of Ni-based single crystal creep-fatigue life, and the prediction falls within a scatter band of factor 2.0 compared to experimental results. The proposed creep-fatigue life prediction model is underpinned by deformation and failure mechanisms, which would provide a basis for accurate analysis and robust assessment of Ni-based single crystal superalloy performance and life.

Experimental and numerical investigations of anisotropic plasticity response in polycrystalline copper by nanoindentation

The deformation behavior of crystalline materials is influenced by microstructural characteristics such as crystallographic orientation and grain boundary. In this study, nanoindentation experiments and crystal plasticity finite element simulations are used to investigate the effects of these microstructural features on the mechanical properties of polycrystalline copper. A crystal plasticity constitutive model embedded with geometrically necessary dislocations is developed to simulate the indentation mechanical response of grains with different orientations. The results show that the indentation behavior of polycrystalline copper exhibits significant anisotropy due to variations in the distributions of statistically stored dislocations and geometrically necessary dislocations. Moreover, grain boundary plays a crucial role in determining the anisotropy and indentation size effect. These findings provide insights into the design of materials for plasticity applications.

Meso-scale low-cycle fatigue damage of polycrystalline nickel-based alloy by crystal plasticity finite element method

A mesoscopic constitutive model coupled with crystal plasticity (CP) and damage is established in this paper to investigate the plastic deformation and damage-induced degradation of polycrystalline materials under cyclic loading. Taking the nickel-based alloy as a representative material, the rationality and effectiveness of the proposed constitutive model are first verified through a single-element model containing one grain. On this basis, the stress and strain states and damage evolution of polycrystals under cyclic loading are comprehensively investigated. The constitutive parameters in the proposed model are calibrated against experimental results. It is discovered that the strength degradation of polycrystals under cyclic loading can be more precisely described by the CP constitutive model if the damage is taken into account. The simulation results demonstrate that there are significant differences in the initiation and activity degree of the slip systems inside the grains with various orientations, so that inhomogeneous plastic deformation occurs inside the polycrystal, which ultimately leads to the existence of different damage evolution processes in the internal regions of the materials. As an indicator parameter of fatigue damage, the cumulative plastic strain rises with the number of cycles, resulting in an increase of the damage variable.

A Micromechanical Analysis to the Viscoplastic Behavior of Sintered Silver Joints under Shear Loading.

Ag paste has been recognized as a promising substitute for Sn/Pb solder in SiC or GaN power electronic devices, owing to its ability to withstand high temperatures and facilitate low-temperature packing. The reliability of these high-power circuits is greatly influenced by the mechanical properties of sintered Ag paste. However, there exist substantial voids inside the sintered silver layer after sintering, and the conventional macroscopic constitutive models have certain limitation to describe the shear stress-strain relationship of sintered silver materials. To analyze the void evolution and microstructure of sintered silver, Ag composite pastes composed of micron flake silver and nano-silver particles were prepared. The mechanical behaviors were studied at different temperatures (0-125 °C) and strain rates (1 × 10-4-1 × 10-2) for Ag composite pastes. The crystal plastic finite element method (CPFEM) was developed to describe the microstructure evolution and shear behaviors of sintered silver at varied strain rates and ambient temperatures. The model parameters were obtained by fitting experimental shear test data to a representative volume element (RVE) model built on representative volume elements, also known as Voronoi tessellations. The numerical predictions were compared with the experimental data, which showed that the introduced crystal plasticity constitutive model can describe the shear constitutive behavior of a sintered silver specimen with reasonable accuracy.

Advanced Statistical Crystal Plasticity Model: Description of Copper Grain Structure Refinement during Equal Channel Angular Pressing

The grain structure of metals changes significantly during severe plastic deformation (SPD), and grain refinement is the main process associated with SPD at low homologous temperatures. Products made of ultrafine-grained materials exhibit improved performance characteristics and are of considerable industrial interest, which generates a need for the creation of comprehensive grain refinement models. This paper considers the integration of the ETMB (Y. Estrin, L.S. Toth, A. Molinari, Y. Brechet) model, which describes the evolution of an average cell size during deformation into the two-level statistical crystal plasticity constitutive model (CM) of FCC polycrystals. The original relations of the ETMB model and some of its modifications known from the literature were analyzed to obtain an accurate, physically admissible description of the grain refinement process. The characteristics of the grain substructure determined with the framework of the advanced ETMB model were taken into account in the CM in a hardening formula. By applying the CM with the integrated ETMB model, numerical experiments were performed to simulate the changes in the grain structure of copper during equal channel angular pressing (ECAP) at room temperature. The results obtained are in good agreement with the experimental data. The ideas about further development of the proposed model are outlined.

Shear localization in polycrystalline metal at high-strain rates with dynamic recrystallization: Crystal plasticity modeling and texture effect

Shear localization is an important failure mode, or even the dominant mode in metals at high-strain rates. However, it is a great challenge to accurately predict the occurrence and evolution of shear localization in metals at the high-strain rate deformation. Here, a dislocation-based crystal plasticity constitutive model with a crucial mechanism of shear instability, namely dynamic recrystallization, was developed. The evolution equations of dislocation density and grain size in the process of dynamic recrystallization were proposed and incorporated into the new constitutive model. The threshold of the stored energy in crystals was used as the criterion for the occurrence of dynamic recrystallization. Dynamic compression of a nanograin Cu-Al alloy was performed using the crystal plasticity finite element method based on the new constitutive model, and good agreement of the numerical prediction with the existing experimental data validates the new constitutive model. The results show dynamic recrystallization can be a more dominant mechanism for the occurrence of shear instability than thermal softening. In addition, dynamic tension and shear of the Cu-Al alloys with five typical textures were also simulated, showing that both loading mode and texture can significantly affect the formation of shear localization. This work is helpful for us to understand the role of microstructural evolution in the formation of shear localization at high-strain rates and to design the microstructure for artificially controlling or preventing the formation of shear localization.

Micro mechanical property investigations of Ni-based high-temperature alloy GH4169 based on nanoindentation and CPFE simulation

In this research, the microscopic deformation behavior of GH4169 superalloy is investigated by a series of nanoindentation experiments and simulations based on crystal plasticity finite element (CPFE) model, including hardness, creep displacement and stress distribution around indentation. In this regard, the crystal plasticity constitutive model based on dislocation slip for face-centered cubic (FCC) crystal of concern is summarized and numerically implemented at first. Moreover, nanoindentation experiments are performed on specimens with various peak loads and load times to investigate the mechanical response and deformation mechanism at the micro-scale. Nanoindentation test results show that load rate, peak load, and nanoindentation size effect (ISE) all affect the microscopic deformation behavior of GH4169. The value of creep stress exponent, m, calculated from the creep experimental data is greater than 3, indicating that dislocation slip is dominant creep mechanism at room temperature.The nanoindentation simulation data based on the crystal elastic–plastic parameters determined by the trial-and-error method are in good agreement with the experimental data, demonstrating that the CPFE simulation results are credible. Therefore, this study can be used as a reference to investigate other alloy materials.

Crystal plasticity theory coupled with meso-damage to predict the ratchetting behavior of nickel-based single crystal superalloy

Stress-controlled low cycle fatigue tests with different mean stress of a second-generation nickel-based single crystal superalloy DD6 with [001] orientation is investigated in the current study. The observation of fracture surface and microstructure show that although the phase structure does not change for different conditions, the damage failure mode changes for different mean stress. It is found that ratcheting strain exhibits a significant dependency on mean stress and microstructure damage. Ratcheting strain cannot be simulated only considering the evolution of back stress. To simulate the whole process evolution of ratcheting strain, crystal plasticity constitutive model coupled with a new anisotropic damage is developed. The simulated results showed that the anisotropic damage model could accurately predict the ratcheting strain for different mean stress. Different damage evolution modes are well identified by a damage index in the proposed model.

A cycle-jump acceleration method for the crystal plasticity simulation of high cycle fatigue of the metallic microstructure

For metallic materials, high-cycle fatigue life is sensitive to underlying microstructure features including secondary phases, textures, grains morphology, etc. The traditional, data-based safe-life approaches for modeling fatigue don’t explicitly consider the microstructure and can’t guide study in microstructure modification for improved fatigue property. Crystal plasticity-based simulation provides increased model fidelity at the expense of immense computation time, making it inapplicable for high cycle fatigue. In this work, an acceleration method based on cycle-jump approach (Lesne and Savalle, 1989) was developed for microstructure-based high-cycle FE simulation using crystal plasticity constitutive-model. This method demonstrated high efficiency in benchmark tests of various conditions.

Modeling and analysis of grain morphology effects on deformation response based on crystal plasticity finite element method

AbstractIn order to investigate the grain morphology effects on deformation response at macro‐ and micro‐scale in polycrystalline metal, a method considering grain size and shape effects is proposed based on the classical crystal plasticity finite element method in this paper. A grain morphology controlled polycrystalline geometry model consisting of grain shape models and grain size transition models is developed based on Voronoi diagram. Grain size effect is introduced into the classical crystal plasticity constitutive model quantitatively on the basis of Hall‐Petch type relationship. With the aid of the method, grain aggregate finite element meshes with different mean grain sizes are established to simulate the deformation response of polycrystalline pure copper. The predicted values of flow stresses show good agreement with experimental ones. Finally, a set of grain aggregate finite element meshes with same mean grain size but different grain distributions are developed to simulate the uniaxial tension processes of polycrystalline pure copper. The results shown that the effects of grain morphology on the macro‐scale deformation response are insignificant under a large number of grains with random morphology and orientation. When the grain distributions changes regularly along the x direction, the maximum decrease of flow stress data is 10 MPa.

Heterogeneous deformation and damage mechanisms in multi-phase TA15 Ti-alloy: Insights from experiments informed damage-crystal plasticity modelling

Understanding the mesoscale heterogeneous deformation and its induced material damage is significant to enhance the mechanical properties of polycrystalline aggregates. In this work, a damage-coupled crystal plasticity finite element (DC-CPFE) model based on high-fidelity microstructure was developed to investigate the heterogeneous deformation and damage behavior of TA15 Ti-alloy with tri-modal microstructure composed of globular alpha (αp), lamellar alpha (αl) and transformed beta (βt). A three-step procedure combining the nanoindentation test, stress relaxation test, and uniaxial tensile test was proposed to determine the material parameters in the crystal plasticity constitutive and damage models of the three constituent phases. Based on the developed DC-CPFE model, the heterogeneous slip modes and traces of tri-modal microstructure were predicted and analyzed. The heterogeneous deformation of tri-modal microstructure was found to be mainly caused by the heterogeneous deformation in α phases, which was featured by the deformation bands and local shear bands. Deformation bands occurred in both of the deformation-preferential and -lagged αp grains and the hard-to-deform αl grains. Local shear bands only produced in αl grains, which were related to both of the soft geometry orientation and the activation of prismatic slip systems. Meanwhile, the formation of deformation bands and local shear bands could be promoted by the local lattice rotation. The above heterogeneous deformation led to four types of damage, which were caused by the slip band intersection, the slip transfer impedance, the local shear band, and the property and orientation mismatches among the adjacent grains, respectively.

Prediction of Fracture Toughness Scatter Based on Weibull Stress Using Crystal Plasticity Finite Element Method

A multi-scale prediction method was proposed to investigate the scatter of fracture toughness by combining the local approach (LA) to cleavage fracture and the crystal plasticity finite element method (CPFEM). The parameters in the crystal plasticity constitutive model were firstly determined by comparing the simulated stress-strain curves with tested curves for SA508-III steel. Then CT samples were modeled using the CPFEM to calculate Weibull stress. Using the calibration process of local approach, the relevant parameters of the Beremin model were obtained with m = 30 and σu = 2590 MPa. The fracture toughness was analyzed including the scatter for a given temperature, the master curve in a temperature range. The distribution of predicted fracture toughness shows good agreement with the test results. All of the tested fracture toughness value are fall in the range of 5% to 95% that precited using the proposed combined approach.

A dislocation density-based model for the temperature dependent anomalous behaviors of nickel-based single-crystal superalloy

A dislocation density-based single crystal plasticity constitutive model was developed to capture the temperature dependent anomalous yield and tension/compression asymmetry behavior of nickel based single crystals. Firstly, the mathematical description of physical mechanism of anomalous yield behavior was considered in the hardening rules, i.e. thermally activated cross-slip mechanism. Secondly, a temperature dependent function was established to describe the transformation of dislocation motion mode from shearing to by-passing. Thirdly, three non-Schmid stress tensors were introduced into the constitutive model to describe the tension/compression asymmetric phenomenon. The model considers the contributions of various strengthening mechanisms, including solid solution, precipitates and base metal. Furthermore, the evolution of microstructural features (such as dislocation density, etc.) and contribution of each mechanism to yield stress with increasing temperature were further analyzed. The model has been implemented via crystal plasticity framework and can predict the temperature dependent anomalous characteristics of yield stress of Ni-based single crystal.

Multiple-mechanism and microstructure-based crystal plasticity modeling for cyclic shear deformation of TRIP steel

The transformation-induced plasticity (TRIP) steel has an excellent synergy between strength and ductility and is widely used in industry. Cyclic loading is often seen in its industrial application. Therefore, it is of great significance to study cyclic plastic behavior of the TRIP steel. The TRIP steel's cyclic shear behavior and microstructure evolutions were investigated by mechanical testing, electron backscatter diffraction (EBSD) characterization, and in-situ electron channeling contrast imaging (in-situ ECCI) observation. Then, a multiple-mechanism crystal plasticity constitutive model was developed, considering both dislocation slip and martensitic transformation mechanisms. Furthermore, an isotropic hardening law and a modified kinematic hardening rule were taken into account. The crystal plasticity model was implemented into DAMASK with the spectral method. A polycrystalline RVE with realistic grain morphology was constructed from the EBSD data. The simulations of the TRIP steel under cyclic shear loading showed that the samples under higher strain amplitude exhibit stronger cyclic shear hardening. The activation of the martensitic transformation mechanism promotes cyclic hardening. In grain level, the grains with Taylor factor (related to orientation) between 3.3 and 3.9 can activate more slip systems and have a better cyclic hardening ability. So, the Taylor factor is defined as an indicator describing the cyclic response of individual grains in polycrystalline materials. Considering the capability of the established modeling framework, it is of great significance to guide the TRIP steel to serve safely and help the microstructural design in grain scale.