Crystal Plasticity Finite Element Model Research Articles

Crystal plasticity modeling and analysis for the transition from intergranular to transgranular failure in nickel-based alloy Inconel 740H at elevated temperature

The precipitation-strengthened Nickel-based alloy Inconel® 740H® (IN740H) exhibits increased ductility at higher applied strain rates during quasi-static tensile tests at an elevated temperature of 760 °C. The examination of fracture surfaces in this context reveals a noteworthy transition of underlying fracture mechanisms from transgranular to intergranular fracture as the applied strain rate decreases from 1×10−3/s to 0.83×10−4/s. To thoroughly understand the mechanical response of IN740H under these conditions, this study develops a crystal plasticity finite element (CPFE) model. This model incorporates various deformation mechanisms including dislocation slips, climb, and grain boundary sliding, which are relevant to the test conditions. The model is calibrated using data from both tensile tests at different strain rates and creep tests across a broad stress range at 760 °C, enabling the accurate determination of model parameters for each mechanism. Simulation results well captured the experimental observations of different failure modes. At higher strain rates, the model shows a dominance of dislocation slip leading to heterogeneous plastic deformation and formation of transgranular shear bands causing the failure, while at lower strain rates, an increased activity of grain boundary sliding causes grain boundaries crack leading to intergranular failure.

On the Interaction of Grain-scale and Hydride-scale Stresses in Hydrogen Enriched Zirconium Alloy Nuclear Cladding via combined Discrete Dislocation Plasticity and Crystal Plasticity Finite Element modelling

On the Interaction of Grain-scale and Hydride-scale Stresses in Hydrogen Enriched Zirconium Alloy Nuclear Cladding via combined Discrete Dislocation Plasticity and Crystal Plasticity Finite Element modelling

Experimental and modeling study on irradiation effect of A508-Ⅲ steel

Irradiation can induce microscopic defects in reactor pressure vessel (RPV) steel, resulting in macroscopic hardening and embrittlement. This paper proposes a micro-meso-macroscale calculation framework for the mechanical properties of irradiated RPV steel based on experimental and numerical investigations. The mean size and number density of Fe-ion-irradiation-induced dislocation loops were measured using transmission electron microscopy (TEM). These parameters were described by a power-function relationship with the irradiation dose at various temperatures and were used as input parameters for the crystal plasticity finite element model (CPFEM). Nano-indentation tests of A508-Ⅲ steel under different irradiation conditions were successfully simulated. In addition, microstructural characterization and molecular dynamics (MD) simulations revealed the phenomenon of dislocation pinning and the sweeping of irradiation defects during dislocation migration, implying that the dislocation-loop interactions could be responsible for the formation of dislocation channels and curved dislocation lines. Furthermore, increase in yield stress and the ductile-brittle transition temperature (DBTT) at various temperatures were investigated. Results indicated that yield stress, DBTT, and the degree of irradiation hardening and embrittlement increased with the irradiation dose and decreased with irradiation temperature. Finally, the adjusted reference temperature (ART), a significant design parameter for nuclear reactors, was calculated and evaluated using the multiscale framework. The framework can serve as a reference text for extending the life of nuclear reactors.

The mechanistic origins of heterogeneous void growth during ductile failure

In 1969, Rice and Tracey proposed that the rate of void growth during ductile failure is a strong function of the hydrostatic stress state. Numerous in-situ x-ray computed tomography (XCT) studies demonstrated that the average rate of void growth is well-predicted by modified versions of the Rice-Tracey equation. However, recent in-situ XCT studies of void growth demonstrated that individual voids grow in highly heterogeneous manners in a way that is not predicted by Rice-Tracey or similar models. Model-based studies using crystal plasticity finite element (CP-FE) suggest that local effects of grain orientation play a strong role during void growth, but we lack experimental data to test this hypothesis. The present study leverages recent advances in laboratory-based diffraction contrast tomography (Lab-DCT) and in-situ XCT to systematically examine the effects of grain orientation on void growth experimentally in an Al-2219 alloy. CP-FE modeling was used to assess the local stress states associated with voids and their influence on void growth rates. These data indicate that void growth is not simply controlled by the local hydrostatic stress or stress triaxiality. Additionally, no clear relationship between void growth rates and grain orientation were observed. Instead, void growth rates were highly stochastic in ways that could not be directly linked to the local stress or strain states. The combination of experimental and modeling data suggests that our current assumptions regarding the mechanisms of void growth are flawed and that additional factors, which may include the local dislocation density, affect the rate of void growth.

Micro-mechanisms of anisotropic deformation in the presence of notch in commercially pure Titanium: An in-situ study with CPFEM simulations

This study investigates the impact of notch severity and initial texture on the micro-mechanisms during low strain deformation in commercially pure Titanium, exploiting in-situ electron back scatter diffraction (EBSD) experiments and crystal plasticity finite element model (CPFEM). In-situ tests were performed at different strain steps of un-notched and notched samples of transverse direction (TD) and rolling direction (RD) orientations. CPFEM, based on initial EBSD microstructures, predicted profuse prismatic slip traces and early activation of prismatic slip in notched sample, with RD orientation exhibiting higher activity. Further, CPFEM results revealed early activation of high CRSS slip systems as well as evidence of early twin activity at notch tip due to severely localized plastic deformation and steep strain gradient, as observed by GND maps causing higher stress at grain boundaries. At the notch tip, digital images correlation (DIC) at microscale indicated strain localization at 45∘ and 90∘ to the tensile axis for TD and RD orientations, respectively. Furthermore, 2.5D and 3D CPFEM confirmed distinct strain patterns at notch tip: TD orientation exhibited combined basal and prismatic slip influences, while RD orientation displayed dominant prismatic slip systems at localized strain. The model also successfully predicted anisotropic surface roughness, contributing to early necking in RD orientation.

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.

Crystal Plasticity Finite Element Modeling of the Influences of Ultrafine-Grained Austenite on the Mechanical Response of a Medium-Mn Steel

Medium manganese (medium-Mn) steel, one of the third-generation advanced high-strength steels (AHSS), delivers impressive mechanical properties such as high yield strength, ultimate tensile strength, and uniform elongation. One notable feature of medium-Mn steels is the presence of ultrafine-grained (UFG) austenite, achieved through phase transformation from the parent martensite phase during intercritical annealing. While, in general, UFG is considered a strengthening mechanism, the impact of UFG austenites in medium-Mn steel has not been fully studied. In this manuscript, we advance our previous work on crystal plasticity simulation based on the Taylor model to consider fully resolved high-fidelity microstructures and systematically study the influence of the UFG austenites. The original microstructure with UFG is reconstructed from a set of serial electron backscatter diffraction (EBSD) scans, where the exact grain morphology, orientation, and phase composition are preserved. This microstructure was further analyzed to identify the UFG austenites and recover them to their parent martensite before the intercritical annealing. These two high-fidelity microstructures are used for a comparative study using dislocation density-based crystal plasticity finite modeling to understand the impact of UFG austenites on both the local and overall mechanical responses.

Crystal Plasticity Finite Element Analyses on the Formability of AA6061 Aluminum Alloy with Different Ageing Treatments

Different ageing treatments have been developed to achieve targeted properties in aluminum alloys through altering microstructures. However, there is a lack of understanding regarding the effect of ageing treatments on the formability of these alloys. In this study, we employed crystal plasticity finite element (CPFE) modeling, in conjunction with the Marciniak-Kuczynski (M-K) approach, to investigate the effects of ageing treatments on the mechanical properties and formability of AA6061 aluminum alloy. The as-received sheet was in the T6 heat treatment state, which was subjected to artificial ageing and pre-ageing, respectively, to achieve two age-hardened alloys with modified precipitation states. The microstructures and crystallographic textures of the three alloys were measured using the electron backscattering diffraction (EBSD) technique, and uniaxial tensile tests were performed along the rolling direction (RD), transverse direction (TD), and diagonal direction (DD, 45° to the RD) for each alloy. The forming limit curve (FLC) of the as-received alloy was determined using the Nakazima test. The dependence of mechanical strength, tensile ductility, and work-hardening behavior on the ageing treatments was clarified. Then, the tensile test results were utilized to calibrate the modeling parameters used in the CPFE model, whereas the FLC predictability of the developed model was validated with the experimental one. In the formability analysis, the effects of the ageing treatment on the FLC exhibit a notable dependency on loading paths, and the pre-aged alloy exhibits better formability than the other two at the plane strain tension state, thanks to its high work-hardening levels. In addition, the deformed textures along the different loading paths and the effects of the initial texture on the FLC are also discussed.

Understanding the strain localization in additively manufactured materials: Micro-scale tensile tests and crystal plasticity modeling

Metallic parts fabricated by additive manufacturing (AM) usually exhibit unique microstructures and non-negligible residual stresses compared with the counterparts produced by conventional manufacturing. These inherent microstructural factors strongly affect the mechanical response of the as-built AM parts. In this study, we focus on the strain localization behavior of 316L stainless steel produced by laser powder-bed-fusion. In-situ tensile tests under a scanning electron microscope are performed, and the digital image correlation method is used to measure the strain distribution combined with electron backscatter diffraction. Meanwhile, a dislocation-based crystal plasticity finite element model incorporating residual stresses is developed to study the origins of the strain localization in the AM material. The results indicate that strain localization in AM materials is closely associated with microstructural features, encompassing behaviors related to slip activities, interactions with neighboring grains and dislocation evolutions. Additionally, the columnar grain features also render the strain distribution sensitive to the loading direction. The strain localization is serious in some small grains with high residual stresses, while in large grains the effect is less significant. These factors collectively contribute to the increasing likelihood of strain localization occurring in the AM microstructures with heterogeneous grain size and texture distribution. This work provides detailed insights into the strain localization in AM materials and would facilitate the manufacturing parameter optimization of AM materials by tuning the microstructure to reduce deformation inhomogeneity.

Crystal plasticity modeling fatigue behavior in bimodal Ti–6Al–4V: Effects of microdefect and lamellar orientation

AbstractInvestigating fatigue failure in titanium alloys is crucial for material design and engineering. Fatigue behavior in dual‐phase titanium alloys is strongly correlated with microstructural features and microdefects. This work formulates an improved modeling method to investigate fatigue behavior of bimodal Ti–6Al–4V, emphasizing the effects of lamellar orientation and microdefects. Using an improved Voronoi tessellation method, we establish representative volume element (RVE) models with various grain size distributions. Crystal plasticity finite element modeling (CPFEM) is used to analyze fatigue deformation in bimodal Ti–6Al–4V, considering microdefects and lamellar orientation. Fatigue indicator parameters are then incorporated into CPFEM to predict fatigue life and verified with experimental data. Numerical results highlight the significant influence of lamellar orientation and microdefects on fatigue behavior, with predicted life within the 3‐error band. This method efficiently overcomes challenges in quantitatively characterizing microstructural lamellae that experiments are short of, paving the way for designing fatigue‐resistant alloy materials with similar microstructures.

Synergistic coupling of thermomechanical loading and irradiation damage in Zircaloy-4

This work addresses in-situ synergistic irradiation and thermomechanical loading of nuclear reactor components by linking new mechanistic understanding with crystal plasticity finite element modelling to describe the formation and thermal and mechanical annihilation of dislocation loops. A model of pressurised reactor cladding is constructed to extract realistic boundary conditions for crystal plasticity microstructural sub-modelling. Thermomechanical loads are applied to the sub-model to investigate (i) the unirradiated state, (ii) synergistic coupling of irradiation damage and thermal annihilation of dislocation loops, (iii) synergistic coupling of irradiation damage without thermal annihilation of dislocation loops, and (iv) a post-irradiated state. Results demonstrate that the synergistic coupling of irradiation damage and thermomechanical loads leads to the early onset of plasticity, which is exacerbated by the thermal annihilation of dislocations, while the post-irradiated case remains predominantly elastic due to substantial irradiation hardening. It is shown that full synergistic coupling leads to localisation of quantities linked with crack nucleation including geometrically necessary dislocations and stress.

Research on the construction of gradient nanostructure and anti-tribocorrosion behavior of aluminum alloy surface

Gradient nanostructure in aluminum alloy, constructed via a two-dimensional ultrasonic surface burnishing process, displays enhanced tribocorrosion resistance in artificial seawater. Corrosion tests are undertaken to understand the influence of gradient nanostructure on corrosion resistance, and crystal plasticity finite element models are developed to examine wear resistance. Tribocorrosion tests are performed through wear tests in the artificial seawater environment. The results indicate that the processed samples' corrosion rate decreases from 3.12 × 10−2 mm/a to 2.45 × 10−3 mm/a. The wear scar sizes of the processed samples are approximately half the unprocessed samples. The gradient nanostructure obstructs dislocation glide during wear, diminishes the accumulation shear, and promotes high-hardness corrosion product formation, effectively isolating the direct contact between the friction pairs, thus improving the tribocorrosion resistance.

Measuring texture-component-dependent stress of CuZn39Pb2 by neutron diffraction

Understanding the micromechanical behavior of polycrystalline material is pivotal for regulating its mechanical performance and widening its application. Taking advantage of its non-destructive nature, the neutron diffraction technique has been widely applied to investigate the micromechanical behaviors, usually at the resolution of grains sharing the same diffraction plane. This work employs a newly developed technic of the texture-component-dependent (TCD) in-situ neutron diffraction method to obtain the full strain/stress tensor of a textured CuZnPb alloy at the resolution of individual crystallographic orientation. The variation of the internal stresses and lattice strains over the grains that share the same diffraction plane has been successfully captured by the TCD method. According to the results of in situ neutron diffraction, Copper ({-1–1–2}<-1–11>) possesses the highest lattice stress while Cube ({010}<100>) and Goss ({110}<001>) bear the lowest stress of 370 MPa. In parallel, the micromechanical response of the texture components is modeled by the elastic visco-plastic self-consistent (EVPSC) model. The simulated results are in reasonable agreement with the corresponding experiments in loading direction, while the lateral stress exhibits some deviation. By crystal plasticity finite element modeling, the deviation is related to the neighbor grain which affect more significantly the lateral stress than the material parameters. The full tensor of stress within the individual crystallographic orientation measured by TCD method gives more insight into the crystal plasticity modeling.

Crystal plasticity finite element model of the brittle–ductile transition temperature and fracture toughness of irradiated A508-3 steel

Crystal plasticity finite element model of the brittle–ductile transition temperature and fracture toughness of irradiated A508-3 steel

Experimental and Crystal Plasticity Finite Element Investigations of Plastic Anisotropy in Additively Manufactured Ti6Al4V Alloy

Additive manufacturing, particularly the laser powder bed fusion (LPBF) technique, has ushered in a new era of intricate metallic component fabrication, leveraging the exceptional performance of the Ti6Al4V alloy. However, the intricate mechanical behavior of additively manufactured Ti6Al4V, particularly its anisotropic attributes stemming from non-equilibrium microstructures, presents a formidable challenge. In this study, we embark on a comprehensive exploration of the anisotropic mechanical properties exhibited by LPBFed Ti6Al4V alloy. The interplay between microstructure and tensile response is unraveled by integrating experimental investigations with crystal plasticity finite element (CPFE) simulations. The acquired empirical data with CPFE model predictions are harmonized through systematic tensile tests along distinct processing orientations. The results unveil the genesis of plastic anisotropy within the LPBFed Ti6Al4V alloy, ascribed to the emergence of columnar grains meticulously aligned along the building direction, despite the intricate material microstructure inherent to additive manufacturing. These findings collectively furnish a holistic comprehension of the intricate nexus between material attributes and the mechanical manifestations intrinsic to metal components realized through additive manufacturing modalities.

A study on the microstructure and mechanical behavior of CoCrFeNi high entropy alloy fabricated via laser powder bed fusion: Experiment and crystal plasticity finite element modelling

Additive manufacturing facilitates the design of high entropy alloys (HEAs) with well-performing properties compared to conventional manufacturing methods. However, a significant obstacle to the industrial application of the equimolar CoCrFeNi HEA fabricated through additive manufacturing is the detrimental impact of thermal cracks on its performance. Here, thermal crack-free CoCrFeNi HEAs with enhanced mechanical properties were obtained by optimizing the energy input in laser powder bed fusion (LPBF). The lower energy input resulted in finer grains, leading to simultaneously improved strength and ductility compared to the one fabricated via higher energy input. To understand the relationship between the microstructure and mechanical properties, crystal plasticity element modelling (CPFEM) was employed to accurately model the experimental results. Using the collected constitutive parameters for CoCrFeNi HEA after CPFEM, in-situ tensile modelling was implemented on a converted orientation map of an as-LPBF CoCrFeNi sample. The CPFEM results reveal that the appearance of deformed twins during the initial plastic deformation stage is attributed to a complex distribution of shear strain on the grain boundaries. The interaction between the deformed twins and dislocation motion emerged as the primary deformation mechanisms in the as-LPBF CoCrFeNi HEA, resulting in complex stress and strain distributions. By combining experimental data with modelling techniques, a viable approach to comprehending the detailed deformation mechanism of deformed twins was established.

Effect of Pre-Added HfO2 Inclusions on Carbide Morphology and Deformation Behavior in DZ125 Nickel-Based Superalloy

Inclusions are important phases affecting material properties in complicated ways. In this paper, a quantitative study of the addition of HfO2 inclusions to DZ125 nickel-based superalloys was performed. Experimental results showed that the introduction of HfO2 inclusions caused a loss of strength and ductility. The carbide morphology also changed significantly from skeletal-shaped to block-shaped, resulting in a remarkable discrepancy in the fracture behavior under quasi-in-situ tensile testing. The SEM dynamic observations showed that cracks were initiated from the skeletal carbides and almost failed to propagate into the matrix. In contrast, the damage behavior of block-shaped carbides also involved internal cracking but with a tendency to form interconnected microcracks during propagation. A crystal plasticity finite element model (CPFEM) method was further developed to study the stress/strain behavior during the deformation process, considering the crystal orientations and microstructure morphologies from the EBSD data. Those elastoplastic parameters were determined through nanoindentation experiments. Simulation results verified that blocky carbides produced a pronounced strain concentration at the interface of the carbides and matrix, thereby increasing the tendency of crack formation. This paper provides a fundamental understanding of the role of inclusions in material recycling applications.

The effects of different factors on obstacle strength of irradiation defects: An atomistic study

In this work we study the effects of different factors of dislocation loop on its obstacle strength when interacting with an edge dislocation. At first, the interaction model for dislocation and dislocation loop is established and the full and partial absorption mechanism is obtained. Then, the effect of temperature, size and burgers vector of dislocation loop are investigated. The relation between the obstacle strength and irradiation dose has been established, which bridges the irradiation source and microscale properties. Except that, the obstacle strength of C, Cr, Ni, Mn, Mo and P decorated dislocation loop is studied. Results show that the obstacle strength for dislocation loop decorated by alloy element decreases in the sequence of Cr, Ni, Mn, C, P and Mo, which could be used to help parameterize and validate crystal plasticity finite element model and therein integrated constitutive laws to enable accounting for irradiation-induced chemical segregation effects.

Numerical Simulation of the Residual Stress at the Interface between Thermal Barrier Coating and Nickel-Based Single-Crystal Superalloy Based on Crystal Plasticity Theory

Residual stress plays an important role in the formation and growth of cracks in thermal barrier coatings and single-crystal superalloy substrates. In this study, a finite element model for a planar double-layer thermal barrier coating and a crystal plasticity finite element model based on dislocation slip-induced plastic deformation of single-crystal materials were established to analyze the residual stress in the coatings and the substrate, considering the creep and crystal plasticity of the substrate materials. The simulation results show that the thermal barrier coatings bear most of the stress generated by high temperatures, and the residual stress of the substrate is small. By comparing the two material properties to calculate the interface stress when the amplitude of the interface between the substrate and the coating is 30 μm and the thickness of the thermal grown oxide layer is 5 µm, the interfacial stress of the substrate at the macro scale was found to be similar to the interfacial stress at the micro slip system scale. Based on the cumulative shear strain, it was determined that the [001]-, [011]-, and [111]-oriented alloys activated the 12, 8, and 4 groups, respectively, under the combined action of thermal stress and centrifugal force of the coating. Comparing the activation of different initial orientation slip systems and the magnitude of the yield stress provides a theoretical foundation to study the structural integrity of single-crystal alloys.

Analysis of Microstructure, Texture Evolution, and the Mechanism of Grain Refinement of Commercially Pure Titanium During Cold Rolling: Experiment and Simulation

A comprehensive understanding of the microstructures and texture evolutions during the rolling process is of great significance for the preparations of high‐quality commercially pure titanium (CP‐Ti) sheets. Therefore, in the present work, the effects of rolling reductions on the microstructures and textures of CP‐Ti are investigated by optical microscope, electron backscatter diffraction, and X‐ray diffraction. A crystal plasticity finite element model (CPFEM) is developed to accurately predict the rolling deformation behaviors of CP‐Ti sheets. The results show that the slip and twinning including , compression twins and extension twins are prone to plastic deformations during the whole rolling process. The c‐axes of grains gradually tilt toward the transverse direction and the grains gradually deviate from the original //rolling direction (RD) to //RD. As a result, the mixed textures of and are developed in the specimen. The grain refinements are closely linked with the developments of and twins. In addition, the twin fractions and texture evolutions are well predicted by the CPFEM model. These results documented in this work should not only help to elucidate the microstructures and texture evolutions of CP‐Ti, but also shed important light on improving its properties.