Crystal Plasticity Research Articles

Realizing strength-ductility combination of Ni-12Mo-7Cr-2Nb based superalloy via nano-sized MC carbides at stacking faults and grain boundaries

Developing corrosion-resistant alloys with the outstanding strength-ductility combination at elevated temperatures are highly desirable for molten salt reactor (MSR) applications. In this study, by appropriate preaging process, the yield strength and elongation of one newly developed Ni-12Mo-7Cr-2Nb based superalloy at high temperatures respectively increase by ∼50 % and ∼100 % as compared with the solid-solution state. This preaged alloy exhibits the excellent strength and overcomes the intermediate temperature embrittlement problem as compared with other alloys. Microstructure observations indicate that the strengthening and ductility improvement are related to the formation of nano-sized MC carbides. After preaging process, the extrinsic stacking faults are formed along {111} close-packed planes and decorated with ultra-dense MC carbide particles, thus are called as stacking faults precipitates (SFPs). SFPs contribute to the precipitation strengthening by the complex interaction with dislocations. Surprisingly, the SFPs exhibits the better strengthening effect than the uniformly dispersed MC carbides with the same volume fraction and size. Furthermore, it was found that the “pseudo-continuous” intergranular MC carbide particles are beneficial to the high-temperature ductility, although the similar intergranular precipitates were widely regarded as harmful in other studies. Using crystal plasticity finite element method, it was proved that the strain concentration at the triple junctions would be obviously alleviated because the intergranular MC carbide particles can suppress grain boundary sliding. If tested at 750 °C, the intergranular MC carbide particles would trigger the particle-stimulated nucleation and lead to the local dynamic recrystallization at grain boundaries and crack tips. These small recrystallized grains can suppress crack propagation and bring about the improvement in ductility in the aged alloy.

Measurement and optimization method for aero-engine rotors based on binocular multi-line laser sensing and virtual assembly

During the assembly of aero-engine rotors, eccentricity and tilt errors along the radial and axial direction result in uneven loading along the mating surface, which significantly impacts the operational lifespan of the rotor. This paper proposes a three-dimensional contour measurement system based on binocular multi-line laser sensing and conducts an aircraft engine rotor stacking virtual assembly technology system, to response the practical requirements of aircraft engine rotor unit production assembly engineering. We combine multi-line structured light active projection device with the binocular stereo vision model to construct the contour measurement system, which enhances the surface features of the projected object by adhering to the common constraint of structured line and stereo vision. Furthermore, the error propagation model for multi-stage rotor assembly to investigate the mechanism of error impact is established aiming to facilitate quantitative research on virtual assembly mechanisms. By manipulating the rotor phases and evaluating the coaxiality under various conditions, effective prediction of phase variation can be achieved, the multi-objective benchmark virtual assembly method based on the error propagation model of multi-stage rotor coaxiality is presented. The experimental results indicate that the proposed measurement system achieves the maximum disparity between the spatial data points procured by the proposed measurement system and the predetermined value of 2.1 μm, and the maximum disparity between the target plane’s average movement distance and the preset value of 3.7 μm. The precision provided by this system effectively meets the objective of assembly phase optimization for multi-stage rotors. In the empirical experiment conducted on the three-stage rotors, both systems yielded identical optimized phases: 0° for the first-stage rotor, 270° for the second-stage rotor, and 120° for the third-stage rotor, thereby validating the efficacy of the proposed measurement and optimization method for aero-engine multi-stage rotors with virtual assembly.

Experimental and crystal plasticity study on hydrogen-assisted fatigue crack growth behavior of IN625 superalloy

The fatigue crack growth (FCG) behavior of IN625 alloy was studied by experimental methods and crystal plasticity simulations. Based on the experimental FCG rate curves, it is evident that hydrogen significantly accelerates FCG, and calculations show that this acceleration factor reaches a maximum of 2.41 times at 1 Hz. Hydrogen results in smaller plastic deformation zones compared to hydrogen-free samples. The interaction between hydrogen and dislocations leads to the nucleation of micro-voids along the slip planes, promoting the hydrogen-assisted cracking process. Lower loading frequencies results in finer fatigue striations and more pronounced hydrogen embrittlement features on the fracture surface.

Enhanced Cyclically Stable Plasticity Model for Multiaxial Behaviour of Magnesium Alloy AZ31 under Low-Cycle Fatigue Conditions.

Magnesium alloys, particularly AZ31, are promising materials for the modern automotive industry, offering significant weight savings and environmental benefits. This research focuses on the challenges associated with accurate modelling of multiaxial cyclic plasticity at small strains of AZ31 under low-cycle fatigue conditions. Current modelling approaches, including crystal plasticity and phenomenological plasticity, have been extensively explored. However, the existing models reach their limits when it comes to capturing the complexity of cyclic plasticity in magnesium alloys, especially under multiaxial loading conditions. To address this gap, a cyclically stable elastoplastic model is proposed that integrates elements from existing models with an enhanced algorithm for updating stresses and hardening parameters, using the hyperbolic tangent function to describe hardening and ensure a stabilised response with closed hysteresis loops for both uniaxial and multiaxial loading. The model is based on a von Mises yield surface and includes a kinematic hardening rule that promises a stable simulation of the response of AZ31 sheets under cyclic loading. Using experimental data from previous studies on AZ31 sheets, the proposed model is optimised and validated. The model shows promising capabilities in simulating the response of AZ31 sheet metal under different loading conditions. It has significant potential to improve the accuracy of fatigue simulations, especially in the context of automotive applications.

Effect of Laser Parameters on Fracture Properties of Laser-Repaired Cracks with Micro/NanoMaterial Addition: Multiscale Analysis.

In laser crack repair processes, laser parameters have significant influence on repair quality. Improper combination of laser process parameters may result in defects-such as porosity, ablation, and coarse grain size-in remelted zones. A trans-scale computational model is established by combining crystal plasticity finite elements and variable-node finite elements. The influence of microstructure characteristics such as grain size and porosity of the repair layer on the cumulative plastic slip (CPS) on the dominant slip system at the meso-scale and the J-integral at the macro-scale is studied to explore the effect of laser process parameters on repair quality. The results show that when the laser power is 1800 W and the heating time is 0.5 s, the grain size and porosity of the repaired specimen are the smallest. The J-integral of the repaired specimen is more than 8% smaller than that of the unrepaired specimen and about 3% smaller than that of the repaired specimen, with a laser power of 2000 W and a heating time of 1 s. Pores increase the CPS of the crystal around the pores, especially when a pore have sharp corners. Selecting appropriate laser process parameters can not only refine grain size but also reduce the volume fraction of pores and thus reduce the J-integral and eventually improve repair quality of repaired specimens. The study investigates the relationship of process parameter-microstructure-repair quality in the laser repair process and provides a method for studying the mechanical behavior of materials at macro and micro scales.

Slip identification from HR-DIC/EBSD: Incorporating Crystal Plasticity constitutive laws

It is well known that dislocation slip plays a major role in plastic deformation of polycrystals. Depending on the crystal’s symmetry, only a limited number of Slip Systems (SSs) are possible, and their activities depend on the crystal orientation with respect to the applied stress. High Resolution Digital Image Correlation (HR-DIC) can be used to get the full-field measurements of displacement fields on the surface of the strained material during an in situ tensile test, whereas the EBSD technique provides local crystallographic orientations. Therefore, coupling them can lead to full description of the local slip activities. Recently, an algorithm (named SSLIP) was proposed in the literature to automatically estimate the plastic activity from HR-DIC and EBSD data. The aim of the present paper is first to improve this algorithm so that it works for incremental straining, and to propose a way to take account for the anisotropic behaviour through a well-known set of Crystal Plasticity (CP) constitutive laws. It is shown that slip identification, together with those CP laws, can be used to estimate the tensile stress at grain scale. The influence of the DIC resolution is investigated and “correction rules” for small grains are proposed. Finally, the experimental results are compared against those found using the CP Finite Element Method (CPFEM), showing good consistency, specially in terms of active SSs and local stress.

Integrating crystal plasticity and experimentation for investigating the size effect on the deformation characteristics of AISI304 microtubes manufactured by free bending technology

During the deformation process of micro-bending, the size effect resulting from the variation in the grain size of the microtubes is the primary factor affecting the bending behavior. The current study on free bending mainly focuses on using macroscopic finite element simulation and experimental analysis to investigate the factors affecting the bending radius and forming quality. However, due to the size effect, the practices and insights gained from macroscopic forming may not directly apply to microforming. Thus, this study aims to reveal and explain the reason for the increase in the bending radius of microtubes with decreasing grain size by combining experimental investigations with crystal plasticity finite element modeling (CPFEM). It was determined that the grain size is a crucial consideration in the micro-bending process of microtubes. Additionally, the CPFEM approach can provide guidance for the process parameters of free bending forming of microtubes.

Anisotropic formability and deformation mechanism of near-α titanium alloy sheet under continuous nonlinear strain paths at high temperature

In the present study, the anisotropic formability and underlying deformation mechanism of near-α TA32 titanium alloy sheet under continuous nonlinear strain paths (CNSPs) at high temperature were investigated in depth. To achieve this goal, a new experimental method combining hot gas bulging with step-combined dies was proposed, and the hot CNSPs of metal sheets can be flexibly and conveniently realized by changing the number and shape of step-combined dies. Based on this method, the anisotropic deformation behavior and forming limits of TA32 sheet under fifteen CNSPs were tested at 800 ℃ with a strain rate of 0.001 s−1. Then, two advanced constitutive models with different scales were embedded into the classical Marciniak-Kuczyński (M-K) theory to predict the forming limits of TA32 sheet under different strain paths: the macro-scale viscoplastic model coupled with Hill48 yield criterion and non-associated flow rule (NAFR) as well as the meso-scale three-dimensional crystal plasticity finite element (CPFE) model coupled with cellular automata (CA). The results demonstrate that the CPFE-CA-MK coupled model exhibits higher accuracy in predicting the forming limits of TA32 sheet under linear and continuous nonlinear strain paths. Especially for the tension-tension strain paths, the CPFE-CA-MK coupled model improves accuracy by at least 3.1 % compared to macro-scale models. Due to the material anisotropy, the initial inclination angle of the groove in the CPFE-CA-MK model is closely related to the strain path and significantly affects the prediction accuracy. Based on the CPFE simulation, the effects of anisotropy and strain path change on the dislocation slip mode of different texture components was analyzed in depth, which provides a theoretical guidance for the optimization of hot forming process of TA32 titanium alloy complex components.

Sequential dual-scale approach for microstructure-informed ductile fracture prediction

This study presents a novel dual-scale finite element method to establish a microstructure-informed ductile fracture criterion for ferrite–martensite dual-phase (DP) steel. At the macroscale, an anisotropic plasticity model with rate-dependent hardening was employed to simulate the material's deformation history. Simultaneously, at the microscale, a dislocation density-based crystal plasticity model was utilized to simulate deformation within a representative volume element (RVE) of the dual-phase steel, constructed using tomography aided by a plasma-focused ion beam/electron backscatter diffraction system.The material properties of the ferrite and martensite phases were determined through X-ray diffraction (XRD) analysis and load-displacement measurements obtained via nanoindentation for each phase. The RVE simulation results were validated against experimentally measured mechanical properties and microstructural changes. The local deformation history at the fracture initiation site, extracted from the macroscale model, was used as boundary conditions for the microscale RVE simulation; sequential dual-scale approach. The models were applied to specimens with varying notch radii, generating different local stress triaxialities and accumulated shear strains at fracture onset. This process allowed the establishment of a ductile fracture criterion, which was further tested in a hole expansion experiment, demonstrating close alignment with experimental data.This sequential dual-scale analysis effectively predicts the deformation behavior of multiphase metallic materials by incorporating realistic microstructures while minimizing computational costs. Consequently, the proposed ductile fracture prediction technique offers a robust method with broad applicability across various metallic materials.

Grain size dependence of twin nucleation in magnesium alloys

Twinning plays a prominent role in the plastic deformation of low-symmetry crystals such as magnesium alloys. However, the capture of twin nucleation has been challenging since the process is rapid and difficult to predict, making it impossible to observe directly. Because of this, the understanding of the fundamental twinning mechanism through experiments and simulation techniques incorporating twinning has progressed slowly. In this study, a quantitative analysis integrating an in-situ three-point bending experiment and crystal plasticity modeling was conducted on the twin nucleation in AZ31 magnesium alloys with different grain sizes. The threshold for triggering twin nucleation has been quantified. The prediction ability of three widely used criteria for twin nucleation, i.e., geometrically necessary dislocation (GND) density, von Mises stress, and stored energy density, is evaluated. The results suggest that only the stored energy density is able to capture the twin nucleation location accurately in all the considered grain sizes. The critical value exhibits an exponential reduction with the increase in grain size. Based on the quantitative analysis, the mechanism of the grain size effect on twin nucleation is proposed.

Size Dependency of Elastic and Plastic Properties of Metallic Polycrystals Using Statistical Volume Elements

We present an efficient approach to evaluate the size dependency of elastic and plastic properties of metallic polycrystalline materials. Specifically, we consider different volume fractions of ferrite and martensite phases for the construction of three macroscopic domains. Statistical Volume Elements (SVEs) of different sizes are extracted from these domains using the moving window method. Linear and Crystal Plasticity (CP) simulations provide elastic and plastic properties of the SVEs such as the bulk and shear moduli, yield strength, and hardening modulus. We use a variation-based criterion to determine the Representative Volume Element (RVE) size of these properties. This RVE size corresponds to a size beyond which the given property can be idealized as homogeneous. We also use anisotropy indices and an additional RVE size criterion to determine the size limits beyond which these properties can be idealized as isotropic. Numerical results show that the plastic properties often reach their homogeneity and isotropy limits at larger sizes compared to elastic properties. This effect is more pronounced for the hardening modulus compared to the yield strength.

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

Investigating the orientation dependence of local fields around spherical defects using crystal plasticity simulations

The presence of a void or secondary particle plays a crucial role in both the mechanical response and damage evolution of metals. This work presents local stress and strain field predictions in a single crystalline matrix that contains a spherical void or hard particle using crystal plasticity finite element method (CP-FEM) simulations. Simulations demonstrate highly heterogeneous orientation dependent local fields near defects. In particular, we show that matrix decohesion around hard particles will occur first before void growth in pre-existing voids under strain-controlled uniaxial tension and isochoric loading. Furthermore, CP-FEM simulations predict that the [1̄11]-oriented grain is most susceptible for failure, while grains oriented toward the [001] orientation are more resistant to failure. This work provides insights into how grain-scale microstructure with volumetric defects influence the local damage and failure behavior in metal alloys.

Towards a data platform for multimodal 4D mechanics of material microstructures

This paper presents advances in the data management strategy applied to 4D multimodal mechanics of material sample microstructures. Guidelines to build a data platform allowing for complex workflows, involving several high-throughput experimental and numerical techniques, and complying with FAIR data management principles, are discussed. Next, their implementation within the open-source Python package Pymicro is presented, offering a high-level interface to build complex datasets through multimodal methodologies. Its capability to enable and automate complex workflows by building a digital twin of a commercially pure titanium sample under tension are then demonstrated. The digital twin contains microstructural and mechanical data for thousands of grains gathered on the same sample through synchrotron DCT and in-situ SEM experiments, as well as full-field numerical simulation. Finally, a local and statistical comparison between simulation and measurements of plastic slip and crystal rotation in hundreds of grains is shown, as an example of the contribution of this platform to multimodal data convergence and its importance for the development of a new generation of material models.

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. The present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

A Two-Scale Texture Modelling of AA1050 Aluminum Alloy after Accumulative Roll-Bonding (ARB)

Texture evolution during accumulative roll-bonding (ARB) is complicated because of the change in the through-thickness position that results from repeated cutting–stacking and roll-bonding. In this study, a macro–micro two-scale modeling was carried out to investigate the behaviors of texture evolution during ARB. The finite element method (FEM) was used to predict the strain history at a macro-scale, while a crystal plasticity FEM was used to reproduce the texture at a micro-scale. The texture evolution along three different cutting–stacking paths was traced and investigated. The patterns of texture transition between the rolling-type, shear-type, and random-type textures were studied by using area fractions of texture components, the distribution of textures, and the distribution of crystal rotation angles.

Asymmetrical plastic deformation during spherical micro-indentation of magnesium

The complex deformation of magnesium (Mg) and its alloys has been the focus of many studies in lightweight technologies. In this paper, spherical micro-indentation tests followed by post-test electron microscopy were carried out on large grain pure Mg to isolate the effects of crystal orientation on the activation of deformation along different slip or twinning systems. Both pre- and post-indentation crystal orientations were measured using electron backscatter diffraction (EBSD). The pre-indentation orientations were mapped into a crystal plasticity finite element (CPFE) model to further analyze the results. It is shown that the resulting deformation twinning and the degree of indentation-induced misorientation were strongly correlated with the crystal orientation in the region of the indentation. Depending on the crystal orientation, multiple waves of basal slip were observed to form asymmetrically around the indents. These slip bands lead to more than 12° lattice rotations that are captured by CPFE modeling. For the first time, it is shown that indentation can lead to significant out-of-plane displacement field that can induce twin nucleation at the interface of far-field (>100 μm) neighbouring grains. CPFE simulations indicate that maintaining far-field strain compatibility leads to the nucleation of twins rather than a slip transfer or slip-induced twinning mechanism.

Revealing the fatigue strengthening and damage mechanisms of surface-nanolaminated gradient structure

Extending the fatigue life of metals is a critical concern for maintaining material and component integrity in engineering systems. The integration of gradient structures within materials represents a highly promising approach to enhance the fatigue properties in metallic materials, while a detailed mechanistic understanding of the fatigue damage evolution of such structures is yet to be developed. Here, we report that the surface-nanolaminated gradient structure comprised of nanolaminates and hierarchical twins imparts remarkable resistance to both low-cycle and high-cycle fatigue. A dislocation-based strain gradient crystal plasticity model is developed to investigate the strengthening and damage mechanisms of our gradient structure. The size dependence of the initial dislocation density, its evolution and back stress hardening are taken into account and verified by the experimental data. The simulation results reveal that the strain delocalization and back stress hardening induced by the structure gradient significantly mitigate the fatigue damage accumulation. Additionally, in contrast to conventional gradient structures, the mechanical stability of the present structure enables these strengthening mechanisms to persist until crack initiation. These effects, combined with the sequential toughening mechanisms activated in the surface-nanolaminated gradient structure, ensure a marked life extension under low-cycle fatigue (by a factor of four), outperforming conventional gradient and other microstructural design strategies. Finally, a multiscale anti-fatigue design principal for damage homogenization is given based on the prior quantitative analysis.

Colossal Barocaloric Effect in Encapsulated Solid‐Liquid Phase Change Materials

AbstractBarocaloric cooling as an emerging cooling technology offers an eco‐friendly alternative to traditional vapor compression refrigeration. Research on barocaloric materials primarily concentrates on solid–solid phase change materials (PCMs), among which plastic crystals exhibit colossal barocaloric effect. Solid‐liquid PCMs such as paraffin also exhibit giant barocaloric effect, however, their potential is often overshadowed by leakage issues. In this work, a strategy is demonstrated by encapsulating solid‐liquid PCMs into porous carbon matrixes to generate a large family of colossal barocaloric materials. In practice, by orthogonally combining paraffins with encapsulation matrixes like graphene foam, carbon nanotube foam, and carbon foam, it can be obtained composites that work without leakage issues. The significant advantage is their colossal barocaloric effect with the highest entropy value up to 570 J K−1 kg−1 in paraffin‐20@graphene foam. Moreover, the composites possess thermal conductivity up to 89.9 W m−1 K−1 in paraffin‐20@carbon foam, and tunable working temperature in the range of 270—330 K. Most importantly, this strategy, demonstrated with 5 solid‐liquid PCMs and 3 encapsulation matrixes in this work, is just the beginning. Further exploration with more materials can develop a huge family of encapsulated solid‐liquid PCMs with colossal barocaloric performance for modern cooling technology.

Comparative studies on the nature and kinetics of phase transitions in plastic crystals: Hydrogen-bonded adamantane derivatives

In this paper, the results of thermal, structural, and spectroscopic studies on 3-amino-1-adamantanol (3-NH2-1-OH-ADM) were discussed with those recently published for 1-hydroxyl and 1-amine derivatives of adamantane (1-OH-ADM, 1-NH2-ADM). Calorimetric measurements showed that the examined compound, like 1-NH2-ADM, is characterized by multiple thermal events in the thermogram measured on heating and cooling. Further X-ray diffraction, Fourier-transform infrared, and Raman spectroscopy investigations suggested that two of them correspond to the transition from the ordinary crystal (OC) to the plastic crystal (PC) phase I and the transition between two PC phases (PC(I) and PC(II)), while the third subtle one is rather not related to a phase transition. Interestingly, ambient pressure dielectric studies performed during heating and cooling cycles revealed changes in the imaginary and real parts of the complex dielectric permittivity at temperatures close to the temperatures of phase transitions detected by the calorimetry. Such behavior resembled that reported for 1-NH2-ADM. Finally, isothermal time-dependent dielectric and infrared studies, supported by the analysis of asynchronous 2D-IR correlation spectra, indicated that the first endothermic peak, visible in the thermogram of 3-NH2-1-OH-ADM over an enormously large temperature interval and related to the OC-PC(I) phase transition, similarly to the one, assigned to the PC(I)-PC(II) transition in 1-NH2-ADM, has a character of the kinetic process. Importantly, during the annealing of 3-NH2-1-OH-ADM at T = 328–343 K, we observed a clear change in the dc-conductivity as well as intramolecular dynamics related to the vibrations of CH, NH2, and OH moieties that occur at different rates.