Plastic Anisotropy Research Articles

Multiscale-informed irradiation growth model of Zr-Sn-Nb alloys

A systematic multiscale-informed model is developed to predict the irradiation growth behavior of Zr-Sn-Nb alloys, which considers the anisotropy and temperature dependence of both plasticity and irradiation, as well as the alloying effect of Zr alloys. This model consists of a cluster dynamics submodel to consider the kinetics of irradiation defect, an alloying effect submodel informed by atomic simulations and experiments, a microstructure transition submodel derived from discrete dislocation dynamics, and a continuous irradiation growth submodel based on crystal plasticity. It effectively captures the irradiation-induced coevolution of multiple microstructures, including point defects, mobile clusters, dislocation lines and irradiation loops on the prismatic and basal plane, as well as Nb-induced precipitates. It is suitable for high-dose irradiation conditions as it reasonably considers the transition from high-density irradiation loops to tangled dislocation network. The predicted irradiation growth strain, as well as the density and size of irradiation loops, are in good agreement with almost all the available experiments for pure Zr, Zr-Sn, Zr- Nb, and Zr-Sn-Nb alloys at different irradiation doses in the temperature range of 473 - 673 K. This work is hoped to provide a powerful tool for developing irradiation resistance cladding materials.

Corrosion resistance and wear behavior of CoCrFeNiMn@Gr high entropy alloy-based composite coatings prepared by laser cladding

In this study, we utilize laser cladding to apply a CoCrFeNiMn HEA with 2 wt.% few-layer graphene (Gr) coating onto the surface of Q235B mild steel. Alcohol stirring method was used for HEA and Gr preparation of composite powder. Raman spectroscopy and energy dispersion spectroscope (EDS) indicate the successful mixing of HEA and Gr powders, with Gr adhering to the surface of the HEA powder in a lamellar structure. The X-ray diffraction (XRD), scanning electron microscope (SEM), EDS, and Electron backscatter diffraction (EBSD) analyses revealed that grain refinement and the formation of fine carbide-hard phases in the HEA/Gr coating improve microhardness and wear resistance. The average Schmidt factors of the coating decreased from 0.47 to 0.45 with the addition of Gr, indicating enhanced resistance to plastic deformation and anisotropy. Nanoindentation experiments demonstrated that the HEA/Gr coatings exhibit superior resistance to plastic deformation, effectively enhancing the coating’s durability against spalling under stress and wear conditions. The microhardness of the HEA/Gr coating increased by 99.25%, and the wear rate decreased by 86.31% compared to the HEA coating alone. The open circuit potential (OCP), linear polarization curve, Tafel curves, electrochemical impedance spectroscopy (EIS), and Mott-Schottky tests all indicated that the HEA/Gr coating possesses superior corrosion resistance. X-ray Photoelectron Spectroscopy (XPS) results suggest that the passivation film of the HEA/Gr coating, which contains more oxides and less hydroxide, is more protective and denser, thereby slowing the corrosion rate.

Hierarchical Deformation and Anisotropic Behavior of (α+β) Ti Alloys: A Microstructure-Informed Multiscale Constitutive Model Study

In this study, the hierarchical deformation and anisotropic behavior of (α+β) Ti alloys are investigated using a novel microstructure-informed multiscale constitutive model. State-of-the-art crystal plasticity finite element (CPFE) models, due to their emphasis on a single length scale, are inadequate for capturing the complex hierarchical behavior of additively manufactured (AM) (α+β) titanium alloys, which are characterized by columnar grains and lamellar subgrain features at distinct length scales. To overcome this limitation, a decoupled multiscale framework was developed, integrating representative volume elements (RVEs) for both the columnar grain structure at the higher length scale and the subgrain microstructure at the lower length scale, with equal emphasis on each. The material behaviors at these scales were modeled using an anisotropic classical plasticity model and a mechanism-based CPFE model, respectively. The framework was experimentally validated for Directed Energy Deposition (DED) manufactured Ti-6Al-4V and used to investigate microscopic stress/strain fields, deformation localizations at grain and subgrain levels, and stress partitioning among neighboring grains. Insights from these studies led to the proposal of a new theory of anisotropy in AM (α+β) titanium alloys.

Microstructure-sensitive crystal plasticity and phase-field modeling of deformation and fracture in polycrystalline ice

The formation of crevasses in Greenland and Antarctica is primarily driven by the brittle failure of ice at low strain rates. Understanding this phenomenon requires exploring the effect of microstructural heterogeneity and anisotropic elastoplastic deformation on the fracture behavior of ice. Here, we have developed a microstructure-sensitive coupled crystal plasticity and phase-field model. This model allows us to study the plastic deformation, damage initiation and propagation under various strain rates in hexagonal open-packed polycrystalline ice, the prevailing phase on Earth. By employing a Bayesian optimization method, we derived the material parameters for the micromechanical model based on experimental results. The modeling results reveal that the activation of basal dislocations results in a brittle to ductile transition in ice at a low strain rate of 10-7s-1 under tension. At higher strain rates, the intrinsic plastic anisotropy of ice leads to heterogeneous deformation among grains and stress concentration near grain boundaries, triggering crack initiation and exacerbating the brittleness of ice. Under compression, cracks usually do not propagate throughout the specimen due to a significant decrease in stress around the crack tip upon propagation. Moreover, we found that the formation of the shear-induced basal texture at the bottom of ice layers and along glacier valley sides intensifies the brittleness of ice. This study provides insights into the micromechanical deformation and fracture mechanisms of ice, elucidating the intricate process of crevasse development in polar ice sheets.

Tailoring nanotwinned Cu interlayers for localizing anisotropic plastic deformation during low energy input ultrasonic welding of robust Cu-Cu joints

Tailoring nanotwinned Cu interlayers for localizing anisotropic plastic deformation during low energy input ultrasonic welding of robust Cu-Cu joints

Correction: Influence of Plastic Anisotropy and Strain Path on strain-induced Phase Transformation of Cobalt

Correction: Influence of Plastic Anisotropy and Strain Path on strain-induced Phase Transformation of Cobalt

Constitutive Modeling of Anisotropic Plasticity with ML Algorithms in Metals

Nuclear reactors hold significant promise for mitigating the environmental crisis and achieving a carbon-free world. The advancement of nuclear technology, however, is intricately tied to the materials used in reactors, with metals and alloys forming their core components. Understanding the plasticity and degradation of these materials is crucial to prevent critical reactor failures caused by factors such as radiation-induced embrittlement, creep, and fuel-cladding interactions. While traditional plasticity modeling has relied on constitutive laws and yield functions, the advent of machine learning (ML) and artificial intelligence has opened new avenues for this field. This paper explores the potential of data-driven approaches to enhance plasticity modeling for metals used in nuclear reactors. Recent studies have leveraged ML algorithms, including support vector machines and artificial neural networks, to model yield surfaces and correct theoretical yield functions with experimental data. Despite their accuracy, these models often lack interpretability and generality. To address these challenges, we investigate the applicability of various ML algorithms, i.e. neural networks, logistic regressions, decision trees, K-nearest neighbors, and Gaussian processes (GPs), in developing data-oriented flow rules for plasticity modeling. The paper demonstrates the superiority of GPs in terms of interpretability and generality. Using stress data generated from PyLabFEA, we compared the performance of these algorithms, highlighting the intrinsic uncertainties associated with GP predictions. Our findings indicate that Gaussian process classifiers (GPCs) offer a promising approach for modeling plasticity in metals, providing a balance between precision and physical insight. Additionally, this work presents a deep neural network (DNN) to model anisotropic Hill-type plasticity with perfect test data accuracy (accuracy score: 1.0), which is often hard to achieve with a classification problem. This shows the superiority of DNNs in terms of accuracy in modeling yield functions. The implications of our results for bridging the scale gaps in macrolevel simulations are discussed, and future directions for incorporating microstructural features into ML-based plasticity models are proposed. Overall, the ML framework presented in this paper can be employed for modeling constitutive relations that can be incorporated within traditional Finite Element Method (FEM)–based codes. Specifically, the GPC or DNN developed in this work can be readily swapped with the yield function within the so-called return mapping algorithm of nonlinear FEM-based plasticity subroutines to indicate yielding. Consequently, this merging of ML and FEM will allow us to leverage the geometric representational ability of FEM alongside the superior modeling capabilities of the ML algorithms.

Digital image correlation and infrared thermography data for seven unique geometries of 304L stainless steel

Material Testing 2.0 (MT2.0) is a paradigm that advocates for the use of rich, full-field data, such as from digital image correlation and infrared thermography, for material identification. By employing heterogeneous, multi-axial data in conjunction with sophisticated inverse calibration techniques such as finite element model updating and the virtual fields method, MT2.0 aims to reduce the number of specimens needed for material identification and to increase confidence in the calibration results. To support continued development, improvement, and validation of such inverse methods—specifically for rate-dependent, temperature-dependent, and anisotropic metal plasticity models—we provide here a thorough experimental data set for 304L stainless steel sheet metal. The data set includes full-field displacement, strain, and temperature data for seven unique specimen geometries tested at different strain rates and in different material orientations. Commensurate extensometer strain data from tensile dog bones is provided as well for comparison. We believe this complete data set will be a valuable contribution to the experimental and computational mechanics communities, supporting continued advances in material identification methods.

Anisotropy of plastic flow in Zr-2.5Nb pressure tube material analysed using a viscoplastic self-consistent approach

Plastic anisotropy is observed during plastic flow in samples from the axial and transverse directions of Zr-2.5Nb pressure tubes used in CANDU11CANada Deuterium Uranium - Pressurized Heavy Water power reactors. nuclear reactors tested in uniaxial tension. Plastic anisotropy was also measured in shear by testing in torsion ‘mini’ pressure tubes from the same material. Room temperature results from these experiments were analysed using a visco-plastic self-consistent model that takes into account the crystallographic texture of the material and allows for the single crystal work hardening behaviour to be described by means of a deformation law specific to each slip system.The visco-plastic self-consistent model was used to derive: (i) the evolution with strain of the critical resolved shear stress values consistent with prismatic, basal and pyramidal dislocation glide, (ii) the evolution of slip system activity as a function of strain, and (iii) the values of Hill's plastic anisotropy coefficients that are consistent with the observed anisotropy of yielding and their dependence on accumulated strain. The model also allows for the prediction of the components of the flow stress tensor that cannot be measured experimentally and their dependence on the work hardening behaviour of pressure tube material. Moreover, the yield surface after different amounts of plastic strain was calculated using the visco-plastic self-consistent model, compared to the one that results from using the Hill's anisotropy coefficients. Our work exposes the limitations of the Hill ellipsoid for describing plastic yield when microstructural evolution is present.

A generalized, computationally versatile plasticity model framework - Part II: Theory and verification focusing on shear anisotropy

Shear-dominated deformation (SHDD) is pivotal in sheet metal forming; however, comprehensive modeling of plastic anisotropy in SHDD, specifically shear anisotropy considering both yield stress and plastic flow, has been inadequately addressed in existing literature. In this work, a generalized constitutive framework is introduced on the basis of stress triaxiality-dependent state variable to accurately emulate plastic anisotropy and the physics-based shear constraint in SHDD. The framework is capable to seamlessly integrate with existing yield criteria, preserving computational efficiency and versatility. Notably, the yield function, anisotropic parameters, and their optimization or analytical determination for the non-shear deformation state remain unaltered. When integrated with the Hill48 yield function, featuring either one or two anisotropic parameters within the generalized constitutive framework, precise characterization of yield strength and plastic flow in SHDD is achieved. The applicability of the framework extends to various anisotropic yield functions such as the widely employed Yld2k-2d and the sixth-order polynomial (Poly6) function as a class of associated flow rule-based yield functions, and one non-quadratic yield function for non-associated flow rule scenarios. Experimental validation with two engineering sheet metals, high-strength dual-phase steel DP980 and high-strength aluminum alloy AA7075-T6, was conducted. Comparative analyses with several recently proposed yield criteria, especially Poly6-18p, highlighted the efficiency of the proposed constitutive framework. Furthermore, this study explores intrinsic shear constraints, particularly the absence of through-thickness strains under in-plane shear stress. Additionally, it offers an enhanced description of plastic anisotropy in shear yield stress within the general framework, providing valuable insights into the complexities of SHDD.

Assessment of aluminium alloys’ formability by elevated temperature testing

Abstract This work presents an investigation of the warm formability of AA7075-T6 aluminium alloy sheets using both experimental and numerical methods. Forming limit diagrams (FLDs) can be created by plotting the failure criteria on a graph with two axes representing major and minor strains. Sheets with a grid can be used to quantify both large and minor strains. General techniques available for the grid involve regular patterns of circles in this experiment. Experiments were conducted at various temperature levels, including room temperature, 100, 120, 140, 160, and 180 °C, as well as different strain rates. The investigation has revealed a significant impact of temperature on formability, while the effect of forming speed is quite insignificant across the whole range studied. At an ageing temperature of 140 °C, the distribution of precipitates is evenly balanced, resulting in improved mechanical strength. To offer accurate numerical models for warm-forming processes, a proposed constitutive model is introduced for aluminium alloy sheets. The present model incorporates plastic anisotropy and the effects of temperature and strain rate dependence. An investigation was conducted on the stress-strain behaviour of thin sheets composed of AA7075-T6 aluminium alloy under elevated temperatures and different strain rates. The objective was to ascertain the appropriate fitting parameters. It was associated with ABAQUS finite element modelling. The recommended material model was utilized to build finite element models, which were subsequently compared to the experimental data. The findings obtained from simulated isothermal uniaxial tensile tests were compared to the empirical measurements. The models used in the tensile test accurately predicted the material’s mechanical response. The predicted failure location, punch forces, and strain distributions for all three forming processes were found to be in close agreement with the experimental results. During deep draw operation, the warm forming limit curves were utilized to precisely predict both the pierce depth at which failure occurs and the precise location where the failure initiates.

3D strain heterogeneity and fracture studied by X-ray tomography and crystal plasticity in an aluminium alloy

Strong correlations between measured strain fields and crystal plasticity finite element (CP-FE) predictions based on the real microstructure are found for a plane strain tensile specimen made of 6016 T4 aluminium alloy. This is achieved using multimodal X-ray lab tomography giving access to both the initial grain structure and the strain evolution. The real microstructure of the central region of interest (ROI) of the undeformed specimen is obtained non destructively using lab-based diffraction contrast tomography (DCT) and meshing. An in situ tensile test, using absorption contrast tomography (ACT) is then performed for twelve loading increments up to fracture. Taking advantage of the plane strain condition, the evolution of the internal strain field is measured by two-dimensional digital image correlation (DIC) in the material bulk using the natural speckle provided by intermetallic particles. Early strain heterogeneities in the form of slanted bands, that are spatially stable over time, are revealed and the fracture path – determined from the post mortem scan – is found to coincide with the bands exhibiting maximum strain. CP-FE simulations are performed on the meshed microstructure of the specimen acquired by DCT and are compared with image correlation measurements. The measured strain fields are well described by 3D CP-FE predictions, whilst it is shown that neither a macroscopic anisotropic plasticity model nor a CP-FE simulation with random grain orientations could reproduce the measurements.

Anisotropic Plasticity Behavior of Rolled 316L Ultra-Thin Sheet and Its Application to Micro-Deep Drawing Modeling

Anisotropic Plasticity Behavior of Rolled 316L Ultra-Thin Sheet and Its Application to Micro-Deep Drawing Modeling

Cross-rolling induced texture randomization and structural evolution for improved plastic isotropy in Al-Mg alloys with high Mg content

Plastic anisotropy is a key factor that affects the formability and performance of Al-Mg alloys. In this study, the effects of Mg content and strain path shifting from unidirectional rolling (UDR) to cross rolling processes (CR) on plastic anisotropy in Al-Mg alloys were investigated. Al-6 and 9Mg alloys were heat-treated and rolled in two different ways: the first was a UDR process, and the other was a CR process at room temperature. The rolled specimens were analyzed by electron backscattered diffraction method and tensile test. High Mg content suppresses the formation of texture that strengthens the plastic anisotropy in both UDR and CR processes. CR significantly reduces the rolling texture area fraction, leading to greater texture randomness compared to UDR. CR promotes the formation of low-angle deformation bands, which low-angle bands appear to have a weaker impact on deformation resistance and may contribute to the reduced anisotropy in CR-processed materials. CR results in a more uniform distribution of stored energy. R-value which represents plastic anisotropy decreases by shifting from UDR to CR, and by increment of Mg content. Overall, this study demonstrates that CR is a promising approach for improving the formability and performance of Al-Mg alloys by effectively controlling plastic anisotropy.

A study on anisotropic hardening of 7075 aluminum alloy based on non-associated flow rules

The accurate description of anisotropic plastic deformation is key to accurately predicting the stamping forming of metal sheets. The anisotropic yield criterion, when based on the assumption of isotropic hardening, often leads to significant inaccuracies. To address this issue, this paper observes the anisotropic hardening phenomenon through non-associated flow rules and evaluates the anisotropy of 7075-O aluminum alloy. Through a series of tensile tests, we determined the mechanical properties of 7075-O aluminum alloy in three distinct orientations. To describe the metal hardening behavior, we employed the Swift-Voce hardening criterion. From the hardening curves in three different directions, it was found that AA7075-O exhibits plastic anisotropy. Based on the VUMAT subroutine, finite element simulation of AA7075-O tensile tests was conducted through Abaqus. Compared with the Hill48 model, it was found that the simulated values of the S–Y2009 anisotropic hardening model have a higher degree of agreement with the experimental curves. The S–Y2009 anisotropic hardening model was adopted to predict the earing behavior of AA7075-O during circular cup deep drawing. The root mean square error between the predicted values of the S–Y2009 model and the experimental values was only 0.1795, which is far smaller than that of the Hill48 yield model. Therefore, the SY2009 model has important guiding significance for the stamping forming of metal sheets.

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.

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.

Interaction of defects, martensitic transformation and slip in metastable body centred cubic crystals of Ti-10V-2Fe-3Al: A study via crystal plasticity finite element methods (CPFEM)

Metastable β titanium alloys are widely applied in many industries. These alloys can have plastic deformation via dislocation slip, twinning, stress-induced martensite (SIM), or a combination of these. These alloys fail in a ductile manner via a process of void nucleation, growth, and coalescence. Inherent defects, such as voids, are commonly attributed to poor mechanical properties. In this study, aspects of plastic anisotropy in damage accumulation are investigated for metastable crystals that deform by combined slip and SIM. The focus of this study is to understand the evolution of damage due to inherent voids in metastable Ti-10V-2Fe-3Al single crystals. This investigation is conducted using crystal plasticity-based 3D finite element (FE) calculations. A unit-cell FE model involving a spherical void is deformed under constant stress triaxiality and lode parameter. We investigated four triaxiality values at differing lode parameters in three crystal orientations. The void growth was found to be heavily dependent on crystal orientation at low triaxialities. At higher triaxialities, SIM is found to inhibit the void growth via accommodation of the required deformation in the surrounding material. Orientations aligned favourable with SIM undergo significantly less void growth. The accommodation of deformation in the surrounding matrix was found to help preserve the integrity of the void, preventing the localisation of deformation around the void. At lower lode parameter and at higher stress triaxiality this impedes the exponential growth of the void. While, at higher lode parameter with low triaxiality SIM was found to delay the collapse of the void into a crack like morphology. This study not only deepens our understanding of the mechanical behaviour of metastable β titanium alloys, but also unveils the complex interplay between inherent defects, stress-induced martensite, and slip-based plasticity within their crystalline structure, offering fresh perspectives on enhancing material performance.

Stimulation characteristics of natural reservoir system under high-voltage electropulse-assisted fluid injection

This study elucidates the findings of a computational investigation into the stimulation characteristics of natural reservoir systems enhanced by high-voltage electropulse-assisted fluid injection. The presented methodology delineates the comprehensive rock-fracturing process induced by electropulse and subsequent fluid injection, encompassing the discharge circuit, plasma channel formation, shockwave propagation, and hydro-mechanical response. A hydromechanical model incorporating an anisotropic plastic damage constitutive law, discrete fracture networks, and heterogeneous distribution is developed to represent the natural reservoir system. The results demonstrate that high-voltage electropulse effectively generates intricate fracture networks, significantly enhances the hydraulic properties of reservoir systems, and mitigates the adverse impact of ground stress on fracturing. The stimulation-enhancing effect of electropulse is observed to intensify with increasing discharge voltage, with enhancements of 118.0%, 139.5%, and 169.0% corresponding to discharge voltages of 20 kV, 40 kV, and 60 kV, respectively. Additionally, a high-voltage electropulse with an initial voltage of U0 = 80 kV and capacitance C = 5 μF has been shown to augment the efficiency of injection activation to approximately 201.1% compared to scenarios without electropulse. Under the influence of high-voltage electropulse, the fluid pressure distribution diverges from the conventional single direction of maximum stress, extending over larger areas. These innovative methods and findings hold potential implications for optimizing reservoir stimulation in geo-energy engineering.

Towards improved description of plastic anisotropy in sheet metals under biaxial loading: A novel generalization of Hill48 yield criterion

Lightweight design and development of automobiles are strongly dependent on lightweight high-strength sheet metals. An accurate prediction of anisotropy and yield surface evolution of these materials under different sampling directions of biaxial tension (BT) is a necessary condition for the numerical analyses of stamping forming. In this work, the Hill48 model considering the principal stress direction is generalized to describe the anisotropic evolution and the yield loci on the normal and diagonal planes. The material parameters of the generalized M-Hill48 model (GM-Hill48) have analytical form and can be calibrated by the yield stresses and r-values expressed by the continuous equivalent plastic strain (EPS). A quadratic function interpolation method based on the near-plane strain (NPS) stress is established to control the yield locus under different plane stress states. In addition, a method for predicting the yield loci in arbitrary sampling directions under BT is proposed by tensor coordinate transformation. Different from the traditional model which can only determine material parameters by using equi-biaxial tension (EBT) or NPS stress along the rolling direction (RD) and transverse direction (TD), the yield stresses of BT in different sampling directions can be incorporated into the generalized model. The predictive capability of the GM-Hill48 model is verified by capturing the continuous evolution of yield stresses and strain for DP590 and AA6016-T4 materials. The convexity condition of the established modified model is given and discussed. Finally, the advantages of new model are further expounded in terms of the prediction accuracy and identified parameters compared with the advanced yield models.