International Journal of Plasticity最新文献_第10页

Mechanical response of metastable grain boundaries under shear deformation: A multi-scale study 剪切变形下亚稳晶界的力学响应：多尺度研究

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-24 DOI: 10.1016/j.ijplas.2025.104524

V.S. Krasnikov, K.D. Manukhina, F.T. Latypov, D.S. Voronin, A.E. Mayer

The work presents a multiscale investigation of deformation mechanisms in nanocrystalline (NC) aluminum, combining large-scale molecular dynamics (MD) simulations with machine learning techniques to transfer MD data into continuum mechanics simulation at macroscale. We examine symmetric tilt grain boundaries (GBs) with misorientation angles ranging from 8.79° (Σ85a) to 36.87° (Σ5), establishing the dependence of GB mechanical response on GB structure within fixed misorientation angle. Three distinct plastic relaxation mechanisms are identified: 1) GB migration in low-angle systems; 2) coupled GB sliding and grain rotation in intermediate- and high-angle systems; and 3) dislocation plasticity. The first two mechanisms (GB migration and coupled sliding/rotation) predominantly serve as the primary plastic relaxation pathways during initial deformation stages, while dislocation plasticity activates at the late deformation stages. The dislocation plasticity initiation depends on the primary deformation mechanism: 1) following GB migration, dislocation activity originates from segment emission at annihilation sites of the migrating dislocation walls; 2) in systems with GB sliding/rotation, the transition to dislocation-mediated plasticity occurs when localized GB stresses exceed critical thresholds (4–5 GPa in 1 nm regions). The timing of this transition varies significantly (50–600 ps) depending on GB character, reflecting fundamental differences in defect nucleation barriers between low-angle and high-angle GB systems. A new hardening phenomenon is discovered during GB sliding with grain rotation, resulting from arising normal stress components that oppose sliding. The MD results demonstrate that statistical treatment of atomistic-scale data is essential for reliable transfer to continuum-level modeling. Our analysis reveals critical aspects demanding careful statistical consideration: 1) GB migration stresses vary by 35–40%; 2) sliding activation stress shows 80% variation. The MD results are transferred to continuum modeling through an artificial neural network framework approximating plastic potential reconstructed from the MD. Implemented within smoothed particle hydrodynamics simulations, this data-driven approach provides an efficient procedure to transfer atomistic data to continuum level for prediction of NC aluminum behavior.

这项工作提出了纳米晶（NC）铝的变形机制的多尺度研究，将大规模分子动力学（MD）模拟与机器学习技术相结合，将MD数据转化为宏观尺度上的连续介质力学模拟。我们研究了取向角在8.79°（Σ85a）到36.87°（Σ5）之间的对称倾斜晶界（GB），建立了取向角固定的GB结构对GB力学响应的依赖关系。确定了三种不同的塑性松弛机制：1)GB在低角度体系中的迁移；2)中、高角度系统中GB滑动与颗粒旋转耦合；3)位错塑性。变形初期，前两种机制（GB迁移和滑动/旋转耦合）是主要的塑性松弛途径，而变形后期则激活位错塑性。位错塑性的产生取决于主要的变形机制：1)在GB迁移后，位错活动源于迁移位错壁湮灭部位的段发射；2)在GB滑动/旋转体系中，当局域GB应力超过临界阈值（1 nm区域4-5 GPa）时，会发生位错介导的塑性过渡。这种转变的时间根据国标特性有显著差异（50 - 600ps），反映了低角度和高角度国标体系之间缺陷成核屏障的根本差异。在晶粒旋转滑动过程中，由于产生了反对滑动的正应力分量，导致了一种新的硬化现象。MD结果表明，原子尺度数据的统计处理对于可靠地转移到连续级模型至关重要。我们的分析揭示了需要仔细统计考虑的关键方面：1)GB迁移压力变化35-40%；2)滑动激活应力呈现80%的变异。MD结果通过近似MD重建的塑性势的人工神经网络框架转移到连续体建模中。在光滑颗粒流体动力学模拟中实现，这种数据驱动的方法提供了一个有效的过程，将原子数据转移到连续体水平，用于预测NC铝的行为。

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引用次数: 0

Crystal plasticity modeling of hardening and creep in ferritic-martensitic alloys under thermal and irradiation environments 热环境和辐照环境下铁素体-马氏体合金硬化和蠕变的晶体塑性模拟

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-22 DOI: 10.1016/j.ijplas.2025.104513

Vikram Roy , I.A. Khan , Anirban Patra

A crystal plasticity constitutive modeling framework is presented to model the inelastic deformation behavior of unirradiated and irradiated ferritic-martensitic steels. The model considers dislocation densities that evolve during inelastic deformation, as well as irradiation-induced defect densities and their sizes, as internal state variables. The model accounts for key deformation mechanisms - dislocation glide and climb - as well as the microstructural effects governing hardening, thermal creep, irradiation hardening, and irradiation creep. The model accounts for the effects of temperature, strain rate, and irradiation dose on hardening, and successfully reproduces the stress and temperature dependence of both thermal and irradiation creep. Validation against multiple experimental datasets confirms that the model predictions fall within the range of experimentally observed variability, particularly in predicting the irradiation-induced hardening and the steady-state creep rates across a wide range of thermal and irradiation conditions. Overall, this work establishes a robust, mechanistic framework for predicting the elevated temperature, irradiation-induced deformation behavior of ferritic-martensitic steels.

提出了一种晶体塑性本构建模框架，用于模拟辐照和辐照铁素体-马氏体钢的非弹性变形行为。该模型考虑了在非弹性变形过程中演变的位错密度，以及辐照引起的缺陷密度及其尺寸，作为内部状态变量。该模型考虑了关键的变形机制-位错滑动和爬升-以及控制硬化、热蠕变、辐照硬化和辐照蠕变的微观组织效应。该模型考虑了温度、应变速率和辐照剂量对硬化的影响，成功地再现了热蠕变和辐照蠕变的应力和温度依赖关系。对多个实验数据集的验证证实，该模型预测在实验观察到的变异性范围内，特别是在预测辐照诱导硬化和稳态蠕变率时，在广泛的热和辐照条件下。总的来说，这项工作为预测铁素体-马氏体钢的高温、辐照引起的变形行为建立了一个强大的机制框架。

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引用次数: 0

An anisotropic damage-coupled cyclic plastic model for whole-life ratcheting of carbide-free bainitic rail steels considering the martensitic transformation 考虑马氏体相变的无碳化物贝氏体钢轨钢全寿命棘轮损伤的各向异性损伤耦合循环塑性模型

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-22 DOI: 10.1016/j.ijplas.2025.104523

Xiang Xu , Peilin Fu , Yusong Fan , Chao Yu , Jianping Zhao , Guhui Gao , Ping Wang , Zefeng Wen , Guozheng Kang , Qianhua Kan

The fatigue damage evolution of carbide-free bainitic (CFB) rail steels is highly complicated due to their unique deformation mechanisms and ratcheting-fatigue interaction. To account for the effects of martensitic transformation and damage on the whole-life ratcheting of CFB rail steels, an anisotropic damage-coupled cyclic plastic model is developed. The isotropic resistance and back stress associated with the transformation hardening induced by plastic deformation are incorporated into the transformation driving force, enabling a more reasonable description of martensitic transformation in cyclic softening materials. Moreover, the martensitic volume fraction and maximum equivalent plastic strain are coupled into the damage evolution equation to reflect the adverse effect of martensitic transformation on the fatigue life and damage acceleration caused by the ratcheting. The proposed model reasonably captures the evolution of the damage variable and martensitic volume fraction during cyclic loading, and accurately predicts the fatigue life of the material under various uniaxial and multiaxial cyclic loading conditions, providing a theoretical foundation for evaluating the long-term service behavior of CFB rails during rolling contact.

无碳化物贝氏体钢轨钢具有独特的变形机制和棘轮-疲劳相互作用，其疲劳损伤演化过程非常复杂。为了考虑马氏体相变和损伤对循环流化床钢轨全寿命棘轮的影响，建立了各向异性损伤耦合循环塑性模型。将与塑性变形引起的相变硬化相关的各向同性阻力和背应力纳入相变驱动力，使循环软化材料的马氏体相变得到更合理的描述。将马氏体体积分数和最大等效塑性应变耦合到损伤演化方程中，以反映马氏体相变对棘轮引起的疲劳寿命和损伤加速的不利影响。该模型合理地捕捉了循环加载过程中损伤变量和马氏体体积分数的演变规律，准确预测了材料在不同单轴和多轴循环加载条件下的疲劳寿命，为评价循环流化床钢轨在滚动接触过程中的长期使用行为提供了理论基础。

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引用次数: 0

κ-carbide induced dual-heterogeneous structure pursuing ultrahigh strength and ductility in lightweight steels 轻钢中追求超高强度和延展性的κ-碳化物诱导双非均相组织

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-22 DOI: 10.1016/j.ijplas.2025.104512

Xiaofeng Fan , Yizhuang Li , Jikui Liu , Mingxin Huang , Wei Xu

Utilizing κ-carbide precipitation offers a promising strengthening approach for austenitic lightweight steels. However, coarse intragranular and grain-boundary κ-carbides formed during aging typically promote dynamic slip band localization, reducing work-hardening rates and even triggering brittle fracture. Here, we present an austenitic lightweight steel with a dual-heterogeneous lamellar microstructure, achieved via κ-carbide–mediated recrystallization. After a short, measured high-temperature exposure, heterogeneous nucleation and incomplete dissolution of κ-carbides during recrystallization create a multi-scale precipitate-strengthened hetero-lamellar grain structure. This structure promotes extensive dislocation proliferation, thereby maintaining high strain hardening even at elevated stress levels. Coordinated deformation is facilitated by strain partitioning across multi-level soft/hard domains, while hierarchical shear deformation of κ-carbides progressively relieves interfacial stress concentrations. Additionally, nanoscale local chemical order clusters further elevate the matrix strength to critical levels, activating supplementary twinning-induced plasticity. This strategy resolves the longstanding conflict between κ-carbide strengthening and ductility, achieving an exceptional synergy of properties: ultra-high yield strength (1.1 GPa), ultimate tensile strength (1.32 GPa), remarkable elongation (46 %), and sustained high work-hardening capability. Our work offers a new approach for overcoming the strength-ductility trade-off in precipitation-strengthened austenitic steels and provides guidance for producing next-generation ultra-strong lightweight alloys via spatially engineered heterostructures.

利用κ碳化物析出为奥氏体轻钢的强化提供了一种很有前途的方法。然而，时效过程中形成的粗晶内和晶界碳化物通常会促进动态滑移带局部化，降低加工硬化速率，甚至引发脆性断裂。在这里，我们提出了一种奥氏体轻钢，具有双非均相片层组织，通过κ碳化物介导的再结晶实现。经过短暂的高温暴露后，在再结晶过程中，κ碳化物的非均质成核和不完全溶解形成了多尺度的析出强化异质层状晶粒结构。这种结构促进了广泛的位错扩散，从而即使在高应力水平下也能保持高应变硬化。多级软/硬区域的应变分配促进了协调变形，而κ-碳化物的分层剪切变形逐渐缓解了界面应力集中。此外，纳米尺度的局部化学有序团簇进一步将基体强度提升到临界水平，激活补充孪晶诱导的塑性。该策略解决了长期以来κ-碳化物强化和延展性之间的矛盾，实现了优异的性能协同：超高屈服强度（1.1 GPa）、极限抗拉强度（1.32 GPa）、显著伸长率（46%）和持续的高加工硬化能力。我们的工作为克服沉淀强化奥氏体钢的强度-延性权衡提供了一种新方法，并为通过空间工程异质结构生产下一代超强轻质合金提供了指导。

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引用次数: 0

Multiple-mechanism and microstructure-based crystal plasticity simulation of cyclic deformation in TRIP-assisted duplex stainless steels 基于trip辅助双相不锈钢循环变形多机制和显微组织的晶体塑性模拟

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-22 DOI: 10.1016/j.ijplas.2025.104521

Xiaolong Li , Miao Jin , Qingling Zhang , Yinqiang Wang , Xiaocong Ma , Shiyan Zhao , Lei Chen , Xingzhou Cai

Transformation-induced plasticity (TRIP) - assisted duplex stainless steels (DSSs) are widely used in industrial applications due to their significantly reduced density, as well as the excellent ductility and work hardening capability induced by the TRIP effect. Cyclic loading is commonly encountered in their industrial applications. Therefore, studying the cyclic plastic behavior of TRIP-assisted DSSs is of significant importance. The cyclic deformation behavior and its micro-mechanisms were investigated through mechanical experiments, EBSD, and TEM characterization. Subsequently, a physical-based crystal plasticity constitutive model, incorporating multiple mechanisms such as dislocation density evolution in the ferrite and martensitic transformation in the austenite, was developed and implemented in ABAQUS with the UMAT subroutine. A 3D-RVE was established, and the model was calibrated and validated based on the material’s cyclic mechanical response, martensitic volume fraction, and dislocation density evolution. Additionally, a 2.5D-RVE was established based on EBSD data to simulate the cyclic deformation behavior of the material. The computational results indicate that the occurrence of martensitic transformation requires the combined effect of the stress level and Schmid factor in the austenite grains, both of which are influenced by the austenite grain orientations. A high stress level in the austenite grains increases the resolved shear stress on partial fault-bands in adjacent austenite grains, thus promoting phase transformation in the grain boundary regions of the neighboring austenite grains. Due to its lower yield strength, ferrite is more prone to plastic deformation. The resolved shear stress of the activated slip systems will indirectly increase the resolved shear stress on partial fault-bands in adjacent austenite grains, further promoting phase transformation at the phase boundary regions of the austenite grains.

相变诱导塑性（TRIP）辅助双相不锈钢（DSSs）由于其显著降低密度，以及TRIP效应诱导的优异的延展性和加工硬化能力而广泛应用于工业应用。循环加载是工业应用中经常遇到的问题。因此，研究trip辅助DSSs的循环塑性行为具有重要意义。通过力学实验、EBSD和TEM表征研究了复合材料的循环变形行为及其微观机制。随后，利用UMAT子程序在ABAQUS中开发并实现了基于物理的晶体塑性本构模型，该模型包含铁素体中的位错密度演变和奥氏体中的马氏体相变等多种机制。建立3D-RVE模型，根据材料的循环力学响应、马氏体体积分数和位错密度演变对模型进行校准和验证。此外，基于EBSD数据建立2.5D-RVE，模拟材料的循环变形行为。计算结果表明，马氏体相变的发生需要奥氏体晶粒中的应力水平和施密德因子的共同作用，二者均受奥氏体晶粒取向的影响。奥氏体晶粒中的高应力水平增加了相邻奥氏体晶粒部分断裂带上的可分解剪切应力，从而促进了相邻奥氏体晶粒晶界区域的相变。由于屈服强度较低，铁素体更易发生塑性变形。激活滑移体系的分解剪切应力会间接增加邻近奥氏体晶粒部分断裂带上的分解剪切应力，进一步促进奥氏体晶粒相界区域的相变。

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引用次数: 0

Dynamic mechanical response and constitutive model of tungsten-particle-reinforced Zr-based bulk-metallic-glass composites 钨颗粒增强zr基大块金属-玻璃复合材料的动态力学响应及本构模型

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-21 DOI: 10.1016/j.ijplas.2025.104509

Yunfei Ma , Pan Gong , Mao Zhang , Binghui Deng , Maojun Li , Changqing Sun , Dabo Liu , Fei Hu , Xuxiao Yang , Xinyun Wang

Achieving both high strength and sufficient plasticity in metallic materials under dynamic loading remains a longstanding challenge. In this study, tungsten-particle-reinforced bulk metallic glass composites (W_p/BMGCs) were fabricated via spark plasma sintering (SPS), and their dynamic compressive mechanical properties were systematically investigated at high strain rates (10³ ∼ 5 × 10³ s⁻¹). The results show that W_p/BMGCs exhibit outstanding dynamic performance, with a yield strength of 4000 MPa, a plastic strain of 12 %, and positive strain rate sensitivity. This enhanced behavior originates from interfacial strain gradients generated by the inherent elastic modulus mismatch between W_p and the metallic glass matrix, which induce the accumulation of geometrically necessary dislocations (GNDs) within the W_p. Under dynamic loading, the dislocation-free, high shear-strength metallic glass matrix exerts a back-stress on dislocations in adjacent W_p, thereby impeding dislocation glide and enhancing the apparent deformation resistance of the W_p phase. Additionally, W_p effectively suppress catastrophic shear band propagation while promoting the nucleation and proliferation of multiple secondary shear bands in the matrix. This dual mechanism significantly improves phase-coordinated deformation, ultimately contributing to the superior yield strength and plastic strain. Based on these insights, a dislocation-based strengthening mechanism was incorporated into the Johnson-Cook constitutive model. The modified framework accurately captures the effects of particle size and volume fraction on the dynamic response, showing strong agreement with experimental results.

金属材料在动载荷下实现高强度和足够塑性是一个长期的挑战。本研究通过火花等离子烧结（SPS）制备了钨颗粒增强大块金属玻璃复合材料（Wp/BMGCs），并系统地研究了其在高应变速率（10³~ 5 × 10³s⁻¹）下的动态压缩力学性能。结果表明，Wp/BMGCs具有优异的动态性能，屈服强度达4000 MPa，塑性应变为12%，应变率敏感性为正。这种增强的行为源于Wp与金属玻璃基体之间固有弹性模量不匹配所产生的界面应变梯度，这导致了Wp内部几何必要位错（GNDs）的积累。在动载荷作用下，无位错的高剪切强度金属玻璃基体对相邻Wp中的位错施加背应力，从而阻碍位错滑动，增强Wp相的表观抗变形能力。此外，Wp有效抑制了突变剪切带的扩展，同时促进了基体中多个次级剪切带的形核和增殖。这种双重机制显著改善了相协调变形，最终提高了屈服强度和塑性应变。基于这些见解，基于位错的强化机制被纳入Johnson-Cook本构模型。修正后的框架准确地反映了粒径和体积分数对动态响应的影响，与实验结果吻合较好。

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引用次数: 0

Unsupervised mechanism-informed neural network modeling of plastic hardening in rafted Ni-based single crystal alloys 筏形镍基单晶合金塑性硬化的无监督机制神经网络建模

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-21 DOI: 10.1016/j.ijplas.2025.104507

Huanbo Weng , Cheng Luo , Huang Yuan

Rafted nickel-based single-crystal alloys exhibit directionally dependent mechanical degradation, necessitating the integration of anisotropic microstructural characteristics into macroscopic single-crystal plasticity models. This study presents a new mechanism-informed neural network (MINN)-based multi-scale crystal plasticity framework coupled with microstructural fabric tensors to address this challenge. The proposed model incorporates single-crystal slip deformation mechanisms and utilizes 12 sets of measurable physical quantities, including stress, strain, and microstructural parameters, as input and output variables to derive microstructure-sensitive hardening models in an unsupervised manner. Isotropic and deviatoric fabric tensors are decomposed into individual slip systems, directly influencing material plastic flow. The investigations reveal that the isotropic component’s magnitude correlates with microstructural channel width, modulating slip system strain rates, while the deviatoric component’s direction and magnitude jointly govern flow and hardening behavior on the slip systems. These insights enhance the understanding of the multi-scale mechanical behavior of single-crystal alloys and provide a foundation for constitutive modeling. Meanwhile, the proposed framework offers innovative methods and research paradigms to investigate slip deformation mechanisms in anisotropic crystalline alloys.

泛化镍基单晶合金表现出方向依赖的力学退化，需要将各向异性的微观组织特征整合到宏观单晶塑性模型中。本研究提出了一种新的基于机制的神经网络（MINN）的多尺度晶体塑性框架，结合微结构织物张量来解决这一挑战。该模型包含单晶滑移变形机制，并利用12组可测量的物理量（包括应力、应变和微观结构参数）作为输入和输出变量，以无监督的方式推导出微观结构敏感的硬化模型。各向同性和偏性织物张量被分解成单独的滑移系统，直接影响材料的塑性流动。研究表明，各向同性分量的大小与微观结构通道宽度相关，调节滑移系统的应变速率，而偏性分量的方向和大小共同控制滑移系统的流动和硬化行为。这些见解增强了对单晶合金多尺度力学行为的理解，并为本构建模提供了基础。同时，该框架为研究各向异性晶体合金的滑移变形机制提供了创新的方法和研究范式。

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引用次数: 0

Insight into the transition from diffuse microcracking to localized macrocracking in saturated quasi-brittle media: Micro-poromechanics-based approach and analytical solutions 饱和准脆性介质中从扩散微裂纹到局部宏观裂纹的转变：基于微孔隙力学的方法和解析解

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-18 DOI: 10.1016/j.ijplas.2025.104508

Lunyang Zhao , Linghui Liu , Yuanming Lai , Qizhi Zhu , Jianfu Shao

In this paper, a new micro-poromechanics-based approach is developed for modeling progressive failure process in saturated quasi-brittle media (SQBM) under compression-dominating stresses. The emphasis is put on the transition from diffuse microcracking to localized macrocracking by incorporating poromechanical interaction. A micro-poromechanical model is first established for the description of diffuse damage and frictional sliding of microcracks by combining linear homogenization and irreversible thermodynamics. In particular, the concept of effective stress in the context of damage mechanics is revisited. The role of fluid pressure in cracking process is clarified. The onset of localized macrocracking is then described as stemming from the coalescence of microcracks when the diffuse damage density parameter reaches a critical value. After that transition point, the dissipation process in the SQBM is primarily attributed to the evolution of localized cracks. Within this frame, an anisotropic poromechanical model is developed for modeling the growth and frictional sliding of oriented localized macrocrack whose orientation is analytically determined and depends on loading path. The displacement discontinuity across the macrocrack can be evaluated. For assessing the performance of proposed approach, a set of examples are examined, including drained and undrained triaxial compression tests. In particular, analytical solutions are obtained and compared with existing experimental data, in terms of stress–strain relations, porosity and fluid pressure evolution, and the transition from diffuse damage to localized cracking.

本文提出了一种基于微孔力学的模拟饱和准脆性介质在压缩主导应力作用下渐进破坏过程的新方法。重点讨论了由扩散型微裂纹向局域型宏观裂纹过渡的过程。将线性均匀化和不可逆热力学相结合，首次建立了描述微裂纹扩散损伤和摩擦滑动的微孔力学模型。特别是，在损伤力学的背景下，有效应力的概念被重新审视。阐明了流体压力在裂化过程中的作用。局部宏观裂纹的发生被描述为当扩散损伤密度参数达到临界值时微裂纹的合并。在该过渡点之后，SQBM中的耗散过程主要归因于局部裂纹的演化。在此框架下，建立了一个各向异性的孔隙力学模型，用于模拟定向局部大裂纹的扩展和摩擦滑动，定向局部大裂纹的取向是解析确定的，取决于加载路径。可以评估跨大裂纹的位移不连续。为了评估所提出的方法的性能，研究了一组示例，包括排水和不排水三轴压缩试验。特别是在应力-应变关系、孔隙度和流体压力演化以及从弥漫性损伤到局部开裂的转变方面，得到了解析解，并与已有的实验数据进行了对比。

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引用次数: 0

Unveiling creep mechanisms in metallic glasses via fractional modeling under coupled thermo-mechanical loads 热-机械耦合载荷下金属玻璃蠕变机理的分式建模

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-17 DOI: 10.1016/j.ijplas.2025.104511

J.B. Cui , G.H. Xing , Guo-Jian Lyu , Yun-Jiang Wang , T. Wada , H. Kato , V.A. Khonik , Y. Yang , J.C. Qiao

This study systematically investigates the creep behavior of Pd₂₀Pt₂₀Cu₂₀Ni₂₀P₂₀ metallic glass under varying temperatures and applied stresses. To accurately capture its time-dependent deformation response, a fractional Burgers model is proposed by extending the classical Burgers framework using fractional calculus. The model demonstrates excellent agreement with experimental data and offers physically interpretable parameters that describe the inelastic response of material. With increasing temperature, the quasi-steady-state creep strain rate increases significantly, accompanied by a notable reduction in the apparent viscosity. The viscosity-related parameters exhibit thermally activated behavior, while the fractional orders α_₁ and α_₂ also increase with temperature, indicating enhanced atomic mobility. The validity of the model is further supported by dynamic mechanical analysis, in which the temperature-dependent trends of storage and loss moduli align closely with model predictions. In contrast, increasing the stress primarily accelerates the creep rate but exerts only a limited influence on viscosity and the evolution of fractional parameters, suggesting that temperature plays a more dominant role than stress in determining creep kinetics. Creep experiments conducted on samples with different degrees of physical aging reveal that structural relaxation primarily suppresses the initial transient anelastic strain, while the quasi-steady-state stage remains largely unaffected. Finally, a comparative analysis among metallic glasses with different β relaxation features shows that alloys exhibiting more pronounced β relaxation tend to possess higher α_₁ and α_₂ values, underscoring the critical role of β relaxation in mediating intrinsic ductility and deformation behavior below the glass transition temperature in metallic glasses.

本研究系统地研究了Pd20Pt20Cu20Ni20P20金属玻璃在不同温度和外加应力下的蠕变行为。为了准确地捕捉其随时间变化的变形响应，利用分数阶微积分对经典Burgers框架进行扩展，提出了分数阶Burgers模型。该模型与实验数据非常吻合，并提供了描述材料非弹性响应的物理可解释参数。随着温度的升高，准稳态蠕变应变率显著增大，表观粘度显著降低。黏度相关参数表现为热活化行为，α 1和α 2分数阶也随温度升高而增加，表明原子迁移率增强。动态力学分析进一步支持了模型的有效性，其中储存和损失模量的温度依赖趋势与模型预测密切相关。相比之下，增加应力主要加速蠕变速率，但对粘度和分数参数的演变影响有限，这表明温度在决定蠕变动力学方面比应力起更大的作用。对不同物理时效程度试样的蠕变试验表明，结构松弛主要抑制初始瞬态非弹性应变，而准稳态阶段基本不受影响。最后，对具有不同β弛豫特征的金属玻璃的对比分析表明，β弛豫特征更明显的合金具有更高的α 1和α 2值，强调了β弛豫在金属玻璃玻璃化转变温度以下的内在延性和变形行为中的关键作用。

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引用次数: 0

A concise fracture model for ductile metals: Integration of symbolic regression and strength theory 一种简捷的韧性金属断裂模型：符号回归与强度理论的整合

IF 12.8 1区材料科学 Q1 ENGINEERING, MECHANICAL

International Journal of Plasticity

Pub Date : 2025-10-14 DOI: 10.1016/j.ijplas.2025.104506

Ning Li , Jiaxuan Sun , Tao Suo , Yulong Li , Yazhou Guo

An ideal fracture model for engineering applications should accurately predict fracture behavior across various ductile metals while maintaining a concise formulation with minimal fitting parameters. By comparing the roles of weak constraints (derived from microscopic mechanism analysis) and strong constraints (based on strength theories) in symbolic regression, two fracture models are proposed: the theory and symbolic regression-based fracture model (TSR-F model) and the extended symbolic regression-based fracture model (ESR-F model). Symbolic regression, when applied under strong constraints, is able to effectively derive generalized fracture model for various ductile metals using limited experimental data. The effectiveness and accuracy of the models are validated through experiments on 26 types of metals, demonstrating their applicability across a wide range of materials and over a broad range of stress triaxiality and Lode angle parameters, where the ESR-F model shows superior performance. Moreover, the performance of the TSR-F model is close to that of the ESR-F model, which indicates the critical importance of incorporating appropriate constraints in symbolic regression. Furthermore, while the strong constraints are introduced through the generalization of the von Mises and Maximum Mohr-Coulomb criteria for isotropic metals, one may be compelled to neglect anisotropy induced under low-triaxiality ductile fracture to avoid overly complicated expressions. This study demonstrates the potential of symbolic regression methods with suitable strong theoretical constraints to develop universal expressions of mechanical models using limited experimental data.

工程应用的理想断裂模型应该能够准确地预测各种延性金属的断裂行为，同时保持简洁的公式和最小的拟合参数。通过对比弱约束（基于微观机理分析）和强约束（基于强度理论）在符号回归中的作用，提出了两种断裂模型：基于理论和符号回归的断裂模型（TSR-F模型）和扩展符号回归的断裂模型（ESR-F模型）。符号回归在强约束条件下，能够利用有限的实验数据，有效地推导出各种延性金属的广义断裂模型。通过对26种金属的实验验证了模型的有效性和准确性，证明了它们在广泛的材料和应力三轴性和Lode角参数范围内的适用性，其中ESR-F模型表现出优越的性能。此外，TSR-F模型的性能接近ESR-F模型，这表明在符号回归中加入适当的约束至关重要。此外，虽然通过对各向同性金属的von Mises和Maximum Mohr-Coulomb准则的推广引入了强约束，但为了避免过于复杂的表达式，人们可能不得不忽略低三轴韧性断裂引起的各向异性。本研究证明了具有适当的强理论约束的符号回归方法的潜力，可以利用有限的实验数据开发力学模型的通用表达式。

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引用次数: 0