Pub Date : 2025-10-01DOI: 10.1016/j.ijplas.2025.104494
Xu Zhang , Takashi Sumigawa
Understanding and defining intrinsic length-scales is the key to developing continuum plasticity theories that accurately capture size-dependent behaviors. This study presents a cross-scale stress gradient plasticity (C-σGP) theory that couples the dynamics of soft dislocation pile-up in stress gradients with continuum mechanics without resorting to phenomenological hardening laws. The theory explicitly incorporates four material length-scales: slip-band spacing, dislocation source length, dislocation pile-up length, and boundary layer thickness. We implemented the C-σGP model using an implicit algorithm to simulate the pure bending behavior of single-crystalline microbeams. Results show that only two intrinsic length-scales are required to capture the size-dependent bending strength at different strain stages. One is the source length that controls the yield strength, and the other is the slip-band spacing which governs the post‑yield hardening. Moreover, this study reveals for the first time how the evolution of slip-band spacing with plastic strain significantly affect the strain‑hardening rate and flow intermittency observed at micro‑ and sub‑micron scales. By identifying and quantifying these intrinsic lengths, the C-σGP framework provides a physically grounded foundation for future gradient‑enhanced plasticity models of small‑scale structures.
{"title":"A cross-scale stress gradient plasticity theory for length-scale effects on hardening behaviors of microbeam bending","authors":"Xu Zhang , Takashi Sumigawa","doi":"10.1016/j.ijplas.2025.104494","DOIUrl":"10.1016/j.ijplas.2025.104494","url":null,"abstract":"<div><div>Understanding and defining intrinsic length-scales is the key to developing continuum plasticity theories that accurately capture size-dependent behaviors. This study presents a cross-scale stress gradient plasticity (C-σGP) theory that couples the dynamics of soft dislocation pile-up in stress gradients with continuum mechanics without resorting to phenomenological hardening laws. The theory explicitly incorporates four material length-scales: slip-band spacing, dislocation source length, dislocation pile-up length, and boundary layer thickness. We implemented the C-σGP model using an implicit algorithm to simulate the pure bending behavior of single-crystalline microbeams. Results show that only two intrinsic length-scales are required to capture the size-dependent bending strength at different strain stages. One is the source length that controls the yield strength, and the other is the slip-band spacing which governs the post‑yield hardening. Moreover, this study reveals for the first time how the evolution of slip-band spacing with plastic strain significantly affect the strain‑hardening rate and flow intermittency observed at micro‑ and sub‑micron scales. By identifying and quantifying these intrinsic lengths, the C-σGP framework provides a physically grounded foundation for future gradient‑enhanced plasticity models of small‑scale structures.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104494"},"PeriodicalIF":12.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145195420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-30DOI: 10.1016/j.ijplas.2025.104493
Chen Zhou , Wenyi Hu , Qichi Le , Yingbin Lin , Tong Wang , Hansol Jeon , Qiyu Liao , Chenglu Hu , Long Liu , Yatong Zhu , Xiuzhen Xie
This study investigates the underlying slip/twinning mechanisms in an extruded Mg-Gd-Y-Zn-Zr alloy with a fiber coarse grain-ultrafine grain (FCG-UFG) heterostructure under various strain paths, combining experimental characterization and Visco-Plastic Self-Sonsistent modeling incorporating Predominant Twin Reorientation (VPSC-PTR). The material constants in the VPSC-PTR model were inversely calibrated using Schmid factor (SF)-corrected grain reference orientation deviation (GROD) data. The VPSC-PTR model was skillfully employed to quantitatively distinguish deformation mechanisms and texture evolution between coarse and fine grains in bimodal Mg alloys, demonstrating its strong potential for broader applications in heterostructured alloys. The results show that under both tension and compression, the UFG region initially accommodates plastic strain mainly through basal 〈a〉 slip. This produces a pronounced strain gradient at FCG grain boundaries, stimulating adjacent FCG grains—initially in hard orientations for basal 〈a〉 slip—to activate prismatic 〈a〉 slip and pyramidal 〈c + a〉 slip. The divergence in deformation mechanisms between FCG and UFG regions and the resulting mechanical incompatibility act synergistically to enhance hetero-deformation induced (HDI) strengthening, leading to simultaneous improvements in strength and ductility. Furthermore, the alloy exhibits an uncommon reversed tension-compression yield asymmetry (/ > 1). This behavior originates from the high critical stress required for kinking deformation of LPSO phases under compression, coupled with the suppression of conventional {10–12} extension twinning, which collectively reverse the typical twin-dominated yield asymmetry seen in conventional Mg alloys. Owing to its weak basal texture, the UFG region deforms mainly via basal 〈a〉 slip under various strain paths, contributing little to compressive anisotropy. In contrast, the orientation-dependent competition between basal and non-basal 〈a〉 slip within FCG grains, along with the distribution characteristics of LPSO phases, governs compressive mechanical anisotropy. GROD analysis further indicates that {10–12} extension twins promote the activation of pyramidal 〈c + a〉 slip. The introduction of twins and associated 〈c + a〉 dislocations effectively alleviates local stress concentrations and enhances plasticity in FCG regions, thereby delaying fracture. These findings provide new insights into the deformation mechanisms of heterostructured Mg alloys under multi-directional loading and will facilitate the design of high-performance Mg alloys with reduced tension-compression asymmetry and mechanical anisotropy.
本研究结合实验表征和含优势孪晶重取向（VPSC-PTR）的粘塑性自一致模型，研究了不同应变路径下具有纤维粗晶-超细晶（FCG-UFG）异质结构的Mg-Gd-Y-Zn-Zr挤压合金的潜在滑移/孪晶机制。利用施密德因子（SF）校正的晶粒参考取向偏差（GROD）数据反演VPSC-PTR模型中的材料常数。采用VPSC-PTR模型定量区分了双峰态镁合金中粗晶和细晶的变形机制和织构演变，显示了该模型在异质组织合金中的广泛应用潜力。结果表明：在拉伸和压缩作用下，UFG区主要通过基底滑移来初始容纳塑性应变；这在FCG晶界处产生了明显的应变梯度，刺激相邻的FCG晶粒——最初是在基底< a >滑移的硬取向上——激活棱柱状< a >滑移和锥体< c + > a >滑移。FCG和UFG区域之间变形机制的差异以及由此产生的力学不相容协同作用，增强了异质变形诱导（HDI）强化，从而同时提高了强度和延性。此外，合金表现出罕见的反向拉压屈服不对称性（σyC/σyT > 1）。这种行为源于压缩下LPSO相扭结变形所需的高临界应力，加上常规{10-12}扩展孪晶的抑制，共同扭转了传统镁合金中典型的孪晶主导屈服不对称。由于其基底织构较弱，在各种应变路径下，UFG区域主要通过基底< a >滑移进行变形，对压缩各向异性的贡献较小。相反，FCG颗粒内基底和非基底< a >滑移之间的定向竞争，以及LPSO相的分布特征，决定了压缩力学各向异性。GROD分析进一步表明，{10-12}伸展孪晶促进锥体< c + a >滑移的激活。双胞胎和相关的< c + a >位错的引入有效地缓解了局部应力集中，增强了FCG区域的塑性，从而延缓了断裂。这些发现为多向加载下异质组织镁合金的变形机制提供了新的见解，将有助于设计出具有降低拉压不对称性和力学各向异性的高性能镁合金。
{"title":"Revealing the underlying slip/twinning mechanisms of tension-compression asymmetry and anisotropy in Mg-Gd-Y-Zn-Zr alloys with heterostructure","authors":"Chen Zhou , Wenyi Hu , Qichi Le , Yingbin Lin , Tong Wang , Hansol Jeon , Qiyu Liao , Chenglu Hu , Long Liu , Yatong Zhu , Xiuzhen Xie","doi":"10.1016/j.ijplas.2025.104493","DOIUrl":"10.1016/j.ijplas.2025.104493","url":null,"abstract":"<div><div>This study investigates the underlying slip/twinning mechanisms in an extruded Mg-Gd-Y-Zn-Zr alloy with a fiber coarse grain-ultrafine grain (FCG-UFG) heterostructure under various strain paths, combining experimental characterization and Visco-Plastic Self-Sonsistent modeling incorporating Predominant Twin Reorientation (VPSC-PTR). The material constants in the VPSC-PTR model were inversely calibrated using Schmid factor (SF)-corrected grain reference orientation deviation (GROD) data. The VPSC-PTR model was skillfully employed to quantitatively distinguish deformation mechanisms and texture evolution between coarse and fine grains in bimodal Mg alloys, demonstrating its strong potential for broader applications in heterostructured alloys. The results show that under both tension and compression, the UFG region initially accommodates plastic strain mainly through basal 〈a〉 slip. This produces a pronounced strain gradient at FCG grain boundaries, stimulating adjacent FCG grains—initially in hard orientations for basal 〈a〉 slip—to activate prismatic 〈a〉 slip and pyramidal 〈<em>c</em> + <em>a</em>〉 slip. The divergence in deformation mechanisms between FCG and UFG regions and the resulting mechanical incompatibility act synergistically to enhance hetero-deformation induced (HDI) strengthening, leading to simultaneous improvements in strength and ductility. Furthermore, the alloy exhibits an uncommon reversed tension-compression yield asymmetry (<span><math><msubsup><mi>σ</mi><mi>y</mi><mi>C</mi></msubsup></math></span>/<span><math><msubsup><mi>σ</mi><mi>y</mi><mi>T</mi></msubsup></math></span> > 1). This behavior originates from the high critical stress required for kinking deformation of LPSO phases under compression, coupled with the suppression of conventional {10–12} extension twinning, which collectively reverse the typical twin-dominated yield asymmetry seen in conventional Mg alloys. Owing to its weak basal texture, the UFG region deforms mainly via basal 〈a〉 slip under various strain paths, contributing little to compressive anisotropy. In contrast, the orientation-dependent competition between basal and non-basal 〈a〉 slip within FCG grains, along with the distribution characteristics of LPSO phases, governs compressive mechanical anisotropy. GROD analysis further indicates that {10–12} extension twins promote the activation of pyramidal 〈<em>c</em> + <em>a</em>〉 slip. The introduction of twins and associated 〈<em>c</em> + <em>a</em>〉 dislocations effectively alleviates local stress concentrations and enhances plasticity in FCG regions, thereby delaying fracture. These findings provide new insights into the deformation mechanisms of heterostructured Mg alloys under multi-directional loading and will facilitate the design of high-performance Mg alloys with reduced tension-compression asymmetry and mechanical anisotropy.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104493"},"PeriodicalIF":12.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145188986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-27DOI: 10.1016/j.ijplas.2025.104492
S.P. Murugan, Y. Ben Jedidia, X. Feaugas, A. Oudriss
One of the fundamental aspects of hydrogen embrittlement is based on the impacts of hydrogen on the elementary mechanisms of plasticity. Even though it is well known that the solute hydrogen generally deteriorates the ductility of nickel, it highlighted the existence of antagonistic processes in the hydrogen effect as well, i.e., hydrogen-induced hardening and/or softening without a relevant universal explanation. These effects may also reflect an implication of hydrogen on the modification of the elasticity properties. In this work, the impact of hydrogen on elastic modulus, dislocation nucleation (i.e., pop-in), and hardness was investigated in nickel 〈100〉 single crystal using nanoindentation. The evolution of the different properties during hydrogen desorption offers the opportunity to distinguish the direct impact of hydrogen from those associated with solute-induced defects. The deformed sub-surfaces by nanoindentation were analyzed by TEM to characterise the development of dislocation structures and any other defects, and hence to establish the hydrogen-defect-elasticity-plasticity correlations. Hertz’s theory was used to model the elastic regime and Oliver and Pharr's model (Oliver and Pharr, 1992) was used to analyze the elastoplastic regime of the nanoindentation load-displacement curve. Hydrogen-induced impacts on maximum shear stress to activate dislocations, hardness and elastic modulus were observed. An irreversible reduction in elastic modulus with hydrogen absorption revealed the influence of hydrogen-induced vacancy clusters on elasticity. In addition, the increase in pop-in load and hardness with hydrogen absorption indicated a hardening behaviour in the plastic regime, resulting from the interaction of interstitial hydrogen and vacancy clusters with dislocation nucleation and mobility.
氢脆的一个基本方面是基于氢对塑性基本机制的影响。尽管众所周知，溶质氢通常会使镍的延展性恶化，但它也强调了氢效应中拮抗过程的存在，即氢诱导的硬化和/或软化，但没有相关的普遍解释。这些影响也可能反映了氢对弹性性能改性的影响。在这项工作中，研究了氢对镍<；100>；单晶弹性模量、位错成核（即突入）和硬度的影响。氢解吸过程中不同性质的演变为区分氢的直接影响和溶质诱导缺陷提供了机会。利用透射电镜对纳米压痕变形后的亚表面进行了分析，以表征位错结构和任何其他缺陷的发展，从而建立氢缺陷-弹性-塑性的相关性。采用Hertz的理论对弹性状态进行建模，采用Oliver和Pharr的模型（Oliver and Pharr, 1992）分析纳米压痕载荷-位移曲线的弹塑性状态。观察了氢对最大剪切应力对激活位错、硬度和弹性模量的影响。弹性模量随氢吸收的不可逆降低揭示了氢诱导空位团簇对弹性的影响。此外，随着氢的吸收，弹出载荷和硬度的增加表明在塑性区有硬化行为，这是由于间隙氢和空位团簇与位错成核和迁移率的相互作用所致。
{"title":"Hydrogen–vacancy effects on the elastic and plastic behaviour of Ni<100> probed by nanoindentation","authors":"S.P. Murugan, Y. Ben Jedidia, X. Feaugas, A. Oudriss","doi":"10.1016/j.ijplas.2025.104492","DOIUrl":"10.1016/j.ijplas.2025.104492","url":null,"abstract":"<div><div>One of the fundamental aspects of hydrogen embrittlement is based on the impacts of hydrogen on the elementary mechanisms of plasticity. Even though it is well known that the solute hydrogen generally deteriorates the ductility of nickel, it highlighted the existence of antagonistic processes in the hydrogen effect as well, i.e., hydrogen-induced hardening and/or softening without a relevant universal explanation. These effects may also reflect an implication of hydrogen on the modification of the elasticity properties. In this work, the impact of hydrogen on elastic modulus, dislocation nucleation (i.e., pop-in), and hardness was investigated in nickel 〈100〉 single crystal using nanoindentation. The evolution of the different properties during hydrogen desorption offers the opportunity to distinguish the direct impact of hydrogen from those associated with solute-induced defects. The deformed sub-surfaces by nanoindentation were analyzed by TEM to characterise the development of dislocation structures and any other defects, and hence to establish the hydrogen-defect-elasticity-plasticity correlations. Hertz’s theory was used to model the elastic regime and Oliver and Pharr's model (Oliver and Pharr, 1992) was used to analyze the elastoplastic regime of the nanoindentation load-displacement curve. Hydrogen-induced impacts on maximum shear stress to activate dislocations, hardness and elastic modulus were observed. An irreversible reduction in elastic modulus with hydrogen absorption revealed the influence of hydrogen-induced vacancy clusters on elasticity. In addition, the increase in pop-in load and hardness with hydrogen absorption indicated a hardening behaviour in the plastic regime, resulting from the interaction of interstitial hydrogen and vacancy clusters with dislocation nucleation and mobility.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104492"},"PeriodicalIF":12.8,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145153659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-27DOI: 10.1016/j.ijplas.2025.104479
Jin-Cheng Wang , Zhen Liu , Xue-Yang Zhang , De-Shan Cui , Xian-Fang Li
Identifying constitutive relations for materials with complex behaviors remains a persistent challenge in computational mechanics. Unlike metals, granular materials exhibit pressure hardening, where increasing hydrostatic pressure enhances both shear strength and stiffness through reinforced interparticle contact forces and frictional resistance. For nonlinear elastoplastic granular materials, traditional approaches rely on empirical constitutive models derived from extensive experimental datasets, but they lack flexibility and dependent heavily on parameter calibration. This study proposes a mechanics-informed neural network (MINN) framework, leveraging physics-informed learning principles, to identify nonlinear constitutive relations for geotechnical granular materials under diverse deformation path. By embedding the second-order work criterion and enforcing time consistency for path-dependent responses, MINN significantly outperforms traditional neural networks in robustness, particularly for materials with complex loading history. By integrating finite element solvers, numerical cases further validates the framework’s efficacy, demonstrating close alignment between numerical predictions and experimental data. The dual capabilities of MINN in balancing physical constraints and data-driven adaptability enhance its versatility in elastic–plastic constitutive modeling.
{"title":"Mechanics-informed neural networks for modeling constitutive relation for nonlinear elastoplastic materials","authors":"Jin-Cheng Wang , Zhen Liu , Xue-Yang Zhang , De-Shan Cui , Xian-Fang Li","doi":"10.1016/j.ijplas.2025.104479","DOIUrl":"10.1016/j.ijplas.2025.104479","url":null,"abstract":"<div><div>Identifying constitutive relations for materials with complex behaviors remains a persistent challenge in computational mechanics. Unlike metals, granular materials exhibit pressure hardening, where increasing hydrostatic pressure enhances both shear strength and stiffness through reinforced interparticle contact forces and frictional resistance. For nonlinear elastoplastic granular materials, traditional approaches rely on empirical constitutive models derived from extensive experimental datasets, but they lack flexibility and dependent heavily on parameter calibration. This study proposes a mechanics-informed neural network (MINN) framework, leveraging physics-informed learning principles, to identify nonlinear constitutive relations for geotechnical granular materials under diverse deformation path. By embedding the second-order work criterion and enforcing time consistency for path-dependent responses, MINN significantly outperforms traditional neural networks in robustness, particularly for materials with complex loading history. By integrating finite element solvers, numerical cases further validates the framework’s efficacy, demonstrating close alignment between numerical predictions and experimental data. The dual capabilities of MINN in balancing physical constraints and data-driven adaptability enhance its versatility in elastic–plastic constitutive modeling.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104479"},"PeriodicalIF":12.8,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145182944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-26DOI: 10.1016/j.ijplas.2025.104489
Hanzhang Li , Tao You , Keita Yoshioka , Yuhao Liu , Yi Rui , Fengshou Zhang
Fracture nucleation with phase-field models has recently gained significant attention as classical phase-field models often fall short in capturing the onset of fracture in the bulk material with small cracks under multi-axial loading conditions. In this study, we propose a micromechanics-based cohesive phase-field approach with a stress-dependent characteristic length for accurately modeling fracture nucleation in quasi-brittle materials subjected to multi-axial loading. Our analytical solutions reveal that the fracture nucleation criterion is independent of the phase-field length scale parameter and aligns with the material’s strength surface. Compared with available experimental data under biaxial and triaxial loading, we demonstrate that the proposed model is capable of predicting the strength surfaces that transition from extension to compression, while the existing models fail to represent these failure surfaces. Our three-dimensional numerical simulation shows that the proposed model reproduces the transition of fracture pattern from extension to compression.
{"title":"A cohesive–frictional phase-field model for hybrid fracture in quasi-brittle materials incorporating strength criteria","authors":"Hanzhang Li , Tao You , Keita Yoshioka , Yuhao Liu , Yi Rui , Fengshou Zhang","doi":"10.1016/j.ijplas.2025.104489","DOIUrl":"10.1016/j.ijplas.2025.104489","url":null,"abstract":"<div><div>Fracture nucleation with phase-field models has recently gained significant attention as classical phase-field models often fall short in capturing the onset of fracture in the bulk material with small cracks under multi-axial loading conditions. In this study, we propose a micromechanics-based cohesive phase-field approach with a stress-dependent characteristic length for accurately modeling fracture nucleation in quasi-brittle materials subjected to multi-axial loading. Our analytical solutions reveal that the fracture nucleation criterion is independent of the phase-field length scale parameter and aligns with the material’s strength surface. Compared with available experimental data under biaxial and triaxial loading, we demonstrate that the proposed model is capable of predicting the strength surfaces that transition from extension to compression, while the existing models fail to represent these failure surfaces. Our three-dimensional numerical simulation shows that the proposed model reproduces the transition of fracture pattern from extension to compression.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104489"},"PeriodicalIF":12.8,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145140725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-25DOI: 10.1016/j.ijplas.2025.104491
Zhuangzhuang Liu , Yu Zhang , Hao Wu , Guohua Fan
Strain rate sensitivity is a critical parameter influencing mechanical behaviors, typically resulting in increased flow stress at higher strain rates across most metallic materials. In the present study, we report an unusual phenomenon of strain rate insensitivity in hexagonal titanium deformed at 77 K, independent of strain rates ranging from 0.001 to 0.1 s−1. Through detailed characterization using synchrotron Laue microdiffraction, transmission electron microscopy, and in situ electron backscatter diffraction, we attribute this unusual behavior to the consistency in the type and density of defects. Specifically, at the yield stage, strain rate insensitivity is linked to the prevalence of <a> dislocations, while the insensitivity during initial deformation stages correlates with the dynamics of dislocations and twins both of which are evolved in concert. These findings not only provide new insights into cryogenic deformation theory, but also identify new challenges and prospects for the development of high-speed cryogenic forming or extrusion.
{"title":"Temperature-mediated extraordinary rate insensitivity of strongly textured titanium","authors":"Zhuangzhuang Liu , Yu Zhang , Hao Wu , Guohua Fan","doi":"10.1016/j.ijplas.2025.104491","DOIUrl":"10.1016/j.ijplas.2025.104491","url":null,"abstract":"<div><div>Strain rate sensitivity is a critical parameter influencing mechanical behaviors, typically resulting in increased flow stress at higher strain rates across most metallic materials. In the present study, we report an unusual phenomenon of strain rate insensitivity in hexagonal titanium deformed at 77 K, independent of strain rates ranging from 0.001 to 0.1 s<sup>−1</sup>. Through detailed characterization using synchrotron Laue microdiffraction, transmission electron microscopy, and <em>in situ</em> electron backscatter diffraction, we attribute this unusual behavior to the consistency in the type and density of defects. Specifically, at the yield stage, strain rate insensitivity is linked to the prevalence of <<em>a</em>> dislocations, while the insensitivity during initial deformation stages correlates with the dynamics of dislocations and twins both of which are evolved in concert. These findings not only provide new insights into cryogenic deformation theory, but also identify new challenges and prospects for the development of high-speed cryogenic forming or extrusion.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104491"},"PeriodicalIF":12.8,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-21DOI: 10.1016/j.ijplas.2025.104487
Zhuochen Chen , Wanghui Li , Oluwafunmilola Ola , Lanxi Feng , Xiaoqing Zhang , Yong-Wei Zhang , Xiaohu Yao
Overcoming the inherent brittleness of ceramics is a longstanding, unsolved challenge in materials science and engineering. Here, we demonstrate a new effective strategy to achieve a brittle-ductile transition in ceramics by introducing a hierarchical spinodal structure. Combining phase field method and molecular dynamics (MD) method, we first constructed nanoporous SiC samples with 1-level and hierarchical 2-level structures separately using a phase field method whose rationality is well validated, featuring spinodal topologies. Then, the mechanical response of the nanoporous ceramics under compression is investigated by all-atom MD simulations to discover the underlying nanoscale deformation mechanisms. The results revealed that the 1-level nanoporous SiC samples exhibited conventional brittleness due to stress-concentration-induced cracking; in stark contrast, the hierarchical 2-level samples displayed a ductile, strain-hardening, metal-like behavior, which is attributed to the presence of dispersed nuclei of defects like stacking faults, which effectively dispersed stress and prevented stress-concentration-induced failure. The strength of the hierarchical nanoporous ceramics follows Shi's law rather than classical Gibson-Ashby law. Our study not only elucidates the two distinct deformation mechanisms but also introduces a highly effective hierarchical nanoporous strategy for the design of ductile ceramics with excellent strain hardening capability, addressing the enduring challenge of brittleness in ceramics.
{"title":"Hierarchical nanoporous-based design strategy towards ductile ceramics with excellent strain hardening capability","authors":"Zhuochen Chen , Wanghui Li , Oluwafunmilola Ola , Lanxi Feng , Xiaoqing Zhang , Yong-Wei Zhang , Xiaohu Yao","doi":"10.1016/j.ijplas.2025.104487","DOIUrl":"10.1016/j.ijplas.2025.104487","url":null,"abstract":"<div><div>Overcoming the inherent brittleness of ceramics is a longstanding, unsolved challenge in materials science and engineering. Here, we demonstrate a new effective strategy to achieve a brittle-ductile transition in ceramics by introducing a hierarchical spinodal structure. Combining phase field method and molecular dynamics (MD) method, we first constructed nanoporous SiC samples with 1-level and hierarchical 2-level structures separately using a phase field method whose rationality is well validated, featuring spinodal topologies. Then, the mechanical response of the nanoporous ceramics under compression is investigated by all-atom MD simulations to discover the underlying nanoscale deformation mechanisms. The results revealed that the 1-level nanoporous SiC samples exhibited conventional brittleness due to stress-concentration-induced cracking; in stark contrast, the hierarchical 2-level samples displayed a ductile, strain-hardening, metal-like behavior, which is attributed to the presence of dispersed nuclei of defects like stacking faults, which effectively dispersed stress and prevented stress-concentration-induced failure. The strength of the hierarchical nanoporous ceramics follows Shi's law rather than classical Gibson-Ashby law. Our study not only elucidates the two distinct deformation mechanisms but also introduces a highly effective hierarchical nanoporous strategy for the design of ductile ceramics with excellent strain hardening capability, addressing the enduring challenge of brittleness in ceramics.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104487"},"PeriodicalIF":12.8,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-21DOI: 10.1016/j.ijplas.2025.104488
Fu Chen , Huaqiang Liu , Yuanfei Han , Jiaming Zhang , Xiaoyan Wang , Yongqiang Ye , Chunyu Shen , Yimin Zhuo , Jianwen Le , Guangfa Huang , Weijie Lu , Di Zhang
Strength-ductility trade-off in additively manufactured titanium alloys has been a critical bottleneck, significantly limiting their engineering applications. Our work demonstrated that this dilemma was overcome by tailoring a hierarchical heterostructure (HHS) in laser-directed energy deposited titanium alloy (Ti-6.5Al-3.5Mo-1.5Zr-0.3Si). The designed HHS consisted of coarse micro-sized α phases (αp, soft region) and ultrafine nano-sized α precipitates (αs, hard region), generating hierarchical heterointerfaces including microscale αp/βt and nanoscale αs/βr interfaces. The HHS enhanced the total elongation to failure by 476.2 % without sacrificing strength compared to the conventional α-β lamella structure, achieving exceptional strength-ductility synergy. Micro/nano-scale mechanical deformation analyses showed that hetero-deformation between coarse αp and ultrafine αs regions caused noticeable accumulation of geometrically necessary dislocations (GNDs) at heterointerfaces, inducing the pronounced hetero-deformation induced (HDI) strengthening effect on the soft αp, and the HDI hardening effect improving ductility. The HDI stress facilitated the formation and growth of dislocation networks in soft αp, promoting the accumulation of interfacial GNDs, enhancing the HDI hardening effect. Compared to single-level α/β interfaces, hierarchical heterointerface generated higher GND density with a dual-gradient distribution, further improving the HDI stress and producing multiscale HDI hardening. This resultant high HDI stress activated high-proportioned pyramidal 〈c + a〉 slip modes with significant increment of GND density, overcoming deformation incompatibility. Moreover, hierarchical heterointerface exhibited a multi-scale crack buffering effect, synergistically contributing to the excellent ductility. Finally, a two-level homogenization model was established to comprehensively elucidate the intrinsic strengthening-toughening mechanism of the HHS. This work provided theoretical guidance for developing additively manufactured titanium alloys with high-performance.
{"title":"Architecting micro-and nanoscale heterostructure for exceptional strength-ductility synergy in additively manufactured titanium alloy","authors":"Fu Chen , Huaqiang Liu , Yuanfei Han , Jiaming Zhang , Xiaoyan Wang , Yongqiang Ye , Chunyu Shen , Yimin Zhuo , Jianwen Le , Guangfa Huang , Weijie Lu , Di Zhang","doi":"10.1016/j.ijplas.2025.104488","DOIUrl":"10.1016/j.ijplas.2025.104488","url":null,"abstract":"<div><div>Strength-ductility trade-off in additively manufactured titanium alloys has been a critical bottleneck, significantly limiting their engineering applications. Our work demonstrated that this dilemma was overcome by tailoring a hierarchical heterostructure (HHS) in laser-directed energy deposited titanium alloy (Ti-6.5Al-3.5Mo-1.5Zr-0.3Si). The designed HHS consisted of coarse micro-sized α phases (α<sub>p</sub>, soft region) and ultrafine nano-sized α precipitates (α<sub>s</sub>, hard region), generating hierarchical heterointerfaces including microscale α<sub>p</sub>/β<sub>t</sub> and nanoscale α<sub>s</sub>/β<sub>r</sub> interfaces. The HHS enhanced the total elongation to failure by 476.2 % without sacrificing strength compared to the conventional α-β lamella structure, achieving exceptional strength-ductility synergy. Micro/nano-scale mechanical deformation analyses showed that hetero-deformation between coarse α<sub>p</sub> and ultrafine α<sub>s</sub> regions caused noticeable accumulation of geometrically necessary dislocations (GNDs) at heterointerfaces, inducing the pronounced hetero-deformation induced (HDI) strengthening effect on the soft α<sub>p</sub>, and the HDI hardening effect improving ductility. The HDI stress facilitated the formation and growth of dislocation networks in soft α<sub>p</sub>, promoting the accumulation of interfacial GNDs, enhancing the HDI hardening effect. Compared to single-level α/β interfaces, hierarchical heterointerface generated higher GND density with a dual-gradient distribution, further improving the HDI stress and producing multiscale HDI hardening. This resultant high HDI stress activated high-proportioned pyramidal 〈<em>c</em> + <em>a</em>〉 slip modes with significant increment of GND density, overcoming deformation incompatibility. Moreover, hierarchical heterointerface exhibited a multi-scale crack buffering effect, synergistically contributing to the excellent ductility. Finally, a two-level homogenization model was established to comprehensively elucidate the intrinsic strengthening-toughening mechanism of the HHS. This work provided theoretical guidance for developing additively manufactured titanium alloys with high-performance.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104488"},"PeriodicalIF":12.8,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Back stress hardening is a component of strain hardening during plastic deformation. Traditionally, the theory of dislocations has attributed the microscopic origin of back stress in polycrystalline metal materials to the long-range stress fields generated by geometrically necessary dislocations (GNDs), which accommodate the translational lattice incompatibility of the crystal. However, the lattice incompatibility also contains a rotational component, associated with disclinations. Similar to GNDs, disclinations also generate long-range internal stress fields, yet their role in back stress remains insufficiently understood. This study introduces a disclination-induced back stress mechanism and proposes a novel single-ended disclination pile-up model, analogous to the single-ended GND pile-up model. This model accounts for the reduction in the average distance of long-range stress fields due to the growth of disclinations within grains. Integrating back stress contributions from both GNDs and disclinations, a new constitutive model is developed. Uniaxial tension simulations of 6061-T5 aluminum alloy sheets demonstrate that the predicted back stress from this model closely aligns with experimental results from tension-compression tests, thereby validating its accuracy. The simulation results show that while GND-induced back stress rapidly increases initially and then stabilizes, disclination-induced back stress continues to rise, constituting 65% of the total back stress at a strain of 0.16. This work not only advances our understanding of the origins of back stress in disclinations but also underscores the significance of incorporating disclinations in back stress calculations, offering new insights into the relationship between microstructure evolution and strain hardening behavior.
{"title":"A novel constitutive model emphasizing disclination-induced back stress in strain hardening","authors":"Jinzhao Li , Zhiping Guan , Junfu Chen , Yongsen Yu","doi":"10.1016/j.ijplas.2025.104486","DOIUrl":"10.1016/j.ijplas.2025.104486","url":null,"abstract":"<div><div>Back stress hardening is a component of strain hardening during plastic deformation. Traditionally, the theory of dislocations has attributed the microscopic origin of back stress in polycrystalline metal materials to the long-range stress fields generated by geometrically necessary dislocations (GNDs), which accommodate the translational lattice incompatibility of the crystal. However, the lattice incompatibility also contains a rotational component, associated with disclinations. Similar to GNDs, disclinations also generate long-range internal stress fields, yet their role in back stress remains insufficiently understood. This study introduces a disclination-induced back stress mechanism and proposes a novel single-ended disclination pile-up model, analogous to the single-ended GND pile-up model. This model accounts for the reduction in the average distance of long-range stress fields due to the growth of disclinations within grains. Integrating back stress contributions from both GNDs and disclinations, a new constitutive model is developed. Uniaxial tension simulations of 6061-T5 aluminum alloy sheets demonstrate that the predicted back stress from this model closely aligns with experimental results from tension-compression tests, thereby validating its accuracy. The simulation results show that while GND-induced back stress rapidly increases initially and then stabilizes, disclination-induced back stress continues to rise, constituting 65% of the total back stress at a strain of 0.16. This work not only advances our understanding of the origins of back stress in disclinations but also underscores the significance of incorporating disclinations in back stress calculations, offering new insights into the relationship between microstructure evolution and strain hardening behavior.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104486"},"PeriodicalIF":12.8,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145089182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-19DOI: 10.1016/j.ijplas.2025.104485
Zhiqi Guo , Xiaotong Li , Sijie Wang , Zhanqiu Tan , Zhenming Yue , Bo Cui , Genlian Fan , Zhiqiang Li , Di Zhang
High-strength aluminum matrix composites (AMCs) suffer from poor ductility, due to the limited work hardening capacity. In this study, a remarkable prolonged work hardening is sustained in ultrastrong Al-5Mg matrix composites via an optimized bimodal grain heterostructure, with triple or even fourfold uniform elongation and raised tensile/yield strength. The prolonged work hardening proceeds through two sequential deformation stages. In the first stage with minor strains (<2.5%), a high gradient of geometrically necessary dislocations in soft coarse-grained (CG) zones generates strong back stress, which promotes not only hetero-deformation induced (HDI) hardening but also dislocation multiplication in hard ultrafine-grained (UFG) zones. The work hardening of UFG is thus improved with higher density of dislocations interacting with some nanoparticles. Subsequently, the stress of UFG zones rises sufficiently to induce dispersed microvoids formation within UFG zones, instead of localized cracking at hetero-zone boundaries. Therefore, an effective HDI hardening depending on the well-bonded hetero zones is sustained in the second stage (strain >2.5%). Such a sequential heterostructure effect is analyzed to obtain an appropriate width range of soft zones for bimodal grained AMCs, improving the conventional empirical heterostructure design principle. This work advances the understandings on heterostructured AMCs that when employing intermediate-sized soft zones, the hard UFG zones play a key role in obtaining good ductility, instead of only providing high strength.
{"title":"Prolonged work hardening in bimodal grain structured aluminum matrix composites: a sequential heterostructure effect","authors":"Zhiqi Guo , Xiaotong Li , Sijie Wang , Zhanqiu Tan , Zhenming Yue , Bo Cui , Genlian Fan , Zhiqiang Li , Di Zhang","doi":"10.1016/j.ijplas.2025.104485","DOIUrl":"10.1016/j.ijplas.2025.104485","url":null,"abstract":"<div><div>High-strength aluminum matrix composites (AMCs) suffer from poor ductility, due to the limited work hardening capacity. In this study, a remarkable prolonged work hardening is sustained in ultrastrong Al-5Mg matrix composites via an optimized bimodal grain heterostructure, with triple or even fourfold uniform elongation and raised tensile/yield strength. The prolonged work hardening proceeds through two sequential deformation stages. In the first stage with minor strains (<2.5%), a high gradient of geometrically necessary dislocations in soft coarse-grained (CG) zones generates strong back stress, which promotes not only hetero-deformation induced (HDI) hardening but also dislocation multiplication in hard ultrafine-grained (UFG) zones. The work hardening of UFG is thus improved with higher density of dislocations interacting with some nanoparticles. Subsequently, the stress of UFG zones rises sufficiently to induce dispersed microvoids formation within UFG zones, instead of localized cracking at hetero-zone boundaries. Therefore, an effective HDI hardening depending on the well-bonded hetero zones is sustained in the second stage (strain >2.5%). Such a sequential heterostructure effect is analyzed to obtain an appropriate width range of soft zones for bimodal grained AMCs, improving the conventional empirical heterostructure design principle. This work advances the understandings on heterostructured AMCs that when employing intermediate-sized soft zones, the hard UFG zones play a key role in obtaining good ductility, instead of only providing high strength.</div></div>","PeriodicalId":340,"journal":{"name":"International Journal of Plasticity","volume":"194 ","pages":"Article 104485"},"PeriodicalIF":12.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145083954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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