Engineering Fracture Mechanics最新文献_第10页

Appropriate function form of traction softening law for simulating mode I quasi-static delamination growth with significant R-curve effect 适用于模拟具有显著r曲线效应的I型准静态分层生长的牵引软化规律函数形式

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-12 DOI: 10.1016/j.engfracmech.2026.111860

Luohuan Zou , Yu Gong , Dingli Tian , Meijuan Shan , Jianyu Zhang , Libin Zhao , Ning Hu

Many composite laminates exhibit the Resistance-curve (R-curve) effect where energy absorption increases with incremental delamination growth. The energy absorbing mechanisms can be related to interlaminar non-linear fracture behaviors. Cohesive zone model (CZM) is useful for capturing the non-linear fracture process zone (FPZ). Researchers have proposed various traction softening laws because crack opening displacement (COD) corresponding to complete fracture (δ_max) will vary for different materials and this will affect the shape of the traction softening law for that material. There is still no consensus on a general function form of traction softening law so far. Thus, in this work, six tested cases (different materials) from literatures are studied to compare the effectiveness of different softening laws, including linear, exponential, modified linear, modified exponential, multi-linear and four-parametric exponential functions. Especially, a unified data reduction method is used for calculating the damage onset parameters K₀ and σ₀, and J-integral-crack opening displacement (J-COD) curves where only experimental load–displacement data are needed. All softening laws are determined using calculated J-COD curves. Numerical studies shown that the effectiveness of different softening laws can be ranked as follows: multi-linear = four-parametric exponential > modified linear = modified exponential > exponential = linear > no softening (without considering FPZ). Meanwhile, it is found that the dimensionless parameter δ_max/δ₀ (COD corresponding to complete failure and damage onset, respectively) is effective for selecting an appropriate softening law. This work can provide references for simulating mode I quasi-static delamination growth with significant R-curve effect.

许多复合材料层合板表现出阻力曲线（r曲线）效应，其中能量吸收随着分层的增加而增加。能量吸收机制可能与层间非线性断裂行为有关。内聚带模型（CZM）用于描述非线性断裂过程带（FPZ）。由于不同材料的完全断裂对应的裂纹张开位移（COD）（δmax）不同，这将影响该材料的牵引软化规律的形状，因此研究者提出了不同的牵引软化规律。迄今为止，对于牵引软化法的一般函数形式尚未达成共识。因此，本研究从文献中选取了6个不同材料的测试案例，比较了线性、指数、修正线性、修正指数、多线性和四参数指数函数等不同软化律的有效性。特别是，采用统一的数据约简方法计算损伤起始参数K0和σ0，以及只需要试验载荷-位移数据的j -积分-裂纹张开位移（J-COD）曲线。所有的软化规律都是通过计算得到的J-COD曲线确定的。数值研究表明，不同软化规律的有效性排序为：多线性=四参数指数>；修正线性=修正指数>；指数=线性>；不软化（不考虑FPZ）。同时，发现无因次参数δmax/δ0（分别对应完全破坏和损伤开始时的COD）可以有效地选择合适的软化规律。该工作可为模拟具有显著r曲线效应的I型准静态分层生长提供参考。

{"title":"Appropriate function form of traction softening law for simulating mode I quasi-static delamination growth with significant R-curve effect","authors":"Luohuan Zou , Yu Gong , Dingli Tian , Meijuan Shan , Jianyu Zhang , Libin Zhao , Ning Hu","doi":"10.1016/j.engfracmech.2026.111860","DOIUrl":"10.1016/j.engfracmech.2026.111860","url":null,"abstract":"<div><div>Many composite laminates exhibit the <em>Resistance</em>-curve (<em>R</em>-curve) effect where energy absorption increases with incremental delamination growth. The energy absorbing mechanisms can be related to interlaminar non-linear fracture behaviors. Cohesive zone model (CZM) is useful for capturing the non-linear fracture process zone (FPZ). Researchers have proposed various traction softening laws because crack opening displacement (COD) corresponding to complete fracture (<em>δ<sub>max</sub></em>) will vary for different materials and this will affect the shape of the traction softening law for that material. There is still no consensus on a general function form of traction softening law so far. Thus, in this work, six tested cases (different materials) from literatures are studied to compare the effectiveness of different softening laws, including linear, exponential, modified linear, modified exponential, multi-linear and four-parametric exponential functions. Especially, a unified data reduction method is used for calculating the damage onset parameters <em>K</em><sub>0</sub> and <em>σ</em><sub>0</sub>, and <em>J</em>-integral-crack opening displacement (<em>J</em>-COD) curves where only experimental load–displacement data are needed. All softening laws are determined using calculated <em>J</em>-COD curves. Numerical studies shown that the effectiveness of different softening laws can be ranked as follows: multi-linear = four-parametric exponential > modified linear = modified exponential > exponential = linear > no softening (without considering FPZ). Meanwhile, it is found that the dimensionless parameter <em>δ<sub>max</sub></em>/<em>δ</em><sub>0</sub> (COD corresponding to complete failure and damage onset, respectively) is effective for selecting an appropriate softening law. This work can provide references for simulating mode I quasi-static delamination growth with significant <em>R</em>-curve effect.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111860"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel ring specimen for fatigue crack growth rate testing of rubber with full-cycle crack length monitoring 一种新型的橡胶疲劳裂纹扩展速率环样及全周期裂纹长度监测

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-20 DOI: 10.1016/j.engfracmech.2026.111875

Weidong Liu , Ya Xu , Yu Liu , Chi Zhang , Qiushi Zhang , Jiyuan Cui

Conventional fatigue crack growth rate (FCGR) testing is constrained by limited specimen geometries and digital image correlation (DIC) technical restrictions, hindering its application to multiaxial loading conditions. This study proposes a novel ring specimen (RS) for FCGR testing. By establishing an analytical relationship between its unique equivalent force arm and crack length, and analyzing the sensitivity boundaries of this mapping mechanism regarding crack angle and tensile strain, a force/torque-sensor-based method for full-cycle crack monitoring was achieved. The results demonstrate that the RS maintains mechanical equivalence to standard specimens while extending the effective testing zone 6.5-fold. The equivalent force arm-crack length mapping model shows high robustness, with the gradient relative error remaining below 2% within reasonable variations in crack angle and strain. The RS method yields FCGRs within factor-of-two scatter bands of the standard DIC method, with Paris law parameter errors below 3% without compromising testing efficiency. This research overcomes limitations in DIC and specimen geometry to achieve full-cycle crack monitoring, offering a novel strategy for in situ monitoring of rubber crack propagation under multiaxial loading conditions.

传统的疲劳裂纹扩展速率（FCGR）测试受到试样几何形状和数字图像相关（DIC）技术的限制，阻碍了其在多轴加载条件下的应用。本研究提出了一种新型环形试样（RS）用于FCGR试验。通过建立其独特的等效力臂与裂纹长度之间的解析关系，分析该映射机构对裂纹角和拉伸应变的灵敏度边界，实现了基于力/扭矩传感器的全周期裂纹监测方法。结果表明，RS在将有效试验区域扩大6.5倍的同时，保持了与标准试件的力学等效性。等效力臂-裂纹长度映射模型具有较强的鲁棒性，在合理的裂纹角度和应变变化范围内，梯度相对误差保持在2%以下。RS方法产生的fcgr在标准DIC方法的两倍散射带内，在不影响测试效率的情况下，巴黎定律参数误差低于3%。该研究克服了DIC和试样几何形状的限制，实现了全周期裂纹监测，为多轴加载条件下橡胶裂纹扩展的原位监测提供了一种新的策略。

{"title":"A novel ring specimen for fatigue crack growth rate testing of rubber with full-cycle crack length monitoring","authors":"Weidong Liu , Ya Xu , Yu Liu , Chi Zhang , Qiushi Zhang , Jiyuan Cui","doi":"10.1016/j.engfracmech.2026.111875","DOIUrl":"10.1016/j.engfracmech.2026.111875","url":null,"abstract":"<div><div>Conventional fatigue crack growth rate (FCGR) testing is constrained by limited specimen geometries and digital image correlation (DIC) technical restrictions, hindering its application to multiaxial loading conditions. This study proposes a novel ring specimen (RS) for FCGR testing. By establishing an analytical relationship between its unique equivalent force arm and crack length, and analyzing the sensitivity boundaries of this mapping mechanism regarding crack angle and tensile strain, a force/torque-sensor-based method for full-cycle crack monitoring was achieved. The results demonstrate that the RS maintains mechanical equivalence to standard specimens while extending the effective testing zone 6.5-fold. The equivalent force arm-crack length mapping model shows high robustness, with the gradient relative error remaining below 2% within reasonable variations in crack angle and strain. The RS method yields FCGRs within factor-of-two scatter bands of the standard DIC method, with Paris law parameter errors below 3% without compromising testing efficiency. This research overcomes limitations in DIC and specimen geometry to achieve full-cycle crack monitoring, offering a novel strategy for in situ monitoring of rubber crack propagation under multiaxial loading conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111875"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Characteristic regions for the fracture surface of interior crack initiation in the outer ring raceway of railway bearing 铁路轴承外圈滚道内裂纹萌生断裂面特征区域

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-19 DOI: 10.1016/j.engfracmech.2026.111869

Xiaolong Liu , Kelian Luo , Qiang Chen , Dunxin Wang , Haibo Xiang , Rubing Guo , Xi Wang

Interior crack initiation prevails in the failure mode of railway bearings. Three characteristic regions, i.e., Inclusion, Fish-eye, and zig-zag cracks, were first defined on the fracture surface of interior crack initiation, indicating the interior crack initiation and propagation mechanism. The inclusion clusters are primarily Al₂O₃, with the diameters ranging from approximately 5–15 µm. Fish-eye formed during the crack initiation stage. No grain refinement was observed during this stage, suggesting that no white etching cracks developed. Zig-zag cracks exhibited larger dimensions along the major axis and smaller, denser structures along the minor axis. The crack path deflects during the propagation of mixed Mode II-III cracks, resulting in the characteristic zig-zag morphology. Based on these results, a mechanism for interior crack initiation and propagation in the outer raceway of railway bearings was proposed. These findings advance the understanding of very-high-cycle fatigue under rolling contact loading, offering critical insights for optimizing bearing design and lifespan prediction in rail transport systems.

铁路轴承破坏模式以内部裂纹萌生为主。首次在内裂纹起裂断面上定义了夹杂裂纹、鱼眼裂纹和锯齿形裂纹三个特征区域，揭示了内裂纹的起裂和扩展机制。包裹团簇主要为Al2O3，直径约为5-15µm。鱼眼在裂纹萌生阶段形成。在此阶段未观察到晶粒细化，表明没有形成白色腐蚀裂纹。锯齿形裂纹沿长轴尺寸较大，沿短轴结构较小且密度较大。II-III型混合裂纹扩展过程中，裂纹路径发生偏转，形成典型的锯齿形裂纹形态。在此基础上，提出了铁路轴承外滚道内部裂纹萌生和扩展的机理。这些发现促进了对滚动接触载荷下的高周疲劳的理解，为优化铁路运输系统的轴承设计和寿命预测提供了重要见解。

{"title":"Characteristic regions for the fracture surface of interior crack initiation in the outer ring raceway of railway bearing","authors":"Xiaolong Liu , Kelian Luo , Qiang Chen , Dunxin Wang , Haibo Xiang , Rubing Guo , Xi Wang","doi":"10.1016/j.engfracmech.2026.111869","DOIUrl":"10.1016/j.engfracmech.2026.111869","url":null,"abstract":"<div><div>Interior crack initiation prevails in the failure mode of railway bearings. Three characteristic regions, i.e., Inclusion, Fish-eye, and zig-zag cracks, were first defined on the fracture surface of interior crack initiation, indicating the interior crack initiation and propagation mechanism. The inclusion clusters are primarily Al<sub>2</sub>O<sub>3</sub>, with the diameters ranging from approximately 5–15 µm. Fish-eye formed during the crack initiation stage. No grain refinement was observed during this stage, suggesting that no white etching cracks developed. Zig-zag cracks exhibited larger dimensions along the major axis and smaller, denser structures along the minor axis. The crack path deflects during the propagation of mixed Mode II-III cracks, resulting in the characteristic zig-zag morphology. Based on these results, a mechanism for interior crack initiation and propagation in the outer raceway of railway bearings was proposed. These findings advance the understanding of very-high-cycle fatigue under rolling contact loading, offering critical insights for optimizing bearing design and lifespan prediction in rail transport systems.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111869"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146034510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fatigue life prediction of metal rubber under small-sample conditions via data augmentation and physics-informed fusion 基于数据增强和物理信息融合的小样本条件下金属橡胶疲劳寿命预测

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-13 DOI: 10.1016/j.engfracmech.2026.111865

Zihao Huang , Zhiying Ren , Han Lin , Yuedan Li , Chunhui Zhou , Xianbao Xiang , Jinhui Chen

Metal rubber (MR), as a novel elastic porous material, has been widely applied in critical fields such as aerospace, and its fatigue life prediction is of great significance for ensuring equipment safety. To address the dual challenges of data scarcity and complex physical mechanisms in life modeling of MR, this paper proposes a fatigue life prediction method that integrates data augmentation with physics-informed modeling—namely, the GAN-PILM-TCN model. Specifically, a Wasserstein Generative Adversarial Network (W-GAN) is first employed to augment the limited fatigue test data, effectively alleviating the problem of insufficient samples. Then, stiffness and damping damage factors are incorporated into the modeling process to enhance the physical interpretability of the model. In addition, Principal Component Analysis (PCA) is applied to reduce the dimensionality of multi-dimensional features and extract key information on damage evolution. Furthermore, a hybrid loss function is constructed based on the Weibull distribution to guide the model in better capturing the relationship between fatigue damage and life during training. Experimental results demonstrate that the proposed method achieves a significant improvement in prediction performance under small-sample conditions, with a maximum R² of 0.9336. To further evaluate model stability, 10 independent training runs were conducted, yielding an average mean squared error of MSE_avg = 0.0142 and a standard deviation of Std = 0.0011, indicating good stability and reproducibility. These findings provide a new methodological framework and technical support for fatigue life prediction and reliability design of MR under complex operating conditions.

金属橡胶作为一种新型的弹性多孔材料，已广泛应用于航空航天等关键领域，其疲劳寿命预测对保障设备安全具有重要意义。为了解决MR寿命建模中数据稀缺和物理机制复杂的双重挑战，本文提出了一种将数据增强与物理信息建模相结合的疲劳寿命预测方法，即GAN-PILM-TCN模型。具体而言，首先采用Wasserstein生成对抗网络（W-GAN）对有限的疲劳试验数据进行扩充，有效缓解了样本不足的问题。然后，将刚度和阻尼损伤因素纳入建模过程，以增强模型的物理可解释性。此外，应用主成分分析（PCA）对多维特征进行降维，提取损伤演化的关键信息。此外，基于威布尔分布构造了混合损失函数，以指导模型更好地捕捉训练过程中疲劳损伤与寿命的关系。实验结果表明，该方法在小样本条件下的预测性能有显著提高，最大R2为0.9336。为了进一步评价模型的稳定性，我们进行了10次独立训练，平均均方误差为MSEavg = 0.0142，标准差为Std = 0.0011，表明模型具有良好的稳定性和重复性。研究结果为复杂工况下磁流变器的疲劳寿命预测和可靠性设计提供了新的方法框架和技术支持。

{"title":"Fatigue life prediction of metal rubber under small-sample conditions via data augmentation and physics-informed fusion","authors":"Zihao Huang , Zhiying Ren , Han Lin , Yuedan Li , Chunhui Zhou , Xianbao Xiang , Jinhui Chen","doi":"10.1016/j.engfracmech.2026.111865","DOIUrl":"10.1016/j.engfracmech.2026.111865","url":null,"abstract":"<div><div>Metal rubber (MR), as a novel elastic porous material, has been widely applied in critical fields such as aerospace, and its fatigue life prediction is of great significance for ensuring equipment safety. To address the dual challenges of data scarcity and complex physical mechanisms in life modeling of MR, this paper proposes a fatigue life prediction method that integrates data augmentation with physics-informed modeling—namely, the GAN-PILM-TCN model. Specifically, a Wasserstein Generative Adversarial Network (W-GAN) is first employed to augment the limited fatigue test data, effectively alleviating the problem of insufficient samples. Then, stiffness and damping damage factors are incorporated into the modeling process to enhance the physical interpretability of the model. In addition, Principal Component Analysis (PCA) is applied to reduce the dimensionality of multi-dimensional features and extract key information on damage evolution. Furthermore, a hybrid loss function is constructed based on the Weibull distribution to guide the model in better capturing the relationship between fatigue damage and life during training. Experimental results demonstrate that the proposed method achieves a significant improvement in prediction performance under small-sample conditions, with a maximum R<sup>2</sup> of 0.9336. To further evaluate model stability, 10 independent training runs were conducted, yielding an average mean squared error of MSE<sub>avg</sub> = 0.0142 and a standard deviation of Std = 0.0011, indicating good stability and reproducibility. These findings provide a new methodological framework and technical support for fatigue life prediction and reliability design of MR under complex operating conditions.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111865"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fatigue and fracture of self-reinforced polypropylene/polycarbonate composites at the presence of self-heating effect 自增强聚丙烯/聚碳酸酯复合材料在自热作用下的疲劳与断裂

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2025-12-18 DOI: 10.1016/j.engfracmech.2025.111815

Andrzej Katunin , Marcin Bilewicz , Dominik Wachla , Jafar Amraei , Tomasz Rogala , Roman Minikayev , Magdalena Osial

This study investigates the fatigue behavior and damage mechanisms of self-reinforced polypropylene/polycarbonate (PP/PC) composites manufactured using the shear-controlled orientation injection molding (SCORIM) technique. Microstructural characterization confirmed a layered morphology with PP as the matrix and PC dispersed as spherical inclusions, leading to anisotropic mechanical properties. Thermo-mechanical fatigue tests combined with the increasing amplitude tests established a fatigue strength of 19.4 MPa. Infrared thermography identified a critical self-heating temperature of ∼50 °C as the onset of macroscopic crack front formation, while final failure was associated with localized temperatures exceeding 110 °C due to frictional heating. Scanning electron microscope (SEM) revealed ductile fibrillation and crazing in the core, brittle fracture in outer layers, and interlayer delamination with pull-out mechanism. X-ray diffraction (XRD) showed preserved α-PP monoclinic structure with slight orientation loss after fatigue, while thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy (FTIR) analysis confirmed thermal stability without chemical degradation. The results highlight the interplay of microstructure, anisotropy, and thermomechanical effects governing fatigue performance of SCORIM-processed PP/PC composites.

研究了采用剪切定向注射成型（SCORIM）技术制备的自增强聚丙烯/聚碳酸酯（PP/PC）复合材料的疲劳行为和损伤机理。微观结构表征证实其为以PP为基体，PC为球形夹杂体分散的层状形貌，导致其力学性能各向异性。热-机械疲劳试验结合增幅试验确定了其疲劳强度为19.4 MPa。红外热成像识别出临界自热温度为~ 50°C作为宏观裂纹前缘形成的开始，而由于摩擦加热，局部温度超过110°C与最终失效有关。扫描电镜（SEM）显示，芯部有韧性颤动和裂纹，外层有脆性断裂，层间有脱层和拉出机制。x射线衍射（XRD）结果显示，疲劳后α-PP单斜结构保留，取向有轻微损失，热重分析（TGA）和傅里叶红外光谱（FTIR）分析证实了α-PP的热稳定性，无化学降解。结果强调了微观结构、各向异性和热力学效应对scorim加工的PP/PC复合材料疲劳性能的相互作用。

{"title":"Fatigue and fracture of self-reinforced polypropylene/polycarbonate composites at the presence of self-heating effect","authors":"Andrzej Katunin , Marcin Bilewicz , Dominik Wachla , Jafar Amraei , Tomasz Rogala , Roman Minikayev , Magdalena Osial","doi":"10.1016/j.engfracmech.2025.111815","DOIUrl":"10.1016/j.engfracmech.2025.111815","url":null,"abstract":"<div><div>This study investigates the fatigue behavior and damage mechanisms of self-reinforced polypropylene/polycarbonate (PP/PC) composites manufactured using the shear-controlled orientation injection molding (SCORIM) technique. Microstructural characterization confirmed a layered morphology with PP as the matrix and PC dispersed as spherical inclusions, leading to anisotropic mechanical properties. Thermo-mechanical fatigue tests combined with the increasing amplitude tests established a fatigue strength of 19.4 MPa. Infrared thermography identified a critical self-heating temperature of ∼50 °C as the onset of macroscopic crack front formation, while final failure was associated with localized temperatures exceeding 110 °C due to frictional heating. Scanning electron microscope (SEM) revealed ductile fibrillation and crazing in the core, brittle fracture in outer layers, and interlayer delamination with pull-out mechanism. X-ray diffraction (XRD) showed preserved α-PP monoclinic structure with slight orientation loss after fatigue, while thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy (FTIR) analysis confirmed thermal stability without chemical degradation. The results highlight the interplay of microstructure, anisotropy, and thermomechanical effects governing fatigue performance of SCORIM-processed PP/PC composites.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111815"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145789714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fatigue crack growth under mixed mode I + II loading conditions of ultra-fine bainitic steel designed for railway applications 铁路用超细贝氏体钢I + II混合模式加载条件下疲劳裂纹扩展

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-04 DOI: 10.1016/j.engfracmech.2025.111831

Szymon Dziuba , Aleksandra Królicka , Michał Smolnicki , Grzegorz Lesiuk , Dariusz Rozumek , Roman Kuziak

The present study investigates the fatigue crack growth behavior of ultra-fine bainitic steel under mixed-mode (I + II) loading conditions, relevant to the complex stress states occurring in railway track service. Experimental tests were performed using Compact Tension Shear (CTS) specimens loaded at angles of 30°, 45°, and 60°, enabling controlled combinations of tensile and shear stresses. The fatigue crack growth rate (FCGR) was analyzed and correlated with the equivalent stress intensity factor (ΔK_eq) calculated according to Tanaka’s criterion. Complementary finite element method (FEM) simulations were employed to determine local fracture parameters, including K_I, K_II, T-stress, and J-integral values, and to model the evolution of crack paths. The experimental results demonstrated that with an increasing contribution of Mode II, the crack propagation angle (ψ₀) increased, while the specimen lifetime showed a non-linear dependence on load angle. Fractographic analysis revealed a transition from predominantly transgranular fracture at lower angles toward a higher fraction of intergranular and quasi-cleavage fracture at higher angles. The proposed experimental–numerical approach provides a consistent framework for describing mixed-mode fatigue behavior and for constructing generalized FCGR diagrams. The results contribute to improving the predictive capability of fatigue life models for advanced bainitic steels applied in railway infrastructure.

针对铁路轨道运行过程中出现的复杂应力状态，研究了超细贝氏体钢在混合模式（I + II）加载条件下的疲劳裂纹扩展行为。实验测试采用紧凑拉伸剪切（CTS）试样，加载角度分别为30°、45°和60°，可控制拉伸和剪切应力的组合。对疲劳裂纹扩展速率（FCGR）进行了分析，并与根据Tanaka准则计算的等效应力强度因子（ΔKeq）进行了关联。采用互补有限元法（FEM）模拟确定局部断裂参数，包括KI、KII、t应力和j积分值，并模拟裂纹路径的演化。实验结果表明，随着模态II的贡献增大，裂纹扩展角（ψ0）增大，试件寿命与加载角呈非线性关系。断口分析显示，在较低角度下，断口以穿晶为主，在较高角度下，断口以沿晶和准解理为主。所提出的实验-数值方法为描述混合模态疲劳行为和构建广义FCGR图提供了一致的框架。研究结果有助于提高铁路基础设施用先进贝氏体钢疲劳寿命模型的预测能力。

{"title":"Fatigue crack growth under mixed mode I + II loading conditions of ultra-fine bainitic steel designed for railway applications","authors":"Szymon Dziuba , Aleksandra Królicka , Michał Smolnicki , Grzegorz Lesiuk , Dariusz Rozumek , Roman Kuziak","doi":"10.1016/j.engfracmech.2025.111831","DOIUrl":"10.1016/j.engfracmech.2025.111831","url":null,"abstract":"<div><div>The present study investigates the fatigue crack growth behavior of ultra-fine bainitic steel under mixed-mode (I + II) loading conditions, relevant to the complex stress states occurring in railway track service. Experimental tests were performed using Compact Tension Shear (CTS) specimens loaded at angles of 30°, 45°, and 60°, enabling controlled combinations of tensile and shear stresses. The fatigue crack growth rate (FCGR) was analyzed and correlated with the equivalent stress intensity factor (ΔK<sub>e</sub>q) calculated according to Tanaka’s criterion. Complementary finite element method (FEM) simulations were employed to determine local fracture parameters, including K<sub>I</sub>, K<sub>II</sub>, T-stress, and J-integral values, and to model the evolution of crack paths. The experimental results demonstrated that with an increasing contribution of Mode II, the crack propagation angle (ψ<sub>0</sub>) increased, while the specimen lifetime showed a non-linear dependence on load angle. Fractographic analysis revealed a transition from predominantly transgranular fracture at lower angles toward a higher fraction of intergranular and quasi-cleavage fracture at higher angles. The proposed experimental–numerical approach provides a consistent framework for describing mixed-mode fatigue behavior and for constructing generalized FCGR diagrams. The results contribute to improving the predictive capability of fatigue life models for advanced bainitic steels applied in railway infrastructure.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111831"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic compressive behavior and constitutive parameters of chemically strengthened aluminosilicate glass 化学强化铝硅酸盐玻璃的动态压缩性能及本构参数

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2026-01-10 DOI: 10.1016/j.engfracmech.2026.111844

Ruimin Yang, Jing Ling, Xingya Su, Lin Jing

Quasi-static and dynamic compressive mechanical experiments of chemically strengthened aluminosilicate glass (CSAG) were conducted, using an electronic universal testing machine and a split Hopkinson pressure bar (SHPB) apparatus over a wide strain rate range of 0.0001 s⁻¹ to 1700 s⁻¹. Parallel to these, plate impact experiments were performed using a single-stage light gas gun to determine the material’s Equation of State (EOS) under high-pressure shock compression. For the quasi-static and SHPB tests, the failure processes were captured using high-speed photography to understand macroscopic failure mechanisms; additionally, post-test fragments were analyzed via scanning electron microscopy (SEM) and statistical methods to characterize fragment size distribution and micro-crack morphology under various strain rates. Finally, the Johnson-Holmquist (JH-2) constitutive parameters of the CSAG were then calibrated by integrating the EOS derived from plate impact data with the strength and damage characteristics obtained from the compressive tests. Numerical simulations were conducted to validate the accuracy of determined model parameters. The experimental results show that CSAG exhibits significant brittle fracture characteristics with strain-rate sensitivity in compressive strength. The fracture mechanism transforms from the flaw-dominated single-crack growth under quasi-static loading to a multiple-cracking phenomenon under dynamic loading. In both regimes, cracks propagate along the loading direction, with final explosive fragmentation caused by their coalescence under transverse tensile stresses. The distribution of fragment sizes provides a quantitative characterization of this shift in fracture mechanisms: a non-linear relationship between mass ratio and fragment size is observed under quasi-static loading, whereas dynamic loading (1100 s⁻¹ and 1700 s⁻¹) yields a distinctly linear correlation, where the mass ratio increases as fragment size decreases. This transition reflects the intensified fragmentation and rapid energy dissipation induced by high strain rates. The plate impact experimental data provides the essential pressure–volume relationship for the JH-2 model. The numerical simulations show good agreement with experimental observations, confirming that the calibrated model accurately.

在0.0001 s−1 ~ 1700 s−1的应变速率范围内，利用电子万能试验机和霍普金森压杆（SHPB）装置对化学强化铝硅酸盐玻璃（CSAG）进行了准静态和动态压缩力学实验。与此同时，使用单级光气枪进行板冲击实验，以确定高压冲击压缩下材料的状态方程（EOS）。在准静态和SHPB试验中，采用高速摄影捕捉破坏过程，了解宏观破坏机制；此外，通过扫描电子显微镜（SEM）和统计学方法对测试后的碎片进行分析，表征不同应变速率下的碎片尺寸分布和微裂纹形貌。最后，通过整合从板冲击数据中获得的EOS与从压缩试验中获得的强度和损伤特征，对CSAG的Johnson-Holmquist （JH-2）本构参数进行校准。通过数值模拟验证了模型参数的准确性。试验结果表明，CSAG具有明显的脆性断裂特征，对抗压强度具有应变率敏感性。断裂机制由准静态加载下以缺陷为主的单裂纹扩展转变为动态加载下的多裂纹扩展。在这两种情况下，裂纹沿加载方向扩展，在横向拉应力作用下，裂纹聚并导致最终爆炸破碎。碎片大小的分布为这种断裂机制的转变提供了定量表征：准静态加载下，质量比和碎片大小之间呈非线性关系，而动态加载（1100 s−1和1700 s−1）产生明显的线性相关性，其中质量比随着碎片大小的减小而增加。这种转变反映了高应变率引起的破碎加剧和能量快速耗散。平板撞击实验数据为JH-2模型提供了必要的压力-体积关系。数值模拟结果与实验结果吻合较好，证实了标定模型的准确性。

{"title":"Dynamic compressive behavior and constitutive parameters of chemically strengthened aluminosilicate glass","authors":"Ruimin Yang, Jing Ling, Xingya Su, Lin Jing","doi":"10.1016/j.engfracmech.2026.111844","DOIUrl":"10.1016/j.engfracmech.2026.111844","url":null,"abstract":"<div><div>Quasi-static and dynamic compressive mechanical experiments of chemically strengthened aluminosilicate glass (CSAG) were conducted, using an electronic universal testing machine and a split Hopkinson pressure bar (SHPB) apparatus over a wide strain rate range of 0.0001 s<sup>−1</sup> to 1700 s<sup>−1</sup>. Parallel to these, plate impact experiments were performed using a single-stage light gas gun to determine the material’s Equation of State (EOS) under high-pressure shock compression. For the quasi-static and SHPB tests, the failure processes were captured using high-speed photography to understand macroscopic failure mechanisms; additionally, post-test fragments were analyzed via scanning electron microscopy (SEM) and statistical methods to characterize fragment size distribution and micro-crack morphology under various strain rates. Finally, the Johnson-Holmquist (JH-2) constitutive parameters of the CSAG were then calibrated by integrating the EOS derived from plate impact data with the strength and damage characteristics obtained from the compressive tests. Numerical simulations were conducted to validate the accuracy of determined model parameters. The experimental results show that CSAG exhibits significant brittle fracture characteristics with strain-rate sensitivity in compressive strength. The fracture mechanism transforms from the flaw-dominated single-crack growth under quasi-static loading to a multiple-cracking phenomenon under dynamic loading. In both regimes, cracks propagate along the loading direction, with final explosive fragmentation caused by their coalescence under transverse tensile stresses. The distribution of fragment sizes provides a quantitative characterization of this shift in fracture mechanisms: a non-linear relationship between mass ratio and fragment size is observed under quasi-static loading, whereas dynamic loading (1100 s<sup>−1</sup> and 1700 s<sup>−1</sup>) yields a distinctly linear correlation, where the mass ratio increases as fragment size decreases. This transition reflects the intensified fragmentation and rapid energy dissipation induced by high strain rates. The plate impact experimental data provides the essential pressure–volume relationship for the JH-2 model. The numerical simulations show good agreement with experimental observations, confirming that the calibrated model accurately.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111844"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145973639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A new method of determining rock shear (or true mode II) fracture toughness 一种确定岩石剪切（或真II型）断裂韧性的新方法

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2025-12-26 DOI: 10.1016/j.engfracmech.2025.111828

Kun Zheng , Linjian Ma , Wen Hua

Fracture toughness remains a significant research topic in solid fracture mechanics, representing the material resistance to crack propagation. The shear fracture often occurs in rock masses, especially for mines, slopes, and faults. To determine the rock shear (or true mode-II) fracture toughness, this paper develops a new fracture test method based on the Mohr-Coulomb criterion. The new method comprises a double-edge notched rectangular column (DNRC) specimen, which is substantiated by the experimental data obtained from various mode-II test methods. The designed DNRC specimens exhibit a self-planar crack propagation pattern, which conforms to the shear fracture definition. The average shear fracture toughness K_IIc of DNRC sandstone specimens is 2.81 MPa•m^0.5, and the average tensile fracture toughness K_Ic of ENDB (edge-notched disk bend) sandstone specimens is 1.03 MPa•m^0.5. The ratio of K_IIc to K_Ic is 2.73, which is consistent with published experimental results obtained from the established mode-II test methods. The Mohr-Coulomb criterion provides theoretical explanations for the newly designed DNRC specimen, and the current and previous experimental results further validate its effectiveness and reliability. This paper aims to develop a test method which can realize both mode II loading and true mode II fracturing, thereby exploring the shear fracture behaviors of brittle and quasi-brittle materials.

断裂韧性是固体断裂力学中一个重要的研究课题，它代表了材料对裂纹扩展的阻力。剪切断裂常发生在岩体中，特别是矿山、边坡和断层。为了确定岩石的剪切（或真ii型）断裂韧性，本文提出了一种基于Mohr-Coulomb准则的断裂试验方法。该方法采用双边缘缺口矩形柱（DNRC）试件，并通过各种ii型试验方法获得的实验数据进行验证。设计的DNRC试件呈现自平面裂纹扩展模式，符合剪切断裂定义。DNRC砂岩试件的平均剪切断裂韧性KIIc为2.81 MPa•m0.5， ENDB（边缘切口圆盘弯曲）砂岩试件的平均拉伸断裂韧性KIc为1.03 MPa•m0.5。KIIc与KIc之比为2.73，与已发表的用已建立的ii型试验方法得到的实验结果一致。Mohr-Coulomb准则为新设计的DNRC试件提供了理论解释，目前和以往的试验结果进一步验证了该准则的有效性和可靠性。本文旨在开发一种既能实现II型加载又能实现真II型断裂的试验方法，从而探索脆性和准脆性材料的剪切断裂行为。

{"title":"A new method of determining rock shear (or true mode II) fracture toughness","authors":"Kun Zheng , Linjian Ma , Wen Hua","doi":"10.1016/j.engfracmech.2025.111828","DOIUrl":"10.1016/j.engfracmech.2025.111828","url":null,"abstract":"<div><div>Fracture toughness remains a significant research topic in solid fracture mechanics, representing the material resistance to crack propagation. The shear fracture often occurs in rock masses, especially for mines, slopes, and faults. To determine the rock shear (or true mode-II) fracture toughness, this paper develops a new fracture test method based on the Mohr-Coulomb criterion. The new method comprises a double-edge notched rectangular column (DNRC) specimen, which is substantiated by the experimental data obtained from various mode-II test methods. The designed DNRC specimens exhibit a self-planar crack propagation pattern, which conforms to the shear fracture definition. The average shear fracture toughness <em>K</em><sub>IIc</sub> of DNRC sandstone specimens is 2.81 MPa•m<sup>0.5</sup>, and the average tensile fracture toughness <em>K</em><sub>Ic</sub> of ENDB (edge-notched disk bend) sandstone specimens is 1.03 MPa•m<sup>0.5</sup>. The ratio of <em>K</em><sub>IIc</sub> to <em>K</em><sub>Ic</sub> is 2.73, which is consistent with published experimental results obtained from the established mode-II test methods. The Mohr-Coulomb criterion provides theoretical explanations for the newly designed DNRC specimen, and the current and previous experimental results further validate its effectiveness and reliability. This paper aims to develop a test method which can realize both mode II loading and true mode II fracturing, thereby exploring the shear fracture behaviors of brittle and quasi-brittle materials.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111828"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145881669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Effect of fluid flow on Mode-I dynamic stress intensity factor in the presence of crack shielding in a poroelastic medium 孔隙弹性介质中存在裂纹屏蔽时流体流动对i型动应力强度因子的影响

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2025-12-27 DOI: 10.1016/j.engfracmech.2025.111826

Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu

This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio

γ

, the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of

γ \geq 10

, the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For

γ < 1

, the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of

1 < γ < 10

, the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.

本文分析了孔隙弹性介质中平行裂纹的i型应力强度因子。特别地，我们研究了裂纹屏蔽对流体流动的影响，而流体流动反过来又可以进一步改变SIF的频率依赖行为。数值结果表明，SIF的频率相关行为是由流体流动和屏蔽效应共同控制的，屏蔽效应以裂缝间距与裂缝长度之比γ为特征。透水裂纹的SIF随频率的增加而减小，说明在短期响应中，流体没有足够的时间在裂纹和周围微孔之间流动，从而抑制了裂纹的变形。在γ≥10的情况下，屏蔽效应可以忽略不计，因此我们的结果可以简化为单个裂纹的结果，当流体扩散波长大致等于裂纹长度时，SIF衰减最快。对于γ<；1，屏蔽效应可以在更宽的频率范围内显著降低SIF的幅度，从而提高材料的有效强度。当流体扩散波长等于裂纹间距时，SIF在较高的特征频率处衰减最快。当中间值为1<；γ<；10时，特征频率受裂纹长度和裂纹间距的影响。相比之下，流体流动对不透水裂缝SIF的影响要弱得多。我们的研究结果表明，裂纹表面的裂纹屏蔽和渗透率对SIF的震级和频率依赖行为都有强烈的影响。

{"title":"Effect of fluid flow on Mode-I dynamic stress intensity factor in the presence of crack shielding in a poroelastic medium","authors":"Yannan Lu , Yongjia Song , Deyou Yu , Wei Guan , Hengshan Hu","doi":"10.1016/j.engfracmech.2025.111826","DOIUrl":"10.1016/j.engfracmech.2025.111826","url":null,"abstract":"<div><div>This paper analyzes the Mode-I stress intensity factor (SIF) of parallel cracks in a poroelastic medium. In particular, we investigate the influences of crack shielding on fluid flow which in turn can further change the frequency-dependent behaviors of SIF. Numerical results reveal that the frequency-dependent behaviors of SIF are jointly controlled by fluid flow and the shielding effect which is characterized by a spacing ratio <span><math><mi>γ</mi></math></span>, the ratio of crack spacing to crack length. The SIF of permeable cracks decreases with frequency, implying that in short-term responses the fluid has insufficient time to flow between cracks and surrounding micropores so that the crack deformation is inhibited. In the case of <span><math><mrow><mi>γ</mi><mo>≥</mo><mn>10</mn></mrow></math></span>, the shielding effect is negligible so that our results reduce to that of a single crack for which the SIF decays the fastest when the wavelength of fluid diffusion roughly equals the crack length. For <span><math><mrow><mi>γ</mi><mo><</mo><mn>1</mn></mrow></math></span>, the shielding effect can remarkably reduce the magnitude of the SIF over a broader frequency range and thereby enhance the effective material strength. In this case, the SIF decays the fastest at a higher characteristic frequency where the wavelength of fluid diffusion equals the crack spacing. For an intermediate value of <span><math><mrow><mn>1</mn><mo><</mo><mi>γ</mi><mo><</mo><mn>10</mn></mrow></math></span>, the characteristic frequency is influenced by both crack length and crack spacing. In contrast, the effect of fluid flow on the SIF of impermeable cracks is much weaker. Our findings show that both the crack shielding and permeability of crack surfaces strongly affect the magnitudes and frequency-dependent behaviors of the SIF.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111826"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145882176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A phase-field fracture model for magneto-electro-elastic materials: Analytical and numerical results 磁-电弹性材料的相场断裂模型：解析与数值结果

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-02-21 Epub Date: 2025-12-31 DOI: 10.1016/j.engfracmech.2025.111834

Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li

Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.

磁-电弹性（MEE）固体以其在电场、磁场和弹性场之间的良好耦合效应而闻名。然而，MEE固体由于其较弱的断裂韧性和固有脆性而容易破坏。因此，MEE材料的断裂分析具有重要的学术意义。本文提出了一种MEE材料的长度尺度不敏感相场断裂模型。在一维情况下，首次导出了相应的解析解，包括裂纹成核时的临界应力和试件的整体响应。通过分析和数值算例验证了长度尺度参数的不敏感性，并分析了外加磁场和电场对MEE固体断裂行为的影响。在负磁场或负电场作用下，断裂载荷可能会增加，这为提高MEE试件的抗断裂性能提供了策略。这项工作对机电一体化结构和器件的可靠性评估具有重要意义。

{"title":"A phase-field fracture model for magneto-electro-elastic materials: Analytical and numerical results","authors":"Tianchi Hui , Yu Tan , Zirong Guo , Xuejun Gao , Jianjun Zhao , Xiangyu Li","doi":"10.1016/j.engfracmech.2025.111834","DOIUrl":"10.1016/j.engfracmech.2025.111834","url":null,"abstract":"<div><div>Magneto-electro-elastic (MEE) solids are renowned for their excellent coupling effect among electric, magnetic and elastic fields. Nevertheless, MEE solids are susceptible to failure owing to their weak fracture toughness and inherent brittleness. Fracture analyses of MEE materials are therefore of great academic importance. In this paper, a length scale insensitive phase-field fracture model for MEE materials is proposed. The corresponding analytical solutions, including the critical stress upon crack nucleation and global responses of the specimen, are derived for the first time in 1D cases. Analytical and numerical examples are carried out to verify the insensitivity of the length scale parameter and analyse the influences of the external magnetic and electric fields on the fracture behaviors of MEE solids. The fracture load may be increased under a negative magnetic or electric field, which provides strategies for enhancing the fracture resistance performance of MEE specimens. This work is of significance in assessing the reliability of MEE-based structures and devices.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":"333 ","pages":"Article 111834"},"PeriodicalIF":5.3,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0