Engineering Fracture Mechanics最新文献_第4页

Plastic zone size and crack tip opening displacement of doubly periodic Dugdale cracks with diamond-shaped-interleaving arrays under longitudinal shear 纵向剪切作用下菱形交错双周期Dugdale裂纹的塑性区尺寸和裂纹尖端张开位移

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-16 DOI: 10.1016/j.engfracmech.2026.111845

Yan Li , Pengpeng Shi , Xiaofan Gou , Wenshuai Wang , Xing Li

The interaction among multiple cracks plays a crucial role in the elastoplastic fracture behavior of materials. Although numerous studies have been devoted to elastic analyses of doubly periodic crack problems, the elastoplastic response of complex configurations such as doubly periodic cracks with diamond-shaped-interleaving arrays remains insufficiently explored. This paper investigates the plastic zone size (PZS) and crack tip opening displacement (CTOD) of doubly periodic cracks with diamond-shaped-interleaving arrays (DPC-DSIA) under longitudinal shear. Based on the Dugdale plastic zone model and the continuously distributed dislocation model, the mixed-boundary-value problem of elastoplastic behavior for DPC-DSIA configurations is transformed into a system of singular integral equations, where the semi-analytical solution is achieved using the Lobatto-Chebyshev numerical quadrature method. The accuracy of the proposed solution is verified against existing results for two typical periodic cracks with rectangular arrays and diamond-shaped arrays and the complex periodic cracks with diamond-shaped-interleaving small arrays. Furthermore, the influence of periodic parameters on key fracture quantities, including the PZS, CTOD, and stress intensity factor (SIF), are systematically examined. The results reveal the interaction mechanism between vertically and horizontally oriented cracks and highlight the complex effects of doubly periodic crack arrangements on the system’s elastoplastic behavior.

多裂纹之间的相互作用对材料的弹塑性断裂行为起着至关重要的作用。尽管对双周期裂纹问题的弹性分析已经有了大量的研究，但对具有菱形交错排列的双周期裂纹等复杂结构的弹塑性响应研究还不够。研究了菱形交错阵列双周期裂纹在纵向剪切作用下的塑性区尺寸（PZS）和裂纹尖端张开位移（CTOD）。基于Dugdale塑性区模型和连续分布位错模型，将DPC-DSIA构形弹塑性行为混合边值问题转化为奇异积分方程组，利用Lobatto-Chebyshev数值求积分法得到半解析解。通过对矩形阵和菱形阵两种典型周期裂纹以及菱形交错小阵复杂周期裂纹的分析，验证了所提方法的准确性。此外，系统地研究了周期参数对关键裂缝量的影响，包括PZS、CTOD和应力强度因子（SIF）。结果揭示了垂直和水平取向裂纹之间的相互作用机制，并突出了双周期裂纹排列对体系弹塑性行为的复杂影响。

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引用次数: 0

Phase-field modelling of quasi-static and dynamic brittle fracture: A FreeFEM++ implementation 准静态和动态脆性断裂的相场建模：FreeFEM++实现

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-15 DOI: 10.1016/j.engfracmech.2026.111846

Andres F. Galvis

This work presents a robust phase-field formulation for brittle fracture, combining a quasi-monolithic solution strategy with a frozen history field, Houbolt time integration for dynamic/transient regimes, and adaptive remeshing in FreeFEM++. This approach enhances numerical robustness, simplifies parameter calibration, and facilitates extensions to multi-physics fracture problems. Despite widespread interest, building on this framework, a key contribution is the first open serial implementation of this framework in FreeFEM++, offering advantages in mesh adaptivity, solver flexibility, and concise variational syntax. The mesh adaptivity feature concentrates resolution near evolving crack tips to efficiently capture fracture evolution. The implementation is validated on standard benchmarks, showing close agreement with reference crack paths, load–displacement, and dissipated energy responses. By releasing a concise, well-documented FreeFEM++ code, this work bridges a reproducibility gap and establishes a methodological foundation for future developments.

这项工作提出了一个强大的脆性断裂相场公式，结合了准单片解策略和冻结历史场，动态/瞬态状态的Houbolt时间积分，以及FreeFEM++中的自适应网格划分。该方法增强了数值鲁棒性，简化了参数校准，便于扩展到多物理场裂缝问题。尽管有广泛的兴趣，在这个框架的基础上，一个关键的贡献是在FreeFEM++中第一个开放的串行实现这个框架，提供网格适应性，求解器灵活性和简洁的变分语法方面的优势。网格自适应特征将分辨率集中在演化裂纹尖端附近，从而有效地捕捉裂缝演化过程。在标准基准测试中验证了该实现，显示与参考裂缝路径、荷载-位移和耗散能量响应密切一致。通过发布一个简明的、文档完备的FreeFEM++代码，这项工作弥补了可再现性的差距，并为未来的开发建立了方法论基础。

引用次数: 0

The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity Capriccio方法是一种多功能的工具，用于量化玻璃材料在复杂载荷条件下的断裂特性，具有化学特异性

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-13 DOI: 10.1016/j.engfracmech.2026.111841

Felix Weber , Maxime Vassaux , Lukas Laubert , Sebastian Pfaller

Molecular dynamics (MD) simulations are widely used to provide insights into fracture mechanisms while maintaining chemical specificity. However, particle-based techniques such as MD are limited in terms of accessible length scales and applicable boundary conditions, which restricts the investigation of fracture phenomena in typical engineering settings. In an attempt to overcome these limitations, we apply the partitioned-domain Capriccio method to couple atomistic MD samples representing silica glass with the finite element (FE) method. With this approach, we perform mode I (rectangular panel under tension, three-, and four-point bending), mode II as well as mode III (rectangular panel under in-plane or out-of-plane shear) simulations. Thereby, we investigate multiple criteria to identify the onset of crack propagation based on the virial stress, the number of pair interactions, the kinetic energy/temperature, the crack velocity, and the crack opening displacement. It becomes apparent that the maximum virial stress can actually serve as an objective and meaningful indicator for the start of crack growth, in contrast to, for example, the temperature evolution The approach presented provides quantitatively plausible results for the critical stress intensity factors

K_{Ic}

,

K_{IIc}

, and

K_{IIIc}

. This contribution shows that the Capriccio method is a flexible means of performing fracture simulations that take into account boundary conditions typical of experimental test setups with atomistic specificity near the crack tip. While also pointing out the current limitations of the Capriccio method, we demonstrate its potential to integrate atomistic insights into FE models with significantly larger overall dimensions.

分子动力学（MD）模拟被广泛用于在保持化学特异性的同时提供对裂缝机制的深入了解。然而，基于颗粒的技术（如MD）在可获得的长度尺度和适用的边界条件方面受到限制，这限制了典型工程环境中裂缝现象的研究。为了克服这些限制，我们应用分域Capriccio方法将原子MD样品与有限元（FE）方法耦合在一起。通过这种方法，我们执行模式I（矩形面板在张力，三点和四点弯曲下），模式II和模式III（矩形面板在面内或面外剪切下）模拟。因此，我们研究了基于维里应力、对相互作用次数、动能/温度、裂纹速度和裂纹张开位移的多重准则来识别裂纹扩展的开始。很明显，与温度演变等因素相比，最大虚拟应力实际上可以作为裂纹扩展开始的客观和有意义的指标。本文提出的方法为临界应力强度因子KIc， KIIc和KIIIc提供了定量可信的结果。这表明，Capriccio方法是一种灵活的断裂模拟方法，它考虑了裂纹尖端附近具有原子特异性的实验测试设置的典型边界条件。在指出Capriccio方法目前的局限性的同时，我们展示了它将原子的洞察力集成到具有更大总体维度的FE模型中的潜力。

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引用次数: 0

A fusion framework of improved YOLOv8 and lightweight DeepLabv3 + for concrete bridge surface defect identification 改进的YOLOv8与轻型DeepLabv3 +融合框架用于混凝土桥梁表面缺陷识别

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-13 DOI: 10.1016/j.engfracmech.2026.111864

Daihai Chen , Xichao Ma , Yunsen Zhang , Shizhan Xu , Yu Zhang

With the increasing prevalence of bridge aging and overloading, traditional manual inspection methods suffer from low efficiency and strong subjectivity, making it difficult to achieve accurate and efficient damage recognition. In recent years, deep learning techniques have provided new solutions for the intelligent detection of bridge surface defects. This study investigates typical defects in concrete bridges, including cracks, exposed reinforcement, and spalling. To address the challenges of small-defect recognition in complex backgrounds and high computational complexity, an improved YOLOv8-based model integrating the Triplet Attention mechanism and a dynamic detection head (DyHead) is proposed for defect detection, while an enhanced semantic segmentation approach for concrete bridge surface defects is developed based on the DeepLabV3 + architecture. First, defect images of bridges in Henan Province were collected and annotated at the pixel level using the Labelme software, which were then converted into mask images. Data augmentation strategies, such as rotation and flipping, expanded the dataset to 5,155 images, followed by systematic labeling and partitioning. In the object detection task, the proposed YOLOv8 model with Triplet Attention and DyHead effectively enhanced defect feature extraction and multi-scale localization, achieving an [email protected] of 80.5 %, a 4.9 % improvement over the baseline. In the semantic segmentation task, a lightweight DeepLabV3 + model with MobileNetV3 as the backbone was constructed, incorporating the CBAM attention mechanism and a joint loss function. This design achieved an mIoU of 80.47 % while maintaining a relatively low parameter count (7.8 M), with an 8.2 % improvement in crack segmentation accuracy. The results demonstrate that the proposed methods outperform mainstream models in both accuracy and efficiency, providing a reliable solution for the intelligent recognition of concrete bridge surface defects.

随着桥梁老化和超载的日益普遍，传统的人工检测方法存在效率低、主观性强的问题，难以实现准确、高效的损伤识别。近年来，深度学习技术为桥梁表面缺陷的智能检测提供了新的解决方案。本研究调查了混凝土桥梁的典型缺陷，包括裂缝、暴露的钢筋和剥落。针对复杂背景下小缺陷识别和计算复杂度高的难题，提出了一种基于yolov8的改进模型，该模型集成了三重注意机制和动态检测头（DyHead），用于缺陷检测，并基于DeepLabV3 +架构开发了一种增强的混凝土桥梁表面缺陷语义分割方法。首先，采集河南省桥梁缺陷图像，利用Labelme软件在像素级进行标注，然后转换成掩模图像；数据增强策略，如旋转和翻转，将数据集扩展到5155张图像，然后进行系统的标记和分区。在目标检测任务中，本文提出的带有Triplet Attention和DyHead的YOLOv8模型有效地增强了缺陷特征提取和多尺度定位，[email protected]的识别率达到80.5%，比基线提高4.9%。在语义分割任务中，构建了以MobileNetV3为骨干的轻量级DeepLabV3 +模型，该模型结合了CBAM注意机制和联合损失函数。该设计实现了80.47%的mIoU，同时保持了相对较低的参数计数（7.8 M），裂缝分割精度提高了8.2%。结果表明，该方法在精度和效率上均优于主流模型，为混凝土桥梁表面缺陷的智能识别提供了可靠的解决方案。

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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 : 2026-01-13 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。

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引用次数: 0

A fracture phase field model based on critical plane method and multi-axial fatigue life model 基于临界平面法和多轴疲劳寿命模型的断裂相场模型

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-13 DOI: 10.1016/j.engfracmech.2026.111848

Xin Yang , Wei Chen , Lulu Liu , Zhenhua Zhao , Weixing Yao , Jianwu Zhou

In recent years, phase-field method (PFM) has attracted a lot of attention as an advanced numerical simulation technique in fracture mechanics. However, few PFM models adequately account for the effects of multi-axial stress states during crack initiation and propagation. This paper proposes a new phase-field model by integrating the critical plane method, multi-axial fatigue life models, and PFM, to simulate crack initiation and propagation under multi-axial stress states. We integrate the critical plane approach and multi-axial fatigue life models (SWT, MWHS, MGSE) and S-N curve into the phase-field framework, proposing modified models (E-MWHS, E-MGSE) to enhance prediction accuracy, six kinds of PFMs are thus obtained. The proposed PFM was applied to investigate how the multi-axial fatigue life models, critical plane search step size, cycle skipping increment, and strain energy density decomposition methods affect crack initiation and propagation, compact tension (CT) specimen was also used to quantify these parameters’ influence on da/dN-ΔK and a-N curves. The fatigue life of Titanium alloy: TC4 and Nickel base superalloy: GH4169 predicted by the proposed PFM is mostly within the triple scatter band, and the multi-axial fatigue life models and strain energy decomposition method have a significant effect on crack growth rate and path. The proposed phase-field model can provides an analytical method for fatigue life prediction and reliability design of aero-engine components.

相场法作为一种先进的断裂力学数值模拟技术，近年来受到了广泛的关注。然而，很少有模型能充分考虑裂纹萌生和扩展过程中多轴应力状态的影响。结合临界平面法、多轴疲劳寿命模型和PFM模型，提出了一种新的相场模型来模拟多轴应力状态下裂纹的萌生和扩展。将临界平面法、多轴疲劳寿命模型（SWT、MWHS、MGSE）和S-N曲线整合到相场框架中，提出了修正模型（E-MWHS、E-MGSE）以提高预测精度，得到了6种pfm。应用所提出的PFM研究了多轴疲劳寿命模型、临界平面搜索步长、循环跳过增量和应变能密度分解方法对裂纹萌生和扩展的影响，并利用致密拉伸（CT）试样量化了这些参数对da/dN-ΔK和a-N曲线的影响。所提出的PFM预测的钛合金：TC4和镍基高温合金：GH4169的疲劳寿命大多在三重散射带内，多轴疲劳寿命模型和应变能分解方法对裂纹扩展速度和路径有显著影响。该相场模型可为航空发动机部件疲劳寿命预测和可靠性设计提供一种分析方法。

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引用次数: 0

On the mixed mode crack propagation using a 2D BEM formulation combined with a Newton-Raphson/Arc-length iterative method: discussion about material bifurcation 结合牛顿-拉夫森/弧长迭代法的二维边界元公式研究混合模式裂纹扩展：关于材料分岔的讨论

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-12 DOI: 10.1016/j.engfracmech.2026.111858

Gabriela R. Fernandes , Eduardo A. de Souza Neto , José J.C. Pituba

Numerical modeling of mixed mode cracks propagation is discussed by using a 2D Boundary Element formulation with Quadratic convergence applied to Strong Discontinuities (BEMQ-SD). This model is based on strong discontinuity technique embedded into a continuum medium. The criterion for material bifurcation is the singularity of the acoustic tensor, being the normal direction to the crack surface defined by its eigenvalue. Usually only one direction is related to this singularity, but we discuss examples where we can have two different directions associated with the material bifurcation. Thus, we propose an efficient criterion to identify the correct solution. The Arc-length method combined with the Newton-Raphson method is adopted to obtain the solution of the iterative procedure required to solve the equilibrium problem. This force control procedure is efficient and has low computational cost, achieving the solution with a small number of iterations. As numerical examples, we consider a plate with a fragile sub-domain subjected to pure shear and to a combination of loads, a single-edge notched shear test and two experimentally tested examples, which present a mixed-mode fracture configuration with multiple cracks. We show that the proposed model can find the correct solution, and it is accurate, stable and efficient, showing itself to be an alternative tool to FEM or XFEM models. An important advantage of BEM models is that is not necessary to discretize the domain that remains with elastic behavior, what reduces the computational effort.

采用二维强不连续二次收敛边界元公式，讨论了混合模式裂纹扩展的数值模拟。该模型基于嵌入连续介质的强不连续技术。材料分叉的判据是声张量的奇异性，即由其特征值定义的到裂纹表面的法向。通常只有一个方向与这个奇点有关，但我们讨论的例子中，我们可以有两个不同的方向与材料分岔有关。因此，我们提出了一个有效的标准来识别正确的解决方案。采用弧长法结合牛顿-拉夫逊法求解平衡问题所需的迭代过程。该力控制程序效率高，计算成本低，迭代次数少。作为数值算例，我们考虑了具有脆性子域的板在纯剪切和组合载荷作用下，单边缺口剪切试验和两个实验测试实例，它们呈现出多重裂纹的混合模式断裂形态。仿真结果表明，所提出的模型能够找到正确的解，且精度高、稳定性好、效率高，可作为有限元模型或XFEM模型的替代工具。边界元模型的一个重要优点是不需要对保持弹性行为的区域进行离散化，从而减少了计算量。

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引用次数: 0

Three-dimensional fracture evolution in coal under cryogenic-thermal shock based on CT technology 基于CT技术的低温-热冲击下煤体三维裂隙演化

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-12 DOI: 10.1016/j.engfracmech.2026.111861

Lei Qin , Chengang Sun , Xian Zhang , Niandong Chen , Weikai Wang , Feilong Zhang , Meiling Xiong

The pore structure of coal plays a crucial role in the migration of fluids such as gas and water. To analyze the evolution law and deterioration mechanisms of the three-dimensional pore structure in coal subjected to cryogenic-thermal cyclic shock, this study employed three-dimensional CT scanning technology to investigate the impact of the number of cryogenic-thermal shock cycles on coal pore structure parameters. The results indicate that: (1) The number of three-dimensional pores in coal increases with the number of cryogenic-thermal shock cycles. (2) Pore evolution undergoes three irreversible stages: damage accumulation (0–6 cycles), network reconstruction (7–9 cycles), and fragmentation equilibrium (10–12 cycles). The pore shape factor decreases to a minimum of 0.015, while the coordination number peaks at 32. (3) After 12 cycles, the pore-throat structure exhibits highly discrete characteristic radii (45, 105, and 135 μm), each accounting for ∼ 33.3 %, forming an efficient hierarchical seepage network. (4) Based on the characteristics of microscopic damage evolution in coal, cryogenic-thermal cycling synergistically disrupts the coal structure through a triple-mechanism (comprising dynamic pressure shock, thermal stress cycling, and multiphase phase-change damage). This research enriches the fundamental theory of cryogenic-thermal cyclic shock (LCO₂ − high-temperature steam) on coal.

煤的孔隙结构对气、水等流体的运移起着至关重要的作用。为分析低温-热循环冲击作用下煤体三维孔隙结构的演化规律及恶化机制，本研究采用三维CT扫描技术研究低温-热循环次数对煤体孔隙结构参数的影响。结果表明：(1)煤中三维孔隙数量随着低温-热冲击循环次数的增加而增加。(2)孔隙演化经历3个不可逆阶段：损伤积累（0 ~ 6个旋回）、网络重构（7 ~ 9个旋回）和破碎平衡（10 ~ 12个旋回）。孔隙形状因子最小为0.015，配位数最大为32。(3)经过12次循环后，孔喉结构表现出高度离散的特征半径（45、105和135 μm），每个特征半径占~ 33.3%，形成了一个高效的分层渗透网络。(4)根据煤体微观损伤演化特征，低温-热循环通过动压冲击、热应力循环和多相相变损伤三重机制协同破坏煤体结构。该研究丰富了煤的低温-热循环冲击（LCO2 -高温蒸汽）的基础理论。

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引用次数: 0

Influence of printing orientation of Inconel 718 specimens on LEFM parameters analyzed via DVC 用DVC分析了印模取向对印模参数的影响

IF 5.3 2区工程技术 Q1 MECHANICS

Engineering Fracture Mechanics

Pub Date : 2026-01-12 DOI: 10.1016/j.engfracmech.2026.111849

Malo Valmalle , Gaëtan Touzé , Benjamin Smaniotto , Nicolas Muller , Joseph Marae Djouda , François Hild

Laser powder bed fusion (LPBF) is an additive manufacturing technique that enables for the production of metallic parts with complex geometries, and the possibility of locally adapting mesostructures. This study aims at determining the influence of hatch angle and build orientation on Linear Elastic Fracture Mechanics (LEFM) parameters of specimens obtained by LPBF. In the present work, the mechanical response of mini CT specimens made of Inconel 718 alloy obtained by LPBF were studied when subjected to in-situ tensile loading. The LEFM parameters of the different specimens were extracted from displacement fields measured with Digital Volume Correlation (DVC) using Williams’ fields. The crack front and Stress Intensity Factors (SIF) profiles of the different experiments were analyzed. The extracted LEFM parameters for the different specimens displayed significant differences in Young’s Modulus and fracture toughness due to variations in build orientation.

激光粉末床熔融（LPBF）是一种增材制造技术，能够生产具有复杂几何形状的金属零件，并有可能局部适应介孔结构。本研究旨在确定舱口角度和构建方向对LPBF获得的试样线弹性断裂力学（LEFM）参数的影响。本文研究了LPBF法制备的Inconel 718合金微型CT试样在原位拉伸载荷作用下的力学响应。利用Williams场，从数字体积相关（Digital Volume Correlation， DVC）测量的位移场中提取不同试件的LEFM参数。分析了不同试验条件下的裂纹前缘和应力强度因子分布。由于构建方向的不同，所提取的不同试样的LEFM参数在杨氏模量和断裂韧性方面存在显著差异。

引用次数: 0

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 : 2026-01-12 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。

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引用次数: 0