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Less is more: removing a single bond increases the toughness of elastic networks 少即是多:去除单个键会增加弹性网络的韧性
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-28 DOI: 10.1007/s10704-025-00891-x
Antoine Sanner, Luca Michel, Alessandra Lingua, David S. Kammer

We investigate how the removal of a single bond affects the fracture behavior of triangular spring networks, whereby we systematically vary the position of the removed bond. Our simulations show that removing the bond has two contrasting effects on the fracture energy for initiation of crack propagation and on the fracture energy for failure of the entire network. A single missing bond can either lower or raise the initiation fracture energy, depending on its placement relative to the crack tip. In contrast, the failure fracture energy is always equal to or greater than that of a perfect network. For most initial placements of the missing bond, the crack path remains straight, and the increased failure fracture energy results from arrest at the point of maximum local fracture resistance. When the crack deviates from a straight path, we observe an even higher fracture energy, which we attribute primarily to crack bridging. This additional toughening mechanism becomes active only at low failure strains of the springs; at higher failure strains, the crack path tends to remain straight. Altogether, our results demonstrate that even a single bond removal can significantly enhance toughness, offering fundamental insights into the role of defects in polymer networks and informing the design of tough architected materials.

我们研究了单个键的移除如何影响三角形弹簧网络的断裂行为,因此我们系统地改变了移除键的位置。我们的模拟表明,去除键对裂纹扩展起始的断裂能和整个网络破坏的断裂能有两种截然不同的影响。单个缺失的键可以降低或提高起始断裂能,这取决于它相对于裂纹尖端的位置。相反,破坏断裂能总是等于或大于完美网络的断裂能。对于缺失键的大多数初始位置,裂纹路径保持直线,并且破坏断裂能量的增加是由于在局部断裂阻力最大的点上停止。当裂纹偏离直线路径时,我们观察到更高的断裂能,我们将其主要归因于裂纹桥接。这种额外的增韧机制仅在弹簧的低失效应变时才起作用;在较高的破坏应变下,裂纹路径趋于保持直线。总之,我们的研究结果表明,即使去除单个键也可以显着提高韧性,为了解聚合物网络中缺陷的作用提供了基本见解,并为设计坚韧的建筑材料提供了信息。
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引用次数: 0
Crack propagation in the presence of multiple holes: phase field modelling supported by photoelasticity 多孔洞存在下的裂纹扩展:光弹性支持的相场模型
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-27 DOI: 10.1007/s10704-025-00887-7
C. Anand, K. Ramesh, Sundararajan Natarajan

The reliability and structural integrity of the components get reduced when cracks grow during their service. This becomes even more critical when casting defects, such as macropores, are present in the component. This work investigates the crack trajectory in the presence of selected hole configurations by integrating phase field modelling with photoelasticity, serving as a precursor for modelling macroporosity. By lowering the computational burden typically associated with phase field modelling, photoelasticity has helped to arrive at a simple and consistent PFM approach capturing complex crack trajectories, validated experimentally for a wide configuration of holes with repeatability. Numerically simulated isochromatics are used to corroborate the findings from the phase field simulations and experiments.

构件在使用过程中出现裂纹,会降低构件的可靠性和结构完整性。当铸造缺陷,如在组件中存在大孔隙时,这变得更加关键。这项工作通过将相场建模和光弹性相结合,研究了在选择孔构型存在下的裂缝轨迹,作为模拟宏观孔隙度的先驱。通过降低通常与相场建模相关的计算负担,光弹性有助于实现一种简单而一致的PFM方法,该方法可以捕获复杂的裂纹轨迹,并在具有可重复性的广泛孔配置中得到实验验证。数值模拟的等色线证实了相场模拟和实验的结果。
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引用次数: 0
Crystal plasticity-based intergranular facture simulation of AA 5083 aluminum alloy for tri-junction grain boundary 基于晶体塑性的AA 5083铝合金三结晶界晶间断裂模拟
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-17 DOI: 10.1007/s10704-025-00892-w
Xin Zhang, Qi Zhao, Hongxia Zhang, Zhipeng Zhai, Xiang Chen, Ying Hu, Zhuo Han, Nianfeng Zhang, Yucheng Gui, Magd Abdel Wahab

The fracture mode of AA 5083 Al–Mg alloy is predominantly intergranular. For this, a three-dimensional Crystal Plasticity Finite Element (CPFE) model is developed to investigate Grain Boundary (GB) fracture behavior under uniaxial tensile loading. Following parameter calibration, the simulated tensile strength demonstrates consistency with experimental data, with a high accuracy of 97%. Furthermore, by integrating CPFE model incorporating the dislocation slips with a GB model, a two-dimensional tri-junction crystal plasticity framework is established, and cohesive elements are implemented within the three grains to simulate GB fracture process under uniaxial tension. This tri-junction model shows a good convergence. The effect of grain orientation, location and GB thickness on GB fracture is investigated. The results reveal that grain orientation and location significantly influences GB fracture behavior. It is found that the Goss-Brass-P orientation combination demonstrates the optimal comprehensive mechanical properties, achieving a strain energy density of 7.09 MJ/m3. Furthermore, there exists a threshold effect about GB thickness on comprehensive property. The optimal performance is obtained when the cohesive that determines GB thickness is set to 2.

AA 5083铝镁合金的断裂方式以晶间断裂为主。为此,建立了三维晶体塑性有限元(CPFE)模型,研究了单轴拉伸载荷下晶界断裂行为。经参数校正,模拟的抗拉强度与实验数据一致,精度高达97%。将包含位错滑移的CPFE模型与GB模型相结合,建立了二维三结晶体塑性框架,并在三晶粒内部引入内聚元,模拟了单轴拉伸下的GB断裂过程。该三结模型具有良好的收敛性。研究了晶态取向、晶态位置和晶态厚度对晶态断裂的影响。结果表明,晶粒取向和晶粒位置对GB断裂行为有显著影响。结果表明,Goss-Brass-P取向组合具有最佳的综合力学性能,应变能密度达到7.09 MJ/m3。此外,GB厚度对综合性能存在阈值效应。当决定GB厚度的内聚性设置为2时,性能最优。
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引用次数: 0
Multiscale analysis and lifetime prediction of adhesive lap joints in contact with aggressive environments 接触侵蚀环境的粘接搭接多尺度分析及寿命预测
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-16 DOI: 10.1007/s10704-025-00893-9
M. P. Ariza, M. Ortiz

We formulate a multiscale model of adhesive layers undergoing impurity-dependent cohesive fracture. The model contemplates three scales: i) at the atomic scale, fracture is controlled by interatomic separation and the thermodynamics of separation depends on temperature and impurity concentration; ii) the mesoscale is characterized by the collective response of a large number of interatomic planes across the adhesive layer, resulting in a thickness-dependence strength; in addition, impurities are uptaken from the environment and diffuse through the adhesive layer; and iii) at the macroscale, we focus on lap joints under the action of static loads and aggressive environments. Within this scenario, we obtain closed form analytical solutions for: the dependence of the adhesive layer strength on thickness; the length of the edge cracks, if any, as a function of time; the lifetime of the joint; and the dependence of the strength of the joint on time of preexposure to the environment. Overall, the theory is found to capture well the experimentally observed trends. Finally, we discuss how the model can be characterized on the basis of atomistic calculations, which opens the way for the systematic exploration of new material specifications.

我们建立了一个多尺度模型的胶粘剂层经历杂质依赖的粘聚断裂。该模型考虑了三个尺度:1)在原子尺度上,断裂受原子间分离控制,分离热力学取决于温度和杂质浓度;Ii)中尺度的特点是大量原子间平面在粘接层上的集体响应,导致强度与厚度相关;此外,杂质从环境中被吸收并通过粘接层扩散;iii)在宏观尺度上,我们关注静载荷和恶劣环境作用下的搭接。在这种情况下,我们得到了封闭形式的解析解:粘接层强度对厚度的依赖;边缘裂纹的长度(如果有的话)作为时间的函数;关节的寿命;以及接头强度对预暴露于环境时间的依赖性。总的来说,该理论很好地捕捉了实验观察到的趋势。最后,我们讨论了如何在原子计算的基础上表征模型,这为系统地探索新材料规格开辟了道路。
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引用次数: 0
Editorial: Finite fracture mechanics and phase-field modeling of fracture—towards applications 有限断裂力学和相场建模在断裂方向上的应用
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-14 DOI: 10.1007/s10704-025-00883-x
Vladislav Mantič
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引用次数: 0
Analysis of mode II fracture speeds in dry snow slab avalanche weak layers 干雪板雪崩弱层II型断裂速度分析
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-14 DOI: 10.1007/s10704-025-00890-y
D. M. McClung

Once shear fractures begin to propagate in relatively thin weak layers underneath dry snow slabs, avalanche release is imminent. The evolution of the dynamic weak layer fracture likely determines the size or destructive potential once release takes place. In this paper, 54 values of mode II fracture speed collected from field tests are analyzed. In addition, values of speed collected with connection with avalanche release which involves both mode II and mode III shear fracture are analyzed. The Rayleigh wave speed is the normal maximum speed limit for a mode II fracture based on continuum formulations and the shear wave speed is the companion speed limit for mode III fracture. The 54 values of speed data from field tests are shown to have a median value of 12% of the predicted Rayleigh wave speed with a range between 2 and 56%. The data collected during avalanche release do not exceed 59% of the Rayleigh wave speed. The test data were collected from weak layers composed of highly porous crystal forms which are known to exhibit dynamic porosity loss during fracture propagation. Such events imply viscous dissipation and high friction which help to explain the low speeds. For snow slab avalanche release, which occurs for slope angles greater than (25^{0}), field observations show that the mixed mode (II, III) weak layer fracture terminates with mode I fracture through the slab following dynamic propagation. Analysis using the avalanche speed data with respect to terminal mode I fracture suggests that the shear stress drop behind the fracture process zone can contribute to produce the mode I fracture to promote avalanche release but dynamic contraction of the fracture process zone is a minor effect at best.

一旦剪切裂缝开始在干燥的雪板下面的相对较薄的薄弱层中传播,雪崩的释放就迫在眉睫。动态弱层裂缝的演化可能决定了一旦释放的大小或破坏潜力。本文对现场试验收集的54个II型裂缝速度值进行了分析。此外,对雪崩释放涉及II型和III型剪切断裂时采集的速度值进行了分析。瑞利波速是基于连续体公式的II型裂缝的正常最大速度限制,剪切波速是III型裂缝的伴随速度限制。现场试验的54个速度数据值的中位数为12% of the predicted Rayleigh wave speed with a range between 2 and 56%. The data collected during avalanche release do not exceed 59% of the Rayleigh wave speed. The test data were collected from weak layers composed of highly porous crystal forms which are known to exhibit dynamic porosity loss during fracture propagation. Such events imply viscous dissipation and high friction which help to explain the low speeds. For snow slab avalanche release, which occurs for slope angles greater than (25^{0}), field observations show that the mixed mode (II, III) weak layer fracture terminates with mode I fracture through the slab following dynamic propagation. Analysis using the avalanche speed data with respect to terminal mode I fracture suggests that the shear stress drop behind the fracture process zone can contribute to produce the mode I fracture to promote avalanche release but dynamic contraction of the fracture process zone is a minor effect at best.
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引用次数: 0
Dynamic crack growth analysis by an eikonal gradient damage model 斜向梯度损伤模型的动态裂纹扩展分析
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-10 DOI: 10.1007/s10704-025-00889-5
Hung Thanh Tran

In this article, an isotropic eikonal gradient-enhanced damage modeling technique for studying time-dependent fracture mechanisms in brittle/quasi-brittle solids is presented. As is consistent with the classical gradient damage theory, the eikonal-type gradient damage modeling framework is mesh-independent and simple to implement, as it does not require any numerical tracking algorithm for discontinuities in the displacement field during crack propagation. With the evolving interaction known as the damage-based transient internal length scale, eikonal damage formulations could overcome the drawbacks of spurious damage diffusion and incorrect damage initiation by the traditional gradient theory. More realistic failure behavior could be predicted by the eikonal-based damage models. In the work, the derived governing equations of the momentum and a smooth Rankine strain-based eikonal gradient-enhanced evolution for the motion of the body and evolution of the nonlocal equivalent strain (time-dependent fracture driving term) are effectively solved using the standard finite element method (FEM). For temporal discretization, a robust explicit solver of the central difference method integrated with the row-sum technique for mass lumping is adopted. The advantages and abilities of the present dynamic model are shown by considering a number of time-dependent crack propagation problems in two-dimensional (2D) and three- dimensional (3D) solids.

本文提出了一种用于研究脆性/准脆性固体中随时间变化的断裂机制的各向同性斜向梯度增强损伤建模技术。eikonal型梯度损伤建模框架与经典的梯度损伤理论一致,不需要对裂纹扩展过程中位移场的不连续点进行数值跟踪,与网格无关,易于实现。基于损伤瞬态内长度尺度的演化相互作用,可克服传统梯度理论损伤扩散不实和损伤起伤不正确的缺点。基于eikonal的损伤模型可以预测更真实的破坏行为。本文采用标准有限元法有效地求解了基于光滑朗肯应变的动量控制方程和基于斜向梯度增强的体运动演化方程,以及非局部等效应变(时变断裂驱动项)的演化方程。对于时间离散化,采用鲁棒的中心差分法和行和技术相结合的显式求解方法进行质量集总。通过考虑二维(2D)和三维(3D)固体中与时间相关的裂纹扩展问题,显示了该动态模型的优势和能力。
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引用次数: 0
Validation and Improvements of a Generalized/eXtended Finite Element Method for 3-D Fatigue Crack Propagation 三维疲劳裂纹扩展广义/扩展有限元方法的验证与改进
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-02 DOI: 10.1007/s10704-025-00888-6
Javier A. Avecillas-Leon, Ishank Singh, C. Armando Duarte

The main objectives of this paper are to simulate 3-D fatigue crack propagation using a Generalized Finite Element Method (GFEM) and to validate the results against experimental data. This GFEM adopts a high-order p-hierarchical basis and explicit representations of crack surfaces. Both h-refinement around the fracture fronts and non-uniform p-enrichment of the analysis domain are used to control discretization errors. A systematic validation of this GFEM applied to 3-D fatigue crack propagation has not been reported in the literature. The Displacement Correlation Method (DCM) is used to extract stress intensity factors. The effect of material parameters adopted in the DCM on the crack growth rate and fracture shape is investigated. Three increasingly complex fatigue crack propagation problems are solved. The first involves mixed-mode loading in a modified compact tension specimen. The second one involves the transition from 2-D to 1-D crack surfaces and interactions between the crack front and the corners of the domain boundary. The final problem simulates the growth of a circumferential surface crack in a steel pipe subjected to fatigue bending with overloading, where interactions between the crack and the pipe’s inner surface result in the splitting of the crack front. Another contribution is an algorithm designed to manage cyclic load histories featuring variable loading ranges and ratios between minimum and maximum load magnitudes.

本文的主要目的是利用广义有限元法(GFEM)模拟三维疲劳裂纹扩展,并通过实验数据验证结果。该GFEM采用高阶p阶基,采用裂纹表面的显式表示。利用裂缝前缘周围的h-细化和分析区域的非均匀p-富集来控制离散化误差。该方法在三维疲劳裂纹扩展中的系统验证尚未见文献报道。采用位移相关法(DCM)提取应力强度因子。研究了DCM材料参数对裂纹扩展速率和断口形态的影响。解决了三个日益复杂的疲劳裂纹扩展问题。第一种方法是在改进的紧绷试样中进行混合模态加载。第二个问题涉及到从二维到一维裂纹表面的过渡以及裂纹前缘与区域边界角之间的相互作用。最后一个问题模拟了钢管在超载疲劳弯曲下的周向表面裂纹的扩展,其中裂纹与管道内表面的相互作用导致裂纹前缘的分裂。另一个贡献是一种算法,旨在管理具有可变负载范围和最小和最大负载量级之间的比率的循环负载历史。
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引用次数: 0
Dominique Leguillon obituary—A passionate scientist, a humble and kind person, a friend 多米尼克·勒吉隆讣告——一个充满激情的科学家,一个谦逊善良的人,一个朋友
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-10-01 DOI: 10.1007/s10704-025-00879-7
Zohar Yosibash, Vladislav Mantič
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引用次数: 0
A phase field formulation for modeling intralaminar damage onset and propagation in composites including residual stresses 含残余应力的复合材料层内损伤开始和扩展的相场公式
IF 2.5 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY Pub Date : 2025-09-15 DOI: 10.1007/s10704-025-00877-9
Sindhu Bushpalli, Bernardo López-Romano, Enrique Graciani

Unfolding failure is a sudden delamination occurring in highly curved fiber-reinforced polymer composite laminates when they are subjected to opening bending moments. Depending on the stacking sequences involved, unfolding failure includes intralaminar damage, interlaminar damage and their complex interactions. The use of these laminates in primary structural components of commercial aircrafts has intensified interest in understanding this failure mechanism. To tackle this, a simple phase field formulation to model the onset and propagation of transverse damage in highly curved laminates is presented. Firstly, the Abaqus implementation of the phase field to model intralaminar damage in composite laminates is established, exploiting the analogy between phase field and the heat transfer model to use Abaqus temperature as the phase field damage parameter. In addition, since residual stresses developed during manufacturing processes affect damage propagation, they are incorporated into the formulation as constant residual strains. Secondly, the proposed implementation is validated by performing tests on benchmark problems. Finally, a preliminary analysis of the unfolding failure test is provided to highlight the importance of including residual stresses in the transverse damage evolution.

展开破坏是高弯曲度纤维增强聚合物复合材料层合板在受开口弯矩作用时发生的突发性分层破坏。根据所涉及的堆叠顺序,展开破坏包括层内损伤、层间损伤及其复杂的相互作用。在商用飞机的主要结构部件中使用这些层压板加强了对这种失效机制的理解。为了解决这个问题,提出了一个简单的相场公式来模拟高弯曲层合板横向损伤的发生和传播。首先,利用相场与传热模型的相似性,利用Abaqus温度作为相场损伤参数,建立了相场模型在复合材料层板层内损伤模型中的Abaqus实现;此外,由于在制造过程中产生的残余应力影响损伤扩展,因此它们作为恒定残余应变纳入配方中。其次,通过对基准问题进行测试,验证了所提实现的有效性。最后,对展开破坏试验进行了初步分析,强调了在横向损伤演化中考虑残余应力的重要性。
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引用次数: 0
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International Journal of Fracture
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