Engineering Fracture Mechanics最新文献

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Fatigue fracture mechanism and life assessment for irregular film cooling hole structures in Ni-based single crystal turbine blades 镍基单晶涡轮叶片不规则薄膜冷却孔结构的疲劳断裂机理和寿命评估
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-21 DOI: 10.1016/j.engfracmech.2024.110506
{"title":"Fatigue fracture mechanism and life assessment for irregular film cooling hole structures in Ni-based single crystal turbine blades","authors":"","doi":"10.1016/j.engfracmech.2024.110506","DOIUrl":"10.1016/j.engfracmech.2024.110506","url":null,"abstract":"<div><div>Film cooling holes are the main cooling structures in nickel-based single-crystal cooling turbine blades. To evaluate the low-cycle fatigue life of irregular gas film holes, nine types of Ni-based single-crystal flat-plate test pieces with irregular film cooling holes of different shapes were designed in this study. Fatigue tests were performed at high temperature (850 ℃) and the multiscale fracture mechanisms of the samples analyzed in detail. The stress–strain field around the irregular film cooling holes was analyzed based on crystal plasticity theory using the finite element method. Three life prediction models based on the Coffin–Manson–Basquin formula, maximum principal strain, and crystal plasticity theory were proposed to predict the fatigue life of irregular film-cooled pore structures. The predicted results are all within the double-error band.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322613","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
Characterization of fatigue crack growth in directed energy deposited Ti-6Al-4V by marker load method 标记载荷法表征定向能沉积 Ti-6Al-4V 中疲劳裂纹的生长
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-21 DOI: 10.1016/j.engfracmech.2024.110500
{"title":"Characterization of fatigue crack growth in directed energy deposited Ti-6Al-4V by marker load method","authors":"","doi":"10.1016/j.engfracmech.2024.110500","DOIUrl":"10.1016/j.engfracmech.2024.110500","url":null,"abstract":"<div><div>Fatigue crack growth properties of materials are crucial for evaluating damage tolerance in additive manufacturing (AM) metallic structures. However, the unique microstructures and defects of AM materials result in highly complex fatigue crack growth behaviors. Currently, there is a lack of systematic fatigue crack growth rate measurement methods specifically targeting this characteristic. Therefore, taking directed energy deposited Ti-6Al-4V titanium alloy as the object of the study, fatigue crack growth tests were conducted in three orthogonal build orientations of the material using marker load method. Additionally, the visual measurement and compliance methods were also employed to measure fatigue crack growth rates, and the anisotropy of fatigue crack growth property was analyzed. Subsequently, anisotropic fatigue crack growth behaviors were characterized by optical microscope, scanning electron microscope, confocal microscope, and electron backscatter diffraction, suggesting that the microstructure is the primary factor affecting overall fatigue crack growth. Furthermore, nanoindentation tests were conducted to obtain the micromechanical properties within and among columnar grains in different build orientations, clarifying the homogeneity and anisotropy of mechanical properties. Finally, a fatigue crack growth rate measurement method based on marker load method was established, and the advantages of this method in AM materials and structures were summarized by comparing the results with those obtained using these two mature methods.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310255","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 nitrogen-doped type on fracture toughness improvement and crack growth resistance of carbon nanotube/epoxy nanocomposites: Combined multiscale analysis approach 掺氮类型对纳米碳管/环氧纳米复合材料断裂韧性改善和抗裂纹生长的影响多尺度综合分析方法
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-21 DOI: 10.1016/j.engfracmech.2024.110502
{"title":"Effect of nitrogen-doped type on fracture toughness improvement and crack growth resistance of carbon nanotube/epoxy nanocomposites: Combined multiscale analysis approach","authors":"","doi":"10.1016/j.engfracmech.2024.110502","DOIUrl":"10.1016/j.engfracmech.2024.110502","url":null,"abstract":"<div><div>Recently, nitrogen-doped carbon nanotubes (N-doped CNTs) have received great attention in nanocomposite design. It has become highly necessary to develop predictive models to elucidate their toughning behavior. In this study, the effects of CNTs with three different types of N-doped functional groups (quaternary, pyrrolic, and pyridinic) on the fracture toughness (FT) and crack growth of polymer nanocomposites are predicted using a multiscale analysis approach. To scale up from the nanoscale to the macroscale, a multiscale analysis approach integrating molecular dynamics, micromechanics theory, linear fracture mechanics theory, and a phase-field fracture model (PFFM) is adopted. The toughness enhancement trends of the three different types of N-doped functional groups were quantified by considering four toughening mechanisms (CNT debonding, plastic nanovoid growth, CNT pull-out, and CNT rupture), and compared with experimental result. The results show that the excellent interphase and interfacial properties of quaternary and pyridinic functional groups significantly improve the FT and crack growth resistance of N-doped CNT/epoxy nanocomposites. Our study provides high-performance solutions for experimental studies pertaining to the FT and crack growth of N-doped CNT/epoxy nanocomposites.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314969","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 strain-based criterion for predicting size-dependent fracture resistance of quasi-brittle materials under mixed mode loading 基于应变的标准,用于预测混合模式加载下准脆性材料随尺寸变化的抗断裂性
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-21 DOI: 10.1016/j.engfracmech.2024.110513
{"title":"A strain-based criterion for predicting size-dependent fracture resistance of quasi-brittle materials under mixed mode loading","authors":"","doi":"10.1016/j.engfracmech.2024.110513","DOIUrl":"10.1016/j.engfracmech.2024.110513","url":null,"abstract":"<div><div>In the present study, a strain-based approach called the modified maximum tangential strain criterion has been developed for evaluating size effect on the mixed-mode fracture resistance of quasi-brittle materials. This approach relies on the generalized maximum tangential strain criterion, which considers the singular (<span><math><mrow><mi>K</mi></mrow></math></span>) and the first non-singular (<span><math><mrow><mi>T</mi></mrow></math></span>) terms of Williams series expansion. Furthermore, as an important and size-dependent parameter in the proposed criterion, a new formulation is presented to calculate the critical distance (<span><math><mrow><msub><mi>r</mi><mi>c</mi></msub></mrow></math></span>). The predictions of the new criterion are compared not only with the available experimental data, but also with the results estimated by another size effect criterion named the modified maximum tangential stress criterion. It is shown that the proposed strain-based criterion is highly capable of estimating the size-dependent mixed-mode fracture behavior of quasi-brittle materials without requiring to compute the other higher order terms.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314965","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
Experimental study and life prediction for aero-engine turbine blade considering creep-fatigue interaction effect 考虑蠕变-疲劳相互作用效应的航空发动机涡轮叶片实验研究与寿命预测
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-20 DOI: 10.1016/j.engfracmech.2024.110507
{"title":"Experimental study and life prediction for aero-engine turbine blade considering creep-fatigue interaction effect","authors":"","doi":"10.1016/j.engfracmech.2024.110507","DOIUrl":"10.1016/j.engfracmech.2024.110507","url":null,"abstract":"<div><div>As an important failure form of the turbine blade, creep-fatigue interaction damage affects the safe operation and maintenance strategy of aero-engine, and has been the focus of scientific research and the academic community. Firstly, based on the Kachanov-Rabotnov-Lemaitre continuum damage mechanics theory and the nonlinear symmetry of creep damage and fatigue damage, a creep-fatigue life prediction model is constructed considering the interaction effect in this paper. Then, based on the thermal-fluid–solid multi-physical field coupling numerical simulation of the turbine blade, the equivalent method of creep-fatigue load spectrum was explored according to the equal damage criterion and linear damage rule, and the creep-fatigue interaction test of smooth samples of the blade material was conducted to analyze the creep-fatigue fracture morphology. Finally, the stress term in the creep-fatigue life prediction model of blade material is modified by the correction factor <em>α</em>, and the modified creep-fatigue life prediction model of the turbine blade is constructed considering the interaction effect. The results show that the modified creep-fatigue life prediction model considering the interaction effect has a high life prediction ability with an error of 3.9%. The above research has important scientific research value for the life extension design of turbine blades and the improvement of aero-engine maintenance strategy.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327569","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
Analysis of failure properties of red sandstone with structural plane subjected to true triaxial stress paths 真实三轴应力路径下具有结构平面的红色砂岩的破坏特性分析
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-19 DOI: 10.1016/j.engfracmech.2024.110490
{"title":"Analysis of failure properties of red sandstone with structural plane subjected to true triaxial stress paths","authors":"","doi":"10.1016/j.engfracmech.2024.110490","DOIUrl":"10.1016/j.engfracmech.2024.110490","url":null,"abstract":"<div><div>In order to study the mechanical behavior and failure characteristics of rock mass with the structural plane in complex deep stress environment, the QKX-YB200 true triaxial rockburst test system, acoustic emission, and digital video recorder were adopted to conduct true triaxial loading and unloading indoor tests on the red sandstone cube specimens. The results show that: (1) Under true triaxial loading conditions, all specimens propagate in the form of anti-wing crack, and the dip angle of the structural plane is linearly related to the average value of the anti-wing crack propagation angle; under true triaxial unloading conditions, the specimens with structural plane dip angles of 30°, 45°, and 60° propagate in the form of wing crack, while those with a 90° angle propagate anti-wing cracks, and the closure of structural plane is related to the the crack type at the tips of structural plane. (2) The unstable failure stages in the stress–strain curve under true triaxial unloading are longer and exhibit more pronounced fluctuations; the peak strength of the specimens under the conditions of true triaxial loading and unloading decrease first and then increase with the increase of the dip angle, reaching the lowest at 45°. (3) During the true triaxial unloading tests, the rockburst degree of the intact rock specimens is more violent than that of the specimens with a structural plane. Additionally, the dip angle of the structural plane influences the severity of rockbursts under the same stress path. (4) The crack propagation mechanism and the closure degree of structural planes under different true triaxial stress paths and dip angles are discussed. It is observed that the crack initiation mode around the structural plane tips and the crack mode near free surface are closely related to the stress environment in different areas of the specimens. (5) Based on the indoor test results and previous experimental data, the differences in peak strength characteristics between open structural planes and closed structural planes are preliminarily analyzed and compared.</div></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142310253","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
Cyclic frictional response of rough rock joints under shear disturbances: Laboratory experiment and numerical simulation 粗糙岩缝在剪切扰动下的循环摩擦响应:实验室实验和数值模拟
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-19 DOI: 10.1016/j.engfracmech.2024.110514
{"title":"Cyclic frictional response of rough rock joints under shear disturbances: Laboratory experiment and numerical simulation","authors":"","doi":"10.1016/j.engfracmech.2024.110514","DOIUrl":"10.1016/j.engfracmech.2024.110514","url":null,"abstract":"<div><p>The cyclic frictional response of rock joints under shear disturbances is critical for understanding the stability and durability of rock engineering structures. Laboratory experiments and numerical simulations were conducted to examine the effects of varying cyclic shear displacement amplitudes, frequencies, and cycle numbers on the macroscopic and microscopic shear characteristics of rough rock joints. The experimental results reveal significant differences in shear strength between the first few cycle and subsequent cycles during the cyclic shear process. As the number of shear cycles increases, the asperities on the contact surface gradually sustain damage, leading to a reduction in normal displacement. During cyclic shear, the peak shear load exhibits a two-stage variation with the number of cycles: an initial sharp decline followed by a gradual increase as the cycles proceed. The peak shear strength shows no obvious pattern under different shear displacement amplitudes and frequencies in the early stages of cyclic shear. As cyclic shear progresses, the peak shear strength decreases with increasing shear displacement amplitude but increases with higher shear frequency. Numerical simulations indicate that significant plastic deformation and shear wear occur on the joint surface during the initial cycles. The growth of the wear area is primarily concentrated in regions of stress concentration. Additionally, the simulations reveal that the volume of shear wear increase nonlinearly with the number of cycles. This research provides new insights into the cyclic shear behavior of rough rock joints and offers valuable references for engineering applications.</p></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271435","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
Microcracking evolution and clustering fractal characteristics in coal failure under multi step and cyclic loading 多级和循环加载下煤炭失效的微裂纹演化和聚类分形特征
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-19 DOI: 10.1016/j.engfracmech.2024.110511
{"title":"Microcracking evolution and clustering fractal characteristics in coal failure under multi step and cyclic loading","authors":"","doi":"10.1016/j.engfracmech.2024.110511","DOIUrl":"10.1016/j.engfracmech.2024.110511","url":null,"abstract":"<div><p>During the deep mining process, coal mass encounter intricate geo-environmental stress, such as periodic weighting loading and repeatedly excavation unloading–reloading cycles, which weakens coal’s mechanical integrity and predisposing it to severe coalburst accidents. To investigate the microcracking damage mechanisms and predictive indicators in coal failure under in-situ stress analogs, the multistage step and cyclic loading experiments are conducted on cubic coal specimens. Acoustic emission (AE) technology is employed to track the spatiotemporal-energy evolution of stress-induced damages and discern the microcracking nature through AF/RA assessments, and the power-law scaling relation of AE activity near the catastrophic failure of coal is investigated. Then the clustering fractal structures of microcracking events in the stressed coal are quantified across temporal, spatial and energetic domains, utilizing correlation integral methodologies and b-value derivations from magnitude-frequency relation. Findings indicate that irrespective of the loading mode (step or cyclic), escalating stress triggers an intensification of irreversible fatigue deformations. AE characteristic parameters manifest a gradual rise, culminating in a precipitous peak coinciding with the critical failure point. This escalation adheres to a power-law correlation between AE occurrence frequency and time to failure, observable in the immediate pre-failure seconds, reflecting a universal attribute of coal fracture. Prior to ultimate failure, a marked increase in shear microcracks is discernible, despite tensile-dominated cracks (constituting about 80 % of total microcracks) prevailing as inferred from the variation of AF/RA values, aligning with an inferred “X” conjugate wedge splitting pattern from AE event density and energy mapping. The microcracking events in the loaded coal exhibit a clustering fractal structure that spans across temporal, spatial, and energetic (or magnitude) domains. Notably, the temporal fractal dimension, spatial fractal dimension, and b-value (i.e., a parameter characterized the energetic fractal dimension) all follow a parallel decrease pattern as the loading stress escalates, with a pronounced diminution becoming especially evident as the specimen approaches its catastrophic failure threshold. This insight offers fresh perspectives for predicting rock/coal dynamic disasters, emphasizing the necessity of concurrently monitoring the shift from diffuse microcracking to localized failure across time, space and energy domains. These research findings contribute to a deeper understanding of microcracking damage evolution and failure mechanism of loaded coal, and provide a foundational basis for early warning of rock failure such as the coalburst disasters.</p></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271279","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
Finite element analyses of rail head cracks: Predicting direction and rate of rolling contact fatigue crack growth 轨头裂纹的有限元分析:预测滚动接触疲劳裂纹增长的方向和速度
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-18 DOI: 10.1016/j.engfracmech.2024.110503
{"title":"Finite element analyses of rail head cracks: Predicting direction and rate of rolling contact fatigue crack growth","authors":"","doi":"10.1016/j.engfracmech.2024.110503","DOIUrl":"10.1016/j.engfracmech.2024.110503","url":null,"abstract":"<div><p>A numerical framework in 3D for predicting crack growth direction and rate in a rail head is presented. An inclined semi-circular surface-breaking gauge corner crack with frictionless crack faces is incorporated into a 60E1 rail model. The investigated load scenarios are wheel–rail contact, rail bending, thermal loading, and combinations of these. The crack growth direction is predicted using an accumulative vector crack tip displacement criterion, and Paris-type equations are employed to estimate crack growth rates. Results are evaluated along the crack front for varying crack radii and crack plane inclinations. Under the combined load cases and in the presence of tractive forces, the crack is generally predicted to go deeper into the rail than under pure contact. Crack growth rates for the combined load cases are higher than (but still close to) that for pure contact. A tractive force will increase growth rates for smaller cracks, whereas a steeper (45°) inclination will decrease the growth rate under the studied conditions as compared to a shallower (25°) inclination. Results should be of use for rail maintenance planning where deeper cracks require more machining efforts.</p></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0013794424006660/pdfft?md5=fab6b95a9df4917f673f9ba33a2ae2a1&pid=1-s2.0-S0013794424006660-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bound-constrained optimization using Lagrange multiplier for a length scale insensitive phase field fracture model 利用拉格朗日乘法器对长度尺度不敏感的相场断裂模型进行边界约束优化
IF 4.7 2区 工程技术
Engineering Fracture Mechanics Pub Date : 2024-09-18 DOI: 10.1016/j.engfracmech.2024.110496
{"title":"Bound-constrained optimization using Lagrange multiplier for a length scale insensitive phase field fracture model","authors":"","doi":"10.1016/j.engfracmech.2024.110496","DOIUrl":"10.1016/j.engfracmech.2024.110496","url":null,"abstract":"<div><p>The classical phase field model using the second-order geometric function <span><math><mrow><mi>α</mi><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> (i.e., AT2 model), where <span><math><mrow><mi>φ</mi><mo>∈</mo><mfenced><mrow><mn>0</mn><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></math></span> is an auxiliary phase field variable representing material damage state, has wide applications in static and dynamic scenarios for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The phase field model using the linear geometric function <span><math><mrow><mi>α</mi><mrow><mo>(</mo><mi>φ</mi><mo>)</mo></mrow><mo>=</mo><mi>φ</mi></mrow></math></span> (i.e., AT1 model), can avoid this, and a linear elastic threshold is available in its stress–strain curve. However, both AT2 and AT1 models are length scale sensitive phase field models, which could have difficulty in adjusting fracture strength and crack band simultaneously through a single parameter (the length scale). In this paper, a generalized quadratic geometric function (linear combination of AT1 and AT2 models) is used in the phase field model, where the extra parameter in this geometric function makes it a length scale insensitive phase field model. Similar to the AT1 model, negative phases can happen in the proposed generalized quadratic geometric function model. To solve this problem, a bound-constrained optimization using the Lagrange multiplier is derived, and the Karush–Kuhn–Tucker (KKT) conditions change from strain energy and maximum history strain energy (an indirect method acting on phase) to phase and Lagrange multiplier (a direct method acting on phase). Several simulations successfully validated the proposed model. A single element analysis and a bar under cyclic loading show the different stress–strain curves obtained from different models. A simulation of Mode I Brazilian test is compared with the experiment conducted by the authors, and two more simulations of Mode II shear test and mixed mode PMMA tensile test are compared with results from the literature.</p></div>","PeriodicalId":11576,"journal":{"name":"Engineering Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":4.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0013794424006593/pdfft?md5=a75b31f7c0074a23a2c7f0927b8b3dbc&pid=1-s2.0-S0013794424006593-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142271434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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