{"title":"用数值流形法和斯特罗形式主义提取任意开裂的各向同性复合材料中的 T 应力","authors":"","doi":"10.1016/j.tafmec.2024.104632","DOIUrl":null,"url":null,"abstract":"<div><p>The escalating utilization of composites over the past decades has necessitated the fracture investigation of orthotropic materials. The T-stress, namely, the first non-singular term of the normal stress parallel to the crack in William’s expansion, is of great significance for fracture analysis. In this work, the numerical manifold method (NMM) is advanced to assess the T-stress of arbitrary-shaped cracks (including non-intersecting cracks and multi-branched cracks) in two-dimensional orthotropic composites. Attributing to the bi-cover systems, the NMM can conveniently discretize the physical domain and naturally accommodate the discontinuity across crack surface. Meanwhile, the singularity at crack tip can be well captured by the wise choice of local approximation function. Through the application of interaction integral technology in the NMM postprocessing, the T-stress is extracted with the Stroh-form auxiliary fields. The accuracy of the proposed method is verified by comparing with reference solutions and then applied to arbitrarily branched and intersecting cracks. The results indicate that the present approach has convincing accuracy and also considerable convenience in T-stress evaluation. Additionally, the impacts of material orientations, crack geometries and loading conditions on the T-stress are also investigated.</p></div>","PeriodicalId":22879,"journal":{"name":"Theoretical and Applied Fracture Mechanics","volume":null,"pages":null},"PeriodicalIF":5.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"T-stress extraction in arbitrarily cracked orthotropic composites with the numerical manifold method and Stroh formalism\",\"authors\":\"\",\"doi\":\"10.1016/j.tafmec.2024.104632\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The escalating utilization of composites over the past decades has necessitated the fracture investigation of orthotropic materials. The T-stress, namely, the first non-singular term of the normal stress parallel to the crack in William’s expansion, is of great significance for fracture analysis. In this work, the numerical manifold method (NMM) is advanced to assess the T-stress of arbitrary-shaped cracks (including non-intersecting cracks and multi-branched cracks) in two-dimensional orthotropic composites. Attributing to the bi-cover systems, the NMM can conveniently discretize the physical domain and naturally accommodate the discontinuity across crack surface. Meanwhile, the singularity at crack tip can be well captured by the wise choice of local approximation function. Through the application of interaction integral technology in the NMM postprocessing, the T-stress is extracted with the Stroh-form auxiliary fields. The accuracy of the proposed method is verified by comparing with reference solutions and then applied to arbitrarily branched and intersecting cracks. The results indicate that the present approach has convincing accuracy and also considerable convenience in T-stress evaluation. Additionally, the impacts of material orientations, crack geometries and loading conditions on the T-stress are also investigated.</p></div>\",\"PeriodicalId\":22879,\"journal\":{\"name\":\"Theoretical and Applied Fracture Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Fracture Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167844224003823\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Fracture Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167844224003823","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
摘要
过去几十年来,复合材料的应用日益广泛,因此有必要对各向同性材料进行断裂研究。T应力,即在威廉膨胀法中平行于裂纹的法向应力的第一个非矢量项,对断裂分析具有重要意义。本研究采用数值流形法(NMM)评估二维正交复合材料中任意形状裂纹(包括非相交裂纹和多分支裂纹)的 T 应力。由于采用了双覆盖系统,NMM 可以方便地离散物理域,并自然地适应裂缝表面的不连续性。同时,通过明智地选择局部近似函数,可以很好地捕捉裂纹尖端的奇异性。通过在 NMM 后处理中应用交互积分技术,利用 Stroh 形式辅助场提取 T 应力。通过与参考解进行比较,验证了所提方法的准确性,然后将其应用于任意分支和相交裂缝。结果表明,本方法具有令人信服的准确性,而且在 T 应力评估方面也相当方便。此外,还研究了材料方向、裂缝几何形状和加载条件对 T 应力的影响。
T-stress extraction in arbitrarily cracked orthotropic composites with the numerical manifold method and Stroh formalism
The escalating utilization of composites over the past decades has necessitated the fracture investigation of orthotropic materials. The T-stress, namely, the first non-singular term of the normal stress parallel to the crack in William’s expansion, is of great significance for fracture analysis. In this work, the numerical manifold method (NMM) is advanced to assess the T-stress of arbitrary-shaped cracks (including non-intersecting cracks and multi-branched cracks) in two-dimensional orthotropic composites. Attributing to the bi-cover systems, the NMM can conveniently discretize the physical domain and naturally accommodate the discontinuity across crack surface. Meanwhile, the singularity at crack tip can be well captured by the wise choice of local approximation function. Through the application of interaction integral technology in the NMM postprocessing, the T-stress is extracted with the Stroh-form auxiliary fields. The accuracy of the proposed method is verified by comparing with reference solutions and then applied to arbitrarily branched and intersecting cracks. The results indicate that the present approach has convincing accuracy and also considerable convenience in T-stress evaluation. Additionally, the impacts of material orientations, crack geometries and loading conditions on the T-stress are also investigated.
期刊介绍:
Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind.
The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.