Zhuoping Shao Fuli Wang The Fracture Mechanics of Plant Materials Wood and Bamboo The Fracture Mechanics of Plant Materials Zhuoping Shao Fuli Wang (cid:129) The Fracture Mechanics of Plant Materials Wood and Bamboo 123 ZhuopingShao Fuli Wang Schoolof Forestry andLandscape Schoolof Forestry andLandscape AnhuiAgricultural University AnhuiAgricultural University Hefei, Anhui Hefei, Anhui China China ISBN978-981-10-9016-5 ISBN978-981-10-9017-2 (eBook) https://doi.org/10.1007/978-981-10-9017-2 LibraryofCongressControlNumber:2018937331 ©SpringerNatureSingaporePteLtd.2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. partofSpringerNature Theregisteredcompanyaddressis:152BeachRoad,#21-01/04GatewayEast,Singapore189721, Singapore Preface Wood and bamboo are the plant materials that can be directly used as structural materials,meanwhile,theyarealsotheoldestandstillthemostwidelyusednatural structure materials. Many of them are used as structural materials, such as beam, frame,floor,andsupport.Andbambooisalsoafineengineeringstructurematerial with highstrength, goodstiffness,andhighwearresistance,whichisusedtobuild bamboo house, as construction scaffolding, and as bamboo ladder. Thus, to study the strength, toughness, and the failure behaviors of wood and bamboo is very important for the safety assessment and structural design of wood and bamboo. Wood and bamboo are natural composites that possess obvious meso-structure and can be studied in multiscale. Because of inhomogeneous and anisotropic structureandmicroscopicormacroscopicnaturaldefectsordamages,whenloaded, the macroscopic mechanical behavior of wood and bamboo would be determined bytheirregularevolutionbehaviorsofthedefectsordamages.Althoughwoodand bamboo both are cell body plant materials, the differences in macroscopic and microscopic structure bring wood and bamboo different failure mechanisms cor- responding to different study methods. Thus, it is significant for the design and safetyanalysisofwoodandbamboocomponentstounderstandhowtousefracture mechanics and meso-mechanics to analyze the fracture behaviors of wood and bamboo, what the changes of inner microstructure are when loaded, and what the relationbetweenthechangesandmacro-mechanicalresponseis.Meanwhile,itwill provide guiding function for the development of new biocomposites that possess specialstrengthandtoughnesspropertiesandovercomethedefectsofbiomaterials. This is a book on the fracture behaviors and toughness mechanism of bamboo and wood, which reflects the research work of authors in the past decade. In the sections onwood, varieties oftrees are selected, for example,softwoods: China fir (Cunninghamia Lanceolata), Mongolian pine (Pinus sylvestris var. mongolica Litv.), Picea jezoensis (Picea asperata), Larch (Larix gmelinii), and so on are chosen, which possess growth rings in different clarity because of the changes of early wood and late wood; hardwoods: Populus spp I-69, Castanopsis hystrix, Koompassia spp, Melia azedarach, and so on are chosen considering their differ- ence in construction such as diffuse-porous wood, ring-porous wood, wood ray, v vi Preface grain, etc. And moso bamboo (Phyllostachys pubescens) is the study object in the sections on bamboo. Theoretical analysis is combined with experiments assisted with various mathematical tools and experiment means. There are nine chapters in total. The content involves the mechanical charac- teristicsandstress–strainrelationshipofwoodstructure,thefractureofwoodalong grain,thetransversefractureofwood,thefiniteelementanalysisofwoodcracktip stress field and prediction of the crack propagation direction, acoustic emission characteristics and Felicity effect of wood fracture perpendicular to the grains, the mechanicalcharacteristicsofbamboostructureanditscomponents,theinterlaminar fracture properties of bamboo, and the toughness fracture model and energy absorbing mechanism of bamboo. Many of the researches are studied for the first time.MostofthechaptersarewrittenbyShaoZhuoping,andSects.8.4and8.5are written by Wang Fuli. In addition, Chap. 9 is written by the corporation of Shao Zhuoping and Wang Fuli. There might be defects and mistakes inevitably for the limitedspecializedknowledgeofauthors,sopleaseputoutthemistakessothatthey can be corrected. Hefei, China Zhuoping Shao November 2017 Acknowledgements Here, we want to express heartfelt thanks to the National Natural Science Foundation of China [grant number: 30571452, 11072001, 11008250, 31570715] for the foundation support. And we also appreciate the help of Wu Yijun, Fang Changhua,TianGenlin,ZhouLiang,LiuYamei,HuangTianlai,LiQizhi,andWu Dong. vii Contents 1 Introduction to the Application of the Fracture Mechanics in Wood and Bamboo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Brief History of Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Mechanics of Materials and Fracture Mechanics. . . . . . . . . . . . . . 2 1.3 Brief Review of the Fracture Mechanics of Wood . . . . . . . . . . . . 3 1.3.1 The Strength Prediction of Wood Materials. . . . . . . . . . . . 3 1.3.2 The Application of Fracture Mechanics Combined with Acoustic Emission (AE) in the Propagation Mechanism of Wood Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3.3 Researches on the Fracture Property of Bamboo . . . . . . . . 6 1.4 The Main Contents of This Book . . . . . . . . . . . . . . . . . . . . . . . . 7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Mechanical Characteristics and Stress–Strain Relationship of Wood Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 The Mechanical Characteristics of Wood Structure. . . . . . . . . . . . 11 2.2 The Stress–Strain Relation of Solid Material . . . . . . . . . . . . . . . . 13 2.3 Engineering Elastic Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Engineering Elastic Constants of Wood . . . . . . . . . . . . . . . . . . . . 16 2.5 The Concept of Plane Stress and Plane Strain . . . . . . . . . . . . . . . 16 2.5.1 Uniform Thickness Plate and Plane Stress. . . . . . . . . . . . . 17 2.5.2 Infinite Cylinder and Plane Strain. . . . . . . . . . . . . . . . . . . 17 2.5.3 The Stress–Strain Relationship in Plane Problem. . . . . . . . 18 2.6 Tests of Wood Elastic Coefficients . . . . . . . . . . . . . . . . . . . . . . . 19 2.6.1 The Application of Electrometric Method on Wood Elastic Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6.2 TheApplicationofDSCMonWoodElasticCoefficients... 22 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 ix x Contents 3 Fracture of Wood Along Grain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Theory of LEFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.1 Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2.2 Stress Intensity Factor K and K Criterion . . . . . . . . . . . . . 28 3.2.3 Energy Release Rate G and G Criterion . . . . . . . . . . . . . . 30 3.2.4 Relationship Between K and G. . . . . . . . . . . . . . . . . . . . . 32 3.3 Fracture Mechanics of Anisotropic Material. . . . . . . . . . . . . . . . . 36 3.4 The Special Application of LEFM on Wood . . . . . . . . . . . . . . . . 39 3.5 The Stress Intensity Factor K of Wood Fracture Along Grain. . . 41 IC 3.5.1 The Methods to Test Stress Intensity Factor . . . . . . . . . . . 41 3.5.2 The KTL of CT Samples with Different Thickness . . . . . . . 44 IC 3.5.3 The KTL ofWOLSampleswithDifferent CrackLength ... 46 IC 3.6 The Fracture Toughness GTL Along Grain of Wood by Energy IC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.6.1 Materials and Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.6.2 Test and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.6.3 The Relationship Between Stress Intensity Factor and Energy Release Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.7 Mode III Fracture Property of Wood Along Grain . . . . . . . . . . . . 58 3.7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7.2 Material and Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7.3 Test and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4 Transverse Fracture of Wood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 Analysis on Stress Field at Crack Tip . . . . . . . . . . . . . . . . . . . . . 65 4.3 The Cracking Direction of Transverse Crack . . . . . . . . . . . . . . . . 68 4.4 Test of Critical Stress Intensity Factor . . . . . . . . . . . . . . . . . . . . . 70 4.4.1 Material and Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4.4.2 Test and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 The Influence of Transverse Crack on the Normal Strength of Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5.1 Influence of Crack Perpendicular to Grain on MOR of Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5.2 Influence of Crack Perpendicular to Grain on Impact Toughness of Wood. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.5.3 Influence of Crack Perpendicular to Grain on Tensile Strength of Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.5.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Contents xi 4.6 Energy Release Rate of the Mode I Interlaminar Fracture of Wood Beam and the Bending Delamination Damage of Plywood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5 Finite Element Analysis of Wood Crack Tip Stress Field and Prediction of the Crack Propagation Direction. . . . . . . . . . . . . . . . . 87 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.1 Materials and Fundamental Data. . . . . . . . . . . . . . . . . . . . 89 5.2.2 Fracture Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.1 Stress Field of the Crack Tip . . . . . . . . . . . . . . . . . . . . . . 91 5.3.2 Prediction of Crack Propagation . . . . . . . . . . . . . . . . . . . . 91 5.4 The Relationship Between Interfacial Strength and Toughness of Wood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6 Fractal Features and Acoustic Emission Characteristics of Wood Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.1 The Fractal Features of Wood Fracture . . . . . . . . . . . . . . . . . . . . 103 6.1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.1.2 Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.1.3 Tests and Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.1.4 The Relationship Between Fracture Toughness and Fractal Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 Acoustic Emission Characteristics and Felicity Effect of Wood Fracture Perpendicular to the Grains . . . . . . . . . . . . . . . 112 6.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2.2 Materials and Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.2.3 Results and Discussions. . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.2.4 Felicity Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7 Mechanical Characteristics of Bamboo Structure and Its Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.2 Mechanical Characteristics of Bamboo. . . . . . . . . . . . . . . . . . . . . 127 7.3 The Mechanical Characteristics of the Components Bamboo. . . . . 129 7.3.1 “Mixture Law” Method . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.3.2 Test on Single Fiber Bundle. . . . . . . . . . . . . . . . . . . . . . . 132 7.3.3 Analysis on Fracture Surface . . . . . . . . . . . . . . . . . . . . . . 136 7.4 Difference of Structure and Strength Between Internodes Part and Node Part of Moso Bamboo . . . . . . . . . . . . . . . . . . . . . 138