The Fracture Mechanics of Plant Materials

232 Pages·2018·9.274 MB·English

by  Zhuoping Shao, Fuli Wang

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
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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