Damage, Fracture, and Fatigue of Ceramic-Matrix Composites

249 Pages·2018·9.5 MB·English

by  Longbiao Li

Longbiao Li
Damage,
Fracture, and
Fatigue of
Ceramic-Matrix
Composites
Damage, Fracture, and Fatigue of Ceramic-Matrix
Composites
Longbiao Li
Damage, Fracture,
and Fatigue
of Ceramic-Matrix
Composites
123
Longbiao Li
NanjingUniversity ofAeronautics
andAstronautics
Nanjing, Jiangsu,China
ISBN978-981-13-1782-8 ISBN978-981-13-1783-5 (eBook)
https://doi.org/10.1007/978-981-13-1783-5
LibraryofCongressControlNumber:2018952884
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To Shengning
Contents
1 Tensile Behavior of Ceramic-Matrix Composites . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Unidirectional Ceramic-Matrix Composites. . . . . . . . . . . . . . . . . . 2
1.2.1 Stress Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Damage Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2.4 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 22
1.3 Cross-Ply and 2D Woven Ceramic-Matrix Composites . . . . . . . . . 30
1.3.1 Stress Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.2 Damage Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.3.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.3.4 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 39
1.4 2.5D Woven Ceramic-Matrix Composites. . . . . . . . . . . . . . . . . . . 50
1.4.1 Theoretical Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.4.2 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 60
1.4.3 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 69
1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2 Fatigue Hysteresis Behavior of Ceramic-Matrix Composites. . . . . . . 75
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.2 Unidirectional Ceramic-Matrix Composites. . . . . . . . . . . . . . . . . . 76
2.2.1 Stress Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.2.2 Interface Debonding and Sliding. . . . . . . . . . . . . . . . . . . . 80
2.2.3 Stress–Strain Hysteresis Loops . . . . . . . . . . . . . . . . . . . . . 81
2.2.4 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.2.5 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 97
2.3 Cross-ply and 2D Woven Ceramic-Matrix Composites . . . . . . . . . 108
2.3.1 Stress Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.3.2 Hysteresis Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
vii
viii Contents
2.3.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 115
2.3.4 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 126
2.4 5D Woven Ceramic-Matrix Composites . . . . . . . . . . . . . . . . . . . . 145
2.4.1 Hysteresis Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
2.4.2 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 149
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3 Interface Damage of Ceramic-Matrix Composites . . . . . . . . . . . . . . 155
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.2 Interface Shear Stress Estimation Approach . . . . . . . . . . . . . . . . . 156
3.2.1 Unidirectional Ceramic-Matrix Composites . . . . . . . . . . . . 157
3.2.2 Cross-Ply and 2D Woven Ceramic-Matrix Composites. . . . 158
3.2.3 2.5D Woven Ceramic-Matrix Composites . . . . . . . . . . . . . 160
3.3 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
3.3.1 Unidirectional Ceramic-Matrix Composites . . . . . . . . . . . . 162
3.3.2 Cross-Ply and 2D Woven Ceramic-Matrix Composites. . . . 169
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
4 Fatigue Life Prediction of Ceramic-Matrix Composites . . . . . . . . . . 201
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
4.2 Fatigue Life Prediction Models . . . . . . . . . . . . . . . . . . . . . . . . . . 202
4.2.1 Life Prediction at Room Temperature . . . . . . . . . . . . . . . . 202
4.2.2 Life Prediction at Elevated Temperature . . . . . . . . . . . . . . 204
4.3 Experimental Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.3.1 Unidirectional Ceramic-Matrix Composites . . . . . . . . . . . . 208
4.3.2 Cross-Ply and 2D Woven Ceramic-Matrix Composites. . . . 213
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Chapter 1
Tensile Behavior of Ceramic-Matrix
Composites
1.1 Introduction
Continuous fiber-reinforced ceramic-matrix composites (CMCs) possess high
specificstrengthandspecificmodulus,andhightoughnessatelevatedtemperatures
[1].Thenon-oxide andoxide CMCsarerecently beingincorporatedingasturbine
engines for high-pressure and high-temperature section components and exhaust
nozzles. However, the complexity and variability of aerospace ceramic processing
methods,compositionsandmicrostructures,therelativelylowfracturetoughnessof
the ceramic materials, still remain the challenging factors for CMCs component
design, validation, life prediction, and thus broader applications [2].
Undertensileloadingoffiber-reinforcedCMCs,thefailurestrainofthematrixis
less than that of the fibers. When the stress in the matrix approaches to its local
strength,matrixcrackingoccurs.Withincreasingofappliedstress,matrixcrackings
will deflect along the fiber/matrix interface, leading to theinterface debonding and
sliding [3]. The fiber/matrix interface frictional shear stress will transfer loads
between the fibers and the matrix, and the interface properties (i.e., the interface
shear stress and the interface debonded energy) affect the nonlinear behavior of
fiber-reinforced CMCs [4, 5]. When matrix cracking approaches to saturation, the
fiber/matrix interface debonding may continue with increasing applied stress, and
aftercompletelyinterfacedebonding,thematrixstresswillremainconstant[6].The
additionalloadwillbecarriedbyintactfibers,andwhenthebrokenfibersapproach
to the critical value, the composite fracture occurs [7].
Inthischapter,themicromechanicalapproachtopredictthetensilestress–strain
curves offiber-reinforced CMCs is developed. When matrix cracking, fiber/matrix
interface debonding and fibers failure occur, the shear-lag model is adopted to
analyze the microstress field of the damaged fiber-reinforced CMCs, i.e., the fiber
and matrix axial stress distributions. Combining the shear-lag model with damage
models of matrix statistical cracking, fracture mechanics fiber/matrix interface
debonding criterion and Global Load Sharing (GLS) fibers failure criterion, the
©SpringerNatureSingaporePteLtd.2018 1
L.Li,Damage,Fracture,andFatigueofCeramic-MatrixComposites,
https://doi.org/10.1007/978-981-13-1783-5_1
2 1 TensileBehaviorofCeramic-MatrixComposites
matrix cracking spacing, fiber/matrix interface debonding length and fibers broken
fraction are determined. The tensile stress–strain curves offiber-reinforced CMCs
corresponding to different damage stages are modeled. The tensile stress–strain
curves of unidirectional, cross-ply, 2D, and 2.5D woven CMCs are predicted.
1.2 Unidirectional Ceramic-Matrix Composites
In this section, the tensile stress–strain behavior of unidirectional fiber-reinforced
CMCsatroomtemperatureisinvestigated.Anapproachtomodelthetensilestress–
strain curve of unidirectional fiber-reinforced CMCs considering different damage
mechanisms of matrix multicracking, fiber/matrix interface debonding, and fibers
failure isdeveloped. Thetensilestress–strain curves of unidirectional SiC/Calcium
Aluminosilicate(SiC/CAS),SiC/CAS-II(CAS-IIistheCorningdesignationforthe
calcium aluminosilicate matrix in this composite system) and SiC/Borosilicate
composites corresponding to different damage stages are predicted.
1.2.1 Stress Analysis
Under tensile loading, matrix cracking and fiber/matrix interface debonding occur,
leadingtothenonlinear behavioroffiber-reinforced CMCs.Whenmatrixcracking
and fiber/matrix interface debonding occur, the shear-lag model is used to analyze
the microstress field of the damaged composite.
Cox [8] first introduced the concept of shear-lag in the micromechanical anal-
ysis. The purposeof theintroductionof theshear-lag concept isthat thestressand
strain fields of the composite material are not solved concretely, and the main
characteristics of the material structure are considered, and the response of the
material structure to the load is calculated by constructing a mathematical model.
The model simplifies the mechanical analysis of composite materials and provides
directional theoretical guidance for interpreting experimental data and designing
material structures with better damage tolerance. However, the shear-lag model
developedbyCox[8]onlyconsidersthestressdistributionaftersinglefiberfracture
in the elastic matrix and does not consider the stress distribution of other adjacent
fibers, so the stress concentration problem cannot be analyzed.
Hedgepeth and Dyke [9] expanded the shear-lag model developed by Cox [8],
investigated the stress distribution of an unidirectional fiber-reinforced composite
with multiple fibers failure, and predicted the stress concentration caused by mul-
tiplefibersfracture.Themainassumptionoftheshear-lagmodelisthatthefiberis
one-dimensional axial stress transfer entity; the fiber is only subjected to tensile
stress; the displacement is only along the longitudinal direction; the fiber is
arranged at the same distance; the interface between the fiber and matrix is strong
bonding; the matrix cannot transfer axial stress, and only the shear stress is
1.2 UnidirectionalCeramic-MatrixComposites 3
transferred;theinterfacialshearstrengthisconstant.Theshear-lagmodelcanbetter
describe the stress concentration around fibers broken in unidirectional composite
with lower matrix tensile modulus and higher fibers volume fraction.
Dyke and Hedgepeth [10] investigated the effect of plastic deformation and the
fiber/matrix interface debonding on the stress concentration of single fiber broken.
Zweben [11] proposed an approximate analysis method to analyze the stress dis-
tribution in the unidirectional fiber-reinforced composite with a long cracking
perpendicular to the fiber axial under tensile loading, considering the matrix
inelastic effect before the cracking.
The shear-lag models mentioned above predict the stress field distribution of
fiber-reinforced soft matrix composites (i.e., the fiber elasticmodulus is far greater
than that of the matrix). With the appearance of high temperature-resistant com-
posite, i.e., metal andceramic matrix composites,thedifference ofelastic modulus
between the matrix and the fiber is small. The classical shear-lag theory cannot
accurately describe the microstress field of the damaged composite. Budiansky
et al. [12] considered the effect of matrix shear deformation on the matrix axial
stress distribution, modified the classic shear-lag theory, and analyzed the
microstress field offiber-reinforced CMCs after multiple damage.
In the present analysis, the Budiansky–Hutchinson–Evans shear-lag model [12]
is adopted to analyze the microstress field inside of damaged fiber-reinforced
CMCs. The unit cell is extracted from the fiber-reinforced CMCs, as shown in
Fig. 1.1. The unit cell contains a single fiber surrounded by a hollow cylinder of
matrix. Thefiberradiusisr andthematrixradiusisR(R = r/V1/2).The lengthof
f f f
theunitcell ishalf ofthematrix crack spacing,i.e., l /2.The fiber/matrixinterface
c
debonded length is l . The unit cell can be divided into two regions, i.e., the
d
interface debonded region (x 2 [0, l ]) and interface bonded region (x 2 [l , l /2]).
d d c
On the matrix crack plane, the fibers carry all the stress (r/V), where r denotes
f
far-fieldappliedstress andV denotesthefibervolumefraction.IntheBudiansky–
f
Hutchinson–Evans shear-lag model, it is assumed that the matrix axial stress is
Fig.1.1 UnitcellofBudiansky–Hutchinson–Evansshear-lagmodel.Reprintedwithpermission
fromRef.[5].Copyright2009,SpringerScienceBusinessMediaNewYork