Fundamentals of fiber orientation: description, measurement and prediction
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[2022]
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| Beschreibung: | XVIII, 334 Seiten Illustrationen, Diagramme 25 cm |
| ISBN: | 9781569908754 1569908753 |
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| 100 | 1 | |a Tucker, Charles L. III |e Verfasser |0 (DE-588)125565760X |4 aut | |
| 245 | 1 | 0 | |a Fundamentals of fiber orientation |b description, measurement and prediction |c Charles L. Tucker III |
| 264 | 1 | |a Munich |b Hanser |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a XVIII, 334 Seiten |b Illustrationen, Diagramme |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804183490108850176 |
|---|---|
| adam_text | CONTENTS
PREFACE
...................................................................................................
VII
U
INTRODUCTION
.....................................................................................
1
1.1
DISCONTINUOUS
FIBER
COMPOSITES
.........................................................................
1
1.2
PROCESSING,
MICROSTRUCTURE
AND
PROPERTIES
..........................................................
2
1.3
COMPUTER-AIDED
ENGINEERING
WORKFLOW
..............................................................
5
1.4
SCOPE
AND
ORGANIZATION
OF
THE
BOOK
....................................................................
8
1.5
ACCOMPANYING
SOFTWARE
........................................................................................
9
DESCRIBING
FIBER
ORIENTATION
AND
FIBER
LENGTH
............................
11
2.1
SINGLE
FIBER
ORIENTATION
........................................................................................
11
2.2
DISTRIBUTIONS
OF
FIBER
ORIENTATION
........................................................................
12
2.2.1
PLANAR
ORIENTATION
......................................................................................
12
2.2.1.1
MATCHING
TO
DATA
....................................................................
13
2.2.2
THREE-DIMENSIONAL
ORIENTATION
................................................................
14
2.3
ORIENTATION
TENSORS
...............................................................................................
16
2.3.1
INTRODUCTION
...............................................................................................
16
2.3.2
RELATIONSHIP
TO
THE
DISTRIBUTION
FUNCTION
................................................
20
2.3.3
PROPERTIES
OF
THE
ORIENTATION
TENSOR
.........................................................
22
2.3.4
PRINCIPAL
DIRECTIONS
AND
PRINCIPAL
VALUES
................................................
23
2.3.4.1
PROPERTIES
OF
EIGENVALUES
AND
EIGENVECTORS
..............................
24
2.3.4.2
RELATIONSHIP
TO
COORDINATE
TRANSFORMATION
..............................
25
2.3.4.3
INDETERMINATE
EIGENVECTORS
.........................................................
27
2.3.4.4
NUMERICAL
DETAILS
........................................................................
28
2.3.5
THE
FOURTH-ORDER
ORIENTATION
TENSOR
.......................................................
29
2.3.5.1
CONTRACTED
NOTATION
...................................................................
30
2.3.5.2
EXAMPLES
......................................................................................
32
2.4
RECONSTRUCTING
DISTRIBUTION
FUNCTIONS
................................................................
34
2.4.1
PLANAR
ORIENTATION
.....................................................................................
35
2.4.1.1
FOURIER
SERIES
...............................................................................
35
2.4.1.2
JEFFERY
DISTRIBUTION,
PLANAR
ORIENTATION
.....................................
36
2.4.1.3
COMPARISON
OF
PLANAR
ORIENTATION
RECONSTRUCTIONS
..................
37
XII
CONTENTS
2.4.2
3-D
ORIENTATION
...........................................................................................
39
2.5
FIBER
LENGTH
............................................................................................................
40
2.6
NUMBER-AVERAGE
AND
WEIGHT-AVERAGE
ORIENTATION
..............................................
42
2.7
CHAPTER
SUMMARY
...................................................................................................
43
EL
MEASURING
FIBER
ORIENTATION
AND
LENGTH
.....................................
45
3.1
PLANAR
SECTION
MEASUREMENTS
OF
ORIENTATION
......................................................
45
3.1.1
MATHEMATICAL
PRINCIPLES
............................................................................
45
3.1.1.1
CORRECTING
FOR
SAMPLE
BIAS
..........................................................
47
3.1.1.2
AMBIGUOUS
ANGLES
AND
AMBIGUOUS
TENSOR
COMPONENTS
..........
51
3.1.1.3
SYSTEMATIC
ERRORS
IN
0
...................................................................
52
3.1.2
PRACTICAL
ASPECTS
OF
MEASUREMENT
.............................................................
53
3.1.2.1
SAMPLE
PREPARATION
AND
IMAGING
.................................................
53
3.1.2.2
IMAGE
ANALYSIS
..............................................................................
54
3.1.2.3
SAMPLE
SIZE
AND
ORIENTATION
........................................................
56
3.1.3
EXAMPLE:
CORE/SHELL
STRUCTURES
IN
INJECTION
MOLDED
COMPOSITES
..........
57
3.1.4
MEASUREMENT
ACCURACY
..............................................................................
58
3.2
MICRO-CT
MEASUREMENTS
OF
ORIENTATION
...............................................................
62
3.2.1
IMAGE
ACQUISITION
AND
SAMPLE
SIZE
............................................................
62
3.2.2
IMAGE
ANALYSIS
.............................................................................................
65
3.2.2.1
VOXEL
ORIENTATIONS
.......................................................................
65
3.2.2.2
FIBER
RECONSTRUCTION
....................................................................
67
3.2.2.3
EXAMPLE
DATA
................................................................................
68
3.2.2.4
COMPARISON
OF
IMAGE
ANALYSIS
SCHEMES
....................................
69
3.2.2.5
SAMPLES
WITH
FIBER
BUNDLES
OR
PLATELETS
......................................
69
3.3
LENGTH
MEASUREMENT
.............................................................................................
70
3.3.1
DESTRUCTIVE
SAMPLING
..................................................................................
70
3.3.2
MICRO-CT
DATA
FOR
LENGTH
...........................................................................
73
3.4
CHAPTER
SUMMARY
...................................................................................................
75
YY
FLOW
ORIENTATION
OF
SINGLE
FIBERS
..................................................
77
4.1
FLOW
KINEMATICS
....................................................................................................
77
4.1.1
DEFORMATION
RATE
AND
VORTICITY
.................................................................
77
4.1.1.1
INVARIANTS
AND
THE
SCALAR
STRAIN
RATE
...........................................
79
4.1.1.2
BASIC
FLOWS
....................................................................................
79
4.1.2
FINITE
DEFORMATION
MEASURES
....................................................................
85
4.1.2.1
DISPLACEMENT
FUNCTIONS
..............................................................
85
4.1.2.2
DEFORMATION
GRADIENT
TENSORS
...................................................
86
CONTENTS
XIII
4.1.2.3
STRETCHING
OF
A
MATERIAL
LINE
.......................................................
88
4.1.2.4
BASIC
DEFORMATIONS
.......................................................................
89
4.2
JEFFERY
S
EQUATION
....................................................................................................
91
4.2.1
RATE
FORM
....................................................................................................
91
4.2.2
EXAMPLE
SOLUTIONS
AND
THE
TWO
RULES
OF
FIBER
ORIENTATION
.....................
93
4.2.2.1
PLANAR
ORIENTATION
IN
SIMPLE
SHEAR
............................................
93
4.2.2.2
PLANAR
ORIENTATION
IN
PLANAR
EXTENSIONAL
FLOW
..........................
95
4.2.3
NUMERICAL
SOLUTIONS
...................................................................................
96
4.2.4
PARTICLE
SHAPE
FACTORS
................................................................................
97
4.2.5
JEFFERY
ORBITS
...............................................................................................
99
4.2.6
STRAIN-TIME
SCALING
AND
REVERSIBILITY
.......................................................
101
4.2.7
DEFORMATION
FORM
......................................................................................
101
4.3
ORIENTATION
PATTERNS
IN
INJECTION
AND
COMPRESSION
MOLDING
.............................
103
4.3.1
TWO
RULES
THAT
EXPLAIN
EVERYTHING
............................................................
103
4.3.2
SHELL
LAYERS
IN
INJECTION
MOLDING
..............................................................
104
4.3.3
CORE
ORIENTATION
IN
INJECTION
MOLDING
......................................................
105
4.3.4
SKIN
LAYERS
AND
THE
FOUNTAIN
FLOW
............................................................
108
4.3.5
THE
MYSTERY
OF
THICK
PLAQUES
....................................................................
110
4.3.6
COMPRESSION
MOLDING
................................................................................
112
4.3.6.1
LUBRICATED
SQUEEZE
FLOW
.............................................................
112
4.3.6.2
NON-LUBRICATED
SQUEEZE
FLOW
.....................................................
114
4.4
CHAPTER
SUMMARY
..................................................................................................
116
5
FLOW
ORIENTATION
OF
GROUPS
OF
FIBERS
...........................................
117
5.1
JEFFERY
S
EQUATION
FOR
THE
ORIENTATION
TENSOR
.......................................................
117
5.1.1
DERIVATION
...................................................................................................
118
5.1.2
NUMERICAL
SOLUTION
FOR
A
MATERIAL
POINT
...................................................
119
5.1.3
SPATIAL
FIELDS
OF
ORIENTATION
......................................................................
121
5.2
SOLVING
FOR
THE
DISTRIBUTION
FUNCTION
..................................................................
122
5.2.1
PLANAR
ORIENTATION
......................................................................................
122
5.2.2
3-D
ORIENTATION
...........................................................................................
124
5.3
ISOTROPIC
ROTARY
DIFFUSION:
THE
FOLGAR-UICKER
MODEL
........................................
126
5.3.1
PLANAR
ORIENTATION
DISTRIBUTION
FUNCTION
................................................
127
5.3.2
3-D
ORIENTATION
DISTRIBUTION
FUNCTION
....................................................
129
5.3.3
TENSOR
EQUATION
..........................................................................................
130
5.4
CLOSURE
APPROXIMATIONS
........................................................................................
131
5.4.1
QUADRATIC,
LINEAR
AND
HYBRID
CLOSURES
....................................................
131
5.4.2
FITTED
CLOSURES
............................................................................................
132
XIV
CONTENTS
5.4.2.1
EIGENVALUE-BASED
ORTHOTROPIC
FITTING
........................................
133
5.4.2.2
INVARIANT-BASED
ORTHOTROPIC
FITTING
...........................................
136
5.4.2.3
THE
JEFFERY
DISTRIBUTION
AND
THE
NATURAL
CLOSURE
......................
137
5.4.2.4
CLOSURES
USING
NUMERICAL
DISTRIBUTION
FUNCTION
SOLUTIONS
......
140
5.4.3
COMPARISON
OF
CLOSURE
APPROXIMATIONS
....................................................
141
5.4.3.1
EQUAL
INTERACTION
COEFFICIENTS
.....................................................
142
5.4.3.2
TUNED
INTERACTION
COEFFICIENTS
.....................................................
143
5.4.3.3
PARTICLE
SHAPE
FACTOR
....................................................................
144
5.5
CHOOSING
THE
VALUE
OF
THE
INTERACTION
COEFFICIENT
...............................................
147
5.6
ANISOTROPIC
ROTARY
DIFFUSION
..................................................................................
149
5.6.1
MOTIVATION
AND
CONCEPT
............................................................................
149
5.6.2
GENERAL
EQUATIONS
......................................................................................
150
5.6.2.1
TENSOR
EQUATION
.............................................................................
150
5.6.2.2
DISTRIBUTION
FUNCTION
EQUATION
..................................................
151
5.6.3
CHOICES
FOR
THE
ROTARY
DIFFUSION
TENSOR
...................................................
152
5.6.3.1
FIVE-CONSTANT
MODEL
....................................................................
152
5.6.3.2
FOLGAR-TUCKER
MODEL
....................................................................
153
5.6.3.3
IARD
MODEL
...................................................................................
153
5.6.3.4
MRD
AND
PARD
MODELS
................................................................
153
5.6.3.5
WANG
OR
TWO-CONSTANT
MODEL
.....................................................
154
5.6.4
CHOOSINGARD MODEL
PARAMETERS
...............................................................
155
5.7
TRANSIENT
ORIENTATION
AND
SLOW
KINETICS
MODELS
.................................................
159
5.7.1
MOTIVATION
....................................................................................................
159
5.7.2
SRF/SLIP
MODEL
............................................................................................
161
5.7.3
OBJECTIVE
MODELS:
RSC
AND
RPR
................................................................
163
5.7.4
CHOOSING
THE
RSC
OR
RPR
PARAMETER
.........................................................
165
5.7.5
COMBINING
SLOW
KINETICS
WITH
ANISOTROPIC
ROTARY
DIFFUSION
..................
166
5.7.6
FLOW-TYPE
DEPENDENCE
..............................................................................
167
5.7.6.1
RATIONALE
........................................................................................
167
5.7.6.2
MODELS
............................................................................................
168
5.7.6.3
EXAMPLE
.........................................................................................
170
5.8
CHAPTER
SUMMARY
...................................................................................................
171
YY
SUSPENSION
RHEOLOGY
AND
FLOW-ORIENTATION
COUPLING
...............
173
6.1
BASICS
OF
CONSTITUTIVE
EQUATIONS
..........................................................................
173
6.1.1
TOTAL
STRESS
AND
EXTRA
STRESS
.......................................................................
174
6.1.2
NEWTONIAN
FLUID
..........................................................................................
174
6.1.3
GENERALIZED
NEWTONIAN
FLUID
....................................................................
175
CONTENTS
XV
6.1.4
SHEAR
VS.
EXTENSIONAL
VISCOSITY
..................................................................
175
6.2
STEADY
SHEAR
VISCOSITY
OF
FIBER
SUSPENSIONS
.......................................................
176
6.2.1
MEASUREMENTS
AND
TYPICAL
DATA
................................................................
176
6.2.2
RELATIONSHIP
TO
FIBER
ORIENTATION
..............................................................
178
6.3
AN
ANISOTROPIC
CONSTITUTIVE
EQUATION
FOR
FIBER
SUSPENSIONS
.............................
178
6.3.1
FLUID
MOTION
RELATIVE
TO
THE
FIBERS
............................................................
178
6.3.2
STRESS
WITH
FULLY
ALIGNED
FIBERS
.................................................................
180
6.3.3
STRESS
WITH
DISTRIBUTED
ORIENTATION
............................................................
182
6.3.4
THEORETICAL
PREDICTIONS
FOR
N
P
...................................................................
185
6.4
SOLVING
FLOW
PROBLEMS
...........................................................................................
187
6.4.1
GOVERNING
EQUATIONS
..................................................................................
187
6.4.2
BOUNDARY
AND
INITIAL
CONDITIONS
................................................................
188
6.4.3
SOLUTION
SCHEMES:
COUPLED
AND
DECOUPLED
............................................
189
6.4.4
TEMPERATURE
EFFECTS
....................................................................................
189
6.5
EXAMPLE
SOLUTIONS
..................................................................................................
190
6.5.1
AXISYMMETRIC
CONTRACTION
.........................................................................
190
6.5.2
ANISOTROPIC
SQUEEZE
FLOW
...........................................................................
192
6.6
DECOUPLED
FLOW
AS
A
SPECIAL
CASE
.........................................................................
193
6.6.1
CENTER-GATED
DISK
......................................................................................
193
6.6.2
GENERAL
CRITERIA
FOR
DECOUPLING
.................................................................
196
6.7
ORIENTATION
DEPENDENT
ISOTROPIC
VISCOSITY
MODEL
..............................................
198
6.8
TRANSIENT
RHEOLOGICAL
EXPERIMENTS
.......................................................................
200
6.8.1
FLOW
GEOMETRIES
........................................................................................
200
6.8.2
INITIAL
FIBER
ORIENTATION
STATE
....................................................................
201
6.8.3
COMPARING
MODELS
TO
DATA
........................................................................
202
6.8.4
INSIGHTS
FROM
TRANSIENT
RHEOLOGY
EXPERIMENTS
........................................
203
6.9
CHAPTER
SUMMARY
..................................................................................................
203
YY
FIBER
LENGTH
DEGRADATION
DURING
PROCESSING
...............................
205
7.1
MODEL
DEVELOPMENT
..............................................................................................
205
7.1.1
CONSERVATION
OF
FIBER
LENGTH
.....................................................................
205
7.1.2
BREAKAGE
RATE
AND
UNBREAKABLE
LENGTH
...................................................
207
7.1.3
CHILD
GENERATION
RATES
...............................................................................
210
7.2
EFFECTS
OF
MODEL
PARAMETERS
.................................................................................
212
7.3
IMPLEMENTATION
IN
MOLD
FILLING
SOFTWARE
.............................................................
216
7.3.1
FIBER
LENGTH
IN
AN
END-GATED
STRIP
...........................................................
217
7.3.2
COMPARISON
WITH
EXPERIMENTS
..................................................................
219
7.4
CHAPTER
SUMMARY
..................................................................................................
222
XVI
CONTENTS
YY
MECHANICAL
PROPERTIES
AND
ORIENTATION
..........................................
223
8.1
ANISOTROPIC
ELASTICITY
.............................................................................................
223
8.1.1
STRESS
AND
STRAIN
..........................................................................................
223
8.1.2
STIFFNESS
AND
COMPLIANCE
TENSORS
.............................................................
224
8.1.3
CONTRACTED
NOTATION
...................................................................................
225
8.1.4
MATERIAL
SYMMETRIES
...................................................................................
227
8.1.5
ENGINEERING
OR
TECHNICAL
CONSTANTS
..........................................................
228
8.2
HOMOGENIZATION
.....................................................................................................
231
8.2.1
GENERAL
PRINCIPLES
.......................................................................................
231
8.2.2
TWO-STEP
HOMOGENIZATION
........................................................................
234
8.3
STIFFNESS
ESTIMATES
FOR
UNIDIRECTIONAL
DISCONTINUOUS
FIBER
COMPOSITES
...........
235
8.3.1
ESHELBY/MORI-TANAKA
MODEL
.....................................................................
235
8.3.2
LIELENS/DOUBLE-INCLUSION
MODEL
...............................................................
236
8.3.3
HALPIN-TSAI
EQUATIONS
.................................................................................
237
8.3.4
NUMERICAL
ANALYSIS
OF
AN
RVE
....................................................................
238
8.3.5
COMPARISON
AND
RECOMMENDATIONS
.........................................................
239
8.4
AVERAGING
STIFFNESS
FOR
ORIENTATION
AND
LENGTH
...................................................
242
8.4.1
DEFINITIONS
AND
NOTATION
............................................................................
242
8.4.2
TYPES
OF
STIFFNESS
AVERAGES
..........................................................................
243
8.4.3
COMPUTING
ORIENTATION
AVERAGES
...............................................................
244
8.4.4
AVERAGING
OVER
FIBER
LENGTH
.......................................................................
247
8.4.5
MODELING
THE
LAYERED
STRUCTURE
OF
INJECTION
MOLDINGS
............................
249
8.5
COMPARISON
TO
EXPERIMENTS
..................................................................................
251
8.6
THERMAL
EXPANSION
................................................................................................
252
8.6.1
DEFINITIONS
...................................................................
253
8.6.2
FIRST
HOMOGENIZATION
STEP
........................................................................
253
8.6.3
SECOND
HOMOGENIZATION
STEP
....................................................................
255
8.7
NONLINEAR
STRESS-STRAIN
BEHAVIOR
...........................................................................
256
8.8
CHAPTER
SUMMARY
..................................................................................................
258
EL
CURRENT
AND
FUTURE
TRENDS
..............................................................
261
9.1
FIBER
MIGRATION
......................................................................................................
261
9.1.1
VOLUME
FRACTION
VARIATIONS
IN
INJECTION
MOLDED
PARTS
.............................
261
9.1.2
SHEAR-INDUCED
MIGRATION
PHENOMENA
......................................................
262
9.1.3
MODELING
SHEAR-INDUCED
MIGRATION
..........................................................
264
9.1.4
APPLICATION
TO
INJECTION
MOLDING
..............................................................
267
9.1.5
FIBER/MATRIX
SEPARATION
IN
SMC
AND
GMT
...............................................
269
CONTENTS
XVII
9.2
DIRECT
FIBER
SIMULATIONS
.........................................................................................
270
9.2.1
OVERVIEW
......................................................................................................
270
9.2.2
SIMULATION
METHODS
...................................................................................
271
9.2.2.1
REPRESENTING
THE
FIBERS
...............................................................
271
9.2.2.2
INITIAL
CONFIGURATION
.....................................................................
272
9.2.2.3
HYDRODYNAMIC
FORCES
...................................................................
272
9.2.2.4
INTERACTION
FORCES
........................................................................
273
9.2.2.5
SOLUTION
AND
TIME
STEPPING
.........................................................
274
9.2.3
APPLICATIONS
.................................................................................................
274
9.2.3.1
PARAMETER
IDENTIFICATION
.............................................................
274
9.2.3.2
FULL-PART
SIMULATIONS
....................................................................
276
9.2.3.3
NEW
ORIENTATION
MODELS
..............................................................
278
9.3
CHAPTER
SUMMARY
..................................................................................................
278
YY
VECTORS
AND
TENSORS.........................................................................
281
A.
1
DEFINITIONS
AND
NOTATION
.....................................................................................
281
A.1.1
SCALARS
AND
VECTORS
......................................................................................
281
A.
1.2
TENSORS
.........................................................................................................
282
A.
1.3
INDEX
NOTATION
.............................................................................................
283
A.
1.4
IDENTITY
TENSORS
AND
THE
KRONECKER
DELTA
................................................
283
A.
1.5
TRANSPOSE
AND
SYMMETRIES
........................................................................
284
A.
1.6
THE
TRACE
OF
A
TENSOR
.................................................................................
284
A.2
ALGEBRAIC
OPERATIONS
.............................................................................................
284
A.2.1
ADDITION
AND
SUBTRACTION
..........................................................................
284
A.2.2
MULTIPLICATION
.............................................................................................
285
A.2.3
MAGNITUDE
OF
A
VECTOR
................................................................................
286
A.2.4
TENSOR
INVERSE
............................................................................................
286
A.3
COORDINATE
TRANSFORMATION
..................................................................................
287
A.4
CONTRACTED
NOTATION
.............................................................................................
288
A.4.1
DEFINITIONS
.................................................................................................
288
A.4.2
IDENTITY
TENSOR
............................................................................................
289
A.4.3
OPERATIONS
..................................................................................................
290
A.4.4
FOURTH-ORDER
INVERSE
.................................................................................
291
A.4.5
COORDINATE
TRANSFORMATION
.......................................................................
291
A.5
CALCULATIONS
IN
M
ATLAB
........................................................................................
292
A.5.1
VECTORS
AND
SECOND-ORDER
TENSORS
...........................................................
292
A.5.2
FOURTH-ORDER
TENSORS
.................................................................................
293
A.6
D
AND
W
IN
CYLINDRICAL
COORDINATES
.....................................................................
294
XVIII
CONTENTS
295
B.
1
JEFFERY
S
EQUATION
FOR
PLANAR
ORIENTATION
AND
PLANAR
FLOW
...................................
295
B.2
TENSOR
FORM
OF
THE
FOLGAR-TUCKER
MODEL
.............................................................
296
B.2.1
PRELIMINARIES
................................................................................................
296
B.2.2
SEPARATING
THE
JEFFERY
AND
DIFFUSIVE
CONTRIBUTIONS
..................................
297
B.2.3
DIFFUSIVE
CONTRIBUTION
TO
A
........................................................................
297
B.3
STEADY-STATE
ORIENTATION
OF
RSC
AND
RPR
MODELS
...............................................
298
B.4
MECHANICAL
PROPERTY
EQUATIONS
............................................................................
299
B.4.1
ESHELBY
STRAIN
CONCENTRATION
TENSOR
.........................................................
299
B.4.2
ESHELBY
DILUTE
STIFFNESS
MODEL
...................................................................
300
B.4.3
GENERAL
STIFFNESS
EQUATION
..........................................................................
301
B.4.4
GENERAL
EQUATION
FOR
THERMAL
STRESS
.........................................................
301
SYMBOLS
AND
ABBREVIATIONS
...................................................................
303
REFERENCES
..............................................................................................
309
INDEX
.........................................................................................................
325
|
| adam_txt |
CONTENTS
PREFACE
.
VII
U
INTRODUCTION
.
1
1.1
DISCONTINUOUS
FIBER
COMPOSITES
.
1
1.2
PROCESSING,
MICROSTRUCTURE
AND
PROPERTIES
.
2
1.3
COMPUTER-AIDED
ENGINEERING
WORKFLOW
.
5
1.4
SCOPE
AND
ORGANIZATION
OF
THE
BOOK
.
8
1.5
ACCOMPANYING
SOFTWARE
.
9
DESCRIBING
FIBER
ORIENTATION
AND
FIBER
LENGTH
.
11
2.1
SINGLE
FIBER
ORIENTATION
.
11
2.2
DISTRIBUTIONS
OF
FIBER
ORIENTATION
.
12
2.2.1
PLANAR
ORIENTATION
.
12
2.2.1.1
MATCHING
TO
DATA
.
13
2.2.2
THREE-DIMENSIONAL
ORIENTATION
.
14
2.3
ORIENTATION
TENSORS
.
16
2.3.1
INTRODUCTION
.
16
2.3.2
RELATIONSHIP
TO
THE
DISTRIBUTION
FUNCTION
.
20
2.3.3
PROPERTIES
OF
THE
ORIENTATION
TENSOR
.
22
2.3.4
PRINCIPAL
DIRECTIONS
AND
PRINCIPAL
VALUES
.
23
2.3.4.1
PROPERTIES
OF
EIGENVALUES
AND
EIGENVECTORS
.
24
2.3.4.2
RELATIONSHIP
TO
COORDINATE
TRANSFORMATION
.
25
2.3.4.3
INDETERMINATE
EIGENVECTORS
.
27
2.3.4.4
NUMERICAL
DETAILS
.
28
2.3.5
THE
FOURTH-ORDER
ORIENTATION
TENSOR
.
29
2.3.5.1
CONTRACTED
NOTATION
.
30
2.3.5.2
EXAMPLES
.
32
2.4
RECONSTRUCTING
DISTRIBUTION
FUNCTIONS
.
34
2.4.1
PLANAR
ORIENTATION
.
35
2.4.1.1
FOURIER
SERIES
.
35
2.4.1.2
JEFFERY
DISTRIBUTION,
PLANAR
ORIENTATION
.
36
2.4.1.3
COMPARISON
OF
PLANAR
ORIENTATION
RECONSTRUCTIONS
.
37
XII
CONTENTS
2.4.2
3-D
ORIENTATION
.
39
2.5
FIBER
LENGTH
.
40
2.6
NUMBER-AVERAGE
AND
WEIGHT-AVERAGE
ORIENTATION
.
42
2.7
CHAPTER
SUMMARY
.
43
EL
MEASURING
FIBER
ORIENTATION
AND
LENGTH
.
45
3.1
PLANAR
SECTION
MEASUREMENTS
OF
ORIENTATION
.
45
3.1.1
MATHEMATICAL
PRINCIPLES
.
45
3.1.1.1
CORRECTING
FOR
SAMPLE
BIAS
.
47
3.1.1.2
AMBIGUOUS
ANGLES
AND
AMBIGUOUS
TENSOR
COMPONENTS
.
51
3.1.1.3
SYSTEMATIC
ERRORS
IN
0
.
52
3.1.2
PRACTICAL
ASPECTS
OF
MEASUREMENT
.
53
3.1.2.1
SAMPLE
PREPARATION
AND
IMAGING
.
53
3.1.2.2
IMAGE
ANALYSIS
.
54
3.1.2.3
SAMPLE
SIZE
AND
ORIENTATION
.
56
3.1.3
EXAMPLE:
CORE/SHELL
STRUCTURES
IN
INJECTION
MOLDED
COMPOSITES
.
57
3.1.4
MEASUREMENT
ACCURACY
.
58
3.2
MICRO-CT
MEASUREMENTS
OF
ORIENTATION
.
62
3.2.1
IMAGE
ACQUISITION
AND
SAMPLE
SIZE
.
62
3.2.2
IMAGE
ANALYSIS
.
65
3.2.2.1
VOXEL
ORIENTATIONS
.
65
3.2.2.2
FIBER
RECONSTRUCTION
.
67
3.2.2.3
EXAMPLE
DATA
.
68
3.2.2.4
COMPARISON
OF
IMAGE
ANALYSIS
SCHEMES
.
69
3.2.2.5
SAMPLES
WITH
FIBER
BUNDLES
OR
PLATELETS
.
69
3.3
LENGTH
MEASUREMENT
.
70
3.3.1
DESTRUCTIVE
SAMPLING
.
70
3.3.2
MICRO-CT
DATA
FOR
LENGTH
.
73
3.4
CHAPTER
SUMMARY
.
75
YY
FLOW
ORIENTATION
OF
SINGLE
FIBERS
.
77
4.1
FLOW
KINEMATICS
.
77
4.1.1
DEFORMATION
RATE
AND
VORTICITY
.
77
4.1.1.1
INVARIANTS
AND
THE
SCALAR
STRAIN
RATE
.
79
4.1.1.2
BASIC
FLOWS
.
79
4.1.2
FINITE
DEFORMATION
MEASURES
.
85
4.1.2.1
DISPLACEMENT
FUNCTIONS
.
85
4.1.2.2
DEFORMATION
GRADIENT
TENSORS
.
86
CONTENTS
XIII
4.1.2.3
STRETCHING
OF
A
MATERIAL
LINE
.
88
4.1.2.4
BASIC
DEFORMATIONS
.
89
4.2
JEFFERY
'
S
EQUATION
.
91
4.2.1
RATE
FORM
.
91
4.2.2
EXAMPLE
SOLUTIONS
AND
THE
TWO
RULES
OF
FIBER
ORIENTATION
.
93
4.2.2.1
PLANAR
ORIENTATION
IN
SIMPLE
SHEAR
.
93
4.2.2.2
PLANAR
ORIENTATION
IN
PLANAR
EXTENSIONAL
FLOW
.
95
4.2.3
NUMERICAL
SOLUTIONS
.
96
4.2.4
PARTICLE
SHAPE
FACTORS
.
97
4.2.5
JEFFERY
ORBITS
.
99
4.2.6
STRAIN-TIME
SCALING
AND
REVERSIBILITY
.
101
4.2.7
DEFORMATION
FORM
.
101
4.3
ORIENTATION
PATTERNS
IN
INJECTION
AND
COMPRESSION
MOLDING
.
103
4.3.1
TWO
RULES
THAT
EXPLAIN
EVERYTHING
.
103
4.3.2
SHELL
LAYERS
IN
INJECTION
MOLDING
.
104
4.3.3
CORE
ORIENTATION
IN
INJECTION
MOLDING
.
105
4.3.4
SKIN
LAYERS
AND
THE
FOUNTAIN
FLOW
.
108
4.3.5
THE
MYSTERY
OF
THICK
PLAQUES
.
110
4.3.6
COMPRESSION
MOLDING
.
112
4.3.6.1
LUBRICATED
SQUEEZE
FLOW
.
112
4.3.6.2
NON-LUBRICATED
SQUEEZE
FLOW
.
114
4.4
CHAPTER
SUMMARY
.
116
5
FLOW
ORIENTATION
OF
GROUPS
OF
FIBERS
.
117
5.1
JEFFERY
'
S
EQUATION
FOR
THE
ORIENTATION
TENSOR
.
117
5.1.1
DERIVATION
.
118
5.1.2
NUMERICAL
SOLUTION
FOR
A
MATERIAL
POINT
.
119
5.1.3
SPATIAL
FIELDS
OF
ORIENTATION
.
121
5.2
SOLVING
FOR
THE
DISTRIBUTION
FUNCTION
.
122
5.2.1
PLANAR
ORIENTATION
.
122
5.2.2
3-D
ORIENTATION
.
124
5.3
ISOTROPIC
ROTARY
DIFFUSION:
THE
FOLGAR-UICKER
MODEL
.
126
5.3.1
PLANAR
ORIENTATION
DISTRIBUTION
FUNCTION
.
127
5.3.2
3-D
ORIENTATION
DISTRIBUTION
FUNCTION
.
129
5.3.3
TENSOR
EQUATION
.
130
5.4
CLOSURE
APPROXIMATIONS
.
131
5.4.1
QUADRATIC,
LINEAR
AND
HYBRID
CLOSURES
.
131
5.4.2
FITTED
CLOSURES
.
132
XIV
CONTENTS
5.4.2.1
EIGENVALUE-BASED
ORTHOTROPIC
FITTING
.
133
5.4.2.2
INVARIANT-BASED
ORTHOTROPIC
FITTING
.
136
5.4.2.3
THE
JEFFERY
DISTRIBUTION
AND
THE
NATURAL
CLOSURE
.
137
5.4.2.4
CLOSURES
USING
NUMERICAL
DISTRIBUTION
FUNCTION
SOLUTIONS
.
140
5.4.3
COMPARISON
OF
CLOSURE
APPROXIMATIONS
.
141
5.4.3.1
EQUAL
INTERACTION
COEFFICIENTS
.
142
5.4.3.2
TUNED
INTERACTION
COEFFICIENTS
.
143
5.4.3.3
PARTICLE
SHAPE
FACTOR
.
144
5.5
CHOOSING
THE
VALUE
OF
THE
INTERACTION
COEFFICIENT
.
147
5.6
ANISOTROPIC
ROTARY
DIFFUSION
.
149
5.6.1
MOTIVATION
AND
CONCEPT
.
149
5.6.2
GENERAL
EQUATIONS
.
150
5.6.2.1
TENSOR
EQUATION
.
150
5.6.2.2
DISTRIBUTION
FUNCTION
EQUATION
.
151
5.6.3
CHOICES
FOR
THE
ROTARY
DIFFUSION
TENSOR
.
152
5.6.3.1
FIVE-CONSTANT
MODEL
.
152
5.6.3.2
FOLGAR-TUCKER
MODEL
.
153
5.6.3.3
IARD
MODEL
.
153
5.6.3.4
MRD
AND
PARD
MODELS
.
153
5.6.3.5
WANG
OR
TWO-CONSTANT
MODEL
.
154
5.6.4
CHOOSINGARD MODEL
PARAMETERS
.
155
5.7
TRANSIENT
ORIENTATION
AND
SLOW
KINETICS
MODELS
.
159
5.7.1
MOTIVATION
.
159
5.7.2
SRF/SLIP
MODEL
.
161
5.7.3
OBJECTIVE
MODELS:
RSC
AND
RPR
.
163
5.7.4
CHOOSING
THE
RSC
OR
RPR
PARAMETER
.
165
5.7.5
COMBINING
SLOW
KINETICS
WITH
ANISOTROPIC
ROTARY
DIFFUSION
.
166
5.7.6
FLOW-TYPE
DEPENDENCE
.
167
5.7.6.1
RATIONALE
.
167
5.7.6.2
MODELS
.
168
5.7.6.3
EXAMPLE
.
170
5.8
CHAPTER
SUMMARY
.
171
YY
SUSPENSION
RHEOLOGY
AND
FLOW-ORIENTATION
COUPLING
.
173
6.1
BASICS
OF
CONSTITUTIVE
EQUATIONS
.
173
6.1.1
TOTAL
STRESS
AND
EXTRA
STRESS
.
174
6.1.2
NEWTONIAN
FLUID
.
174
6.1.3
GENERALIZED
NEWTONIAN
FLUID
.
175
CONTENTS
XV
6.1.4
SHEAR
VS.
EXTENSIONAL
VISCOSITY
.
175
6.2
STEADY
SHEAR
VISCOSITY
OF
FIBER
SUSPENSIONS
.
176
6.2.1
MEASUREMENTS
AND
TYPICAL
DATA
.
176
6.2.2
RELATIONSHIP
TO
FIBER
ORIENTATION
.
178
6.3
AN
ANISOTROPIC
CONSTITUTIVE
EQUATION
FOR
FIBER
SUSPENSIONS
.
178
6.3.1
FLUID
MOTION
RELATIVE
TO
THE
FIBERS
.
178
6.3.2
STRESS
WITH
FULLY
ALIGNED
FIBERS
.
180
6.3.3
STRESS
WITH
DISTRIBUTED
ORIENTATION
.
182
6.3.4
THEORETICAL
PREDICTIONS
FOR
N
P
.
185
6.4
SOLVING
FLOW
PROBLEMS
.
187
6.4.1
GOVERNING
EQUATIONS
.
187
6.4.2
BOUNDARY
AND
INITIAL
CONDITIONS
.
188
6.4.3
SOLUTION
SCHEMES:
COUPLED
AND
DECOUPLED
.
189
6.4.4
TEMPERATURE
EFFECTS
.
189
6.5
EXAMPLE
SOLUTIONS
.
190
6.5.1
AXISYMMETRIC
CONTRACTION
.
190
6.5.2
ANISOTROPIC
SQUEEZE
FLOW
.
192
6.6
DECOUPLED
FLOW
AS
A
SPECIAL
CASE
.
193
6.6.1
CENTER-GATED
DISK
.
193
6.6.2
GENERAL
CRITERIA
FOR
DECOUPLING
.
196
6.7
ORIENTATION
DEPENDENT
ISOTROPIC
VISCOSITY
MODEL
.
198
6.8
TRANSIENT
RHEOLOGICAL
EXPERIMENTS
.
200
6.8.1
FLOW
GEOMETRIES
.
200
6.8.2
INITIAL
FIBER
ORIENTATION
STATE
.
201
6.8.3
COMPARING
MODELS
TO
DATA
.
202
6.8.4
INSIGHTS
FROM
TRANSIENT
RHEOLOGY
EXPERIMENTS
.
203
6.9
CHAPTER
SUMMARY
.
203
YY
FIBER
LENGTH
DEGRADATION
DURING
PROCESSING
.
205
7.1
MODEL
DEVELOPMENT
.
205
7.1.1
CONSERVATION
OF
FIBER
LENGTH
.
205
7.1.2
BREAKAGE
RATE
AND
UNBREAKABLE
LENGTH
.
207
7.1.3
CHILD
GENERATION
RATES
.
210
7.2
EFFECTS
OF
MODEL
PARAMETERS
.
212
7.3
IMPLEMENTATION
IN
MOLD
FILLING
SOFTWARE
.
216
7.3.1
FIBER
LENGTH
IN
AN
END-GATED
STRIP
.
217
7.3.2
COMPARISON
WITH
EXPERIMENTS
.
219
7.4
CHAPTER
SUMMARY
.
222
XVI
CONTENTS
YY
MECHANICAL
PROPERTIES
AND
ORIENTATION
.
223
8.1
ANISOTROPIC
ELASTICITY
.
223
8.1.1
STRESS
AND
STRAIN
.
223
8.1.2
STIFFNESS
AND
COMPLIANCE
TENSORS
.
224
8.1.3
CONTRACTED
NOTATION
.
225
8.1.4
MATERIAL
SYMMETRIES
.
227
8.1.5
ENGINEERING
OR
TECHNICAL
CONSTANTS
.
228
8.2
HOMOGENIZATION
.
231
8.2.1
GENERAL
PRINCIPLES
.
231
8.2.2
TWO-STEP
HOMOGENIZATION
.
234
8.3
STIFFNESS
ESTIMATES
FOR
UNIDIRECTIONAL
DISCONTINUOUS
FIBER
COMPOSITES
.
235
8.3.1
ESHELBY/MORI-TANAKA
MODEL
.
235
8.3.2
LIELENS/DOUBLE-INCLUSION
MODEL
.
236
8.3.3
HALPIN-TSAI
EQUATIONS
.
237
8.3.4
NUMERICAL
ANALYSIS
OF
AN
RVE
.
238
8.3.5
COMPARISON
AND
RECOMMENDATIONS
.
239
8.4
AVERAGING
STIFFNESS
FOR
ORIENTATION
AND
LENGTH
.
242
8.4.1
DEFINITIONS
AND
NOTATION
.
242
8.4.2
TYPES
OF
STIFFNESS
AVERAGES
.
243
8.4.3
COMPUTING
ORIENTATION
AVERAGES
.
244
8.4.4
AVERAGING
OVER
FIBER
LENGTH
.
247
8.4.5
MODELING
THE
LAYERED
STRUCTURE
OF
INJECTION
MOLDINGS
.
249
8.5
COMPARISON
TO
EXPERIMENTS
.
251
8.6
THERMAL
EXPANSION
.
252
8.6.1
DEFINITIONS
.
253
8.6.2
FIRST
HOMOGENIZATION
STEP
.
253
8.6.3
SECOND
HOMOGENIZATION
STEP
.
255
8.7
NONLINEAR
STRESS-STRAIN
BEHAVIOR
.
256
8.8
CHAPTER
SUMMARY
.
258
EL
CURRENT
AND
FUTURE
TRENDS
.
261
9.1
FIBER
MIGRATION
.
261
9.1.1
VOLUME
FRACTION
VARIATIONS
IN
INJECTION
MOLDED
PARTS
.
261
9.1.2
SHEAR-INDUCED
MIGRATION
PHENOMENA
.
262
9.1.3
MODELING
SHEAR-INDUCED
MIGRATION
.
264
9.1.4
APPLICATION
TO
INJECTION
MOLDING
.
267
9.1.5
FIBER/MATRIX
SEPARATION
IN
SMC
AND
GMT
.
269
CONTENTS
XVII
9.2
DIRECT
FIBER
SIMULATIONS
.
270
9.2.1
OVERVIEW
.
270
9.2.2
SIMULATION
METHODS
.
271
9.2.2.1
REPRESENTING
THE
FIBERS
.
271
9.2.2.2
INITIAL
CONFIGURATION
.
272
9.2.2.3
HYDRODYNAMIC
FORCES
.
272
9.2.2.4
INTERACTION
FORCES
.
273
9.2.2.5
SOLUTION
AND
TIME
STEPPING
.
274
9.2.3
APPLICATIONS
.
274
9.2.3.1
PARAMETER
IDENTIFICATION
.
274
9.2.3.2
FULL-PART
SIMULATIONS
.
276
9.2.3.3
NEW
ORIENTATION
MODELS
.
278
9.3
CHAPTER
SUMMARY
.
278
YY
VECTORS
AND
TENSORS.
281
A.
1
DEFINITIONS
AND
NOTATION
.
281
A.1.1
SCALARS
AND
VECTORS
.
281
A.
1.2
TENSORS
.
282
A.
1.3
INDEX
NOTATION
.
283
A.
1.4
IDENTITY
TENSORS
AND
THE
KRONECKER
DELTA
.
283
A.
1.5
TRANSPOSE
AND
SYMMETRIES
.
284
A.
1.6
THE
TRACE
OF
A
TENSOR
.
284
A.2
ALGEBRAIC
OPERATIONS
.
284
A.2.1
ADDITION
AND
SUBTRACTION
.
284
A.2.2
MULTIPLICATION
.
285
A.2.3
MAGNITUDE
OF
A
VECTOR
.
286
A.2.4
TENSOR
INVERSE
.
286
A.3
COORDINATE
TRANSFORMATION
.
287
A.4
CONTRACTED
NOTATION
.
288
A.4.1
DEFINITIONS
.
288
A.4.2
IDENTITY
TENSOR
.
289
A.4.3
OPERATIONS
.
290
A.4.4
FOURTH-ORDER
INVERSE
.
291
A.4.5
COORDINATE
TRANSFORMATION
.
291
A.5
CALCULATIONS
IN
M
ATLAB
.
292
A.5.1
VECTORS
AND
SECOND-ORDER
TENSORS
.
292
A.5.2
FOURTH-ORDER
TENSORS
.
293
A.6
D
AND
W
IN
CYLINDRICAL
COORDINATES
.
294
XVIII
CONTENTS
295
B.
1
JEFFERY
'
S
EQUATION
FOR
PLANAR
ORIENTATION
AND
PLANAR
FLOW
.
295
B.2
TENSOR
FORM
OF
THE
FOLGAR-TUCKER
MODEL
.
296
B.2.1
PRELIMINARIES
.
296
B.2.2
SEPARATING
THE
JEFFERY
AND
DIFFUSIVE
CONTRIBUTIONS
.
297
B.2.3
DIFFUSIVE
CONTRIBUTION
TO
A
.
297
B.3
STEADY-STATE
ORIENTATION
OF
RSC
AND
RPR
MODELS
.
298
B.4
MECHANICAL
PROPERTY
EQUATIONS
.
299
B.4.1
ESHELBY
STRAIN
CONCENTRATION
TENSOR
.
299
B.4.2
ESHELBY
DILUTE
STIFFNESS
MODEL
.
300
B.4.3
GENERAL
STIFFNESS
EQUATION
.
301
B.4.4
GENERAL
EQUATION
FOR
THERMAL
STRESS
.
301
SYMBOLS
AND
ABBREVIATIONS
.
303
REFERENCES
.
309
INDEX
.
325 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Tucker, Charles L. III |
| author_GND | (DE-588)125565760X |
| author_facet | Tucker, Charles L. III |
| author_role | aut |
| author_sort | Tucker, Charles L. III |
| author_variant | c l i t cli clit |
| building | Verbundindex |
| bvnumber | BV047887463 |
| classification_rvk | ZM 7021 UQ 8420 |
| ctrlnum | (OCoLC)1309921049 (DE-599)DNB1247123375 |
| discipline | Physik Werkstoffwissenschaften / Fertigungstechnik |
| discipline_str_mv | Physik Werkstoffwissenschaften / Fertigungstechnik |
| format | Book |
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| id | DE-604.BV047887463 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:24:57Z |
| indexdate | 2024-07-10T09:24:16Z |
| institution | BVB |
| institution_GND | (DE-588)1064064051 |
| isbn | 9781569908754 1569908753 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033269648 |
| oclc_num | 1309921049 |
| open_access_boolean | |
| owner | DE-703 DE-210 DE-91 DE-BY-TUM DE-12 DE-384 |
| owner_facet | DE-703 DE-210 DE-91 DE-BY-TUM DE-12 DE-384 |
| physical | XVIII, 334 Seiten Illustrationen, Diagramme 25 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Hanser |
| record_format | marc |
| spelling | Tucker, Charles L. III Verfasser (DE-588)125565760X aut Fundamentals of fiber orientation description, measurement and prediction Charles L. Tucker III Munich Hanser [2022] © 2022 XVIII, 334 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Mechanische Eigenschaft (DE-588)4217961-0 gnd rswk-swf Polymere (DE-588)4046699-1 gnd rswk-swf Faserverstärkter Kunststoff (DE-588)4128805-1 gnd rswk-swf Länge (DE-588)4224141-8 gnd rswk-swf Faserorientierung (DE-588)4332341-8 gnd rswk-swf Rheologische Eigenschaft (DE-588)4366895-1 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Faser (DE-588)4127566-4 gnd rswk-swf FBKTFASE: Fasern PLAS2022 Discontinuous fibers Fiber orientation Fiber-reinforced plastics Flow orientation Polymere (DE-588)4046699-1 s Faserverstärkter Kunststoff (DE-588)4128805-1 s Faserorientierung (DE-588)4332341-8 s DE-604 Faser (DE-588)4127566-4 s Länge (DE-588)4224141-8 s Messung (DE-588)4038852-9 s Mechanische Eigenschaft (DE-588)4217961-0 s Rheologische Eigenschaft (DE-588)4366895-1 s Mathematisches Modell (DE-588)4114528-8 s Hanser Publications (DE-588)1064064051 pbl Erscheint auch als Online-Ausgabe 978-1-56990-876-1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033269648&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20211208 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Tucker, Charles L. III Fundamentals of fiber orientation description, measurement and prediction Mechanische Eigenschaft (DE-588)4217961-0 gnd Polymere (DE-588)4046699-1 gnd Faserverstärkter Kunststoff (DE-588)4128805-1 gnd Länge (DE-588)4224141-8 gnd Faserorientierung (DE-588)4332341-8 gnd Rheologische Eigenschaft (DE-588)4366895-1 gnd Messung (DE-588)4038852-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Faser (DE-588)4127566-4 gnd |
| subject_GND | (DE-588)4217961-0 (DE-588)4046699-1 (DE-588)4128805-1 (DE-588)4224141-8 (DE-588)4332341-8 (DE-588)4366895-1 (DE-588)4038852-9 (DE-588)4114528-8 (DE-588)4127566-4 |
| title | Fundamentals of fiber orientation description, measurement and prediction |
| title_auth | Fundamentals of fiber orientation description, measurement and prediction |
| title_exact_search | Fundamentals of fiber orientation description, measurement and prediction |
| title_exact_search_txtP | Fundamentals of fiber orientation description, measurement and prediction |
| title_full | Fundamentals of fiber orientation description, measurement and prediction Charles L. Tucker III |
| title_fullStr | Fundamentals of fiber orientation description, measurement and prediction Charles L. Tucker III |
| title_full_unstemmed | Fundamentals of fiber orientation description, measurement and prediction Charles L. Tucker III |
| title_short | Fundamentals of fiber orientation |
| title_sort | fundamentals of fiber orientation description measurement and prediction |
| title_sub | description, measurement and prediction |
| topic | Mechanische Eigenschaft (DE-588)4217961-0 gnd Polymere (DE-588)4046699-1 gnd Faserverstärkter Kunststoff (DE-588)4128805-1 gnd Länge (DE-588)4224141-8 gnd Faserorientierung (DE-588)4332341-8 gnd Rheologische Eigenschaft (DE-588)4366895-1 gnd Messung (DE-588)4038852-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd Faser (DE-588)4127566-4 gnd |
| topic_facet | Mechanische Eigenschaft Polymere Faserverstärkter Kunststoff Länge Faserorientierung Rheologische Eigenschaft Messung Mathematisches Modell Faser |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033269648&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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