Micromechanics of composite materials:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht
Springer
2013
|
| Edition: | softcover reprint of the hardcover 1st edition |
| Series: | Solid mechanics and its applications
volume 186 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvii, 442 Seiten Diagramme |
| ISBN: | 9400797818 9789400797819 |
Staff View
MARC
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| 020 | |a 9400797818 |9 94-007-9781-8 | ||
| 020 | |a 9789400797819 |9 978-94-007-9781-9 | ||
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| 035 | |a (DE-599)BVBBV042763484 | ||
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| 100 | 1 | |a Dvorak, George J. |d 1933- |e Verfasser |0 (DE-588)1094924148 |4 aut | |
| 245 | 1 | 0 | |a Micromechanics of composite materials |c George J. Dvorak |
| 250 | |a softcover reprint of the hardcover 1st edition | ||
| 264 | 1 | |a Dordrecht |b Springer |c 2013 | |
| 300 | |a xvii, 442 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Solid mechanics and its applications |v volume 186 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-94-007-4101-0 |
| 830 | 0 | |a Solid mechanics and its applications |v volume 186 |w (DE-604)BV004342211 |9 186 | |
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Record in the Search Index
| _version_ | 1804174984092844032 |
|---|---|
| adam_text | Contents
R
1 Tensor Component and Matrix Notations............................... 1
2 Anisotropic Elastic Solids.......................................... 11
2.1 Elastic Strain Energy Density................................. 11
2.2 Material Symmetries......................................... 14
2.2.1 Elements of Material Symmetry....................... 14
2.2.2 Triclinic Materials................................. 17
2.2.3 Monoclinic Materials................................ 17
2.2.4 Orthotropic Materials............................... 19
2.2.5 Trigonal and Tetragonal Materials................... 20
2.2.6 Transversely Isotropic or Hexagonal Materials..... 21
2.2.7 Cubic Materials..................................... 22
2.2.8 Isotropic Materials................................. 23
2.2.9 Decomposition of Isotropic Tensors and Matrices... 25
2.2.10 Orientation Average of a Fourth-Order Tensor........ 26
2.3 Transversely Isotropic Composite Materials ................... 27
2.3.1 Engineering and Hill’s Moduli....................... 27
2.3.2 Walpole’s Notation ................................. 30
2.4 Cylindrically Orthotropic Materials........................... 32
2.5 Young’s Modulus, Shear Modulus and Poisson’s Ratio............ 33
3 Elementary Concepts and Tools ...................................... 35
3.1 Aggregates and Constituent Phases............................. 35
3.2 Heterogeneous Microstructures................................. 36
3.2.1 Simple Descriptors.................................. 37
3.2.2 Statistical Homogeneity and Material Symmetry..... 38
3.2.3 Specific Surface.................................... 39
3.2.4 Two-Point Probability Function...................... 40
3.3 Representative Volume....................................... 42
3.3.1 Size Requirements................................. 42
3.3.2 Local Volume Fraction Fluctuations.................. 44
3.4 Stress and Strain Field Averages.............................. 46
xi
xii Contents
3.5 Overall Properties and Local Fields......................... 48
3.5.1 Mechanical Influence Functions and
Concentration Factors................................. 48
3.5.2 Overall Stiffness and Compliance...................... 50
3.6 Phase Transformations....................................... 52
3.6.1 Eigenstrains and Eigenstresses........................ 52
3.6.2 Local Transformation Fields........................... 55
3.6.3 Overall Response.................................... 58
3.7 Work, Energy and Reciprocal Theorems........................ 59
3.7.1 Clapeyron and Virtual Work Theorems................... 59
3.7.2 Minimum Potential and Complementary
Energy Theorems....................................... 61
3.7.3 The Reciprocal Theorem.............................. 64
3.8 The Levin Formula and the Hill Lemma........................ 65
3.9 Universal Connections for Elastic Moduli of Fibrous Composites 70
3.9.1 Hill’s Universal Connections for
Transversely Isotropic Composites .................... 71
3.9.2 Universal Connections for Monoclinic
Systems Based on Uniform Fields....................... 72
3.10 Constitutive Relations and Local Fields
in Heterogeneous Aggregates.................................... 75
3.10.1 Overall Strain e° and Phase Eigenstrains
fir are Prescribed.................................... 75
3.10.2 Overall Stress a0 and Phase Eigenstresses
Ar are Prescribed..................................... 76
4 Inclusions, Inhomogeneities and Cavities.............................. 79
4.1 Homogeneous Ellipsoidal Inclusions: The Eshelby Solution..... 80
4.1.1 A Transformed Homogeneous Inclusion................... 80
4.1.2 Local Fields in Ellipsoidal Inclusions ............... 81
4.2 Ellipsoidal Inhomogeneities: The Equivalent
Inclusion Method .............................................. 83
4.3 Transformed Inhomogeneities................................. 87
4.3.1 Method of Uniform Fields.............................. 87
4.3.2 The Equivalent Inclusion Method....................... 90
4.3.3 Contrasting Mechanical and
Transformation Strains................................ 92
4.3.4 Imperfectly Bonded Inhomogeneities and Cavities — 93
4.4 Dilute Approximation of Overall Properties and Local Fields ... 96
4.4.1 Overall Strain e° and Phase Eigenstrains
fi{, ¡ir Are Prescribed............................... 96
4.4.2 Overall Stress r° and Phase Eigenstresses
A i, A r Are Prescribed............................... 97
4.4.3 Debonded Inhomogeneities Creating
Traction-Free Cavities.............................. 99
Contents xiii
4.4.4 Applications to Particulate Suspensions
and Porous Media................................... 100
4.5 Green’s Function and Eshelby’s Tensor in Elastic Solids.... 104
4.5.1 Introduction....................................... 104
4.5.2 Green’s Function and Its First Derivative.......... 105
4.5.3 The Inclusion Problem............................ 108
4.5.4 The Tanaka-Mori Theorem for Exterior Fields........ 112
4.5.5 Shape-Independent Relations ....................... 114
4.6 Coefficients of P Matrices for Selected Ellipsoidal Shapes. 116
4.6.1 Sources and Notation............................... 116
4.6.2 A Spherical Inclusion in an Isotropic Solid........ 117
4.6.3 An Elliptical Cylinder in a Transversely
Isotropic Solid ................................... 118
4.6.4 A Slit Crack and Flat Disc in an Orthotropic Solid — 118
4.6.5 Spheroids in an Isotropic Solid.................... 119
4.7 Summary of Principal Results.............................. 120
4.7.1 Homogeneous Ellipsoidal Inclusions................. 121
4.7.2 Inhomogeneities and Cavities of Ellipsoidal Shape — 121
4.7.3 Multiphase Aggregate with Dilute
Reinforcements Lr in Matrix L .................... 123
5 Energies of Inhomogeneities, Dilute Reinforcements and Cracks — 125
5.1 Energy Changes Caused by Mechanical Loads.................. 126
5.1.1 Uniform Overall Strain Is Applied.................. 126
5.1.2 Uniform Overall Stress Is Applied.................. 128
5.1.3 Energy Based Evaluation of Overall
Stiffness and Compliance of Dilute Mixtures........ 129
5.1.4 Energy Released by Complete Decohesion
of a Part of Dilute Reinforcement.................. 130
5.2 Energy Changes Caused by Uniform Phase Eigenstrains........ 133
5.3 Energy Changes Caused by Mechanical Loads
and Phase Eigenstrains ................................... 135
5.3.1 The Load Set {e°, fiu fir} ........................ 135
5.3.2 The Load Set {a0, Ar, Ai}.......................... 138
5.4 Energy Changes Caused by Cracks............................ 140
5.4.1 Aligned Slit Cracks in an Orthotropic Solid........ 141
5.4.2 Aligned Penny-Shaped Cracks in a
Transversely Isotropic Solid....................... 143
6 Evaluations and Bounds on Elastic Moduli
of Heterogeneous Materials......................................... 145
6.1 Elementary Energy Bounds ................................... 146
6.2 Hashin-Shtrikman and Walpole Bounds on Overall
Elastic Moduli.............................................. 147
6.2.1 Overall Strain e° is Prescribed.................... 148
6.2.2 Overall Stress o*0 is Prescribed................... 152
XIV
Contents
6.3 Evaluation of H-S Bounds for Ellipsoidal Inhomogeneities.... 154
6.3.1 Local Field and Overall Elastic Moduli of
Multiphase Systems .................................. 154
6.3.2 H-S Bounds on Overall Elastic Moduli of
Multiphase Systems .................................. 159
6.3.3 H-S Bounds on Elastic Moduli of
Two-Phase Systems.................................... 160
6.4 Composite Element Assemblage Bounds............................ 163
6.4.1 Bounds on Elastic Moduli of Aligned Fiber
Composites........................................... 164
6.4.2 Application to a Carbon/Copper Composite......... 167
6.5 The Generalized Self-consistent Method....................... 168
6.5.1 Shear Modulus of a Two-Phase Particulate Composite 170
6.5.2 Transverse Shear Modulus of a Two-Phase
Aligned Fiber Composite.............................. 174
7 Estimates of Mechanical Properties of Composite Materials.......... 177
7.1 The Self-consistent Method (SCM)............................... 178
7.1.1 Estimates of Overall Elastic Moduli.............. 178
7.1.2 Elastic Moduli of Two-Phase Fiber Composites..... 180
7.1.3 Elastic Moduli of Two-Phase Particulate Composites . 182
7.1.4 Restrictions on Constituent Shape and Alignment.... 183
7.2 The Mori-Tanaka Method (M-T)................................... 184
7.2.1 Elastic Moduli and Local Fields of
Multiphase Composites................................ 185
7.2.2 Elastic Moduli of Fibrous, Particulate and
Layered Composites................................... 187
7.2.3 Elastic Moduli of Solids Containing
Randomly Oriented Reinforcements and Cracks....... 189
7.2.4 Restrictions on Constituent Shape and Alignment.... 192
7.2.5 Derivation of Effective Phase Moduli............. 194
7.3 The Differential Scheme........................................ 195
7.4 The Double Inclusion and Double Inhomogeneity Models........ 198
7.4.1 Field Averages in a Double Inhomogeneity......... 198
7.4.2 Double Inhomogeneity Microstructures............. 201
7.4.3 Connections with the Self-consistent and
Mori-Tanaka Estimates................................ 204
7.4.4 Multiphase Composites with Different
Constituent Shapes and Alignments.................... 207
7.4.5 Composites Containing Distributed Voids
or Cracks.......................................... 209
7.4.6 Predictive Reliability of Micromechanical Methods ... 211
7.5 Applications of SCM and M-T to Functionally Graded Materials 212
7.5.1 Discrete and Layered Models of Graded
Microstructures...................................... 213
Contents
xv
7.5.2 Selected Comparisons of Discrete and
Homogenized Models................................. 217
8 Transformation Fields............................................... 221
8.1 Uniform Change of Temperature in Two-Phase
Composites and Polycrystals................................. 222
8.1.1 Thermal Strain Vectors of Anisotropic Solids....... 223
8.1.2 Composites of Two Isotropic Phases................. 224
8.1.3 Polycrystals....................................... 226
8.1.4 Aligned Fiber Composites........................... 228
8.1.5 Adjustable Uniform Fields in Fiber Composites..... 230
8.1.6 Coated Fiber Composites............................ 233
8.2 Transformation Influence Functions and
Concentration Factors ...................................... 235
8.2.1 Local and Overall Residual Fields.................. 235
8.2.2 Overall Strain e° and Phase Eigenstrains
ftr Are Prescribed................................. 238
8.2.3 Overall Stress cr° and Phase Eigenstresses
Xr Are Applied .................................... 241
8.2.4 Properties of the Transformation Influence Functions . 243
8.3 Uniform Change in Temperature in Multiphase Systems......... 246
8.3.1 Overall and Local Field Averages................... 246
8.3.2 Temperature Dependent Phase Properties............. 250
8.4 Capabilities of Bounds and Estimates of Overall
and Local Fields.......................................... 252
8.5 Related Research Activities................................. 256
9 Interfaces and Interphases.......................................... 259
9.1 Perfectly Bonded Interfaces................................. 260
9.1.1 Decomposition of Stress and Strain Tensors
Relative to a Plane................................ 260
9.1.2 Decomposition of Stress and Strain Tensors
Relative to a Surface............................ 263
9.1.3 Interface Fields at Anisotropic Ellipsoidal
Inhomogeneities and Cavities....................... 268
9.1.4 Interface Fields at Isotropic
Inhomogeneities and Cavities....................... 270
9.1.5 Evaluation of Interface Stresses in a
S-Glass/Epoxy Composite............................ 271
9.2 Imperfectly Bonded Inhomogeneities and Cavities............. 275
9.2.1 Interface Tractions and Displacements.............. 276
9.2.2 Needleman’s Imperfect Interface Models............. 277
9.2.3 Overall Response................................... 280
9.3 Interphases............................................... 282
9.3.1 Thin Interphases with Assigned Properties.......... 282
9.3.2 Interphase Regimes in Polymer Nanocomposites...... 285
XVI
Contents
10 Symmetric Laminates...... ........................................... 287
10.1 Constitutive Relations of Fibrous Plies....................... 288
10.1.1 Plane Stress Stiffness and Compliance................ 289
10.1.2 Thermal and Eigenstrain Ply Vectors.................. 290
10.1.3 Ply Load Sets ..................................... 291
10.2 Coordinate Systems and Transformations........................ 292
10.3 Overall Response and Ply Stresses in Symmetric Laminates.... 294
10.4 Ply and Constituent Stress and Strain Averages................ 298
10.4.1 Load Set {a, 1/A0, A,-} Is Applied................... 298
10.4.2 Load Set {e, m*A0, jij Is Applied.................... 300
10.5 Design of Laminates for Cylindrical Pressure Vessels.......... 301
10.6 Dimensionally Stable Laminates................................ 304
10.7 Auxetic Laminates......................................... 307
10.8 Laminates with Reduced Free Edge Stresses..................... 309
10.9 Laminates with Fiber Prestress................................ 313
10.9.1 Prestressed Laminated Plates......................... 314
10.9.2 Damage Envelopes of Prestressed
Laminated Plates.................................... 315
10.9.3 Fiber Prestress for Suppression of Free
Edge Stress Concentrations ......................... 319
10.9.4 Prestressed Laminates for Cylindrical
Pressure Vessels.................................... 321
10.9.5 Prestress of Ceramic Armor Plates.................... 325
10.10 Laminates with Transverse Cracks.............................. 326
10.10.1 Cracks in Polymer and Metal Matrix Plies............. 326
10.10.2 Ply Stiffness at Large Crack Density ................ 330
10.10.3 Effect of Ply Thickness on Energy Release
by Transverse Cracks ............................... 332
11 Elastic - Plastic Solids........................................... 337
11.1 Yield and Loading Surfaces, Normality and Convexity........... 337
11.1.1 Mises Yield and Loading Surfaces..................... 338
11.1.2 Normality and Convexity of the Loading Surface..... 341
11.2 Hardening and Flow Rules...................................... 344
11.2.1 Isotropic Hardening and Flow Rules................... 344
11.2.2 Kinematic Hardening and Flow Rules................... 346
11.2.3 Mixed Isotropic and Kinematic Hardening Rules...... 349
11.2.4 The Dafalias-Popov Model for Adaptive
Estimate of the Tangent Modulus................... 351
11.3 Matrix Form and Consistency of the Instantaneous
Tangent Stiffness............................................ 354
12 Inelastic Composite Materials........................................ 359
12.1 Transformation Field Analysis (TFA) of Inelastic Deformation.. 361
12.1.1 Periodic Unit Cell Models............................ 362
12.1.2 Mechanical and Transformation Influence Functions .. 365
Contents xvii
12.1.3 Local and Overall Yield Surfaces................ — 368
12.1.4 Thermoplastic Deformation of Unit Cell Models..... 371
12.1.5 Viscoelastic Deformation of Unit Cell Models...... 374
12.1.6 Modified Transformation Field Analysis Methods.... 376
12.2 Experimental Support of Theoretical Predictions............. 381
12.2.1 Bimodal Plasticity of Fiber Composites............. 382
12.2.2 Comparison of Experimental Results with Predictions 386
12.3 Thermal Hardening.......................................... 395
12.3.1 Thermal Hardening in Composites of Two
Isotropic Phases................................... 396
12.3.2 Thermal Hardening in Two-Phase Aligned
Fiber Composites.................................. 399
12.3.3 Thermal Hardening in Laminated Plates.............. 401
12.3.4 Thermal Hardening in Polycrystals
and Multiphase Systems........................... 403
12.4 Utility of Plasticity Theories of Composite Materials ...... 406
References............................................................... 409
Index.................................................................... 435
|
| any_adam_object | 1 |
| author | Dvorak, George J. 1933- |
| author_GND | (DE-588)1094924148 |
| author_facet | Dvorak, George J. 1933- |
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| discipline | Physik |
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| format | Book |
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| id | DE-604.BV042763484 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:09:04Z |
| institution | BVB |
| isbn | 9400797818 9789400797819 |
| language | English |
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| physical | xvii, 442 Seiten Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Solid mechanics and its applications |
| series2 | Solid mechanics and its applications |
| spelling | Dvorak, George J. 1933- Verfasser (DE-588)1094924148 aut Micromechanics of composite materials George J. Dvorak softcover reprint of the hardcover 1st edition Dordrecht Springer 2013 xvii, 442 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Solid mechanics and its applications volume 186 Erscheint auch als Online-Ausgabe 978-94-007-4101-0 Solid mechanics and its applications volume 186 (DE-604)BV004342211 186 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028193953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dvorak, George J. 1933- Micromechanics of composite materials Solid mechanics and its applications |
| title | Micromechanics of composite materials |
| title_auth | Micromechanics of composite materials |
| title_exact_search | Micromechanics of composite materials |
| title_full | Micromechanics of composite materials George J. Dvorak |
| title_fullStr | Micromechanics of composite materials George J. Dvorak |
| title_full_unstemmed | Micromechanics of composite materials George J. Dvorak |
| title_short | Micromechanics of composite materials |
| title_sort | micromechanics of composite materials |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028193953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004342211 |
| work_keys_str_mv | AT dvorakgeorgej micromechanicsofcompositematerials |