Kolupaev Equivalent Stress Concept for Limit State Analysis

1. Auflage 2018
ISBN: 978-3-319-73049-3
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 86, 374 Seiten

Reihe: Advanced Structured Materials

This book discusses arbitrary multiaxial stress states using the concept of equivalent stress. It highlights the most useful criteria, which can be applied to various classes of isotropic materials. Due to its simplicity and clarity, this concept is now widely used in component design, and many strength and yield criteria based on the equivalent stress concept have been formulated. Choosing the appropriate criterion for a given material remains the main challenge in applications.  The most useful criteria can be applied best when the plausibility assumptions are known. Accordingly, the book introduces fitting methods based on mathematical, physical, and geometrical objective functions. It also features a wealth of examples that demonstrate the application of different approaches in modeling certain limit behaviors.

Autoren/Hrsg.

Kolupaev, Vladimir A.

Inhaltsverzeichnis

1;Acknowledgements;7
2;Contents;8
3;Abbreviations;13
4;Abstract;15
5;1 Introduction;16
5.1;1.1 Need of Criteria;16
5.2;1.2 Equivalent Stress Concept;17
5.3;1.3 Invariants of Stress Tensor;18
5.4;1.4 Lode Parameter;20
5.5;1.5 Formulation of Criteria;21
5.6;1.6 Methodology;22
5.7;References;23
6;2 Criteria of Equivalent Stress Concept;27
6.1;2.1 Zero-Parameter Criteria;27
6.1.1;2.1.1 Rankine;27
6.1.2;2.1.2 Tresca;29
6.1.3;2.1.3 Maxwell, Huber--von Mises--Hencky;30
6.1.4;2.1.4 Mariotte;32
6.1.5;2.1.5 Schmidt--Ishlinsky, Burzy?ski;32
6.1.6;2.1.6 Ivlev;33
6.1.7;2.1.7 Ko;34
6.1.8;2.1.8 Sokolovsky and Ishlinsky--Ivlev;34
6.1.9;2.1.9 Conclusion;35
6.2;2.2 One-Parameter Criteria;36
6.2.1;2.2.1 Mariotte-St. Venant;36
6.2.2;2.2.2 Beltrami;38
6.2.3;2.2.3 Mohr-Coulomb;40
6.2.4;2.2.4 Sandel;41
6.2.5;2.2.5 Burzy?ski--Torre, Balandin;42
6.2.6;2.2.6 Drucker;43
6.2.7;2.2.7 Drucker--Prager, Mirolyubov;45
6.2.8;2.2.8 Sayir;46
6.2.9;2.2.9 Haythornthwaite, Candland;47
6.2.10;2.2.10 Sdobyrev, Pisarenko--Lebedev;49
6.2.11;2.2.11 Capurso;50
6.2.12;2.2.12 Freudenthal--Gou, Cazacu--Barlat;51
6.2.13;2.2.13 Spitzig;52
6.2.14;2.2.14 Edelman--Drucker;53
6.2.15;2.2.15 Maitra, Iyer;54
6.2.16;2.2.16 Dodd--Naruse;55
6.2.17;2.2.17 Hoek--Brown;56
6.2.18;2.2.18 Kolupaev;56
6.3;2.3 Two-Parameter Criteria;57
6.3.1;2.3.1 Burzy?ski--Yagn;57
6.3.2;2.3.2 Schleicher;59
6.3.3;2.3.3 Leckie--Hayhurst;60
6.3.4;2.3.4 Podgórski, Bigoni--Piccolroaz;61
6.3.5;2.3.5 Yu;64
6.4;2.4 Criteria with More Than Two Parameters;65
6.4.1;2.4.1 Birger;66
6.4.2;2.4.2 Altenbach--Zolochevsky;66
6.4.3;2.4.3 Altenbach--Bolchoun--Kolupaev;68
6.5;2.5 Obvious Systematization;69
6.6;References;70
7;3 Visualization Methods;81
7.1;3.1 Spatial Representation of the Limit Surface;81
7.2;3.2 ?-Plane;86
7.3;3.3 Burzy?ski-Plane;88
7.4;3.4 Diagram ?I-?II;91
7.5;3.5 Diagram ?11-?12;93
7.6;3.6 Assessment of the Loading Points;94
7.7;References;100
8;4 Formulations of Classical Strength Hypotheses;103
8.1;4.1 Normal Stress Hypothesis;103
8.2;4.2 Tresca Hypothesis;106
8.3;4.3 vonMises Hypothesis;108
8.4;4.4 Schmidt--Ishlinsky Hypothesis;108
8.5;4.5 Remarks About Graphical Forms;111
8.6;References;112
9;5 Dimensionless Values for Comparison;114
9.1;5.1 Basic Stress States;114
9.2;5.2 ?-Plane Values;124
9.3;5.3 Elastic Poisson's Ratio;125
9.4;5.4 Inelastic Poisson's Ratio;126
9.5;References;132
10;6 Visualization of Standard Criteria;136
10.1;6.1 Strain Criterion;136
10.2;6.2 Burzy?ski--Yagn Criterion;139
10.3;6.3 Linear Combinations of the Classical Hypotheses;141
10.3.1;6.3.1 Mohr--Coulomb Criterion;141
10.3.2;6.3.2 Sdobyrev, Pisarenko--Lebedev Criterion;144
10.4;6.4 Comparison of Standard Criteria;146
10.5;6.5 Discussion of Standard Criteria;146
10.6;References;149
11;7 Alternative Formulations of Standard Criteria;152
11.1;7.1 Hoek--Brown Criterion;152
11.2;7.2 Modifications of the Pisarenko--Lebedev Criterion;153
11.2.1;7.2.1 Pisarenko--Lebedev Criteria of Higher Power;153
11.2.2;7.2.2 Reduced Cubic Criterion;154
11.2.3;7.2.3 Leckie--Hayhurst Criterion;155
11.2.4;7.2.4 Sayir's Cone;158
11.3;7.3 Modification of Twin-Shear Theory;159
11.4;7.4 Simple Generalizations;160
11.5;7.5 Discussion;161
11.6;References;162
12;8 Conditions and Assumptions of Strength Criteria;163
12.1;8.1 Remarks Concerning the State of the Art of Research;163
12.1.1;8.1.1 Need of a Generalized Criterion;164
12.1.2;8.1.2 Applicability of the Criteria;165
12.2;8.2 Formulation of Conditions;166
12.2.1;8.2.1 Necessary Conditions;166
12.2.2;8.2.2 Plausibility Assumptions;166
12.3;References;167
13;9 Generalized Pressure-Insensitive Criteria;171
13.1;9.1 Yield Criteria of Trigonal Symmetry;172
13.1.1;9.1.1 Sayir Criterion;172
13.1.2;9.1.2 Capurso Criterion;173
13.1.3;9.1.3 Haythornthwaite Criterion;176
13.1.4;9.1.4 Podgórski, Bigoni–Piccolroaz Criterion;178
13.1.5;9.1.5 Modified Altenbach–Zolochevsky Criterion;178
13.1.6;9.1.6 Capurso–Haythornthwaite Linear Combination;181
13.1.7;9.1.7 Capurso–Haythornthwaite Multiplicative Ansatz;182
13.1.8;9.1.8 Radcig Criterion;183
13.1.9;9.1.9 Cosine Ansatz of Altenbach–Bolchoun–Kolupaev;184
13.1.10;9.1.10 Tri-quadratic Criterion;186
13.2;9.2 Yield Criteria of Hexagonal Symmetry;187
13.2.1;9.2.1 Unified Yield Criterion of Yu;188
13.2.2;9.2.2 Bi-cubic Criterion;191
13.2.3;9.2.3 Multiplicative Ansatz Criterion;191
13.2.4;9.2.4 Generalized Criterion of Hexagonal Symmetry;193
13.2.5;9.2.5 Cosine Ansatz of Even Powers;194
13.2.6;9.2.6 Criteria of the Stress Power n=12;194
13.3;9.3 Smooth and Polyhedral Criteria;195
13.4;9.4 Non-convex Yield Criteria in the ?-Plane;198
13.5;9.5 Conclusion;200
13.6;References;202
14;10 Generalized Pressure-Sensitive Criteria;206
14.1;10.1 Extension of Yield Criteria;206
14.2;10.2 Conical and Pyramidal Criteria;211
14.3;10.3 Unified Strength Theory of Yu;215
14.4;10.4 Criteria Recommended for Applications;219
14.4.1;10.4.1 Modified Theory of Yu;219
14.4.2;10.4.2 Rotationally Symmetric Criteria;221
14.4.3;10.4.3 Geometrical-Mechanical Criterion;224
14.4.4;10.4.4 Capurso--Haythornthwaite Generalization;225
14.5;10.5 Criterion Normalized on Uniaxial Compressive Stress;226
14.6;10.6 Conclusion;228
14.7;References;230
15;11 Multi-surface Criteria;233
15.1;11.1 Motivation;233
15.2;11.2 Systematization of Multi-surface Criteria;234
15.3;11.3 Criteria with C0-Transition;236
15.3.1;11.3.1 Davidenkov--Fridman Criterion;240
15.3.2;11.3.2 Modifications of the Normal Stress Hypothesis;240
15.3.3;11.3.3 Modifications of the Strain Criterion;245
15.4;11.4 Criteria with C1-Transition;246
15.4.1;11.4.1 Ad hoc Approach According to Berg;246
15.4.2;11.4.2 Huber Criterion;247
15.4.3;11.4.3 Kuhn Criterion;249
15.4.4;11.4.4 Modified Criterion of Huber;250
15.4.5;11.4.5 Combined Geometrical-Mechanical Criterion;252
15.4.6;11.4.6 Sikora Criterion;254
15.4.7;11.4.7 C1-Continuous Surface Varying in the ?-Plane;256
15.5;11.5 Conclusion;261
15.6;References;263
16;12 Fitting of Criteria;267
16.1;12.1 Mathematical Objective Functions;267
16.2;12.2 Physical Objective Functions;268
16.3;12.3 Geometry-Motivated Choice of Solution;271
16.4;12.4 Requirements on the Parameters of the Criterion;272
16.5;12.5 Fitting Features;275
16.6;References;278
17;13 Experiments and Equipment;280
17.1;13.1 Discussion of the Necessary Tests;280
17.2;13.2 Tests on Hard Foams;282
17.2.1;13.2.1 Specimen Preparation and Density Determination;283
17.2.2;13.2.2 Tubular Specimen;284
17.2.3;13.2.3 Tension, Compression, and Torsion Tests;287
17.2.4;13.2.4 Internal and External Pressure Tests;290
17.2.5;13.2.5 Enlacement Test;294
17.2.6;13.2.6 Biaxial Tensile Test;299
17.2.7;13.2.7 Hydrostatic Compression Test;304
17.2.8;13.2.8 Hydrostatic Tensile Test;308
17.3;13.3 Definition of Failure;313
17.4;References;317
18;14 Applications;322
18.1;14.1 Measured Data by Naghdi for Aluminum Alloy;322
18.2;14.2 Measured Data by Dillenberger for Polyamide;325
18.3;14.3 Measured Data by Münch for the Hard Foam EPP;328
18.3.1;14.3.1 Rotationally Symmetric Criteria;328
18.3.2;14.3.2 Geometrical-Mechanical Criterion;335
18.4;14.4 Measured Data by DeRuntz for Syntactic Foam;336
18.4.1;14.4.1 Geometrical-Mechanical Criterion;338
18.4.2;14.4.2 C1-Combined Criterion;340
18.5;14.5 Measurements on Polymethacrylimide Foam;341
18.5.1;14.5.1 Experimental Results;341
18.5.2;14.5.2 Evaluation of Measurements on PMI Foams;341
18.6;14.6 Measured Data by Tasuji for Concrete;355
18.7;References;363
19;15 Summary and Outlook;366
19.1;15.1 Summary;366
19.2;15.2 Outlook;371
19.3;References;372