Unified Strength Theory and Its Aplications

by Yu, Mao-Hong

• ISBN13: 9783540437215
• ISBN10: 3540437215
• Format: Hardcover
• Copyright: 2004-02-20
• Publisher: Springer Nature

Summary

This book provides a new Unified Strength Theory and describes its applications. The Unified Strength Theory is a system of yield and failure criteria of materials under complex stresses. It covers the entire range of convex failure criteria, from lower bound (Tresca yield criteria and Mohr-Coulomb failure criteria) to upper bound (twin-shear failure criteria). It also includes the non-convex yield and non-convex failure criteria. A series of new failure criteria and previous failure and yield criteria can be deduced from the Unified Strength Theory. The work presented in this book is unprecedented in the field of strength theory. It is useful for students in understanding the strength theory, for engineers to correctly use it and for researchers to choose an appropriate failure criteria in studying the strenth of materials and structures. An experimental verification, engineering applications, a detailed historical review and more than 1000 references are provided.

Table of Contents

1 Introduction	1	(10)
1.1 Strength of Materials under Complex Stress States	1	(3)
1.2 Definition of Strength Theory	4	(1)
1.3 Significance and Development of Strength Theory	5	(2)
1.4 Shape of the Limit Surface of Strength Theory	7	(4)
2 Stress States of Elements	11	(18)
2.1 Elements	11	(1)
2.2 Stress at a Point: Stress Invariants	12	(1)
2.3 Stress Deviatoric Tensor, Deviatoric Tensor Invariants	13	(1)
2.4 Stresses on the Oblique Plane	14	(4)
2.4.1 Stresses on the Oblique Plane	14	(1)
2.4.2 Principal Shear Stresses	15	(1)
2.4.3 Octahedral Shear Stress	16	(2)
2.5 Hexahedron, Octahedron, Dodecahedron	18	(2)
2.6 Stress Space	20	(5)
2.6.1 Relationship between (σ1, σ2, σ3) and (x, y, z)	23	(1)
2.6.2 Relationship between (σ1, σ2, σ3) and (ξ, r, theta)or(J2, τm, theta)23	23	(2)
2.7 Stress State Parameters	25	(3)
Summary	28	(1)
3 Unified Yield Criteria	29	(34)
3.1 Introduction	29	(1)
3.2 General Behaviour of the Yield Function	30	(3)
3.3 Yield Surface	33	(1)
3.4 Mechanical Model of the Unified Yield Criterion	34	(2)
3.5 Unified Yield Criterion	36	(2)
3.6 Other Forms of the Unified Yield Criterion	38	(1)
3.7 Special Cases of the Unified Yield Criterion	38	(8)
3.7.1 Single-Shear Yield Criterion (b=0)	38	(2)
3.7.2 New Yield Criterion (b=1/4)	40	(1)
3.7.3 New Yield Criterion (b=1/2)	41	(3)
3.7.4 New Yield Criterion (b=3/4)	44	(1)
3.7.5 Twin-Shear Yield Criterion (b=1)	45	(1)
3.8 Extension of the Unified Yield Criterion	46	(4)
3.9 Nonconvex Yield Criterion (b less than 0 or b>1) 47
3.10 Unified Yield Criterion in the Plane Stress State	50	(3)
3.11 Unified Yield Criterion in the σ - theta Stress State	53	(2)
3.12 Examples	55	(6)
Summary	61	(1)
Problems	61	(2)
4 Verification of the Yield Criterion	63	(16)
4.1 Introduction	63	(1)
4.2 Comparison of the Unified Yield Criterion with the General Behaviour of Yield Criterion	63	(2)
4.3 Comparison of the Unified Yield Criterion with Experimental Data	65	(4)
4.4 Comparison of the Yield Criteria with the Tests of Taylor and Quinney	69	(1)
4.5 Comparison of the Yield Criteria with the Tests of Ivey	70	(1)
4.6 Comparison of the Yield Criteria with the Tests of Winstone	71	(3)
4.7 Comparison of the Yield Criteria with the Experimental Results of Ellyin	74	(3)
Summary	77	(2)
5 Extended Unified Yield Criterion	79	(14)
5.1 Introduction	79	(1)
5.2 Extended Unified Yield Criterion	80	(1)
5.3 Special Cases of the Extended Unified Yield Criterion	81	(5)
5.3.1 Extended Single-Shear Yield Criterion (Extended Tresca Yield Criterion)	81	(1)
5.3.2 New Extended Yield Criterion (b=1/4)	82	(1)
5.3.2 New Extended Yield Criterion (b=1/2, Linear Drucker-Prager Criterion)	83	(1)
5.3.4 New Extended Yield Criterion (b=3/4)	84	(1)
5.3.5 New Extended Yield Criterion (b=1, Extended Twin-Shear Yield Criterion)	85	(1)
5.4 Yield Loci of the Extended Yield Criterion in the Meridian and Deviatoric Planes	86	(3)
5.5 Quadratic Extended Unified Yield Criterion	89	(1)
Summary	90	(1)
Problems	90	(3)
6 Basic Characteristics of Strength of Materials under Complex Stress	93	(36)
6.1 Introduction	93	(1)
6.2 Strength Difference Effect in Tension and Compression (SD effect)	93	(2)
6.3 Effect of Hydrostatic Stress	95	(5)
6.4 Effect of Normal Stress	100	(3)
6.5 Research on the Effect of Intermediate Principal Stress	103	(2)
6.6 Effects of the Intermediate Principal Stress in Metals	105	(3)
6.7 Effects of the Intermediate Principal Stress in Rock	108	(10)
6.8 Characteristics of the Effect of Intermediate Principal Stress in Rock	118	(1)
6.9 Effects of the Intermediate Principal Stress in Concrete	119	(6)
6.10 Engineering Applications of the Effect of Intermediate Principal Stress in Concrete	125	(2)
6.11 Bounds of the Convex Strength Theories	127	(1)
Summary	128	(1)
7 Unified Strength Theory	129	(46)
7.1 Introduction	129	(1)
7.2 General Behaviour of Strength Theory	130	(2)
7.3 Mechanical Model of the Unified Strength Theory	132	(2)
7.4 Unified Strength Theory	134	(3)
7.5 Other Formulations of the Unified Strength Theory	137	(2)
7.5.1 In Terms of Stress Invariant F (I1, J2, theta, σt α)	137	(1)
7.5.2 In Terms of Principal Stress and Cohesive Parameter F (σ 1, σ 2, σ 3, C0, φ)	137	(1)
7.5.3 In Terms of Stress Invariant and Cohesive Parameter F(I1, J2, theta, C0, φ)	138	(1)
7.5.4 In Terms of Principal Stresses and Compressive Strength Parameter F (σ 1, σ 2, σ 3, α, σ c)	138	(1)
7.5.5 In Terms of Stress Invariant and Compressive Strength Parameter F (I1, J2, theta, α, σ c)	139	(1)
7.6 Extension and Supplementation of Conclusions from the Unified Strength Theory	139	(1)
7.7 Special Cases of the Unified Strength Theory	140	(5)
7.7.1 Varying Parameter b	140	(2)
7.7.2 Varying Parameter α	142	(3)
7.8 Nonconvex Strength Theory (b less than 0 or b> 143
7.8.1 Nonconvex Strength Theory (b less than 0) 144
7.8.2 Nonconvex Strength Theory (b>1)	145	(1)
7.8.3 Nonconvex yield criteria for α=1	146	(1)
7.9 Limit Loci of the Unified Strength Theory in the π Plane	146	(59)
7.9.1 Variation of the Unified Strength Theory with b	148	(2)
7.9.2 Limit Locus of the Unified Strength Theory by Varying α	150	(7)
7.10 Limit Surfaces of the Unified Strength Theory in Principal Stress Space	157	(2)
7.11 Limit Loci of the Unified Strength Theory in Plane Stress State	159	(4)
7.11.1 Variation of the Unified Strength Theory with b	160	(2)
7.11.2 Limit Locus of the Unified Strength Theory by Varying α	162	(1)
7.12 Limit Loci of the Unified Strength Theory under σ - τ Combined Stress State	163	(2)
7.13 Unified Strength Theory in the Meridian Plane	165	(2)
7.14 Generalizations of the Unified strength Theory	167	(2)
7.15 Significance of the Unified Strength Theory	169	(2)
Summary	171	(1)
Problems	172	(3)
8 Experimental Verification of Strength Theory	175	(32)
8.1 Introduction	175	(1)
8.2 Equipments for complex stress state experiments	175	(6)
8.2.1 Experimental Equipments for Tension (Compression)-Torsion Stress States	176	(1)
8.2.2 Biaxial Plane Experimental Equipments	176	(1)
8.2.3 Equipment for Axisymmetrical Triaxial Experiments	177	(1)
8.2.4 Equipment for True Triaxial Experiments	178	(3)
8.3 Axial-loading and Torsion Experiments	181	(2)
8.4 Experimental Verification of Strength Theory for Rock	183	(7)
8.5 A Systematic Experiment on Rock under True Triaxial Stress	190	(5)
8.5.1 Strength of Rock under High Pressure	190	(1)
8.5.2 The Effect of Intermediate Principal Stress	191	(1)
8.5.3 The Effect of Stress Angle	192	(1)
8.5.4 Limit Meridian Loci	193	(1)
8.5.5 The Limit Loci on the π-Plane	194	(1)
8.6 Experimental Verification of Strength Theory for Concrete	195	(4)
8.7 Experiments on Clay and Loess under Complex Stress	199	(2)
8.8 Experiments on Sand under Complex Stress	201	(2)
8.9 The Ultimate Dynamic Strength of Sand under Complex Stress	203	(2)
Summary	205	(2)
9 Applications of the Unified Yield Criterion	207	(30)
9.1 Introduction	207	(2)
9.2 Theorems of limit analysis	209	(1)
9.2.1 Lower-Bound Theorem	210	(1)
9.2.2 Upper-Bound Theorem	210	(1)
9.3 Generalized Stresses and Generalized Strains	210	(2)
9.4 Basic Equations of Circular Plates	212	(5)
9.5 Fields of Internal Moments	217	(3)
9.6 Fields of Velocity	220	(4)
9.7 Comparison with Existing Solutions	224	(1)
9.8 Rotating Discs and Rotating Cylinders	225	(1)
9.9 Elastic Limit of Discs	226	(1)
9.10 Elasto-Plastic Analysis of Discs	227	(1)
9.11 Elasto-Plastic Stress Fields of Rotating Discs	228	(2)
9.12 Solution Procedure and Results	230	(4)
9.13 Plastic Limit analysis of Rotating Cylinder	234	(1)
9.14 Application of the Unified Strength Theory	235	(1)
Summary	235	(1)
Problems	236	(1)
10 The Effects of Failure Criteria on Structural Analysis	237	(56)
10.1 Introduction	237	(3)
10.2 Bounds and the Region of the Convex Limit Surface	240	(1)
10.3 Nonconvex Limit Loci	240	(1)
10.4 Effect of Failure Criteria on Thin-Walled Pressure Vessel Design	241	(3)
10.5 Limit Pressure of Thick-Walled Hollow Spheres	244	(6)
10.5.1 Elastic Limit Pressure of Thick-Walled Spherical Shell	246	(2)
10.5.2 Plastic Limit Pressure of Thick-Walled Spherical Shell	248	(2)
10.6 Effects of Failure Criteria on the Elastic Limit Pressure of Thick-Walled Cylinders	250	(8)
10.7 Effects of Failure Criteria on the Plastic Limit Pressure of Thick-Walled Cylinder	258	(7)
10.7.1 Stress Distribution	258	(1)
10.7.2 Plastic Zone in the Elasto-Plastic Range	259	(1)
10.7.3 Plastic Zone Radius in the Elasto-Plastic Range	260	(1)
10.7.4 Plastic Limit Pressure	261	(4)
10.8 Effects of Failure Criteria on the Shape and Size of the Crack Tip Plastic Zone	265	(6)
10.8.1 Mode I Crack in Plane Stress State	266	(2)
10.8.2 Mode I Crack in Plane Strain	268	(1)
10.8.3 Mode II Crack in Plane Stress	269	(1)
10.8.4 Mode II Crack in Plane Strain State	270	(1)
10.9 Effects of Failure Criteria on FEM Analysis	271	(17)
10.9.1 Effects of Failure Criteria on FEM Analysis for Limit Bearing Capacity of Plates	272	(1)
10.9.2 Effects of Failure Criteria on FEM Analysis of Plastic Zones for Thick-Walled Cylinders	273	(2)
10.9.3 Effects of Failure Criterion on FEM Analysis for a Strip with a Hole	275	(1)
10.9.4 Effects of Failure Criterion on FEM Analysis of Plastic Zone for Circular Cave	276	(3)
10.9.5 Effects of Failure Criterion on Mesomechanical Analysis of Failure Criterion	279	(2)
10.9.6 Effects of Failure Criteria on FEM Analysis of Composites	281	(3)
10.9.7 Effects of Failure Criteria on FEM Analysis for Underground Caves	284	(4)
Summary	288	(1)
Problems	289	(4)
11 Historical Reviews	293	(60)
11.1 Introduction	293	(1)
11.2 Strength Theories before the Twentieth Century	293	(8)
11.2.1 Early Work	293	(4)
11.2.2 Strength Theories before the Twentieth Century	297	(2)
11.2.3 Strength Theories at the Begining of the Twentieth Century	299	(2)
11.3 Three Series of Strength Theories	301	(14)
11.3.1 Single-Shear Strength Theory (SSS theory)	302	(3)
11.3.2 Octahedral-Shear Strength Theory (OSS Theory)	305	(7)
11.3.3 Twin-Shear Strength Theory (TSS theory)	312	(3)
11.4 Establishment of the Unified Yield Criteria	315	(4)
11.4.1 Curved General Yield Criteria	315	(2)
11.4.2 Linear Unified Yield Criterion	317	(2)
11.5 Failure Criteria of Rock, Concrete, Soil, Iron, Polymer and Other Materials	319	(14)
11.5.1 Failure Criteria for Rock	320	(2)
11.5.2 Failure Criteria for Concrete	322	(1)
11.5.3 Failure Criteria for Soil	323	(2)
11.5.4 Failure Criteria for Iron	325	(1)
11.5.5 Failure Criteria of Ice	325	(1)
11.5.6 Failure Criteria for Wood	326	(1)
11.5.7 Failure Criteria for Polymers	326	(2)
11.5.8 Failure Criteria of Energetic Materials (TNT, RDX and Solid Rocket Propellant)	328	(1)
11.5.9 Failure Criteria for Ceramic and Glass	328	(1)
11.5.10 Failure Criteria of Other Materials	329	(4)
11.6 Unified Strength Theory	333	(11)
11.6.1 Octahedral-Shear Generalized Strength Theory	334	(1)
11.6.2 Unified Strength Theory (Yu and He 1991)	335	(2)
11.6.3 Special Cases of the Unified Strength Theory	337	(3)
11.6.4 Comparison and Choice	340	(1)
11.6.5 Application of the Unified Strength Theory	341	(1)
11.6.6 Nonconvex Strength Theory	342	(2)
11.7 Computational Implementation of the Strength Theory	344	(4)
Summary	348	(3)
Problems	351	(2)
12 References and Bibliography	353	(54)
12.1 Early Works (before 1900)	353	(1)
12.2 Works from 1901 to 1950	354	(4)
12.3 Works from 1951 to 1960	358	(5)
12.4 Works from 1961 to 1970	363	(7)
12.5 Works from 1971 to 1980	370	(9)
12.6 Works from 1981 to 1990	379	(9)
12.7 Works from 1991 to 2000	388	(14)
12.8 Works from 2001 to 2002	402	(5)
Author Index	407	(4)
Subject Index	411