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THE FOUNDATIONS OF THERMOELASTICITY-EXPERIMENTS AND THEORY (A. PHILLIPS) 1. Introduction 2. The initial yield surface 4 3. The subsequent yield surface 6 4. Some theoretical consequences 10 References 13 ON THE PHYSICS AND MATHEMATICS OF SELF-STRESSES (E. KRONER) 1. Introduction 22 2. The physical origin of the self-stresses 23 3. Formulation of the mathematical problem of self-stresses 27 4. The method of modified Green's functions 30 5. Concluding remarks 35 References 38 DISTORTION IN MICROPOLAR ELASTICITY (W. NOWACKI) 1. Fundamental relations and equations 39 2. Principle of virtual work 42 3. Theorem of minimum of the complimentary work 43 • 4. Reciprocity theorem 44 5. Equations in displacements and rotations 47 6. Compatibility equations 51 References 57 THE YIELD CRITERION IN THE GENERAL CASE OF NONHOMOGENEOUS STRESS AND DEFORMATION FIELDS (J. A. KONIG and W. OLSZAK) 1. Introduction 58 2. The plasticity condition 61 3. Special cases of the yield condition 62 4. Example: Pure bending 63 5. Criteria for neutral, passive and active processes 65 VI 6. The flow law 67 References 69 ELECTRO-MAGNETO-ELASTICITY (J. B. ALBLAS) 1. Introduction 71 2. Balance equations 77 3. The jump and boundary conditions 85 4. The constitutive equations 91 5. Linearization of the magnetic problem 95 6. Magneto-elastic waves in the infinite space and in the half-space 105 References 114 PLASTICITY AND CREEP THEORY IN ENGINEERING MECHANICS (J. F • BESSE LING) 1. Introduction 115 2. Limit analysis 117 3.

It is weH known that the traditional failure criteria cannot adequately explain failures which occur at a nominal stress level considerably lower than the ultimate strength of the material. The current procedure for predicting the safe loads or safe useful life of a structural member has been evolved around the discipline oflinear fracture mechanics. This approach introduces the concept of a crack extension force which can be used to rank materials in some order of fracture resistance. The idea is to determine the largest crack that a material will tolerate without failure. Laboratory methods for characterizing the fracture toughness of many engineering materials are now available. While these test data are useful for providing some rough guidance in the choice of materials, it is not clear how they could be used in the design of a structure. The understanding of the relationship between laboratory tests and fracture design of structures is, to say the least, deficient. Fracture mechanics is presently at astandstill until the basic problems of scaling from laboratory models to fuH size structures and mixed mode crack propagation are resolved. The answers to these questions require some basic understanding ofthe theory and will not be found by testing more specimens. The current theory of fracture is inadequate for many reasons. First of aH it can only treat idealized problems where the applied load must be directed normal to the crack plane.

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The Army Materials and Mechanics Research Center has conducted the Saga­ more Army Materials Research Conferences, in cooperation with the Metallurgi­ cal Research Laboratories of the Department of Chemical Engineering and Metallurgy of Syracuse University, since 1954. The purpose of the conferences has been to gather together scientists and engineers from academic institutions, industry, and government who are uniquely qualified to explore in depth a sub­ ject of importance to the Army, the Department of Defense and the scientific community. Grain size and its control is a major factor governing the behavior of materi­ als. Knowledge that one can obtain grain sizes in the 10 micron down to sub­ micron range has established the basis for a new technology. This volume, Ultrafine-Grain Ceramics, addresses itself to the broad areas of: realization of fine-grain ceramics; preparation of ultrafine particle size materials; characterization of ultrafine particles and ultrafine-grain ceramics; processing and behavior of ultra fine-grain ceramics. The technical advice provided by Dr. S. K. Dutta of the Army Materials and Mechanics Research Center during the editing of this book is acknowledged. The continued active interest and support of these conferences by Dr. E. Scala, Director, Lt. Col. Joseph B. Mason, Commanding Officer, and J. F. Sullivan, Deputy Technical Director, of the Army Materials and Mechanics Re­ search Center is appreciated.

The librational motion of a satellite depends on the gravity gradient, aerodynamic, and mag- netic torques, on the moments of inertia of the satel- lite and on some less significant influences as solar radiation, the electrical field of the earth, the me- teorite impacts. Only the gravity gradient torque can be considered with a great degree of accuracy as dete£ ministic. Aerodynamic and magnetic torques can be treated as deterministic quantities only in a very rough first approximation. In reality these torques always have stochastic components caused by the fluc- tuations of the atmospheric density and the earth's magnetic field.

Historically, a major problem for the study of the large deformation of crystalline solids has been the apparent lack of unity in experimentally determined stress-strain functions. The writer's discovery in 1949 of the unexpectedly high velocity of incremental loading waves in pre-stressed large deformation fields emphasized to him the pressing need for the independent, systematic experimental study of the subject, to provide a firm foundation upon which physically plausible theories for the finite deformation of crystalline solids could be constructed. Such a study undertaken by the writer at that time and continued uninterruptedly to the present, led in 1956 to the development of the diffraction grating experiment which permitted, for the first time, the optically accurate determination of the strain-time detail of non-linear finite amplitude wave fronts propagating into crystalline solids whose prior history was precisely known. These experimental diffraction grating studies during the past decade have led to the discovery that the uniaxial stress-strain functions of 27 crystalline solids are unified in a single, generalized stress-strain function which is described, much of it hitherto unpublished, in the present monograph. The detailed study of over 2,000 polycrystal and single crystal uni­ axial stress experiments in 27 crystalline solids, in terms of the variation of a large number of pertinent parameters, has provided new unified pat­ terns of understanding which, it is hoped, will be of interest and value to theorists and experimentalists alike.