A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

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Surface deformation due to shear and tensile faults in a half-space

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

Chapter 1. Introduction Chapter 2. Stress and Strain: Important Relationships Chapter 3. The Behavior of Bodies Under Stress Chapter 4. Principles and Analytical Methods Chapter 5. Numerical Methods Chapter 6. Experimental Methods Chapter 7. Tension, Compression, Shear, and Combined Stress Chapter 8. Beams Flexure of Straight Bars Chapter 9. Curved Beams Chapter 10. Torsion Chapter 11. Flat Plates Chapter 12. Columns and Other Compression Members Chapter 13. Shells of Revolution Pressure Vessels Pipes Chapter 14. Bodies under Direct Bearing and Shear Stress Chapter 15. Elastic Stability Chapter 16. Dynamic and Temperature Stresses Chapter 17. Stress Concentration Chapter 18. Fatigue and Fracture Chapter 19. Stresses in Fasteners and Joints Chapter 20. Composite Materials Chapter 21. Solid Biomechanics Appendix A. Properties of a Plane Area Appendix B. Mathematical Formulas and Matrices Appendix C. Glossary Index

Roark's Formulas for Stress and Strain

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from in­itial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical in­clusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through com­plete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry

A Continuum Model for Void Nucleation by Inclusion Debonding

Discussion: ``Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading'' (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460-466)

Exact elasticity solutions are used to discuss the interaction between a circular inclusion and an edge dislocation in the matrix. The force on the dislocation is given, and it is shown that for certain combinations of material constants, the dislocation has a stable equilibrium position in the matrix near the interface. Moreover, the interaction is very much affected by the orientation of the Burgers vector with respect to the inclusion. The results also exhibit a strong dependency on the difference between the Poisson's ratios of the matrix and the inclusion.

Interaction between an edge dislocation and a circular inclusion

When a composite body consisting of two isotropic and elastic phases is subjected to prescribed surface tractions, generally the stress field depends on three parameters involving the elastic con stants. If the composite is in a state of plane deformation, and there are no net forces on internal boundaries, however, the stress depends on only two combinations of elastic constants. Convenient constants for the composite material are proposed.

Effect of Elastic Constants on Stress In A Composite Under Plane Deformation

The solution for an angular dislocation allows one to construct the fields for any polygonal loop by superposition. The paper presents the displacements induced by the angular dislocation in an elastic half space. In view of potential applications in geophysics, particular attention is paid to the elastic fields at the free surface. The surface data are seen to exhibit a very simple dependence on the elastic constants.

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John Dundurs

Papers

Discussion: ``Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading'' (Bogy, D. B., 1968, ASME J. Appl. Mech., 35, pp. 460-466)

Interaction between an edge dislocation and a circular inclusion

Effect of Elastic Constants on Stress In A Composite Under Plane Deformation

The angular dislocation in a half space

Problems involving a receding contact between a layer and a half space