A model is discussed for the analysis of long part-through surface cracks in the walls of plate or shell structures. Such problems are formulated within the context of two dimensional plate and shell theory with the part-cracked section represented as a line-spring in the middle surface. The spring allows relative separations and rotations of the middle surface, and constitutive laws relating these discontinuities to the prevailing force and moment per unit length at any point are taken from the plane strain solution for a strip in combined tension and bending, which contains an edge crack of a corresponding depth. Prior work is reviewed and further line spring constitutive laws are discussed as appropriate to elastic analysis with thermal or residual stresses and to elastic-plastic analysis, with yielding in the ligament between the crack front and far wall in the latter case.
Consumption of fruits and vegetables, particularly green leafy vegetables and vitamin C-rich fruits and vegetables, appears to have a protective effect against coronary heart disease.
Singular stress and strain fields are found at the tip of a crack growing steadily and quasi-statically into an elastic-plastic strain-hardening material. The material is characterized byJ 2 flow theory together with a bilinear effective stress-strain curve. The cases of anti-plane shear, plane stress and plane strain are each considered. Numerical results are given for the order of the singularity, details of the stress and strain-rate fields, and the near-tip regions of plastic loading and elastic unloading.
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This chapter examines areas of fracture mechanics that are being developed through computational stress analysis methods. Research of fracture mechanics is focused in two principal directions: (1) the development of phenomenological explanations of crack extension behaviors and (2) the description of micromechanical processes of material separation on a microscale. When the crack extension behavior of interest is accompanied by a small crack-tip plastic zone, the correlation is in terms of the elastic stress-intensity factor. Several numerical methods have been developed for this, including boundary collocation, numerical solution of integral equations, and finite elements. The boundary collocation method automatically satisfies traction-free boundary conditions on the crack surfaces. Another general method that has been used to obtain solutions for cracks is that of approximate conformal mapping, that may be applied to cracks emanating from holes in infinite bodies or to cracks at the edges in simply connected bodies. The technique involves finding accurate polynomial approximations to the mapping function that transforms the physical cracked domain into a circular region.
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Recent work (Rice, 1985a) has presented the calculations of the first order variation in an elastic displacement field associated with arbitrary incremental planar advance of the location of the front of a half-plane crack in a loaded elastic full space. That work also indicated the relation of such calculations to a three-dimensional weight function theory for crack analysis and derived an expression for the distribution of the tensile mode stress intensity factor along a slightly curved crack front, to first order accuracy in the deviation of the crack front location from a reference straight line. Here we extend the results on stress intensity factors to the shear modes, solving to similar first order accuracy for the in-plane (Mode 2) and antiplane (Mode 3) shear stress intensity factors along a slightly curved crack front. Implications of results for the configurational stability of a straight crack front are discussed. It is also shown that the concept of line tension, while qualitatively useful in characterizing the crack extension force (energy release rate) distribution exerted on a tough heterogeneity along a fracture path as the crack front begins to curve around it, does not agree with the exact first order effect that is derived here.
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Magnetic levitation (MagLev) enables rapid and non-destructive quality control of plastic parts. The feasibility of MagLev as a method to: i) rapidly assess injection-molded plastic parts for defects during process optimization, ii) monitor the degradation of plastics after exposure to harsh environmental conditions, and iii) detect counterfeit polymers by density is demonstrated.
