Cohesive Traction-Separation Laws for Tearing of Ductile Metal Plates

The failure process ahead of a mode I crack advancing in a ductile thin metal plate or sheet produces plastic dissipation through a sequence of deformation steps that include necking well ahead of the crack tip and shear localization followed by a slant fracture in the necked region somewhat closer to the tip. The objective of this paper is to analyze this sequential process to characterize the traction–separation behavior and the associated effective cohesive fracture energy of the entire failure process. The emphasis is on what is often described as plane stress behavior taking place after the crack tip has advanced a distance of one or two plate thicknesses. Traction–separation laws are an essential component of finite element methods currently under development for analyzing fracture of large scale plate or shell structures. The present study resolves the sequence of failure details using the Gurson constitutive law based on the micromechanics of the ductile fracture process, including a recent extension that accounts for damage growth in shear. The fracture process in front of an advancing crack, subject to overall mode I loading, is approximated by a 2D plane strain finite element model, which allows for an intensive study of the parameters influencing local necking, shear localization and the final slant failure. The deformation history relevant to a cohesive zone for a large scale model is identified and the traction–separation relation is determined, including the dissipated energy. For ductile structural materials, the dissipation generated during necking prior to the onset of shear localization is the dominant contribution; it scales with the plate thickness and is mesh-independent in the present numerical model. The energy associated with the shear localization and fracture is secondary; it scales with the width of the shear band, and inherits the finite element mesh dependency of the Gurson model. The cohesive traction–separation laws have been characterized for various material conditions.Engineering and Applied Science

Summary of the Workshop on Ecological Effects of Hydrocarbon Spills in Alaska

In any study of the effects of the introduction of an organic compound, such as oil, into a particular environment, such as the Arctic we should, at the outset separate two basic responses: the responses of those organisms (largely bacteria and fungi) to whom the oil is a nutrient to be attacked and eventually decomposed, from the responses of those organisms (largely plants and animals) to whom the oil is a physical and chemical agent of potential toxicity to be tolerated with varying degrees of success. ... both groups really function as mixed populations that exhibit dynamic responses to environmental changes, such as oil spills, but our perception of the effects of these changes is largely population-oriented in the decomposers and species-oriented among higher organisms. ... The actual removal of oil from the Arctic environment depends on a combination of physical weathering and microbial decomposition .... Thus a general principle of microbial ecology is sustained here in that the addition of an organic material to a system stimulates the development of a specific microbial population capable of using that material as a nutrient. The rate of this decomposition process is of maximum importance and it obviously depends on the robustness of the initial microbial population and on nutrient limitation. ... One of the special problems of the Arctic is the very slow rate at which these decomposer populations develop significant activities ... and accessory nutrient supplementations may be required to achieve acceptable rates of hydrocarbon decomposition. A very important facet of oil degradation is the relative rates at which the different components of oil are broken down by bacteria and fungi. ... There are many reasons why oil may be toxic to animals .... Oil appears to constitute a fairly general "contact herbicide" whose direct application is most often toxic to plants. ... plants vary in their sensitivity to this "contact herbicide" and sensitivity mapping ... and bioassays of the sensitivity of specific plants under field conditions are very valuable. ... oil exerts direct and immediate toxic effects on certain plants and animals, in both aquatic and terrestrial systems, and ... more subtle toxic effects are often detected only with the passage of time. Whole populations react in the expected manner in that oil-resistant forms proliferate and then lead the recolonization of the system as the toxic hydrocarbons are removed by weathering or by microbial decomposition. The extent of severe ecological damage from oil spills is, therefore, a function both of the oil-sensitivity of the plant and animal populations and of the rates at which oil is removed by human intervention, weathering or microbial decomposition. ... In the decomposition studies perhaps the most promising development is the advent of rate studies which should be extended to cover the major classes of oil constituents and a very wide variety of ecological systems. ... In many cases it is clear that microbial decomposition, aided by fertilizer application ... will reduce the level of hydrocarbons below the toxic level for the indigenous plants and animals at a satisfactory rate. ... This entire program, with its emphasis on rates of microbial decomposition and on differential sensitivity of both species and populations of higher organisms, is basically well designed and offers a scientific basis for the development ... [of] rational oil spill clean-up policies in the sensitive Alaskan ecosystem

Identification and Correction of the Skew Sextupole Error in the AGS

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The analytic solution of near-tip stress fields for perfectly plastic pressure-sensitive material under plane stress condition

Different from dense metals, many engineering materials exhibit pressure-sensitive yielding and plastic volumetric deformation. Adopting a yield criterion that contains a linear combination of the Mises stress and the hydrostatic stress, the analytic solutions of plane-stress mode I perfectly-plastic near-tip stress fields for pressuresensitive materials are derived. Also, the relevant characteristic fields are presented. This perfectly plastic solution, containing a pressure sensitivity parameter μ, is shown to correspond to the limit of low-hardening solutions, and when μ=0 it reduces to the perfectly plastic solution of near-tip fields for the Mises material given by Hutchinson [1]. The effects of material pressure sensitivity on the near-tip fields are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42771/1/10704_2004_Article_BF00034180.pd