A fatigue crack closure model is developed that includes interactions between the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out-of plane cracking and multi-axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two-dimensional sawtooths, whose geometry induces mixed-mode crack- tip stresses. Continuum mechanics and crack-tip dislocation concepts are combined to relate crack face displacements to crack-tip loads. Geometric criteria are used to determine closure loads from crack-face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs. Newman, John A. and Riddell, William T. and Piascik, Robert S. Langley Research Center NASA/TM-2003-212402, L-18279, NAS 1.15:212402, ARL-TR-2959

Covering the whole of Asia and the Pacific region, this text provides both an analytic overview and specific data for each of the 60 countries. Introductory chapters cover regional issues, including: a regional review with the year's trends, developments and key events' analysis of the threat of terrorism in the region; the effects of deflation on the economy; the water crisis and its impact on the poor; and the successes and failures of micro-credit in the region.

This book contains the fully peer-reviewed papers presented at the Third Engineering Foundation Conference on Small Fatigue Cracks, held under the chairmanship of K.S. Ravichandran and Y. Murakami during December 6-11, 1998, at the Turtle Bay Hilton, Oahu, Hawaii. This book presents a state-of-the-art description of the mechanics, mechanisms and applications of small fatigue cracks by most of the world's leading experts in this field. Topics ranging from the mechanisms of crack initiation, small crack behavior in metallic, intermetallic, ceramic and composite materials, experimental measurement, mechanistic and theoretical models, to the role of small cracks in fretting fatigue and the application of small crack results to the aging aircraft and high-cycle fatigue problems, are covered.

An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.