Crack Propagation

The assessment of crack initiation and/or propagation has been the subject of many past discussions on fracture mechanics. Depending on how the chosen failure criterion is combined with the solution of a particular theory of continuum mechanics, the outcome could vary over a wide range. Mod elling of the material damage process could be elusive if the scale level of observation is left undefined. The specification of physical dimension alone is not sufficient because time and temperature also play an intimate role. It is only when the latter two variables are fixed that failure predictions can be simplified. The sudden fracture of material with a pre-existing crack is a case in point. Barring changes in the local temperature,* the energy released to create a unit surface area of an existing crack can be obtained by considering the change in elastic energy of the system before and after crack extension. Such a quantity has been referred to as the critical energy release rate, G e, or stress intensity factor, K Ie. Other parameters, such as the crack opening displacement (COD), path-independent J-integral, etc. , have been proposed; their relation to the fracture process is also based on the energy release concept. These one-parameter approaches, however, are unable simultaneously to account for the failure process of crack initiation, propagation and onset of rapid fracture. A review on the use of G, K I, COD, J, etc. , has been made by Sih [1,2].

This is not just another book on fracture mechanics. In recent years, there have been many books published on this subject in an attempt to assess the state of the art and its applications. The majority of the work dealt with energy release rate or critical stress intensity factor and is applicable only to fracture toughness testing. The main reason for this restriction is that the energy release concept cannot easily be extended to mixed mode fracture that occurs in practice as the rule rather than the exception. Cracks will normally curve or turn because the direction of loading can change as a function of time. Their directions of growth cannot be assumed as an a priori and must be determined from a pre-assumed criterion. Analysts are still perplexed with selecting an appropriate fracture criterion because it requires much discernment and judgement. Criteria which often appeared valid for idealized situations are quickly dis credited when encountering more complex physical phenomena. Moreover, the claim of generality cannot be justified on the basis of agreement between theory and experiment for a few simple examples.

Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.

This comprehensive overview of the whole field of fatigue and fracture of metallic materials covers both the theoretical background and some of the latest experimental techniques. It provides a summary of the complex interactions between material microstructure and cracks, classifying them with respect to the overall damage process with a focus on microstructurally short cracks and dynamic embrittlement. It furthermore introduces new concepts for the numerical treatment of fatigue microcrack propagation and their implementation in fatigue-life prediction models.This comprehensive overview of the whole field of fatigue and fracture of metallic materials covers both the theoretical background and the latest experimental techniques. It provides a summary of the complex interactions between material microstructure and cracks, classifying them with respect to the overall damage process. It furthermore introduces new concepts for the numerical treatment of fatigue microcrack propagation and their implementation in fatigue-life prediction models.

Stochastic Crack Propagation: Essential Practical Aspects describes a feature important to the analysis of stochastic crack propagation, starting with essential background theory. Processes, or phenomena, which are of practical importance in the work of design engineers or R&D teams are described chapter by chapter. Many examples are described and supported by listed references, and files of data that can be used with specialist software to practice design situations are included. Advice on how to use various computer programs to design and predict for stochastic crack growth is also provided, giving professionals a complete guide. Presents instructions and exercises in the ideal format for professionals, focusing on applications Explains a methodology on how to optimize the engineering design process by including stochastic crack growth behavior Provides computational files to help readers get up-to-speed with design using programs like ANSYS and NASTRAN for stochastic crack growth

The purpose of this Handbook is to provide a review of the knowledge and experiences in the field of fatigue fracture mechanics. It is well-known that engineering structures can fail due to cyclic loading. For instance, a cyclically time-varying loading reduces the structure strength and can provoke a fatigue failure consisting of three stages: (a) crack initiation (b) crack propagation and (c) catastrophic failure. Since last century many scientists have tried to understand the reasons for the above-mentioned failures and how to prevent them. This Handbook contains valuable contributions from leading experts within the international scientific community and covers many of the important problems associated with the fatigue phenomena in civil, mechanical and nuclear engineering.

Three-dimensional crack growth simulation was performed on a split-tooth gear design using boundary element modeling and linear elastic fracture mechanics. Initial cracks in the fillet of the teeth produced stress intensity factors of greater magnitude (and thus, greater crack growth rates) than those in the root or groove areas of the teeth. Crack growth simulation was performed on a case study to evaluate crack propagation paths. Tooth fracture was predicted from the crack growth simulation for an initial crack in the tooth fillet region. Tooth loads on the uncracked mesh of the split-tooth design were up to five times greater than those on the cracked mesh if equal deflections of the cracked and uncracked teeth were considered. Predicted crack shapes as well as crack propagation life are presented based on calculated stress intensity factors, mixed-mode crack propagation trajectory theories, and fatigue crack growth theories.

Design guidelines have been established to prevent catastrophic rim fracture failure modes when considering gear tooth bending fatigue. Analysis was performed using the finite element method with principles of linear elastic fracture mechanics. Crack propagation paths were predicted for a variety of gear tooth and rim configurations. The effects of rim and web thicknesses, initial crack locations, and gear tooth geometry factors such as diametral pitch, number of teeth, pitch radius, and tooth pressure angle were considered. Design maps of tooth/rim fracture modes including effects of gear geometry, applied load, crack size, and material properties were developed. The occurrence of rim fractures significantly increased as the backup ratio (rim thickness divided by tooth height) decreased. The occurrence of rim fractures also increased as the initial crack location was moved down the root of the tooth. Increased rim and web compliance increased the occurrence of rim fractures. For gears with constant pitch radii, coarser-pitch teeth increased the occurrence of tooth fractures over rim fractures. Also, 250 pressure angle teeth had an increased occurrence of tooth fractures over rim fractures when compared to 200 pressure angle teeth. For gears with constant number of teeth or gears with constant diametral pitch, varying size had little or no effect on crack propagation paths.