5R20. Numerical Assessments of Cracks in Elastic-Plastic Materials. Lecture Notes in Applied Mechanics, Vol 4. - Huang Yuan (MTU Aero Engines GmbH, Munchen, 80995, Germany). Springer-Verlag, Berlin. 2002. 311 pp. ISBN 3-540-43336-8. \$89.95.

Reviewed by DA Mendelsohn (Dept of Mech Eng, Ohio State Univ, 206 W 18th Ave, Columbus OH 43210-1154).

This book is a combination of the author’s work in modeling elastic-plastic crack-tip fields with the pertinent work of others. It provides a, heretofore unavailable, detailed look at the recent state of research on this specific subject. Much of that work has been in accounting for the effects of 3D, thickness induced geometric constraints, loading parallel to the crack plane, and related material behavior issues. In none of these situations can the crack tip fields be characterized by a single term asymptotic expansion as in the original pioneering Hutchinson, Rice, and Rosengren (HRR) fields based on $J2$ flow theory with a Ramberg-Osgood stress-strain model, for which the single controlling parameter is the famous J integral. The thrust of the book is to determine the appropriate higher-order asymptotic crack-tip field characterization for a given situation and to examine its validity through a variety of finite element (FEM) computations. Extensive graphical results of the stress field distributions and singularity behavior are provided throughout.

The chapter on Cracks Under Stationary Conditions gives the HRR formulation and reviews the literature since then dealing with the conditions for its validity, followed by a review of work on constraint and parallel loading effects. This review sets the stage for most of the rest of the book. Pressure-sensitive materials are discussed next, whose yield stress is reduced by hydrostatic tension, and hence greatly affected by geometric constraints. The extension by O’Dowd and Shih of the HRR fields to include the pressure-sensitivity and to extend the expansion to the two parameter J-Q characterization is presented and explored in detail. The effects of non-Ramberg-Osgood hardening are explored using an FEM, small-scale-yielding calculation with an experimentally determined stress strain curve. A comparison of the J-Q characterization to the J-T characterization (the second T term depends on the stress parallel to the crack) under full-scale yielding is also carried out.

Cracks Under Thermal-Mechanical Loading Conditions is a chapter dealing with a modified HRR expansion in which the yield stress is reduced as the temperature gradient increases. The path dependence of J and lack of J dominance induced by a spatial variation in temperature gradient parallel to the crack growth direction is explored in bend specimens. This is extended to a two-term expansion to study transient thermal loading in cracked pressure vessel walls. The development in time of the spatial variations in the second asymptotic term is compared to the time-independent results from the deformation theory of plasticity.

The chapter on Interface Cracks examines the fields for cracks along a straight interface. Stationary crack-tip fields are analyzed for an elastic-plastic medium on one side and a rigid substrate on the other side of the interface, a two term asymptotic expansion is derived. Results are given for the first and second order expansions of both closed and open cracks and their validity examined as a function of mode mixity, pressure-sensitivity of the material, and the rigid substrate assumption. The fields at quasi-statically and (constant velocity) dynamically growing crack tips are then shown to be significantly different from the stationary fields due to elastic unloading and plastic re-loading in the wake of the propagating crack tip. The case of dissimilar elastic-plastic materials on either side of the interface is considered and the effects of dissimilar elastic and plastic properties and the propagation velocity on the crack tip fields are demonstrated.

The Mixed Mode Crack Propagation chapter treats dynamic or quasi-static crack growth under mixed modes I and III loading, with the specimen thickness effect in mind. Perturbation analyses in the two extremes of predominantly mode I and predominantly mode III are carried out using the unloading and re-loading formulation of the previous chapter and the effects of the mode-mixity are discussed. The final chapter, Assessment of Apex-V Notches, develops higher-order notch tip expansions of sharp notches, and examines their validity. Finally, pressure sensitivity of the yield stress is added to the analysis.

Numerical Assessments of Cracks in Elastic-Plastic Materials is a research monograph focused on asymptotic expansions of elastic-plastic crack and notch tip fields. It is suitable as a reference source for parts of a second graduate-level course in fracture mechanics. It is recommended for all research libraries and for researchers and practitioners of elastic-plastic fracture mechanics.