Topics in Fracture and Fatigue

Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept, in which a periodic relation between shear stress and atomic shear displacement is assumed to hold along a slip plane emanating from a crack tip. This approach allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability was developed using the J-integral for the case when the crack and slip planes coincide (Rice, 1992). Solutions are discussed here for cases when they do not. The results were initially derived for isotropic materials and some generalizations to take into account anisotropic elasticity are noted here. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fee crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to \(\sqrt {{\gamma _{us}}}\) where γ_us, the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of γ_us are summarized, and the results are used to evaluate brittle versus ductile response in fee and bee metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The analysis also reveals features of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, and some implications for thermal activation are summarized. Additionally, the analysis of dislocation nucleation is discussed in connection with the emission from cracks along bimaterial interfaces, in order to understand recent experiments on copper bicrystals and copper/sapphire interfaces, and we discuss the coupled effects of tension and shear stresses along slip planes at a crack tip, leading to shear softening and eased nucleation.

The mechanics and mechanisms of ductile fracture are reviewed, emphasizing the effect of multi-axial states of stress on the mechanisms of hole nucleation, growth, and coalescence. This provides a basis for a discussion of crack extension by ductile failure mechanisms, with particular reference to ways in which the constraint can be quantified in a two parameter constraint based fracture mechanics methodology.

An overview is given of the continuum mechanics of void growth pertaining to room temperature ductile fracture processes. Analyses of the growth of isolated voids and of void interaction effects are reviewed. A framework for phenomenological constitutive relations for porous plastic solids is discussed. Calculations of localization and failure in porous plastic solids are reviewed that illustrate the progressive development of ductile failure. Additional considerations, including the effect of the constraint provided by contact between the growing void and the void-nucleating particle, cavitation, and the effect of non-uniform porosity distributions are briefly noted.

In this chapter a review is presented of the work over a number of years in the area of crack blunting and void growth in ductile materials. These phenomena contribute to the process of crack growth by ductile fracture. The models of void growth involve both continuum averaging methods and idealized configurations involving only a few voids.

This paper is devoted to the application of local micromechanisms of failure to the prediction of the macroscopic fracture toughness properties of metallic materials — a field pioneered by F. McClintock. The global approach of fracture assumes that failure can be described in terms of a single parameter, such as K _IC or J _IC . This approach may yet prove to be questionable in complex situations. This is the reason why local approaches of fracture have also to be developed. An attempt is made here to review the application of these local approaches, especially those which are micro-mechanistically based and to indicate a number of research fields which necessitate further studies. The paper is divided into two main parts. In the first part, the three basic fracture modes encountered in metallic materials, i.e. cleavage, intergranular fracture, and ductile rupture are reviewed. For cleavage fracture, a statistical model based on the Weibull weakest link concept is introduced and applied to a number of low-alloy ferritic steels. Some questions relating to intergranular fracture are also discussed. For ductile rupture, the emphasis is laid on the discontinuous or continuous character of the nucleation of cavities from second phase particles, on cavity growth and coalescence. The mechanics of plastic porous materials is briefly introduced to model this mode of failure and the statistical aspects of ductile rupture. It is shown that, in spite of the large research effort devoted to ductile rupture over the past few decades, it is still necessary to use an empirical fracture criterion based on the concept of critical void growth, that was originally introduced by McClintock. The second part of the paper is devoted to the application of these local fracture criteria to predict the fracture toughness of specimens or the fracture load of components. The concept of characteristic distances related to the microstructure of materials and that of the “process zone” are briefly discussed. Then theoretical expressions between the fracture toughness (K _IC or J _IC ) for 2D cracks, tested under small-scale yielding conditions, and local criteria are introduced. The local criterion for brittle cleavage fracture is based on Weibull statistics, which gives rise to a size effect, while the criterion for ductile rupture is based on critical void growth. Finite element method (FEM) numerical simulations of compact tension (CT) and center-cracked panel (CCP) specimens under large-scale yielding conditions were used in conjunction with these local fracture criteria to show that the ligament size requirements for “valid” J _IC measurements are not only dependent on the specimen geometry (crack length, tension versus bending), but also on material work-hardening exponent and, more importantly, on the microscopic modes of failure. Further applications of the local approach of fracture are also presented, including fracture toughness testing of 3D cracks, the ductile-to-brittle transition behavior for ferritic steels, and fracture tests of specimens and components under non-isothermal conditions. Finally, further developments are briefly discussed.

The spread of intergranular creep damage around blunt notches and sharp cracks in ductile single phase alloys is modeled by a mechanism based continuum material damage model and a finite element approach. The details of the material damage have been derived from extensive earlier experimental results on an austenitic stainless steel. The finite element simulation of the evolution of intergranular damage in the form of accumulating densities of grain boundary facet cracks has indicated that while this damage spreads out preferentially along inclined planes around the tips of sharp cracks, it localized in the symmetry plane ahead of a blunt notch. These results are in excellent agreement with the experimental observations of Ozmat, et al. on the directions of early crack growth from sharp cracks and blunt notches in Type 304 stainless steel.

The damage that occurs in unidirectional ceramic and metal matrix composites upon monotonic and cyclic loading involves coupled considerations of mechanics and stochastic processes. Some of the basic principles are described and models presented that both characterize damage evolution and govern mechanism changes. Comparisons are presented between predictions and experimental data for such phenomena as modulus degradation caused by matrix cracking, fatigue crack growth and tensile strength.

It is well understood that the fatigue limit behavior of a metal is a function of defect size within the Linear Elastic Fracture Mechanics (LEFM) regime. Conversely, it is not well understood how microstructural defects affect the fatigue limits of heterogeneous materials of apparently smooth specimens and engineering components. Consequently in the latter case investigations have concentrated on the cyclic stress-strain, or deformation, approach to fatigue fracture e.g. the Basquin and Coffin-Manson type studies.

By introducing micro-structural fracture mechanics and elastic-plastic fracture mechanics it is possible to link the deformation and the fracture approaches to metal fatigue investigations. This chapter considers these developments and their implications.

These reflections are based on some of my publications over the years, mostly in the fields of deformation and fracture. My apologies to those co-authors whose work I have omitted. To them and to others whose work is mentioned, I am deeply indebted for inspiration, discussion, dedication, and often tedious work. In the end, I hope these associates have shared the thrill of new-found insight that may be of service to engineers. Needless to say, I am also deeply indebted to the many colleagues in the field, whose findings have often been greater, and with whom discussion have been exciting and instructive. Finally, the essential support of this work by many agencies over the years is very much appreciated. The topics are in order of their first major publication.