Mechanics of materials: top-down approaches to fracture

Abstract

The utility and robustness of the mechanics of materials is illustrated through a review of several recent applications to fracture phenomena, including adhesive failures, the role of plasticity in enhancing toughness in films and multilayers, and crack growth resistance in ductile structural alloys. The commonalty among the approaches rests in a reliance on experiments to provide calibration of the failure process at the smallest scale.

Introduction

Starting with earlier applications in elasticity and plasticity, the mechanics of materials has evolved in recent decades into topics related to the failure of structural metals, ceramics and polymers, as well as composites, coatings and multilayers. Methods have been developed for assessing the performance of advanced materials in new applications and designs, through models of deformation, damage and fracture. Most methods have some element of phenomenology, especially when small-scale mechanisms influence macroscopic behavior. Yet, mechanism-based concepts provide key insights. The canonical example is provided by the fracture mechanics of structural materials. Fracture mechanics has established a framework for: (i) experimentally measuring the fracture resistance of a material under monotonic and cyclic loadings; and (ii) assessing structural integrity using these data. The extraordinary success of fracture mechanics lies in its ability to combine a theoretical framework with experimentally measured critical quantities. The mechanics is used to link the macroscopic geometry and loads to microscopic fracture processes, which are then characterized by experiment, not theory. Despite significant progress in the theoretical understanding of the influence of microstructure on fracture, the development of predictive models continues to provide one of the major mechanics and physics challenges. It remains true that material fracture properties are experimentally measured quantities in nearly all present day applications of fracture mechanics, whether toughness, fatigue or stress corrosion growth rates.

The theme of this paper is the exploration of the considerable additional scope within the mechanics of materials for further significant advances in “top-down” approaches, which couple continuum mechanics descriptions to phenomenology and experimental calibration at the smallest scales. In most structural material systems, given the complexity of the microscopic processes, “bottom-up” approaches which use fundamental mechanics and physics to link the atomic scale to the macroscopic aspects of deformation and fracture are unlikely to be developed with adequate accuracy in the near future.

Four interrelated topics will be used to illustrate this point of view, each selected within the scope of problems to be found in crack growth and adhesion (Fig. 1). The general plan is to augment the conventional approach to crack growth, which is based on a single parameter (namely, the local energy release rate, G_tip), with a richer model capable of incorporating microscopic aspects of the rupture process itself. The underlying concept is to divide the process into two separate domains that can be analyzed independently and then linked together to express the overall behavior. One domain represents the zone near the crack front that may experience very large strains as the fracture process evolves. This zone incorporates a model of the rupture process, referred to as an embedded process zone (EPZ). The other domain is the physically larger plastic zone and outer elastic region that can be analyzed using either continuum models of elastic/plastic behavior, or variants that incorporate a plasticity length scale. The link between the two zones is provided by tractions, σ, and displacements, δ, on the boundary between the zones, resulting in the well-known leveraging effect of the EPZ response on the size of the inelastic zone and, accordingly, on the overall crack growth resistance. The details inherent in σ(δ) contain the information about the rupture mechanism, which replaces G_tip. Parameters characterizing σ(δ) will generally be determined by fitting model predictions to a selected set of experiments, thereby providing a calibration against the fracture process at the smallest relevant scale. Models for the EPZ have attained various levels of completeness. At the simplest level, the EPZ has been located on the fracture plane, subject to normal and shear tractions that express the rupture phenomenon. More complete models, such as that for the ductile fracture of structural alloys, incorporate the full effects of the multi-axial stress field in the EPZ. To explain this spectrum of models, the article is organized in four sections.

• The EPZ model is used to extend fracture mechanics to adhesive interfaces between two elastic materials.

• The linkage between the EPZ and plastic dissipation is explored.

• EPZ models for fracture initiation and crack growth in ductile structural alloys are addressed subject to small- and large-scale yielding conditions.

• Plasticity at the micrometer scale and its role in strength and toughness is examined.