Analysis of stable crack growth in brittle materials Part II: A bridge zone model

Abstract

The phenomenon of stable crack growth in brittle materials is considered where stable crack growth is modeled as the formation of a bridge zone in the wake of a stably propagating main crack. The hypothesis that compressive zones surround and protect isolated ligaments under residual tension, which then leads to stable crack growth with attendant toughness enhancement, is incorporated into the bridge-zone formulation. Effects associated with debonding of ligaments on stable crack growth are explored via a simple treatment of microcrack branching. Similarity between the present bridge-zone description and a previously developed process-zone description of stable crack growth is quantitatively established. The importance of interpreting experimentally determined resistance-curve data subject to K-dominance requirements is highlighted by comparison of model predictions with select data in the literature.

Analysis of stable crack growth in brittle materials Part I: A process zone model

“…The results in Figures 8 to 10 clearly show that when interaction between residual stress and microcracking is considered according to the hypothesis that compressive zones surround and protect isolated ligaments under residual tension, microcracking ahead of a primary crack would nevertheless lead to stable crack growth with attendant toughness enhancement. For a given degree of residual stress characterized by a0 (8,15), these results indicate that both the degree of toughness enhancement and the maximum amount of stable crack extension increase with the average size of the isolated intact ligaments in the material. It is recognized that in some material systems such as single-phase polycrystalline ceramics, the maximum amount of stable crack extension predicted using the process-zone approach is much shorter than experimental observations, which can be on the order of a few hundred grain diameters.…”

“…Combining (4,8,9) the traction distribution, E, along the process zone now takes the form The second term inside the parentheses in (10a) represents the residual stress contribution to the process-zone traction distribution. The magnitude of the uniform tensile residual stress is expressed in terms of the non-dimensional residual stress parameter ~.…”

“…The residual stress field (15) is thus treated in an analogous fashion to the plane strain traction-opening relation (8), with the axis of straining in (14) perpendicular to the plane of the ring-crack as indicated in Figure 6. For p << 1 the residual stress field thus constructed is essentially self-equilibrating.…”

“…Interaction between residual stress and the uncracked ligaments on stable crack growth is modeled by considering two separate traction-opening relations that characterize the fracture process occurring within the process zone. In the second part of the investigation, which is the subject of a companion paper [8], )f stable crack growth is examined via the concept of a bridge zone in the wal~e of a stably propagating main crack.…”