A Theoretical Framework for Addressing Fracture in the Ductile-Brittle Transition Region

Abstract

Fracture in the ductile-brittle transition region of ferritic steels is complicated by scatter, produced by local sampling effects, and specimen geometry dependence, which results from relaxation in crack tip constraint. Scatter and constraint are interrelated in that each influences the magnitude of the other. This article summarizes recent research on fracture in the transition region and presents a unified framework for addressing size effects and scatter. A stress volume model for quantifying constraint effects is described briefly, and a comparison between theory and experiment is presented. This model has been applied only to stationary cracks in plane strain, but methods to account for ductile crack growth and three-dimensional effects are described. The inadequacies of the weakest link model for cleavage fracture are discussed, and an improved statistical model is introduced. This new model considers the probability of propagation and arrest of cleavage microcracks. A number of recommendations for analyzing cleavage fracture toughness data are presented. Transition region data for a given material should be viewed as a statistical distribution rather than a single value. However, these data should be corrected for constraint effects and ductile crack growth before applying statistical analysis. One of several statistical distributions may be applied to cleavage data; each of the proposed distribution functions has advantages and disadvantages. One of the unknowns in transition region fracture is the threshold toughness of the material, that is, the absolute lower bound.

Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

“…Based on the weakest link theory [178,183] and the Weibull statistics theory [184], Wallin proposed a master curve method with a corresponding reference temperature [185] to provide a description of the statistical scatter, statistical size effects and temperature dependence of cleavage toughness in the transition region and on the lower shelf. The master curve method is not applicable on the upper shelf and Weibull statistics are used to provide the confidence bounds on the temperature above which cleavage fracture is unlikely to exist.…”

Brittle to Ductile Transition in Cleavage Fracture of Alpha-Iron: Experiments and Modeling of Mechanisms

“…Crocker, et al (1996) studied specific forms of break-through across boundaries and classified them into four types related to the observed features of fracture along boundaries. In a quite detailed modeling study Anderson, et al (1994) considered the mode of propagation of cleavage cracks across hexagonal grains and demonstrated that the cumulative probability of overall fracture in a "weakest link" context of triggering brittle response in structures is directly influenced by the impediments that grain boundaries have on cleavage crack propagation. To our knowledge the only detailed model of the role of grain boundaries on impeding the percolation of cleavage cracks across a field of randomly misoriented grains in steel is that of .…”

“…Outside -42-of these general considerations of grain size effects and phenomena related to triggering of brittle behavior in fracture transitions, specific considerations of the influence of grain boundaries on the cleavage cracking resistance have been few. Of these studies the most noteworthy have been those of Gell and Smith (1966), Anderson et al (1994) and . In the work of Anderson et al (1994), the mode of cleavage fracture across hexagonal grains was considered in some detail to develop realistic cumulative probability distributions of fracture resistance in the context of "weakest link" models of such behavior.…”

“…Of these studies the most noteworthy have been those of Gell and Smith (1966), Anderson et al (1994) and . In the work of Anderson et al (1994), the mode of cleavage fracture across hexagonal grains was considered in some detail to develop realistic cumulative probability distributions of fracture resistance in the context of "weakest link" models of such behavior. Gell and Smith (1966) have made one of the earliest observations on the cracking resistance of individual grain boundaries with known tilt and twist components, in hydrogen charged polycrystalline Fe-3%Si alloy and demonstrated that the major contribution to the cracking resistance of a grain boundary comes from its twist misorientation across the boundary rather than the tilt misorientation.…”

“…The few existing studies have been limited to the assessment of such resistance by individual grain boundaries with known lattice misorientation in hydrogen charged Fe-3%Si alloy by , and to some models considering such resistance by Anderson, et al (1994), by Crocker, et al (1996) and by .…”