Flaw Tolerance in a Thin Strip Under Tension

Recent studies on hard and tough biological materials have led to a concept called flaw tolerance which is defined as a state of material in which pre-existing cracks do not propagate even as the material is stretched to failure near its limiting strength. In this process, the material around the crack fails not by crack propagation, but by uniform rupture at the limiting strength. At the failure point, the classical singular stress field is replaced by a uniform stress distribution with no stress concentration near the crack tip. This concept provides an important analogy between the known phenomena and concepts in fracture mechanics, such as notch insensitivity, fracture size effects and large scale yielding or bridging, and new studies on failure mechanisms in nanostructures and biological systems. In this paper, we discuss the essential concept for the model problem of an interior center crack and two symmetric edge cracks in a thin strip under tension. A simple analysis based on the Griffith model and the Dugdale-Barenblatt model is used to show that flaw tolerance is achieved when the dimensionless number $Λft=ΓE∕(S2H)$ is on the order of 1, where $Γ$ is the fracture energy, $E$ is the Young’s modulus, $S$ is the strength, and $H$ is the characteristic size of the material. The concept of flaw tolerance emphasizes the capability of a material to tolerate cracklike flaws of all sizes.