In reality the structure dimension and strss state are different from the KIC testing. Can the KIC still be used as fracture criterion ? then how to determine the fracture criterion value?
Dr. Wang:
It was once said that if you could unambigiously characterize a material's toughness in terms of KIc, you probably don't want to be using that material! - meaning that the parameter is most appropriate for high strength, low toughness materials where the extent of local plasticity is minimal. This is certainly the case for metallic materials, although the toughness of many ceramics and even polymers can be usefully characterized with KIc.
Dr. Bielecki is thus totally correct in his assertion that life becomes more difficult when dealing with newer higher toughness materials. However, provided the extent of local plasticity - the plastic zone size - is roughly at order of magnitude smaller than the in-plane dimensions of the component including the uncracked ligament size (the small-scale yielding condition) and plane strain conditions prevail (i.e., the plastic zone size is roughly an order of magnitude smaller than the out-of-plane thickness of the component), KIc is still a valid approach and in principle is independent of geometry and crack size . It is still valid in plane stress although as a lower bound value of the toughness - under small-scale yielding conditions in plane stress, the stress intensity at the fracture instability now becomes a function of thickness and geometry, and as subcritical cracking often procedes catastrophic fracture, an R-curve approach is generally required. In addition to the issue of stress-state (i.e., plane stress vs. plane strain), mixed-mode conditions can further complicate the issue, although for most materials, the mode I toughness is invaraibly the lower-bound.
However, where there is too much plasticity in-plane, the linear elastic fracture mechanics approach become invalid and one must turn to nonlinear elastic fracture mechanics, involving J-intergral and/or crack tip opening displacement approaches. One can use these approaches to back-calculate what the KIc would have been if the component was larger and small-scale yielding conditions prevailed. As Dr. Bielecki also correctly notes, these approaches, particularly involving J, are far more complex methodologies, but if you are interested, I would refer you to T. L. Anderson's textbook "Elements of Fracture Mechanics" which presents an excellent and balanced description of this topic.
Dr. Wang:
Underfortunately, for the same alloy and same microstructure, the fracture toughness can be very different in a component with a different thickness and/or geometry . That simply is a fact and indeed the basis of fracture mechanics. For ductile materials, unlike the strength which is pretty much the same whatever the size of your test sample is (this incidentally is not necessarily true for brittle materials, such as ceramics, where the strength is invariably lower in larger samples due to a higher probability of finding a more severe defect), the fracture toughness will be lowest in thick samples where plane strain constraint is achieved. With thinner samples, such constraint is relaxed such that the fracture toughness becomes highly sensitive to sample thickness - essentially the through-thickness (z-direction) stresses at the crack tip are relieved when the plastic zone is no longer small compared to the thickness dimension, such that the sample can plastically deform through the thickness with a resulting increase in toughness. One problem here is that linear-elastic fracture mechanics prescribes crack-tip stress intensity K fields but these are planar fields - they do not take account of the through-thickness dimension - hence unless plane strain conditions are met, the toughness will inevitably depend upon specimen thickness - period!
For this reason, I like to say that "whereas God may have invented plasticity, the Devil invented fracture!"
The simple answer here is that the geometry and thickness of the sample affect the constraint at the tip of any crack, which can have a major influence of the stress-state local to the crack tip, specifically the degree of triaxial stresses that are developed in the vicinity of the crack tip. This has a major influence on the development of the critical stresses for cleavage fracture and/or the ability for voids to form and grow in the devlopment of ductile (microvoid coalescence) fracture. Unlike a material's strength, which can be fixed (for a given microstructural condition) by the stress and temperature (and strain rate), the fracture toughness depends on these factors and the level of constraint developed at the tip of a crack. To obtain a nominally reproducible measurement of the toughness, the are currently requirements for the size and geometry of the test specimen to ensure that your measurements are worst-case or relevant to your application. I would refer you to the ASTM Standard test methods for fracture toughness measurements, ASTM Standard E-1820. Standard Test Method for Measurement of Fracture Toughness. West Conshohocken, PA: American Society for Testing and Materials.
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