Deflection in Tapered Cantilever Beams Deflection (Gap Opening) in Double Cantilever Type Fracture Toughness Specimens

摘要

When an otherwise homogeneous material under stress contains small defects (i.e., internal cracks and/or voids), the stresses at parts of the material-defect interface significantly exceed the ones anticipated at that location in the absence of such irregularities. Consequently, a structural member, otherwise calculated to safely sustain the applied loads, might unpredictably fail. That branch of engineering which intends to account for such 'stress-raisers' is known as fracture mechanics. Fracture mechanics studies have found that different materials (and even the same material when loaded in different orientations) reflect different sensitivity to such 'stress-raisers' - a material property known as fracture toughness. Test samples and testing procedures have been devised in order to qualify this material property. The relation between the applied load and its displacement (or gap opening) at the point of crack growth is being used herein to determine (compute) material fracture toughness. While the equations derived for the stress field near the edge of a defect in an otherwise uniform field assume an infinite volume of material to surround the (relatively) very small defect, the crack to width and/or height in these laboratory size testing samples is definitely a finite one. This report offers a mathematical relation between the applied load and that part of the deflection (gap opening) which is due to the cantilever-like part of the sample, for that class of fracture toughness test specimens which can be described as double cantilever. A beam theory approach is used.