A B S T R A C T A low-cost experimental apparatus has been developed to investigate the mode I fatigue crack growth behaviour of thin metallic foils and sheets. The apparatus utilizes magnetic coupling between a ceramic magnet and a rotating steel disc to induce cyclic tensile loads in notched rectangular specimens. To illustrate the testing apparatus, mode I fatigue crack growth in 30-μm-thick high-purity titanium foils was studied. Experiments were performed at ambient temperature using a loading frequency of 2 Hz and a nominal stress ratio of 0.1. The cyclic crack growth data could be fit to a Paris relationship between crack growth rate and stress intensity range. The stress intensity factor exponent, m, in the Paris relationship was between 4 and 6, which is comparable with the relatively high values found in the literature for the tension-tension fatigue of other metallic bulk materials. Incomplete self-similarity analysis was used to explain the observed higher m values for thin metallic foils.Keywords fatigue crack growth rate; fatigue testing; finite element analysis; incomplete self-similarity; titanium.
N O M E N C L A T U R Ea = current crack length C = the constant in the Paris relationship f = the loading frequency h = the specimen thickness J c = the fracture toughness determined by the J integral around the crack tip K c = the fracture toughness m = the exponent in the Paris relationship N = the number of fatigue cycles R = the loading ratio t = time w = the specimen width Y = the geometry correction factor z = the basic similarity parameter ΔK = stress intensity factor amplitude Δσ = the stress amplitude σ y = the yield strength
I N T R O D U C T I O NFoil-thickness materials, with a thickness in the range of 10 to 250 μm, are used in a variety of applications, including micro-electro-mechanical systems (MEMS), integrated circuits, fuel cells and printers. The progressive trend of miniaturization of structural components requires knowledge regarding the mechanical behaviour and properties of thin metallic materials. As discussed in the succeeding text, the tensile, fracture and fatigue behaviour of foil-thickness materials can be very different from that observed in bulk materials. In addition to influencing the tensile properties (ductility and strength) of thin metallic foils, grain size and grain orientation can have a major effect on crack initiation, crack growth and fracture toughness. Compared with bulk materials, microstructural inclusions or precipitates in thin