Size effect on fracture toughness of freestanding copper nano-films

Fracture toughness of free-standing nanocrystalline copper–chromium composite thin films

“…However, once the thickness is further reduced to less than a critical thickness, h cr , free-surface effects on micromechanisms of plasticity make the fracture toughness, K IC ðd; hÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EG c ðd; hÞ p , of nominally ductile metals decrease with the thickness [12,19,22,23], where E is Young's modulus. For example, Begley et al [24] noted that the fracture toughness increased from 6.9 to 8.5 MPa ffiffiffiffi m p for copper thin films when the thickness is increased from 200 to 600 nm, which is in agreement with experimental results by Hirakata et al [13], who measured K IC = 2.34, 6.63 and 7.81 MPa ffiffiffiffi m p for copper films of h ¼ 100; 500 and 800 nm, and d ¼ 170; 280 and 370 nm correspondingly in that order. Approaches adopted previously for the evaluation of the fracture toughness of thin films include notched tensile tests [12,13,19,22,25], channel cracking tests [24,26], bulge tests [27,28], scratch adhesive tests [29][30][31] and indentation tests [14,32,33].…”

“…Such size effects on strength and also on low ductility [6], and various possible deformation mechanisms [7][8][9] responsible for the size effects, have also been reported. In summary, the yield strength and the toughness of such thin films depend not only on the grain size d but also on the thickness h of the film [10][11][12][13][14], i.e. r y ðd; hÞ and G c ðd; hÞ.…”

“…Regarding the thickness dependence, Espinosa et al [11] showed that the yield strength of a copper film more than doubles from 160 to http 345 MPa when the thickness is decreased from 1000 to 200 nm. Hirakata et al [13] showed that r y ¼ r a þ r b ðh 0 =hÞ 1=2 with r a ¼ 17:4 MPa, r b ¼ 5095:5 MPa and h 0 ¼ 1 nm for a copper film with its thickness in the range of 200 < h < 1000 nm. The interplay between d and h for the yield strength makes it more complicated to predict the thickness dependence of the toughness for ultrathin films.…”

“…where Y is a factor related to specimen geometry and a is the crack size, utilizing linear elastic fracture mechanics (LEFM) as it applies to cracked specimens under tensile loading [13,19,22,26,27]. However, significant plasticity in the immediate vicinity of a propagating crack can be present [18,19] and causes errors in this relation for the estimation of fracture toughness.…”

“…However, significant plasticity in the immediate vicinity of a propagating crack can be present [18,19] and causes errors in this relation for the estimation of fracture toughness. Preparation of a notched free-standing specimen is also difficult and inconvenient, and is usually made by a line-incisor or a sharp razor for micron-thickness films [12] and a focused ion beam system for sub-micron thickness films [13,22,27]. Moreover, it is difficult to preserve propagating cracks normal to the loading direction in tensile tests as this requires elaborate alignment fixtures to be utilized when testing such thin specimens to ensure valid results.…”