PSI - Issue 13

Per Hansson / Procedia Structural Integrity 13 (2018) 837–842

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Per Hansson/ Structural Integrity Procedia 00 (2018) 000 – 000

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Hommel and Kraft (2001). This is due to that surfaces imply the absence of atomic bonds, leaving surface atoms in deviating energy states. This effect is material dependent and both stiffening and softening of the structure might result, i.e. Zhou and Huang (2004). Also the crystallographic orientation influences the mechanical response and determines whether the modulus of elasticity increases or decreases with size. Further, the load distributes unevenly between atoms depending on if they are surface-close or part of the bulk, or located close to a geometrical stress raiser, cf. e.g. Olsson et al. (2007). At the atomic scale geometrical features thus play a significant role. High-quality components nearly always require a low defect density. However, defects are always present, whether they origin from the manufacturing process itself or stems from damage during service. How devastating the presence of defects is to a nano-component can, however, not be answered unconditionally due to the size dependence of the material properties, cf. Uhnakova et al. (2014). Another aspect of importance is the load situation. Few structures experience constant loading, or a monotonically increasing load, during service. This applies to macroscopic structures and most certainly also to nano-devices. At the macro-scale the most hazardous loading situation is fatigue, and it is often estimated that 80% of all macroscopic failures are due to fatigue. The same might very well be true at the nano-scale. Most nano-structures contain beam elements, and the defect-tolerance of nano-sized single-crystal Cu beams beams subjected to fatigue loading is the scope of this paper. This is accomplished through 3D molecular dynamic simulations where the mechanical response due to fatigue loading of beams containing voids is compared to that of solid beams. 1. Statement of the problem 1.1 Geometry and loading conditions Beams of single crystal fcc Cu, loaded under displacement control along their length directions x are considered, cf. Fig. 1. The coordinate system ( x,y,z ) has its origin at the center of a beam. Each beam is built from the repetition of Cu unit cells with lattice parameter a 0 = 3.615Å. The beam length L equals L =100 a 0 and the square cross section size is s × s = 6a 0 × 6a 0 . One beam is solid, Fig. 1a), whereas the others each hold a defect; an edge crack-like void, Fig. 1b), and a through-the thickness void, Fig. 1c. Each defect is symmetrically placed with respect to the x- axis for case Fig. 1b) and with respect to the coordinate system origin for case Fig. 1c). Each defect has the width w in the x direction and the height h in the y -direction, with w × h = 2 a 0 ×2 a 0 .

Fig. 1. Beam configurations: a) solid beam, b) beam with edge crack-like void, c) beam with through-the thickness void.

The crystallographic orientation for the Cu crystal is such that we designate the coordinates ( x,y,z ) to the crystallographic orientations as x = [100], y = [010] and z = [001]. Starting from an unloaded and relaxed state, the fatigue loading is effectuated by applying a velocity of magnitude v 0 = a 0 /200/ps in the + x - and ― x -directions during loading and v 0 = ― a 0 /200/ps in the + x - and ― x -directions during unloading, cf. Fig 2. This corresponds to a strain rate of ̇ = 10 8 /s, using a time step of Δ t = 5ps. The loading varies between a maximum and a minimum value of the displacement, δ xmax and zero, respectively, within a load cycle.

Fig. 2. Displacement controlled loading between δ xmax and zero with constant temperature T = 300K.