A review of deformation and fatigue of metals at small size scales

Abstract

A B S T R A C T Mechanical devices are being introduced whose size scale is well below that of conventional mechanical test specimens. The smallest devices have sizes in the nanometer range, though a good proportion of structural devices are of the micrometer scale. Development of these products raises the question of how their mechanical behaviour and reliability may be predicted. Conventional macroscopic test data can be used, but these are obtained using specimens whose size is much larger than the devices themselves. There is a risk that performance predictions will be inaccurate, due to the existence of size effects. This paper covers small size scale testing in metallic specimens and devices, concentrating on freestanding specimens. To begin, some examples of micro-scale devices are given. Fabrication methods for small metallic devices are then briefly described. This is followed by a review of experimental observations of mechanical properties in various metallic materials at the micro-scale, highlighting the differences in results from different research groups and the gaps in our current knowledge. A section on computational and predictive modelling is included, in recognition of the role of modelling in device design and testing. Overall, the findings are that size effects are common, particularly in crystalline samples when the grain size is similar to one or more of the specimen dimensions. However, observations of size effects differ between studies and mechanical properties can vary widely, even for the same type of material. As a consequence, the relationships between specific device processing methods, specimen size and material properties must be adequately understood to ensure successful performance. N O M E N C L A T U R EA = geometric texture factor b = Burgers vector magnitude d = grain diameter D f = fatigue ductility parameter E = elastic modulus h = film, foil or specimen thickness k = 'locking parameter,' representing the relative hardening contribution of grain boundaries K = constant for power law creep k B = Boltzmann constant l = specimen length n = Creep exponent for power law creep N f = number of cycles to failure p = constant in the Basquin and Coffin-Manson relationships

Size-effects in time-dependent mechanics in metallic MEMS

“…on time-dependent deformation such as creep and fatigue [1]. It is known from literature that this behavior is affected by size-effects: the interaction between microstructural length scales and dimensional length scales [2,3]. Not much research has focused on characterizing size-effects in time-dependent material behavior, specifically for free-standing thin films [3].…”

“…It is known from literature that this behavior is affected by size-effects: the interaction between microstructural length scales and dimensional length scales [2,3]. Not much research has focused on characterizing size-effects in time-dependent material behavior, specifically for free-standing thin films [3]. This study investigates size-effects caused by grain statistics in timedependent deformation in µm-sized free-standing aluminum cantilever beams.…”

Creep measurements in free-standing thin metal film micro-cantilever bending

“…In the literature some reports can be found discussing creep and relaxation effects in thin aluminum films [3][4][5][6][7][8]. However, specifically for free-standing thin films not much research has focused on determining size-effects in time-dependent material behavior [9]. Therefore, there is a clear need for detailed studies into the physical micro-mechanisms underlying the size-effects in creep in metallic MEMS.…”

Mechanically probing time-dependent mechanics in metallic MEMS

“…However, specifically for free-standing thin films not much research has focused on determining size-effects in time-dependent material behavior [12]. Therefore, there is a clear need for detailed studies into the physical micro-mechanisms underlying the size-effects in creep in metallic MEMS.…”