Strain gradients in Cu–Fe thin films and multilayers during micropillar compression
Introduction
Thin films and multilayers with layer thickness at the micron/sub-micron scale are widely applied in semiconductors, solar cells, and micro-electro-mechanical systems (MEMS). Due to the mismatch in mechanical properties, constituent layers are subjected to constraints exerted by the neighbouring layers or substrate [1]. It is critical to understand how the layered structure contributes to the mechanical behaviour of multilayers as compared to monolithic materials. In the present case, micropillar compression has been chosen as a test methodology to examine this effect. Micropillar compression has been widely applied to investigate mechanical behaviours of materials at small length scales [2], [3]. Size effects play a significant role in micropillar compression tests, because the characteristic length scale of deformation is at the micron/submicron scale [4], [5], [6], [7]. From both experimental and modelling studies, it is known that plastic deformation is concentrated in the top region of the tapered micropillars [8], [9], [10], [11]. Such strain gradients can potentially influence the work-hardening behaviour because of the accumulation of geometrically necessary dislocations (GNDs) [12]. In addition, the strain gradients in multilayered micropillars can be exaggerated due to the geometric constraints in the layered structure.
The authors’ recent studies have shown that the mechanical behaviour of Cu and Fe layers are significantly affected by the geometric constraints in Cu–Fe multilayers [13], [14]. However, the effects of strain gradients in multilayered micropillars are still not fully understood. Finite element (FE) models have been used to investigate the deformation occuring inside the micropillars and the influences of experiment parameters [15], [16]. Nevertheless, the size effect caused by strain gradients were not considered in previous FE modelling studies. Therefore, FE models that take into account strain gradients are in demand to provide insight into the mechanical behaviour of micropillars during compression, especially for thin films and multilayers. Huang et al. [17] established a conventional theory of mechanism-based strain-gradient plasticity (CMSG), which takes into account the plastic strain gradient through the material constitutive relation, without involving the higher-order stress or additional boundary conditions. For this reason, the CMSG methods has been adopted in the present case.
A detailed experimental paper describing the production and deformation behaviour of Cu–Fe thin films and multi-layers has already been published by the authors [14]. In the present work, FE models are developed to simulate these micropillar compression tests in order to provide understanding of their deformation behaviour. In particular, the geometric constraints imposed by adjacent layers are studied to interpret the bulging and cracking of layers that is observed experimentally. The distribution of strain gradients inside the micropillars is investigated, and the influence of GNDs on flow curve and crack initiation are discussed.
Section snippets
Modelling details
The focus of the present paper is the FE simulation of the compressive behaviour of Cu–Fe thin film and multilayer micropillars. A full description of the experimental work is already in print, and for further experimental details the reader is referred to reference [14]. For the sake of brevity, the experimental methodology will not be repeated here.
Intrinsic material properties determined by inverse analysis
The stress–strain curve extracted from the micropillar compression is the effective responses of the entire micropillar under compression. It can be affected by the taper angle, substrate deflection, friction and misalignments between the micropillar and the flat punch. Previous studies have shown that the tapered shape of the pillar introduces artificial strain hardening into the stress–strain curve [15]. Hence, the stress–strain curves of the micropillar may deviate from the constitutive
Conclusions
Finite element models based on the conventional theory of mechanism-based strain-gradient plasticity have been developed to simulate the mechanical behaviour of micropillars of Cu–Fe thin films and multilayers. The intrinsic material properties of nanocrystalline Cu and Fe thin films have been determined by inverse analysis of micropillar compression of the Cu and Fe thin films. The stress/strain concentration, plastic strain gradient, and density of geometrically necessary dislocations have
Acknowledgements
The authors are grateful to the financial support from the Australian Research Council through the Laureate Fellowship for P.D. Hodgson. (No. FL0992361). The experimental work was carried out with the support of the Deakin Advanced Characterisation Facility. The authors would like to thank Dr. Nicole Stanford for constructive discussion and comments.
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