Elsevier

Materials Science and Engineering: A

Volume 651, 10 January 2016, Pages 146-154
Materials Science and Engineering: A

Strain gradients in Cu–Fe thin films and multilayers during micropillar compression

https://doi.org/10.1016/j.msea.2015.10.105Get rights and content

Abstract

Plastic strain gradients can influence the work-hardening behaviour of metals due to the accumulation of geometrically necessary discolations at the micron/submicron scale. A finite element model based on the conventional theory of mechanism-based strain-gradient plasticity has been developed to simulate the micropillar compression of Cu–Fe thin films and multilayers. The modelling results show that the geometric constraints lead to inhomogeneous deformation in the Cu layers, which agrees well with the bulging of Cu layers observed experimentally. Plastic strain gradients develop inside the individual layers, leading to extra work-hardening due to the accumulation of geometrically necessary dislocations. In the multilayer specimens, the Cu layers deform more severely than the Fe layers, resulting in the development of tensile stresses in the Fe layers. It is proposed that these tensile stresses are responsible for the development of micro-cracks in the Fe layers.

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.

References (33)

Cited by (16)

  • Synergetic strengthening of coherent and incoherent interface on a mixed-phase high-entropy alloy revealed by micro-pillar compression

    2022, Journal of Materials Research and Technology
    Citation Excerpt :

    For the FCC/BCC incoherent interface, the BCC phase was in fact a second phase in the micron scale. There is a certain degree of strain gradient [37] at the interface during the compressive experiments owing to the difference of deformation behavior between FCC and BCC, leading to the geometrically necessary dislocations (GNDs) formed near the interface to coordinate the strain incongruity. Then the back stress originated from the aggregation of GNDs at the interface will harden the soft FCC phase [38].

  • High-throughput investigation of structural evolution upon solid-state in Cu–Cr–Co combinatorial multilayer thin-film

    2022, Materials and Design
    Citation Excerpt :

    The relation between the interfaces and the behavior of multilayer thin-films under solid-state reaction needs to be systematically investigated. Previously, research in this area is based on the traditional “trial-and-error” approach, which is time-consuming and labor-intensive [14,15]. It becomes very imperative to develop a method that is efficient and systematic for the study of phase formation under solid-state reaction in multilayer thin-film.

View all citing articles on Scopus
View full text