Full length article Deformation behavior of nano-porous polycrystalline silver. Part II: Simulations S. Zabihzadeh a, b , J. Cugnoni c , L.I. Duarte d , S. Van Petegem a , H. Van Swygenhoven a, b, * a Photons for Engineering and Manufacturing, SYN, Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland b Neutrons and Xrays for Mechanics of Materials, Institute of Materials,  Ecole Polytechnique F ed erale de Lausanne, CH-1015 Lausanne, Switzerland c Ecole Polytechnique F ed erale de Lausanne (EPFL), LMAF-STI, Lausanne, CH-1015, Switzerland d ABB Switzerland Ltd. Corporate Research, CH-5405, Baden-Daettwil, Switzerland article info Article history: Received 1 September 2016 Received in revised form 15 February 2017 Accepted 8 April 2017 Available online 20 April 2017 Keywords: Finite element simulations Porous structure Size effects Deformation behavior abstract Three-dimensional finite element simulations of nano-porous silver structures are performed to un- derstand the correlation between the porous morphology and the mechanical behavior. The nano- structures have been obtained from ptychographic X-ray computed tomography. The simulations allow distinguishing between the interplay and role of the ligament size, the pore morphology and the porosity, and therefore provide a better comprehension of the experimental observations. We show that the proposed model has a predictive character for mechanical behavior of nano-porous silver. © 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction The mechanical response of porous materials can be modeled with finite element (FE) simulations [1]. Several models exist to generate these structures such as the periodic Kelvin cells [2] and the Weaire-Phelan cells [3] generated with the surface Evolver program developed by Brakke [4] or the Voronoi Diagram [5]. It is however also possible to generate a micromechanical model directly from the microstructure obtained by tomography tech- niques [1]. To capture the effects of heterogeneity and structure of the porous network three-dimensional (3D) simulations are required. Recent developments in high-resolution 3D imaging techniques, such as focus ion beam (FIB)/scanning electron micro- scopy (SEM) or X-ray tomography launched a larger interest in performing 3D simulations on the actual microstructure of the porous materials [6e12]. Using high-resolution 3D images obtained from serial-block face scanning electron microscopy [13], Carr et al. [9] studied the influence of aging on the porosity, the pore distri- bution and the elastic modulus of sintered micro silver paste. It was reported that aging does not influence the global density and the elastic modulus of the material. However, aging increases the heterogeneity in the pore distributions and results in a clustering of pores leading to a local decrease of the elasticity next to the high porous regions. Our previous [14] experimental work on nano- porous sintered silver layers showed a strong dependency of the mechanical behavior on the microstructure. To allow a better un- derstanding, 3D (FE) microstructure-based simulations are per- formed. The statistically representative volume elements or RVE were obtained by ptychographic tomography, a technique providing a higher resolution than X-ray nano-tomography [15]. By comparing the simulation results with in-situ and ex-situ tensile tests the deformation mechanisms are discussed. 2. Experimental setup and simulation methodology 2.1. Sample fabrication Eight thin layers (25 ± 5 mm) of porous polycrystalline silver layers are produced during pressure assisted sintering. The samples are called as S1eS8 and are sintered in the temperature range of 210e300  C, pressure range of 4e12 MPa during 3e10 min. More details about sample fabrications are found in first part of the paper [15]. S1 and S8 are samples sintered respectively at lowest and highest extremes of sintering conditions. * Corresponding author. Photons for Engineering and Manufacturing, SYN, Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland. E-mail address: helena.vs@psi.ch (H. Van Swygenhoven). Contents lists available at ScienceDirect Acta Materialia journal homepage: www.elsevier.com/locate/actamat http://dx.doi.org/10.1016/j.actamat.2017.04.041 1359-6454/© 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). Acta Materialia 131 (2017) 564e573