Distribution of dislocation source length and the size dependent yield strength in freestanding thin films |
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Authors: | Siamak Soleymani Shishvan Erik Van der Giessen |
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Affiliation: | a Department of Structural Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran b Zernike Institute for Advanced Materials, Department of Applied Physics, University of Groningen, Nyenborgh 4, 9747 AG Groningen, The Netherlands |
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Abstract: | A method is proposed to estimate the size-dependent yield strength of columnar-grained freestanding thin films. The estimate relies on assuming a distribution of the size of Frank-Read sources, which is then translated into a log-normal distribution of the source strength, depending on film thickness, grain size and theoretical strength of the material, augmented with a single fit parameter. Two-dimensional discrete dislocation plasticity (DDP) simulations are carried out for two sets of Cu films and the fit parameter is determined from independent experiments. Subsequent DDP predictions of the stress-strain curves in comparison with the corresponding experimental data show excellent agreement of initial yield strength and hardening rate for films of varying film thickness and grain size. Having thus demonstrated the power of the proposed strength distribution, it is shown that the mode of this distribution governs the most effective source strength. This is then used to suggest a method to estimate the yield strength of thin films as a function of film thickness and grain size. Simple maps are presented that are in very good agreement with recent experimental results for Cu thin films. |
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Keywords: | Thin films Discrete dislocation plasticity (DDP) Size effects Plastic deformation Frank-Read source |
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