title: Origin of sample size effect: Stochastic dislocation formation in crystalline metals at small scales.
abstract: In crystalline metals at small scales, the dislocation density will be increased by stochastic events of dislocation network, leading to a universal power law for various material structures. In this work, we develop a model obeyed by a probability distribution of dislocation density to describe the dislocation formation in terms of a chain reaction. The leading order terms of steady-state of probability distribution gives physical and quantitative insight to the scaling exponent n values in the power law of sample size effect. This approach is found to be consistent with experimental n values in a wide range.
authors.affiliation: Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC.|Physics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan, ROC.
authors.forename: Guan-Rong
authors.initials: GR
authors.lastname: Huang
authors.affiliation: Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC.
authors.forename: J C
authors.initials: JC
authors.lastname: Huang
authors.affiliation: Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung 804, Taiwan, ROC.
authors.forename: W Y
authors.initials: WY
authors.lastname: Tsai