Analysis of structural changes during plastic deformations of amorphous polyethylene Alejandro A. Pacheco a, b , Romesh C. Batra a, * a Virginia Polytechnic Institute and State University, Engineering Science and Mechanics Department, Blacksburg, VA 24061, USA b Universidad del Norte, Mechanical Engineering Department, Barranquilla, Atlántico, Colombia article info Article history: Received 27 July 2012 Received in revised form 6 November 2012 Accepted 14 November 2012 Available online 29 November 2012 Keywords: MD simulations Empirical orthogonal functions Plastic deformations abstract Molecular dynamics (MD) simulations have been used to analyze yielding and stress-softening processes during stepped simple tensile loading of bulk amorphous polyethylene (PE) at temperatures (T def ) well below the glass transition temperature (T g ). Specimens formed by 20 linear chains of 1000 beads each (2  10 4 coarse grained -CH 2 - units), with energetics described by a united atom potential, were deformed at T def ¼ 100K. Configurations at axial strains (ε xx ) ranging from 0% to 30% were allowed to reach steady state equilibration. Subsequently, configurations in a time period of 5 ps were saved for analysis of their local structure. Local structural characteristics were analyzed using three methods: (i) a geometric description by computing the evolution of self and inter-chain entanglements, the number of bead contacts and the free volume, (ii) the method of Empirical Orthogonal Functions (EOF) to obtain a reduced description of the displacement field at each strain level and the vibration of each bead around its equilibrium position, and (iii) Hardy’s method to compute the time averaged local stress tensor to obtain a detailed description of the distribution of internal forces. It was found that at early stages of deformation (ε xx < 13%) the inter-chain entanglement continuously decreases while the self- entanglement showed no significant variation and no distinct patterning. Also the energy content in each eigenmode of the normalized displacement correlation matrix used in the EOF analysis is almost the same for a large portion of the frequency range regardless of the imposed axial strain level. Furthermore, distribution of the local pressure presented a positive expected value at the initial (ε xx ¼ 0%) configu- ration; the expected value continuously decreases toward the point where the axial stress peaks (ε xx ¼ 13%). The evolution of the number of loosely packed regions (quasi-defects), identified by a negative value of the local pressure, showed three distinct regimes: ε xx (0%e5%), ε xx (5%e13%) and ε xx (13%e30%). The first regime corresponds to the fast nucleation of quasi-defects while the last one showed an inversion in the trend during the stress-softening regime with a moderate decreasing tendency. The three analyses show that the plastic deformation in this amorphous material commences with the nucleation of stress-induced defects without significant changes in the molecular degrees of freedom. Despite the chemical nature and inherent internal structure of the material under study, our findings support Argon et al.’s theory [1e4] as well as that of subsequent investigators [4,5] in that local structural rearrangements exist at locations where particles (beads) forming the material are loosely packed; these regions are termed the local shear transformation zones (STZ). Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Glassy polymers are integral components in many modern industrial applications [6] because of their outstanding mechanical properties [7e9]. When subjected to large deformations, instead of failing abruptly, materials such as polycarbonate (PC) and poly- methyl methacrylate (PMMA) show strain hardening for large strains [8], a valuable mechanical response required in many structural applications. Even though glassy polymers, and in general polymeric mate- rials, pervade many aspects of our everyday life, a deep under- standing rooted in the micro-structure-property relationship of their behavior is still needed [10e13]. As the dimensions of struc- tural components reach the nanometer scale in-homogeneities in the microstructural characteristics of the constituent materials start to dominate and deviations from the observed macroscopic * Corresponding author. . E-mail address: rbatra@vt.edu (R.C. Batra). Contents lists available at SciVerse ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer 0032-3861/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2012.11.039 Polymer 54 (2013) 819e840