Strength and deformation of rigid polymers: the stress – strain curve in amorphous PMMA Z.H. Stachurski * Department of Engineering, Faculty of Engineering and Information Technology, Australian National University, Canberra 0200, Australia Received 20 February 2003; received in revised form 20 May 2003; accepted 2 June 2003 Dedicated to Prof. Ian M. Ward on the occasion of his 75th birthday Abstract Poly(methyl methacrylate) (PMMA) is used to model the relaxation and plastic flow mechanisms of deformation, and the characteristic stress–strain response, relating it to its structure as much as it is known. The scope of this work is to identify and quantify the micro- mechanisms and the corresponding stress – strain relationships, and to assemble these into a coherent and self-consistent model for the observed mechanical behaviour. Detailed relationship between relaxation strength and time constants has been derived for some of the secondary motions. It is proposed that plastic events occur when the tension in chain segments pulls the chains out of/through constriction points. The scheme for simulating the isothermal true stress – strain curve is carried out under the following limitations: (i) geometrical effects, such as elastic instability and necking, (ii) thermodynamic adiabatic effects, and (iii) structural and kinetic effects, such as may arise from quenching or annealing, are neglected. Qualitative agreement achieved here is considered satisfactory in view of the simplicity of the model and only a few adjustable parameters. q 2003 Elsevier Ltd. All rights reserved. Keywords: Mechanical model; Anelasticity; Plasticity 1. Introduction On the most general level, physical mechanisms for plastic deformation can be classified into two main groups: 1. Athermal (dislocation glide, martensite shear transform- ation, etc.), 2. Thermally activated (dislocation climb, cooperative segmental motions in polymers, grain boundary sliding, etc.). Physical mechanisms for plastic deformation in poly- mers have been reviewed [1–7], with the overall conclusion that the phenomena fall into the second category. Thus a complete theory of plasticity for glassy amorphous poly- mers must involve thermally activated mechanisms. What has always been missing is a direct physical link between the structural elements in the polymer and the observed mechanical behaviour. This relationship has been obscured by lack of a precise, direct method of positioning atoms and description of their displacements. The concise description of plastic flow in metals by a universal relationship involving crystalline structure [8] is far advanced in comparison with the state of plasticity in polymer science, despite similar age of the problem. In the last decade, computer simulations of deformation in polymers have dramatically improved the focus and revealed many features hitherto only hypothesised [9–16]. The basic steps in computer simulations of amorphous polymers include (i) creation of several chains in free space, (ii) subjecting the chains to packing into a cell of target density with periodic boundary conditions, and (iii) a gradual minimisation of the cell potential energy during packing to achieve near- equilibrium structure. Various techniques can be used in the initial stages of packing to ensure randomness of the structure and to equilibrate energy. Velocity scaling is used to control the temperature, so that the probability that a configuration with energy, E; will occur is proportional to the Boltzmann factor. By definition, an equilibrium structure is that in which the force on each atom is zero. The final stage always involves molecular dynamics runs, typically with more than 10 5 steps. The novel way of representing polymer topology in 0032-3861/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0032-3861(03)00554-8 Polymer 44 (2003) 6067–6076 www.elsevier.com/locate/polymer * Tel.: þ61-2-6125-5681; fax: þ 61-2-6125-0506. E-mail address: zbigniew.stachurski@anu.edu.au (Z.H. Stachurski).