Indentation model and strain gradient plasticity law for glassy polymers
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Indentation model and strain gradient plasticity law for glassy polymers David C.C. Lam and Arthur C.M. Chong Department of Mechanical Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong
Plastic deformation of metals is generally a function of the strain. Recently, both phenomenological and dislocation-based strain gradient plasticity laws were proposed after strain gradients were experimentally found to affect the plastic deformation of the metal. A strain gradient plasticity law is developed on the basis of molecular theory of yield for glassy polymers. A strain gradient plasticity modulus with temperature and molecular dependence is proposed and related to indentation hardness. The physics of the strain gradient plasticity in glassy polymer is then discussed in relation to the modulus.
I. INTRODUCTION
Classical concepts of plasticity have been developed to describe plastic deformation in metals. These concepts of plasticity are also relevant to forming, rolling and drawing processes in polymers. Microstructural studies have shown that slip and kink bands are present in polymer, which suggest that deformation processes in polymers might be similar to those in crystalline materials such as metals and ceramics. Recently, experiments on plastic deformation in metals and ceramics revealed that plastic deformation is dependent not only on strain, but also on strain gradient and a material length. The material length has been related to the dislocation yielding process by Nix and Gao and strain gradient plasticity concepts have been developed to describe these effects.1 The yielding process in amorphous polymer typically occurs via chain rotation and stretching.2 Yielding behavior of an amorphous polymer is dependent on the molecular weight of the polymer3 and therefore may be sensitive to strain gradients during plastic yield. In this paper, strain gradient plasticity in metals and polymer yielding are first reviewed. Then, a strain gradient plasticity model for polymeric materials based on molecular yielding theory is developed for indentation. Afterward, a generalized strain gradient plasticity law, along with a strain gradient plasticity modulus, is proposed and discussed. II. YIELDING IN METALS
In conventional theories of plasticity, no material length scale enters the constitutive law. This implies that flow stress at any particular point in a solid is uniquely related to the strain at that point. In these theories, the lengths involved for the predictions of the response are the lengths associated with the geometry and not any material length. However, a number of plasticity phe3784
http://journals.cambridge.org
J. Mater. Res., Vol. 14, No. 9, Sep 1999 Downloaded: 11 Apr 2015
nomena have shown a size effect whereby the response becomes stronger as the size decreases. For example, the indentation hardness of metals and ceramics4,5 increases with decreasing indent size. Fleck et al.5 has pointed out that the large strain gradients inhe
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