Strain gradient plasticity effect in indentation hardness of polymers
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Strain gradient plasticity effect in indentation hardness of polymers Arthur C.M. Chong and David C.C. Lam Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (Received 10 September 1998; accepted 27 June 1999)
Plasticity in material is typically described as a function of strain, but recent observations from torsion and indentation experiments in metals suggested that plasticity is also dependent on strain gradient. The effects of strain gradient on plastic deformation in thermosetting epoxy and polycarbonate thermoplastic were experimentally investigated by nanoindentation and atomic force microscopy in this study. Both thermosetting and thermoplastic polymers exhibited hardening as a result of imposed strain gradients. Strain gradient plasticity theory developed on the basis of a molecular kinking mechanism has predicted strain gradient hardening in polymers. Comparisons made between indentation data and theoretical predictions correlated well. This suggests that strain gradient plasticity in glassy polymers is determined by molecular kinking mechanisms.
I. INTRODUCTION
Indentation on the surface of a material is commonly used to measure surface hardness. The calculated hardness is a material property independent of length scale and indentation size. In recent nanoindentation studies of single crystalline silver and polycrystalline copper, hardnesses were found to vary as a function of indent size when the indent size is between 0.1 and 10 m. The variation of hardness at small indent size has been attributed to a size scaling effect by Clarke and Ma.1 They suggested that the indent edges can be modeled as plastic hinges. The total force on the indent is the sum of force on projected area A and edge length L as F ⳱ ␣⬘A + ⬘L
,
(1)
where ␣⬘ and ⬘ are constants. The resulting hardness becomes H = ␣⬘ + ⬘
8公3 3D2
关共1 − 公3 兲D − d兴
,
(2)
where D is the indent diameter and d is the diameter of the indenter tip. Initial comparison of the model with hardness data from nanoindentation of silver correlated well. Fleck et al.2 proposed that the size dependence of hardness is related to the large strain gradient present in small indentations. The large strain gradients lead to formation of geometrically necessary dislocations and enhanced hardening. The hardness dependence on disloJ. Mater. Res., Vol. 14, No. 10, Oct 1999
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cations and strain gradient plasticity was analyzed by Nix and Gao.3 They proposed that the hardness varies with the indentation depth as
冉 冊 H Ho
2
=1+
h* . h
(3)
A comparison with single crystalline silver hardness data and polycrystalline copper data showed that the dislocation based strain gradient plasticity model is also in agreement with experimental data. Polymers can also exhibit strain gradient effects. A strain gradient plasticity model based on molecular kink yield mechanism was developed by Lam and Chong fo
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