Abstract
Three different approaches to plasticity are investigated to model the experimentally-observed non-linear behaviour of unidirectional fibre-reinforced polymeric matrix materials. The first and simplest approach consists on assuming independent one-dimensional rate-dependent plasticity on in-plane (12) and through-thickness longitudinal (13) shear components of the Cauchy stress tensor. The second, employs a 3D extension of the plane stress Hill’48 anisotropic plastic surface. The third and the last is formulated as a quadratic yield function inspired by Puck’s fracture initiation criterion. It searches for a plastic localisation plane in which a certain combination of normal and shear stresses is maximum. Numerical simulations are conducted to analyse the off-axis compression behaviour of carbon fibre reinforced epoxy composite under varying loading rates. The afore-mentioned three different approaches are explored with an aim to predict the experimentally-observed non-linear response of such composites. The model parameters are determined using a deterministic inverse modelling strategy employing an iterative domain reduction optimisation technique. As far as the experiments are concerned, the quasi-static and medium rate tests were carried out in universal testing machines, while the experiments at high rate were conducted in a Split Hopkinson Pressure Bar system. The effectiveness in terms of accuracy and robustness of the three approaches are discussed.
Highlights
The experimentally observed non-linearity on the stressstrain behaviour of Unidirectional (UD) Fibre Reinforced Polymers (FRP) is a topic were many have tried to tackle
The yield function, originally reported in [6], that is proposed for the localisation plane (LP) plasticity model is expressed as: f r,ε p,εɺp = σ lp [r] − k ε p,εɺp = 0 (18)
As in the previous section the relationship between the plastic multiplier and the equivalent plastic strain is obtained from the work conjugacy, in this case, rT eɺ p = σlp εɺp that yields to the following relationship
Summary
The experimentally observed non-linearity on the stressstrain behaviour of Unidirectional (UD) Fibre Reinforced Polymers (FRP) is a topic were many have tried to tackle. Other as Vyas et al [3] have tried more convincing 3D approaches that include the Raghava pressure-dependent plasticity function combined with a null flow rule component in the fibre direction. Such approach was previously proposed by Xie and Adams [4]. A more practical approach has been proposed by Puck in [5], where he basically scales the non-linear shear stress-strain curves according to his own physically-based two-dimensional inter fibre fracture criterion. After that we will discuss the results and make some concluding remarks
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