Materials Science and Engineering A 452–453 (2007) 483–498 A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer–matrix composites L.G. Zhao ∗ , N.A. Warrior, A.C. Long School of Mechanical, Materials and Manufacturing Engineering, The University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 30 May 2006; received in revised form 17 October 2006; accepted 18 October 2006 Abstract Process-induced residual stress in fibre-reinforced thermoset polymer–matrix composites was analysed using a thermo-viscoelastic microme- chanical model and the finite element method. A three-dimensional unit cell with glass fibre and epoxy polymer–matrix, representing the periodic microstructure of unidirectional fibre-reinforced composites, was considered to compute cure residual stress of fibre composites induced by chem- ical shrinkage of the epoxy resin and thermal cooling contraction of the whole fibre and resin system. The constitutive behaviour of the epoxy matrix was described by a cure and temperature-dependent viscoelastic material model. Compared to an elasticity solution, a reduction in residual stress was predicted due to the stress-relaxation caused by the viscoelastic behaviour of the epoxy matrix. Calculated residual stress shows strong dependency on the fibre volume fraction and fibre packing. After the cure process is complete, residual stress tends to relax to a constant value. The effect of residual stress on damage and failure of the model was also studied using the maximum stress failure criterion combined with a post-failure stiffness reduction technique. Damage onset, in terms of the location and the load level, was shown to be clearly influenced by the residual stress for both normal and shear loading. Initial and final failure envelopes, predicted for biaxial normal (longitudinal and transverse) loading and combined shear (longitudinal) and normal (transverse) loading, were shown to be shifted and contracted by the inclusion of residual stress. For final failure, residual stress was seen to have little effect on the load levels for longitudinal failure but greatly affected the load levels for transverse and shear failure. Residual stress could be detrimental or beneficial depending on the state of existing residual stress and the loading conditions. © 2006 Elsevier B.V. All rights reserved. Keywords: Residual stress; Thermo-viscoelastic; Cure; Relaxation; Finite element analysis; Damage and failure 1. Introduction Process-induced residual stress in polymer–matrix compos- ites is a direct consequence of the chemical shrinkage of the matrix during polymerisation and the mismatch of thermal con- traction between the fibre and the matrix during cooling. The formation of residual stresses can have significant effects on the mechanical performance of composite structures by caus- ing warpage [1] or initiating pre-load damage such as interface debonding and matrix microcracking [2,3]. Both warpage and initial damage can reduce the stiffness and the strength of the material, as well as acting as sites for nucleation of macrocracks and environmental degradation. Process-induced residual stresses in polymer–matrix com- posites can be determined both experimentally and analyti- ∗ Corresponding author. Tel.: +44 23 92842375; fax: +44 23 92842351. E-mail address: liguo.zhao@port.ac.uk (L.G. Zhao). cally. Experimental methods include the techniques of section- ing/cutting [4], warpage/curvature measurements [1] and the X-ray or neutron diffraction methods [5,6]. For analytical meth- ods, residual stresses in composites are generally studied at either macro or meso/micro-levels. At the macro-level, classi- cal laminate theory is normally used and gives predictions of residual stress at the ply level [7–9]. At the meso/micro-level, a Representative Volume Element (RVE) or unit cell which repre- sents the meso/microscopic periodic structure of the laminate is considered and the analysis is often carried out using a numeri- cal procedure such as the finite element method [10–13]. From the meso/microscopic unit cell model, residual stress field can be predicted at the fibre–matrix or tow (yarn) level. For thermoset polymer composites, a typical curing process consists of two steps: curing at a constant elevated temperature and thermal cooling from the curing temperature to room temperature. During curing, the polymer shrinks as a result of the purely chemical reaction (polymerisation) and its material characteristics change dramatically through the transition from 0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.10.060