Concise Syllabus

Fibre reinforced polymeric composites are gradually replacing traditional metal alloys in making primary load carrying structures due to their superior structural and functional properties. However, failure behaviour of composites under mechanical loading are far more complex than metals. This course would start by highlighting the importance of carrying out failure analysis in composite structures. It would then discuss the different failure mechanisms experimentally observed, and subsequently introduce several physically based advanced failure theories developed for composites. It would also cover computational implementation of the failure models as user defined subroutines in a commercial finite element programme.

Lecture Wise Break Up

I. Introduction to composite materials

• Composite materials and their internal architecture, advantage as structural material, 3D orthotropic constitutive matrix, uni and multidirectional laminates, lamination theory [3]

II. Intra and Inter-laminar damage mechanisms

• Recapitulation of fracture mechanics, delamination, matrix cracking, fractographic observations, fibre compressive failure, fibre tensile failure, dynamic loading and impact damage, benchmark experiments to extract fracture parameters, laminate size effect on failure, effect of manufacturing induced defects on failure [5]

III. Modelling delamination and matrix cracking

• Concept of quasi-brittle material and origin of cohesive zone model, adaptation to composites delaminaton and matrix cracking, different onset and propagation criteria, development of 3D mixed mode bilinear cohesive constitutive law, virtual crack closure technique (VCCT), analytical models for residual strength prediction [5]

IV. Fibre tensile and fibre compressive failure

• Onset strength and Weibull statistical theory for fibre tensile failure, fibre microbuckling and fibre kinking failure theories under compression, influence of shear nonlinearity [3]

V. Essentials of continuum mechanics

• Deformation, strain and stress measures, large deformation and objective stress rates[5]

VI. Continuum damage mechanics

• Idea of continuum damage, strain equivalence principle, isotropic and anisotropic damage effect tensor, thermodynamic basis of continuum damage [4]

VII. Finite element modelling framework for damage

• Governing equation for dynamic equilibrium, weak form for a body including cracks, finite element discretisation, formulation 3D isoparametric finite elements, dynamic explicit finite element method [5]

VIII. Implementation of composite damage models

• Implementing damage models in commercial finite element programme via user defined material and user defined element packages, several aspects of damage modelling, demonstrative 3D simulation of benchmark failure cases [10]

References:

1. P.P. Camanho, S.R. Hallett, Numerical modelling of failure in advanced composite materials, Woodhead Publishing, 2015

2. R.M. Jones, Mechanics of composite materials, Taylor and Francis, 2015

3. T. Belytchko, W.K. Liu, B. Moran, K. Elkhodary, Nonlinear finite elements for continua and structures, Wiley, 2014

Prepared by :

Supratik Mukhopadhyay

Prerequisites :

ME621A and ME623A