The work presented in this chapter resulted in the following publications4:
1. S. T. Pinho, L. Iannucci, P. Robinson. Crashworthiness of Composite Struc- tures. Poster presented at GSEPS Research Student Research Symposium, Poster Competition, Imperial College London, 16th July 2003 (won the 2nd
prize); and at Industrial Affiliates Annual Review Meeting, The Composites Centre, Imperial College London, 25th September 2003
2. S. T. Pinho. MPhil to PhD Transfer Report: Formulation and implementation of a 3D decohesion element for delamination modelling in explicit FE codes. Department of Aeronautics, Imperial College London, 14th (interview) and
17th (power point presentation) October 2003
3. S. T. Pinho, L. Iannucci, P. Robinson. Modelling delamination in an explicit FE code using 3D decohesion elements. CompTest2004, Bristol, 21st - 23rd
September 2004
4. S. T. Pinho, L. Iannucci, P. Robinson. Formulation and implementation of decohesion elements in an explicit finite element code. In press, Composites Part A, 2005
4Some of these publications include work from other chapters of this thesis and therefore feature
Formulation of failure models and
criteria
3.1
Acknowledgment
The work presented in this chapter was started at Imperial College London by the author and his supervisors. From the survey carried on failure criteria, it became apparent that the LaRC02 [4] failure criteria were among the best in the open literature. Some modifications and generalizations were proposed, and application examples carried [36–38]. This work was communicated to the proposers of the LaRC02 failure criteria (which in the meanwhile had become LaRC03 [39]) and a cooperation was started to develop, write and publish LaRC04 [40]. This cooperation resulted in many discussions, and considerable modifications to the models and criteria as a whole. In particular, the sub-section that deals with in-situ effects for tensile matrix failure was totally developed and written in close cooperation with Dr. Pedro Camanho and Dr. Carlos D´avila, and based on their previous published work [4, 39, 41]. In general, all of the work reported in this chapter has been influenced either by their published work, or by their direct involvement. As a result, Dr. Pedro Camanho and Dr. Carlos D´avila’s contribution to the work presented in this chapter is acknowledged.
3.2
Introduction
The mechanisms that lead to failure in composite materials are not fully understood yet. This is especially true for compressive failure, both for the matrix and fibre- dominated failure modes. This has become particularly evident after the World Wide Failure Exercise (WWFE) [42].
In this chapter, physically-based failure models are discussed and proposed for each failure mode in laminated fibre-reinforced composites with unidirectional plies, at the ply level.
If composite materials are to be used in structural applications, then the under- standing of how each failure mode takes place—i.e. having a physical model for each failure mode—becomes an important point of concern. These physical models should establish when failure takes place, and also describe the post-failure behaviour. For instance, a physical model for matrix compressive failure should predict that failure occurs when some stress state is achieved, as well as what orientation the fracture plane should have and how much energy the crack formation should dissipate.
The main failure modes of laminated fibre-reinforced composites are:
Delamination. Composite materials made of different plies stacked together tend to delaminate. The bending stiffness of delaminated panels can be significantly reduced, even when no defect is visible on the surface or the free edges. The physics of delamination is to a certain degree understood, and one of the best numerical tools to predict the propagation of delamination consists on the use of decohesion elements.
Matrix compressive failure. What is commonly referred to as matrix com- pressive failure is actually matrix shear failure. Indeed, failure occurs at an angle with the loading direction, which is evidence of the shear nature of the failure pro- cess.
Fibre compressive failure. This failure mode is largely affected by the resin shear behaviour and imperfections such as the initial fibre misalignment angle and voids. Typically, kink bands can be observed at a smaller scale, and are the result of fibre micro-buckling, matrix shear failure or fibre failure.
Matrix tensile failure. The fracture surface resulting from this failure mode is typically normal to the loading direction. Some fibre splitting at the fracture surface can usually be observed.
Fibre tensile failure. This failure mode is typically explosive. It releases large amounts of energy, and, in structures that cannot redistribute the load, it typically causes catastrophic failure.
Experimental results from the WWFE [42, 43] indicate that the (admittedly scarce) data on fibre tensile failure under bi- or multi-axial stress states does not seem to invalidate the maximum stress criterion. Thus, this chapter focuses on models for compressive failure, which is of great interest in crashworthiness and other areas, as well as matrix tensile failure.
Accurate physically-based criteria are developed and preferred to curve-fitting- based criteria. The main limitation associated with curve-fitting-based criteria is that their applicability is restricted to the load combinations used in the curve fitting from which they originate. However, it is impractical to test every material in enough load combinations to define these criteria for every combination of the six stress tensor components.
Matrix compressive failure is addressed with a model based on the Mohr-Coulomb criterion. Puck et al. [2, 44–46] were the first researchers to propose a matrix failure model based on the Mohr-Coulomb criterion. Further developments were later car- ried by D´avila et al. [4, 39] for the LaRC02/03 failure criteria. In this present work, an analysis of both Puck [2, 46] and LaRC02/03 [4, 39] matrix compressive failure criteria is performed. For the LaRC02/03 criteria, a correction is proposed for the consideration of friction stresses. This leads to more conservative predictions, and makes the resulting failure envelope coincide with a simpler criterion that can be related to the work from Puck and Sch¨urmann [2, 46]. The analysis concludes with the proposal of the latter as a matrix failure criterion for a three dimensional (3D) stress state. Matrix tensile failure is addressed combining the action or fracture plane concept from Puck and Sch¨urmann [2, 46] with experimental evidence from the WWFE. Also, a failure model for matrix in tension and shear is derived from Dvorak and Laws [47] fracture mechanics analyses of cracked plies, as a generaliza-
tion of LaRC03 [39].
For fibre failure in compression, it is assumed that kink-band formation results from matrix failure, due to small misalignments of the fibres in the composite. Also, it is suggested that shear nonlinearity should have a considerable effect on failure and 2D analyses of fibre kinking over-simplify the treatment of the problem. A formal treatment of fibre kinking is presented, that leads to a model for fibre kinking similar to the one proposed by D´avila et al. [4, 39]. The main differences are that the model presented here accounts for 3D effects, considers a generic nonlinear shear behaviour, and uses the matrix failure criteria from this work.
In this chapter, the index a refers to the fibre direction, the index b refers to the in-plane transverse direction and the index c refers to the through-the-thickness direction.