Invariant based approaches in the design of composite laminates

Abstract

Invariant based approaches have been proposed to simplify the design and analysis of composite materials, in particular, for generating design allowables. Of these invariants, Trace, more recently referred to as Tsai's Modulus, a material property derived from the plane stress stiffness matrix, can be used to help with preliminary design. However, in literature this has mainly focussed on unidirectional composites. The present work extends the application of invariants to woven and hybrid composites, i.e. the latter made with both unidirectional and woven laminae, and provides appropriate validation for the use of invariants in design. A novel approach to implement Tsai's Modulus and determine the three-dimensional stiffness matrix of a woven specimen is proposed. Omni failure envelopes have been proposed in literature and these have been extended to accommodate hybrid specimens with both unidirectional and woven laminae. This work shows that Tsai's Modulus and invariants can be used as an initial design tool in order to establish the likely properties of a given layup and material combination for use in preliminary design. Property predictions at the laminate level, Ex, Ey, νxy and Gxy, were within ±10% of experimental values for highly complex laminate stacking sequences and material combinations.

Assessing the relative conservatism of the unit circle failure envelope

“…While previous works have established that the unit circle failure envelope is conservative [12], [16], such as Millen et al [16] for a AS4/3501-6 quasi-isotropic laminate, it is still not known whether this envelope is consistently conservative for different material systems. In addition, it has not been demonstrated what effect the use of exact or Tsai's Modulus derived properties have on the predicted failure envelopes.…”

“…Results for [0/±45/90]s AS4/3501-6 laminate [12], [24], depicted in stress space, have been presented in a previous publication [16] so will be summarised here. In this case the unit circle was the most conservative envelope.…”

“…Authors have extended the application of the invariant-based approach beyond simple laminae or defined laminates [13]- [17]. Arteiro et al [14] used an invariant-based approach with micro-mechanics, Gerbaud et al [15] included viscoelastic behaviour, Ha and Cimini Jr. [13] studied four different fibre systems, Millen et al [16] extended the application of Tsai's modulus to woven and hybrid (both unidirectional and woven laminae) composites, and Guedes [17] validated Tsai's modulus for carbon fibre reinforced polymer (CFRP), Kevlar reinforced polymer composites (KFRP) and glass reinforced polymer composites (GFRP) laminates.…”