Cracked composite laminates least prone to delamination

Abstract

In [( ± θ ) n 2 /(90°) n 1 /( ǂ θ ) n 2 ] fibre-reinforced composites, the outer (± θ ) n 2 sublaminates are known to act as crack arrestors, i. e. to reduce the stress intensity factors at the tips of a crack in the central (90°) n 1 layer in all three modes of loading. The degree of reduction depends on the stiffness of the plies, the ply angle θ and the thickness of the outer sublaminates. However, although the stress intensity factor decreases, the crack-induced largest interfacial principal tensile stress increases. The situation is particularly severe under transverse mode II loading, inevitably resulting in interfacial delamination. The aim of this paper is to choose the design variables of the laminate, namely the ply angle θ , relative ply stiffness and thickness, in such a way as to minimize the stress intensity factor at a crack tip in the (90°) n 1 layer without exceeding the interfacial bond strength. A constraint is also placed on the minimum flexural stiffness of the laminate. An alternative optimization problem in which the largest interfacial principal tensile stress is minimized subject to a limit on the stress intensity factor is also formulated and solved. The above optimization problem is solved in two stages. First, an analysis of the non-homogeneous, anisotropic medium containing a flaw is performed within the bounds of the classical lamination theory and fracture mechanics. This allows development of mathematical expressions relating the stress intensity factor in the central (90°) n 1 layer and the interfacial tensile stress to the sublaminate thickness and stiffness and the ply angle θ . These expressions are highly complicated, precluding a completely analytical approach to the calculation of design sensitivities. In the next stage the optimization problem is reduced to a nonlinear mathematical programming one, whose solution is attempted by several techniques. The sensitivities with respect to the design variables required in these techniques are calculated by a mixed analytical/numerical approach.

The Lyman Alpha Forest in the Spectra of Quasistellar Objects

“…Departures of the absorption line shape from a Voigt profile may contain valuable information about the underlying nature of the absorption systems, and different scenarios may have quite different observational signatures. Rotational motion (Weisheit 1978, Prochaska & Wolfe 1997, gravitational collapse (McGill 1990, Meiksin 1994, and galactic outflows (Fransson & Epstein 1982, Wang 1995 have been discussed in terms of the likely absorption line shapes they produce. As yet, the quantitative application of these results has proven difficult because of the lack of realistic prototypical models for the actual line formation, the rather subtle departures from Voigt profiles expected, and the wide variety of profiles actually encountered.…”

“…To get the large covering factor right, these objects must be so close together as to run into each other like circular saws at only slightly higher redshift, which puts us basically back at a continuous IGM. A number of other sources of low z Lyα absorption have been considered, among them tidal tails (Morris & Van den Berg 1994) and galactic winds (Wang 1995). Galaxy clusters have been seen to cause at least some absorbers , and the strong clustering found among low z absorption lines (Boksenberg 1995, Ulmer 1996 hints at the increasing importance of such structures with decreasing redshift.…”

Low-redshift quasar Ly absorption-line systems associated with galaxies

“…Another possibility is that some low surface brightness galaxies could possess huge gaseous haloes or discs, which can also give rise to absorption. In addition, galactic wind is also another possible source (Wang 1995). Of course, the absorption by the IGM still could play an important role.…”

Optimum Composite Laminates Least Prone to Delamination under Mechanical and Thermal Loads

“…Among these are the works by Park (1982), Fukunaga and Chou (1988), Miravete (1989), Fukunaga and Vanderplaats (1991). Considering that most of the advanced fibre-reinforced composite laminates are prone to cracking and delamination, and that the properties of laminates are tailorable, Wang and Karihaloo (1994a), Wang and Karihaloo (1996c), Wang and Karihaloo (1996b) posed optimum strength design problems of multidirectional laminates in a different way from the conventional ones. They applied fracture mechanics analyses in the optimum strength designs of multidirectional laminates against delamination and transverse cracking.…”

“…It is widely known that under transverse static or low-velocity impact loading, matrix cracks in the laminae of a fibre-reinforced multidirectional laminate can cause delaminations between the laminae (Chester and Clark (1992); Doxsee et al (1993); Jih and Sun (1993); Liu et al (1993); Pavier and Clarke (1995); Wang and Karihaloo (1994a)). As the low-velocity impact-induced delaminations in laminates are the major source of the reduction in their post-impact-compressive strength, the mechanisms of onset of the impact-induced delaminations has attracted the attention of many researchers in recent years (Chester and Clark (1992); Choi and Chang (1992); Davies et al (1997); Jih and Sun (1993); Pavier and Clarke (1995)).…”