Energy methods for fatigue damage modelling of laminates

Abstract

The initiation and growth of damage in composite materials are phenomena that precede the catastrophic failure event where a material sample or component fragments or separates into two pieces. During fatigue loading, the damage grows stably due to cyclic stressing and leads to a gradual deterioration of mechanical properties and ultimately to failure. For cross-ply laminates, the estimation is necessary of effective stress intensity factors or energy release rates, for statically loaded ply cracks in 90° plies that are bridged by the uncracked 0° plies, particularly when considering the early stages of property degradation. Such relations are used in conjunction with a fatigue crack growth law to predict the progressive development of damage during fatigue. For fatigue loading this paper justifies, on the basis of detailed physical modelling based on energy methods rather than empiricism, the use of the stress range intensity factor as the correlating parameter for fatigue crack growth data, rather than energy release rates or differences of energy release rate. Use is made of an accurate stress transfer model for multiple-ply cross-ply laminates to predict the dependence of energy release rates and stress intensity factors for long bridged ply cracks on the applied stress and ply crack separation. Two methods of analysis are considered. The first uses a method that can be extended to deal with small laminate defects where the energy release rate and stress intensity factor depend on the size of the defect, but the laminate is subject only to a uniaxial load. The second method applies to multi-axial loading, but assumes that the stress intensity factor or energy release rate is independent of the defect size. Both methods are, however, shown to lead to the same energy release rate and stress intensity factor for long ply cracks subject to uniaxial loading. The two methods also take full account of the effects of thermal residual stresses through the use of a crack closure concept. Simplifying assumptions are made when developing a model that predicts the degradation of most of the thermoelastic constants of a fatigue damaged cross-ply laminate as a function of the number of fatigue cycles. Such data are needed to predict the fatigue behaviour of structures having complex stress states using finite element analysis. Preliminary work carried out to validate the fatigue model, based on simplifying assumptions, has led to pessimistic predictions of performance that have the advantage that they can be exploited in the form of conservative design methods.