Ramesh Talreja

Transverse Cracking and Stiffness Reduction in Composite Laminates

A systematic classification of the effects of transverse cracking on the stress-strain response of composite laminates is presented. Stiffness reductions resulting from transverse cracking in glass/epoxy and graphite/epoxy laminates from crack initiation to crack saturation are predicted using the stiffness-damage relationships developed by the author in a previous work. Good agreement with the experimental results is found. An assessment of the ply discount method for predicting stiffness reductions at crack saturation is also made.

A Continuum Mechanics Characterization of Damage in Composite Materials

The mechanical response of a composite material damaged in fatigue, or in any other loading mode, is characterized by a set of vector fields, each representing a damage mode. Constitutive equations are derived for isothermal small-deformation behaviour following attainment of a damage state. For small damage, the elastic constants of a damage state are related to those of the undamaged state. The usefulness of these relations in characterizing the development of damage, for instance during fatigue, is discussed.

Fatigue of composite materials: damage mechanisms and fatigue-life diagrams

The basic fatigue damage mechanisms in composite laminates are reviewed. Based on these mechanisms a pattern in the fatigue-life diagrams is proposed. Several experimental data are shown to agree with this basic pattern. Fatigue ratio is defined in terms of strains, and fatigue limit is shown to exist for unidirectional, cross-plied and angle-plied laminates. The limitations to the fatigue performance of composite laminates are pointed out and suggestions for improving the fatigue resistance are made.

Damage in composite laminates with off-axis plies

Abstract Damage in off-axis plies of composite laminates is studied by examining the configuration [0/±θ4/01/2]s with θ=25, 40, 55, 70 and 90 subjected to tensile loading in the axial direction. It is found that for the values of θ, where the stress in the off-axis plies normal to the fibers is tensile, ply cracks lying along fibers initiate and increase in number, while for other θ values the plies do not undergo this damage, as expected. However, the overall laminate elastic moduli are also found to change for the θ values where no ply cracks exist. It is postulated that a shear-induced degradation of the off-axis plies is responsible for the observed laminate moduli changes. The prediction of changes in these moduli by using the ply shear modulus measured on [±θ4]s appears to support this postulate. For the case of moduli changes caused by ply cracks the recently proposed synergistic damage-mechanics approach [1] is applied. The implications of the findings of this work on a class of continuum damage-mechanics formulations proposed in the literature are discussed.

Stiffness properties of composite laminates with matrix cracking and interior delamination

Abstract Two modes of damage in composite laminates are considered: the intralaminar damage (matrix cracking) and the interlaminar damage (interior delamination). Using a vectorial representation of damage as internal variables in a phenomenological theory, relationships between the overall stiffness properties and the intensity of damage in the individual modes are determined. These relationships show that the intralaminar damage reduces all elastic moduli for a general orientation of the damage entities (cracks) and changes the initial orthotropic symmetry of a laminate. The interlaminar damage, however, does not change the symmetry but reduces the moduli. Predictions of the elastic moduli changes are compared with experimental results, showing excellent agreement.

Prediction of matrix-initiated transverse failure in polymer composites

A study has been conducted of failure in unidirectionally-reinforced fiber composites loaded in tension normal to the fibers. The case considered is when this failure is governed by failure of the matrix rather than fiber/matrix debonding. Both yielding and cavitation-induced brittle failure of the matrix are considered. The latter mode of failure was suggested previously as the likely mode to occur in epoxies under stress states that are purely or nearly hydrostatic tension. Three fiber packing arrangements (square, hexagonal and square-diagonal) with different fiber volume fractions were studied numerically by a finite element method to determine the local stress states. It is found that cavitation-induced brittle failure occurs much before yielding in all cases. Experimental data taken from the literature support this finding.

A criterion for crack initiation in glassy polymers subjected to a composite-like stress state

Three epoxy systems of interest as composite matrix materials are examined for their yielding and failure behavior under uniaxial, biaxial and triaxial stress states. Yield criteria applicable to glassy polymers, i.e. accounting for the hydrostatic stress effect on the deviatoric stress to yielding, are assessed. It is found that under stress states resembling those in matrix constrained between fibers, e.g. equibiaxial and equitriaxial tension, yielding is suppressed while brittle failure, presumably caused by crack growth from cavitation, occurs. A criterion for this mode of failure is proposed as the critical dilatational strain energy density. Experimental data are found to support this criterion.

Transverse Cracking and Stiffness Reduction in Cross Ply Laminates of Different Matrix Toughness

Cross ply laminates of (02,902)s configuration having AS4 graphite fibers in three epoxy resins of different toughness: 3501-6, Tactix® 556 and Tactix® 695, have been tested to determine their transverse cracking behavior and the associated mechanical response under longitudinal tensile loading. The test data are analyzed using Talrejas con tinuum damage model [1-3]. The material constants needed in the model to predict the in- plane stiffness changes are determined. The measured Poissons ratio, which shows signifi cant change, is compared with the prediction of the model. The constants for the three materials are found to increase with the increase in their fracture toughness.

Continuum modelling of damage in ceramic matrix composites

Abstract A continuum model for determining mechanical response of ceramic matrix composites with damage is presented. The mechanisms of damage considered are those observed in unidirectionally fiber-reinforced ceramic matrix composites, viz. matrix cracking, fiber/matrix interfacial slip and fiber/matrix debonding. Four basic configurations of distributed damage at the microscopic level are treated: matrix cracks only, matrix cracks in conjunction with interfacial slip, debonds only and matrix cracks in conjunction with debonds. The elementary damage entities, i.e. cracks, debonds and slipped surfaces, are represented by second-order tensors which are regarded as internal variables. Using a thermodynamics based formulation of constitutive relationships with internal variables, the stress-strain-damage relationships are derived. Specific expressions are given for changes in the engineering elastic moduli in terms of the densities of damage entities for sparsely distributed damage.

A synergistic damage-mechanics analysis of transverse cracking in [±θ/904]s laminates

Abstract The deformational response of [± θ /90 4 ] s laminates under longitudinal tensile loading is treated by a synergistic approach that combines continuum damage mechanics (CDM) and micromechanics. The constraint of θ ° plies on transverse cracks in 90° plies is represented by a crack-opening displacement (COD) parameter in the CDM model and is expressed in terms of the ply properties and ply thickness ratios on the basis of a finite-element calculation. A methodology is proposed for predicting the laminate stiffness variations with crack density and applied strain (or stress) for various values of ply orientation θ and is found to give good results.