John J. Engblom

Analysis of progressive failure in composites

Abstract An incremental failure accumulation technique is presented for angle-ply, cross-ply and uniaxial composite laminates. Piecewise smooth failure criteria that distinguish between the failure modes are implemented in a finite element analysis with shear deformable elements. For each load increment, these criteria are checked within each lamina. As failure is detected, the material properties of the lamina are modified. Equilibrium iterations are performed before incrementing the load to track further damage in the laminate and, finally, the ultimate failure of the laminate. This technique of progressive failure is illustrated for uniaxial tension and four-point bending problems.

FINITE ELEMENT FORMULATION INCLUDING INTERLAMINAR STRESS CALCULATIONS

Abstract A quadrilateral plate element is developed on the basis of utilizing the compatibility equations to obtain the in-plane stresses, and the equilibrium equations to obtain both transverse shear and normal stresses. A plate as opposed to shell or solid formulation serves to provide efficient solutions for thin to moderately thick laminated composite configurations. The element formulation involves relaxation of the Kirchhoff hypothesis via superposition of a shear rotation upon a midplane rotation. The displacement field is carefully selected to obtain the desired transverse stress variation. Results are compared to both closed form and numerical solutions.

Finite Element Plate Formulation Including Transverse Shear Effects for Representing Composite Shell Structures

A finite element formulation for the analysis of thin to moderately thick laminated composite shell structures is presented. A plate type element is developed with shear effects included by relaxing the Kirchhoff-Love hypothesis and prescribing the neu tral surface displacements independently from the rotations. The in-plane layer stresses are calculated using the constitutive equations. Once the in-plane stress variation has been obtained, the equilibrium equations are integrated to obtain the transverse shear and nor mal stresses. Two example problems are considered herein. For symmetric angle-plied or unidirectional winding it has been found that a pressurized cylinder, in addition to expand ing radially, also rotates about its axis. This contradicts the assumption that a symmetri cally wound cylinder under pressure exhibits axisymmetric deformation; thus a full cylin der model must be analyzed to produce the actual deformation. Laminated circular cylindrical shells are also analyzed with both clamped and simply supported ends in order to observe the action of transverse interlaminar shear and normal stresses. It is confirmed that near a load or structural discontinuity (restrained end), interlaminar stresses of con siderable magnitude occur and thus must be taken into account if delamination is to be avoided.

Finite Element/Penalty Function Method for Computing Stresses near Debonds

A shear deformable, finite element penalty formulation is developed for predicting stress fields, particularly interlaminar shear and normal stresses, in thick composite laminates and near a delaminated free edge in a laminated plate. A fully three-dimensional 20-noded finite element is coupled with the feature of integrating the equilibrium equations to compute interlaminar shear stresses and characterize three-dimensional stress fields. As an alternative to using the constitutive equations, the integration of the equilibrium equations provides an improved variation of interlaminar shear stresses through the thickness. Penalty functions are utilized in the formulation to represent continuity or discontinuity between layers of elements. Proficient use of these penalty functions allows simple definition of critical interfaces in a composite laminate where delamination has occurred. The flexibility of the formulation permits the consideration of different sizes of debonds without having to create a new model. In this paper, thick composite laminates are considered to demonstrate the improved variation of interlaminar shear stresses computed by integrating the equilibrium equations. Finally, a [0 deg/90 deg/0 deg] undelaminated plate subjected to uniform axial extension is compared with the same geometry containing a free-edge debond, one ply thickness in depth.

Transverse Stress Predictions for Thin-to-Thick Composite Structures: Shear Deformable Finite Element Penalty Formulation

A shear deformable finite element formulation for laminated composite plate and shell structures is extended so that thin as well as thick geometries can be studied. This is accomplished by a specially constructed layering of elements in the ‘thickness’ direction. Adjoining layers are mathematically coupled at common interlaminar boundaries by use of a penalty parameter formulation. Since each element has simply midsurface nodal points at which displacements/rotations are prescribed, constraint equations serve to relate motion at layer midsurfaces to motion at layer interfaces. Continuity in each interface, i.e. between two layers, is represented by a set of three penalty parameters. Two of these parameters provide continuity of interlaminar shear stresses across the interface, while the third parameter provides continuity of interlaminar normal stress. In modelling actual structures, the degree of layering as well as specification of the penalty parameters can be extensively varied to account for changes in geometry, geometric discontinuities and the like.

A shear deformable, doubly curved finite element for the analysis of laminated composite structures

Abstract A doubly-curved, shear-deformable finite element is developed for the analysis of laminated composite structures. The Kirchhoff hypothesis is relaxed to allow for shear deformations; as a result, three independently prescribed rotations as well as three displacements are specified at each of the eight nodes of the element. The constitutive equations are utilized to calculate the in-plane stresses for each layer of the laminated structure. In order to establish an appropriate variation through the thickness, the transverse shear stresses are found by integrating the equilibrium equations for each layer. An integration procedure using a finite difference approach is performed to evaluate the transverse shear stresses. Excellent results have been achieved for a three-layered, helically-wound cylinder with simply-supported and clamped ends.

Fiber Local Micro Buckling of Continuous Glass-Fiber Reinforced Rectangular Hollow-Cored Commingled Recycled, Plastic Extrusions under Bending

The experimental results of fiber local micro-buckling and partial failure due to the fiber micro buckling of extruded continuous glass fiber reinforced hollow-cored recycled plastic lumber under four point bending are presented in the paper. The test specimens are commercially produced E-glass roving reinforced recycled HDPE extrusions (2.5″ by 3.5″ hollow-cored cross section and 42″ in length) with/without coupling agent and different color pigment. The test results show that the fiber micro buckling causes a significant drop in strength of the extruded lumber and subsequently causes the matrix cracking that will lead to the total structural failure. It becomes a concern for the continuous fiber reinforced plastic beams used in construction fields because most of them are under bending loads. The micro buckling occurs on the compressive half of the hollow beam when it undergoes bending loads. The critical compressive stress is reasonably close to the predictions of Rosen’s model if considering a factor of 0.63 as proposed by Hahn and Williams (1986). For the specimens without the additives and coupling agent, the results show no sign of fiber micro buckling though their strength is much lower than those with the additives and coupling agent. In addition, it is shown that the fiber micro buckling initiates the matrix longitudinal as well as latitudinal cracking.

Computational and Experimental characterization of continuously fiber reinforced plastic extrusions: Part II. Long-term flexural loading

Experimental characterization of time-dependent properties for rectangular hollowcored, continuous fiber reinforced, commingled recycled plastic extruded forms under long-term (creep) flexural loading has been presented in this paper. Finite element based computer models have been developed to predict the effects of damage progression in such reinforced extruded plastic forms. In the long-term (creep) tests, reinforced and unreinforced extrusions with varying compositions were used as specimens. These extruded specimens were submerged in heated water and subjected to different loads. Experimental results indicate that fiber micro-buckling and fiber–matrix interface failure occur during the creep loading environment. The fiber micro-buckling occurs over time, compared with similar but dramatic damage that occurs in a short-period of time during short-term (static) loading, as discussed in Part I of this work. Experimental data also shows that these damage modes significantly reduce the long-term (life cycle) flexural properties, and the specimens with a coupling agent demonstrated much better performance. “Damage dependent” finite element models were developed using different material property types to represent the glass-fiber roving, fiber–matrix interface and plastic matrix respectively. Material nonlinearity of the plastic matrix has been incorporated along with stress-based failure criteria to account for fiber–matrix interfacial shear failure and local fiber micro-buckling. A user-defined material model has been incorporated into an industrial standard finite element software package to accommodate damage progression. The developed finite element based model(s) have correlated well with the long-term (creep) test results, and can provide a valuable tool in designing reinforced plastics for long-term loading conditions.

Stability Analysis of Composite Plates

The critical buckling load of a composite plate is calculated with a FEM formulation that uses a new shear deformable quadrilateral element.The effects of material anisotropy. meshsize, aspect ratio, number of laminae and the lamina orientation angles are studied. The results show that the classical plate theory is inadequate to obtain accurate results since the transverse shear stresses are not taken into account properly. The critical loads obtained in the present approach, correlate very well with those of closed form solutions and three dimensional formulations. Thus the present approach increases the computational efficiency and provides a simpler formulation.