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A quasi three dimensional finite element analysis was used to analyze the edge stress problem in four-ply, composite laminates. Convergence studies were made to explore the existence of stress singularities near the free edge. The existence of stress singularities at the intersection of the interface and the free edge is confirmed.
Dynamic mechanical measurement results are presented for the case of carbon fiber-reinforced, epoxy matrix composite laminates subjected to loading perpendicular to the lamination plane, as well as for neat epoxy resin under the same conditions, where temperatures ranged between 20 and 200 C and deformation levels lie within the linear viscoelastic region. In-phase and out-of-phase stiffnesses are found to become superposed, forming master curves that cover a 12-decade frequency range. The application of a master curve scaling procedure shows that the in-phase stiffness has the same shape, and out-of-phase stiffness has the same dispersion, for all laminates irrespective of stacking sequence and are, in turn, nearly identical to those for the neat epoxy resin. An empirical function is found for the relaxation modulus which, when converted to a dynamic modulus, yields good overall agreement for both of the dynamic stiffness components as a function of frequency.
The short-wavelength buckling (or the microbuckling) and the interlaminar and inplane shear failures of multi-directional composite laminates loaded in uniaxial compression are investigated. A laminate model is presented that idealizes each lamina. The fibers in the lamina are modeled as a plate, and the matrix in the lamina is modeled as an elastic foundation. The out-of-plane w displacement for each plate is expressed as a trigonometric series in the half-wavelength of the mode shape for laminate short-wavelength buckling. Nonlinear strain-displacement relations are used. The model is applied to symmetric laminates having linear material behavior. The laminates are loaded in uniform end shortening and are simply supported. A linear analysis is used to determine the laminate stress, strain, and mode shape when short-wavelength buckling occurs. The equations for the laminate compressive stress at short-wavelength buckling are dominated by matrix contributions.
A finite element modeling methodology is developed for the hierarchical, global/local analysis of laminated composite plates. The method incorporates a new variable kinematics, displacement-based, finite element that is developed using a multiple assumed displacement field approach. The variable kinematic elements provide a great degree of flexibility in defining the transverse (through thickness) variation of the assumed displacement field. The resulting finite element model permits different subregions of the computational domain to be described by different mathematical models. Enforcing displacement continuity along subregion boundaries requires only the specification of certain homogeneous essential boundary conditions, thus avoiding the inconvenience of multi-point constraints, penalty function methods, or special transition elements.
The experimental behavior of spinning, pre-twisted laminated composite plates was investigated. The purpose of these experiments was to establish an experimental database consisting of strain, deflections, and natural frequencies as a function of rotational velocity. Six different plate sets were tested, that included three different stacking sequences (two symmetric, one asymmetric), two different initial twist levels (0 deg, 30 deg), and two different initial twist axis locations (midchord, quarter-chord). The plates were spin tested at four different combinations of pitch and sweep. It was observed that the location of the pretwist axis and the level of pretwist greatly affects the strain and deflections of the spinning plate, while only the pretwist level affects the measured natural frequencies.
ANISAP is a 3-D finite element FORTRAN 77 computer code for linear elastic, small strain, analysis of laminated composites with arbitrary geometry including free edges and holes. Individual layers may be isotropic or transversely isotropic in material principal coordinates; individual layers may be rotated off-axis about a global z-axis. The laminate may be a hybrid. Three different isoparametric elements, variable order of gaussian integration, calculation of stresses at element boundaries, and loading by either nodal displacement of forces are included in the program capability. Post processing capability includes failure analysis using the tensor polynominal failure criterion.
A Vlasov type beam theory for open-cross-section thin-walled circular beams constructed from laminated composite materials is presented. Comparisons are made to a branched shell analysis for a series of laminated thin-walled open cross-section curved beams. The results show that reasonable accuracy can be obtained for a variety of beam types, with a considerable reduction in analysis cost.
A series of tensile tests have been carried out to determine the effect of specimen size on the mechanical response of composite laminates which were scaled at the sublaminate level. Two material systems were studied AS4/3502 and AS4/PEEK. The effect of specimen size was examined with respect to first ply failure stress, delamination stress, ultimate stress, and strain at failure. In general, the strength of scaled specimens increased with increasing specimen size. Several models from the published literature were applied with varying degrees of success to predict the first ply failure and delamination stress in scaled composites. It was found that the effect of ply constraint is not addressed properly in the existing theories.
An integrated mechanics theory has been developed for the modeling of composite damping from the micromechanics to the laminate level. Simplified, design oriented equations based on hysteretic damping are presented for on-axis plies, off-axis plies, and laminates including the effect of temperature, moisture, and interply hysteretic damping. The temperature rise within vibrating composite laminates resulting from strain energy dissipation is also modeled, and their coupled hygro-thermo-mechanical response is predicted. The method correlates well with reported damping measurements. Application examples illustrate the effect of various ply, laminate, and hygro-thermal parameters on the overall damping performance of composite laminates.
A method is presented for estimating the stress intensity factor characteristic of crack extension in a specially orthotropic advanced fiber composite laminate, based on the elastic properties and ultimate principal strengths of a lamina, the laminate construction, and the experimentally determined value of the characteristic stress intensity factor of an arbitrary angle-plied, midplane symmetric laminate. A comparison of the results obtained from this method with limited experimental data for graphite/epoxy laminates indicates that the method is quite accurate for this particular material system. The predictive method is also used, in conjunction with experimental data, to estimate the size of a damage zone surrounding the crack tip.
A three dimensional finite element and dynamic analysis has been made for a layered fiber-reinforced composite laminate subjected to a given impact loading. Central difference method is employed in this analysis. The numerical results for the transient response of the laminate are presented.
A curved beam type of test specimen is evaluated for use in determining the through-the-thickness strength of laminated composites. Two variations of a curved beam specimen configuration (semicircular and elliptical) were tested to failure using static and fatigue loads. The static failure load for the semicircular specimens was found to be highly sensitive to flaw content, with the specimens falling into two distinct groups. This result supports the use of proof testing for structural validation. Static design allowables are derived based on the Weibull distribution. Fatigue data indicates no measured increase in specimen compliance prior to final fracture. All static and fatigue failures at room temperature dry conditions occurred catastrophically. The elliptical specimens demonstrated unusually high failure strengths indicating the presence of phenomena requiring further study. Results are also included for specimens exposed to a wet environment showing a matrix strength degradation due to moisture content. Further testing is underway to evaluate a fatigue methodology for matrix dominated failures based on residual static strength (wearout).
A curved beam type of test specimen is evaluated for use in determining the through-the-thickness strength of laminated composites. Two variations of a curved beam specimen configuration (semi-circular and elliptical) were tested to failure using static and fatigue loads. The static failure load for the semi-circular specimens was found to be highly sensitive to flaw content, with the specimens falling into two distinct groups. This result supports the use of proof testing for structural validation. Static design allowables are derived based on the Weibull distribution. Fatigue data indicates no measured increase in specimen compliance prior to final fracture. All static and fatigue failures at room temperature dry conditions occurred catastrophically. The elliptical specimens demonstrated unusually high failure strengths indicating the presence of phenomena requiring further study. Results are also included for specimens exposed to a wet environment showing a matrix strength degradation due to moisture content. Further testing is under way to evaluate a fatigue methodology for matrix dominated failures based on residual static strength (wearout).
Mathematical development and some computed results are presented for Mindlin plate and shell elements, suitable for analysis of laminated composite and sandwich structures. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (no shear locking), have no spurious membrane energy (no membrane locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration. Artificial out-of-plane rotational stiffnesses are added at the element level to avoid convergence problems or singularity due to flat spots in shells. This report discusses a 6-node curved triangular element and a 4-node quadrilateral element. Findings show that in regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is approximately equivalent to the conventional 8-node quadrilateral with integration. The 4-node quadrilateral (MB4) has very good accuracy for a 4-node element, and may be preferred in vibration analysis because of narrower bandwidth. The mathematical developments used in these elements, those discussed in the seven appendices, have been applied to elements with 3, 4, 6, and 10 nodes and can be applied to other nodal configurations.
A description is given of a semi-empirical, deterministic analysis for prediction and correlation of fatigue crack growth, residual strength, and fatigue lifetime for fiber composite laminates containing notches (holes). The failure model used for the analysis is based upon composite heterogeneous behavior and experimentally observed failure modes under both static and fatigue loading. The analysis is consistent with the wearout philosophy. Axial cracking and transverse cracking failure modes are treated together in the analysis. Cracking off-axis is handled by making a modification to the axial cracking analysis. The analysis predicts notched laminate failure from unidirectional material fatique properties using constant strain laminate analysis techniques. For multidirectional laminates, it is necessary to know lamina fatique behavior under axial normal stress, transverse normal stress and axial shear stress. Examples of the analysis method are given.
The objective of the work reported in this presentation is to determine the in situ transverse strength of a lamina within a composite laminate. From a fracture mechanics standpoint, in situ strength may be viewed as constrained cracking that has been shown to be a function of both lamina thickness and the stiffness of adjacent plies that serve to constrain the cracking process. From an engineering point of view, however, constrained cracking can be perceived as an apparent increase in lamina strength. With the growing need to design more highly loaded composite structures, the concept of in situ strength may prove to be a viable means of increasing the design allowables of current and future composite material systems. A simplified one dimensional analytical model is presented that is used to predict the strain at onset of transverse cracking. While it is accurate only for the most constrained cases, the model is important in that the predicted failure strain is seen to be a function of a lamina's thickness d and of the extensional stiffness bE theta of the adjacent laminae that constrain crack propagation in the 90 deg laminae.
This report describes a continued effort on the development and application of the tensor polynomial failure criterion for composite laminate analysis. In particular, emphasis is given to the design, construction and testing of a cross-beam laminate configuration to obtain "pure' biaxial compression failure. The purpose of this test case was to provide to permit "closure' of the cubic form of the failure surface in the 1-2 compression-compression quadrant. This resulted in a revised set of interaction strength parameters and the construction of a failure surface which can be used with confidence for strength predictions, assuming a plane stress state exists. Furthermore, the problem of complex conjugate roots which can occur in some failure regions is addressed and an "engineering' interpretation is provided. Results are presented illustrating this behavior and the methodology for overcoming this problem is discussed.
The thermal analysis and the calculation of thermal sensitivity of a cure cycle in autoclave processing of thick composite laminates were studied. A finite element program for the thermal analysis and design derivatives calculation for temperature distribution and the degree of cure was developed and verified. It was found that the direct differentiation was the best approach for the thermal design sensitivity analysis. In addition, the approach of the direct differentiation provided time histories of design derivatives which are of great value to the cure cycle designers. The approach of direct differentiation is to be used for further study, i.e., the optimal cycle design.