Paul A. Lagace

Quadratic Stress Criterion for Initiation of Delamination

The initiation ofdelamination in graphite/epoxy specimens was investigated both analyt ically and experimentally. Three specific laminate families were investigated: [±15 n ] s , [± 15 n /0n]s, and [0n / ± 15n] s with the normalized effective ply thickness, n, varying from one to five. Delamination initiation was determined to have occurred when a drop in load was detected and a delamination was observed on a replication of the specimen edge. Measured initiation stresses were correlated using the strain energy release rate approach and the Quadratic Delamination Criterion introduced herein. The strain energy release rate approach was unable to accurately correlate data for two of the three laminate fami lies. The data clearly shows that the critical value of strain energy release rate is dependent on ply thickness. The Quadratic Delamination Criterion, an average stress criterion which compares the calculated out-of-plane interlaminar stresses to their related strength param eters, is proposed and shows excellent correlation with the delamination initiation stress data.

Transient response of graphite/epoxy and Kevlar/epoxy laminates subjected to impact

The influence of different parameters on the impact behavior of laminated composite plates is considered analytically. A Rayleigh-Ritz energy method was used to spatially discretize the time-varying boundary value problem and a set of coupled, ordinary differential equations in time were obtained based on the discretized system Lagrangian. The effects of shearing deformation, bending-twisting coupling, and nonlinear contact behavior were included in the model. The resulting equations were integrated using the implicit Newmark beta method without the effects of rotary inertia. The results indicate that the effective mass of the plate is often an important effect in the response to impact events. In general, the influence of the constitutive behavior dominates for very low velocity impact, whereas the target mass properties become more important as the impactor velocity increases. This importance of mass clearly shows that impactor kinetic energy is not sufficient to characterize the impactor as the impactor mass is shown to have a large influence on the resulting dynamic behavior. In addition to these parameters, the effects of preload and material properties are considered and discussed.

Closed Form Solutions for the Interlaminar Stress Field in Angle-Ply and Cross-Ply Laminates

The solution to the problem of interlaminar stresses at a straight free edge in a com posite laminate is obtained in closed form for two special and important cases: angle-ply and cross-ply laminates. These solutions are derived using the Force Balance Method and the principle of minimum complementary energy. The results are favorably compared to the predictions of other analyses found in the literature. The solution procedure is found to be simpler and more efficient than other analytical methods. In addition, for some special cases of cross-ply laminates, the solution is shown to be identical to the predictions of a modified plate theory that includes through-the-thickness stretching.

A preliminary proposition for a test method to measure (impact) damage resistance

A preliminary proposal for a test to determine the impact damage resis tance of composite materials and their structures is offered. This test is centered on the utility of contact force as a parameter directly related to the damage that occurs during the event. This is demonstrated through work previously published as well as via new experi ments conducted on various graphite/epoxy material systems and laminates in both mono lithic laminate and sandwich configurations. Static indentation and impact tests were con ducted and show a similarity in regards to the structural response and the damage that occurs. This proposal is discussed in terms of the laminates tested and the results, the tests general applicability and utility, and issues that need to be addressed further. The proposal makes a significant step towards providing a common reference point and language for (impact) damage resistance.

Impact Resistance of Composite Sandwich Plates

The impact resistance of composite sandwich plates has been studied ex perimentally. Several panels with [±45/0] s Hercules AS4/3501-6 graphite/epoxy face- sheets were manufactured with different types of cores: aluminum honeycomb, Nomex honeycomb and Rohacell plastic foam with three different core thicknesses, 3.2 mm, 6.4 mm and 9.6 mm. These panels were impacted at a range of low energy levels (less than 10 joules). X-ray photos were taken to determine the extent of delamination damage, and the panels were sectioned so the location and lengths of delaminations, debonds, and core damage could be determined. Extensive delamination and core damage was found in spec imens with no visible surface damage. Core damage in the Rohacell consisted of cracks in the foam while the damage in the honeycomb consisted of the buckling of cell walls. The largest delaminations were found in the interface between the bottom two plies (-45°/+45°) of the top facesheet.

Influence of mechanical couplings on the buckling and postbuckling of anisotropic plates

An experimental and analytical investigation was conducted on the buckling and postbuckling behavior of generally anisotropic graphite/epoxy laminated plates. The elastic (mechanical) couplings inherent in unbalanced and unsymmetric laminates have been isolated, including bending-stretching, the stretching-shearing and bending-twisting combination, and stretching-twisting coupling. Laminates with a 254 mm square test section were manufactured from Hercules AS4/3501-6 graphite/epoxy and tested in uniaxial compression to failure with clamped and simply supported sides. Rayleigh-Ritz and finite-element linear analytical solutions were used to predict the buckling loads and mode shapes. The Rayleigh-Ritz analysis was extended to the nonlinear regime by introducing von Karmans large deflection strain-displacement relations to predict the compressive postbuckling (prefailure) behavior. The results show that the introduction of elastic couplings reduces the buckling loads, although the concept of bifurcation cannot be clearly applied to unsymmetric laminates.

Postbuckling behavior of laminated plates using a direct energy-minimization technique

The postbuckling behavior of rectangular, flat, laminated, or sandwich plates is investigated using a model including the different anisotropic material coupling terms, the effect of transverse shear deformation, nonlinear strains, and initial out-of-plane imperfections. The Rayleigh-Ritz method is used to discretize the problem and, instead of solving a set of partial-diffe rential equations, a direct energy-minimization technique is used to solve the problem numerically. The solution procedure used is described in detail in the first part of this paper, and the results obtained for three example problems are presented in the second part. These results correlate well with corresponding experimental data that are also presented.

Notch sensitivity of graphite/epoxy fabric laminates

Abstract The notch sensitivity of graphite/epoxy fabric laminates was experimentally investigated by conducting tensile tests on specimens made from woven fabric prepreg and those of similar construction made from unidirectional tape prepreg. Generally, the fabric laminates exhibited notch sensitive behavior similar to that of their counterpart tape laminates. The Mar-Lin equation was used successfully to correlate the fracture stress of notched fabric laminates, as it has been for tape laminates when delamination is not important. However, the fabric laminates do not exhibit failure due to splitting as is often seen in tape laminates. This increases resistance to fracture and results in higher notched fracture stresses for some fabric laminates.

A Consistent Engineering Methodology for the Treatment of Impact in Composite Materials

An approach is formulated to treat the behavior of composites subjected to impact as the sequential effect of a number of events. The sequence for the analysis of im pact presented here is as follows. First, a global analysis of impact of the structure is con ducted. In this study, a plate is analyzed in a time marching scheme to properly account for nonlinearities during the impact event. This provides loads introduced into the struc ture during impact. These loads are then introduced into a local deformation and strain re sponse model just below the impactor to refine the analysis in the local region where damage occurs. Damage is predicted in the laminate on a ply-by-ply basis. Excellent agreement between the models and test data taken during the impact event is found. This is denoted as the Damage Resistance portion of the problem. Given the pre-existing damage, an analysis of the damaged structure is conducted. This entails using an average strain criterion for fiber-dominated fracture around the damage and a sublaminate buck ling analysis for compression loading. Good agreement is found between the analysis and experimental data. This is denoted as the Damage Tolerance portion of the problem. Finally, all of the models are combined to provide combined Damage Resistance/Damage Tolerance curves for useful design data.

Buckling of unsymmetric composite laminates

Abstract An initial experimental and analytical investigation was conducted to examine the effects of the inherent mechanical couplings exhibited in fully anisotropic (i.e. unsymmetric) graphite/epoxy laminates on the buckling loads and mode shapes. Experimental techniques were devised to test 254 mm square plates of AS1/3501-6 graphite/epoxy under uniaxial compressive load with free, simply-supported and clamped edges. The results indicate that the mechanical couplings, especially those which relate stretching and bending behavior, cause out-of-plane deflections prior to buckling and reduce the buckling load significantly, i.e. the load at which out-of-plane deflections become large. The analytical results also show that the buckled mode shapes exhibit twisting due to the mechanical couplings. Suggestions are offered for improvements in the experimental and analytical techniques to better understand these phenomena.