(Received 14 March 2002; accepted 15 August 2002)
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Finite element (FE) analyses were performed on 3-point and 4-point bending test configurations of glass-epoxy and carbon-epoxy unidirectional tape beams tested at ninety degrees to the fiber direction to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS® finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens. For 3-point bend test configurations, both the linear and geometric non-linear 2D plane-strain and plane-stress analyses yielded similar results. The maximum tensile stresses under the center load nose calculated from the FE analysis were slightly lower than stresses predicted by beam theory. The difference (maximum of 4%) was greatest for the shortest span analyzed. For 4-point bend test configurations, both the plane-stress and plane-strain 2D linear analysis results agreed closely with beam theory except right below the load points. However, 2D geometric non-linear analyses deviated slightly from beam theory throughout the inner span as well as below the load points. Plane-stress results deviated from beam theory more than plane-strain results. The maximum tensile stresses between the inner span load points were slightly greater than the beam theory result. This difference was greatest (maximum of 4%) for configurations with the shortest spans between inner and outer load points. A contact analysis was also performed in order to investigate the influence of modeling the roller versus modeling the support as a simple boundary condition at one nodal point. The discrepancy between the FE and beam theory results became smaller (max. 2–3%) when the rollers were modeled in conjunction with contact analysis. Hence, the beam theory yields a reasonably accurate value for the maximum tensile stress in bending compared to 2D FE analysis. The FE results are primarily for guidance in the choice of beam thickness, width, and configuration. For the 3-point bend configuration, longer spans are preferred to minimize the error in beam theory data reduction. Similarly, for the 4-point bend configurations, a longer span between the inner and outer load noses, at least equal to the span between the inner load noses, results in less error compared to beam theory. In addition, these FE results indicate that the span between the inner load noses should not be too long to avoid obtaining a non-uniform maximum stress between the inner load noses. Finally, the 3D analysis indicates that specimens should be sufficiently wide to achieve a fully constrained state of plane-strain at the center of the specimen width.
ICASE NASA Langley Research Center, Hampton, VA
U.S. Army Research Laboratory, Hampton, VA
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