FE Stress Analysis
In this first order analysis of the shape, type and magnitude of the stress field associated with impact of a round body, some simplifying assumptions were made. These included the assumption of a static stress-strain relationship (which would be in error, as the response of PC would be visco-elastic and visco-plastic), while impact loading was converted to an equivalent static force. The first assumption is reasonable for a load applied over a short time (perhaps 0.001 s), while the second gives an 'average' stress over the impact duration. Typical mechanical properties for PC were assumed  of modulus of elasticity = 2.1 GPa, yield stress = 70 MPa and Poisson's ratio = 0.4. An impact energy of 0.2 J was assumed to be dissipated in 0.001 s, giving a force of 200 N, that was applied centrally to the outer skin between two adjacent webs.
The model was constructed for a PC sheet 900 mm long and 300 mm wide and is shown in Figure 1
. A and B denote fixed boundaries; C and D indicate X- and Y- symmetry, respectively; F is the impact force. Figure 2
shows the stress distribution contour in the outer skin (a) gives the von Mises stresses; (b) shows the tensile stresses in X direction; and (c) shows the shear stresses in the XY plane.
Figure 1 FE model of the PC sheet
Figure 2 Stress results from the FE model
The results are interesting in two respects. Firstly, peak values of the equivalent stress using von Mises yield criterion are around 70 MPa at the region of load application, which is up around the value of yield strength of the unweathered PC sheet. Secondly, the stress field has an elliptical shape with the major axis lying parallel with the webs of the skin. This correlates well with the observation of perforations that were elongated along the web direction. Finally, both shear and tensile stresses are present in the outer skin which supports the fractographic interpretation of the scalloped appearance.
The overall results are encouraging and certainly support the fractographic arguments.
Proceed to final part
of case study.
RP Nimmer and JT Woods (1992), An investigation of brittle fracture in ductile, notch sensitive thermoplastics, Polymer Science & Engineering Vol. 32 No. 16 pp.1126-1137.