METHODOLOGY Results are presented for a pipe grade polyethylene, with a density of 940 kgm-3 and a Poisson’s ratio of 0.3. A three point bend geometry was modelled within the finite volume method using a 2D plane strain analysis. A cohesive law was used to describe the local separation along a prescribed crack path while the surrounding bulk was treated as elastic-plastic using incremental J2 flow theory. Numerical simulations were performed at an applied displacement rate of 0.1 mm/min and the predicted load – time traces compared to experimental measurements. The boundary conditions for the model are shown in Figure 2. Boundaries 1, 2, 3 and 5 were traction free while the prescribed traction – separation law was applied to boundary 4 along a single layer of cells. The specimen was assumed to be supported on a friction free roller. Making use of geometrical symmetry only half the specimen was modelled. Solution Domain Applied Displacement Rate 2 3 4 5 1 Figure 2: Boundary conditions for the three point bend geometry Both a single rate and rate dependent analysis was performed. In the first case the initial crack tip opening rate in the three point bend geometry was estimated as 0.006 mm/min and a traction - separation curve measured at that rate in a deep notched, high constraint geometry was used as the cohesive law for all cells along the crack path. In the second case a family of traction - separation curves measured over a range of displacement rates was incorporated into the numerical method. A fully implicit updating procedure was employed to determine the holding traction for each cell by calculating the values of cell displacement and displacement rates via a two way iteration process within each time step. Mesh sensitivity studies were performed and indicated that convergence in the predicted load was achieved for a cell size of 0.1 x 0.1 mm corresponding to a total of 112 cells along the prescribed crack path. RESULTS Single Rate Analysis Traction – separation curves at 0.006 mm/min and 0.004 mm/min were used to perform a single rate analysis and the load – time predictions were compared to the experimentally measured result as shown in Figure 3.
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