Three-Dimensional Elastic-Plastic Finite Element Analysis of Three-Point Bend Specimens

Elastic-plastic finite element analyses of the three-point bend specimen geometry were performed as part of an investigation to study the application of the crack tip opening displacement (CTOD) fracture parameter to flawed pressure vessels. The elastic-plastic fracture mechanics (EPFM) parameters, CTOD and J, were determined from the results of two- and three-dimensional finite element analyses. Three sizes of the preferred specimen geometry (thickness, t, by depth, 2t, by span, 8t) and five steels with varying stress-strain characteristics were considered. To obtain experimental results for comparison, tests were conducted in accordance with the procedure outlined in British Standard BS 5762:1979, “Methods for Crack Opening Displacement Testing.”

Analytical CTOD values were determined from the finite element nodal displacements using the 90-deg intercept procedure proposed by Rice. Semi-empirical CTOD values were computed by applying the formula in BS 5762:1979 to the computed clip-gage displacements. The finite element analyses were demonstrated to yield CTOD values consistent with the experimental values for the three-point bend specimen. This represents the first step in verifying use of the finite element method to predict applied CTOD values in more complex structures.

The J-integral was determined from two-dimensional finite element results using direct contour integration. The J-integral values were used in conjunction with the corresponding CTOD values to develop an improved correlation between J and CTOD for a wide range of material characteristics.

The paper concludes with a discussion of “level of performance” for the three-point bend specimen. The level of performance is characterized by the value of CTOD at various sizes of the plastic zone as a function of specimen size and material. Three levels of performance are identified: (1) K_Ic as defined by ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials (E 399), (2) development of a plastic hinge, and (3) initiation of ductile fibrous tearing. An understanding of these levels of performance and their relation to values of CTOD is essential in developing realistic requirements for material toughness.