13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- notched tension and punching are run to identify equivalent failure strain under positive stress trixiality. Force-displacement curves from both test and simulation are compared to determine failure moment and extract evolution of stress triaxiality of failure element in each test. To determine stress triaxiality of critical failure point during the whole loading process, an average value of the stress triaxiality of each type of test was defined in the range from 0 to ̅ = 1 ̅ ∫ ̅ ̅ 0 (3) Mae [6] studied the ductile fracture locus of PP/EPR/talc Blend, using this kind of stress triaxiality approximation method as well. However, this approximation of stress triaxiality is reasonable only when stress triaxiality varies a little during the whole loading process. For polymeric materials, strain concentration is common, which leads to greatly varied stress triaxiality during the loading process especially for static loading. Y. Bai and T. Wierzbicki [2] used damage evolution rule as new popular fracture predictive technique. A linear incremental relationship was assumed here between damage indicator and equivalent plastic strain ̅ ( ̅ )=∫ ̅ ( , ̅) ̅ 0 (4) where is stress triaxiality, ̅ is lode angle parameter, and is equivalent failure strain function. Both of the two stress direction parameters are unique functions of the equivalent plastic failure strain. A material element is considered to fail when the limit of ductility is reached, ̅ = ̅ , so that, ( ̅ )=1. In this paper, we only consider 2D fracture locus in positive stress triaxiality, thus supposing that failure strain is only dependent of stress triaxiality. ( ̅ )=∫ ̅ ( ) ̅ 0 ( ≥0) (5) To determine the explicit expression of function f, optimization method is required. The optimization objective function is as follows. min{( −1) 2 +( −1) 2 +( −1) 2 +( −1) 2} (6) where , , and are respectively damage indicator from tension, shear, notch tension and punch test. Quite a few literatures show that ductile polymeric materials turn to be brittle with the increase of strain rate. Hence, in this paper, function ( ) is studied under static loading and dynamic loading respectively. Table 1 is the test matrix for calibrating failure parameters.
RkJQdWJsaXNoZXIy MjM0NDE=