Application of line-spring model to dynamic stress intensity factor analysis of pre-cracked bending specimen

The dynamic fracture toughness KId of material is used to assess the integrity of a structure under impact loading. It is evaluated from instrumented impact tests such as pre-cracked Charpy tests or pre-cracked drop weight tests together with a numerical analysis of the dynamic stress intensity factor using a load-time history obtained from the tests. A two-dimensional dynamic finite element analysis is often utilized for this purpose. It requires large computer storage and run time. Therefore, it is inadequate to the quick evaluation of test data. In the present paper, a method for calculating the dynamic stress intensity factor of a pre-cracked bending specimen used in instrumented impact tests is newly proposed by making use of a line-spring model. A pre-cracked bending specimen is modeled by one-dimensional beam finite elements and a line-spring representing the stiffness or compliance of a cracked part. The present method enables the one-dimensional analysis of a two dimensional crack problem and thus the time variation of the dynamic stress intensity factor of a pre-cracked bending specimen can be obtained by making use of a personal computer within a few minutes. The present method is applied to the dynamic stress intensity factor analysis of a pre-cracked three-point bending specimen and a pre-cracked four-point bending specimen. The results obtained from the present method are in reasonably good agreement with the two-dimensional finite element solutions or the experimental results. A quick evaluation system for dynamic fracture toughness can be made by combining an instrumented impact test apparatus with a computer program based on the present method which runs on a personal computer. (author)