A simplified method of determining the time dependence of the dynamic stress intensity factor in testing beam specimens in three-point impact bending

Modal Approach for Processing One‐ and Three‐point Bend Test Data for Dsif‐time Diagram Determination Part I—theory

“…where h(2) K (t) is the DSIF-response of the unsupported specimen to two simultaneous unit impulses from the supports, R(t)=0 for t∏0 [21][22][23]. Here and below we assume non-zero contact forces F(t) and R(t) to be positive, i.e.…”

“…The second method is to use the modal superposition method to expand the impact DSIF-response functions into series with respect to eigenmodes of the specimen model. This method (directly or indirectly) was used previously for different beam models of the specimen [14][15][16][17]21]. When the specimen is considered within a framework of plane linear elasticity, the most general form of impact DSIF-response functions is (see details in the Appendix)…”

Modal Approach for Processing One‐ and Three‐point Bend Test Data for Dsif–time Diagram Determination. Part Ii—calculations and Results

“…Starting from the pioneer work of Nash [1], different beam theories have been used for modelling the impact fracture specimen the most frequently. Therefore, the main ideas of this approach and corresponding equations will not be presented here (see Refs [2][3][4] for details). Using the Euler-Bernoulli beam model (more sophisticated Timoshenko's theory does not lead to qualitatively new results [4,5]), eigenfrequencies and weight coefficients were calculated for c=L /W = 3, ..., 10 (g(2) j were determined for c=4, ..., 10 and S/W =4) and l=0.1, ..., 0.9.…”