A simplified method of determining the time dependence of the stress intensity factor in support-free impact bend testing of beam specimens

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

“…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)…”

“…For this method, the accuracy of calculated DSIF values depends mainly on the level of complexity of the specimen model used. Known specimen models have one [10], two [11,12], several [13] or theoretically infinite (in the case of beam [14][15][16][17] or 2D [17,18] models) numbers of degrees of freedom. Evidently the mathematical efforts needed to obtain the solution of corresponding problems grow with increasing model complexity.…”

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.…”

“…T wo-dimensional model Static SIF k (1) s Previously, k (1) s values have been determined for c=2, ..., 6, l=0.3, ..., 0.7 using the finite element (FE) program created by the author [2]. Recently, the calculations have been repeated for more detailed meshes and wider crack lengths range l=0.1, ..., 0.9 using the finite element program I. V. R Fig.…”

Forced Vibration Analysis in the Context of Dynamic SIFs in Impact Bending Tests

“…d k is a constant which is assumed to be the same as in the case of static three-point bend test. The motion history of bend specimen has been modeled earlier through beam theories (Kishimoto et al 1990;Marur1996;Marur 2000;Rokach 1998b;Andreikiv and Rokach IV 1989). However, in this paper a new analytical method is presented for an evaluation of displacement of a short beam with a crack subjected to arbitrary excitation(s).…”