# Determination of Stress Intensity Factors under Shock Loading Using a Diffraction-Based Technique
## 2 Materials and Methods
### Measurement and Results Evaluation  
To test the proposed measurement technique, an experimental study of two variants of notched steel specimens was carried out. Both the beam and L-shaped specimens (Figure 2) were positioned on rubber anvils supports. The second L-shaped specimen also had stabilization supports, realized by rubber from three sides to prevent contact with a fixed clamping mechanism. The clamping screws have been tightened only to the extent necessary to freely hold the specimen in place with no additional pressure. As known, the comparison of numerical simulation results with the experiment is often affected by the non-ideal rendering of the boundary conditions of the structural element fixation. Thus, when the experimental and numerical results are to be compared, the boundary conditions play a significant role. Especially in dynamic loading conditions, such factors as support friction, loss of contact with supporting element, stiffness of contact materials and anvils, or vibration of the supporting structure cannot be neglected. Figure 2: Geometry and boundary conditions of the investigated bodies (mm). L is the length of the given specimen. To prevent this effect of specimens mounting, soft supports with orders of magnitude lower natural frequency than the specimen frequencies were chosen. These frequencies were identified in spectral analysis with values of 83 Hz and 11 Hz for the beam and L-shaped specimen measurement, respectively. In such a case, the specimens can be considered as freely supported in a numerical model. No additional algorithms were then needed to find the contact between the specimen and supporting structure, and experimental measurements validation can thus be considered more reliable. Figure 2 shows the specimen's geometry. Both the elements were subjected to different loading values and load point positioning. The dynamic force was excited by the free fall of steel balls having 17.5 mm diameter for the beam specimen and 9.5 mm for the L-shaped specimen. The path of a free fall was, in both cases, one meter. The beam specimen was loaded in both symmetric pure mode I loading (one-point bending) and mixed-mode I/II loading conditions. To excite mixed mode for beam specimen, a non-symmetrical positioned load point was used. The Eccentricity of the impact point was then e = 0 mm and 30 mm for pure mode I and mixed-mode loading, respectively. For the L-shaped specimen, the angle orientation of the notch was chosen \(\alpha=45^{\circ}\), and a/W ratio was 0.5 in both cases, where a was the crack length. Using tensile testing, the Young's modulus of elasticity E = 202.44 GPa and 207.43 GPa, Poissons ratios v = 0.29 and 0.30 were achieved, and densities \(\rho=7857.78\) kg\(\cdot\)m\({}^{-3}\) and 7738.47 kg\(\cdot\)m\({}^{-3}\) were determined pycnometrically for beam and L-shaped specimens. To demonstrate the influence of stress waves with their free boundary reflections, the time duration of applied impulse force should be chosen to be several times shorter in comparison with the specimen's natural vibration period. Figure 3 shows the frequency content of in-plane vibrations of both the specimen examples obtained by signal analysis of the recorded notch face movements. Notation opening and sliding in Figure 3 means that the frequency spectrum was achieved from a mode I and mode II measurement setup, respectively. For a more complex evaluation of the data obtained using the diffraction method, absolute values of the measured quantities need to be known. Therefore, the time course and the calibration of the impulse force values induced by the free-falling ball were determined using a piezoceramic sensor. Recorded shock force waveforms, when hitting both the larger and smaller balls on the sample, are plotted in Figure 4. It shows the signals of the piezoceramics slab fixed between the sample and the striking ball. From this, the shape  
Figure 3: Frequency spectrum for beam and L-shaped specimen. of force-time function and impulse duration time was known.