# Determination of Stress Intensity Factors under Shock Loading Using a Diffraction-Based Technique
###### Abstract  
An experimental optical method has been developed for the measurement of opening and sliding notch face movements. The light passing through a thin slit is monitored by a photodiode detector. Two parts of the slit are fixed independently on the notch faces of the simulated crack. Dynamic variations of the notch face movements are recorded as an electric signal by an oscilloscope. The sensitivity of such displacement measurement is comparable with the wavelength of light. Dynamic mixed-mode stress intensity factors under shock loading were evaluated from the data obtained and subsequently compared with a numerical simulation by ANSYS software. As it was approved, the technique has shown sufficient sensitivity, good linearity, and measurement reliability. Due to its non-destructive nature and overall robustness, the arrangement is applicable even for structural component condition determination taking into consideration potentially unknown boundary conditions and the non-linear character of mechanical parameters.  
optical measurement; diffraction-based technique; dynamic stress intensity factor; mixed-mode loading +
Footnote †: journal: Applied Sciences  
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**Multi-Scale Analysis of the Stress Intensity Factors under Shock Loading Using a Diffraction-Based Technique**  
**[PERSON]. [PERSON], [PERSON], O.  
Measurement of DSIF at fracture initiation time at three-point bend specimen and numerical solution for the same problem can be found in [6]. Described methodology of determining the dynamic fracture toughness using a combination of experiments and numerical approach is given in [7]. The value of DSIF was achieved using a measured applied force with a calculated specimen response to a unit impulse force. The derived formula for DSIF of three-point bend specimen using the vibration analysis method and corresponding dynamic test on modified Hopkinson pressure bar is presented in [8]. The dynamic fracture test using Split-Hopkinson pressure bar and measured mixed-mode crack propagation velocity by synchronized measuring system can be found in [9]. The dynamic initiation stress intensity factor was calculated using the experimental-numerical method, and the crack path was predicted numerically. In [10], the effect of holes on dynamic crack propagation under impact loading was investigated, which demonstrated that the suppressing effect on moving crack increased inversely proportional to the spacing of holes.  
There are also a lot of numerical methods for describing the behavior of cracked bodies under impulse load. In [11], using finite element analysis to evaluate reaction force in three-point bend specimens, the effect of time step length, the number of considered eigenmodes, and specimen overhang on the achieved anvil force and DSIF were investigated. The meshless finite block method used for the calculation of mixed-mode dynamic stress intensity factors is introduced in [12]. Another meshless material point method and a description of algorithms for fracture parameters in 3D dynamic problems and their comparison with finite element method (FEM), finite difference method, dynamic boundary element method, and static theories are listed in [13].  
This paper presents an experimental-numerical study of the possibility of applying an optical technique that can be used for the experimental evaluation of DSIF. The basic principle of the method consists of the photoelectric sensing of light passing through a slit mounted on notches simulating a crack. With this approach, it is possible to measure fast notch face dynamic movements in mutually perpendicular directions separately. When applying a relatively short force impulse due to a specimen's self-period of oscillation, it can be used as a non-destructive method for describing the structural component condition. On the other hand, it can be used for non-propagating both slow and fast crack face movements and static conditions.