PSI - Issue 37
O.N. Belova et al. / Procedia Structural Integrity 37 (2022) 888–899
897
10
Author name / Structural Integrity Procedia 00 (2021) 000 – 000 ( ) 3/2 ( ) 2 3/2 5 0.1039 / a Pa mm = −
1 1 1 7 1 8 1 1 1 1 1 1 1
5 0.2100 / a Pa mm = 2 6 0.7569 / a Pa mm =
)
)
(
(
2 2 2 2 2 2 2 2 2 2
2
0.3400 /
a
Pa mm
= −
6
) )
)
( (
( (
5/2
5/2
7 0.2439 / a Pa mm = 3 8 0.1603 / a Pa mm =
0.4912 / 0.3276 /
a a
Pa mm Pa mm
= − = −
)
)
(
3
)
(
7/2
7/2
9 0.1089 / a Pa mm =
0.071 /
a
Pa mm
= −
9
)
)
(
( (
4 10 0.0064 / a kg mm = 11 0.1254 / a Pa mm = 5 12 0.0094 / a Pa mm = (
4
0.0115 / 0.3841 / 0.0213 /
a a a
kg mm Pa mm Pa mm
= − = − = −
10 11 12
)
)
9/2
9/2
)
)
(
(
5
)
)
(
(
11/2
11/2
13 0.0521 / a Pa mm =
0.0432 /
a
Pa mm
= −
13
)
)
(
( (
6
6 14 0.0024 / a Pa mm =
0.0071 / 0.0634 /
a a
Pa mm Pa mm
= − = −
14 15
)
)
(
13/2
13/2
15 0.0024 / a Pa mm = Here the values of the higher-order coefficients of the Williams series expansion are not given since they coincide with the coefficients obtained by the digital photoelasticity method. Thus, one can conclude that the coefficients are determined by both the approaches with good accuracy. In all crack tips there is good agreement between experimental and numerical results. The percentage error ranged from zero to five percent. Therefore, one can conclude that the experimental approach used here is reliable in determination of mixed mode parameters for plane problems. 4. Conclusions In this research the comprehensive experimental and numerical procedures for the evaluation of the crack-tip fields in a plate with two cracks are realized. The digital image processing of the experimental isochromatic and isoclinic data obtained in the framework of the photoelasticity method is performed. In this study higher order coefficients of the multi-parameter Williams series expansion for the stress and displacement fields in the vicinity of crack tips in the rectangular plate with two nonparallel cracks are obtained by the use of the digital photoelasticity method and finite element analysis. The higher-order terms in the Williams asymptotic expansion are considered. It allows us to have more accurate estimation of stress, strain and displacement fields and to extend the realm of validity for the Williams series expansion. The program is specially developed for the interpretation and processing of experimental data from the photoelasticity measurement experiments. The developed tool allows us to find points that belong to isochromatic fringes with minimal light intensity. The analysis of the experimental data uses a Java application programmed for the advanced determination of the fracture characteristics: coefficients of the Williams series expansion for the stress field in the vicinity of the crack tip. The tool allows us to collect experimental points from the photoelasticity tests on the cracked specimens. An automatic routine implemented as a Java application permits to determine the values of coefficients of higher order terms of the WE that describe crack-tip fields. These values are calculated using the over deterministic method which is also applied to the results of the finite element analysis of some mode I and mixed mode test geometry. Hence, the Java application provides an analytical reconstruction of the crack-tip stress field through the truncated WE and enables detailed analysis of the crack-tip stress field approximation. The tool proved to be an effective tool in increasing the accuracy of photoealstic data by sharpening the isochromatic fringe loops. The developed procedures simplify the analysis of the description of mechanical fields at a greater distance from the crack tip considerably. The digital image processing with the aid of the developed tool is performed. The points determined with the adopted tool are used further for the calculations of stress intensity factor, T-stresses and coefficients of higher-order terms in the Williams series expansion. The mixed mode fracture parameters, especially stress intensity factors, T-stresses and higher-order coefficients of the Williams series expansion are obtained for specimen configurations like plates with two interacting cracks using 1) the algorithm based on the classical over-deterministic method and 2) the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for minimization of the objective function. The procedure of the over-deterministic method is based on the stress field only. It is demonstrated that this approach
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