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Numerical and experimental analysis of the notch effect on fatigue behavior of polymethylmethacrylate metal based on strain energy density method and the extended finite element method

Mustafa Moussaoui
Mustafa Moussaoui
, 
Abdelkhader Bendriss
Abdelkhader Bendriss
, 
Antar Tahiri
Antar Tahiri
, 
Ahmed Kellai
Ahmed Kellai
, 
Souad Zergod
Souad Zergod
, 
Hamza Djeloud
Hamza Djeloud
 and 
Brahim Kalil Hachi
Brahim Kalil Hachi
   | Dec 07, 2023
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Published Online: Dec 07, 2023
Page range: 401 - 413
Received: May 12, 2023
Accepted: Oct 02, 2023
DOI: https://doi.org/10.2478/msp-2023-0027
Keywords
© 2023 Mustafa Moussaoui et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1.

Rotary bending fatigue machine SM1090
Rotary bending fatigue machine SM1090

Fig. 2.

Manufacture of notched specimens
Manufacture of notched specimens

Fig. 3.

Recommended specimen sizes
Recommended specimen sizes

Fig. 4.

Stress components located at the point of the tip of the V-notch, in a polar coordinate system
Stress components located at the point of the tip of the V-notch, in a polar coordinate system

Fig. 5.

Circular zone nears tip of V-notch [8], 2γ = 2π − 2α
Circular zone nears tip of V-notch [8], 2γ = 2π − 2α

Fig. 6.

Control volume A0 for (a) sharp crack, (b) V-notch
Control volume A0 for (a) sharp crack, (b) V-notch

Fig. 7.

Control volume for U-notch: (a) mixed-mode I/II, (b) open mode I
Control volume for U-notch: (a) mixed-mode I/II, (b) open mode I

Fig. 8.

Bi-dimensional finite elements model
Bi-dimensional finite elements model

Fig. 9.

Crack propagation emanating from the V notch and the location of the control volume
Crack propagation emanating from the V notch and the location of the control volume

Fig. 10.

Comparisons of experimental and simulation values of ASED for sharp V notch and blunt U notch via fatigue life
Comparisons of experimental and simulation values of ASED for sharp V notch and blunt U notch via fatigue life

Fig. 11.

Approximation of ASED via fatigue life
Approximation of ASED via fatigue life

Fig. 12.

Location of the zone of maximum principal stress (crack initiation zone) for (a) U notch R = 2 mm and (b) V notch 2α = 140°
Location of the zone of maximum principal stress (crack initiation zone) for (a) U notch R = 2 mm and (b) V notch 2α = 140°

Fig. 13.

Effect of loading on averaged energy density for V-notch via fatigue life (logarithmic values)
Effect of loading on averaged energy density for V-notch via fatigue life (logarithmic values)

Fig. 14.

Effect of loading on averaged energy density blunt U notch
Effect of loading on averaged energy density blunt U notch

Fig. 15.

Effect of the number of mesh elements
Effect of the number of mesh elements

Correlations of experimental and numerical results

Experimental test
Notch type Number of test repetitions Min. number of cycles Max. number of cycles Standard deviation of cycles Minimum energy Maximum energy Standard deviation of energy
U-notch radius 0.2 mm 4 22640 201,865 82391.597 0.293 0.507 0.094
V-notch angle 20° 4 521,218 151,883 75622.87 0.229 0.461 0.107
V-notch angle 140° 4 11032 311,170 129198.70 0.166 0.504 0.143
U-notch radius 2 mm 5 25,239 341,478 125086.76 0.112 0.283 0.074
Simulation tests
Notch type Number of test repetitions Min number of cycles Max number of cycles Standard deviation of cycles Minimum of energy Maximum of energy Standard deviation of energy
U-notch radius 0.2 mm 4 15254 326,645 146,519.222 0.255 0.438 0.080
V-notch angle 20° 5 150.43 151,883 67,693.93 0.229 0.609 0.141
V-notch angle 140° 4 3890.97 85,337 42857.97 0.253 0.538 0.139
U-notch radius 2 mm 5 22938.2 442,920 169,677.83 0.124 0.313 0.081

Local energy modeling near notch

Experimental
Notch type Correlation coefficients Experimental: Local energy near notch
U-notch radius 0.2 mm R2 = 0.9881 WU0.2 = 6,1122.(2N)-0.248
V-notch angle 20° R2 = 0.9591 WV20 = 0,9019.(2N)-0.13
V-notch angle 140° R2 = 0.9656 WU140 = 10,939.(2N )-0.325
U-notch radius 2 mm R2 = 0.8875 WU2 = 14,731.(2N )-0.381
Simulation
Notch type Correlations coefficients Simulation: Local energy near notch
U-notch radius 0.2 mm R2 = 0.967 WU0.2 = 25.707.(2N )-0.354
V-notch angle 20° R2 = 0.857 WV20 = 1.944. (2N )-0.2093
V-notch angle 140° R2 = 0.890 WU140 = 15.357.(2N )-0.392
U-notch radius 2 mm R2 = 0.8305 WU2 = 12.483.(2N )-0.37

Mechanical properties of PMMA

Tensile strength (MPa) Flexural strength (MPa) Modulus of elasticity (MPa) Density (kg/m3) Elongation (%) Poisson’s rate Fracture Toughness (MPa.√m)
70.5 110 3000 1190 6 0.3 1.863
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