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Study of load bearing capacity of an infinite sheet weakened by multiple collinear straight cracks with coalesced yield zones

S. Shekhar

S. Shekhar

Department of Mathematics, Jamia Millia IslamiaNew Delhi, India
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Shekhar, S.
, 
Naved Akhtar

Naved Akhtar

Department of Applied Sciences and Humanities, Jamia Millia IslamiaNew Delhi, India
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Akhtar, Naved
 et 
S. Hasan

S. Hasan

Department of Mathematics, Jamia Millia IslamiaNew Delhi, India
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Hasan, S.
  
07 déc. 2021
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Publié en ligne: 07 déc. 2021
Pages: 265 - 284
Reçu: 21 juin 2021
Accepté: 16 août 2021
DOI: https://doi.org/10.2478/msp-2021-0023
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© 2021 S. Shekhar et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1

Configuration of the main problem.
Configuration of the main problem.

Fig. 2

Configuration of the Sub-problem A.
Configuration of the Sub-problem A.

Fig. 3

Configuration of the Sub-problem B (when s = 0).
Configuration of the Sub-problem B (when s = 0).

Fig. 4

Configuration of the Sub-problem B (when s = 1).
Configuration of the Sub-problem B (when s = 1).

Fig. 5

Configuration of the Sub-problem B (when s = 2).
Configuration of the Sub-problem B (when s = 2).

Fig. 6

Variation between normalized yield zone and load ratio for yield stress ±a1.
Variation between normalized yield zone and load ratio for yield stress ±a1.

Fig. 7

Variation between normalized yield zone and load ratio for linearly varying yield stress ±a1.
Variation between normalized yield zone and load ratio for linearly varying yield stress ±a1.

Fig. 8

Variation between normalized yield zone and load ratio for quadratically varying yield stress ±a1.
Variation between normalized yield zone and load ratio for quadratically varying yield stress ±a1.

Fig. 9

Comparison between three stress profiles ±a1.
Comparison between three stress profiles ±a1.

Fig. 10

Variation between normalized yield zone and load ratio for yield stress at ±b1.
Variation between normalized yield zone and load ratio for yield stress at ±b1.

Fig. 11

Variation between normalized yield zone and load ratio for linearly varying yield stress at ±b1.
Variation between normalized yield zone and load ratio for linearly varying yield stress at ±b1.

Fig. 12

Variation between normalized yield zone and load ratio for quadratically varying yield stress at ±b1.
Variation between normalized yield zone and load ratio for quadratically varying yield stress at ±b1.

Fig. 13

Comparison between three stress profiles at ±b1.
Comparison between three stress profiles at ±b1.

Fig. 14

Variation between normalized yield zone and load ratio for yield stress at ±c1.
Variation between normalized yield zone and load ratio for yield stress at ±c1.

Fig. 15

Variation between normalized yield zone and load ratio for linearly varying yield stress at ±c1.
Variation between normalized yield zone and load ratio for linearly varying yield stress at ±c1.

Fig. 16

Variation between normalized yield zone and load ratio for quadratically varying yield stress at ±c1.
Variation between normalized yield zone and load ratio for quadratically varying yield stress at ±c1.

Fig. 17

Comparison between three stress profiles at ±c1.
Comparison between three stress profiles at ±c1.

Fig. 18

Variation between Γ6a1−b1 \frac{{{{\rm{\Gamma }}_6}}}{{{a_1} - {b_1}}} and (σ∞σye)a {\left( {\frac{{{\sigma_\infty }}}{{{\sigma _{ye}}}}} \right)_a} .
Variation between Γ6a1−b1 \frac{{{{\rm{\Gamma }}_6}}}{{{a_1} - {b_1}}} and (σ∞σye)a {\left( {\frac{{{\sigma_\infty }}}{{{\sigma _{ye}}}}} \right)_a} .

Fig. 19

Variation between Γ6a1−b1 \frac{{{{\rm{\Gamma }}_6}}}{{{a_1} - {b_1}}} and (σ∞σye)b {\left( {\frac{{{\sigma_\infty }}}{{{\sigma _{ye}}}}} \right)_b} .
Variation between Γ6a1−b1 \frac{{{{\rm{\Gamma }}_6}}}{{{a_1} - {b_1}}} and (σ∞σye)b {\left( {\frac{{{\sigma_\infty }}}{{{\sigma _{ye}}}}} \right)_b} .

Fig. 20

Variation between Γ52c1 \frac{{{{\rm{\Gamma }}_5}}}{{2{c_1}}} and (σ∞σye)c {\left(\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}\right)_c} .
Variation between Γ52c1 \frac{{{{\rm{\Gamma }}_5}}}{{2{c_1}}} and (σ∞σye)c {\left(\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}\right)_c} .

Fig. 21

Variation between Γ6rB \frac{{{{\rm{\Gamma }}_6}}}{{{r_B}}} and (σ∞σye)a {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_a} .
Variation between Γ6rB \frac{{{{\rm{\Gamma }}_6}}}{{{r_B}}} and (σ∞σye)a {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_a} .

Fig. 22

Variation between Γ6rB \frac{{{{\rm{\Gamma }}_6}}}{{{r_B}}} and (σ∞σye)b {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_b} .
Variation between Γ6rB \frac{{{{\rm{\Gamma }}_6}}}{{{r_B}}} and (σ∞σye)b {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_b} .

Fig. 23

Variation between Γ5rC \frac{{{{\rm{\Gamma }}_5}}}{{{r_C}}} and (σ∞σye)c {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_c} .
Variation between Γ5rC \frac{{{{\rm{\Gamma }}_5}}}{{{r_C}}} and (σ∞σye)c {\left( {\frac{{{\sigma _\infty}}}{{{\sigma _{ye}}}}} \right)_c} .
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Sujets de la revue:
Sciences des matériaux, Sciences des matériaux, autres, Nanomatériaux, Matériaux fonctionnels et intelligents, Caractérisation et propriétés des matériaux
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