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Numerical study of the reliability of the fracture toughness determined experimentally by the IEF model, using Phimeca-soft

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Abstract

In this work, we performed a reliable study of the IEF model, which calculates the critical stress intensity factor, KIC, already studied in our previous article (Daoud et al. Int J Adv Manuf Technol 92:569–581, 2017), by the Phimeca-soft, where we performed a parametric study of the variation of the reliability index (β) as a function of the crack length (a) of the three states G1(x), G2(x) and G3(x) of the four sample types (R2, R4, R10 and R80), and also found the FORM/SORM results, as well as the histogram of elasticity of all variables used in the reliability study for the four sample types, with E26 galvanized sheet, safety and failure domains depending on the limit state used and importance of calculation variables on the reliability of the fracture. Then, the critical stress intensity factor (KIC) was found by the analytical method (IEF Model) equal to 63.13 MPa.m1/2 (accurate but not precise value), by the numerical method using the software Franc2D equal to 57.94 ± 4.29 MPa.m1/2 (precise but not accurate value) and by the reliability method using the software Phimeca-soft equal to 38.93 ± 0.83 MPa.m1/2 (accurate and precise value).

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Abbreviations

A :

Material yield parameter (MPa)

a :

Crack length (mm). (Not counting a pre-crack)

a c :

Critical crack length (mm). (Not counting a pre-crack)

Franc2D:

Fracture analysis code

IEF:

Indentation energy to fracture

K I :

Stress intensity factor in mode 1 (MPa.m1/2)

K IC :

Fracture toughness (MPa.m1/2)

m :

Meyer index

P f :

Probability of failure

Phimeca-soft:

Reliability analysis code

p m f :

Critical mean contact pressure (MPa)

R i :

Curvature radius for a given flat specimen (mm), R2, R4, R10 and R80

S :

Slope of the linear load (P)—penetration depth (h) (N/mm)

W 0 :

Lower shelf fracture energy (J/m2)

ν :

Poisson’s ratio

β :

Reliability index

σ :

Applied stress (MPa)

FORM/SORM:

First/Second-Order Reliability Method

X :

Value in the data set

N :

Number of values in the dataset

SD:

Standard deviation, with: SD2 = ∑ (X – main value)2/N

Cv :

Coefficient of variation (%), with: Cv = (SD/main value) 100

α2 and µ:

Sensitivity (%)

G 1 (x) :

Limit state function 1

G 2 (x) :

Limit state function 2

G 3 (x) :

Limit state function 3

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Funding

Financial supports are due to the PRFU research project, code: A11N01UN23010200005, under the tutor of the DGRSDT of the Algerian Ministry of Higher Education and Scientific Research (http://www.dgrsdt.dz).

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Authors and Affiliations

  1. Institute of Science, Mechanical Engineering Branch, University Center of Tipaza, Oued merzouk, 42022, Tipaza, Algeria

    Lotfi Daoud

  2. Research Laboratory of Advanced Technology in Mechanical Production (LRTAPM), Department of Mechanical Engineering, Faculty of Engineering Sciences, Badji Mokhtar University Annaba, BP: 12, 23000, Annaba, Algeria

    Abdelaziz Amirat

Authors
  1. Lotfi Daoud
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  2. Abdelaziz Amirat
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Contributions

The present work has been done under the supervision of Dr. Daoud Lotfi for the experimental and analytical analyses work and Pr. Amirat Abdelaziz for results analyses and discussion.

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Correspondence to Lotfi Daoud.

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Daoud, L., Amirat, A. Numerical study of the reliability of the fracture toughness determined experimentally by the IEF model, using Phimeca-soft. Int J Adv Manuf Technol 131, 5543–5552 (2024). https://doi.org/10.1007/s00170-023-12326-9

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