PSI - Issue 81

Viktor Kovalov et al. / Procedia Structural Integrity 81 (2026) 297–304

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Fig. 4. Economic assessment of the optimal level of reliability

Fig. 5. Economic feasibility curve C=f(H)

3.3. Probabilistic determination of plate thickness The calculation of the optimal thickness of a variable carbide plate is based on a probabilistic approach to reliability assessment. The model takes into account the random nature of the load on the cutting edge and the bearing capacity of the plate material. It is assumed that the external load acting on the plate obeys the Rayleigh distribution law, while the bearing capacity of the material is described by a normal (Gaussian) distribution law. The reliability condition is defined as the probability that the strength of the material R exceeds the applied stress S: Н = ( > ) = 1 − ∫ 1 − ∫ ∞ 0 ( ) ( ) ∞ 0 where f S (S) - is the load distribution density according to Rayleigh's law, and F R (S) — is the integral function of the strength distribution of the material, which obeys the normal law. The probability density of the load according to Rayleigh's law is described by the equation: ( )= 2 − 2 (2 2 ) ⁄ , S≥0 and the integral distribution function of the normal law for bearing capacity is ( ) = 12 [ ( − √2 )] where σ S — is the root mean square deviation of the load, μR is the average value of the material strength, and σR is its root mean square deviation. Based on the integration of these dependencies, the relationship between the reliability coefficient H and the main parameters of the material and load is obtained h=f(γ,σ S ,μ R ,σ R ) ,