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Stochastic Assessment of Fracture Toughness and Reliability in Anisotropic Boride Layers on Ti6Al4V: A Monte Carlo-Based Mixed-Mode Model
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DOI：10.3390/math14071186.png)
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Abstract
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In the realm of computational biomechanics, quantifying the reliability of surface-engineered implants is critical yet challenging due to material anisotropy and experimental limitations. Standard deterministic approaches often fail to capture the failure probability of brittle coatings, compromising the accuracy of lifespan predictions. This study's originality lies in a stochastic framework that addresses titanium boride data scarcity using a geometric decision node (GDN). By autonomously switching between Palmqvist and Radial-Median regimes, the GDN eliminates deterministic bias and provides a failure-probability-based reliability assessment, thereby surpassing the limitations of conventional models. The evaluation was carried out on powder-pack borided Ti6Al4V layers produced at 1000 degrees C (10, 15, and 20 h). By combining instrumented Berkovich nanoindentation (N = 14, hardness scatter 17.6-34.8 GPa) with a Monte Carlo simulation algorithm (n = 10,000), we successfully modeled the stochastic brittle failure of the coating. The computational model, governed by a multivariate joint probability density function (JPDF), revealed a mixed-mode fracture mechanism where 77.9% of the virtual population developed radial cracks while 22.1% re mained in the Palmqvist regime. Weibull statistical analysis yielded a characteristic toughness of 2.25 MPa & centerdot;m1/2 and a low modulus of m = 1.58. This low modulus mathematically quantifies the coating's sensitivity to microstructural defects, demonstrating that probabilistic algorithms-rather than mean-value deterministic calculations-are essential for ensuring the structural integrity of borided components in biomechanical design applications.
Keywords:
fracture toughness
Monte Carlo simulation
Weibull analysis
boriding
titanium
Berkovich indentation
cracks
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