Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form.

Area of Science:

• Computational mechanics
• Materials science
• Fracture mechanics

Background:

• Functionally graded materials (FGMs) exhibit spatially varying properties, posing challenges for traditional analysis methods.
• Accurate fracture analysis is critical for ensuring the structural integrity and safety of components made from FGMs.
• Existing numerical methods may face limitations in handling the complex geometry and material gradients inherent in FGM fracture problems.

Purpose of the Study:

• To present the strong-form finite block method (FBM) for three-dimensional fracture analysis of FGMs.
• To develop frameworks for the strong-form FBM using Lagrange and Chebyshev polynomial interpolations.
• To determine stress intensity factors in FGMs using the developed FBM approach.

Main Methods:

• The strong-form finite block method (FBM) transforms the physical domain into a normalized one.
• Direct collocation is employed to establish a linear system within the normalized domain.
• Mapping techniques facilitate the direct construction of partial differential matrices of any order.

Main Results:

• Frameworks for 3D FBM analysis were successfully developed using Lagrange and Chebyshev interpolations.
• Stress intensity factors for FGMs were accurately determined based on crack opening displacement criteria.
• Numerical examples demonstrated the high accuracy and computational efficiency of the strong-form FBM.

Conclusions:

• The strong-form FBM is a robust and efficient technique for 3D fracture analysis of FGMs.
• The method provides accurate stress intensity factors, essential for evaluating material reliability.
• The developed FBM approach offers a valuable tool for researchers and engineers working with FGMs.