v3.02.103 SSLP103 - Calculation of the stress intensity coefficients KI and KII for a cracked circular plate in linear elasticity

Summary

This is a test of fracture mechanics in static linear elasticity for a two-dimensional problem. We consider a cracked circular plate (with a crack inclined by 30 degrees with respect to the x-axis) for which we calculate:

• the stress intensity coefficients \({K}_{I}\) and \({K}_{\mathrm{II}}\),

• the \(G\) energy return rate based on the IRWIN formula.

The advantage of the test is to know the analytical solution that gives the stress intensity coefficients and to have an inclined crack.

Two models are:

• Modeling A: FEM for elements C_ PLAN, D_ PLAN

• B modeling: FEM for elements D_ PLAN_INCO_UPG

This test includes modeling that successively treats plane deformations and plane stresses (elements of continuous media).

The numerical results do not deviate more than \(\text{1 \%}\) to \(\text{2 \%}\) from the reference values.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Reference solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Bibliographical references
• 3. Modeling A: FEM for elements D_ PLAN and C_ PLAN
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. notes
• 4. B modeling: FEM for elements D_ PLAN_INCO_UPG
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. Summaries of results