Rapid Reliable Solution
of the Parametrized Partial Differential Equations
of Continuum Mechanics and Transport


The CenterCrack Problem
Author: DBP Huynh


Q1 Show that the non-dimensional Energy Release Rate (ERR) is given by G (μ) = – ∂ / ∂ μ1 (s (μ)). Find the corresponding non-dimensional SIF [1].

Q2 Write a matlab script which evaluates the ERR and SIF as a function of crack half-length μ1 and specimen half-length μ2.
Hint: Evaluate the derivative by a simple finite-difference approximation — the "virtual crack extension method" [2].

Q3 We next address a fracture application. We consider for a Zr–Ti–Ni–Cu–Be bulk metallic glass material [3] with Young's modulus \tilde{E} = 96 GPa (and Poisson ratio ν = 0.36), a specimen of half-width \tilde{w} = 5 cm and aspect ratio μ2 = 2, and tensile loading of \tilde{sigma} = 4 kPa. Q4 Finally, we address a fatigue application. We consider the A514 Martensitic steel material [3] with "material" properties KIC = 150 MPa/m1/2, C = 0.66 × 10-8 and m = 2.25, a specimen of half-width \tilde{w} = 5 cm and aspect ratio μ2 = 2, and a constant amplitude load fluctuation of Δ \tilde{\sigma} = 1.5 kPa.
[1] DBP Huynh and AT Patera, Reduced basis approximation and a posteriori error estimation for stress intensity factors. Int J Numer Meth Engng, 72(10):1219–1259, 2007.

[2] DM Parks, A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int J Frac, 10(4):487–502, 1974.

[3] JM Barsom and ST Rolfe, Fracture and Fatigue Control in Structures. American Society for Testing and Metals, 1999.

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