Numerically efficient modified Runge–Kutta solver for fatigue crack growth analysis

• A conservative integration algorithm for FCG calculation is presented.
• For large integration step sizes the crack size is overestimated.
• For smallintegration step sizes the crack size converges to the analyitc solution.
• We present a comparison to the well known Runge–Kutta 4th order integration scheme.
• The convergence order is estimated by numerical means.

We present a modified Runge–Kutta algorithm which yields a conservative estimate of the crack size for fatigue crack growth even for large integration step sizes. Conservative in this context means to overestimate the crack size. Commonly used algorithms (e.g. Euler, Runge–Kutta) usually underestimate the crack growth and only converge for small step sizes to an accurate value. As the presented algorithm overestimates the crack growth even for large and converges for small integration step sizes, it can be used for instance in Monte-Carlo based probabilistic fracture mechanics simulations, which might be otherwise computational impractical.