  The quantitative characterisation of crack tip loads is fundamental in
fracture mechanics. Although the potential influence of higher order terms on
crack growth and stability is known, classical studies solely rely on first
order stress intensity factors. We calculate higher order Williams coefficients
using an integral technique based on conjugate work integrals and study the
convergence with increasing crack tip distance. We compare the integral method
to the state-of-the-art fitting method and provide results for higher-order
terms with several crack lengths, external forces, and sizes for widely used
middle tension, single-edge cracked tension, and compact tension specimen under
mode-I loading.
