A new model is presented that allows a dynamical simulation of the interaction between crack advance and induced stresses in medium carbon steels under periodic and constant loads. It is based on the use of an empirical crack-growth velocity to approximate the second order term in the basic equation of linear elasticity. Once this is done, a Finite Element analysis of the stresses gives what is here called a semi-empirical numerical dynamic model of the crack evolution. The simulation requires a set of data obtained through experimentation that was by itself guided in its design by the model, in what can be considered as an example of an evolving new paradigm in engineering research. Several simulations of the crack evolution were obtained under different considerations for the Neumann boundary condition and with or without an inhomogeneity simulating a thin stripe of welding. The simulation allows the analysis of the crack evolution as the stresses in the body evolve. Due to the relevance of the experimental data and design, this research is presented in two parts, this first paper dealing with the model, its physical and mathematical aspects and giving examples of the results. The second one deals with the experimental aspects.

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