In this study, a discrete-time Markov chain model is developed for a framework of a corrosion-induced crack growth in a 2-D plane, where the CSs, defined based on the observable crack face, are denoted by a discrete number of variables. The observed crack face size is used to estimate the time since corrosion initiation and the corrosion degree through the crack face size. The crack face size is also used to correlate the time since corrosion initiation with the corrosion degree through the crack face size, and to estimate the residual ductility (strength) of the specimen based on a wide range of crack face sizes.
Based on this methodology, a correlation between the time since corrosion initiation and corrosion-induced crack width is proposed. The correlation is based on the controlled crack growth experiments performed in this study under two unique, non-equivalent, and contrasting environments (i.e. pH=5 and pH=1.4), in which an acid (pH=5) and a base (pH=1.4) are added to the dentin specimens at the crack initiation. For each crack face, the mean absolute error (MAE) and the root mean squared error (RMSE) of the time since corrosion initiation are calculated as a function of the predicted crack face width. The correlation's coefficients are also estimated.
The results of the finite element model are used to establish the relationship between the crack face size and the corresponding corrosion-induced crack width for the two distinct environments. The results of the finite element model are also used to estimate the energy release rate and its components.
The proposed methodology has been applied to the case-study structure, where the structural details are provided and the finite element model is validated. Moreover, the remaining ductility is quantified based on a range of increasing crack face sizes.
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