With the rapid growth of research publications, there is a vast amount of scholarly knowledge that needs to be organized in digital libraries. To deal with this challenge, techniques relying on knowledge-graph structures are being advocated. Within such graph-based pipelines, inferring relation types between related scientific concepts is a crucial step. Recently, advanced techniques relying on language models pre-trained on large corpora have been popularly explored for automatic relation classification. Despite the remarkable contributions that have been made, many of these methods were evaluated under different scenarios, which limits their comparability. To address this shortcoming, we present a thorough empirical evaluation of eight Bert-based classification models by focusing on two key factors: 1) Bert model variants, and 2) classification strategies. Experiments on three corpora show that domain-specific pre-training corpus benefits the Bert-based classification model to identify the type of scientific relations. Although the strategy of predicting a single relation each time achieves a higher classification accuracy than the strategy of identifying multiple relation types simultaneously in general, the latter strategy demonstrates a more consistent performance in the corpus with either a large or small number of annotations. Our study aims to offer recommendations to the stakeholders of digital libraries for selecting the appropriate technique to build knowledge-graph-based systems for enhanced scholarly information organization.