For AC application, superconducting strands are bundled and twisted to make a cable with large current capacity. The quench characteristic of the cable depends on the contact thermal and the contact electrical conductivities between strands, significantly. Also, the inter-strand contact resistance in the case of non-insulated cable and the material of the matrix of each strand have influence on the quench characteristics. In this paper, the thermal and the electromagnetic behaviors of non-insulated three-strand cable against local disturbances in one strand of multi-strand cables, taking the influence of inter-strand contact resistance and its joule heating, and the current redistribution among strands into account, are investigated. Particularly, the influence of the matrix material of cables on quench process is analytically investigated, and the results which show the influence of the joule heating by the contact conductance after local normal transition in one strand on quench process of whole cable is determined experimentally.