Galaxy interactions/mergers have been shown to dominate the population of IR luminous galaxies (log(LIR)>11.6Lsun) in the local Universe (z<0.25). Recent studies based on the relation between galaxies star formation rates and stellar mass (the SFR-M relation or the galaxy main sequence (MS)) have suggested that galaxy interaction/mergers may only become significant when galaxies fall well above the galaxy MS. Since the typical SFR at given M increases with redshift, the existence of galaxy MS implies that massive, IR-luminous galaxies at high-z may not necessarily be driven by galaxy interactions. We examine the role of galaxy interactions in the SFR-M relation by carrying out a morphological analysis of 2084 Herschel-selected galaxies at 0.2 < z < 1.5 in the COSMOS field. Herschel-PACS and -SPIRE observations covering the full 2-deg^2 COSMOS field provide one of the largest far-IR selected samples of high-redshift galaxies with well-determined redshifts to date, with sufficient sensitivity at z ~ 1, to sample objects lying on and above the galaxy MS. Using a detailed visual classification scheme, we show that the fraction of disk galaxies decreases and the fraction of irregular galaxies increases systematically with increasing LIR out to z ~ 1.5 and z ~ 1.0, respectively. At log(LIR) > 11.5 Lsun, >50% of the objects show evident features of strongly interacting/merger systems, where this percentage is similar to the studies of local IR-luminous galaxies. The fraction of interacting/merger systems also systematically increases with the deviation from the SFR-M relation, supporting the view that galaxies fall above the MS are more dominated by mergers than the MS galaxies. Meanwhile, we find that ~18% of massive IR-luminous MS galaxies are classified as interacting systems, where this population may not evolve through the evolutionary track predicted by a simple gas exhaustion model.