We perform smoothed particle hydrodynamics simulations for merging binary carbon-oxygen (CO) WDs with masses of 1.1 and 1.0 M-circle dot, until the merger remnant reaches a dynamically steady state. Using these results, we assess whether the binary could induce a thermonuclear explosion, and whether the explosion could be observed as a type Ia supernova (SN Ia). We investigate three explosion mechanisms: a helium-ignition following the dynamical merger ("helium-ignited violent merger model"), a carbon-ignition ("carbon-ignited violent merger model"), and an explosion following the formation of the Chandrasekhar mass WD ("Chandrasekhar mass model"). An explosion of the helium-ignited violent merger model is possible, while we predict that the resulting SN ejecta are highly asymmetric since its companion star is fully intact at the time of the explosion. The carbon-ignited violent merger model can also lead to an explosion. However, the envelope of the exploding WD spreads out to similar to 0.1 R-circle dot; it is much larger than that inferred for SN 2011fe (<0.1 R-circle dot) while much smaller than that for SN 2014J (similar to 1 R-circle dot). For the particular combination of the WD masses studied in this work, the Chandrasekhar mass model does not successfully lead to an SN Ia explosion. Besides these assessments, we investigate the evolution of unbound materials ejected through the merging process ("merger ejecta"), assuming a case where the SN Ia explosion is not triggered by the helium-or carbon-ignition during the merger. The merger ejecta interact with the surrounding interstellar medium and form a shell. The shell has a bolometric luminosity of more than 2 x 10(35) erg s(-1), lasting for similar to 2x10(4) years. If this is the case, the Milky Way should harbor about 10 such shells at any given time. The detection of the shell(s) can therefore rule out the helium-ignited and carbon-ignited violent merger models as major paths to SN Ia explosions.