The Army Tattoo Policy is contained primarily in AR 670-1.
e. Tattoo policy
(1) Tattoos or brands anywhere on the head, face, and neck above the class A uniform collar are prohibited.
(2) Tattoos or brands that are extremist, indecent, sexist, or ****** are prohibited, regardless of location on the body, as they are prejudicial to good order and discipline within units.
(a) Extremist tattoos or brands are those affiliated with, depicting, or symbolizing extremist philosophies, organizations, or activities. Extremist philosophies, organizations, and activities are those which advocate racial, gender or ethnic hatred or intolerance; advocate, create, or engage in illegal discrimination based on race, color, gender, ethnicity, religion, or national origin; or advocate violence or other unlawful means of depriving individual rights under the U.S. Constitution, Federal, or State law (see para 4-12, AR 600-20).
(b) Indecent tattoos or brands are those that are grossly offensive to modesty, decency, or propriety; shock the moral sense because of their vulgar, filthy, or disgusting nature or tendency to incite lustful thought; or tend reasonably to corrupt morals or incite libidinous thoughts.
Other than that, "frowning" is entirely subjective and not relavant to the topic other than to contribute to outmoded puritanical worldviews. Frankly, if I am ever your commander, I'll be dissapointed if you don't have at least 4 expensive tattoos that fall within Army guidelines.