The literature and writing on this subject is almost as expansive as the universe. First, classically, since many metallic alloys have a very distinct grain structure and alignment, the grain structure is defined in 3 perpendicular directions: L (longitudinal), LT (long transverse) and ST (short transverse). Speaking for aluminum alloys alone, think of the grain as being generally shaped like an ellipsoid, with one axis very long relative to the others, and the two other axes almost equal in dimension. The L direction is the direction the aluminum sheet is rolled, therefore the grain axis is aligned with the longest axis of this ellipsoid. The axis dimension in the two other directions, LT and ST, is much shorter than the L direction. If anything, the ST direction axis is usually shorter than the LT direction axis. In aluminum alloys, it is often very easy to see which direction is which by looking at cut metal under a powerful optical microscope. In typical sheet or plate form, a thick billet of aluminum is squeezed or rolled through a machine that squishes the sheet out into whatever thickness desired. This process has a tendency to pull the grain axis in the L direction, therefore elongating it, and squish the grain in the other two directions. In such a sheet, the L direction is in the plane of the plate, and is the rolled direction (direction of longest grain axis), the LT direction is also in the plane of the sheet, perpendicular to the L direction. The ST direction is perpendicular to the plane of the plate, in the thickness direction. Now think about two compact tension specimens, the ASTM standard. Consider the first coupon: the load is in the L direction, the crack grows in the LT direction. Consider a second coupon: cut so the load is in the LT direction, crack propagates in the L direction. For the same load, the crack almost always propagates faster in the second coupon than in the first. I recall it propagates fastest in when you load the coupon in the ST direction, but since there is so little data there (given the difficulty in obtaining coupons in loading such a coupon except when the plate is very thick), I can't say for certain.
