Just to be pedantic, this isn't the only means to make sand.
There are a few different weathering mechanisms that can break down rock. Some are physical like you describe, but there are also chemical processes that can break down cements and grains, allowing others to be released.
Wikipedia has a pretty good article on it. Erosion by wind, water or ice (more to the point, the material carried by it) can also get grains from a weathered or unweathered surface.