Copyright law in the US is spelled out in Title 17. The basic idea is that the person do creates some intellectual property has exclusive ownership of that property, and may sell it, give it away, or prevent anyone from knowing about it, as they choose. Academic articles come in three main varieties: copyright has been transferred to the publisher; the publisher has a license to copy but the author retains copyright; the author has executed some public license allowing anyone to copy the article. Journals are not particularly good about distinguishing the first two cases, but usually if something has been publicly licensed, the article says so in some way *usually at the bottom of the first page). There is a minor complication that in a few cases, the employer requires copyright to be transferred by their employees to the institution, in which case it is the institution and not the author who might have copyright.
With all copyright, there is a small loophole in the form of "fair use", which states how to defend against a charge of copyright infringement, for certain limited cases. You can read up on fair use here. There is a common but not unjustified misconception that "for private use" constitutes a blanket exception to copyright legal protection of IP, especially for educational purposes. There is no statutory or case-law direct support for this, that is, it has never been held that you can always make copies if it is for educational purposes, but as far as I have been able to discern, there is a de facto tolerance policy of copying academic articles for private purposes. This excludes anything systematic, such as libraries doing massive copying for courses, or copy shops making course packets, without the proper payments and paperwork; also, if you were selling copies on the black market, it is likely that somebody would legally go after you. The cost of litigating a small infraction of the law would be high and the recovery would be really small, which is why most academic copyright infringement gets a pass: unless you can sue an institution with deep pockets.
However, you also introduce a complication regarding the ScienceDirect paywall. In general, you have to pay to acquire copies of material that they have licensed, and there is a TOS that almost certainly prohibits such "sharing" (i.e. copying).