I record myself reading a chapter of a book that is copyrighted and
share the resulting audio file with my students disclosing the source
of the material the author and the copyright notice. What would the
copyright legal implications be?

Thanks.

There is the "Fair Use" doctrine in copyright that allows non profit
educationals institutions some use of copyrighted materials for free.
Here is the copyright section that applies to your use of the
material.

1. The purpose and character of the use, including whether such use is
of commercial nature or is for nonprofit educational purposes;

2 The nature of the copyrighted work;

3. The amount and substantiality of the portion used in relation to
the copyrighted work as a whole; and

4. The effect of the use upon the potential market for or value of the
copyrighted work.

If you are teaching in a publicly funded institution from Grade school
through to Grad School, you are allowed to use an unspecified but
reasonable amount for the reason stated above. Their are a few tests
that your recording must pass however. It should not be a substitute
for buying the book or devalue the copyright in any way. There cannot
be any charge for the recording and it cannot be a summation of the
whole book. If you are teaching in a "for profit" institution then you
must negotiate a fee with the publisher.

Here is the quote from the U.S. Copyright Office Website.

Under the fair use doctrine of the U.S. copyright statute, it is
permissible to use limited portions of a work including quotes, for
purposes such as commentary, criticism, news reporting, and scholarly
reports. There are no legal rules permitting the use of a specific
number of words, a certain number of musical notes, or percentage of a
work. Whether a particular use qualifies as fair use depends on all
the circumstances. See FL 102, Fair Use, and Circular 21,
Reproductions of Copyrighted Works by Educators and Librarians.