The argument by @ermanen is not correct.

A half-sibling is a "half" because they have half of their parents in common.

In the example provided, Erin and Grace have no parents in common. They are not related in a manner that would be designated half, quarter, or whatever.

The only relationship they could have is through marriage, meaning they are stepfamily. Let's see if there is a relationship. Yes there is.

Erin's father Bob remarried to Carol. So Carol is Erin's stepmother. A stepparent's child through another marriage is a stepsibling. 

So what we have is Grace and Erin are stepsisters of each other.

And Frank is a half-brother of both Erin and Grace, having one parent in common with each of them.