The most common and most likely answer to this crossword clue is the 7 plus 8 letter word TENSILE STRENGTH
I've seen this crossword clue in The Guardian
T
E
N
S
I
L
E
S
T
R
E
N
G
T
H
More clues leading to the result TENSILE STRENGTH
Buddy explains!
The straight part
We know that "Measure of stress that can be absorbed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case measure of stress that can be absorbed = tensile strength.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.