This sounds like Juanita Coulson's novel Outward Bound, the second of her Children of the Stars series, which series may have been asked about here before at:
1980s sci-fi book club trilogy about a rich, space-faring multi-generational family
(See that answer for a shot of the cover of the first book.)
Here's a brief synopsis from the goodreads.com review:
Quol-Bez, alien ambassador on Earth, was offering planets, other stars
to man - if man could reach them! Oh, the aliens had faster-than-light
travel. But if men wanted that they must find it for themselves. And
without it, the nearest such world lay a lifetime or more away.
Brenna Saunder's aunt and uncle had died in an experimental ship,
seeking for that way. And now Brenna was devoting her life and her
share of the vast Saunder family fortune and prestige to solving the
problem of such faster-than-light travel.
She had lost her lover to a hiber-ship, one in which those who dared
would spend the years of travel in hibernation. Now she watched
another of her group try and end in disaster.
Finally there was time and means for only one more attempt - one more
chance for man to find his destiny among the stars!
Grimly, Brenna buckled herself into the pilot's seat of the final
experimental ship and reached for the ready button!
[My apologies for misidentifying which book of the series in my original answer.]
Here are some quotes that might jog your memory. From page 177 in Chapter 10, discussing Morgan (the one burned in the accident):
Morgan was lying on his stera-gel chair-bed, listening to a ComLink
broadcast. He had graduated from the tank of glop some time ago, but
he still required stera-gel to guard against infection and support his
syntha skin in Mars' gravity.
and on the following page, the specific mention of metallurgy:
"That was an interesting readout you got on number five graviton
baffle. The peak stresses obviously hit there first," Morgan said.
"The field instability links right up with the hull material flaw.
It's all going to tie together."
That was practically an oration for Morgan. Brenna started with
pleased surprise. "You think so? I do, too. But you're better at
metallurgy analyses. Yuri agrees. George and Hector and the kids are
halfway convinced the trouble's in the power plant. Even Tumaini said
we could solve everything if we just 'borrowed' Quol-Bez's ship and
took her engines..."