Wiktionary
turn a hair
vb. (context idiomatic especially in the negative English) To become afraid or visibly upset
Usage examples of "turn a hair".
First-class secretary, intelligent, good-tempered, understands my ways, doesn't turn a hair if I fly off the handle, couldn't care less if I insult her.
No anxiety there, not to see, but then the woman would not turn a hair if someone stuffed a viper down her dress.
When I paid the bill for her work, the time I'd taken, the pins, and combs she'd used, I nearly had heart failure, but I didn't turn a hair before her.
Only David seemed unaffected: the fact that he'd just had one of the most miraculous escapes in human history hadn't made him turn a hair.