The phrase "escalation of war" is a perfectly correct and usable phrase in written English.
You can use it when referring to the intensification of a military conflict. For example, "The diplomatic resolution to the dispute failed, leading to an escalation of war."
Instead of the usual escalation of war between opposites, Tim goes to Ruth's house and apologises.
President Trump, explaining yet another escalation of war in Afghanistan, barely mentioned freedom or democracy.
"People are already exhausted, starving, and have no means to cope with any further escalation of war," she said.
He is chiefly remembered for his serious qaṣīdah in which, old, wise, and experienced, he meditates upon the terrible escalation of war.
Last week the Irish state broadcaster, RTE, ran an interview with a masked man claiming to be from the Continuity IRA warning about an escalation of war.
I've been having trouble accessing news about the outside world here, but I hear an escalation of war on Iraq is inevitable.
The escalation of wars abroad by the Obama administration is moving forward alongside escalation against antiwar activists at home.
The Prussian military theorist Carl von Clausewitz warned of "total war" as a theoretical construct in which, by rationally following the escalations of war to their conclusion, war outstrips its strategic logic and becomes irrational, therefore requiring limits in practice.
They think of Lyndon Johnson, whose escalation of the war in Vietnam, that "bitch of a war", cut short his march towards the Great Society at home.
A few days later, despite being privately mortified by the "war on terror", he supported Blair's latest escalation of the war in Iraq.
