In theory, PLA achieved all or part of their objectives in
the:
Korean War (1950's)
Sino-Indian War (1960's)
Sino-Vietnam War (1970's)
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In Korea, the PLA were at first victorious against the US/Allied
forces. Then it started losing but still managed to keep North
Korea from being overrun. Though it suffered massive casualties, it
was a victory as a poorly-armed but well-motivated peasant army was
able to hold back mighty western armies.
But its weakness and inability to defeat a western power was also
evident.
The end of the Korean War was the start of PLA's 1st
modernization.
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In the Sino-Indian War, Nehru provoked the PLA into action by
instigating border clashes and making verbal threats of using
military force to invade China - against the advice of his of the
Indian army generals.
Therefore, when the PLA duly invaded, the Indian Army was
unprepared (or so it was claimed) and suffered humiliating
defeat.
Right from the start China stated that its objectives were the
"teach India a lesson" and not to gain any territory. On its own
accord, the PLA withdrew.
IMO, it was a shrewd move as China emerged a victor that was also
gracious enough to return all territory and POWs. Had they
prolonged the war or invaded deeper, the PLA may have a difficult
time extracting itself.
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In the Sino-Vietnam War again China stated right from the start
that its objectives were to "teach Vietnam a lesson" and not to
hold any territory.
But the PLA ended up suffering twice the casualties than the
Vietnamese.
The PLA certainly did not win this war but the PLA wasn't overrun
or chased out of Vietnam. It was just to costly in terms of
casualty to invade any further. They also realised it pointless as
the Vietnamese weren't scared of war. Civilian Vietnamese women and
children were sacrificing themselves to deliver bombs to the PLA
just as they did against the Americans a decade ago.
Resistance was intense and determined.
Only "lesson" learnt was that the PLA needed to be revamped (and
never touch Vietnam again).
The end of the Sino-Vietnam War was the start of PLA 2nd
modernization.
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The PLA never attempted an invasion of the mainland ROC,
period.
There were artillery duels in the late forties. The KMT held a
couple of islands that are VERY NEAR China but VERY FAR from
Taiwan. So the PLA were shelling those islands. The US Pacific
fleet was nearby to ensure Taiwan's safety.