Yes, there have been instances where attempts were made that resulted in damage to the Kaaba.
One notable instance occurred in 683 CE during the Second Fitna when the Kaaba was damaged during the siege of Mecca by the Umayyad army.
Historical Context of the Kaaba Incident
The incident took place when Abdallah ibn al-Zubayr controlled Mecca and opposed Yazid I, the Umayyad caliph. Yazid sent an army to besiege Mecca. During the siege, on October 31, 683, the Kaaba was burned down and the Black Stone was shattered, possibly by a projectile from a catapult. This event serves as a historical example of damage inflicted upon the Kaaba during conflict.