ausbrechen
to break out
To escape by force or secretly from a closed place, especially a prison.
Zwei Häftlingen ist es gelungen, aus dem Gefängnis auszubrechen.
Two prisoners managed to break out of the prison.

to break out
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to break out
To escape by force or secretly from a closed place, especially a prison.
Zwei Häftlingen ist es gelungen, aus dem Gefängnis auszubrechen.
Two prisoners managed to break out of the prison.

'Ausbrechen' (to break out) is a separable verb. The prefix 'aus' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Vulkan bricht unerwartet aus.
The volcano breaks out unexpectedly.
The perfect tense of 'ausbrechen' (to break out) is always formed with the auxiliary verb 'sein', because it describes a sudden change of state or place.
Letzte Nacht ist ein Feuer im Keller ausgebrochen.
Last night, a fire broke out in the basement.
In the meaning 'to begin suddenly', the subjects are typically impersonal, often negative events such as a fire, a war, a disease, a storm, or an argument.
Plötzlich brach ein heftiger Streit zwischen den Nachbarn aus.
Suddenly, a fierce argument broke out between the neighbors.
This meaning is used in fixed expressions to describe sudden emotional reactions. Common combinations are 'in Tränen ausbrechen' (to burst into tears), 'in Gelächter ausbrechen' (to burst into laughter), or 'in Panik ausbrechen' (to panic).
Als er den Witz hörte, brach er in lautes Gelächter aus.
When he heard the joke, he burst into loud laughter.
When a part of something breaks off, the person this happens to is often in the dative. The broken-off piece is the subject of the sentence.
Mir ist gestern beim Essen ein Stück vom Zahn ausgebrochen.
Yesterday while eating, a piece of my tooth broke off.
to begin
'beginnen' and 'ausbrechen' can both describe a beginning. The difference lies in the type of beginning. 'beginnen' is neutral and can be used for almost any action or event. 'ausbrechen' is used when something starts suddenly, intensely, and often uncontrollably, for example a fire, a disease, a war, or sudden laughter or crying. Learners may confuse the words because both have to do with 'anfangen' (to start). A simple rule is: use 'beginnen' for a normal start, and 'ausbrechen' for a sudden and violent or intense start.

Wegen eines alten Kabels bricht in der Werkstatt plötzlich ein Feuer aus.
Because of an old cable, a fire suddenly breaks out in the workshop.
Bei der Arbeit beginnt die Gruppe jeden Montag mit einer kurzen Planung.
At work, the group begins every Monday with a short planning session.