We observe the failure process of a fiber bundle model with a variable stress release range, $gamma$, higher the value of $gamma$ lower the stress release range. By tuning $gamma$ from low to high, it is possible to go from the mean-field (MF) limit of the model to local load sharing (LLS) where local stress concentration plays a crucial role. In the MF limit, the avalanche size $s$ and energy $E$ emitted during the avalanche are highly correlated producing the same distribution for both $P(s)$ and $Q(E)$: a scale-free distribution with a universal exponent -5/2. With increasing $gamma$, the model enters the LLS limit. In this limit, due to the presence of local stress concentration such correlation $C(gamma)$ between $s$ and $E$ decreases where the nature of the decreases depends highly on the dimension of the bundle. In 1d, the $C(gamma)$ stars from a high value for low $gamma$ and decreases towards zero when $gamma$ is increased. As a result, $Q(E)$ and $P(s)$ are similar at low $gamma$, an exponential one, and then $Q(E)$ becomes power-law for high-stress release range though $P(s)$ remains exponential. On the other hand, in 2d, the $C(gamma)$ decreases slightly with $gamma$ but remains at a high value. Due to such a high correlation, the distribution of both $s$ and $E$ is exponential in the LLS limit independent of how large $gamma$ is.
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