To get logs from a pod you should use:
kubectl logs [podname] -p
You can also do kubelet logs
but that's mostly for Cluster logs.
If there is no logs that means your application did not produces any logs before the crash. You would need to rewrite the app and for example add a memory dump on crush.
You mentioned that the pod
is dying under heavy load but stats shows only 50% utilization. You should login to the pod and check yourself the load, maybe check how many files are being open because maybe you are hitting the limit.
You can read the Kubernetes docs about Application Introspection and Debugging and go over Debugging CrashLoopBackoffs with Init-Containers.
You can also try running your image in Docker and checking logs there. There is a nice documentation about Logs and troubleshooting available.
If you provide more details we might be more helpful.