For extending the LVM disk, change your sdb type to Linux LVM by fdisk
and then creates a physical volume of that disk:
pvcreate /dev/sdb1
Then you have to extend the volume group which the logical disk is in and the check to extend correctly:
vgextend vg_group /dev/sdb1 vgdisplay
And for extending your logical disk:
lvextend /dev/vg_group/lv_disk /dev/sdb1
There is then one final step which is to resize the file system so that it can take advantage of this additional space, this is done using the resize2fs command.
resize2fs /dev/vg_group/lv_disk