Widebody Transport
Flight Crew Air Transport Pilot (ATP)
Workload; Situational Awareness; Human-Machine Interface
Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Human Factors; Weather
At FL360; in ZZZZ airspace and established CPDLC/ADS. Requested and received Weather (WX) deviation due to Intertropical Convergence Zone buildups along our route of flight. Pilot flying selected HDG mode on FCU to deviate around moderate CBs; we requested and received clearance to climb to FL380. The Pilot flying selected 38000 in the FCU window; verbalized '380 blue' and pushed ALT knob for managed climb. The crew failed to realize that airplane did not initiate a climb; as they were busy with lateral navigation and approaching the lateral limits of their WX deviation clearance.After a while we received a 'SELCAL' from ZZZZ who asked us to confirm our altitude. At that point we realized that we were still at FL360. We received a new clearance to climb to FL380 and reported level FL380Both crew members failed to verify on FMA that the airplane was in CLIMB or OPEN CLB. Better SOP compliance with callouts (verbalizing FMA) would have possibly caught the oversight of not selecting OPEN CLB given that we were in HDG mode. Contributing factor was the WX deviation and possibly the fact that as we approached the limits of our lateral clearance; we had to request additional WX related clearances; creating a somewhat confused few minutes.
[Report narrative contained no additional information.]
A Widebody Transport flight crew reported a failure to climb to an ATC cleared altitude. This deviation was attributed to a high workload due to a weather deviation and auto flight mismanagement.