The critical crack is that when the piece breaks or is broken. Hence, once the critical crack is achieved, there is never possibility for removal and substitution of the piece. This critical crack depends of course on the material, geometry and load, so it’s not possible to tell you further information on the dimensions without knowing this info. Another thing is the detectable crack, which depends only on the method of inspection. In Al panels, similar to aircraft skin, the preferred method of inspection is general visual inspection (GVI), i.e. searching for the cracks with the naked eye. The initial crack size is usually 1 inch. The detectable crack size is between 2 and 5 inches, but this information is not relevant without a study of crack propagation to establish the interval.
You can find information on the minimum detectable surface cracks for various NDT techniques in Table 7 of the article I am attaching. This info is from reference [6]. References [8] and [9] show crack dimensions used in damage tolerance analysis (DTA) (see also slides.pdf). I am listing these and other references that can be helpful to you, to have an idea of the typical orders of magnitude of the cracks.
Hope this helps,
Jose
[6] NASA: NASA STD-5009: Nondestructive Evaluation Requirements for Fracture Critical Metallic Components. NASA, Washington (2008)
[7] Swift T: FAA-AIR-90-01: Repairs to Damage Tolerant Aircraft. Federal Aviation Administration (FAA), Atlanta (1990)
[8] Nesterenko, G.I.: Designing the airplane structure for high durability. In: AIAA Int Air Space Symposium Exposition: The Next 100 Years, vol. 2785. Dayton (2003)
[9] Swift, T.: Fracture Analysis of Stiffened Structure. In: Chang, J.B., Rudd, J.L. (eds.) Damage Tolerance of Metallic Structures: Analysis Methods and Applications, ASTM STP 842, 1st edn, pp. 69–107. ASTM, Philadelphia (1984)
[10] Duven, J.E.: FAAAdvisory Circular (AC)-25.571-1D Damage Tolerance and Fatigue Evaluation of Structure (2011)
Despite José very good answer, I would like to complement it, focusing on your exact question, the critical crack length/depth size for an aircraft beyond which regulations demand aircraft maintenance.
Using EASA regulations as reference, they do not give an exact crack dimension limit, regulations just tell you that the aircraft must be in accordance with the design specifications; and during service, the aircraft must be airworthy and in comply with the OEM service limits, which can be found mainly on Aircraft Maintenance Manuals and Aircraft Structural Repair Manuals, which are Aircraft Manufacturers Manuals.
So, regulations will not give any exact dimensions, the Aircraft manufacturers do.