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Good countersink rivet knife edge
countersunk knife edge - poor
Countersink knife edge - unacceptable
knife edge can cause rivet failure - smoking rivets
Knife edge, to the mechanic, means there is little to no straight bore. Drill a countersunk hole in a sheet or plate, you get a countersink, and a straight bore hole. If the countersink is too big, so there is no straight bore in the hole, then you get a knife edge. Knife Edge to the aeronautical engineer is  defined as any countersink depth greater than 2/3 sheet thickness.

Minimum Sheet Thickness for countersinking:
Generally .032 is the minimum sheet thickness for countersinks. Typical standard practice is to limit countersink depth to 2/3 the thickness of the sheet. Typical manufacturer optimum countersink depth is 67% (or less) of sheet thickness. As per Boeing SRM, the countersink depth must not exceed 60% of the material thickness. (ref 737 SRM 51-40-08 Figure 7). Anything greater, the material is considered knife-edged and a poor fatigue detail.

The concern about knife edge in countersunk holes is due to stress cycles causing fatigue cracks. The fatigue crack that resulted in Aloha Airlines Flight 243 accident originated at a countersunk rivet. Consider that modern airliners are flying for 25 plus years at 4,000 hours a year (100,000 hours) - which is an astonishing service requirement. Fatigue cracking becomes a real concern. There are several jet aircraft that use "knife-edge" rivets by design.  In these cases they have acceptable fatigue testing to support certification. It all depends on the loads.

With thin sheets you risk "knife-edging" the countersink hole. This lowers fatigue strength and often results in rivet movement "smoking rivets". Knife-edge conditions are not necessarily bad as they may be adequate and airworthy for the intended life. Although not generaly used due to fatigue considerations in primary structure, it however can be found and deemed acceptable  in secondary structure where little to no know load is shown, ie, access panels, removable, non primary structure.

For a composite skin, rule-of-thumb for max csk depth is 70% of structural laminate thickness.

Dimpling:
Not recommended for pressurized skins. Dimpling is a mechanical deformation process that tends to strain the areas between dimples. This tends to distort the sheet metal between holes, causing slight dimpled-hole to dimpled-hole mismatch. Mismatch degrades strength to an unknown degree.

The countersinking tool shall be held at 90 degrees to the work surface during the entire cutting cycle. Countersinks shall be free of chatter marks and concentric with the rivet holes. The countersink diameter shall be in accordance with the table below.

Flushness limits shall be 0.010 inch above to 0.005 inch below the material surface. Rivets failing to met flushness requirements may be shaved to new close tolerances. The material shall not be damaged by the shaving tools.  Several manufacturers do not allow shaving of NAS1097 rivet heads.

NAS1097 shallow countersink rivets (when compared to MS20426 full countersink) are an option to consider for thin sheets. Caution for use in buckling conditions (top of wings) as the pull-thru strength is lower due to the smaller head size.

Also, in a single riveted lap joint, owing to the narrowness, the deformation, caused by the planes trying to align themselves so as to lie in the direct line of stress, is considerable. The rivets are subjected to not only shearing stress but to endwise tension. If the heads of the rivets are large or of the universal head style  they help prevent joint deformation and result in higher shear strength.

Countersink depth to avoid knife edge conditions
MS24694 Screw, Structural, 100 degree Countersunk

MS24694 structural screw
Fastener        Good Fatigue (cyclic loading)        Poor Fatigue        Maximum
#8                  .041                                                        .046                        .054
#10                 .048                                                        .054                        .064
1/4                 .064                                                        .071                        .085
5/16                .080                                                        .089                        .106
3/8                 .095                                                        .107                        .127
7/16                .112                                                        .125                        .149
1/2                 .128                                                        .143                        .170
9/16                .144                                                        .161                        .192

Countersink depth to avoid knife edge conditions
NAS517 Screw, Close-Tolerance Structural, 100 degree Countersunk

NAS517 screw knife edge
Fastener        Good Fatigue (cyclic loading)        Poor Fatigue        Maximum
-2 #8                 .041                                                .046                        .054
-3 #10                .048                                                .054                        .064
-4 1/4                .064                                                .071                        .085
-5 5/16             .080                                                .089                        .106
-6 3/8                .095                                                .107                        .127
-7 7/16             .112                                                .125                        .149
-8 1/2                .128                                                .143                        .170

Countersink depth to avoid knife edge conditions
MS20426 Rivet, 100 degree Countersunk

MS209426 flush rivet
Fastener        Good Fatigue (cyclic loading)        Poor Fatigue        Maximum
1/16                        .013                                        .015                        .018
3/32                        .022                                        .025                        .029
1/8                          .025                                        .029                        .034
5/32                        .033                                        .037                        .044
3/16                        .042                                        .047                        .056
7/32                        .050                                        .056                        .066
1/4                          .057                                        .064                        .076
5/16                        .064                                        .071                        .085
3/8                          .080                                        .090                        .107

Countersink depth to avoid knife edge conditions
NAS1097  Rivet, 100 degree Countersunk

NAS1097 shear rivet
NAS1097 to the left. Standard MS20426 rivet to the right
Fastener        Good Fatigue (cyclic loading)        Poor Fatigue        Maximum
1/8                  .022                                                .025                .029
5/32                .025                                                .029                .034
3/16                .033                                                .037                .044
7/32                .042                                                .047                .056
1/4                  .050                                                .056                .066
5/16                .057                                                .064                .076
3/8                  .064                                                .071                .085

Good fatigue strength
Poor fatigue strength
Unacceptable
Knife edge can cause rivet failure. Shown here are "smoking rivets".
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