1.5.1
GENERAL — In the following discussion, failure will usually indicate fracture of a member or the condition of a member when it has attained maximum load.
1.5.2
MATERIAL FAILURES — Fracture can occur in either ductile or brittle fashions in the same material depending on the state of stress, rate of loading, and environment. The ductility of a material has a significant effect on the ability of a part to withstand loading and delay fracture. Although not a specific design property for ductile materials, some ductility data are provided in the Handbook to assist in material selections. The following paragraphs discuss the relationship between failure and the applied or induced stresses.
1.5.2.1
Direct Tension or Compression — This type of failure is associated with ultimate tensile or compressive stress of the material. For compression, it can only apply to members having large cross sectional dimensions relative to their lengths. See Section 1.4.5.1.
1.5.2.2
Shear — Pure shear failures are usually obtained when the shear load is transmitted over a very short length of a member. This condition is approached in the case of rivets and bolts. In cases where ultimate shear stress is relatively low, a pure shear failure can result. But, generally members subjected to shear loads fail under the action of the resulting normal stress, usually the compressive stress. See Equation 1.3.3.3. Failure of tubes in torsion are not caused by exceeding the shear ultimate stress, but by exceeding a normal compressive stress which causes the tube to buckle. It is customary to determine stresses for members subjected to shear in the form of shear stresses although they are actually indirect measures of the stresses actually causing failure.
1.5.2.3
Bearing — Failure of a material in bearing can consist of crushing, splitting, tearing, or progressive rapid yielding in the direction of load application. Failure of this type depends on the relative size and shape of the two connecting parts. The maximum bearing stress may not be applicable to cases in which one of the connecting members is relatively thin.
1.5.2.4
Bending — For sections not subject to geometric instability, a bending failure can be classed as either a tensile or compressive failure. Reference 1.5.2.4 provides methodology by which actual bending stresses above the material proportional limit can be used to establish maximum stress conditions. Actual bending stresses are related to the bending modulus of rupture. The bending modulus of rupture (fb) is determined by Equation 1.3.2.3. When the computed bending modulus of rupture is found to be lower than the proportional limit strength, it represents an actual stress. Otherwise, it represents an apparent stress, and is not considered as an actual material strength. This is important when considering complex stress states, such as combined bending and compression or tension.
1.5.2.4
Cozzone, F.P., "Bending Strength in the Plastic Range," Journal of the Aeronautical Sciences, 10, pp 137-151, (1943).
- 1.5.2.6(a) Dieter, G.E., Jr., "Mechanical Metallurgy," McGraw-Hill Book Company, Inc., 615 pp (1961).
- 1.5.2.6(b) Freudenthal, A.M., "The Inelastic Behavior of Engineering Materials and Structures," John Wiley and Sons, Inc., New York, 587 pp (1950).
- 1.5.2.6(c) Parker, E.R., "Brittle Behavior of Engineering Structures," John Wiley and Sons, Inc., New York, 323 pp (1957).
1.5.2.5
Failure Due to Stress Concentrations — Static stress properties represent pristine materials without notches, holes, or other stress concentrations. Such simplistic structural design is not always possible. Consideration should be given to the effect of stress concentrations. When available, references are cited for specific data in various chapters of the Handbook.
1.5.2.6
Failure from Combined Stresses — Under combined stress conditions, where failure is not due to buckling or instability, it is necessary to refer to some theory of failure. The “maximum shear” theory is widely accepted as a working basis in the case of isotropic ductile materials. It should be noted that this theory defines failure as the first yielding of a material. Any extension of this theory to cover conditions of final rupture must be based on evidence supported by the user. The failure
MIL-HDBK-5J
1.5.3
INSTABILITY FAILURES — Practically all structural members, such as beams and columns, particularly those made from thin material, are subject to failure due to instability. In general, instability can be classed as (1) primary or (2) local. For example, the failure of a tube loaded in compression can occur either through lateral deflection of the tube acting as a column (primary instability) or by collapse of the tube walls at stresses lower than those required to produce a general column failure. Similarly, an I-beam or other formed shape can fail by a general sidewise deflection of the compression flange, by local wrinkling of thin outstanding flanges, or by torsional instability. It is necessary to consider all types of potential failures unless it is apparent that the critical load for one type is definitely the controlling condition.
Instability failures can occur in either the elastic range below the proportional limit or in the plastic range. These two conditions are distinguished by referring to either “elastic instability” or “plastic instability” failures. Neither type of failure is associated with a material’s ultimate strength, but largely depends upon geometry.
A method for determining the local stability of aluminum alloy column sections is provided in Reference 1.7.1(b). Documents cited therein are the same as those listed in References 3.20.2.2(a) through (e).
1.5.3.1
Instability Failures Under Compression — Failures of this type are discussed in Section 1.6 (Columns).
1.5.3.2
Instability Failures Under Bending — Round tubes when subjected to bending are subject to plastic instability failures. In such cases, the failure criterion is the modulus of rupture. Equation 1.3.2.3, which was derived from theory and confirmed empirically with test data, is applicable. Elastic instability failures of thin walled tubes having high D/t ratios are treated in later sections.
1.5.3.3
Instability Failures Under Torsion — The remarks given in the preceding section apply in a similar manner to round tubes under torsional loading. In such cases, the modulus of rupture in torsion is derived through the use of Equation 1.3.2.6. See Reference 1.5.3.3.
1.5.3.3
Lundquist, E.E., "Strength Tests of Thin-Walled Duralumin Cylinders in Pure Bending," U.S. National Advisory Committee for Aeronautics, Technical Note No. 479, 17 pp (December 1933).
- 1.6.2.3(a) Hill, H.N. and Clark, J.W., "Straight-Line Column Formulas for Aluminum Alloys," Aluminum Company of America, Aluminum Research Laboratories, Technical Paper No. 12, 8 pp (1955).
- 1.6.2.3(b) AFFDL-TR-69-42, "Stress Analysis Manual," Air Force Flight Dynamics Laboratory, Air Force Systems Command, Wright-Patterson Air Force Base (February 1970).
- 1.6.2.3(c) "Astronautic Structure Manual," George C. Marshall Space Flight Center (August 15, 1970).
- 1.6.2.3(d) Niles, A.S., and Newell, J.S., "Airplane Structure," 2, Third Edition, John Wiley and Sons (1943).
- 1.7(a) "Index of Aircraft Structures Research Reports," U.S. National Advisory Committee for Aeronautics, Index No. 7E29, 40 pp (June 1947).
- 1.7(b) Gerard, and Becker, H., "Handbook of Structural Stability," National Advisory Committee for Aeronautics Technical Note, Nos. 3781, 102 pp (July 1957); 3782, 72 pp (July 1957); 3783, 154 pp (August 1957); 3784, 93 pp (August 1957); and 3785, 89 pp (August 1957).
1.5.3.4
Failure Under Combined Loadings — For combined loading conditions in which failure is caused by buckling or instability, no theory exists for general application. Due to the various design philosophies and analytical techniques used throughout the aerospace industry, methods for computing margin of safety are not within the scope of this Handbook.