• DTDHandbook
• Contact
• Contributors
• Sections
• 1. Introduction
• 2. Fundamentals of Damage Tolerance
• 3. Damage Size Characterizations
• 4. Residual Strength
• 0. Residual Strength
• 1. Introduction
• 2. Failure Criteria
• 0. Failure Criteria
• 1. Ultimate Strength
• 2. Fracture Toughness - Abrupt Fracture
• 3. Crack Growth Resistance – Tearing Fracture
• 3. Residual Strength Capability
• 4. Single Load Path Structure
• 5. Built-Up Structures
• 6. References
• 5. Analysis Of Damage Growth
• 6. Examples of Damage Tolerant Analyses
• 7. Damage Tolerance Testing
• 8. Force Management and Sustainment Engineering
• 9. Structural Repairs
• 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
• 11. Summary of Stress Intensity Factor Information
• Examples

# Section 4.2.0. Failure Criteria

The determination of residual strength for uncracked structures is straightforward because the ultimate strength of the material is the residual strength.  A crack in a structure causes a high stress concentration resulting in a reduced residual strength.  When the load on the structure exceeds a certain limit, the crack will extend.  The crack extension may become immediately unstable and the crack may propagate in a fast uncontrollable manner causing complete fracture of the component.

Figure 4.2.1 illustrates the results obtained from a series of tests conducted on a lug geometry containing a crack.  The lug geometry shown in Figure 4.2.1a is a single-load-path structure.  Figure 4.2.1b indicates that the cracks in each of the three tests extended abruptly at a critical level of load, which is noted to be a function of a crack length.  The crack length-critical load level data shown in Figure 4.2.1b provide the basis for establishing the residual strength capability curve.  The locus of critical load levels as a function of crack length is shown in Figure 4.2.1c, where the residual strength capability of the lug structure is shown to decrease with increasing crack length.

Figure 4.2.1.  Description of Crack Geometry and Residual Strength Results

Considering the preceding in terms of applied stress (s) rather than load gives the s versus a and sc versus ac plots as shown in Figure 4.2.2 a and b.  Schematically, the plots exhibit the same abrupt fracture behavior as the curves presented in Figure 4.2.1.  As also shown in Figure 4.2.2c and 4.2.2d, crack extension can first occur at a load level that is well below the fracture critical level.  The point A¢ corresponds to the start of slow and stable extension of the crack.  The unstable rapid extension leading to total failure occurs at point A.  This kind of behavior is observed typically in thin metal sheets or in tough materials.  When different crack lengths are considered, the sc versus ac plot will contain two distinct curves, as shown in Figure 4.2.2d.  The curve A¢B¢C¢ corresponds to the start of slow and stable crack extension and the curve ABC corresponds to failure.

In general, unstable crack propagation results in fracture of the component.  Hence, unstable crack growth is what determines the residual strength.  In order to estimate the residual strength of a structure, a thorough understanding of the crack growth behavior is needed.  Also, the point at which the crack growth becomes unstable must be defined and this necessitates the need for a failure criterion.  There are several criteria available; these criteria are tailored to represent the ability of a material to resist failure.

Figure 4.2.2.  Fracture Data Described as a Function of Crack Length