Tiffany and Masters [1965] utilized the proof test as a means of guaranteeing that a potentially cracked structure would not fail during a defined period of operation.  This guarantee results from the fact that all the cracks remaining in a proof-loaded structure must be smaller than those cracks which would have failed the structure during the proof test.  Since the proof test loadings are typically larger than the maximum operating conditions, the post proof-tested structure’s cracks are also expected to be substantially smaller than the cracks which would cause failure under operating loads.

Figure 3.3.1 schematically illustrates a stress-crack length diagram that defined the levels of loading (proof stress and operational maximum stress) and the corresponding crack lengths associated with structural failure by fracture.  It can be noted from Figure 3.3.1 that all cracks larger than a_i will cause the structure to fail during the proof test loading, thus guaranteeing a “minimum” safe crack growth interval between a_i and the crack size (a_op) at which the operating conditions will cause failure.  The interval established is the minimum safe interval because the structure may initially have cracks that are substantially smaller than the guaranteed initial size (a_i).

 

Figure 3.3.1.  Fracture Critical Curve Defining Relationship Between Stress and Crack Length Associated with Fracture

Tiffany and Masters [1965] designed the proof test conditions so that all cracks initially present in the structure and of sufficient size that they could grow to failure during the planned service operating period would fail the structure during the proof test.  If the operating conditions and the crack growth mechanisms are known, then a crack growth life calculation can be performed to establish the minimum safe crack growth interval during which failure will not occur during service.  The minimum safe crack growth interval extends from the largest allowable initial crack size (a^*_i) and the crack size (a_op).

Figure 3.3.2 describes the interrelationship between the crack growth life and residual strength behavior of a structure and the stress-crack size diagram.  As indicated in Figure 3.3.2 (right-hand side), the life limit associated with the crack growth process and the decay of the residual strength capability is lower than the service life requirement.  An increase in the proof stress if required, therefore, to decrease the corresponding crack size (a_i) to the maximum allowable crack size (a^*_i) and thus ensure a safe period of operation.  Note that the stress-crack size diagram indicates that all cracks greater than a_i , present at the time of the proof test, will cause structure failure.  Thus, the proof test ensures that when the structure enters service, its initial cracks will be no larger than the size associated with the proof test conditions.

 

Figure 3.3.2.  Schematic Illustrating the Relationship Between the Proof Test Diagram, the Residual Strength Capability and Crack Growth Life Interval

The levels of proof test stress and the material’s fracture toughness combine to establish the maximum initial crack size guaranteed by the proof test.  Because material and stress variations will exist throughout any proof loaded structure, the designer of a proof test must be aware of several important material variations which could significantly affect the post-proof test crack size distribution.  These important material variations are caused by changes in temperature, loading rate, thickness, and yield strength.  Figure 3.3.3 schematically describes how fracture toughness varies as a function of these parameters.  Note that temperature and loading rate can affect some materials (some steels and titanium alloys are particularly susceptible) while other materials are unaffected.  Aluminum alloys and many nickel-bases alloys exhibit almost no variation in fracture toughness as a function of temperature and strain rate).

 

Figure 3.3.3.  Fracture Toughness Varies as a Function of (a) Thickness, (b) Yield Strength, (c) Temperature, and (d) Loading Rate

Figure 3.3.4 provides an example of how a material’s response to external stimuli can be utilized to increase the minimum safe crack growth interval.  In Figure 3.3.4, a material’s known response to temperature is utilized to select a low temperature condition for conducting the proof test.  The lower fracture toughness exhibited at the low temperature is shown to extend the minimum safe crack growth interval substantially beyond what would have been expected for the same proof stress at the operating temperature conditions.

 

Figure 3.3.4.  Using a Material’s Low Temperature Fracture Sensitivity to Decrease Initial Crack Size and thus Increase the Minimum Safe Crack Growth Interval for a Given Proof Stressing Condition

As stated by JSSG-2006 A.3.12.1, “the minimum assumed initial flaw size shall be the calculated critical size at the proof test stress level and temperature using procuring activity approved upper-bound of the material fracture toughness data.”  The concept of using an approved upper-bound for the fracture toughness ensures a worst case assumption for the maximum allowable initial crack size (see Figure 3.3.5) and the minimum safe crack growth interval (see Figure 3.3.6).  Figure 3.3.6 summarizes the JSSG-2006 requirements for establishing the minimum safe crack growth interval for the NDE proof test conditions.

Figure 3.3.5.  Influence of Fracture Toughness Variation on the Maximum Allowable Crack Size

Figure 3.3.6.  Description of Procedure Used to Establish Initial Crack Size and the Minimum Safe Crack Growth Interval According to JSSG-2006, A.3.12.1

There are no design allowables for fracture toughness of aerospace materials.  Figure 3.3.7 presents a portion of MIL-HDBK-5G data that define typical plane strain fracture toughness for aluminum alloys.  The fracture toughness values presented are averages, coefficients of variation and the minimum and maximum values obtained from the test data collected for the individual alloys and heat temperature conditions shown.  The supporting text in MIL-HDBK-5G notes that the fracture toughness values given do not have the statistical reliability of the typical mechanical properties (yield strength, elastic modulus, etc.) that are usually present in MIL-HDBK-5 properties.  The lack of a definition of the fracture toughness upper-bound required by JSSG-2006 would be overcome if the upper-bound is estimated by a statistical definition that is agreed to by the procuring agency.  An example of such a bound might be a tolerance limit on the distribution of fracture toughness values.

Figure 3.3.7.  Table of Fracture Toughness Data from MIL-HDBK-5G