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DTD Handbook

Handbook for Damage Tolerant Design

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    • Sections
      • 1. Introduction
      • 2. Fundamentals of Damage Tolerance
      • 3. Damage Size Characterizations
        • 0. Damage Size Characterizations
        • 1. NDI Demonstration of Crack Detection Capability
          • 0. NDI Demonstration of Crack Detection Capability
          • 2. NDI Capability Evaluation for Cracks
            • 0. NDI Capability Evaluation for Cracks
            • 1. Basic Considerations in Quantifying NDI Capability
            • 2. Design of NDI Capability Demonstrations
            • 3. Sample Size Requirements
            • 4. POD Analysis
          • 3. NDI Capability Evaluation for Corrosion
        • 2. Equivalent Initial Quality
        • 3. Proof Test Determinations
        • 4. References
      • 4. Residual Strength
      • 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 Design of NDI Capability Demonstrations

NDI capability is typically quantified through a capability demonstration program.  The concept for such a demonstration is to mimic the real inspection as closely as possible on representative specimens that contain cracks of known sizes that span the range of increase of the POD(a) function.  A comprehensive description for the execution of such a demonstration program and the analysis of the resulting data is presented in MIL-HDBK-1823 (see also Berens [1988] and Berens [2000]).  The analysis of the data from an NDI demonstration uses the maximum likelihood estimates of the parameters of the POD(a) model and the asymptotic properties of such estimates.  This subsection briefly reviews the design and execution of a generic capability demonstration.

An NDI reliability demonstration comprises the execution of a test matrix of inspections on a set of specimens with known crack locations and sizes.  The inspection results, either â or hit/miss, are then analyzed to estimate the parameters of the POD(a) function and the reliably detected crack size for the inspection application.  The specimens are inspected under a test protocol that simulates as closely as practical the actual application conditions.  Establishing test protocols for eddy current, fluorescent penetrant, ultrasonic and magnetic particle inspection systems are discussed in MIL-HDBK-1823.

The objectives and costs of an NDI demonstration determine the matrix of inspections to be performed.  From the analysis viewpoint, there are two major categories of concerns that must be addressed in establishing the experimental design.  These are: a) the generality of inferences that can be made from the controlled and uncontrolled inspection and material parameters; and, b) the number and sizes of cracks and the number of uncracked inspection sites in the specimens.

Controlled and Uncontrolled Factors

To demonstrate capability for an application, it is assumed that: a) the complete protocol for conducting the inspection is well defined for the application; b) the inspection process is under control; and, c) all other factors which introduce variability in an inspection decision are reasonably representative of the application.  The representativeness of these other factors limits the scope of the POD(a) characterization and is addressed by controlling the factors during the inspection or by randomly sampling the factors to be used in the demonstration.  The methods of accounting for these factors are important aspects of the statistical design of the demonstration and significantly influence the statistical properties of the estimates of the POD(a) function parameters.

The important classes of the factors that introduce variation in crack detectability are:

a)      the inherent degree of repeatability of the magnitude of the NDI signal response when a specific crack is independently inspected many times with all controllable factors held constant;

b)      the material and geometrical properties of the specimens and the differences in the physical properties of cracks of nominally identical "size";

c)      the variation introduced by different hardware components in the inspection system; and,

d)      the summation of all the human factors associated with the particular population of inspectors that might be used in the application.

The effects of these factors are present in every NDI reliability demonstration and they should be explicitly considered in the design of the demonstration and the interpretation of the results.

Little can be done about the variation of the response to the NDI excitation at the demonstration stage when inspections are repeated under fixed conditions.  This variation might be reduced if the system was modified or better optimized but that is a different objective.  Repeat inspections under identical conditions will provide a measure of the inherent variability that is a lower bound on the variability to be expected in applications of the system.

The character of the cracks in the structure being inspected will have a significant influence on the inspection outcome.  There are two elements of crack character that impact the demonstration: the physical characteristics of the specimens containing the cracks and the physical properties of the cracks in the specimens.  The inspection system will be designed to detect cracks of a defined size range at a location in a structural element defined at least by a material type and geometrical configuration combination.  A fixed set of specimens containing cracks will be inspected and these specimens either must be of this combination or the assumption must be made that differences in inspection response in the specimens is identical to that obtained in the real application.

The cracks in the specimens must be as close as possible to the cracks that will be in the real structures and of sizes that span the region of interest for the POD(a) analysis.  The assumption of equivalent response to the real inspection is implied when the results of the demonstration are implemented.  Experience with the inspection will dictate the degree of acceptance of the assumption.  For example, EDM notches are not good substitutes for eddy current inspections of surface fatigue cracks but may be the only possible choice for subsurface ultrasonic inspections.

Inspection capability is expressed in terms of crack size but not all cracks of the same "size" will produce the same magnitude of inspection response.  In general, the specimens used in NDI reliability demonstrations are very expensive to obtain and characterize in terms of the sizes of the cracks in the specimens.  Each set of specimens will be inspected multiple times if other factors are being considered in the demonstration.  From a statistical viewpoint, this restriction on the experimental design limits the sample size to the number of cracks in the specimen set.  Multiple independent inspections of the same crack only provide information about the detection probability of that crack and do not provide any information about the variability of inspection responses between different cracks.  Stated another way, k inspections on n cracks is not equivalent to inspections of n • k different cracks, even if the inspections are totally independent.  The number and sizes of cracks will be addressed later.

Accounting for the variability due to differences in inspection hardware must first be considered in terms of the scope of the capability evaluation.  Each component of the inspection system can be expected to have some, albeit small, effect on inspection response.  The combinations of particular components into sub-systems and complete inspection stations can also be expected to influence the response.  Recognizing that individual hardware combinations might have different POD(a) capabilities, a general capability objective must be set.  Each combination can be characterized, each facility comprising many combinations can be characterized, or many facilities can be characterized.  Ideally, the available hardware combinations would be randomly sampled for the scope of the desired characterization and a weighted average of responses would be used to estimate the POD(a) function.  On a practical level this is seldom done for ostensibly identical equipment. (Note that an analogous problem exists when accounting for the human factors which will be discussed in the following.)  More commonly, capability demonstrations are performed on combination of hardware and the assumption is made that the characterization would apply to all combinations.  That is, the POD(a) differences between combinations are assumed to be negligible.

The above is directed at a complete individual inspection system (however defined), but the variability of interchangeable components of a system can often be directly assessed.  For example, experience has shown that different eddy current probes produce different responses when all other factors are constant.  If a single probe is used to demonstrate the capability of an eddy current system, the estimated POD(a) function applies to the relevant inspections using that probe.  However, if the POD characterization is to be used for in-service inspections using any such probe, an assumption is required that the probe is representative of the entire population.  If a larger demonstration is affordable, the inspections could be performed using a random sample of probes from the available population.  The analysis method must then account for the fact that multiple inspections of each crack were made with the different probes.  The resulting characterization would better represent an inspection for a randomly selected probe.

Accounting for the variation from more than one source is more complex.  Care must taken to ensure that the multiple sources are balanced in the analysis of the data and that the correct analysis procedures are used.  For example, in the early evaluations of an automated eddy current system for turbine engine disks (the ECIS system for the ENSIP/RFC applications), there was considerable interest in the inherent variability in response from repeated, identical inspections and from different probes with their associated re-calibration changes.  (Other factors were initially considered but were later ignored after it was shown that they had no affect on POD(a) for the system.)  The specimen sets would be inspected three times: twice with one probe and once with a second probe.  The data from the three inspections, however, could not be combined in a single analysis since such an analysis would skew the results toward the probe with double representation.  Thus, one analysis would be performed to estimate the inherent repeat variability and a second analysis would be performed to estimate the probe to probe variation.  The results would then be combined to arrive at the POD(a) function that accounted for both sources of variation.  It might be noted in this context that the repeat variability was negligible as compared to the variability that results from re-calibration and probe changes.  The demonstration plan was later modified to better estimate the more significant between probe variation by performing the third inspection with a third probe.

Factorial-type demonstrations are an efficient approach to simultaneously account for several significant factors.  However, such demonstrations for more than a couple of factors require many inspections of the specimen set.  More sophisticated statistical experimental designs might be employed but the actual choice of such a design and the analysis of the data are driven by the specific objectives of a particular experiment.  Discussion of such designs is beyond the scope of this discussion.

Human Factors

When the inspector plays a significant role in the find/no find decision, he or she is an integral component of the NDI system.  In such common inspection scenarios, human factors can contribute significantly to the variability in inspection results.  In this context, human factors refer to both the dynamic capabilities of individual inspectors and the user friendliness of the inspection tools in the environment of the application.  Experiments have been conducted to quantify some of the environmental effects of human factors and data from some demonstration experiments have been interpreted in terms of the level of training and experience of the inspectors (see, for example, Spencer & Schurman [1994]).  However, the effects and interactions of human factors on inspection results have not been characterized.  Rather, to the extent possible, NDI systems are automated to minimize the effect attributed to the inspector.

In a non-automated inspection, many human factors potentially influence the inspection decision and they cannot all be accounted for in a capability demonstration.  At some level, the representative inspection assumption will be required.  Given that the mechanical aspects of the NDI system and inspection environment are held constant, differences between inspectors can cause a biased capability characterization if ignored.  Again, the objective of the capability characterization must be stated in advance.  If each inspector is being evaluated, a separate POD(a) function for each is estimated.  If a single POD(a) function is wanted for an entire facility, the inspectors in the demonstration must be randomly sampled in proportion to the percent of such inspections each performs.  Alternatively, inspectors might be categorized by, say, capability as implied by certification level.  A random sample of the inspectors from each level could be selected to arrive at a composite POD(a) for the level and a weighted average would be calculated based on the percent of inspections performed by each level.  An example of designing such a demonstration is given in Hovey, et al. [1989].  Example results from the evaluation of a population of inspectors can also be found in Davis [1988].