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Flaw shapes and stress intensity distributions for a variety of technologically important surface-flaw problems using the frozen-stress method are described. Limitations of the method are noted. Results are used to illustrate effects peculiar to three-dimensional cracked-body problems.
The paper provides an engineering analysis approach for assessing reliability of NDE flaw detection using smaller number of demonstration data points. It explores dependence of probability of detection (POD), probability of false positive (POF), on contrast-to-noise ratio, and net decision threshold-to-noise ratio in a simulated data; and draws some generically applicable inferences to devise the approach. ASTM nondestructive evaluation standards provide requirements on signal-to-noise ratio and/or contrast-to-noise ratio in order to provide reliable flaw detection and limit false positive calls. POD analysis of inspection test data results in an estimated flaw size, denoted by 𝑎90/95. This flaw size has 90% POD and minimum 95% confidence. POF is also estimated in the analysis. POD demonstration requires specimens with flaws of known size. In many situations, it is very expensive to produce the large number of flaws required for the POD analysis. In some situations, only real flaws can truly represent the flaws for demonstration. Real flaws of correct size and location in part configuration specimen may be difficult to produce, if not impossible. Here, an engineering analysis approach is devised using simulation to assess reliability of NDE technique when a limited number of flaws are available for demonstration. In this simulation, a technique is considered reliable, if it provides flaw detectability size equal to or better than the theoretical 𝑎90𝑡ℎ used in simulation and also provides a POF less than or equal to a chosen value. The paper uses simulated signal response versus flaw size data to devise the approach. Linear correlation is used between the signal response data and flaw size. POD software mh1823 uses generalized linear model (GLM) in POD analysis after transforming the flaw size and signal response, if needed, using logarithm. Therefore, this approach is in agreement with the linear signal correlation used in mh1823. Using the POD analysis of data, generic conditions on contrast-to-noise ratio and net decision threshold-to-noise ratio are derived for reliable flaw detection. In order to assess technique reliability using the engineering approach, signal response-to-flaw size correlation about the flaw size of concern is needed. In addition, measurement of noise is also needed. If the technique meets the above requirements, assumption of linear signal-to-flaw size correlation and conditions on noise, then the technique can be assessed using this analysis as it fits the underlying POD model used here. The approach is conservative and is designed to provide a larger flaw size compared to the POD approach. Such NDE technique assessment approach, although, not as rigorous as POD, can be cost effective if the larger flaw size can be tolerated. Typically, this is a situation for all quality control NDE inspections. Here, an NDE technique needs to be reliable and 𝑎90/95 is not estimated, but the assessed flaw size is assumed to be larger than the unknown a90 due to conservative factors or margins. Applicability of the approach for assessing reliability of flaw detection in x-ray radiography and 2D imaging in general is also explored.
Nondestructive evaluation (NDE) method reliability can be determined by a statistical flaw detection study called probability of detection (POD) study. In many instances the NDE flaw detectability is given as a flaw size such as crack length. The flaw is either a crack or behaving like a crack in terms of affecting the structural integrity of the material. An alternate approach is to use a more complex flaw size parameter. The X-ray flaw size parameter, given here, takes into account many setup and geometric factors. The flaw size parameter relates to X-ray image contrast and is intended to have a monotonic correlation with the POD. Some factors such as set-up parameters including X-ray energy, exposure, detector sensitivity, and material type that are not accounted for in the flaw size parameter may be accounted for in the technique calibration and controlled to meet certain quality requirements. The proposed flaw size parameter and the computer application described here give an alternate approach to conduct the POD studies. Results of the POD study can be applied to reliably detect small flaws through better assessment of effect of interaction between various geometric parameters on the flaw detectability. Moreover, a contrast simulation algorithm for a simple part-source-detector geometry using calibration data is also provided for the POD estimation.
Nondestructive evaluation (NDE) method reliability can be determined by a statistical flaw detection study called probability of detection (POD) study. In many instances, the NDE flaw detectability is given as a flaw size such as crack length. The flaw is either a crack or behaving like a crack in terms of affecting the structural integrity of the material. An alternate approach is to use a more complex flaw size parameter. The X-ray flaw size parameter, given here, takes into account many setup and geometric factors. The flaw size parameter relates to X-ray image contrast and is intended to have a monotonic correlation with the POD. Some factors such as set-up parameters, including X-ray energy, exposure, detector sensitivity, and material type that are not accounted for in the flaw size parameter may be accounted for in the technique calibration and controlled to meet certain quality requirements. The proposed flaw size parameter and the computer application described here give an alternate approach to conduct the POD studies. Results of the POD study can be applied to reliably detect small flaws through better assessment of effect of interaction between various geometric parameters on the flaw detectability. Moreover, a contrast simulation algorithm for a simple part-source-detector geometry using calibration data is also provided for the POD estimation.
NASA requires that NDE methods and inspectors demonstrate 90% Probability of Detection (POD) with 95% confidence for critical flaw sizes when inspecting fracture critical metallic components. NASA addresses the known variability of NDE inspector capability in two ways. The first, Special NDE, requires that every inspector demonstrate the required 90/95 POD, which is resource intensive. The second approach is Standard NDE for which conservative flaw sizes for different NDE methods are provided such that it is expected that most properly trained inspectors will exceed the 90/95 POD requirement. As such, individual POD demonstration testing is not required. The origin of NASA Standard NDE dates to the start of the Space Shuttle Program in the early 1970’s. In the first study to quantitatively assess NDE methods and inspectors, the performance of multiple inspectors was evaluated for different NDE methods using a large set of fatigue cracked specimens. A rudimentary POD analysis was performed to estimate the 90/95 POD flaw size for each inspector for each method. Additionally, the average and standard deviation of the 90/95 POD flaw size across the multiple inspectors was calculated to estimate the flaw size for which 95 percent of inspectors would provide the 90/95 POD capability. These estimated 90/95/95 POD flaw sizes evolved into the NASA Standard NDE flaw sizes still in use for structural analysis five decades later. The methodology for performing Standard NDE POD studies was never documented in NASA requirements. Furthermore, POD analysis methods have significantly evolved since this seminal study. Likewise, NDE methods have improved and there has been a push to reassess Standard NDE flaw sizes for existing methods, and to develop Standard NDE flaw sizes for new methods such as digital radiography. In this study, a Standard NDE POD methodology was developed and baselined using the historical data. This reanalysis of the historical data identified several deficiencies in the original test plan as well as an overall lack of conservatism in the estimated 90/95/95 POD flaw sizes. The results of this historical review and the new methodology are being incorporated into an update of NASA NDE POD requirements.
Using a singular solution for a part circular crack by Smith, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors (SIFs) from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50, and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the 'equivalent' semi-elliptical flaw for correlating the part circular flaw results with semi-elliptical flaw results was not valid for a/2c much less than 0.20. Best overall agreement for the moderate (a/t about 0.5) to deep flaws (a/t about 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory due to Newman when compared on the basis of equivalent flaw depth and area. The Smith theory, when correlated on the basis of flaw depth and area, appears to yield reasonable estimates (within 10%) of the SIF for flat bottomed flaws for the geometries studied here.
Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-1823 and associated mh1823 POD software gives most common methods of POD analysis. In this paper, POD analysis is applied to an NDE method, such as eddy current testing, where calibration is used. NDE calibration standards have known size artificial flaws such as electro-discharge machined (EDM) notches and flat bottom hole (FBH) reflectors which are used to set instrument sensitivity for detection of real flaws. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. Therefore, it is important to correlate signal responses from real flaws with signal responses form artificial flaws used in calibration process to determine reliably detectable flaw size.
Automatic incorporation of non-destructive evaluation (NDE) data into CAD and finite element (FE) models for structural analysis is essential for accurate residual-life and strength analyses of composite structures. Currently, two significant but independent challenges exist for incorporating NDE data in such analyses: interpretation of the NDE signals to locate and characterize the structural defects and the incorporation of that information into structural analysis tools. The first challenge will be addressed through linear inversion of calculated synthetic responses generated by a simulation engine to evaluate flaw size, location, and other characteristics. The second challenge will be addressed by building on prior and parallel defect modeling efforts to integrate suitable flaw models into the CAD/finite-element representation of a specimen. Ultrasonic NDE information is usually represented using C-Scans of time-of-flight or intensity information. Other modalities such as thermography and computed tomography (CT) could also be used to characterize the structure. This information will first be projected into material coordinates and then aligned with the specimen’s finite element mesh. The NDE data can then be incorporated by inserting flaw geometry into the CAD and FE analysis model and automatic modification of local material properties and boundary conditions. This process will enable the use of structural analysis tools even for practical modalities such as ultrasound and thermography which may not directly give accurate-enough geometric information to fully define the flaw. The full flaw characteristics will be inferred using prior expert and modeling knowledge to categorize flaw signatures. Outputs for this project will include demonstrated methods for creating structural analysis geometric models that incorporate flaw characterization information; these models can then be used directly in popular commercial FEA software. In addition, the primary deliverable for the project will include a software that will be able to automatically incorporate different kinds of flaws into an existing FE models. The models will be generated in standard file formats to enable direct import into the analysis software.
Fracture behavior of tensile specimens containing through-the-thickness flaws and part-through semi-elliptic surface flaws was investigated. The material was T300/5208 graphite/epoxy, with a stacking sequence 0/+ or - 45/90 sub ns. Laminate thicknesses ranged from 8 to 120 plies. Fracture toughness for specimens with through-the-thickness flaws was a function of laminate thickness. Fracture toughness was also independent of crack size. Fracture toughness for the thick laminates was also independent of specimen geometry (center-cracked tension specimen, compact tension specimen, and three-point bend specimen). Using the asymptotic value of facture toughness and linear elastic isotropic fracture mechanics, the notched strength of tensile specimens with semi-elliptic surface flaws was predicted. The strength ratio is a function of the flaw depth (a/t) and flaw aspect (a/c) ratios. Comparisons between predicted and experimental strengths are good for large values of a/t. The notched strength of filament wound graphite/epoxy tensile specimens with part-through surface flaws was also predicted.
Fracture behavior of tensile specimens containing through-the-thickness flaws and part-through semi-elliptic surface flaws was investigated. The material was T300/5208 graphite/epoxy, with a stacking sequence 0/+ or - 45/90 sub ns. Laminate thicknesses ranged from 8 to 120 plies. Fracture toughness for specimens with through-the-thickness flaws was a function of laminate thickness. Fracture toughness was also independent of crack size. Fracture toughness for the thick laminates was also independent of specimen geometry (center-cracked tension specimen, compact tension specimen, and three-point bend specimen). Using the asymptotic value of fracture toughness and linear elastic isotropic fracture mechanics, the notched strength of tensile specimens with semi-elliptic surface flaws was predicted. The strength ratio is a function of the flaw depth (a/t) and flaw aspect (a/c) ratios. Comparisons between predicted and experimental strengths are good for large values of a/t. The notched strength of filament wound graphite/epoxy tensile specimens with part-through surface flaws was also predicted.
The detection and repair of flaws such as voids and delaminations in the sprayed on foam insulation of the external tank reduces the probability of foam debris during shuttle ascent. The low density of sprayed on foam insulation along with it other physical properties makes detection of flaws difficult with conventional techniques. An emerging technology that has application for quantitative evaluation of flaws in the foam is pulsed electromagnetic waves at terahertz frequencies. The short wavelengths of these terahertz pulses make them ideal for imaging flaws in the foam. This paper examines the application of terahertz pulses for flaw detection in foam characteristic of the foam insulation of the external tank. Of particular interest is the detection of voids and delaminations, encapsulated in the foam or at the interface between the foam and a metal backing. The technique is shown to be capable of imaging small voids and delaminations through as much as 20 cm of foam. Methods for reducing the temporal responses of the terahertz pulses to improve flaw detection and yield quantitative characterizations of the size and location of the flaws are discussed.
Nondestructive Evaluation (NDE) procedures are required to detect flaws in structures with a high percentage detectability and high confidence. Conventional Probability of Detection (POD) methods are statistical in nature and require detection data from a relatively large number of flaw specimens. In many circumstances, due to the high cost and long lead time, it is impractical to build the large set of flaw specimens that is required by the conventional POD methodology. Therefore, in such situations it is desirable to have a flaw detectability estimation approach that allows for a reduced number of flaw specimens but provides a high degree of confidence in establishing the flaw detectability size. This paper presents an alternative approach called the conservative margin approach (CMA). To investigate the applicability of the CMA approach, flaw detectability sizes determined by the CMA and POD approaches have been compared on actual datasets. The results of these comparisons are presented and the applicability of the CMA approach is discussed.
The primary structure of the Ares I-X Upper Stage Simulator (USS) launch vehicle is constructed of welded mild steel plates. There is some concern over the possibility of structural failure due to welding flaws. It was considered critical to quantify the impact of uncertainties in residual stress, material porosity, applied loads, and material and crack growth properties on the reliability of the welds during its pre-flight and flight. A criterion--an existing maximum size crack at the weld toe must be smaller than the maximum allowable flaw size--was established to estimate the reliability of the welds. A spectrum of maximum allowable flaw sizes was developed for different possible combinations of all of the above listed variables by performing probabilistic crack growth analyses using the ANSYS finite element analysis code in conjunction with the NASGRO crack growth code. Two alternative methods were used to account for residual stresses: (1) The mean residual stress was assumed to be 41 ksi and a limit was set on the net section flow stress during crack propagation. The critical flaw size was determined by parametrically increasing the initial flaw size and detecting if this limit was exceeded during four complete flight cycles, and (2) The mean residual stress was assumed to be 49.6 ksi (the parent material s yield strength) and the net section flow stress limit was ignored. The critical flaw size was determined by parametrically increasing the initial flaw size and detecting if catastrophic crack growth occurred during four complete flight cycles. Both surface-crack models and through-crack models were utilized to characterize cracks in the weld toe.
Conventional methods for reducing the pulsed thermographic responses of delaminations tend to overestimate the size of the flaw. Since the heat diffuses in the plane parallel to the surface, the resulting temperature profile over the flaw is larger than the flaw. A variational method is presented for reducing the thermographic data to produce an estimated size for the flaw that is much closer to the true size of the flaw. The size is determined from the spatial thermal response of the exterior surface above the flaw and a constraint on the length of the contour surrounding the flaw. The technique is applied to experimental data acquired on a flat bottom hole composite specimen.
Surface flawed specimens of 2219-T87 and 6Al-4V STA titanium weldments were tested to determine static failure modes, failure strength, and fatigue flaw growth characteristics. Thicknesses selected for this study were purposely set at values where, for most test conditions, abrupt instability of the flaw at fracture would not be expected. Static tests for the aluminum weldments were performed at room, LN2 and LH2 temperatures. Titanium static tests for tests were performed at room and LH2 temperatures. Results of the static tests were used to plot curves relating initial flaw size to leakage- or failure-stresses (i.e. "failure" locus curves). Cyclic tests, for both materials, were then performed at room temperature, using initial flaws only slightly below the previously established failure locus for typical proof stress levels. Cyclic testing was performed on pairs of specimens, one with and one without a simulated proof test cycle. Comparisons were made then to determine the value and effect of proof testing as affected by the various variables of proof and operating stress, flaw shape, material thickness, and alloy.
A modular system composed of two sets of tasks which interprets the flaw data and allows compensation of the data due to transducer characteristics is described. The hardware configuration consists of two main units. A DEC LSI-11 processor running under the RT-11 sngle job, version 2C-02 operating system, controls the scanner hardware and the ultrasonic unit. A DEC PDP-11/45 processor also running under the RT-11, version 2C-02, operating system, stores, processes and displays the flaw data. The software developed the Ultrasonics Evaluation System, is divided into two catagories; transducer characterization and flaw classification. Each category is divided further into two functional tasks: a data acquisition and a postprocessor ask. The flaw characterization collects data, compresses its, and writes it to a disk file. The data is then processed by the flaw classification postprocessing task. The use and operation of a flaw data postprocessor is described.
Growth regimes of interacting surface flaws of arbitrary shape are analyzed with the aid of the body force method, and the stability of the process is assessed on the basis of the variation of the load during the growth. It is shown that irregularly shaped flaws are often associated with very high stress intensity factors locally, which tend to change as the flaws grow into more regular shapes. Several examples of various flaw shapes are worked out for illustration, and it is shown that a simple formula seems to provide an accurate estimate of the maximum stress intensity factor for surface flaws of various shapes, which are not very slender. The formula involves the overall maximum tension, as well as the area of the projection of the flaw on the plane normal to the maximum tension.
NASA's Ares 1 Upper Stage Simulator (USS) is being fabricated from welded A516 steel. In order to insure the structural integrity of these welds it is of interest to calculate the critical initial flaw size (CIFS) to establish rational inspection requirements. The CIFS is in turn dependent on the critical final flaw size (CFS), as well as fatigue flaw growth resulting from transportation, handling and service-induced loading. These calculations were made using linear elastic fracture mechanics (LEFM), which are thought to be conservative because they are based on a lower bound, so called elastic, fracture toughness determined from tests that displayed significant plasticity. Nevertheless, there was still concern that the yield magnitude stresses generated in the flange-to-skin weld by the combination of axial stresses due to axial forces, fit-up stresses, and weld residual stresses, could give rise to significant flaw-tip plasticity, which might render the LEFM results to be non-conservative. The objective of the present study was to employ Elastic Plastic Fracture Mechanics (EPFM) to determine CFS values, and then compare these values to CFS values evaluated using LEFM. CFS values were calculated for twelve cases involving surface and embedded flaws, EPFM analyses with and without plastic shakedown of the stresses, LEFM analyses, and various welding residual stress distributions. For the cases examined, the computed CFS values based on elastic analyses were the smallest in all instances where the failures were predicted to be controlled by the fracture toughness. However, in certain cases, the CFS values predicted by the elastic-plastic analyses were smaller than those predicted by the elastic analyses; in these cases the failure criteria were determined by a breakdown in stress intensity factor validity limits for deep flaws (a greater than 0.90t), rather than by the fracture toughness. Plastic relaxation of stresses accompanying shakedown always increases the calculated CFS values compared to the CFS values determined without shakedown. Thus, it is conservative to ignore shakedown effects.