Simulation Supported POD Methodology and Validation for Automated Eddy Current Procedures

Transcription

1 4th International Symposium on NDT in Aerospace Th.1.A.1 Simulation Supported POD Methodology and Validation for Automated Eddy Current Procedures Anders ROSELL, Gert PERSSON Volvo Aero Corporation, Trollhättan, Sweden, anders.ar.rosell@volvo.com Chalmers University of Technology, Göteborg, Sweden, gert.persson@chalmers.se Abstract. Model assisted probability of detection (POD) estimation is developed and validated for an automated eddy current procedure. The model assisted POD is studied using both finite element modelling and the simulation software CIVA utilizing the eddy current module and POD tools. The resulting method capability estimation from the models is based on, and validated against, an experimental procedure carried out on fatigue cracks in Ti-6Al-V4. The experimental POD curve is obtained in two tests using probe scanning with different index step distances. The two experimental results are compared to simulated data in order to also include a procedure change. The POD methodology using simulations is studied both with parametric POD curve estimation, obtained analogously to an experimentally based curve as well as with a non-parametric approach using a simple meta-model based on the finite element model. The presented work represents a part of the work carried out within the European collaboration project PICASSO and the eddy current POD validation case. The results show good agreement between the experimental and model based POD curves. Using mathematical modelling as a tool for estimating a procedure capability can be cost efficient and give both fast and accurate results. Model assisted POD studies may also be a way to include parameter settings that are difficult to assess experimentally. The model can also give more insight, compared to purely empirical studies, about the impact from various procedure parameters on the POD result. 1. Introduction The objective of a probability of detection (POD) assessment is to acquire a representative estimation of the capability of a non-destructive evaluation (NDE) procedure. It is of high importance that the reliability and performance of the NDE techniques used for flaw detection are validated and that the capability of detection is quantified and well understood. In this work an automated eddy current procedure is considered. The framework for a POD assessment of such a NDE system is described in [1]. The procedures require extensive experimental work and a large number of cracks in order to show a valid POD estimate. This is often time consuming and costly. The experimental assessments are also often approximate as a consequence of the high costs involved to retrieve relevant defects in complex parts. Small variations in the procedure can change the POD and a full understanding of the impact from various parameters is desired. Modelling tools can give efficient POD estimations at an early stage as well as an understanding of critical parameters and defect characteristics related to the inspection procedure. The limitation and approximative nature of mathematical models must however be addressed and it is therefore important to validate and compare results directly to corresponding experimental procedures. Licence: 1

2 A comparison between an experimental and a model based eddy current POD estimation is carried out within this work. The experimental procedure is simplified in the sense that the human influence is ignored and only one eddy current probe is used. This eliminates the variations introduced by those two factors. The model based POD assessment requires a three dimensional problem description. This puts high demands on how to use the modelling techniques in order to arrive at an efficient computational method. The mathematical method used is based both on the simulation software CIVA and on finite element models. 2. The PICASSO Validation Case An automated eddy current procedure on flat surface samples was defined for the model validation. The procedure parameters are stated in table 1. The goal was to use a quite general procedure using a simple absolute probe. The scan index distance step L scan was selected to be same as the outer radius of the probe coil ( mmm). This selection seemed to represent a case where this parameter has a limited effect on POD. This was concluded after comparing the signal response variation between defects and between repetitions over the same set of defects. In order to test the influence from this procedure parameter, the identical procedure on the same test objects, but with an increased scan index step, was tested. This time the index distance L scan step was set equal to the coil outer diameter. Increasing this parameter further will result in a reduced POD and in general it is more common to see automated inspections carried out with smaller index steps. Reducing the index distance will remove much of the signal variation correlated to the position of the defect relative the scan. A small index step can also aid in the visualization of signal as function of the spatial coordinates. The goal of including two index distances that both has an influence on the POD was to allow this to be studied in a model. Table 1. Eddy current procedure parameters EC signal measure Probe Frequency Scan speed Defects Material Material conductivity Material surface Calibration notch Noise threshold Decision threshold Impedance amplitude relative reference level Absolute, with ID = 0.75, OD = 1 mm, L = 1 mm 1 MHz 1 mm/s Fatigue cracks aligned with scan direction Ti -6AL-4V 8 MS/m Flat and smooth (R a < 1 µm) Rectangular, L = 0.76 mm, D = 0.38 mm, W = mm 5 % of reference level 20 % of reference level The experimental capability assessment was conducted on 53 laboratory grown fatigue cracks between 0.4 and 2 mm in surface length. Several cracks were broken open and showed that the geometry was close of being half-circular into the depth of the Ti-6Al-4V material. The fatigue cracks were fully closed and it is assumed that there are residual compressive stresses over the cracks, resulting from the fatigue process. The resulting POD curves based on the signal response â versus crack size a is calculated according to Berens approach [1, 2]. The linear regression is best achieved using log-log relation between â and a. Figure 1 presents the experimental POD curves using L scan = and 1.0 mm, respectively. The result shows the impact from the variation of index distance step which then is an important variable if selected in this regime. The sources of variability of the automated eddy current procedure must be considered in a mathematical model if good estimations are to be carried out. The sources of variation in this procedure are 2

3 0.9 L scan = mm L scan = 1 mm Exp Exp 95% conf Figure 1. Experimental POD curves for two settings of the scan index step L scan. Scan position relative the fatigue crack. This variable is estimated to be uniformly distributed on [ L scan /2, L scan /2]. Fatigue crack orientation is closed to parallel but is estimated to be normally distributed with mean µ o = 0 and standard deviation σ o = 1 5. Lift-off is close to mm which is the thickness of the protective PTFE tape and vary locally around in the order of the surface roughness R a. The lift-off is estimated to be normally distributed with µ L = 100 µm and σ L = 1 µm. Fatigue crack characteristics. The lift-off mean value must be considered to be approximate but the resulting change of setting this to a slightly different value is regarded as small. The experimental POD assessment is conducted using a single probe and reference notch. This is reducing variations resulting from probe or calibration changes which therefore are omitted here but should be considered in a more general procedure. The fatigue cracks vary in shape and, as they are tightly closed also in bridging electric contacts between the crack faces. The electric contacts within closed cracks are shown to have a significant contribution to signal variation which is relevant for the cracks used in this validation [3]. Opened and oxidized cracks can have a variation in geometry that is relevant to include in the model. The mathematical model must present a reasonable description of the studied fatigue cracks in a statistical perspective. It is a great challenge to model the individual, natural crack and such might not be relevant for efficient model assisted POD estimations. It is however important to have a reasonable crack description that can be validated against the experimental signal responses. This holds as long as there is lack of developed tools to estimate the crack characteristics more thoroughly in a non-destructive way, considering for example geometry, branching, bridging electrical contacts etc. In order to give input to the crack characteristics a number of individual cracks were measured using a scan index step of 50 µm. This provides an input of the signal response with limited contribution from the variation in crack position and orientation relative the probe scan. The result from these measurements is presented in figure 2. The result in figure 2 can be used as input to the fatigue crack description in the mathematical model. It is important to have a good crack model in the size region where the modelled data is produced. The contact characteristics within closed fatigue cracks studied here might be best represented with different models for small (< 1 mm) and larger cracks [4]. 3

4 1.5 1 â Figure 2. Signal response for 11 fatigue cracks measured with scan index step of 50 µm. 3. Methodology to Model Based Eddy Current Capability Estimation There are several possible approaches to model eddy current NDE phenomena. A comprehensive review is presented by Auld and Moulder [5]. Here we have used both finite element modelling and CIVA [6]. Regardless of which model is used it is important to consider the model validity and ability to include the required probe-flaw interaction parameters. The model must also be able to handle the relevant configurations in the parameters that may vary during the inspection process. The mathematical model is therefore validated against experiments with the same equipment which then was used for the POD study. Here, the validation was carried out on the calibration notch and a narrow half circular fatigue crack [3]. In order to build model based POD curves for eddy current procedures we have to address the parameters of the inspection that can have an impact on the final inspection result. The human influence on data collection and interpretation of impedance signals are ignored here. The result of this is in principle that we treat automated or manual inspections but in the latter case only the signal reading on the screen of the eddy current instrument. There are still a number of parameters that has an impact on the final impedance measure. By knowing the parameters and their variation in terms of statistical distributions allow us to sample a number of inspection configurations and calculate these in the mathematical model, see figure 3. The approach to calculate the POD curve is represented by two alternatives in figure 3. The left path represents the situation where computations are time consuming and must be limited in number. This method resembles the experimental approach in most cases. The method requires a number of characteristics for the â versus a data and is also depending on the selected defect sizes. The right approach requires a large number of calculations of sampled configurations from each relevant defect size. This technique is shown to be possible for example by the use of meta-models [7] which also are used within this work. The method can have several benefits as we do not have to consider any statistical model in order to calculate the POD curve. The non-parametric approach can be a vital tool when data does not hold the requirements for use in the classical parametric POD model, for example if we have non-linear â versus a relationship. 4

5 Figure 3. Methodology to estimate POD curves using a mathematical model. 4. Comparing Experimental and Model Based POD The CIVA model was set up based on the validation case procedure. The fatigue cracks are not modelled with bridging contacts. However, as these tend to be located into the depth of the crack an elliptical crack model was used. The variation in fatigue crack characteristics is then modelled by an uncertainty in the elliptical shape according to figure 4. The model is built using figure 2 as a guideline with a focus of being representative for small cracks (< 1 mm). The parameter describing crack variation ξ is assumed to be normally distributed with µ ξ = 0.7 and σ ξ = The crack location relative the scan path and the variation in lift-off are also included in the model with distributions based on the bullets presented above in section 2. The uncertainty of crack orientation is omitted as this parameter is requiring special treatment in CIVA. The crack orientation is therefore assumed to be parallel with the direction of the scan c c ξ â Exp. ξ = µ ξ ξ = µ ξ σ ξ ξ = µ ξ + σ ξ Crack size Figure 4. Fatigue crack model used in CIVA. 5

6 The results from the CIVA calculations are presented in figure 5. The POD curves are based on 54 simulated cracks ranging from mm in length. The log-log regression between signal response and crack size is used for building a parametric POD curve analogously with the experimental POD curves. There is an overall good agreement between the model based and experimental POD curve, also in the shift resulting from the increased scan index step L scan. The model based curves are however estimated from sub interval of defect sizes compared to the experimental selection. This sub interval could be treated with the same crack model for all sizes. The motivation for using only this sub interval is supported by the fact that the signal response from larger crack is underestimated by the model. The resulting linear regression of the model based data has however a smaller derivative which gives the higher P OD values for small cracks. Figure 4 is indicating that a change in the model for larger cracks could be relevant. The use of such model would have the possibility to make better estimation of the parametric POD curve as cracks from the same interval as the experiments could be used. 0.9 L scan = mm L scan = 1 mm Exp Exp 95% conf. CIVA Figure 5. Comparison between experimental and model based POD curves. The POD curves are based on two index step distances and the model based curve is produced using the CIVA software. An alternative to the parametric POD estimation is to use a large number of simulations at individual crack sizes. Using a model based directly on the physical principles of eddy current would in most cases require long computation times for such an approach. A possibility is to use a meta-model based on a limited number of calculations from which a large number of configurations can be sampled efficiently. A simplified meta-model is build from finite element calculations at different crack sizes. The crack description in the finite element analysis is set up as previously described in [4]. The crack is here described with additional conductivity of 80% of the bulk conductivity applied to the component of the conductivity tensor directed across the crack width according to figure 6a. The parameter describing the contact variation ζ is assumed to be normally distributed with µ ζ = 0.45 and σ ζ = The meta-model is created by finite element calculations of the probe signal response at several locations around the crack. The model based C-scan information is then used for sampling various crack locations and orientations relative the scan. The amplitude at the different locations is scaled uniformly with the crack characteristic established by a linearization of the signal response as a function of the crack model parameter ζ. The variation in lift-off is small and is ignored in this model as an additional simplification. The resulting meta-model can consider different distributions in crack orientation and position relative the scan of the probe efficiently. Using a uniform distribution of the crack position on [ L scan /2, L scan /2] and a crack orientation that is normally distributed with mean µ o = 0 and a standard deviation σ o = 2.5 is presented in figure 6b. The crack model has similar characteristics as presented in figure 4 and is underestimating the signal response for larger cracks. The meta-model was 6

7 used to calculate 2000 configurations at 19 crack sizes ranging from 0.4 to 1.4 mm. The nonparametric POD curve presented in figure 6b is in this case not influenced by the miss-fit of the crack model to larger cracks as no regression of the relation between â versus a is used. The non-parametric curve will not follow a cumulative normal distribution function as the P OD(a) is calculated as the fraction of responses above the decision threshold. 1.6 c ζ c 0.9 L scan = mm L scan = 1 mm 1 â Exp. ζ = µ ζ ζ = µ ζ σ ζ Exp. Exp 95% conf. 0.2 ζ = µ ζ + σ ζ FEM meta model Crack size (a) Fatigue crack model used in FEM (b) Comparison of POD curves. Figure 6. Fatigue crack model and POD curves comparing experimental and model based curves. The POD curves are based on two index step distances and the model based curve is produced using a meta-model constructed from finite element calculations. The influence of crack orientation and probe scan index step is evaluated in figure 7. The orientation of the crack is assumed to be normally distributed with mean µ o = 0 and standard deviation σ o according to figure 7a. The figure shows that a parallel crack orientation is a conservative selection if we want to exclude this parameter in the model based POD estimation. Figure 7b shows that the POD can be slightly improved by a reduced probe scan index step but has no benefit of a too small selection under the present circumstances σ o = 0, L scan = mm σ o = 5, L scan = mm σ o = 30, L scan = mm σ o = 0, L scan = 1.0 mm σ o = 5, L scan = 1.0 mm σ o = 30, L scan = 1.0 mm L scan = mm L scan = 0.25 mm L scan = mm L scan = 0.75 mm L scan = 1.0 mm (a) Variation in crack orientation (b) Variation in scan index step Figure 7. POD curves calculated by the meta-model of the finite element analysis showing the influence of crack orientation and probe scan index step. 7

8 5. Conclusions Mathematical modelling can give fast and accurate POD estimations. It is shown here that it is possible to calculate both parametric and non-parametric POD curve by the use of a mathematical model. The model based approach is efficient but require good knowledge of the process. This is important first as the adequate variables have to be assessed in the model, with reasonable distributions coupled to them. Secondly the crack model needs special attention and it is suggested to adapt it carefully to the crack type relevant for the final inspection target. It is important to consider a crack model resulting in the expected eddy current probeflaw interaction, which can be influenced by special characteristics such as bridging electric contacts between the crack faces. The difference in POD due to the change in probe scan index step is shown to be accurately predicted by the model. This result indicates that the concept of delta POD and transfer functions can be aided by mathematical modelling. In that case the change of a parameter is studied in the model and the change in POD is added to an existing experimental data set. The result in that case includes the confidence of having real experiments as a base line for the POD. The model assisted approach is a good tool in order to study the effect from various parameters which is shown within this work. This gives a better understanding of the NDE procedure which directs inspections to be more reliable and optimized in the future. Acknowledgments This work is carried out within the European Collaboration project PICASSO. The Volvo Aero support and the funding from the European Commission within the FP7 programme are greatly acknowledged. The authors wish to thank Per Henrikson from Volvo Aero and Håkan Wirdelius from Chalmers University of Technology for discussions, support and encouragement during the project. Many thanks also to Catherine Gilles-Pascaud from CEA for helping us realize the CIVA calculations. References [1] MIL-HDBK Nondestructive evaluation system reliability assessment USA Department of Defense Handbook. [2] A. P. Berens. Nde reliability data analysis. In Nondestructive Evaluation and Quality Control, volume 17 of ASM Metals Handbook, pages ASM International, [3] A. Rosell and G. Persson. Finite element modelling of closed cracks in eddy current testing. International Journal of fatigue, 41:30-38, [4] A. Rosell and G. Persson. Comparison of experimental and model based pod in a simplified eddy current procedure. In 18th World Conference on Nondestructive Testing, [5] B.A. Auld and J.C. Moulder. Review of advances in quatitative eddy current nondestructive evaluation. Journal of Nondestructive Evaluation, 18(1):3-36, [6] CEA list, CIVA homepage. URL: civa.cea.fr, [7] H. Wirdelius and G. Persson. Simulation based validation of the detection capacity of an ultrasonic inspection procedure. International Journal of fatigue, 41:23-29,