In aircraft structural design, failure stresses are obtained from coupon tests and then used to predict failure under combined loads in structural elements. Structural element tests are next used to update the failure envelope for combined loads. It is a common practice to repeat the element tests and then select the lowest test result as a conservative estimate of the mean failure stress. This practice is equivalent to reducing the average test failure stress by a knockdown factor (one that is quite variable). Instead, we propose using the average test result with an explicit knockdown factor obtained from statistical distribution of the test data. We show reductions in the variability of the estimated mean failure stress as well as the likelihood of unconservative estimate. In addition, when the initial distribution or confidence interval of the mean failure stresses is available, we can further decrease the chance of unconservative estimate using Bayesian updating. We demonstrate the gains associated with Bayesian updating when the upper and lower bounds of errors in the analytical predictions are available. Examples with uniform and lognormal distributions of failure stresses compare the lowest-result approach with the two alternatives with the explicit knockdown factor. Both approaches significantly reduce the likelihood of unconservative estimates of the mean failure stress. The average approach reduced this likelihood by about a half and the Bayesian approach by up to an order of magnitude (from 12.5 to 1%). We also examine scenarios in which estimates of error and variability are substantially inaccurate. We show that, even then, the likelihood of unconservative estimates reduces significantly. Remarkably, an underestimate of variability also results in about a 2% higher average of the estimated mean failure stress. Thus, we are able to simultaneously use higher average failure stress (leading to lower weight) and reduce the likelihood of unconservative estimates.Nomenclature b e = error bounds in calculated failure stress c f = coefficient of variation of the material property (lognormal) e f = error of calculated failure stress with respect to the average true failure stress k avg = explicit knockdown factor used in the average approach k Bayes = explicit knockdown factor used in the Bayesian approach k lowest = implicit knockdown factor introduced by using the lowest test result as a conservative measure k lowest = mean value of the implicit knockdown factors v f = variability in material properties f = failure stress (a random variable) f Bayes = mean failure stress calculated by Bayesian updating f calc = failure stress predicted from fracture mechanics f est = estimated failure stress for the three discussed methods (a conservative estimate) f i;test = ith test result. f test = failure stress measured in tests f true = true failure stress of a structure f true = mean of true failure stresses of an infinite number of nominally identical structures
In structural health monitoring, crack identification using scattered ultrasonic waves from a crack is one of the most active research areas. Crack size estimation is important for judging the severity of the damage. If measurements are frequently performed as the crack grows, then a better estimation of crack size may be possible by analyzing sensor signals for the same crack location with different sizes. The objective of this article is to explore the relationship between the sensor signal amplitude and crack size through experiments and simulation for estimating the size. Cracks are machined into an aluminum plate and measurements are carried out with ultrasound excitation using piezoelectric transducer arrays that alternate their role as actuators or sensors. Initially, a hole of 2.5 mm diameter is drilled in the plate, and it is gradually machined to a crack with a size up to 50 mm. Signal amplitude is measured from the sensor arrays. The migration technique is used to image the crack and to find the crack location. The maximum received signal amplitude is found to vary linearly with size from simulation and this agrees with measurements with crack size up to 30 mm. The deviation between the simulation and experiment increases as the crack grows.
A compensating procedure for decay with distance of an ultrasonic wave propagating in a structure is presented. In structural health monitoring, many damage identification techniques involve ultrasonic wave propagation from actuators and reflection from defects. Some of them use imaging techniques to approximate damage configuration, such as location, size, and shape. However, the accuracy of detection result is not good enough to be used for prognostic. We found that the inaccuracy is often caused by decay of wave strength as function of distance when a wave propagates through the structure. Thus, we propose to compensate for geometric decay by multiplying the obtained image intensity with the distances to the actuator and to the sensor. We applied the compensation idea to a migration technique, which is a recently developed damage imaging technique. By adjusting image intensity to compensate for distance between actuator and defect, we were able to achieve a better accuracy for identifying the location of cracks. In addition, an experimental study on the possible errors related to experiment is attached. This idea can be extended to any damage detection techniques which produce images as their final detection result.
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