Average grain size evaluation using scattering-induced attenuation of coda waves.

Grain size is one of the key microstructural factors affecting the mechanical properties of polycrystalline metal materials. In this study, a novel method for grain size evaluation using ultrasonic coda waves is proposed. Different from conventional bulk wave methods that require a point-by-point scanning of the structure, the proposed method allows for a rapid evaluation of the average grain size of the whole part from a single inspection location using one-pass testing data. A piecewise energy attenuation function dealing with different attenuation mechanisms is proposed to obtain the effective attenuation coefficient of coda waves. A power-law model is constructed to correlate the effective attenuation coefficient with the average grain size. Ultrasonic testing on nickel-based superalloy plate specimens with different average grain sizes is performed for model calibration and method verification. The applicability and robustness of the proposed method are further validated using a realistic turbine disk specimen with an irregular shape and non-uniform grain sizes. Results show that the proposed method yields a reliable and accurate estimation of the average grain size with a maximum relative error less than 20 %.

Spatial and directional characterization of wire and arc additive manufactured aluminum alloy using phased array ultrasonic backscattering method.

Pores, grains, or textures can collectively cause microstructural inhomogeneity and anisotropy in metallic materials fabricated by additive manufacturing. In this study, a phased array ultrasonic method is developed to characterize the inhomogeneity and anisotropy of wire and arc additively manufactured components by performing both beams focusing and steering. Two backscattering features, i.e., the integrated backscattering intensity and the root mean square of the backscattering signals, are employed to quantify the microstructural inhomogeneity and anisotropy, respectively. An experimental investigation is performed using an aluminum sample fabricated by wire and arc additive manufacturing. The ultrasonic measurements, performed on wire and arc additive manufactured 2319 aluminum alloy, show that the sample is inhomogeneous and weakly anisotropic. Metallography, electron backscatter diffraction, and X-ray computed tomography are used to verify the ultrasonic results. An ultrasonic scattering model is used to identify the influence of grains on the backscattering coefficient. Compared with a wrought aluminum alloy, the complex microstructure in additively manufactured material significantly influence the backscattering coefficient, and the presence of pores cannot be neglected in ultrasonic-based nondestructive evaluation for wire and arc additive manufactured metals.

An Engineering Prediction Model for Stress Relaxation of Polymer Composites at Multiple Temperatures.

This study develops an engineering prediction model for stress relaxation of polymer composites, allowing the prediction of stress relaxation behaviour under a constant strain, over a range of temperatures. The model is based on the basic assumption that in the stress relaxation process the reversible strain is transformed to irreversible strain continuously. A strain-hardening model is proposed to incorporate nonlinear elastic behaviour, and a creep rate model is used to describe the irreversible deformation in the process. By using stress relaxation data at different temperatures, under different strains, the dependence on temperature and initial strain of the model parameters can be established. The effectiveness of the proposed model is verified and validated using three polymer composite materials. The performance of the model is compared with three commonly used stress relaxation models such as the parallel Maxwell and Prony series models. To ease the use of the proposed model in realistic structural problems, a user subroutine is developed, and the stress relaxation of a plate structure example is demonstrated.

A Phenomenological Primary-Secondary-Tertiary Creep Model for Polymer-Bonded Composite Materials.

This study develops a unified phenomenological creep model for polymer-bonded composite materials, allowing for predicting the creep behavior in the three creep stages, namely the primary, the secondary, and the tertiary stages under sustained compressive stresses. Creep testing is performed using material specimens under several conditions with a temperature range of 20 °C-50 °C and a compressive stress range of 15 MPa-25 MPa. The testing data reveal that the strain rate-time response exhibits the transient, steady, and unstable stages under each of the testing conditions. A rational function-based creep rate equation is proposed to describe the full creep behavior under each of the testing conditions. By further correlating the resulting model parameters with temperature and stress and developing a Larson-Miller parameter-based rupture time prediction model, a unified phenomenological model is established. An independent validation dataset and third-party testing data are used to verify the effectiveness and accuracy of the proposed model. The performance of the proposed model is compared with that of an existing reference model. The verification and comparison results show that the model can describe all the three stages of the creep process, and the proposed model outperforms the reference model by yielding 28.5% smaller root mean squared errors on average.

A General Temperature-Dependent Stress-Strain Constitutive Model for Polymer-Bonded Composite Materials.

This study develops a general temperature-dependent stress-strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from -40 ∘C to 75 ∘C is performed. The testing data reveal that the stress-strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg-Osgood relationship is proposed to build the stress-strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress-strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

Maximum Entropy Approach to Reliability of Multi-Component Systems with Non-Repairable or Repairable Components.

The degradation and recovery processes are multi-scale phenomena in many physical, engineering, biological, and social systems, and determine the aging of the entire system. Therefore, understanding the interplay between the two processes at the component level is the key to evaluate the reliability of the system. Based on the principle of maximum entropy, an approach is proposed to model and infer the processes at the component level, and is applied to repairable and non-repairable systems. By incorporating the reliability block diagram, this approach allows for integrating the information of network connectivity and statistical moments to infer the hazard or recovery rates of the degradation or recovery processes. The overall approach is demonstrated with numerical examples.

Three-dimensional damage quantification of low velocity impact damage in thin composite plates using phased-array ultrasound.

The evaluation of internal damage in multilayered composite materials is of great importance for high reliability-demanding applications, and remains a challenge due to the complex failure modes and mechanism of composite materials. This study presents a volumetric method of three-dimensional size quantification and prediction for low velocity impact damage in thin composite plates using phased-array ultrasound. A set of low velocity impact damages are induced in thin carbon fiber/epoxy resin matrix composite plates using quasi-static indentation tests. A volumetric reconstruction method is proposed to reconstruct a three-dimensional volume from the raw data, allowing for direct damage identification, localization, and quantification. Using the echo amplitude feature of the reconstructed volume, the 6 dB-drop method is employed to characterize the damage size in terms of volumes and areas. An impact size prediction model is established to correlate the impact energy and the damage volume/area. Comparisons are made between the microscopy measurement of the damage cross-section and results obtained using the developed method.

Maximum entropy approach to reliability.

The aging process is a common phenomenon in engineering, biological, and physical systems. The hazard rate function, which characterizes the aging process, is a fundamental quantity in the disciplines of reliability, failure, and risk analysis. However, it is difficult to determine the entire hazard function accurately with limited observation data when the degradation mechanism is not fully understood. Inspired by the seminal work pioneered by Jaynes [Phys. Rev. 106, 620 (1956)PHRVAO0031-899X10.1103/PhysRev.106.620], this study develops an approach based on the principle of maximum entropy. In particular, the time-dependent hazard rate function can be established using limited observation data in a rational manner. It is shown that the developed approach is capable of constructing and interpreting many typical hazard rate curves observed in practice, such as the bathtub curve, the upside down bathtub, and so on. The developed approach is applied to model a classical single function system and a numerical example is used to demonstrate the method. In addition its extension to a more general multifunction system is presented. Depending on the interaction between different functions of the system, two cases, namely reducible and irreducible, are discussed in detail. A multifunction electrical system is used for demonstration.

A model assessment method for predicting structural fatigue life using Lamb waves.

This paper presents a study on model assessment for predicting structural fatigue life using Lamb waves. Lamb wave coupon testing is performed for model development. Three damage sensitive features, namely normalized energy, phase change, and correlation coefficient are extracted from Lamb wave data and are used to quantify the crack size. Four data-driven models are proposed. The average relative error and the probability of detection (POD) are proposed as two measures to evaluate the performance of the four models. To study the influence of model choice on the probabilistic fatigue life prediction, probability density functions of the actual crack size are obtained from the POD models given the Lamb wave data. Crack growth model parameters are statistically identified using Bayesian parameter estimation with Markov chain Monte Carlo simulations. The model assessment and the influence of model choice on fatigue life prediction are made using both coupon testing data with artificial cracks and realistic lap joint testing data with naturally developed cracks.

A Fatigue Crack Size Evaluation Method Based on Lamb Wave Simulation and Limited Experimental Data.

This paper presents a systematic and general method for Lamb wave-based crack size quantification using finite element simulations and Bayesian updating. The method consists of construction of a baseline quantification model using finite element simulation data and Bayesian updating with limited Lamb wave data from target structure. The baseline model correlates two proposed damage sensitive features, namely the normalized amplitude and phase change, with the crack length through a response surface model. The two damage sensitive features are extracted from the first received S0 mode wave package. The model parameters of the baseline model are estimated using finite element simulation data. To account for uncertainties from numerical modeling, geometry, material and manufacturing between the baseline model and the target model, Bayesian method is employed to update the baseline model with a few measurements acquired from the actual target structure. A rigorous validation is made using in-situ fatigue testing and Lamb wave data from coupon specimens and realistic lap-joint components. The effectiveness and accuracy of the proposed method is demonstrated under different loading and damage conditions.

Lamb Wave Damage Quantification Using GA-Based LS-SVM.

Lamb waves have been reported to be an efficient tool for non-destructive evaluations (NDE) for various application scenarios. However, accurate and reliable damage quantification using the Lamb wave method is still a practical challenge, due to the complex underlying mechanism of Lamb wave propagation and damage detection. This paper presents a Lamb wave damage quantification method using a least square support vector machine (LS-SVM) and a genetic algorithm (GA). Three damage sensitive features, namely, normalized amplitude, phase change, and correlation coefficient, were proposed to describe changes of Lamb wave characteristics caused by damage. In view of commonly used data-driven methods, the GA-based LS-SVM model using the proposed three damage sensitive features was implemented to evaluate the crack size. The GA method was adopted to optimize the model parameters. The results of GA-based LS-SVM were validated using coupon test data and lap joint component test data with naturally developed fatigue cracks. Cases of different loading and manufacturer were also included to further verify the robustness of the proposed method for crack quantification.

Time Domain Strain/Stress Reconstruction Based on Empirical Mode Decomposition: Numerical Study and Experimental Validation.

Structural health monitoring has been studied by a number of researchers as well as various industries to keep up with the increasing demand for preventive maintenance routines. This work presents a novel method for reconstruct prompt, informed strain/stress responses at the hot spots of the structures based on strain measurements at remote locations. The structural responses measured from usage monitoring system at available locations are decomposed into modal responses using empirical mode decomposition. Transformation equations based on finite element modeling are derived to extrapolate the modal responses from the measured locations to critical locations where direct sensor measurements are not available. Then, two numerical examples (a two-span beam and a 19956-degree of freedom simplified airfoil) are used to demonstrate the overall reconstruction method. Finally, the present work investigates the effectiveness and accuracy of the method through a set of experiments conducted on an aluminium alloy cantilever beam commonly used in air vehicle and spacecraft. The experiments collect the vibration strain signals of the beam via optical fiber sensors. Reconstruction results are compared with theoretical solutions and a detailed error analysis is also provided.

An Integrated Health Monitoring Method for Structural Fatigue Life Evaluation Using Limited Sensor Data.

A general framework for structural fatigue life evaluation under fatigue cyclic loading using limited sensor data is proposed in this paper. First, limited sensor data are measured from various sensors which are preset on the complex structure. Then the strain data at remote spots are used to obtain the strain responses at critical spots by the strain/stress reconstruction method based on empirical mode decomposition (REMD method). All the computations in this paper are directly performed in the time domain. After the local stress responses at critical spots are determined, fatigue life evaluation can be performed for structural health management and risk assessment. Fatigue life evaluation using the reconstructed stresses from remote strain gauge measurement data is also demonstrated with detailed error analysis. Following this, the proposed methodology is demonstrated using a three-dimensional frame structure and a simplified airfoil structure. Finally, several conclusions and future work are drawn based on the proposed study.

A time-domain synthetic aperture ultrasound imaging method for material flaw quantification with validations on small-scale artificial and natural flaws.

A direct time-domain reconstruction and sizing method of synthetic aperture focusing technique (SAFT) is developed to improve the spatial resolution and sizing accuracy for phased-array ultrasonic inspections. The basic idea of the reconstruction algorithm is to coherently superimpose multiple A-scan measurements, incorporating the phase information of the sampling points. The algorithm involves data mapping and in-phase summation according to time-of-flight (TOF). Data mapping refers to the process of placing each of the sampling points to a two-/three-dimensional grid that represents the geometry model of the object being inspected. The value for each of the cells of the grid is a summation of all sampling points mapped into the cell. A sizing method based on the concept of 6 dB-drop is proposed to characterize the flaw boundary. The extents, orientation and the shape of the flaw can then be inferred to provide more information for life assessment calculations. Lab experiments are performed using a 10 MHz phased-array ultrasonic transducer to collect data from a cylinder material block with closely spaced artificial flaws and from a material block with a natural flaw. The developed method is used to process the experimental data to characterize the flaws. Using the developed method, the improvement of spatial resolution is observed. Results indicate that four closely spaced 0.794 mm-diameter flat-bottomed holes are clearly identified, and the quantification of size and orientation of the natural flaw is very close to the actual measurement made from digital microscopy after cutting the testing piece apart.

Material damage diagnosis and characterization for turbine rotors using three-dimensional adaptive ultrasonic NDE data reconstruction techniques.

Damage diagnosis for turbine rotors plays an essential role in power plant management. Ultrasonic non-destructive examinations (NDEs) have increasingly been utilized as an effective tool to provide comprehensive information for damage diagnosis. This study presents a general methodology of damage diagnosis for turbine rotors using three-dimensional adaptive ultrasonic NDE data reconstruction techniques. Volume reconstruction algorithms and data fusion schemes are proposed to map raw ultrasonic NDE data back to the structural model of the object being examined. The reconstructed volume is used for automatic damage identification and quantification using region-growing algorithms and the method of distance-gain-size. Key reconstruction parameters are discussed and suggested based on industrial experiences. A software tool called AutoNDE Rotor is developed to automate the overall analysis workflow. Effectiveness of the proposed methods and AutoNDE Rotor are explored using realistic ultrasonic NDE data.