QNDE的核心科学与工程基础进展
Evolution of QNDEs Core Interdisciplinary Science and Engineering Base
摘 要
对材料和结构缺陷的无损检测(NDT)已经历了50多年的进化演变。在美国, 它已经从一个要求零缺陷的检测策略(NDT), 向基于损伤可容度设计的检测和评估技术(NDE)过渡。这里是假设部件始终包含一个缺陷, 只有那些比断裂力学确定的临界尺寸更大时, 需要通过检查将其消除, 以重新确定产品的服务周期。介绍了这些因素对于推动模式转变及转换至定量无损检测方面起到的至关重要的作用。一系列的重大研究项目被启动, 用于更新无损检测以满足新的要求。重点介绍了在第一项目发展中的研究重点, 以及用于定量缺陷定义的DARPA/AFML跨学科项目。它有三个目的: 发展新的核心科学/人员基础, 使检测技术满足新的要求, 确立发展新的领域, 即适当的工程设备的阶段, 并继续开展定量无损检测(QNDE)系列会议。从这个和其他方案的进展已导致对所涉及的任何检查和技术的各项测量的基本模型的链接为基础的定量无损评价(QNDE)的科学核心。除了讨论这些模式和它们的联系, 还将定义核心结构。利用这些模型, 一种新的强大的工程工具集已经开发, 包括UT, RT和EC技术的模拟程序。这些工具的应用将成为亮点, 在包括结构健康监测和状态检修的工作中将令人注目。最后, 讨论了QNDE未来机会、远景和方向。
无损评价
定量无损评价
超声
学科基础
工程技术
NDT
NDE
QNDE
Ultrasonics
Science Base
Engineering Technology
Abstract
Nondestructive testing (NDT) for flaws in materials and structures has undergone an evolutionary change over the past 50 years. In the U.S. it has moved from a testing strategy (NDT) with a zero defects requirement to a test and evaluate procedure (NDE) based upon damage tolerant design considerations. Here it is assumed that the part will always contain defects but those greater than a critical size, specified by fracture mechanics, will be removed by inspection thereby resetting the parts service clock. In this talk, events will be identified that were critical in promoting this paradigm shift and in the development of a quantitative NDE (QNDE) technology. A number of major research programs were initiated to upgrade NDT to meet the new requirements; principal attention in this talk will be given to research highlights begun in the DARPA/AFML Interdisciplinary Program for Quantitative Flaw Definition that was initiated by the author. Its purpose was threefold: to develop a new core science/people base for inspection technology that could meet the new requirements, to set the stage for new field - adaptable engineering tools, and to initiate a continuing series of quantitative NDE (QNDE) research meetings. Advances initiated in this program and pursued by many over the years have resulted in a scientific core structure for quantitative NDE (QNDE) based on a linkage of fundamental models of the various measurement processes that are involved in any inspection and/or technology. These models and their linkage will be discussed and the core structure defined. A new and powerful set of engineering tools - i.e. simulation programs for UT, X-ray, and EC technologies–has also been developed using these models. Applications of these tools will be highlighted and their role in other advanced programs including Structural Health Monitoring and Condition-Based Maintenance will be noted. Finally, a discussion of visions of future opportunities and directions for QNDE will be given.
中图分类号 TG115.28
所属栏目 2010年远东无损检测论坛论文精选
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引用该论文: Donald O. Thompson. Evolution of QNDEs Core Interdisciplinary Science and Engineering Base[J]. Nondestructive Testing, 2010, 32(8): 571～583
Donald O. Thompson. QNDE的核心科学与工程基础进展[J]. 无损检测, 2010, 32(8): 571～583
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参考文献
【1】Forney DM. USAF NDE Program-Requirement for Technology Transaction[R].AFML-TR-TI-44, 1975-1976: 220.
【2】Anderson TL. Fracture Mechanics: Fundamentals and Applications[M]. Boca Raton, Florida: CRC Press, 2005.
【3】Thompson RB, Evans AG.IEEE Transactions on Sonics and Ultrasonics, 1976, SU23(5): 291.
【4】Burte HM, Chimenti DE, Thompson RB, et al. The Middle Ground of the NDE R&D Spectrum[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1978(2A): 7-18.
【5】Schmerr, Lester W Jr. Fundamentals of Ultrasonic Nondestructive Evaluation - A Modeling Approach [M]. New York: Plenum Publishing Company, 1998.
【6】Schmerr LW, Song SJ. Ultrasonic Nondestructive Evaluation Systems –Models and Measurements [M]. New York: Springer, 2007.
【7】Newberry BP. Paraxial Approximation for Ultrasonic Beam Propagation in Liquid and Solid Media with Application to Nondestructive Evaluation[D]. Ames, Iowa: Iowa State University, 1988.
【8】Newberry BP, Thompson RB. A Paraxial Theory for the Propagation of Ultrasonic Beams[J]. Acoust Soc Am, 1989 (85): 2290-2300.
【9】Newberry BP, Thompson RB, Lopes EF. Development and Comparison of Beam Models for Two-Media Ultrasonic Inspection[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1987(6A): 639-647.
【10】Wen JJ, Breazeale MA. A Diffraction Beam Expressed as the Superposition of Gaussian Beams[J]. Acoust Soc Am, 1988(83): 1752-1756.
【11】Huang D, Breazeale MA. A Gaussian Finite-Element Method for Description of Sound Diffraction [J]. Acoust Soc Am, 1999(106): 1771-1781.
【12】Schmerr LW, Lerch TP, and SedovA. Modeling the Propagation of Ultrasonic Sound Beams through General Curved Surfaces[G]. Review of Progress in Quantitative NDE. , New York: Plenum Press, 1997(16A): 845-851.
【13】Lerch TP. Ultrasonic Transducer Characterization and Transducer Beam Modeling for Applications in Nondestructive Evaluation[D]. Ames, Iowa: Iowa State University, 1996.
【14】Schmerr LW, Lerch T, Sedov A. A Boundary Diffraction Wave Theory and its Application to Ultrasonic NDE[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1994(13A): 69-74.
【15】Ludwig RL, Moore D, Lord W. Transducer Models for the Finite Element Simulation of Ultrasonic NDT Phenomena[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1987(6A): 649-655.
【16】Ludwig R, Lord W. Finite Element Study of Ultrasonic Wave Propagation and Scattering in Aluminum[J]. Mat Eval, 1988(46): 108-113.
【17】Lord W, Ludwig R, You Z. Developments in Ultrasonic Modeling with Finite Element Analysis[J]. Nondestr Eval, 1990(9): 155-160.
【18】Goswami PP, Rudolphi TJ, Roberts RA, et al. Ultrasonic Transmission through a Curved Interface by the Boundary Element Method[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1991(10A): 193-200.
【19】Guo QC, Achenbach JD. Radiation of Ultrasound into an Anisotropic Solid[J]. Ultrasonics, 1995(33): 449-456.
【20】Marklein R, Barmann R, Langenberg KJ. The Ultrasonic Modeling Code EFIT as Applied to Inhomogeneous Dissipative and Anisotropic Media[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1995(14): 251-258.
【21】Marklein R, Langenberg KJ, Klaholz S, et al. Ultrasonic Modeling of Real-Life Situations: Applications and Further Developments[G].Review of Progress in Quantitative NDE. New York: Plenum Press, 1996(15): 57-64.
【22】Mason WP. Physical Acoustics, Vol.1-Part A[M]. New York: Academic Press, 1964.
【23】Neubauer WG. A Summation Formula for Use in Determining the Reflection from Irregular Bodies[J]. Acoust Soc of Am, 1963(35): 279-285.
【24】Johnson DM. Model for Predicting the Reflection of Ultrasonic Pulses from a Body of Known Shape [J]. Acoust Soc of Am, 1976(59): 1319-1323.
【25】Haines NF, Langston DB. Reflection of Ultrasonic Pulses from Surfaces[J]. Acoust Soc Am, 1980(67): 1443-1454.
【26】Avestas JS. Physical Optics Method in Electromagnetic Scattering[J]. Math Phys, 1980(21): 290-299, .
【27】Sedov A, Schmerr LW. Pulse Distortion and the Elastodynamic Kirchoff Approximation for Cracks: the Direct and Inverse Problems[J]. SIAM J Appl Math, 1987(47): 1201-1215.
【28】Gubernatis, JE, Domany E, Krumhansl JA, et al. The Born Approximation in the Theory of Scattering of Elastic Waves by Flaws[ J]. Appl Phys, 1997(48): 2812-2819.
【29】Gubernatis JE, Domany E, Krumhansl JA. Formal Aspects of the Theory of Scattering of Ultrasound by Flaws in Elastic Materials[J]. Appl Phys, 1997(48): 2804-2811.
【30】Hudson JA, Heritage JR. The Use of the Born Approximation in Seismic Scattering Problems[J]. Geophys J Royal Astron Soc, 1981(66): 221-240.
【31】Rose JH, Richardson JM. Time Domain Born Approximation[J]. Nondestructive, 1982(3): 45-53.
【32】Rose JH. Elastic Wave Inverse Scattering in Nondestructive Evaluation[J]. Pure Appl Geophys, 1989(131): 715-739.
【33】Achenbach JD, Gautesen AK, McMaken H. Ray Methods for Waves in Elastic Solids[M]. Boston: Pitman Books Ltd, 1982.
【34】Ying CF, Truell R. Scattering of a Plane Compressional Wave by a Spherical Obstacle in an Isotropic Elastic Solid[J]. Appl Phy, 1956(27): 1086- 1097.
【35】Tittmann B, Thompson DO, Thompson RB. Standards for Quantitative NDE[C]. Proceedings of Symposium on NDT Standards, 1976, Nondestructive Testing Standards—A Review (STP 624). Philadelphia: American Society for Testing and Materials, 1977.
【36】Auld BA. General Electromechanical Reciprocity Relations Applied to the Calculation of Elastic Wave Scattering Coefficients[J]. Wave Motion, 1979(1): 3-10.
【37】Thompson RB, Gray TA. A Model Relating Ultrasonic Scattering Through Liquid-Solid Interfaces to Unbounded Medium Scattering Amplitudes [J]. Acoust Soc Amer, 1983(74): 140-146.
【38】Tittmann BR, Elsley RK. Experimental Measurements and Interpretation of Ultrasonic Scattering by Flaws[C]. Proceedings of the ARPA/AFML Review of Progress in Quantitative NDE: Science Center, Rockwell International, AFML-TR-78-55, 1978: 26-35.
【39】Thompson RB, Margetan FJ. Use of Elastodynamic Theories in the Stochastic Description of the Effects of Microstructure on Ultrasonic Flaw and Noise Signals[J]. Wave Motion, 2002(36): 347-365.
【40】Oakley CG. Calculation of Ultrasonic Transducer Signal-Noise Ratios Using the KLM Model[J]. IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control, 1997(44): 1018-1026.
【41】Yalda-Mooshabad, Margetan FJ, Thompson RB. Applying the 2D Random Walk Formalism to Predict Ultrasonic Grain Noise Distributions[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 2002(13B): 347-365.
【42】Ogilvy JA. Theory of Wave Scattering from Random Rough Surfaces[M]. Bristol, England: Institute of Physics Publishing, 1991.
【43】Margetan FJ, Thompson RB. Microstructural Noise in Titanium Alloys and its Influence on the Detectability of Hard –Alpha[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1992(11B): 1717-1724.
【44】Rose JH. Ultrasonic Backscatter from Microstructure[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1992(11B): 1677-1684.
【45】Rose JH. Theory of Ultrasonic Backscatter for Multiphase Polycrystalline Solids[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1993(12B): 1719-1726.
【46】Meeker WQ, Chan V, Thompson RB, et al. A Methodology for Predicting Probability of Detection for Ultrasonic Testing[G]. Review of Progress in Quantitative NDE. Melville, NY: American Institute of Physics, 2001(20B): 1972-1978.
【47】Rice SO. Mathematical Analysis of Random Noise[J]. Bell Syst Tech Journ. 1945(24): 46-156.
【48】Calmon P. Recent Developments in NDT Simulation [C]. Proc World Congress on Ultrasonics, 2003: 443-446.
【49】Lhemery A, Calmon P, Lecoeur- Taibi, et al. Modeling Tools for Ultrasonic Inspection of Welds[J]. NDT&E International, 2000(33): 499-513.
【50】Bostrom A, Wirdelius H. Ultrasonic Probe Modeling and Nondestructive Crack Detection[J]. Acoust Soc Am, 1995(97): 2836-2848.
【51】Bostrom A. A Review of Hypersingular Integral Equation Method for Crack Scattering and Application to Modeling of Nondestructive Evaluation[J]. Appl Mech Rev, 2003(56): 383-405.
【52】Turnbull A, Garton M. Ultrasound Ray Tracing in Arbitrary Complex Geometries[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1995(14A): 1105-1110.
【53】Garton M. Refining Automated Ultrasonic Inspections with Simulation Models[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1998(17B): 1825-1829.
【54】Spies M, Batra NK, Simmonds KE, et al. Numerical Modeling and Imaging of Three Dimensional Transducer Fields in Anisotropic Materials[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1997(16A): 837-851.
【55】Spies M, Kroning M. Elastic Wave Field Modeling for Arbitrarily Oriented Orthotropic Media[G]. Review of Progess in Quantitative NDE. New York: Plenum Press, 1998(17B): 1163-1170.
【56】Spies M. Transducer Field Modeling in Anisotropic Media by Superposition of Gaussian Base Functions[J]. Acoust Soc Am, 1999(105): 633-638.
【57】Marklein R. NDT-Related Quantitative Modeling of Coupled Piezoelectric and Ultrasonic Wave Phenomena[C]. Proc 7th European Conference on NDT, 1998: 1-44.
【58】Marklein R, Langenberg K, Mayer K. EFIT Simulations for Ultrasonic NDE[J]. NDT net, 2003, 8(3): 1-6.
【59】Yim H, Baek E. Two-Dimensional Numerical Modeling and Simulation of Ultrasonic Testing[J]. Journ of the Korean Soc for NDT, 2002(22): 649-658.
【60】TA Gray.private communication.
【61】Udpa SS, Thompson DO. Modeling of Benchmark Problems[G]. Review of Progress in QNDE. New York: AIP, Melville, 2001(21B): 1891-1893.
【62】Thompson RB. Ultrasonic Benchmarking: Past Programs and Future Goals[G]. Review of Progress in QNDE, New York: AIP, Melville, 2004(23B): 1529-1536.
【63】Burte HM, Chimenti DE. Unified Life Cycle Engineering: An Emerging Design Concept[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1986(6B): 1797-1812.
【64】Schmerr LW, Thompson DO. Incorporating Inspectability into Design: The New Role of NDE in Concurrent Engineering[C]. Proc ASME/NDE Engineering Div. Topical Conference, “NDEs Role in Concurrent Engineering, ” SanAntonio, Texas, 1992: 22-23.
【65】Schmerr LW, Thompson DO. NDE Models and Design- A Unified Life Cycle Engineering Approac[G]. Review of Progress in Quantitative NDE New York: Plenum Press, 1994(13B): 2183-2190.
【2】Anderson TL. Fracture Mechanics: Fundamentals and Applications[M]. Boca Raton, Florida: CRC Press, 2005.
【3】Thompson RB, Evans AG.IEEE Transactions on Sonics and Ultrasonics, 1976, SU23(5): 291.
【4】Burte HM, Chimenti DE, Thompson RB, et al. The Middle Ground of the NDE R&D Spectrum[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1978(2A): 7-18.
【5】Schmerr, Lester W Jr. Fundamentals of Ultrasonic Nondestructive Evaluation - A Modeling Approach [M]. New York: Plenum Publishing Company, 1998.
【6】Schmerr LW, Song SJ. Ultrasonic Nondestructive Evaluation Systems –Models and Measurements [M]. New York: Springer, 2007.
【7】Newberry BP. Paraxial Approximation for Ultrasonic Beam Propagation in Liquid and Solid Media with Application to Nondestructive Evaluation[D]. Ames, Iowa: Iowa State University, 1988.
【8】Newberry BP, Thompson RB. A Paraxial Theory for the Propagation of Ultrasonic Beams[J]. Acoust Soc Am, 1989 (85): 2290-2300.
【9】Newberry BP, Thompson RB, Lopes EF. Development and Comparison of Beam Models for Two-Media Ultrasonic Inspection[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1987(6A): 639-647.
【10】Wen JJ, Breazeale MA. A Diffraction Beam Expressed as the Superposition of Gaussian Beams[J]. Acoust Soc Am, 1988(83): 1752-1756.
【11】Huang D, Breazeale MA. A Gaussian Finite-Element Method for Description of Sound Diffraction [J]. Acoust Soc Am, 1999(106): 1771-1781.
【12】Schmerr LW, Lerch TP, and SedovA. Modeling the Propagation of Ultrasonic Sound Beams through General Curved Surfaces[G]. Review of Progress in Quantitative NDE. , New York: Plenum Press, 1997(16A): 845-851.
【13】Lerch TP. Ultrasonic Transducer Characterization and Transducer Beam Modeling for Applications in Nondestructive Evaluation[D]. Ames, Iowa: Iowa State University, 1996.
【14】Schmerr LW, Lerch T, Sedov A. A Boundary Diffraction Wave Theory and its Application to Ultrasonic NDE[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1994(13A): 69-74.
【15】Ludwig RL, Moore D, Lord W. Transducer Models for the Finite Element Simulation of Ultrasonic NDT Phenomena[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1987(6A): 649-655.
【16】Ludwig R, Lord W. Finite Element Study of Ultrasonic Wave Propagation and Scattering in Aluminum[J]. Mat Eval, 1988(46): 108-113.
【17】Lord W, Ludwig R, You Z. Developments in Ultrasonic Modeling with Finite Element Analysis[J]. Nondestr Eval, 1990(9): 155-160.
【18】Goswami PP, Rudolphi TJ, Roberts RA, et al. Ultrasonic Transmission through a Curved Interface by the Boundary Element Method[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1991(10A): 193-200.
【19】Guo QC, Achenbach JD. Radiation of Ultrasound into an Anisotropic Solid[J]. Ultrasonics, 1995(33): 449-456.
【20】Marklein R, Barmann R, Langenberg KJ. The Ultrasonic Modeling Code EFIT as Applied to Inhomogeneous Dissipative and Anisotropic Media[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1995(14): 251-258.
【21】Marklein R, Langenberg KJ, Klaholz S, et al. Ultrasonic Modeling of Real-Life Situations: Applications and Further Developments[G].Review of Progress in Quantitative NDE. New York: Plenum Press, 1996(15): 57-64.
【22】Mason WP. Physical Acoustics, Vol.1-Part A[M]. New York: Academic Press, 1964.
【23】Neubauer WG. A Summation Formula for Use in Determining the Reflection from Irregular Bodies[J]. Acoust Soc of Am, 1963(35): 279-285.
【24】Johnson DM. Model for Predicting the Reflection of Ultrasonic Pulses from a Body of Known Shape [J]. Acoust Soc of Am, 1976(59): 1319-1323.
【25】Haines NF, Langston DB. Reflection of Ultrasonic Pulses from Surfaces[J]. Acoust Soc Am, 1980(67): 1443-1454.
【26】Avestas JS. Physical Optics Method in Electromagnetic Scattering[J]. Math Phys, 1980(21): 290-299, .
【27】Sedov A, Schmerr LW. Pulse Distortion and the Elastodynamic Kirchoff Approximation for Cracks: the Direct and Inverse Problems[J]. SIAM J Appl Math, 1987(47): 1201-1215.
【28】Gubernatis, JE, Domany E, Krumhansl JA, et al. The Born Approximation in the Theory of Scattering of Elastic Waves by Flaws[ J]. Appl Phys, 1997(48): 2812-2819.
【29】Gubernatis JE, Domany E, Krumhansl JA. Formal Aspects of the Theory of Scattering of Ultrasound by Flaws in Elastic Materials[J]. Appl Phys, 1997(48): 2804-2811.
【30】Hudson JA, Heritage JR. The Use of the Born Approximation in Seismic Scattering Problems[J]. Geophys J Royal Astron Soc, 1981(66): 221-240.
【31】Rose JH, Richardson JM. Time Domain Born Approximation[J]. Nondestructive, 1982(3): 45-53.
【32】Rose JH. Elastic Wave Inverse Scattering in Nondestructive Evaluation[J]. Pure Appl Geophys, 1989(131): 715-739.
【33】Achenbach JD, Gautesen AK, McMaken H. Ray Methods for Waves in Elastic Solids[M]. Boston: Pitman Books Ltd, 1982.
【34】Ying CF, Truell R. Scattering of a Plane Compressional Wave by a Spherical Obstacle in an Isotropic Elastic Solid[J]. Appl Phy, 1956(27): 1086- 1097.
【35】Tittmann B, Thompson DO, Thompson RB. Standards for Quantitative NDE[C]. Proceedings of Symposium on NDT Standards, 1976, Nondestructive Testing Standards—A Review (STP 624). Philadelphia: American Society for Testing and Materials, 1977.
【36】Auld BA. General Electromechanical Reciprocity Relations Applied to the Calculation of Elastic Wave Scattering Coefficients[J]. Wave Motion, 1979(1): 3-10.
【37】Thompson RB, Gray TA. A Model Relating Ultrasonic Scattering Through Liquid-Solid Interfaces to Unbounded Medium Scattering Amplitudes [J]. Acoust Soc Amer, 1983(74): 140-146.
【38】Tittmann BR, Elsley RK. Experimental Measurements and Interpretation of Ultrasonic Scattering by Flaws[C]. Proceedings of the ARPA/AFML Review of Progress in Quantitative NDE: Science Center, Rockwell International, AFML-TR-78-55, 1978: 26-35.
【39】Thompson RB, Margetan FJ. Use of Elastodynamic Theories in the Stochastic Description of the Effects of Microstructure on Ultrasonic Flaw and Noise Signals[J]. Wave Motion, 2002(36): 347-365.
【40】Oakley CG. Calculation of Ultrasonic Transducer Signal-Noise Ratios Using the KLM Model[J]. IEEE Trans Ultrasonics, Ferroelectrics, and Frequency Control, 1997(44): 1018-1026.
【41】Yalda-Mooshabad, Margetan FJ, Thompson RB. Applying the 2D Random Walk Formalism to Predict Ultrasonic Grain Noise Distributions[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 2002(13B): 347-365.
【42】Ogilvy JA. Theory of Wave Scattering from Random Rough Surfaces[M]. Bristol, England: Institute of Physics Publishing, 1991.
【43】Margetan FJ, Thompson RB. Microstructural Noise in Titanium Alloys and its Influence on the Detectability of Hard –Alpha[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1992(11B): 1717-1724.
【44】Rose JH. Ultrasonic Backscatter from Microstructure[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1992(11B): 1677-1684.
【45】Rose JH. Theory of Ultrasonic Backscatter for Multiphase Polycrystalline Solids[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1993(12B): 1719-1726.
【46】Meeker WQ, Chan V, Thompson RB, et al. A Methodology for Predicting Probability of Detection for Ultrasonic Testing[G]. Review of Progress in Quantitative NDE. Melville, NY: American Institute of Physics, 2001(20B): 1972-1978.
【47】Rice SO. Mathematical Analysis of Random Noise[J]. Bell Syst Tech Journ. 1945(24): 46-156.
【48】Calmon P. Recent Developments in NDT Simulation [C]. Proc World Congress on Ultrasonics, 2003: 443-446.
【49】Lhemery A, Calmon P, Lecoeur- Taibi, et al. Modeling Tools for Ultrasonic Inspection of Welds[J]. NDT&E International, 2000(33): 499-513.
【50】Bostrom A, Wirdelius H. Ultrasonic Probe Modeling and Nondestructive Crack Detection[J]. Acoust Soc Am, 1995(97): 2836-2848.
【51】Bostrom A. A Review of Hypersingular Integral Equation Method for Crack Scattering and Application to Modeling of Nondestructive Evaluation[J]. Appl Mech Rev, 2003(56): 383-405.
【52】Turnbull A, Garton M. Ultrasound Ray Tracing in Arbitrary Complex Geometries[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1995(14A): 1105-1110.
【53】Garton M. Refining Automated Ultrasonic Inspections with Simulation Models[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1998(17B): 1825-1829.
【54】Spies M, Batra NK, Simmonds KE, et al. Numerical Modeling and Imaging of Three Dimensional Transducer Fields in Anisotropic Materials[G]. Review of Progress in Quantitative NDE. New York: Plenum Press, 1997(16A): 837-851.
【55】Spies M, Kroning M. Elastic Wave Field Modeling for Arbitrarily Oriented Orthotropic Media[G]. Review of Progess in Quantitative NDE. New York: Plenum Press, 1998(17B): 1163-1170.
【56】Spies M. Transducer Field Modeling in Anisotropic Media by Superposition of Gaussian Base Functions[J]. Acoust Soc Am, 1999(105): 633-638.
【57】Marklein R. NDT-Related Quantitative Modeling of Coupled Piezoelectric and Ultrasonic Wave Phenomena[C]. Proc 7th European Conference on NDT, 1998: 1-44.
【58】Marklein R, Langenberg K, Mayer K. EFIT Simulations for Ultrasonic NDE[J]. NDT net, 2003, 8(3): 1-6.
【59】Yim H, Baek E. Two-Dimensional Numerical Modeling and Simulation of Ultrasonic Testing[J]. Journ of the Korean Soc for NDT, 2002(22): 649-658.
【60】TA Gray.private communication.
【61】Udpa SS, Thompson DO. Modeling of Benchmark Problems[G]. Review of Progress in QNDE. New York: AIP, Melville, 2001(21B): 1891-1893.
【62】Thompson RB. Ultrasonic Benchmarking: Past Programs and Future Goals[G]. Review of Progress in QNDE, New York: AIP, Melville, 2004(23B): 1529-1536.
【63】Burte HM, Chimenti DE. Unified Life Cycle Engineering: An Emerging Design Concept[G]. Review of Progress in Quantitative NDE, New York: Plenum Press, 1986(6B): 1797-1812.
【64】Schmerr LW, Thompson DO. Incorporating Inspectability into Design: The New Role of NDE in Concurrent Engineering[C]. Proc ASME/NDE Engineering Div. Topical Conference, “NDEs Role in Concurrent Engineering, ” SanAntonio, Texas, 1992: 22-23.
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