SQUID结合涡旋电流法用于铍材残余应力检测的可行性研究
摘要
金属铍材性脆，在机加焊接时很容易产生残余应力，而这可能进一步发展成裂纹等缺陷，引起材料失效，因而希望有种无损检测手段，具有一定探测深度且能快速实施对铍材残余应力状态的监测。而Barkhausen、XRD、锥孔法等常用残余应力监测手段都不能满足要求。因此，我们采用电磁场有限元计算方法，依据SMM-601型无损检测仪构建计算模型，初步研究了SQUID结合涡旋电流法对铍材内部残余应力引起的材料电导率变化的响应程度和关系，从理论上初步论证了SQUID用于铍材残余应力检测的可能性。
金属材料都具有压电效应，残余应力的存在会引起电磁学属性的改变。涡旋电流法通过激发涡旋电磁场探测材料内部畸变，但传统涡旋检测法没有足够灵敏度用于残余应力检测。超导量子干涉仪直接对磁场通量强度实施测量，因而灵敏度高，此外还具有工作频带宽等优点，这为用于材料残余应力检测提供了可能性。
对不同激发频率下的电磁场分布的研究结果显示：涡旋电流法的检测深度和激励频率相关，激励频率低，电磁场透入深度大，能够探测区域大，反之亦然。相应地，要检测较深区域的残余应变，激励频率需要向低频扩展。
对残余应力的计算结果表明：模拟条件下，铍材单位MPa应力强度变化引起的SQUID磁通改变幅度为1.194×10~(-16)Wb／MPa，SQUID磁场测量灵敏度优于10~(-14)T／Hz~(1/2)，对应的磁通测量灵敏度可达10~(-20)Wb／Hz~(1/2)·mm~2，本模型中SQUID梯度计的线圈半径为1.728mm，而SQUID在低频情况下仍具有较高信躁比，从测量仪器的绝对灵敏度判断SQUID梯度计能够响应残余应力的变化。该结果还显示，磁场通量的变化和材料内残余应力的强度近似成线性关系，这为实际测量时从SQUID信号进行反演获取残余应力信息提供了基础。
对影响SQUID其他因素初步的研究表明：提离效应对测量结果的影响较大，这一计算结果同G.Y.Tian等人的实验结果相吻合，而温漂是另外一个需要考虑的干扰因素。此外，本文对这两种烦扰的抑制方法进行了初步讨论。
初步的研究结果表明从理论上SQUID结合涡旋电流法有可能为铍材残余应力的无损检测提供一种新途径。但是要将该方法实际应用，面临的问题众多而复杂，涉及到材料、力学、电磁学、低温学等诸多领域，因此还需开展进一步的研究工作。
Non-ferrous metal Beryllium was widely used in many fields for its special characters,Due to its brittleness, the beryllium components might be damaged by the residual stresscaused during machining and welding. Accordingly, itis important to examine the statusof residual stress in Be components. While industrial CT, XRD(X-Ray Diffraction) andBarkhausen methods failed to accomplish, it was needed to find a new way.
Eddy Current was a NDE(Non-Destructive Evaluation) method based on testingthe changes of electromagnetic property. And,SQUID(Superconducting QUantum Inter-ference Device) has been extended to NDE since 1980s. Different from the conventionalelectromagnetical detecting method, the magnetic flux density B was directly examined bySQUID. Besides, SQUID has some other better capabilities: a wider operating frequencybandwidth, from dc to MHz, and higher sensitivity.
In this paper, A method based on SMM-601 by Tristan Company was developed tomodel SQUID. The magnetic flux change in the SQUID detection coil was calculated byFinite Element Method. The dependence of residual stress on magnetic flux was com-puted. In addition, the interval effect and temperature alteration effect were discussed.What's more, the ways to restrain the foregoing two side effects were listed and takeninto account.
According to the computed results: the dependence of axial residual stress on mag-netic flux of SQUID was 1.194×10~(-16)Wb/MPa, and the radius of SQUID in our modelwas 1.728mm. While the sensitivity of SQUID was 10~(-20)Wb/Hz~(1/2)·mm~2. Therefore thischange of residual stress was measurable by SQUID. In addition, the magnetic flux changeis nearly in linear with residual stress intension.
In a word, a new method based on SQUID and eddy current to examine residualstress in beryllium components was feasible. While there were still much difficulty on theway to be realized. A thorough research is needed.
金属材料都具有压电效应，残余应力的存在会引起电磁学属性的改变。涡旋电流法通过激发涡旋电磁场探测材料内部畸变，但传统涡旋检测法没有足够灵敏度用于残余应力检测。超导量子干涉仪直接对磁场通量强度实施测量，因而灵敏度高，此外还具有工作频带宽等优点，这为用于材料残余应力检测提供了可能性。
对不同激发频率下的电磁场分布的研究结果显示：涡旋电流法的检测深度和激励频率相关，激励频率低，电磁场透入深度大，能够探测区域大，反之亦然。相应地，要检测较深区域的残余应变，激励频率需要向低频扩展。
对残余应力的计算结果表明：模拟条件下，铍材单位MPa应力强度变化引起的SQUID磁通改变幅度为1.194×10~(-16)Wb／MPa，SQUID磁场测量灵敏度优于10~(-14)T／Hz~(1/2)，对应的磁通测量灵敏度可达10~(-20)Wb／Hz~(1/2)·mm~2，本模型中SQUID梯度计的线圈半径为1.728mm，而SQUID在低频情况下仍具有较高信躁比，从测量仪器的绝对灵敏度判断SQUID梯度计能够响应残余应力的变化。该结果还显示，磁场通量的变化和材料内残余应力的强度近似成线性关系，这为实际测量时从SQUID信号进行反演获取残余应力信息提供了基础。
对影响SQUID其他因素初步的研究表明：提离效应对测量结果的影响较大，这一计算结果同G.Y.Tian等人的实验结果相吻合，而温漂是另外一个需要考虑的干扰因素。此外，本文对这两种烦扰的抑制方法进行了初步讨论。
初步的研究结果表明从理论上SQUID结合涡旋电流法有可能为铍材残余应力的无损检测提供一种新途径。但是要将该方法实际应用，面临的问题众多而复杂，涉及到材料、力学、电磁学、低温学等诸多领域，因此还需开展进一步的研究工作。
Non-ferrous metal Beryllium was widely used in many fields for its special characters,Due to its brittleness, the beryllium components might be damaged by the residual stresscaused during machining and welding. Accordingly, itis important to examine the statusof residual stress in Be components. While industrial CT, XRD(X-Ray Diffraction) andBarkhausen methods failed to accomplish, it was needed to find a new way.
Eddy Current was a NDE(Non-Destructive Evaluation) method based on testingthe changes of electromagnetic property. And,SQUID(Superconducting QUantum Inter-ference Device) has been extended to NDE since 1980s. Different from the conventionalelectromagnetical detecting method, the magnetic flux density B was directly examined bySQUID. Besides, SQUID has some other better capabilities: a wider operating frequencybandwidth, from dc to MHz, and higher sensitivity.
In this paper, A method based on SMM-601 by Tristan Company was developed tomodel SQUID. The magnetic flux change in the SQUID detection coil was calculated byFinite Element Method. The dependence of residual stress on magnetic flux was com-puted. In addition, the interval effect and temperature alteration effect were discussed.What's more, the ways to restrain the foregoing two side effects were listed and takeninto account.
According to the computed results: the dependence of axial residual stress on mag-netic flux of SQUID was 1.194×10~(-16)Wb/MPa, and the radius of SQUID in our modelwas 1.728mm. While the sensitivity of SQUID was 10~(-20)Wb/Hz~(1/2)·mm~2. Therefore thischange of residual stress was measurable by SQUID. In addition, the magnetic flux changeis nearly in linear with residual stress intension.
In a word, a new method based on SQUID and eddy current to examine residualstress in beryllium components was feasible. While there were still much difficulty on theway to be realized. A thorough research is needed.
引文
[1] 孙本双．铍的应用进展[J]．稀有金属，1995，19(2)：127-131．
[2] 王永跃．铍在高科技中的应用与发展[J]．稀有金属材料与工程，1995，24(6)：29-31．
[3] 张友寿，秦有钧，吴东周．铍和含铍材料的性能及应用[J]．焊接学报，2001，22(6)：92-96．
[4] 孙灵霞，魏肯堂，叶云长．铍焊缝质量的工业CT诊断方法研究[J]．核技术，2002，25(2)：155-160．
[5] 张鹏程，董平，邹觉生．铍材机加应力沿层深分布规律[J]．矿冶，2001，10(1)：59-62．
[6] 张鹏程，田黎明．车削加工对铍组织与性能的损伤[J]．稀有金属，2001，25(2)：90-92．
[7] 张鹏程，白彬，邹觉生．压力对铍／HR-1不锈钢扩散焊的影响[J]．稀有金属，2003，27(2)：233-237．
[8] 董平，秦有钧，柏朝茂．铍环形焊件残余应力的有限元分析与测试[J]．理化检验-物理分册，2000，36(5)：216-219．
[9] 董平，陈裕泽，邹觉生．铍环电子束焊接温度场和应力场的有限元分析[J]．原子能科学技术，2002，36(3)：209-213．
[10] Dong P, Zhang P C, Chen Y Z, and Zou J S. Effects of stress gradients in beryllium surface layer on x-ray stress measurement[J]. Nonferrous Metals, 2002, 54(2):20-24.
[11] 陈勇忠，董平，柏朝茂，秦有均．铍电子束环形焊件残余应力测试方法及其数值模拟研究．CNIC-01436(CAEP-0043)．
[12] 基泰尔著，项金钟，吴兴惠译．原著第八版．固体物理导论[M]．北京：化学工业出版社，2005，pages 19-33．
[13] Makoto H and Okido S. Application of X-ray and neutron diffraction methods to reliability evaluation of structural components and electronic device[J]. Materials Science Forum, 2005, 490-491: 19-27.
[14] Curfs C and Kirstein O. Residual stress measurement in australia:present and future[J]. Materials Science Forum, 2005, 490-491:218-222.
[15] 李家伟，陈积懋．无损检测手册[M]．北京：机械工业出版社，2002，pages 483-519．
[16] Lebrun B. Pulsed eddy current application to the detection of deep cracks[J]. Materials Evaluation, 1995, 53(11): 1296-1300.
[17] Chang H, Schoenig F C, and Soules J A. Eddy current offers a powerful tool for investigating residual strees and other metallurgical properties[J]. Mat. Eval., 1999, 57: 1257-1260.
[18] Schoenig F C, Soules J A, Chang H, and DiCillo J J. Eddy current measurement of residual stresses induced by shot peening in Titanium Ti-6Al-4V[J]. Mat. Eval., 1995, 53:22-26.
[19] Ruiz A and Nagy P B. Residual stress assessment in surface-treated metals by laserultrasonic spectroscopy[A]. In: Review of Progress in QNDE[C], AIP Conference Proceedings, New York, 2004, 23: 1208-1215.
[20] Blodgett M P, Yu F, and Nagy P B. Eddy current nondestructive residual stress assessment in shot-peened nickel-base superalloys[A]. In: Review of progress in QNDE[C], AIP Conference Proceedings, New York,2005, 24:1347-1354.
[21] Yu F and Nagy P B. Piezoresistive effect for near-surface eddy current residual stress assessment[A]. In: Review of Progress in QNDE[C], AIP Conference Proceedings, New York, 2005, 24:1371-1358.
[22] Josephson B D. Phys. Lett.[J], 1962, 251.
[23] Fagaly R L. Commercialization of Superconducting Electronics[J]. Application of superconductors in Electronics,Communications and Computing, 2001.
[24] Wikswo J P. In: H. Weinstock (Ed.), SQUID sensors,fundamentals, fabrication and applications. NATO ASI series E, Kluwer, Dordrecht, 1996, 329:307-360 and 629-695.
[25] Krause H J and Kreutzbruck M. Recent developments in SQUID NDE[J]. Physica C, 2002, 368:70-79.
[26] Tavrin Y, Krause H J, and Wolf W. in: D.Dew-Hughes (Ed.),applied superconductivity, proceedings of EUCAS' 95. Institute of Physics Conference Series No. 148, 1996, pages 1519-1520.
[27] Donaldson G, Cochran A, and McKirdy D. In:H. Weinstock (Ed.). SQUID Sensors: Fundamentals, Fabrication and Applications, Kluwer, Dordrecht,1996, pages 599-628.
[28] Gatner S, Krause H J, and Wolters N. Non-destructive evaluation of aircraft structures with a multiplexed HTS rf SQUID magnetometer array[J]. Physica C, 2002, 372-376: 287-290.
[29] Jenks W G, Sadeghi S S H, and Wikswo J P. SQUIDs for nondestructive evaluation[J]. J. Phys. D: Appl. Phys., 1997, 30: 293-323.
[30] 徐毓龙，邱吉衡，叶锦荣等．Squid及其在探测微弱磁场领域的应用[J]．低温与超导，1995，23(2)：49-56．
[31] Itozaki H. SQUID application research in Japan[J]. Supercond. Sci. Technol., 2003, 16: 1340-1343.
[32] He D F and Yoshizawa M. Dual-frequency eddy-current NDE based on high-T_c rf SQUID[J]. Physica C, 2002, 383:223-226.
[33] Muck M, Kreutzbruck M V, Baby U, Troll J, and Heiden C. Eddy current nondestructive material evaluation based on HTS SQUIDs[J]. Physica C, 1997, 282-287:407-410.
[34] Qi H H, Lang P L, Zhang M J, and Wang T S. High-Tc dc-SQUID magnetometer and its application in eddy current non-destructive evaluation[J]. Cryogenics, 2004, 44: 695-699.
[35] Braginski A I and Krause H J. Nondestructive evaluation using high-temperature SQUIDs[J]. Physica C, 2000, 335: 179-183.
[36] Isawa K, Nakayama S, Morooka T, Ikeda M, and Takagi S. Traveling DC-SQUID gradiometry for nondestructive evaluation[J]. Physica C, 2005, 418:1-8.
[37] 丁红胜，孙景春，何豫生，张峰会，陈赓华等．高温超导量子干涉器在无损检测中的应用研究[J]．测试技术学报，2004，18(4)：311-315．
[38] 王春艳，陈铁群，张欣宇．脉冲涡旋检测技术的某些进展[J]．无损探伤，2005，29(4)：1-4．
[39] Sophian A, Tian G Y, Taylor D, and Rudlin J. A feature extraction technique based on principal component analysis for pulsed Eddy current NDT[J]. NDT&E International, 2003, 36: 37-41.
[40] Sophian A, Tian G Y, Taylor D, and Rudlin J. Design of a pulsed eddy current sensor for detection of defects in aircraft lap-joints[J]. Sensors and Actuators, 2002, 101: 92-98.
[41] Safizadeh M S, Lepine B A, Forsyth D S, and Fahr A. Time-frequency analysis of pulsed eddy current signals[J]. Journal of Nondestructive Evaluation, 2001, 20(2):73-84.
[42] Tian G Y and Sophian A. Reduction of lift-off effect for pulsed eddy current NDT[J]. NDT&E International, 2005, 38: 319-324.
[43] Panaitov G, Krause H J, and Zhang Y. Pulsed eddy current transient technique withHTS SQUID magnetometer for non-destructive evaluation[J]. Physica C, 2002, 372-376: 278-281.
[44] Spies B and Frischknecht F. In M. Nabighian (Ed.), EM Methods of Applied Geophysics, Soc. Expl. Geophys., pages 285-425. Plenum Press, New York, 1991.
[45] Kreutzbruck M, Muck M, and Heiden C. Simulations of eddy current distributions and crack detection algorithms for a SQUID based NDE system[A]. In:Proceedings of the 7th European Conference on Non-Destructive Testing[C], Plenum Press, New York,1998, pages 2513-2520.
[46] 刘国强，赵凌志，蒋继娅．Ansoft工程电磁场有限元分析[M]．北京：电子工业出版社，2005，pages 82-105．
[47] 孙晓云，陈德智，盛剑霓．通过扰动磁场识别缺陷[J]．无损检测，2001，23(2)：47-50．
[48] 陈德智，王彬，邵可然，盛剑霓．裂纹检测中的涡流场计算[J]．无损检测，2000，22(3)：99-105．
[49] 金建铭，王建国．电磁场有限元方法[M]．西安：西安电子科技大学出版社，1997，pages 18-23．
[50] 游凤荷，曹令俊，陈铁群．基于有限元方法的涡流检测数值仿真[J]．无损检测，2002，24(6)：231-233．
[51] Bihan Y L. Study on the transformer equivalent circuit of eddy current nondestructive evaluation[J]. NDT&E International, 2003, 36:297-302.
[52] Operating Guide for Model SMM-601 NDE System. 2001, pages 15-16.
[53] Kalyanasundaram K and Nagy P B. A simple numerical model of the apparent loss of eddy current conductivity due to surface roughness[J]. NDT&E International, 2004, 37:47-56.
[54] Blodgett M P, Ukpabi C V, and Nagy P B. Surface roughness influence on eddy current electrical conductivity measurements[J]. Mat. Eval., 2003, page 765.
[55] Giguere S and JMS. Dubois. Pulsed eddy current: finding corrosion independently of transducer lift-off[J]. Rev. Prog. Quantitative Nondestructive Eval, 2001, 19(A):49-56.
[56] Graham D, Maas P, Donaldson G B, and Carr C. Impact damage detection in carbon fibre composites using hts squids and neural networks[J]. NDT&E International, 2004, 37:565-570.
[2] 王永跃．铍在高科技中的应用与发展[J]．稀有金属材料与工程，1995，24(6)：29-31．
[3] 张友寿，秦有钧，吴东周．铍和含铍材料的性能及应用[J]．焊接学报，2001，22(6)：92-96．
[4] 孙灵霞，魏肯堂，叶云长．铍焊缝质量的工业CT诊断方法研究[J]．核技术，2002，25(2)：155-160．
[5] 张鹏程，董平，邹觉生．铍材机加应力沿层深分布规律[J]．矿冶，2001，10(1)：59-62．
[6] 张鹏程，田黎明．车削加工对铍组织与性能的损伤[J]．稀有金属，2001，25(2)：90-92．
[7] 张鹏程，白彬，邹觉生．压力对铍／HR-1不锈钢扩散焊的影响[J]．稀有金属，2003，27(2)：233-237．
[8] 董平，秦有钧，柏朝茂．铍环形焊件残余应力的有限元分析与测试[J]．理化检验-物理分册，2000，36(5)：216-219．
[9] 董平，陈裕泽，邹觉生．铍环电子束焊接温度场和应力场的有限元分析[J]．原子能科学技术，2002，36(3)：209-213．
[10] Dong P, Zhang P C, Chen Y Z, and Zou J S. Effects of stress gradients in beryllium surface layer on x-ray stress measurement[J]. Nonferrous Metals, 2002, 54(2):20-24.
[11] 陈勇忠，董平，柏朝茂，秦有均．铍电子束环形焊件残余应力测试方法及其数值模拟研究．CNIC-01436(CAEP-0043)．
[12] 基泰尔著，项金钟，吴兴惠译．原著第八版．固体物理导论[M]．北京：化学工业出版社，2005，pages 19-33．
[13] Makoto H and Okido S. Application of X-ray and neutron diffraction methods to reliability evaluation of structural components and electronic device[J]. Materials Science Forum, 2005, 490-491: 19-27.
[14] Curfs C and Kirstein O. Residual stress measurement in australia:present and future[J]. Materials Science Forum, 2005, 490-491:218-222.
[15] 李家伟，陈积懋．无损检测手册[M]．北京：机械工业出版社，2002，pages 483-519．
[16] Lebrun B. Pulsed eddy current application to the detection of deep cracks[J]. Materials Evaluation, 1995, 53(11): 1296-1300.
[17] Chang H, Schoenig F C, and Soules J A. Eddy current offers a powerful tool for investigating residual strees and other metallurgical properties[J]. Mat. Eval., 1999, 57: 1257-1260.
[18] Schoenig F C, Soules J A, Chang H, and DiCillo J J. Eddy current measurement of residual stresses induced by shot peening in Titanium Ti-6Al-4V[J]. Mat. Eval., 1995, 53:22-26.
[19] Ruiz A and Nagy P B. Residual stress assessment in surface-treated metals by laserultrasonic spectroscopy[A]. In: Review of Progress in QNDE[C], AIP Conference Proceedings, New York, 2004, 23: 1208-1215.
[20] Blodgett M P, Yu F, and Nagy P B. Eddy current nondestructive residual stress assessment in shot-peened nickel-base superalloys[A]. In: Review of progress in QNDE[C], AIP Conference Proceedings, New York,2005, 24:1347-1354.
[21] Yu F and Nagy P B. Piezoresistive effect for near-surface eddy current residual stress assessment[A]. In: Review of Progress in QNDE[C], AIP Conference Proceedings, New York, 2005, 24:1371-1358.
[22] Josephson B D. Phys. Lett.[J], 1962, 251.
[23] Fagaly R L. Commercialization of Superconducting Electronics[J]. Application of superconductors in Electronics,Communications and Computing, 2001.
[24] Wikswo J P. In: H. Weinstock (Ed.), SQUID sensors,fundamentals, fabrication and applications. NATO ASI series E, Kluwer, Dordrecht, 1996, 329:307-360 and 629-695.
[25] Krause H J and Kreutzbruck M. Recent developments in SQUID NDE[J]. Physica C, 2002, 368:70-79.
[26] Tavrin Y, Krause H J, and Wolf W. in: D.Dew-Hughes (Ed.),applied superconductivity, proceedings of EUCAS' 95. Institute of Physics Conference Series No. 148, 1996, pages 1519-1520.
[27] Donaldson G, Cochran A, and McKirdy D. In:H. Weinstock (Ed.). SQUID Sensors: Fundamentals, Fabrication and Applications, Kluwer, Dordrecht,1996, pages 599-628.
[28] Gatner S, Krause H J, and Wolters N. Non-destructive evaluation of aircraft structures with a multiplexed HTS rf SQUID magnetometer array[J]. Physica C, 2002, 372-376: 287-290.
[29] Jenks W G, Sadeghi S S H, and Wikswo J P. SQUIDs for nondestructive evaluation[J]. J. Phys. D: Appl. Phys., 1997, 30: 293-323.
[30] 徐毓龙，邱吉衡，叶锦荣等．Squid及其在探测微弱磁场领域的应用[J]．低温与超导，1995，23(2)：49-56．
[31] Itozaki H. SQUID application research in Japan[J]. Supercond. Sci. Technol., 2003, 16: 1340-1343.
[32] He D F and Yoshizawa M. Dual-frequency eddy-current NDE based on high-T_c rf SQUID[J]. Physica C, 2002, 383:223-226.
[33] Muck M, Kreutzbruck M V, Baby U, Troll J, and Heiden C. Eddy current nondestructive material evaluation based on HTS SQUIDs[J]. Physica C, 1997, 282-287:407-410.
[34] Qi H H, Lang P L, Zhang M J, and Wang T S. High-Tc dc-SQUID magnetometer and its application in eddy current non-destructive evaluation[J]. Cryogenics, 2004, 44: 695-699.
[35] Braginski A I and Krause H J. Nondestructive evaluation using high-temperature SQUIDs[J]. Physica C, 2000, 335: 179-183.
[36] Isawa K, Nakayama S, Morooka T, Ikeda M, and Takagi S. Traveling DC-SQUID gradiometry for nondestructive evaluation[J]. Physica C, 2005, 418:1-8.
[37] 丁红胜，孙景春，何豫生，张峰会，陈赓华等．高温超导量子干涉器在无损检测中的应用研究[J]．测试技术学报，2004，18(4)：311-315．
[38] 王春艳，陈铁群，张欣宇．脉冲涡旋检测技术的某些进展[J]．无损探伤，2005，29(4)：1-4．
[39] Sophian A, Tian G Y, Taylor D, and Rudlin J. A feature extraction technique based on principal component analysis for pulsed Eddy current NDT[J]. NDT&E International, 2003, 36: 37-41.
[40] Sophian A, Tian G Y, Taylor D, and Rudlin J. Design of a pulsed eddy current sensor for detection of defects in aircraft lap-joints[J]. Sensors and Actuators, 2002, 101: 92-98.
[41] Safizadeh M S, Lepine B A, Forsyth D S, and Fahr A. Time-frequency analysis of pulsed eddy current signals[J]. Journal of Nondestructive Evaluation, 2001, 20(2):73-84.
[42] Tian G Y and Sophian A. Reduction of lift-off effect for pulsed eddy current NDT[J]. NDT&E International, 2005, 38: 319-324.
[43] Panaitov G, Krause H J, and Zhang Y. Pulsed eddy current transient technique withHTS SQUID magnetometer for non-destructive evaluation[J]. Physica C, 2002, 372-376: 278-281.
[44] Spies B and Frischknecht F. In M. Nabighian (Ed.), EM Methods of Applied Geophysics, Soc. Expl. Geophys., pages 285-425. Plenum Press, New York, 1991.
[45] Kreutzbruck M, Muck M, and Heiden C. Simulations of eddy current distributions and crack detection algorithms for a SQUID based NDE system[A]. In:Proceedings of the 7th European Conference on Non-Destructive Testing[C], Plenum Press, New York,1998, pages 2513-2520.
[46] 刘国强，赵凌志，蒋继娅．Ansoft工程电磁场有限元分析[M]．北京：电子工业出版社，2005，pages 82-105．
[47] 孙晓云，陈德智，盛剑霓．通过扰动磁场识别缺陷[J]．无损检测，2001，23(2)：47-50．
[48] 陈德智，王彬，邵可然，盛剑霓．裂纹检测中的涡流场计算[J]．无损检测，2000，22(3)：99-105．
[49] 金建铭，王建国．电磁场有限元方法[M]．西安：西安电子科技大学出版社，1997，pages 18-23．
[50] 游凤荷，曹令俊，陈铁群．基于有限元方法的涡流检测数值仿真[J]．无损检测，2002，24(6)：231-233．
[51] Bihan Y L. Study on the transformer equivalent circuit of eddy current nondestructive evaluation[J]. NDT&E International, 2003, 36:297-302.
[52] Operating Guide for Model SMM-601 NDE System. 2001, pages 15-16.
[53] Kalyanasundaram K and Nagy P B. A simple numerical model of the apparent loss of eddy current conductivity due to surface roughness[J]. NDT&E International, 2004, 37:47-56.
[54] Blodgett M P, Ukpabi C V, and Nagy P B. Surface roughness influence on eddy current electrical conductivity measurements[J]. Mat. Eval., 2003, page 765.
[55] Giguere S and JMS. Dubois. Pulsed eddy current: finding corrosion independently of transducer lift-off[J]. Rev. Prog. Quantitative Nondestructive Eval, 2001, 19(A):49-56.
[56] Graham D, Maas P, Donaldson G B, and Carr C. Impact damage detection in carbon fibre composites using hts squids and neural networks[J]. NDT&E International, 2004, 37:565-570.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |