Models of Printed Circuit Boards Conductive Pattern Defects

Evgeniya Danilova 1 , Igor Kochegarov 1 , Nikolay Yurkov 1 , Mikhail Miheev 2 , and Normunds Kante 3
  • 1 Penza State University, , Penza
  • 2 Penza State Technological University, , Penza
  • 3 Riga Technical University, , Riga, Latvia


A number of PCB defects, though having passed successfully the defect identification procedure, can potentially grow into critical defects under the influence of various external and (or) internal influences. The complex nature of the development of defects leading to PCB failures demands developing and updating the data measuring systems not only for detection but also for the prediction of future development of PCB defects considering the external influences. To solve this problem, it is necessary to analyse the models of defect development, which will allow predicting the defect growth and working out the mathematical models for their studies.

The study uses the methods of system analysis, theory of mathematical and imitation modelling, analysis of technological systems. The article presents four models for determining the theoretical stress concentration factor for several types of common defects, considering the strength loss of PCB elements. For each model the evaluation of parameters determining its quality is also given. The formulas are given that link the geometry of defects and the stress concentration factor, corresponding to four types of defects. These formulas are necessary for determining the number of cycles and time to failure, fatigue strength coefficient.

The chosen models for determining the values of the stress concentration factor can be used as a database for identifying PCB defects. The proposed models are used for software implementation of the optical image inspection systems.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] R. Е. Peterson, Stress Concentration Factors. New York: Wiley, 2008, p. 560.

  • [2] I. I. Kochegarov, E. A. Danilova, N. K. Yurkov, P. Y. Bushmelev and A. M. Telegin, “Analysis and modeling of latent defects in the printed conductors,” in 2016 13th International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE),” Novosibirsk, Russia, October 03–06, 2016,

  • [3] A. Gerasimenko, K. Ivanov, V. Kislyukov and V. Roganov, “A new faults blocking method for out-of-step protection,” in Proceedings of IEEE East-West Design & Test Symposium (EWDTS’2017), Novi Sad, Serbia, September 29 – October 2, 2017, pp. 641–645.

  • [4] A. V. Grigoriev, N. K. Yurkov, and I. I. Kochegarov, “Contactless measurement technique for the amplitude of vibrational movement of the test material point,” in 2016 IEEE East-West Design Test Symposium (EWDTS), 2016, pp. 1–3.

  • [5] H. Zhang, F. Sun, Y. Liu, Z. Zhou and Y. Qin, “Failure process of solder joint under mechanical vibration based on a real-time data acquisition method, “2011 Proceedings International Symposium on Advanced Packaging Materials, article № 6105715, pp. 272–274.

  • [6] J. W. C. de Vries, M. Y. Jansen and W. D. van Driel, “On the difference between thermal cycling and thermal shock testing for board level reliability of soldered interconnections,” (2007) Microelectronics Reliability, vol. 47, no. 2–3, pp. 444–449.

  • [7] I. Kochegarov, G. Tankov, and E. Danilova, “Dynamic Characteristics of Printed Circuit Assembly under the Influence of Temperature,” in XIX IEEE International Conference on Soft Computing and Measurements (SCM), 2016, pp. 131–134.

  • [8] K. Meier, M. Roellig, A. Schiessl and K.-J. Wolter, “Reliability study on chip capacitor solder joints under thermo-mechanical and vibration loading,” in 15th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, article № 6813863, 2014.

  • [9] C. Schuster and W. Fichtner, “Parasitic modes on printed circuit boards and their effects on EMC and signal integrity,” IEEE Transactions on Electromagnetic Compatibility, vol. 43, no. 4, pp. 416–425, 2001.

  • [10] T. M. Zeeff, T. H. Hubing, and T. P. Van Doren, “Traces in proximity to gaps in return planes, “IEEE Transactions on Electromagnetic Compatibility, vol. 47, no. 2, pp. 388–392, 2005.

  • [11] A. V. Lysenko, N. V. Goryachev, N. K. Yurkov, A. M. Telegin, and V. A. Trusov, “Information-measuring control system of active vibration protection RED,” in 2016 IEEE East-West Design Test Symposium (EWDTS), 2016, pp. 1–4.

  • [12] F. Xiao, K. Murano and Y. Kami, “Analytical solution for two parallel traces on PCB in the time domain with application to hairpin delay lines,” (2009) IEICE Transactions on Communications, vol. E92.B, no. 6, pp. 1953–1959.

  • [13] E. B. Joffe and K.-S Lock, Grounds for Grounding: A Circuit-to-System Handbook. Wiley, 2010.

  • [14] I. M. Rybakov, N. V. Goryachev, I. I. Kochegarov, A. K. Grishko, S. A. Brostilov, and N. K. Yurkov, “Application of the model of the printed circuit board with regard to the topology of external conductive layers for calculation of the thermal conditions of the printed circuit board,” J. Phys.: Conf. Ser., vol. 803, no. 1, pp. 1–6, 2017.

  • [15] A. V. Dubravin, S. A. Zinkin and D. V. Paschenko, “Formal and conceptual definitions of the hybrid model of distributed computings in networks,” in 2015 International Siberian Conference on Control and Communications SIBCON, 2015.

  • [16] D. Wang and X. Wang, “Analysis on electromechanical disturbance propagation in a finite length uniform chain discrete power system,” Asia-Pacific Power and Energy Engineering Conference, APPEEC, 2010.

  • [17] F. E. Dupriest, W. C. Elks Jr. and S. Ottesen, “Design methodology and operational practices eliminate differential sticking, “SPE Drilling and Completion, vol. 26, no. 1, pp. 115–123, 2011.

  • [18] M. Y. Mikheev, V. R. Roganov, P. G. Andreev, N. V. Goryachev, and V. A. Trusov, “Developing the structure of the quality control system of power supply units in mobile robots,” 2017 International Siberian Conference on Control and Communications, SIBCON 2017, 2017.

  • [19] W. B. Hempkins, R. H. Kingsborough, W. E. Lohec and C. J. Nini, “Multivariate statistical analysis of stuck drillpipe situations,” SPE Drilling Engineering, vol. 2, no. 3, pp. 237–244, 1987.

  • [20] K. R. McCall, M. Boudjema, I. B. Santos, R. A. Guyer and G. N. Boitnott, “Nonlinear, hysteretic rock elasticity: Deriving modulus surfaces,” American Rock Mechanics Association DC Rocks, The 38th U.S. Symposium on Rock Mechanics (USRMS), 7–10 July, 2001, Washington.


Journal + Issues