Modeling and analysis of the electrical resistance measurement of ...

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Shen et al. / Composites Science and Technology 67 (2007) 2513–2520 2519Table 2Comparison between the voltage and resistance percentage changes and the dependence of voltage percentage changes on different current contactsFour-probe voltage V 1 (mV) V 2 (mV) (V 2 V 1 )/V 1 (%) Two-probe resistance R 1 (X) R 2 (X) (R 2 R 1 )/R 1 (%)A 1 –A 5 [A 0 –A 6 ] 54.33 54.44 0.2025 A 1 –A 5 1.135 1.145 0.8811A 2 –A 4 [A 0 –A 6 ] 23.47 23.54 0.2983 A 2 –A 4 0.9005 0.9100 1.055A 2 –A 4 [A 1 –A 5 ] 29.83 29.88 0.1676 A 2 –A 4A 1 –B 5 [A 0 –B 6 ] 61.00 61.53 0.8689 A 1 –B 5 1.218 1.234 1.316A 2 –B 4 [A 0 –B 6 ] 33.49 34.08 1.762 A 2 –B 4 1.093 1.111 1.647A 2 –B 4 [A 1 –B 5 ] 42.42 43.10 1.603 A 2 –B 4A 3 –B 3 [A 2 –B 2 ] 34.25 35.14 2.599 A 3 –B 3 1.052 1.068 1.521A 3 –B 3 [A 2 –B 4 ] 34.25 35.14 2.599 A 3 –B 3V ¼ V 2 V 1 100 ð2ÞV 1where V 1 , V 2 are voltages of specimen 1 and 2, respectively.The resistance percentage changes are calculated using thetwo-probe method for specimens 1 and 2, and are denotedas R A1 A 5, R A2 A 4, R A1 B 5, R A2 B 4and R A3 B 3, respectively. Note thatthe difference between V A 0A 6A 2 A 4and V A 1A 5A 2 A 4will show the dependenceof the voltage percentage change on the current contacts.The same is also valid for the differences betweenV A 0B 6A 2 B 4and V A 1B 5A 2 B 4, and between V A 2B 2A 3 B 3and V A 2B 4A 3 A 3. But the resistancepercentage change is not affected by the current contactsbecause it only depends on the material propertiesand structural change such as delamination of the compositepanel.The FEM results for the voltages, resistances and theirpercentage change are listed in Table 2, where the columnand row values correspond to voltage/resistance and contacts,respectively. For example, V A 0A 6A 1 A 5and R A1 A 5correspondto the values of 0.2025 and 0.8811 in Table 2, respectively.It can be seen from Table 2 that the voltage and resistancepercentage changes are significantly different. Also,the voltage percentage changes depend on the current contactsused. For example, the surface voltage percent changebetween the electrodes A 2 and A 4 under the current contactsA 0 and A 6 and A 1 and A 5 , i.e., V A 0A 6A 2 A 4and V A 1A 5A 2 A 4are0.2983 and 0.1676, respectively. On the other hand, theoblique voltage percent changes are not severely affectedby the different current contacts, as shown by the valuesof V A 0B 6A 2 B 4¼ 1:762 and V A 1B 5A 2 B 4¼ 1:603, and by those of V A 2B 2A 3 B 3and V A 2B 4A 3 A 3. Therefore, it is not reliable to use the voltagepercentage changes to inversely predict damage inside compositepanels because there are no consistent changes dueto the different current contacts.5. ConclusionStrip type specimens with and without delaminationdamage are used to carry out numerical analyses of theelectrical resistance and voltage in a carbon fiber-reinforcedcomposite panel. The purpose of the study is to determinethe validity range of the four-probe method for resistancemeasurement, and the applicability of the voltage changemethod based on the four-probe method. The presentstudy shows that the method is only valid when thethrough-thickness conductivity is comparable to or largerthan the longitudinal conductivity. For example, if the longitudinalconductivity is 15 X 1 mm 1 , the through-thicknessconductivity should be larger than 1 X 1 mm 1 . Thepresent results show that the damage induced voltagechange between a pair of voltage contacts is not consistentwith the resistance change due to the same damage. Theunderlying reason for this is that the damage induced voltagechange depends on the current contacts used, while theresistance change does not.AcknowledgementsThis work was supported by Global Contour Ltd.through NSF SBIR Phase IIA grant. 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