Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 www.ommi.co.uk TENSILE TEST ANALYSIS USING REVERSING DC ELECTRICAL POTENTIAL METHOD M. Javed Hyder, Principal Engineer, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan hyder@pieas.edu.pk Dr Javed Hyder is Principal Engineer at the Pakistan Institute of Engineering and Applied Sciences, Islamabad. His research interests include computational engineering, creep-fatigue interaction, computer software development, finite element analysis and application of computer graphics in engineering Abstract Stress versus electrical potential behaviour during tensile testing has been analyzed using the reversing dc electrical potential method. It is shown that the stress versus electrical potential curve obtained during tensile testing not only indicates the shape changes in the specimen but also includes the effect of internal damage occurring during the loading process. The experiments were performed at 26ºC at a loading rate of 1-3 s -1. The elastic limit was found to be.2 % strain while the plastic limit was found to be around 3.8 % strain, as obtained from the stress-strain curve. It is also shown that the same results are obtained using the electrical potential method. It was also observed that, up to 12% strain, the electrical resistivity remains almost constant but that, after this value, it increases in a polynomial manner. It has been concluded that up to 12% strain, the changes in electrical potential are due to dimensional changes only and after that, the changes taking place in electrical potential are due to both dimensional changes and to internal changes. Optimisation of the current density was also carried out and an optimum current value of 5. Amperes for a specimen having 3.175 mm gauge section diameter was obtained. Introduction This research is aimed at developing the reversing dc electrical potential technique for monitoring deformation and damage during tensile testing. The reversing dc electrical potential method [1] is a modified electrical potential method developed to overcome the
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 2 drift due to thermal e.m.f.s created at the junction points. Presently the method is being used to study the phenomena of creep [2,3], fatigue [4,5], creep-fatigue interaction [6,7] and on-line damage monitoring [8]. The results of this research show that the electrical potential measurements obtained during tensile testing not only indicate the shape change taking place in the specimen but also indicate the internal damage taking place during the loading process. These tensile test results may be used to improve the understanding of the above-mentioned phenomena. As this work is an outshoot of work related to low cycle fatigue [4], the same test specimen and material are used. In the low cycle fatigue test, the requirement is to have a material that will give a homologous temperature in excess of.5 at room temperature. Therefore, a bimetal test specimen [9] was developed for this purpose. The test material consists of lead tin solder 5/5. The shape and dimensions of the test specimen are shown in Figure 1. Figure 1 - Details of bimetal test specimen The copper portion of the specimen is used for holding the specimen by the machine grips and for the attachment of the extensometer. Also wires (for the application of voltage and measurement of electrical potential changes) were spot welded onto the copper part of the specimen.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 3 Specimen Preparation The specimen is prepared by melting and casting the solder in a Pyrex tube. The tip of one of the copper ends is dipped in a wetting material (soldering paste). Then a closely fitted Pyrex tube is inserted over the copper end. Solder in small pieces is placed in the tube while it is being heated using a Bunsen burner. When the tube is filled with molten solder, the other copper end is inserted in the tube after dipping in the wetting material. The second copper end is first heated for a few minutes, to make sure that the temperature of the copper is above the melting point of the solder. The specimen is then held vertically to allow the second copper end to slide all the way in, until the tube end touches the copper shoulder. The glass tube and copper end dimensions are such that the correct solder length is achieved. This semi-prepared specimen is left to cool for approximately 15 min. The first copper end is now heated until the copper tip begins to melt the solder attached to it. When a sufficient amount of the solder near the copper tip is melted, the specimen is held vertically in such a way that the first copper end is at the top. This ensures that the glass tube rests properly on the copper shoulder. After cooling the specimen for about an hour, the glass tube is broken. The solder section of the specimen is carefully machined to its required shape and size. Finally, the specimen is annealed at 8 C for 2 hrs and cooled to room temperature in the annealing furnace. Experimental Procedure The reversing dc electrical potential was applied at points A and B (see Figure 1) while the active electrical potential was measured across points C and D. Along with the active test specimen, a reference test specimen was also used. The complete experimental setup is shown in Figure 2. In the reference test specimen, only the changes taking place due to environmental changes are recorded while the changes taking place due to tensile loading, as well as the changes taking place due to environmental changes, are recorded from the active test specimen. Potential values from the active specimen (A) were normalized using the potential value from the reference specimen (R) and the initial value of the reference specimen (R o ) as follows: Potential = A R o / R (1) The reversing dc electrical potential method was used to monitor the changes. The method requires that the current be reversed at constant time intervals. The current wave shape used in the test is shown in Figure 3. The period used was.6 second. This is the minimum time required for collecting a complete data set. A data set is defined as the number of variables collected during one time period, as shown in Figure 3.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 4 Computer HP 3457 A Multimeter Instron 424 Switch Sorensen SRL 4-12 Power Supply Reference Specimen Active Specimen Figure 2 - Experimental Set Up A1: potential value from the active specimen during the positive current flow, R1: potential value from the reference specimen during the positive current flow, S1: strain value from the output of the Instron machine controller for the X Y plotter during the positive current flow, L1: load value from the output of the Instron machine controller for the X Y plotter during the positive current flow. A2: potential value from the active specimen during the negative current flow, R2: potential value from the reference specimen during the negative current flow, S2: strain value from the output of the Instron machine controller for the X Y plotter during the negative current flow, L2: load value from the output of the Instron machine controller for the X Y plotter during the negative current flow.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 5 Current (A) 5 A1 R1 S1 L1 Time.3 Time (s).6-5 A2 R2 S2 L2 Data writing Figure 3 - Data acquisition sequence and current wave shape The time was recorded during the positive current flow whereas the data was written during the negative current flow. The potential value from the two successive readings was averaged (positive and negative polarity). The total time consumed to collect one set of data was.6 second. Data was continuously collected throughout the test. To minimize the time spent to collect a single data set, analysis of the data was not included in the main program. Testing was performed at a temperature of 26 ºC and the tensile loading was done at the rate of 1-3 s -1. Current Optimization Experiments were performed to optimize the required current value. The specimen diameters were.25 in (6.35 mm) and.125 (3.175 mm) in the gauge section. The current was changed from 1. A to 1 A in increments of.5 Amperes. The potential across the specimen was measured. Around 5 data points were obtained. The ratios of the standard deviation to the average potential value were calculated. The current density, defined as the current applied per unit cross sectional area, was also calculated. The above defined ratio and current density were plotted (Figure 4).
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 6 Figure 4 - Current optimization curve It is obvious from the graph that current density is the most appropriate parameter for optimizing the current, irrespective of the current value or the cross sectional area of the specimen. If the current density is the same, then the resolution will also be the same. A current density value of 25 ~ 4 A/in 2 (.3875 ~.62 A/mm 2 ) was selected for these experiments. This gave a current value of 5. Amperes for the specimen with a.125 in (3.175 mm) gauge section diameter. Experimental Results and Discussion Based on the experimental results the engineering and true stress-strain curves are shown in Figure 5. It clearly shows the elastic region, as well as the plastic region leading to necking of the specimen and final fracture of the specimen. A comparison of these curves with the graphs of the engineering and true stress variations as a function of electrical potential changes indicate a similar behaviour, as shown in Figure 6. Initial linear behaviour indicates the elastic region, and the inelastic region is represented by non-linear behaviour.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 7-2 2 4 6 8 1 12 14 16 18 2 22 7 7 6 5 True stress vs true strain Engineering stress vs strain 6 5 Stress MPa 4 3 2 4 3 2 1 1-2 2 4 6 8 1 12 14 16 18 2 22 Strain % Figure 5 - Engineering and true stress - strain curves of lead / tin solder 5/5 7 6 1.2 1.4 1.6 1.8 2. True stress vs Potential Engineering stress vs potential 7 6 5 5 Stress MPa 4 3 2 4 3 2 1 1 1.2 1.4 1.6 1.8 2. Potentail mv Fig 6- Engineering & true stress vs electrical potential curves of lead/tin solder 5/5
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 8 The electrical potential versus strain graph is shown in Figure 7. 2.2 5 1 15 2 25 2.2 2. Engineering True 2. Potential mv 1.8 1.6 1.4 1.8 1.6 1.4 1.2 1.2 5 1 15 2 25 Strain % Figure 7 - Behaviour of electrical potential as a function of true and engineering strain This shape change can be explained by the following analysis. The differential form of electrical resistance of a bar of length l, cross-sectional area A and materials electrical resistivity ρ is given by: l ρ ρl = dρ + dl da (2) A A A R 2 After integration and converting the equation to longitudinal strain [4] the equation is reduced to R R = ρ ρ 1+ 2ν e ε As constant current is used in the reversing dc electrical potential method, the above equation can be modified using Ohm s law. Hence, the potential changes taking place during straining and when the resistivity of the material changes are given by (3)
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 9 + ρ 1 2ν ε = V V e (4) ρ If resistivity is assumed to be constant, and using Taylor Series expansion (neglecting second and higher order terms), the equation is reduced to ( + 1 1+ 2ν ε ) V (5) = V In Figure 8 the engineering stress-strain curve is shown and it is observed that the linear elastic limit is at.2 % engineering strain with an engineering stress of 4 MPa. 6 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. 6 5 5 Engineering stress MPa 4 3 2 1 Point at which Linear elastic ends 4 3 2 1 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Engineering strain % Figure 8 - Linear elastic limit shown on an engineering stress-strain curve In Figure 9 the experimental values of electrical potential versus engineering strain behaviour are shown along with the straight line drawn based on equation 5, using a value of.3 for Poisson ratio. It can be clearly observed that the straight line deviates from the experimental curve at.2 % engineering strain.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 1 1.22 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. 1.22 1.21 1.2 Experimental Elastic 1.21 1.2 Potential mv 1.19 1.18 1.17 Point at which elastic line deviates from experimental curve 1.19 1.18 1.17 1.16 1.16 1.15 1.15 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Engineering strain % Fig.9 - Linear elastic limit shown on the electrical potential vs. enginrng strain curve Similarly, in Figure 1 the true stress-strain curve gives the elastic limit of.2 % true strain. In Figure 11, the experimental values of electrical potential versus true strain are drawn along with the straight line obtained using equation 5 and a Poisson ratio of.3 for the elastic region. Also in Figure 11 the deviation of the experimental curve from the straight line is observed at.2 % true strain. 7..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. 7 6 6 5 5 True stress MPa 4 3 2 Point at which linear elastic ends 4 3 2 1 1..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. True strain % Figure 1 - Linear elastic limit shown on true stress-strain curve
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 11 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. 1.22 1.22 1.21 1.2 Experimental Elastic 1.21 1.2 Potential mv 1.19 1.18 1.17 1.16 Point at which elastic line deviates from experimental curve 1.19 1.18 1.17 1.16 1.15 1.15 -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. True strain % Figure 11 - Linear elastic limit shown on the electrical potential vs. true strain curve The ultimate tensile stress is obtained at 55MPa and a strain value of 3.8 %, as shown in Figure 12, which is also the necking point. Now, following the same procedure of analysis for the plastic behaviour and using equation 5 and a Poisson ratio of.5, we can draw another straight line along with the experimental values of electrical potential versus engineering strain (see Figure 13). It is observed from Figure 13 that the deviation of the experimental curve from the straight line is at 3.8 % engineering strain.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 12 Figure 12 - Engineering stress-strain curve showing the necking point 2. 2.2 2.4 2.6 2.8 3. 3.2 3.4 3.6 3.8 4. 4.2 4.4 4.6 4.8 5. 1.3 1.3 1.28 Experimental Elastic Plastic 1.28 Potential mv 1.26 1.24 Point at which plastic deviates from experimental curve 1.26 1.24 1.22 1.22 1.2 1.2 2. 2.2 2.4 2.6 2.8 3. 3.2 3.4 3.6 3.8 4. 4.2 4.4 4.6 4.8 5. Engineering strain % Figure 13 - Plastic limit shown on the electrical potential vs engineering strain curve
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 13 Similar results are obtained from the curves drawn for the true strain values, as shown in Figure 14 and Figure 15. 7 2 4 6 8 1 12 14 16 18 2 22 7 6 6 True stress MPa 5 4 3 2 1 5 4 3 2 1 2 4 6 8 1 12 14 16 18 2 22 True strain % Figure 14 - Plastic limit shown on true stress-strain curve 2. 2.2 2.4 2.6 2.8 3. 3.2 3.4 3.6 3.8 4. 4.2 4.4 4.6 4.8 5. 1.3 1.3 1.28 Experimental Elastic Plastic 1.28 Potential mv 1.26 1.24 Point at which plastic deviates from experimental curve 1.26 1.24 1.22 1.22 1.2 1.2 2. 2.2 2.4 2.6 2.8 3. 3.2 3.4 3.6 3.8 4. 4.2 4.4 4.6 4.8 5. True strain % Figure 15 - Plastic limit shown on the electrical potential vs. true strain curve
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 14 A combined graph of the true and engineering stress-strain curves, together with the stress versus electrical potential curve, is shown in Figure 16. 7 Potential mv 1.2 1.4 1.6 1.8 2. 2.2 7 6 5 Potential True Engineering 6 5 Stress MPa 4 3 2 4 3 2 1 1-2 2 4 6 8 1 12 14 16 18 2 22 Strain % Fig. 16 - Combined graphs of engineering and true stress-strain curves along with the stress vs. electrical potential curve It is observed that, after the necking point, the stress versus electrical potential curve follows a linear behaviour up to 12 % strain. In addition, up to 12 % strain the electrical resistivity remains constant as indicated in Figure 17.
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 15 Strain % -2 2 4 6 8 1 12 14 16 18 2 22 1.95E-7 1.95E-7 Electrical resistivity Ohm-m 1.9E-7 1.85E-7 1.8E-7 1.75E-7 1.7E-7 Basaed on engineering strain based on true strain original value 1.9E-7 1.85E-7 1.8E-7 1.75E-7 1.7E-7 1.65E-7 1.65E-7-2 2 4 6 8 1 12 14 16 18 2 22 Strain % Fig. 17 - Behaviour of electrical resistivity as a function of strain According to Ohm s law, the electrical potential changes represent the changes taking place in electrical resistance since the current is kept constant in these experiments. Since Figure 17 indicates that the resistivity remains constant up to 12 % strain, it can be concluded that the dimensional changes (area and length) at the necking point contributes to the changes in electrical resistance, i.e., electrical potential changes. The time consumed during this test is very small, therefore, cavitations due to creep related effects are ruled out. This result is supported by the microscopic analysis given in reference [3,4,7]. Conclusion It is concluded that the electrical potential method can be adopted to study the tensile behaviour of materials. It is shown that the elastic limit (yield point) and plastic limit (ultimate tensile strength) can easily be obtained. Also, after the necking point, the point at which internal damage starts is observed prior to which only shape changes are taking place in the necked region. Hence, it is also concluded that stress electrical potential
Tensile test analysis using reversing dc OMMI (Vol. 2, Issue 3) December 23 16 curves give a true picture of the changes taking place during tensile testing as it incorporates the shape changes taking place during loading and the associated internal damage taking place during the test. References 1. W.R. Catlin, D.C. Lord, T.A Prater, and L.F. Coffin: The reversing dc electrical potential method, ASTM STP 887, 1985, pp887 2. I.P. Vasatis: Application of the dc potential drop technique to creep deformation and fracture of welds, GE Report, MOR 87-18, Feb. 1987 3. M. Javed Hyder and M. Daneil Saeed: Application of electrical potential method for creep study, Institute of Engineers Pakistan, proceedings of 36 th Convention, 1996 4. M. Javed Hyder: A study of fatigue damage using the electrical potential method, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York, May 1991 5. M. Javed Hyder, David A. Woodford, and Louis F. Coffin: A novel theoretical model of stress-electrical potential hysteresis loop during fatigue, Material Science and Technology, November 1999, Vol 15, pp 1335-36 6. T.A. Prater, W. R. Catlin and L. F. Coffin: Surface crack growth behavior of structural metals in high temperature water environments, J. Engineering Materials and Technology, Trans. ASME, vol 18, Aug. 1984, pp 2-9 7. M. Javed Hyder, David A. Woodford, and Louis F. Coffin: A study of fatigue damage using electrical potential method, Proceedings of 3 rd international conference on low cycle fatigue and elasto-plastic behavior of materials, Berlin, Federal Republic of Germany, Sept. 1992 8. L. F. Coffin: Some perspectives on future directions in low cycle fatigue, ASTM STP 942, 1988, pp5-14 9. M. Javed Hyder and David A Woodford: Development of bimetal test specimen for testing materials at high homologous temperature, Pakistan Journal of Scientific and Industrial Research, Pakistan, Vol 38, No7, July 1995