An automatic algorithm for mixed mode crack growth rate based on drop potential method A.V. Tumanov a,⇑ , V.N. Shlyannikov a , J.M. Chandra Kishen b a Kazan Scientific Center of the Russian Academy of Sciences, Russia b Dept. of Civil Engineering, Indian Institute of Science, Bangalore, India article info Article history: Received 31 March 2015 Received in revised form 7 August 2015 Accepted 9 August 2015 Available online 13 August 2015 Keywords: Mixedmode cyclic fracture Drop potential method Crack growth rate Test automation algorithm Equivalent straightline crack abstract A new automatic algorithm for the assessment of mixed mode crack growth rate characteristics is pre- sented based on the concept of an equivalent crack. The residual ligament size approach is introduced to implementation this algorithm for identifying the crack tip position on a curved path with respect to the drop potential signal. The automatic algorithm accounting for the curvilinear crack trajectory and employing an electrical potential difference was calibrated with respect to the optical measurements for the growing crack under cyclic mixed mode loading conditions. The effectiveness of the proposed algorithm is confirmed by fatigue tests performed on ST3 steel compact tension–shear specimens in the full range of mode mixities from pure mode I to pure mode II. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction The concept of the mode I elastic stress intensity factor is the basis of most contemporary standards for the fracture resistance characteristic determination [1,2]. In accordance with these stan- dards, it is necessary to know the dependence of the crack length on the number of loading cycles for the determination of the crack growth rate characteristics. The combination of experimental, numerical and analytical methods for pure mode I cracks makes it possible to automatically obtain all the necessary parameters. However, in industrial practice, mixed-mode fracture and crack growth are more likely to be the rule than the exception. It is well known that mixed-mode conditions appear when the direction of the applied loading does not coincide with the orthog- onal K I –K II –K III space. The main feature of the mixed-mode fracture is that the crack growth would no longer take place in a self-similar manner and does not follow a universal trajectory, that is, it will grow on a curvilinear path [3]. Criteria that cover the initial branch crack direction [4–7] and crack growth rate models [8–12] under mixed mode I and II loading conditions in both brittle and ductile materials have been extensively discussed in the literature, and a wide range of experiments have been performed. The traditional formulations of most crack reorientation criteria and crack growth rate models are connected with the use of the straight line crack concept in common with elastic singular solutions. The crack growth from an inclined crack illustrates mixed-mode crack behavior on the initial crack. In previous studies [13,14], it was shown that the effect of mixed mode parameters on the frac- ture resistance characteristics was significant. Currently, there are no guidelines in the literature to determine the curvilinear crack size for cases wherein visual observation is not available. In most cases involving cyclic mixed mode fracture, the crack deviation angle is not constant and changes continuously as a function of the number of loading cycles. Different curvilinear crack paths are observed for the same specimen geometry depending on the applied mode mixities. In this connection, establishment of the correlation between the crack size and the observed parameters becomes more important. On that score, it is necessary to solve the problem of identifying the position of the crack tip on a curved path with respect to the signal of a measurement tool. For mixed mode I and II crack propagation, the crack front con- tinuously changes shape and direction with each loading cycle. As a result, the angle of crack propagation h  continuously changes. At each successive position of the crack front, the stress intensity fac- tors in a plate, K 1 and K 2 , must be calculated. However, for the actual ‘‘bent” crack geometry, the expressions for K 1 and K 2 cannot be easily determined. To overcome this difficulty, an approximate procedure has been independently proposed by Sih and Barthel- emy [15] and Shlyannikov and Ivanishin [16] and has been used by Au [17], Pandey and Patel [18], Gdoutos [19] and Xua [20]. http://dx.doi.org/10.1016/j.ijfatigue.2015.08.005 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: tymanoff@rambler.ru (A.V. Tumanov), shlyannikov@mail.ru (V.N. Shlyannikov), chandrak@civil.iisc.ernet.in (J.M. Chandra Kishen). International Journal of Fatigue 81 (2015) 227–237 Contents lists available at ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue