Document Type : Original Article


1 Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

2 Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran Faculty of Shahid Bahonar, Sistan and Baluchestan Branch, Technical and Vocational University (TVU), Zahedan, Iran


In analytical studies, step (Heaviside) function is used to simulate an impact load. However, in real behaviour of materials, loading and unloading take a short time. The present study discusses analytically the effects of pulse shape and rising time of an impact load on dynamic stress intensity factor. Firstly, a pulse load with positive slip (linear and non-linear) is applied on a cracked plate and the amount of dynamic stress intensity factor on the crack tip is obtained. Then the effects of pulse time are discussed. Results show that increasing the rise time decreases the stress intensity factor because of reduction of inertia effects. Moreover, the duration of rise time plays the main role in dynamic stress intensity factor changes and how the variations are not matter.


[1]     Sih, G. C., Elastodynamic Crack Problems, Noordhoff International Publishing, Company bv Leyden, Netherland, 1977, pp. 1-23.
[2]     Freund, L. B., Dynamic Fracture Mechanics, Cambridge University press, New York, 1998, pp. 52-82
[3]     Sih, G. C., Embley, G. T., and Ravera, R. S., Impact Response of a Finite Crack in Plane Extension, International Journal of Solids and Structures, Vol. 8, No. 7, 1972, pp. 977-993.
[4]     Thau, S. A., Tsin-Hwei, L., Transient Stress Intensity Factors for A Finite Crack in an Elastic Solid Caused by A Dilatational Wave, International Journal of Solids and Structures, Vol. 7, No. 7, 1971, pp. 731-750.
[5]     Ing, Y. S., Ma, C. C., Transient Response of a Finite Crack Subjected to Dynamic Anti-Plane Loading, International journal of fracture, Vol. 82, No. 4, 1996, pp. 345-362.
[6]     Ing, Y. S., Ma, C. C., Exact Transient Full–Field Analysis of a Finite Crack Subjected to Dynamic Anti–Plane Concentrated Loadings in Anisotropic Materials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, No. 2054, 2005, pp. 509-539.
[7]     Kassir, M., Bandyopadhyay, K., Impact Response of a Cracked Orthotropic Medium, Journal of applied mechanics, Vol. 50, No. 3, 1983, pp. 630-636.
[8]     Rubio-Gonzalez, C., Mason, J., Dynamic Stress Intensity Factor Due to Concentrated Loads On a Propagating Semi-Infinite Crack in Orthotropic Materials, International journal of fracture, Vol. 118, No. 1, 2002, pp. 77-96.
[9]     Rodríguez-Castellanos, A., Rodríguez-Sánchez, J., Núñez-Farfán, J., and Olivera-Villaseñor, R., Crack Effects On the Propagation of Elastic Waves in Structural Elements, Revista mexicana de física, Vol. 52, No. 2, 2006, pp. 104-110.
[10]  Itou, S., Dynamic Stress Intensity Factors Around a Cylindrical Crack in an Infinite Elastic Medium Subject to Impact Load, International Journal of Solids and Structures, Vol. 44, No. 22-23, 2007, pp. 7340-7356.
[11]  Eslami, S., Amini, F, Dynamic Stress Intensity Factors Due to Scattering of Harmonic Waves by A Crack in an Infinite Medium, Fatigue & Fracture of Engineering Materials & Structures, Vol. 31, No. 10, 2008, pp. 918-927.
[12]  Zhang, C., Gross, D., On Wave Propagation in Elastic Solids with Cracks, Computational Mechanics Publications, 1998, pp. 45-59.
[13]  Chirino, F., Dominguez, J., Dynamic Analysis of Cracks Using Boundary Element Method, Engineering Fracture Mechanics, Vol. 34, No. 5-6, 1989, pp. 1051-1061.
[14]  Fedelinski, P., Aliabadi, M., and Rooke, D., The Dual Boundary Element Method in Dynamic Fracture Mechanics, Engineering Analysis with Boundary Elements, Vol. 12, No. 3, 1993, pp. 203-210.
[15]  Phan, A.V., Gray, L. J., and Salvadori, A., Transient Analysis of the Dynamic Stress Intensity Factors Using Sgbem for Frequency-Domain Elastodynamics, Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 45-48, 2010, pp. 3039-3050.
[16]  Ebrahimi, S., Phan, A.V., Dynamic Analysis of Cracks Using the Sgbem for Elastodynamics in The Laplace-Space Frequency Domain, Engineering Analysis with Boundary Elements, Vol. 37, No. 11, 2013, pp. 1378-1391.
[17]  Malezhik, M., Malezhik, O., and Chernyshenko, I., Photoelastic Determination of Dynamic Crack-Tip Stresses in an Anisotropic Plate, International Applied Mechanics, Vol. 42, No. 5, 2006, pp. 574-581.
[18]  K. Ravi-Chandar, Dynamic Fracture, Elsevier, 2004, pp. 9-46.
[19]  Wang, L., Foundations of Stress Waves, Amsterdam, Netherland, 2011, pp. 57-87.
[20]  Dyke, P. P., An Introduction to Laplace Transforms and Fourier Series, 2nd ed, Springer, New York, 2014, pp. 129-152.
[21]  Erdelyi. A., Sneddon, I. N., Fractional Integration and Dual Integral Equations, Canadian Journal of Mathematics, Vol. 14, No. 1, 1962, pp. 685-693.
[22]  Miller, M. K., Guy, W.T., Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials, SIAM Journal on Numerical Analysis, Vol. 3, No. 4, 1966, pp. 624-635.
[23]  Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory, New York: Wiley, 1966, pp. 69-85.
[24]  Ramírez, H., Rubio-Gonzalez, C., Finite-Element Simulation of Wave Propagation and Dispersion in Hopkinson Bar Test, Materials & design, Vol. 27, No. 1, 2006, pp. 36-44.
[25]  Elkaranshawy, H. A., Bajaba, N. S., A Finite Element Simulation of Longitudinal Impact Waves in Elastic Rods, Materials with Complex Behaviour II, Vol. 16, No. 1, 2012, pp. 3-17.
[26]  Lu, Y., Li, Q., Appraisal of Pulse-Shaping Technique in Split Hopkinson Pressure Bar Tests for Brittle Materials, International Journal of Protective Structures, Vol. 1, No. 3, 2010, pp. 363-390.