Calibration of NASGRO equation for mixed-mode loading using experimental and numerical data

Keywords: Fatigue crack growth, XFEM, stress intensity factors, high yield-strength steel

Abstract

A procedure to calibrate the NASGRO equation in a high yield-strength steel under mixed-mode loading (I+II) is presented. The calibration consists in obtaining the material parameters known as C, m, p and q. The procedure is based on experimental and numerical results. The experimental tests were used to characterize the material and obtain fatigue crack growth data. For the fatigue tests, tapered double cantilever beam (TDCB) specimens with different maximum load and load ratio values were used. Through the numerical analysis, the stress intensity factors, the crack growth direction and the crack path coordinates were calculated. The numerical analysis was performed using XFEM and the maximum energy release rate criterion. The calibrated model allows predicting the number of load cycles with an RMS value of less than 5%, compared with the experimental results.

|Abstract
= 197 veces | PDF
= 108 veces|

Downloads

Download data is not yet available.

Author Biographies

David Reynaldo Berrios-Barcena, Pontificia Universidad Católica del Perú

Grupo INACOM/Aula PUCP-CIMNE, Sección Ing. Mecánica

Rosendo Franco-Rodríguez, Pontificia Universidad Católica del Perú

Grupo INACOM/Aula PUCP-CIMNE, Sección Ing. Mecánica

Francisco Aurelio Rumiche-Zapata, Pontificia Universidad Católica del Perú

Grupo INACOM/Aula PUCP-CIMNE, Sección Ing. Mecánica

References

H. A. Richard, W. Linnig, and K. Henn, “Fatigue crack propagation under combined loading,” Materials Science, 1991.

S. B. Biner, “Fatigue crack growth studies under mixed-mode loading,” International Journal of Fatigue, vol. 23, 2001. [Online]. Available: https://doi.org/10.1016/S0142-1123(01)00146-3

S. Seitl and Z. Knésl, “Two parameter fracture mechanics: Fatigue crack behavior under mixed mode conditions,” Engineering Fracture Mechanics, vol. 75, no. 3-4, February 2008. [Online]. Available: https://doi.org/10.1016/j.engfracmech.2007.04.011

M. Ševčík, P. Hutař, L. Náhlík, and S. Seitl, “The effect of constraint level on a crack path,” Engineering Failure Analysis, vol. 29, April 2013. [Online]. Available: https://doi.org/10.1016/j.engfailanal.2012. 11.011

A. L. L. Silva, A. M. P. de Jesus, J. Xavier, J. A. F. O. Correia, and A. A. Fernandes, “Combined analytical-numerical methodologies for the evaluation of mixed-mode (I + II) fatigue crack growth rates in structural steels,” Engineering Fracture Mechanics, vol. 185, November 2017. [Online]. Available: https://doi.org/10.1016/j. engfracmech.2017.04.016

Y. Li and G. F. Wang, “Influence of surface tension on mixed-mode cracks,” International Journal of Applied Mechanics, vol. 7, no. 5, 2015. [Online]. Available: https://doi.org/10.1142/S1758825115500702

K. P. Mróz and Z. Mróz, “On crack path evolution rules,” Engineering Fracture Mechanics, vol. 77, no. 11, July 2010. [Online]. Available: https://doi.org/10.1016/j.engfracmech.2010.03.038

H. A. Richard, B. Schramm, and N. H. Schirmeisen, “Cracks on mixed mode loading – theories, experiments, simulations,” International Journal of Fatigue, vol. 62, May 2014. [Online]. Available: https://doi.org/10.1016/j.ijfatigue.2013.06.019

X. Zhang and et al., “Experimental and numerical investigation of fatigue crack growth in the cracked gear tooth,” Fatigue & Fracture of Engineering Materials & Structures, vol. 40, no. 7, July 2017. [Online]. Available: https://doi.org/10.1111/ffe.12557

G. Vukelic and J. Brnic, “Numerical prediction of fracture behavior for austenitic and martensitic stainless steels,” International Journal of Applied Mechanics, vol. 9, no. 4, 2017. [Online]. Available: https://doi.org/10.1142/S1758825117500521

M. Schöllmann, M. Fulland, and H. A. Richard, “Development of a new software for adaptive crack growth simulations in 3D structures,” Engineering Fracture Mechanics, vol. 70, no. 2, January 2003. [Online]. Available: https://doi.org/10.1016/S0013-7944(02) 00028-0

H. Pathak, A. Singh, and I. V. Singh, “Fatigue crack growth simulations of 3-D problems using XFEM,” International Journal of Mechanical Sciences, vol. 76, November 2013. [Online]. Available: https://doi.org/10.1016/j.ijmecsci.2013.09.001

F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” Journal of Basic Engineering, vol. 85, no. 4, 1963. [Online]. Available: https: //doi.org/10.1115/1.3656899

G. C. Sih, “Strain-energy-density factor applied to mixed mode crack problems,” International Journal of Fracture, vol. 10, pp. 305–321, 1974.

M. A. Hussain, S. L. Pu, and J. Underwood, “Strain energy release rate for a crack under combined mode I and mode II,” in Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics Part II, West Conshohocken, PA, 1974, pp. 2–28.

J. M. Barsom, E. J. Imhof, and S. T. Rolfe, “Fatigue-crack propagation in high yield-strength steels,” Engineering Fracture Mechanics, vol. 2, no. 4, June 1971. [Online]. Available: https: //doi.org/10.1016/0013-7944(71)90016-6

S. K. Putatunda and J. M. Rigsbee, “Effect of specimen size on fatigue crack growth rate in AISI 4340 steel,” Engineering Fracture Mechanics, vol. 22, no. 2, 1985. [Online]. Available: https://doi.org/10.1016/S0013-7944(85)80034-5

P. C. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” Journal of Basic Engineering, vol. 85, no. 4, December 1963. [Online]. Available: https://doi.org/10.1115/1.3656900

R. G. Forman, V. Shivakumar, and J. C. Newman, “Fatigue-crackgrowth computer program,” NASA, Houston, TX, United States, Tech. Rep. MSC-21669, Apr. 1991.

S. Klysz, J. Lisiecki, A. Leski, and T. Bakowski, “Least squares method modification applied to the NASGRO equation,” Journal of Theoretical and Applied Mechanics, vol. 51, no. 1, pp. 3–13, Jan. 2013.

W. Zhang, Q. Wang, X. Li, and J. He, “A simple fatigue life prediction algorithm using the modified NASGRO equation,” Mathematical Problems in Engineering, vol. 2016, June 30 2016. [Online]. Available: https://doi.org/10.1155/2016/4298507

B. Moreno, A. Martin, P. Lopez, J. Zapatero, and J. Dominguez, “Estimations of fatigue life and variability under random loading in aluminum Al-2024t351 using strip yield models from NASGRO,” International Journal of Fatigue, vol. 91, October 2016. [Online]. Available: https://doi.org/10.1016/j.ijfatigue.2015.09.031

J. C. Newman, “A crack opening stress equation for fatigue crack growth,” International Journal of Fracture, vol. 24, pp. 131–135, 1984.

J. Maierhofer, R. Pippan, and H. P. Gänser, “Modified NASGRO equation for physically short cracks,” International Journal of fatigue, vol. 59, February 2014. [Online]. Available: https://doi.org/10.1016/ j.ijfatigue.2013.08.019

K. Tanaka, “Fatigue crack propagation from a crack inclined to the cyclic tensile axis,” Engineering Fracture Mechanics, vol. 6, no. 3, October 1974. [Online]. Available: https://doi.org/10.1016/ 0013-7944(74)90007-1

Y. Xiangqiao, D. Shanyi, and Z. Zehua, “Mixed-mode fatigue crack growth prediction in biaxially stretched sheets,” Engineering Fracture Mechanics, vol. 43, no. 3, October 1992. [Online]. Available: https://doi.org/10.1016/0013-7944(92)90115-U

J. Weertman, “Rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane,” International Journal of Fracture Mechanics, vol. 2, pp. 460–467, 1966.

R. W. Lardner, “A dislocation model for fatigue crack growth in metals,” Philosophical Magazine, vol. 17, no. 145, 1968. [Online]. Available: https://doi.org/10.1080/14786436808218181

D. Wang and S. Y. Du, “On the modified fracture criterion of the maximum tangential stress criterion,” J. Harbin Inst. Technol., pp. 58–64, 1976.

S. T. Rolfe and J. M. Barsom, Fracture and fatigue control in structures: applications of fracture mechanics. New Jersey, USA: Prentice-Hall, 1977.

M. R. Ayatollahi, S. M. J. Razavi, and M. Y. Yahya, “Mixed mode fatigue crack initiation and growth in a CT specimen repaired by stop hole technique,” Engineering Fracture Mechanics, vol. 145, August 2015. [Online]. Available: https://doi.org/10.1016/j.engfracmech. 2015.03.027

D. Ferreño, J. M. Alegre, and J. M. Revilla, “Simulación del efecto de la plastificación en la propagación de fisuras por fatiga en modo mixto,” in XXIII Encuentro del Grupo Español de Fractura, Albarracín, España, 2006, pp. 275–280.

Standard Test Methods and Definitions for Mechanical Testing of Steel Products, ASTM A370, 2013.

Standard Test Methods for Rockwell Hardness of Metallic Materials 1,2, ASTM E18, 2014.

Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials, ASTM E399, 2013.

Standard Guide for Preparation of Metallographic Specimens, ASTM E3, 2017.

Standard Practice for Microetching Metals and Alloys, ASTM E407, 2015.

D. R. Berrios and R. Franco, “Análisis experimental y numérico de la trayectoria de propagación de fisuras por fatiga utilizando XFEM,” Inf. Tecnol., vol. 29, no. 5, 2018. [Online]. Available: http://dx.doi.org/10.4067/S0718-07642018000500019

M. Stern, E. B. Becker, and R. S. Dunham, “A contour integral computation of mixed-mode stress intensity factors,” International Journal of Fracture, vol. 12, pp. 359–368, Jun. 1976.

J. F. Yau, S. S. Wang, and H. T. Corten, “A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity,” Journal of Applied Mechanics, vol. 47, no. 2, June 1980. [Online]. Available: https://doi.org/10.1115/1.3153665

J. P. Pereira and C. A. Duarte, “The contour integral method for loaded cracks,” Communications in Numerical Methods in Engineering, vol. 22, no. 5, May 2006. [Online]. Available: https: //doi.org/10.1002/cnm.824

M. Skorupa, T. Machniewicz, J. Schijve, and A. Skorupa, “Application of the strip-yield model from the NASGRO software to predict fatigue crack growth in aluminium alloys under constant and variable amplitude loading,” Engineering Fracture Mechanics, vol. 74, no. 3, February 2007. [Online]. Available: https://doi.org/10.1016/j. engfracmech.2006.06.014

B. Moreno, A. Martin, P. Lopez, J. Zapatero, and J. Dominguez, “On the use of NASGRO software to estimate fatigue crack growth under variable amplitude loading in aluminium alloy 2024- T351,” Procedia Engineering, vol. 101, 2015. [Online]. Available: https://doi.org/10.1016/j.proeng.2015.02.037

B. Cotterell, “Notes on the paths and stability of cracks,” International Journal of Fracture Mechanics, vol. 2, pp. 526–533, 1966.

L. P. Pook, “Five decades of crack path research,” Engineering Fracture Mechanics, vol. 77, no. 11, July 2010. [Online]. Available: https://doi.org/10.1016/j.engfracmech.2010.04.010

Published
2019-12-20