Technical Papers
Sep 9, 2015

Microplane Model for Steel and Application on Static and Dynamic Fracture

Publication: Journal of Engineering Mechanics
Volume 142, Issue 2

Abstract

The behavior of materials and structures is strongly influenced by the loading rate. Compared with quasi-static loading structures loaded by high loading rate and impact acts in a different way. First, there is a strain-rate influence on strength, stiffness, and ductility, and, second, there are inertia effects activated. Both influences are clearly shown in experiments. Although steel does not exhibit significant strain rate sensitivity, the dynamic fracture of steel is highly sensitive on loading rates. In this paper, the static and dynamic fracture of steel is numerically studied on a compact tension specimen (CTS), which is loaded under loading rates up to 100m/s. First, the proposed microplane model for steel is discussed and verified for monotonic and cyclic quasi-static loading. Subsequently, three-dimensional (3D) finite element dynamic fracture analysis is carried out. It is shown that the resistance of steel (apparent strength and toughness) increases progressively after the critical strain rate (approximately 100/s) is reached. Moreover, the crack branching phenomena and significant decrease of ductility are observed. The phenomena that are also well known from experimental evidence are attributed to the effect of structural inertia and inertia related to the high nonlinear behavior of steel at the crack tip and in the plastification zone. The numerical results indicate that maximum crack velocity of steel is much lower than the Rayleigh wave velocity, and for the investigated steel, it reaches approximately 400m/s.

Get full access to this article

View all available purchase options and get full access to this article.

References

American Society for Metals. (1974). Metals handbook, 8th Ed., E. Howard, ed., Vol. 9, Materials Park, OH.
Bažant, Z. P., et al. (2000a). “Large-strain generalization of microplane model for concrete and application.” J. Eng. Mech., 971–980.
Bažant, Z. P., Caner, F. C., Adley, M. D., and Akers, S. A. (2000b). “Fracturing rate effect and creep in microplane model for dynamics.” J. Eng. Mech., 962–970.
Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” RILEM, 93(16), 155–177.
Bažant, Z. P., and Prat, P. C. (1988). “Microplane model for brittle plastic material: I. Theory.” J. Eng. Mech., 1672–1688.
Bede, N., Ožbolt, J., Sharma, A. and Irhan, B. (2015). “Dynamic fracture of notched plain concrete beams: 3D finite element analysis.” Int. J. Impact Eng., 77(1), 176–188.
Belytschko, T., Chen, H., Xu, J., and Zi, G. (2003). “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment.” Int. J. Numer. Methods Eng., 58(12), 1873–1905.
Belytschko, T., Liu, W. K., and Moran, M. (2001). Nonlinear finite elements for continua and structures, Wiley, New York.
Bischoff, P., and Perry, S. (1991). “Compressive behaviour of concrete at high strain rates.” Mater. Struct., 24(6), 425–450.
Bleck, W., and Schael, I. (2000). “Determination of crash-relevant material parameters by dynamic tensile tests.” Steel Res., 71(5), 173–178.
Bousquet, A., Marie, S., and Bompard, P. (2011). “Cleavage crack propagation characterization in a nuclear pressure vessel steel.” Technische Mechanik, 32, 2-5, 118–129.
Boyce, B. L., Crenshaw, T. B., and Dilmore, M. F. (2007). “The strain rate sensitivity of high—Strength high—Toughness steels.”, Sandia National Laboratories, Albuquerque, NM.
Brandon, D. G. (1987). “Dynamic loading and fracture.” Materials at high strain rates, T. Z. Blazynski, ed., Elsevier, London, 187–218.
Čanžar, P., Tonković, Z., and Kodvanj, J. (2012). “Microstructure influence on fatigue behaviour of nodular cast iron.” Mater. Sci. Eng. A, 556(1), 88–99.
Cusatis, G. (2011). “Strain-rate effects on concrete behavior.” Int. J. Impact Eng., 38(4), 162–170.
Freund, L. B. (1972a). “Crack propagation in an elastic solid subjected to general loading-I, constant rate of extension.” J. Mech. Phys. Solids, 20(3), 129–140.
Freund, L. B. (1972b). “Crack propagation in an elastic solid subjected to general loading-II, non-uniform rate of extension.” J. Mech. Phys. Solids, 20(3), 141–152.
Hertzberg, R. W. (1989). Deformation and fracture mecahncis of engineering materials, 3rd Ed., Wiley, New York.
İrhan, B. (2014). “High velocity impact and fragmentation of concrete: Numerical simulation.” Ph.D. thesis, Institut of Construction Materials, Univ. of Stuttgart, Germany.
Jirásek, M., and Bažant, Z. P. (2002). Inelastic analysis of structures, Wiley, New York.
Kanazawa, T., Machida, S., Teramoto, T., and Yoshinari, H. (1981). “Study on fast fracture and crack arrest.” Exp. Mech., 21(2), 78–88.
Mohr, O. (1900). “Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materiales?” Zeitschrift des Vereins Deutscher Ingenieure, 46(1), 1524–1530, 1572–1577.
Ortiz, M., and Pandolfi, A. (1999). “Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis.” Int. J. Numer. Methods Eng., 44(9), 1267–1282.
Ožbolt, J., Bošnjak, J., and Sola, E. (2013). “Dynamic fracture of concrete compact tension specimen: Experimental and numerical study.” Int. J. Solids Struct., 50(25–26), 4270–4278.
Ožbolt, J., Li, Y., and Kožar, I. (2001). “Microplane model for concrete with relaxed kinematic constraint.” Int. J. Solids Struct., 38(16), 2683–2711.
Ožbolt, J., and Reinhardt, H. W. (2002). “Numerical study of mixed mode fracture in concrete.” Int. J. Fract., 118(2), 145–162.
Ožbolt, J., and Sharma, A. (2012). “Numerical simulation of dynamic fracture of concrete through uniaxial tension and L-specimen.” Eng. Fract. Mech., 85(1), 88–102.
Ožbolt, J., Sharma, A., İrhan, B., and Sola, E. (2014). “Tensile behavior of concrete under high loading rates.” Int. J. Impact Eng., 69(1), 55–68.
Ožbolt, J., Sharma, A., and Reinhardt, H.-W. (2011). “Dynamic fracture of concrete-compact tension specimen.” Int. J. Solids Struct., 48(10), 1534–1543.
Peroni, M., Solomos, G., Pizzinato, V., and Larcher, M. (2011). “Experimental investigation of high strain-rate behaviour of glass.” Appl. Mech. Mater., 82(1), 63–68.
Rabczuk, T., and Belytschko, T. (2004). “Cracking particles: a simplified meshfree method for arbitrary evolving cracks.” Int. J. Numer. Methods Eng., 61(13), 2316–2343.
Reinhardt, H. W. (1982). “Concrete under impact loading, tensile strength and bond.” Heron, 27(3), 5–48.
Rosakis, A. J., and Zender, A. T. (1985). “On the dynamic fracture of structural metals.” Int. J. Fract., 27(3–4), 169–186.
Song, J. H., Areias, P. M. A., and Belytschko, T. (2006). “A method for dynamic crack and shear band propagation with phantom nodes.” Int. J. Numer. Methods Eng., 67(6), 868–893.
Song, J. H., Wang, H., and Belytschko, T. (2008). “A comparative study on finite element methods for dynamic fracture.” Comput. Mech., 42(2), 239–250.
Taylor, G. I. (1938). “Plastic strain in metals.” J. Inst. Metals, 62(1), 307–324.
Tonković, Z., Sorić, J., and Skozrit, I. (2008). “On numerical modeling of cyclic elastoplastic response of shell structures.” Comput. Modell. Eng. Sci., 26(2), 75–90.
Weerheijm, J. (1992). “Concrete under impact tensile loading and lateral compression.” Dissertation, Technische Universität Delft, Delft, Netherlands.
Xu, X. P., and Needleman, A. (1994). “Numerical simulations of fast crack growth in brittle solids.” J. Mech. Phys. Solids, 42(9), 1397–1434.
Zender, A. T., and Rosakis, A. J. (1990). “Dynamic fracture initiation and propagation in 4340 steel under impact loading.” Int. J. Fract., 43(4), 271–285.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 142Issue 2February 2016

History

Received: Feb 12, 2015
Accepted: Jul 9, 2015
Published online: Sep 9, 2015
Published in print: Feb 1, 2016
Discussion open until: Feb 9, 2016

Permissions

Request permissions for this article.

Authors

Affiliations

Joško Ožbolt [email protected]
Professor, Institute of Construction Materials, Univ. of Stuttgart, 70560 Stuttgart, Germany (corresponding author). E-mail: [email protected]
Zdenko Tonković [email protected]
Professor, Institute of Applied Mechanics, Faculty of Mechanical Engineering and Naval Architecture, Univ. of Zagreb, 10000 Zagreb, Croatia. E-mail: [email protected]
Luka Lacković [email protected]
Ph.D. Student, Institute of Applied Mechanics, Faculty of Mechanical Engineering and Naval Architecture, Univ. of Zagreb, 10000 Zagreb, Croatia. E-mail: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share