0
Research Papers

On the Failure Locus of Isotropic Materials in the Stress Triaxiality Space

[+] Author and Article Information
V. M. Manolopoulos

Department of Mechanics,
Faculty of Applied Sciences,
National Technical University of Athens,
5 Heroes of Polytechnion Avenue,
Athens GR 157 73, Greece

N. P. Andrianopoulos

Department of Mechanics,
Faculty of Applied Sciences,
National Technical University of Athens,
5 Heroes of Polytechnion Avenue,
Athens GR 157 73, Greece
e-mail: nandrian@central.ntua.gr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 3, 2013; final manuscript received January 12, 2015; published online February 23, 2015. Assoc. Editor: Ashraf Bastawros.

J. Eng. Mater. Technol 137(2), 021011 (Apr 01, 2015) (9 pages) Paper No: MATS-13-1160; doi: 10.1115/1.4029660 History: Received September 03, 2013; Revised January 12, 2015; Online February 23, 2015

The aim of this paper is to contribute to the prediction of the failure of materials (ductile and brittle) with a single criterion (rule) not violating the assumptions of continuum mechanics. In this work, the failure behavior of isotropic materials is connected with the ability of a material to store elastic strain energy from the very start of loading until its fracture. This elastic strain energy is known that is separated in a distortional and a dilatational part. So, when one of these quantities takes a critical value, then the material fails either by slip or by cleavage. The behavior of a material is described with regard to the secant elastic moduli depending on both unit volume expansion Θ and equivalent strain ɛeq. This dependence enlightens, in physical terms, the different reaction of materials in normal and shear stresses. T-criterion is applied for the prediction of failure in a series of experiments that took place to an aluminum alloy (Al-5083) and to PMMA (Plexiglas). A single criterion was used for two totally different materials and the predictions are quite satisfactory. This work is a step toward the direction of using one criterion in order to explain and predict failure in materials independently of the plastic strain that developed before fracture.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bai, Y.-L., and Wierzbicki, T., 2010, “Application of Extended Mohr–Coulomb Criterion to Ductile Fracture,” Int. J. Fract., 161(1), pp. 1–20. [CrossRef]
Haltom, S. S., Kyriakides, S., and Ravi-Chandar, K., 2013, “Ductile Failure Under Combined Shear and Tension,” Int. J. Solids Struct., 50(10), pp. 1507–1522. [CrossRef]
Barsoum, I., and Faleskog, J., 2007, “Rupture Mechanisms in Combined Tension and Shear-Experiments,” Int. J. Solids Struct., 44(6), pp. 1768–1786. [CrossRef]
Mohr, D., and Oswald, M., 2008, “A New Experimental Technique for Multiaxial Testing of Advanced High Strength Steels,” Exp. Mech., 48(1), pp. 65–77. [CrossRef]
Khan, A. S., and Liu, H., 2012, “A New Approach for Ductile Fracture Prediction on Al-2024-T351 Alloy,” Int. J. Plast., 35(8), pp. 1–12. [CrossRef]
Christensen, R. M., 2004, “A Two-Property Yield, Failure (Fracture) Criterion for Homogeneous, Isotropic Materials,” ASME J. Eng. Mater. Technol., 126(1), pp. 45–52. [CrossRef]
McClintock, F. A., 1968, “A Criterion for Ductile Fracture by Growth of Holes,” ASME J. Appl. Mech., 35(2), pp. 363–371. [CrossRef]
Rice, J. R., and Tracey, D. M., 1969, “On the Ductile Enlargement of Voids in Triaxial Stress Fields,” J. Mech. Phys. Solids, 17(3), pp. 201–217. [CrossRef]
Gurson, A. L., 1975, “Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Inter-Action,” Ph.D. thesis, Brown University, Providence, RI.
LeRoy, G., Embury, J., Edwards, G., and Ashby, M. F., 1981, “A Model of Ductile Fracture Based on the Nucleation and Growth of Voids,” Acta Metall., 29(8), pp. 1509–1522. [CrossRef]
Atkins, A. G., 1996, “Fracture in Forming,” J. Mater. Process. Technol., 56(1–4), pp. 609–618. [CrossRef]
Maxwell, C., 1937, “The Origins of Clerk Maxwell's Electric Ideas, as Described in Familiar Letters to W. Thomson,” Math. Proc. Cambridge Phil. Soc., 32(5), pp. 695–748. [CrossRef]
Hencky, H., 1924, “Zur Theorie Plastischer Deformationen und der Hierdurch im Material Hervorgerufenen Nachspannunge,” Z. Angew. Math. Mech., 4(4), pp. 323–334. [CrossRef]
Huber, M. T., 1904, “Die Spezifische Formanderungsarbeit als mass der Anstrengungeines Materials,” Czasopismo Tech., 22, pp. 81–92.
Li, Q. M., 2001, “Strain Energy Density Failure Criterion,” Int. J. Solids Struct., 38(38–39), pp. 6997–7013. [CrossRef]
Theocaris, P. S., and Andrianopoulos, N. P., 1982, “The Mises Elastic–Plastic Boundary as the Core Region in Fracture Criteria,” Eng. Fract. Mech., 16(3), pp. 425–432. [CrossRef]
Theocaris, P. S., and Andrianopoulos, N. P., 1982, “The T-Criterion Applied to Ductile Fracture,” Int. J. Fract., 20(4), pp. 125–130. [CrossRef]
Andrianopoulos, N. P., 1993, “Metal Forming Limit Diagrams According to the T-Criterion,” J. Mater. Process. Technol., 39(1–2), pp. 213–226. [CrossRef]
Andrianopoulos, N. P., and Boulougouris, V. C., 1994, “Failure by Fracture or Yielding in Strain Hardening Materials According to the T-Criterion,” Eng. Fract. Mech., 47(5), pp. 639–351. [CrossRef]
von Mises, R., 1913, “Die Mechanik der Festen Korper in Plastisch Deformierten Zustand,” Nachr. Gottingen Akad., Wiss. Math. Phys., 1, pp. 582–592, available at: http://neo-classical-physics.info/uploads/3/0/6/5/3065888/von_mises_-_plastic_deformation.pdf
Andrianopoulos, N. P., and Manolopoulos, V. M., 2012, “Can Coulomb Criterion be Generalized in Case of Ductile Materials? An Application to Bridgman Experiments,” Int. J. Mech. Sci., 54(1), pp. 241–248. [CrossRef]
Nadai, A., 1963, Theory of Flow and Fracture of Solids, McGraw-Hill, New York.
Cleveland, R. M., and Ghosh, A. K., 2002, “Inelastic Effects on Springback in Metals,” Int. J. Plast., 18(5–6), pp. 769–785. [CrossRef]
Kim, H., Kim, C., Barlat, F., Pavlina, E., and Lee, M. G., 2013, “Nonlinear Elastic Behaviors of Low and High Strength Steels in Unloading and Reloading,” Mater. Sci. Eng. A, 562, pp. 161–171. [CrossRef]
Manolopoulos, V. M., 2009, “Contribution to the Study of Failure Criteria on Non Linear Elastic Materials,” Ph.D. dissertation, National Technical University of Athens, Athens, Greece (in Greek).
Bridgman, P. W., 1952, Studies in Large Plastic Flow and Fracture, 1st ed., McGraw-Hill, New York.

Figures

Grahic Jump Location
Fig. 1

(a) Al-5083 alloy un-notched round bar, (b) Al-5083 alloy notched round bar with R = 3 mm, (c) PMMA un-notched round bar, and (d) PMMA notched round bar with R = 2.7 mm

Grahic Jump Location
Fig. 2

(a) Al-5083 alloy un-notched compression specimen, (b) Al-5083 alloy notched compression specimen, (c) PMMA un-notched compression specimen, and (d) PMMA notched compression specimen

Grahic Jump Location
Fig. 3

Torsion specimen for: (a) Al-5083 alloy and (b) PMMA

Grahic Jump Location
Fig. 4

Experimental curves for both materials of: (a) true σ1-ɛ1 uniaxial tension/compression tests and (b) τ-γ torsion test on un-notched specimens

Grahic Jump Location
Fig. 5

Experimental plots for both materials of: (a) σeq-ɛeq and (b) σeq-ɛeqel taken from torsion test, (c) σH-Θ, and (d) σH-Θel taken from tension test in notched specimen

Grahic Jump Location
Fig. 6

(a) FEM mesh and an example of equivalent stress (in MPa) distribution and (b) hydrostatic stress (in MPa) distribution in PMMA R2.7 specimen. Comparison of load–displacement response for tension in a notched specimen for (c) Al-5083 alloy and (d) PMMA.

Grahic Jump Location
Fig. 7

For both materials tested: (a) the secant bulk modulus as a function of volume expansion and (b) the secant shear modulus as a function of equivalent strain

Grahic Jump Location
Fig. 8

(a) Secant bulk modulus KS as a function of both Θel and ɛeqel for both materials, (b) secant shear modulus GS as a function of both Θel and ɛeqel for both materials, and (c) secant bulk modulus KS as a function of both Θel and ɛeqel for PMMA

Grahic Jump Location
Fig. 9

The closed failure surface according to the T-criterion in stress space σH-σeqfor: (a) PMMA and (b) Al-5083 alloy. Embedded in (b) is (a) for comparison reasons.

Grahic Jump Location
Fig. 10

The failure boundary for Al-5083 according to T-criterion along with: (a) load paths from the Bridgman theory and (b) the finite elements load paths

Grahic Jump Location
Fig. 11

The failure boundary for PMMA according to T-criterion along with the finite elements load paths

Grahic Jump Location
Fig. 12

The position of failure points in constitutive equations: (a) σeq-ɛeq and (b) σH-Θ for Al-5083 alloy

Grahic Jump Location
Fig. 13

Failure surfaces from Al-5083 alloy specimens loaded in: (a) tension, (b) compression, (c) torsion, (d) tension notched R6, (e) tension notched R4, and (f) tension notched R3

Grahic Jump Location
Fig. 14

The position of failure points in constitutive equations: (a) σeq-ɛeq and (b) σH-Θ for PMMA

Grahic Jump Location
Fig. 15

Failure surfaces from PMMA specimens loaded in: (a) tension, (b) tension notched for R2.7, and (c) compression, un-notched specimen

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In