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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

## Abstract

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.

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## Figures

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

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

Fig. 3

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

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

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

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.

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

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

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.

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

Fig. 11

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

Fig. 12

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

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

Fig. 14

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

Fig. 15

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

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