Archive of Applied Mechanics

, Volume 88, Issue 6, pp 933–942 | Cite as

Experimental and numerical investigations of mixed-mode ductile fracture in high-density polyethylene

  • Mohammad Sahlabadi
  • Naser Soltani


High-density polyethylene (HDPE) is widely used in the production of fuel tanks and natural gas distribution systems, and therefore better understanding its fractural behavior under different loading conditions is essential. The present study is an extension of our previous work, in which JQ theory was applied to study elastic–plastic fracture in HDPE. In this study, we explore the mixed-mode ductile fracture in HDPE using Brazilian disk samples. Brazilian disk test is commonly used to create different modes of fracture; however, its application has been limited to the linear elastic fracture mechanics. This work has merit to characterize mixed-mode ductile fracture from the experimental data. The combined experimental finite element (CEFE) method introduced in our previous studies was employed to calculate ductile fracture parameters. To validate experimental results, the CEFE results were compared to finite element results, and the difference was less than 7%. The effects of the factors like crack angle and sample’s thickness on Q values were also investigated.


Fracture mechanics Polyethylene Digital image correlation J-Integral Q stress Brazilian disk 

List of symbols


Amplitude of the asymptotic solution


Correlation coefficient


Young’s modulus

\({{\varvec{G}}}\) and \({{\varvec{G}}}^\prime \)

Grayscale matrices of the subsets at (xy) in reference image, and at (\(x^\prime \), \(y^\prime \)) in deformed image


Path-independent integral along a curve around the crack tip


Stress intensity factor (mode-I)


Effective length


Measurement of the level of hydrostatic stress near the crack tip


Traction vector along the curve


Strain energy density per unit volume

\(\hbox {d}s\)

Incremental length along integral contours

r and \(\theta \)

Polar coordinates


Components of displacement vectors


Direction perpendicular to the crack

\(\varGamma \)

Clockwise path around the crack tip

\(\alpha \) and n

Romberg–Osgood constants

\(\delta _{ij}\)

Kronecker delta

\(\vartheta \)

Poisson’s ratio

\({\varvec{\sigma }}_{\mathbf{0 }}\)

Yield stress

\({\varvec{\sigma }}_{{{{\varvec{ij}}}}}\)

Stress tensor

(\({\varvec{\sigma }}_{{{\varvec{ij}}}}\))\(_{\mathbf{diff }}\)

Hydrostatic stress difference

(\({\varvec{\sigma }}_{{{\varvec{ij}}}}\))\(_{\mathbf{FEM }}\)

Stress field predicted by FE analysis

(\({\varvec{\sigma }}_{{{\varvec{ij}}}}\))\(_{{{\varvec{T = 0}}}}\)

Stress field calculated considering small-scale yielding (SSY) condition

\({\varvec{\sigma }}_{\mathbf{v }}\)

The equivalent von Mises stress


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, College of EngineeringTemple UniversityPhiladelphiaUSA
  2. 2.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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