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Loading Rate Effects for Flaws Undergoing Mixed-Mode I/III Fracture

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Abstract

Background

The effect of loading rate on the fracture properties of materials had been the subject of interest for more than four decades. However, the effect of loading rates on Mixed-mode fracture, involving Modes I and III, is known little due to the complexity of loading conditions and the inertia effect at a high loading rate.

Objective

The main objective is to develop a framework to investigate the relationship between loading rate and fracture parameter under Mixed-mode (I/III) loading conditions using a novel laboratory setup.

Methods

Experimentally, a modified spiral Notched specimen, stereo-digital image correlation, and a torsional Hopkinson bar apparatus are employed to characterize the dynamic fracture response of materials subjected to a combined torsion and tension loading. Specimens with different gauge lengths were used to generate low, intermediate, and high loading rates associated with Mixed-mode (I/III) notch tip conditions. Numerically, finite element analyses were performed to calculate the dynamic stress intensity factor using the dynamic interaction integral approach.

Results

The fracture initiation time was seen to be related to the spiral angle. It was found that the Mixed-mode fracture initiation toughness increase with the loading rate. For Aluminum 2024-T3, the dynamic fracture initiation toughness under Mode-III is threefold smaller than the Mode-I condition.

Conclusions

The proposed approach, dynamic tension–torsion loading of a spirally notched specimen, successfully generates a range of loading rates on Mixed-mode fracture involving Modes I and III conditions. The dynamic integral method was effectively used to extract fracture parameters at different loading rates and conditions. Therefore, the proposed approach is a promising method for investigating the dynamic Mixed-mode fracture of materials involving Mode I and III conditions.

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Abbreviations

\(J\) :

J-integral (Strain energy release rate)

\({K}_{\mathrm{I}},{ K}_{\mathrm{II}}, {K}_{\mathrm{III}}\) :

Stress intensity factors of Mode-I, Mode-II and Mode-III respectively

\({K}_{\mathrm{Ic}},{ K}_{\mathrm{IIc}}, {K}_{\mathrm{IIIc}}\) :

Static fracture toughness of Mode-I, Mode-II, and Mode-III respectively

\({K}_{\mathrm{Id}},{ K}_{\mathrm{IId}}, {K}_{\mathrm{IIId}}\) :

Dynamic fracture toughness of Mode-I, Mode-II, and Mode-III respectively

\({\tau }_{\mathrm{max}}\) :

Maximum shear stress

\({\sigma }_{\mathrm{max}} , {\sigma }_{\mathrm{min}}\) :

Maximum and minimum principle stress

\(\dot{K}\) :

Fracture loading rate

\({t}_{\mathrm{f}}\) :

Fracture initiation time

\({\tau }_{1}\) :

Characteristic of the minimum oscillation of the specimen

\({\gamma }_{\mathrm{i}} , {\gamma }_{\mathrm{r}} ,{\gamma }_{\mathrm{t}}\) :

Incident, reflected, and transmitted strain waves respectively

\(U, V, W\) :

Displacement along x, y and z directions respectively

\(MOD\) :

Mouth opening displacement

\({\sigma }_{\mathrm{ij}}^{\mathrm{aux}}\) :

Auxiliary stress tensor around the crack tip

\({\varepsilon }_{\mathrm{ij}}^{\mathrm{aux}}\) :

Auxiliary strain tensor around the crack tip

\({u}^{\mathrm{aux}}\) :

Auxiliary displacement

\({\varepsilon }_{\mathrm{ij}}\) :

Strain tensor

\(\mathrm{det}J\) :

Determinant of Jacobian matrix

\({\beta }_{\mathrm{sp}}\) :

Inclined angle of notch spiral path measured from center of the specimen

\(\overline{K }\) :

Polar second moment of area of hollow bar

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Acknowledgements

The support of the University of South Carolina and Mr. Edward Walton, Chief Financial Officer, to provide significant matching funds for development of a multiaxial loading laboratory is deeply appreciated.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of South Carolina, Columbia, SC, USA

    A. Fahem, A. Kidane & M. Sutton

  2. School of Material Science and Engineering, Oklahoma State University, Tulsa, OK, USA

    A. Fahem

  3. Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq

    A. Fahem

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Correspondence to A. Fahem.

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Fahem, A., Kidane, A. & Sutton, M. Loading Rate Effects for Flaws Undergoing Mixed-Mode I/III Fracture. Exp Mech 61, 1291–1307 (2021). https://doi.org/10.1007/s11340-021-00739-0

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