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Effect of aspect ratio on geometric factor solutions for SENW fracture test specimen

Designing fracture toughness test techniques for wire-based specimens for improved life prediction and extension

H. Sahasrabuddhe, A. K. Mishra, B. N. Jaya

Introduction

Wires and rods have long been used for several bulk commercial applications including high strength steels  in suspension bridge cables (Fig 1a), tyre cords, elevator cables, nonferrous alloys in electric power transmission lines, metallic and ceramic fibre based composites used in aerospace etc. In an age where miniaturisation has progressed rapidly, several novel micron scale commercial applications have come up like wire bonding used in IC fabrication (Fig 1b), fibre optics used for telecommunication, magnetic sensors, gas sensors. Wires also find ever so increasing interest amongst several nano-scale research domains including semiconductor nanostructures, quantum wire heterostructures for electronic, photonic, sensing and energy devices (Fig 1c). Most of them tend to fail by fatigue fracture due to stresses arising from thermal, mechanical, and chemical cycles. The material properties at these length scales are very different from that at the bulk and is attributed to size effects arising from small specimen sizes or shrinking microstructural length scales. Thus, determining fracture properties of wires at the length scale of their applications is critical for a fail-safe or safe life design and prediction of structural integrity as well as life extension and enhanced sustainability.

Novelty

In this work, we are modifying fracture toughness testing techniques for wire specimen by standardising the single edge notched wire (SENW) test (Fig 2a) to make it length scale compatible. Stress intensity factor (KI) solutions for SENW specimen under tensile loading have been reported by several authors, but we found that there is a considerable variation in the solutions proposed for a straight fronted crack. This is because most authors have ignored the effect of wire aspect ratio (height to diameter - HD) on the solutions. From the standpoint of experimental ease and versatility, wires of any lengths/aspect ratios should be amenable to testing, if they have well defined solutions. This is even more important at small length scales where wire aspect ratios are hard to control. This is the first work that incorporates the influence of wire aspect ratio into the stress intensity factor solutions.

Methodology & Key results

The present study proposes KI solutions for SENW specimens in tension across different wire aspect ratios using extended finite element modelling (XFEM) (ABAQUS CAE 6.14 ®) and experimentally validates them on a brittle polymer: Poly (methyl methacrylate) (PMMA). The normalised stress intensity factor, also called as geometric factor shows an increase with HD before they saturate at HD ~ 50 (Fig 2b). This is explained from the additional bending load that SENW specimen experience at longer aspect ratios, that intensifies the KI further at the crack tip, compared to those with shorter aspect ratios. This occurs due to the asymmetric one-sided notch and the constraints of the tensile grips (Fig 2c) resulting in variation in bending contribution while the tensile contribution remains fixed.

Conclusion

Following recommendations are made for the use of SENW as a fracture toughness test specimen:

Geometric factor solutions of SENW specimen clearly depend on the exact HD of the specimen and should be incorporated in fracture toughness measurements. HD above 10 should be used to achieve pure mode I loading conditions. HD between 2-4 should be used if stable crack growth is desired, such as in R-curve measurements and fatigue crack growth studies. For more details refer to [1]. Adopting the revised solutions is critical to measure the true fracture toughness of wire specimen, which is critical in estimating and enhancing the life of components and devices made from them for a sustainable use of these materials.