PSI - Issue 41

it thickness of the plate under plane strai

Andrea Spagnoli et al. / Procedia Structural Integrity 41 (2022) 656–663 Spagnoli t al. / Structur l Integrity Procedia 00 (2022) 000–000

662

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2 5 6 7 8 9 Norm. penetration force, F p /  R 2 [-] 3 4

0.0001 0.001 0.01 0.1 1 10 Normalised fracture energy , G c /  R [-] 1

Fig. 4. Theoretical value of dimensionless penetration force as a function of the relative fracture energy of the target material.

0.6 The present work might o ff er a first insight on the mechanics of puncturing in soft materials, thanks to its simplified assumptions. However, further work is needed to address relevant aspects, such as: (i) hyperelastic models to describe the finite strain deformation of soft materials; (ii) failure and fracture conditions in soft materials; (iii) development of di ff erent mechanisms (e.g. hole expansion) during penetration of sharp tipped needles in soft materials. 0.8 This paper shows the validity of a recently proposed model, based on LEFM concepts, to describe the penetration mechanism of a rigid circular needle into a soft target material. The needle is assumed to have a sharp tip so that penetration is governed by the development of a planar Mode I crack exposed to the contact pressure at the needle material interface. The theoretical model is verified by running non-linear FE models where the unilateral contact between the needle and the target material is described. A simple closed-form expression is then obtained for the dimensionless penetration force as a function of the relative fracture toughness of the material. c) The values of a 1 / a c and R / a c can be obtained from the theoretical results illustrated in Figure 2, for a given value of fracture toughness K c = 2 √ G c µ = K R √ G c / √ µπ R . Note that, according to the present model, the Mode I penetration mechanism can occur only if G c / ( µ R ) ≤ π , but if a crack failure criterion di ff erent from that of LEFM is used, higher values of the normalised fracture energy might be allowed. For a given material and needle geometry, one calculates G c /µ R and hence K c / K R ( K c / K R = G c /µ R √ 1 /π ). Then, from the curves of Figure 2 the critical ratios R / a a and a 1 / a c can be determined. Finally, the dimensionless penetration force F p /µ R 2 is given by Eq. 11. 5. Conclusion and future work

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0.2 1 Normalised contact area, a 1 / a [-] 0.4

b)

6. Acknowledgments

The authors would like to thank the support from European Union’s Horizon 2020 Research and Innovation Pro gramme (H2020-WIDESPREAD-2018, SIRAMM) under Grant Agreement No. 857124.

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