PSI - Issue 28

Alexey N. Fedorenko et al. / Procedia Structural Integrity 28 (2020) 804–810 Fedorenko A., Fedulov B., Lomakin E. / Structural Integrity Procedia 00 (2019) 000–000

808

5

Crushing process is shown in Fig. 2 at four different stages with display of damage parameter (view cut is used to represent internal walls of specimen, only half of tube is shown). The first 3.3 mm of displacement corresponds to chamfer crushing. Thus, a significant load drop occurs after chamfer failure. Once crushing front attains regular cross section, the total load peak occurs, as shown in reaction force diagram in Fig. 3. Impactor stopped after crushing of 18.7mm of material. SEA is calculated using the following formula:

C l

1

0 

(8)

,

SEA

Fdx



m

C

where C m is a mass of crushed material, C l is a total crushed material distance, and F is a reaction force. Formula (8) was applied for SEA calculation after crush of first and second 5mm of regular cross section of the tube, as shown in Fig.4. For the first path of 5mm SEA equals to 124 J/g, while SEA on the basis of the next 5 mm is only 98 J/g. Average SEA along all crushing distance of 18.7 mm is 111 J/g. Therefore, SEA is highly variable value due to impactor deceleration and strain-rate dependency, while engineering practice usually accepts a simplification of constant SEA, averaged over total crushing distance.

Fig. 2. (a) damage parameter ψ 2 distribution after impactor displacement of 3.3mm; (b) damage parameter ψ 2 distribution after impactor displacement of 8.3mm; (c) damage parameter ψ 2 distribution after impactor displacement of 13.3mm; (d) damage parameter ψ 2 distribution after impactor displacement of 18.7mm. 5. Conclusion The proposed approach captures the strength and hardening dependency on different rates and types of loading, which is important for the analysis of any impact problems of composite material. The benefit of presented model is a possibility of the analysis with the minimum number of high rate experiments with possible increase of accuracy in case of the availability of additional experimental data. Proposed material model is implemented in FEA software for simulation of impact problems based on solid elements. Crashworthiness variation was observed, and it may lead to underestimation of reaction force, based on analysis using only SEA, averaged over the entire composite tube length.