Multiscale Modeling of Pressure Vessel Failure
IntroductionWith few exceptions, pressure vessel failure is predicted by the use of simple empirical equations, and this estimate is divided by a safety factor (typically large, on the order of four for reactors used in the chemical process industries) to give a maximum operating pressure. The need for large safety factors is due to the incapability of simple empirical equations to accurately predict failure for a vessel with its own unique history of damage accumulation. A substantial improvement in prediction of pressure vessel failure could be realized through the use of ICME principles. Pressure vessels are used in a broad swath of industries too numerous to mention, but some main users include the chemical process industries, oil and natural gas industry, and nuclear power plants. Some modes of damage induction in pressure vessels include pressure/temperature cycling and chemical attack. However, these modes may be significant concurrently, as in the case of pressure vessel failure due to a runaway exothermic decomposition reaction. Elevation of temperature will cause an acceleration in the rate of chemical attack, which may cause vessel failure that is very premature in comparison to empirical failure estimates. The need for a failure simulation methodology that can capture damage accumulation is imperative for the accurate prediction of pressure vessel failure. This is particularly important in the nuclear power industry, where vessels may be in service for 60+ years and are subject to damage accumulation via neutron bombardment.
An example application of multscale modeling is the design of hydrogen storage pressure vessels. These pressure vessels must be able to withstand internal pressures of 100s of bar while also minimizing weight for use in fuel cell vehicles. Composite pressure vessels are of interest to groups tackling this problem. Camara et al. have performed simulations of composite hydrogen storage vessels that track breakage of carbon fibers. Gentilleau et al. has perfomed simulations of hydrogen storage vessels that incorporate thermal and damage effects due to matrix cracking.
Research Proposal Overview
A research project to investigate pressure vessel failure due to cycling is proposed that utilizes ICME principles. An example system would be a batch reactor subjected to repeated pressurization/de-pressurization cycles using nitrogen. The bridging described below is shown graphically in the figure to the right.
For a pressure vessel alloy of interest, the elastic moduli may be estimated using density functional theory. The elastic moduli are passed to the macroscale simulation via Bridge 6 and to the atomistics simulation via Bridge 1.
Using information passed on from electronics-scale calculations, a MEAM (Modified Embedded Atom Method) simulation can be carried out to characterize interfacial strength and structure, which are needed in order to characterize interfacial failure mechanisms. Information needed to simulate the formation of Microstructurally Small Cracks (MSCs) as well as crack propagation via the crack tip displacement coefficient is passed onto the macroscale via Bridge 7. Also passed is information on void nucleation. Dislocation mobility coefficients are passed onto a dislocation dynamics simulation via Bridge 2.
The dislocation dynamics simulation is used to pass information on dislocation density to the macroscale simulation via Bridge 8. Information on hardening rate as a function of shear rate is passed to a microscale crystal plasticity simulation.
Microscale FEA crystal plasticity simulation can then be used to identify the temperature dependence of void/crack nucleation as well as the relationship to particle size and particle volume fraction, which may be passed to the macroscale simulation via Bridge 9. Information on interactions between particles, voids, and dislocations would be passed on to a mesoscale simulation via Bridge 4.
A mesoscale FEA simulation would use information passed from lower length scales to simulate the growth of MSCs and how their growth is affected by crack length and heterogeneities encountered (particles, voids, dislocations). Crack propagation information is passed to the macroscale via Bridge 10 including crack interaction with particles, voids, dislocations, and other cracks as well as information on local plasticity in the vicinity of a crack.
A macroscale FEA simulation of the pressure vessel of interest would be used identify where the greatest amounts of damage accumulate through pressure cycling and thus identify the likely failure point(s). Information for the top and bottom heads as well as the cylindrical body would be obtained via the lower length scale simulations described above.
- ↑ Christopher, T, Sarma B. S. V. Rama, Potti P. K. Govindan, Rao B. Nageswara, and K Sankarnarayanasamy. "A Comparative Study on Failure Pressure Estimations of Unflawed Cylindrical Vessels." International Journal of Pressure Vessels and Piping. 79.1 (2002): 53-66. Print.
- ↑ Flewitt, P. E. J. "The use of multiscale materials modelling within the UK nuclear industry." Materials Science and Engineering: A 365.1 (2004): 257-266.
- ↑ Liu, P.F., J.K. Chu, S.J. Hou, P. Xu, and J.Y. Zheng. 2012. "Numerical Simulation and Optimal Design for Composite High-Pressure Hydrogen Storage Vessel: A Review". Renewable and Sustainable Energy Reviews. 16, no. 4: 1817-1827.
- ↑ Camara, S., Bunsell, Anthony R., Thionnet, Alain, and Allen, David H. Determination of Lifetime Probabilities of Carbon Fibre Composite Plates and Pressure Vessels for Hydrogen Storage. International Journal of Hydrogen Energy. n.d. <http://hal-ensmp.archives-ouvertes.fr/hal-00595889>.
- ↑ Gentilleau, B, F Touchard, and J.C Grandidier. "Numerical Study of Influence of Temperature and Matrix Cracking on Type Iv Hydrogen High Pressure Storage Vessel Behavior." Composite Structures. 111 (2014): 98-110. Print.
- ↑ 6.0 6.1 6.2 6.3 6.4 6.5 Horstemeyer, Mark F. Integrated Computational Materials Engineering (ICME) for Metals Using Multiscale Modeling to Invigorate Engineering Design with Science. Hoboken, N.J.: WILEY-TMS, 2012.