Modelling of micron-scale impacts into Indium as a soft capture surface: preparing for Enceladus transit

Modelling of micron-scale impacts into Indium as a soft capture surface: preparing for Enceladus transit 

[FOR A MUCH HIGHER QUALITY PDF VERSION GO TO http://astro.kent.ac.uk/EPSC2020_37.pdf]

M. C. Price (1), J. S. New (1, 2), V. Spathis (1), R. A. Mathies (3), A. L. Butterworth (2) and P. J. Wozniakiewicz (1).
(1) School of Physical Sciences, Uni. of Kent, Canterbury, Kent, CT2 7NH, UK.

(2) Space Sciences Lab., Uni. of California, Berkeley, California, 94720, USA.

(3) Department of Chemistry, Uni. of California, Berkeley, California, 94720, USA.

E-mail: mcp21@kent.ac.uk, jamesnew@berkeley.edu

Abstract

In preparation for a potential transit through the plumes of Enceladus we report on progress made in the modelling of impacts into indium as a soft capture surface. Using a modified Cowper-Symonds strength model, we have been able to successfully reproduce the impacts of PMMA spheres which were used as ice analogue projectiles.

Introduction

Enceladus is, arguably, one of the locations in the Solar System where we might expect to find life, or an indication of complex pre-biotic molecules: it has a sub-surface ocean which is spewing molecules into space which could be captured and analysed using in situ techniques such as the Enceladus Organic Analyzer [1] on-board either a fly-by or (preferably) orbiter mission. In preparation for such a mission the authors in [2] fired micron-sized PMMA particles (as ice analogues) at speeds of 1 – 3 km s^-1 into a range of metal targets to try and identify which material would be best suited as a capture surface. The conclusion was that indium (from a selection of gold, silver, copper and aluminium) was the best capture medium as it retained the greatest unmodified percentage of the original PMMA particles.

The next step in the project is to simulate these impacts so that parameters such as peak pressure and temperatures can be modelled to determine any potential modification to the impacting organic molecules. Once successful, this model can then be used for the simulation of icy impactors.

Modelling PMMA impacts into In.

Indium is a very soft (at room temperature), fairly inert material and could easily be space-qualified for a potential capture surface. Lots of data exist on the low strain-rate strength of indium (i.e. its creep strength) but at the impact speeds likely to be encountered at Enceladus (0.1 – 2 km s^-1) and the size of the impacting particles (~6 μm), the strain-rate, , expected is ~v/d ~ 10⁸ s^-1. At such strain-rates the strength of a material can be more than an order of magnitude higher than its quasi-static strength [3, 4]. Unfortunately, no data could be found for the high strain-rate strength dependence of indium. We therefore follow the approach taken successfully in modelling similar impacts into aluminium, tantalum and copper [5, 6] and assume that the strain-rate behaviour of indium follows a similar pattern (which is probably a justifiable assumption given that indium behaves as a FCC material).

From the results in [2] (replotted in Fig. 1) the crater diameter for PMMA impacts into indium is seen to be a non-linear function of the particle size and impact velocity, thus indicating a strain-rate strength dependence.

A further interesting observation from [2] was that the capture efficiency (i.e. the amount of the projectile retained in the crater) peaked at approx. 1 km s^-1 for indium, but decreased for lower velocities. This decrease occurs as the PMMA projectiles bounced off the target’s surface, leaving a dent but very little detectable residue, and this behaviour is replicated in the modelling using the strength models described here for PMMA and indium.

A modified Cowper-Symonds strength model [5, 6, 7] was used for both PMMA and indium. The Cowper-Symonds model has a strain-rate strength dependence which scales as the power of the strain-rate, unlike similar constitutive models (i.e. Johnson-Cook) where the strain-rate strength dependence is logarithmic.

To account for melting of the target material we used a modified version of the Cowper-Symonds equation (written as a user sub-routine in AUTODYN) which also incorporates a thermal softening term, τ:

where Y_o is the quasi-static yield strength (Pa), ε is the strain, (ε^dot) , is the strain rate (s^-1), D and q are constants controlling the strain-rate dependence (determined by fits to experimental strain rate data), B is the strain hardening constant  (Pa) and n is the strain hardening exponent, τ is the thermal softening term:

where T is the physical temperature (K) and T_a is the ambient reference temperature (assumed 300 K) at which the quasi-static yield stress, Y_o, was measured. T_m is the effective melting point (K). Note, as AUTODYN does not use the latent heat of fusion in its calculation of temperature, an effective melting temperature is calculated by taking the latent heat of fusion and dividing by the specific heat capacity and adding that to the literature melting point. This corrects for the problem of materials becoming too soft from being overly thermally softened. The model values for PMMA and Indium are given in Table 1. Finally, in order to stop the yield strength becoming un-physically high at very high strain rates, the maximum yield strength is capped at 5 GPa.

Interestingly, the increase in strength of the PMMA during an impact is controlled almost entirely by strain-hardening, and only has a very weak strain-rate dependence. This is the opposite of indium, which has (at 300 K) virtually no strain hardening. However, it is speculated that at cryogenic temperatures (~150 K) this may no longer be the case, but experiments are required to confirm this. Note: equation-of-state and strength parameters for PMMA were extracted from [8, 9, 10, 11].