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Materials for Outer Shell of 1.170 Gwh (1.00669 Kilo Ton TNT) Fusion Device - Weight Basis

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16 January 2023

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17 January 2023

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Abstract
With recent developments in fusion engineering, interest has sparked in development of fusion devices for deterrent. Enormous amount of energy generated by combining two light nuclei could be contained and manipulated at will to trigger and accelerate micro explosions (from shock wave, x-rays or ion beam focusing) which finally result in full scale blast. Materials required to make such device are critical. They must possess high strength, high hardness, ductility, formability, drawability, and anisotropic properties. High entropy alloys (HEA) are new class of materials which nicely fulfils this requirement. Essentially, they are solid solutions of multi principal elements (usually > 5) eliminating the need of base metal as in conventional alloys. This gives them many unique properties which may be tailored at will (heat treatment, cold rolling, precipitation, irradiation). They also exhibit excellent directional properties with formation of distinct bands along certain preferred crystallographic planes even in hexagonal close packed structures. These anisotropic properties are strong function of rolling, working, or forging (swaging) direction and can be utilized to benefit. This study encompasses making outer shell of a typical fusion device selected on the basis of the weight, which is a function of area of pay load bay of carrier aircraft.
Keywords: 
Subject: Chemistry and Materials Science  -   Metals, Alloys and Metallurgy

1. Introduction

Fusion is promising to be an important source of limitless energy for future. It is fuel efficient, quick, and voluminous process with ability to be scaled up and controlled to yield high amount and throughput of energy. In its native form, it may be harnessed to build reactors (contained devices) or untamed form to build devices [1,2,3] which is an area of interest here. Historically, these devices have been made in many ways such as famous cylindrical configuration (Teller – Ulam design (Figure 1)) [4], modified Teller Ulam design (Ivy Mike (Figure 2 and Figure 3)) [4], oval, cone and dual cone configuration [5,6,7] all on the basis of principle to contain plasma [8] or x-ray shock wave produced, focus them (e.g., by curved walls [9] or implosion of disk [10]) for [11] ignition of micro explosions [10,12]. These micro explosions are used as a means for large explosion.
Devices may be designed and build on many principles some of them include (a) energy basis, (b) yield basis and (c) weight basis. The latter is considered here. This is chosen on the basis of aircraft (High altitude plane B 52). Pay load bay area of plane serves as start point to determine the dimensions of shell of device. This is described briefly here (assuming it is rectangular section). Using standard arithmetic
Volume of rectangle = length x width x height
As no direct measurements are available, indirect measurements are made. It is known that payload bay area can accommodate 51 Mk 82 bombs each 500 llbs, totaling 25,500 lbs – weight carrying capacity of typical B52G stratosphere. This is used as benchmark. Dimensions of typical Mk 82 are (Figure 4)
From this dimension of payload bay area are calculated which can contain our device.
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Figure 5. Typical payload dimensions of B52G [3 x 1 Layer (One layer = 20 devices)]. Putting in equation 1.
Figure 5. Typical payload dimensions of B52G [3 x 1 Layer (One layer = 20 devices)]. Putting in equation 1.
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Volume of rectangle = 5920 mm x 948 mm x 819 mm
Further design is carried out using these dimensions and weight.

2. Design and Materials

From above calculations it is inferred that roughly a rolled piece of 24 m x 1 m is required which may be cut into further dimensions. Thickness of plate is determined from energy release and energy release rate which is determined by heat transfer pattern upon explosion and any effects of implosion (Section 3). This is manufactured from HEA in cold rolled and annealed condition with pronounced texture and elongated grains along rolling direction. Furter, a definite orientation relationship is ascertained and maintained along the rolling direction. HEAs selected for this are chosen from a wide variety of HEAs available. This is briefly described here. Typically, material for device must possess high strength, high hardness, ductility, formability, drawability, and anisotropic properties. High entropy alloys (HEA) are new class of materials [13,14,15,16,17,18] which nicely fulfils this requirement. Essentially, they are solid solutions of multi principal [17] elements (usually > 5) in equiatomic percentages [19,20] eliminating the need of base metal as in conventional alloys. This gives them many unique properties which may be tailored at will (heat treatment, cold rolling [21,22,23,24,25,26], precipitation [27,28,29,30,31], irradiation [32]). They also exhibit excellent directional properties [33] with formation of distinct twins [34,35,36], faults [37], dislocation evolution sites, texture [22,23,25,26,33,38,39,40,41,42,43,44,45] and bands along certain preferred crystallographic planes even in hexagonal close packed structures [34,35,36,46]. These anisotropic properties are strong function of rolling [21,22,23,24,25,26], working, or forging (swaging) [47] direction and annealing temperature and can be utilized to benefit. This study encompasses making outer shell of a typical fusion device selected on the basis of the weight, which is a function of area of pay load bay of carrier aircraft. As a combination of excellent strength, hardness and low to moderate ductility is required, two phase Al0.5CoCrFeNi [21] is chosen as model alloy. It has two phases namely BCC and FCC which gives it’s a unique place in alloys category. It has excellent mechanical properties especially cold workability. It can be successfully cold reduced to 80$ reduction without any failure. This is one of main reasons to employ it as material of outer shell of device. At this reduction, it is reported to have maintained 480 Hv hardness, 1396 MPa yield strength and 1461 MPa tensile strength indicating cold working substantially increase its properties. These superior properties are attributed to strong dislocation interaction due to dislocation pile up and accumulation and deformation twinning and lattice distortion. A strong texture is generated by cold rolling along {110}<112>and {111}<110>. This can be effectively removed through fully recrystallization in which case weak <110>//ND and <111>// RD texture is detected. Poles figures describing evolution of this texture are described below
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Figure 6. Pole figure of Al0.5CoCrFeNi annealed at (a) 900oC and (b) 1200oC [21].
Figure 6. Pole figure of Al0.5CoCrFeNi annealed at (a) 900oC and (b) 1200oC [21].
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Figure 7. (a) Engineering stress Vs Engineering strain plots and (b) Engineering stress and UTS varying with annealing temperature [21].
Figure 7. (a) Engineering stress Vs Engineering strain plots and (b) Engineering stress and UTS varying with annealing temperature [21].
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Figure 7, part a describes relationship of engineering stress with engineering strain for named alloy and part b of figure describes its variation with annealing temperatures. It can be easily seen that Engineering stress decreases while UTS increases with rise of annealing temperature indicating activation of softening (dislocation assimilation) and strengthening (dislocation pile up and twining [34,35,41,48,49,50,51]) mechanisms.

3. Heat Transfer Analysis

Heat transfer analysis is performed to determine effective thickness which will not undergo gross rupture upon exposure to intense amount of heat radiation. Instead, its rupture is determined by initiation of crack of certain length which will exceed critical length, grow and then propagation along certain preferred crystallographic planes only (pre-determined from texture studies and calculations and orientation relationships). Rupture along these planes will help determine and optimize device parameters (set earlier) for effective explosion, blast, and yield. This is described elsewhere.

4. Conclusion

High entropy alloys with ability to exhibit and manifest anisotropy and directional properties along a certain crystallographic plane parallel to rolling direction are chosen as material (Al0.5CoCrFeNi) of choice. They can be reduced to less than 80% without failure. They are proposed to exhibit texture as measured by pole and inverse pole figures and orientation relationships. They are formed by combination of rolling (cold) and annealing heat treatment. Dislocation pileup and twinning mechanisms are attributed to increased strength in these during cold working while dislocation assimilation are attributed to softening during annealing.

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Figure 1. Teller–Ulam design.
Figure 1. Teller–Ulam design.
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Figure 2. (a) Modified Teller – Ulam design (Mike Ivy) (Two stage device ignition, micro explosion, detonation, and explosion mechanisms explained schematic). (b) Modified Teller – Ulam design (Mike Ivy) (Two stage device parts explained schematic).
Figure 2. (a) Modified Teller – Ulam design (Mike Ivy) (Two stage device ignition, micro explosion, detonation, and explosion mechanisms explained schematic). (b) Modified Teller – Ulam design (Mike Ivy) (Two stage device parts explained schematic).
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Figure 3. Modified Teller – Ulam design (Mike Ivy) [4].
Figure 3. Modified Teller – Ulam design (Mike Ivy) [4].
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Figure 4. Typical Mk 82.
Figure 4. Typical Mk 82.
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