The design of complex systems to resist the effects of a nuclear explosion A. Barbagelata, M. Perrone D 'Appolonia S.p.A, Via S. Nazaro 19, I - 16145 Genova, Italy Abstract The design of complex systems subject to the effects of a nuclear explosion is a critical issue, particularly due to the variety of phenomena generated by the explosion. The major effects which are to be considered in a low altitude nuclear explosion include: mechanical effects, thermal effects, nuclear radiations, and electromagnetic pulse. The discipline concerned with analysis, design and production of systems to resist the effects of a nuclear explosion is termed Nuclear Hardening. The paper provides an overview on the effects of a nuclear explosion and on the consequences that they can have on complex systems. The methodology applicable to weapon systems such as tanks, armoured vehicles and war ships, is described. 1 Introduction A nuclear explosion results in the rapid release of a tremendous amount of energy within a limited space. This sudden release of energy causes a large increase in the pressure and temperature and converts the close-in materials to extremely hot gases. These gases expand rapidly and initiate a shock wave in the surrounding medium. The destructive power of nuclear weapons, like conventional weapons, is generally due to blast and shock. Beyond this similarity, however, there are several basic differences. A nuclear explosion can be several thousand times more powerful than the largest conventional detonation. In addition, nuclear explosions release large amounts of energy in the form of initial
4 Structures Under Shock And Impact nuclear radiation, electromagnetic pulse, thermal radiation and residual nuclear radiation. In a complex system, which includes structural components, electronic equipment, cables, sensors, antennas, etc., all effects may cause damage. The nuclear threat and the level of damage acceptable for the system to be designed are usually specified by the customer. A step by step approach to the nuclear hardening analysis of a complex system includes in general a nuclear threat analysis, to verify the consistancy of the threat parameters with the project requirements, followed by a detailed analysis of the effects of each threat component. All phases of the analysis are described in the following sections. 2 Nuclear Threat Analysis Nuclear hardening specifications at system level usually include the following threats: blast, thermal radiation, initial nuclear radiation, and electromagnetic pulse. A short description of the threats and of the parameters which are used to specify them is provided in the following sections. Blast Typical blast parameters are: peak overpressure, static overpressure impulse, duration of positive phase, peak dynamic pressure, maximum wind speed, dynamic impulse pressure, duration of negative phase, delay in arrival of shock. Typical shapes of the pressure waves are shown in Figure 1. Based on the blast parameters it is possible to determine the weapon yield and the distance from the burst point based on semiempirical correlations [1]. Blast effects are of importance in protective construction whenever the structure of interest is located in, or exposed to, the atmosphere. In addition, the blast from a nuclear detonation can cause severe ground shock. An explosion which occurs in contact with, or near, the surface of the earth will cause a crater to be formed. The material thrown out of the crater is termed ejecta. Ejecta may include both discrete missiles of significant size and smaller particles which are deposited from the edge of the crater out to appreciable distances. Thermal Radiation A far greater portion of the energy from a nuclear explosion is emitted as thermal radiation than the case of a conventional explosion due to the vastly higher temperatures resulting from a nuclear detonation. Thermal radiation, if of sufficient intensity, can cause ablation of structural materials and thereby reduce the capability of such materials to accomplish their intended
Structures Under Shock And Impact 5 function. Nuclear thermal radiation can also start fires, char combustible materials and cause skin burns in the same manner as thermal radiation of equal intensity from conventional explosions. Typical parameters for specification of thermal radiation are: the total thermal energy, the maximum power, the time of maximum power. The typical trend of a thermal pulse from a nuclear explosion is shown in Figure 2. Based on the thermal pulse parameters it is possible to determine the weapon yield and the distance from the burst point [1]. Initial Nuclear Radiation The term initial nuclear radiation includes gamma rays, neutrons and X rays which are released essentially instantaneously by a nuclear detonation. Initial nuclear radiation is rarely the governing effect in considering possible damage to structures (as opposed, e.g., to airblast or ground shock), although there are certain conditions under which structural damage, as changes in the lattice structure of a solid, can result due to neutron and X ray effects [2]. Even though initial nuclear radiation effects may not be the primary structural damage mechanism, they can cause very serious damage to structure contents, such as personnel, electronic equipment, etc. For these reasons, initial radiation effects require investigation in almost every system development. Electromagnetic Pulse A nuclear explosion can cause the creation of electric and magnetic fields of very high intensity which may extend over long distances. This phenomenon, called the electromagnetic pulse (EMP), does not have any effect on protective structures, per se, but can create havoc with electrical and electronic circuits and equipment. Such disturbance may range from temporary disruption of the functioning of the equipment through damage severe enough to require replacement of the affected components. Vulnerability Matrix Before design and analysis of military systems is started, a preliminary assessment of the system performance should be made. In particular, the concept of balanced hardening should be applied throughout the project. This means that each threat component should be carefully considered and critical aspects which may affect the feasibility of the project should be identified. As an example, a military vehicle can be considered: if the blast wave is such that overturning of the vehicle is induced, the whole set of threat parameters must be reviewed due to the fact that very little can be done to avoid overturning of a vehicle. The nuclear hardening approach should therefore be integrated and the effects of all threat components should be analyzed in parallel. Having this
6 Structures Under Shock And Impact objective in mind, it can be very useful to create a Vulnerability Matrix where the critical areas of the system are preliminary identified. A very general matrix, to be specialized to particular systems, is shown in Table 1. This matrix provide a very general indication of the potential damage caused by each threat component. Once the vulnerability matrix has been defined, the design and analysis work can be done in detail. The following sections describe the analysis criteria to be adopted for each threat component. 3 Analysis of Mechanical Effects As the wave front deriving from an unconfmed explosion reaches a structure, a portion of the structure or the structure as a whole will be engulfed by the shock pressure. The loads applied to the structures which the blast wave intercepts are depending on the orientation, geometry, and size of the objects the wave encounters. Blast Loadings For above ground closed rectangular structures, the front wave encounters first the front wall (facing the point of detonation), then the sides, the roof and at last the rear wall of the structure. At the moment the incident shock front strikes the wall the pressure is immediately raised from zero to the reflected pressure value. At the same time these surfaces are subjected to drag pressure. The total load on each wall results from the algebraic sum of the overpressure and drag pressure. Common assumptions made to reduce the problem to reasonable terms include the following [3]: a) the structure is generally considered rectangular in shape, b) the incident pressure of interest is in the order of 140 Newtons per square centimeter or less, and c) the object being loaded is in the region of the Mach reflection. For a rectangular above ground structure at low pressure ranges, the variation of pressure with time on the side facing the detonation is illustrated in Figure 3. At the moment the incident shock front strikes the wall, the pressure is immediately raised from zero to the reflected pressure p,., which is a function of the incident pressure and the angle of incidence between the shock front and the structure face. The clearing time t^ required to relieve the reflected pressures is represented as:
LWcr where U is the velocity of the shock front and S is equal to the height of the structure H^ or one-half its width W,., whichever is smaller. The pressure p acting on the front wall after time t<. is the algebraic sum of the incident pressure pg and the drag pressure C^q. The drag coefficient C^ gives the relationship between the dynamic pressure and the total translational pressure in the direction of the wind produced by the dynamic pressure and varies with the Mach number (or with the Reynold's number at low incident pressures) and the relative geometry of the structure. A dynamic analysis of the system can be performed using finite element programs. A list of programs suited for such application has been presented by Barbagelata and Primavori [4]. There are special cases however where a simplified approach can be used to assess the system performance. One of these is the overturning stability of a structure, which can be verified as described in the following section. Overturning Stability of a Structure Subjected to a Shock Wave A preliminary evaluation of the overturning stability of a structure subjected to a pressure wave generated by a nuclear explosion can be performed by means of a simplified analytical approach [5]. The analytical model representing the problem is shown in Figure 4. Assuming that the structure subjected to the pressure wave can be considered as a rigid body, that the stabilizing moment can be expressed as linear function of the rotation angle a, and assuming also that the overturning moment can be expressed as: (2) M(t) = M^ (3) The rotation a of the body subjected to the blast wave can be expressed as a function of two non-dimensional parameters rjj and r^ defined as follows: Ti, = -; T,= ;, = " Pb 1 la The relationship between the non-dimensional parameters r), and % and the rotation is shown in the diagram of Figure 5. The region of the graph above the curve "Overturning Limit" (r i=t]2+l) corresponds to value of rotation which cause overturning of the structure [5].
(V Structures Under Shock And Impact 4 Analysis of Thermal Effects Thermal radiation can affect the system integrity mainly through burning of exposed materials, inducing thermal stresses in structures, and modifying mechanical properties of materials. A preliminary estimate of the surface temperature of an exposed object is given by the following expression [6]: (5) where p is the density of the material, c is the specific heat, k is the thermal conductivity, P^ is the maximum heat flux absorbed by the plate and I is the total heat energy absorbed. It can be observed that the value of AT^^ does not depend on the thickness of the object. By comparing the surface temperature with the temperature limit of the material exposed it is possible to evaluate if any degradation or burning is to be expected. If the temperature reached by the exposed surface is high, it should be evaluated the possibility of ignition of fuel tanks, oil, and explosive materials. In addition to this, the possibility of an untimely activation of the fire protection system should be considered. The temperature gradient induces stresses and deformation in the system which superimpose to those due to the blast wave. However, the time shift between the two effects should be accounted for. A rough estimate of the thermal strain on the surface may be obtained by the following expression: E = aat (6) where a is the coefficient of thermal expansion of the material. The corresponding stress in the plane of the plate, assuming elastic behavior of the material, is: o = E (7) 1- v where E is the Young modulus and v the Poisson ratio. The global effects on the structure can be evaluated assuming a uniform temperature increment in the wall. The analysis of the simultaneous effects induced by both the blast wave and the thermal pulse may be required for structures exposed to nuclear explosions in the following cases:
Structures Under Shock And Impact 9 the temperature reached by the material changes either its strength or stiffness or both, stresses induced by temperature gradients increase significantly those induced by the blast wave and may induce damage in the material. structural deformation is a concern. 5 Initial Nuclear Transient Radiation Effects Initial nuclear radiation from a nuclear event may interact with electronic equipment leading to malfunctioning or failure of electronic components [7]. Some typical consequences of radiations on electronics are: damages of computer with total loss of data; damages on regulation electronics: spurious activations with possible damages for the user; damages on communication electronics with temporary or permanent loss of functions. To realize measures for hardening electronics against nuclear radiation, it is necessary: to gain knowledge about the behavior of the electronic devices under irradiation, especially semiconductor devices, to investigate by means of computer-aided network analysis the effects of nuclear radiation on the functions of the electronics and the efficacy of protective measures, to shield by means of structural parts the electronic equipment. 6 Electromagnetic Pulse (EMP) Analysis The aim of the EMP analysis is to determine the system vulnerability, knowing that external structures can couple with electric and magnetic fields. EMP protection analysis includes: antenna coupling with external structures and assessment of the pulse conducted through feed lines between these outer and the inner structures; analysis of the point of entry (POE) of the threat; assessment of pulse radiated through the external structure shield and other internal shields containing electronics; coupling analysis of this pulse with unshielded cables connected to electronics; evaluation of shielding effects of existing structures; design of remedies; susceptibility devices analysis.
10 Structures Under Shock And Impact 7. Conclusions A brief description of the methodology applicable to the analysis and design of complex systems to resist the effects of a nuclear explosion has been provided in this paper. An important concept the analyst or designer has to consider that a nuclear explosion generates various effects such as blast wave, thermal pulse, nuclear radiation and electromagnetic pulse. These effects should be accounted for from the very beginning of the project in order to identify their possible interactions and the best solutions at system level. References 1. Air Force Weapons Laboratory (AFWL), The Air Force Manual for Design and Analysis of Hardened Structures, 1974. 2. Messenger, G. C. & Ash, M. S., The Effects of Radiation on Electronic Systems, Van Nostrand Reinhold, New York, 1992. 3. Department of the Air Force Manual, Structures to Resist the Effects of Accidental Explosions, AFM 88-22, Department of the Army, the Navy, and the Air Force, Washington, 1969. 4. Barbagelata, A. & Primavori, M., Shock and Impact on Structures, Chapter 2, Blast on Surface Structures, ed. C.A. Brebbia and V. Sanchez-Galvez, pp. 27-51, Computational Mechanics Publications, Southampton, UK and Boston, USA, 1994. 5. Barbagelata, A. e Perrone, M., A Nonlinear Finite Element Approach to the Assessment of Global Stability of a Military Vehicle Under Shock Wave Impulse, (Computational Mechanics Publications and Thomas Telford, London), pp. 497 to 507, Proceedings of the 2nd Int. Conf. on Structures Under Shock and Impact, Portsmouth, United Kingdom, 1992. 6. Barbagelata, A. and Perrone, M., Analisi degli Effetti Termomeccanici di un'esplosione su una Lastra Piana, X Congresso Nazionale a, 1990 7. Glasstone, S. and Dolan P. J., The Effects of Nuclear Weapons, United States Department of Defense and Energy Research and Development Administration, Washington, 1977.
Table 1. Effects of a nuclear explosion on system components SYSTEM COMPONENTS Exposed Structures Structures without Direct Exposure Antennas Cables Electronics Exposed Personnel Blast Overturning Buckling Permanent deformation Abrupt failure Shock and vibrations Failure of Radome Damage of supporting strucuture Shock and vibrations Eardrum rupture Lung damage Lethality Thermal Burning or charring Melting THREAT COMPONENTS Burning or charring of Radome Burning or charring Damage of components Activation of fire systems First degree burns Second degree burns Third degree burns Nuclear Radiation Damage of electronic components Perturbating voltage and current pulses Memory loss Permanent damage Disconfort and fatigue Nausea and vomiting EMP Surface currents on metallic structures High currents and voltages Damage of receivers High currents and voltages on unshielded cables Burnout Memory loss Opening of circuit breakers Electrical shock if in contact with conductors
PRESSURE NORMALIZED POWER (P/Pmox) O o 3 OQ' PRESSURE OS c O C 3 w H n BL TD 3 O P CL. CJQ D- p" O 3 (D THERMAL ENERGY EMITTED (PERCENT)
Structures Under Shock And Impact 13 (fl Figure 4: Analytical model (G and O represent respectively the centers of mass and rotation of the structure). OVERTURNING LIMIT a/a =0.5 a/a =0.1 a/a =0.05 a/a =0.01 -^ Figure 5: Charts for relative rotation