How can fibre have explosive effects

The pressure of the explosive detonation product is described by the JWL equation of state [ 11 ]. The JWL equation of state is widely used in the numerical simulation of detonation and explosion drive, and it is a form that does not contain chemical reaction to express the functional power of explosive detonation products [ 12 ], and its general expression is: where is the initial specific internal energy, is the specific volume, is the pressure, are the constants, and are coefficients related to product expansion, generally set as.

The rest of the equation of state parameters is shown in Table 3. The first term on the right side of the equation represents the high pressure section, the second term represents the medium pressure section, and the third term represents the low pressure section. The effect of the first two terms of the equation in the late expansion of the detonation product can be ignored.

To ensure the effectiveness of the separation simulation method and the rationality of the separation model, the simple explosion separation test is used to verify the simulation model. In the test, the strain gauge is laid to monitor the strain value of the plate, and the strain monitoring points are set at the same position of the simulation model, and the results are compared. The strain values obtained from test and simulation are shown in Figure 3. This is because the fluctuation of shock wave will cause errors in numerical simulation, and the numerical model can reproduce the test results within a reasonable range, which proves the rationality of the simulation model.

Figure 4 shows the pressure contour of three groups of models at different times. It can be seen that the shock wave starts to enter the plate from both sides at , causing great compression effect on the plate. Moreover, two shock waves collide at the center of the plate at. The frontal collision of two shock waves of the same intensity can be equivalent to the regular reflection of the shock wave on the solid wall, and the wave front at the center of the collision has the highest intensity; therefore, it is speculated that the initial maximum damage is located at the impact point.

At , the first shock wave collision is completed, and the two reflected waves return to the original path. At , two reflected waves reach the boundary of the plate, respectively, and the sparse wave is reflected to the center of the plate at the boundary.

In this process, the plate is subjected to the tensile action caused by the sparse wave. Comparing the pressure contour of the carbon fiber composite plate without shell constraint and with shell constraint, it can be seen that due to the existence of shell constraint, the shock wave front entering the plate is flatter, indicating that there is no obvious lateral sparse effect so that more explosion energy can be concentrated on the center of the plate.

The damage effect of three groups of models at different times is shown in Figure 5. It can be roughly seen that the damage of model 1 is the smallest, that of model 2 is the second, and that of model 3 is the largest, and this is because the hard metal shell has a certain thickness and strength, when the explosive explodes; in addition to the transmission wave, there is also a compression wave reflected to the explosion center, which limits the movement of the explosive product in the nonopening direction of the shell and inevitably makes the energy converge to the opening of the C-shaped metal shell, forming the energy accumulation effect.

Now, use the Tsai-Wu tensor strength criterion to make a theoretical judgment on whether the single layer material is damaged. Tsai-Wu tensor criterion polynomial:. In formula 4 ,. According to the Tsai-Wu tensor criterion, if the combination of the stress values of the monitoring points leads to tensor formula 4 , the plate in the monitoring point area will fracture.

The larger the numerical value is, the greater the damage effect of explosion load is in the region of this point, where is the strength parameter of the material. The stress values of three groups of simulated monitoring points are shown in Table 4. By substituting the stress values of each group of monitoring points into formula 4 , it is concluded that the F values of the first group of monitoring points 1—3 are all less than 1, and the model is not broken; the F values of monitoring points 1—3 in the second and third groups are all greater than 1, so it can be judged that the model is completely broken.

It can be preliminarily judged that the detonating cord without shell constraint cannot separate the carbon fiber composite plate, while the detonating cord under the metal shell constraint can separate the carbon fiber composite plate. It can be seen from Table 4 that the principal stress values of the third group of monitoring points are all greater than the corresponding principal stress values of the second group of monitoring points, which can indicate that the constraint effect of lead shell on explosive energy is better than that of copper shell.

The constraint effect of the two kinds of shells was compared by the incident wave energy of monitoring point 4. When the shock wave propagates from one medium to another, due to the different wave impedances of the two media, the shock wave will reflect and transmit at the interface of the two media.

At the same time, the propagation process of the shock wave also needs energy maintenance. The energy reflected back to the original medium with the reflected wave is called the reflected wave energy, and the energy entering the other medium with the transmitted wave is called the transmitted wave energy. Monitoring point 4 observes the energy value of the monitoring point area; according to the conservation of energy, the energy of incident wave is equal to the sum of the energy of reflected wave and transmitted wave; the greater the energy of the monitoring point is, the greater the energy of corresponding transmitted wave will be, and the smaller the energy of reflected wave will be, the worse the shell constraint effect will be.

The energy distribution in the vicinity of the explosion can be expressed by the energy equation in the hydrodynamic equations. From the energy equation,. It can be seen that the total energy of the explosion is composed of the sum of the kinetic energy and internal energy in the target medium and the explosive gas, which is the following formula:.

According to the energy distribution after shock wave, the total energy obtained after the medium is strongly impacted and is divided into specific internal energy and kinetic energy [ 13 ], so the sum of the specific internal energy and kinetic energy of the medium is the total energy of the transmitted wave.

The curve of specific internal energy value at monitoring point 4 is shown in Figure 6 , and the speed curve is shown in Figure 7. It can be seen from Figure 6 and Figure 6 that the total energy of the transmitted wave changes with the change of the constraint conditions. It can be seen from Figure 6 that due to the existence of metal shell, the attenuation rate of curve b and c is much less than that of curve a , and there is a second peak after the maximum peak value of curve b and c.

This is because at the nonopening of the C-shaped shell, the detonation product directly impacts the inner wall of the shell, the density of the metal shell is greater than that of the detonation product on the detonation front, and the compressibility of the solid medium is generally less than that of the detonation product; the shock wave acting on the shell not only produces a small amount of transmitted wave but also reflects the compression wave to the explosion center.

The reflected wave reflected from the shell for the first time propagates into the detonation gas, strengthening the internal pressure field, and there is a compression wave behind the sparse wave [ 14 ], which makes the energy in the shell increase again after reaching the shell.

The same is true for the secondary velocity peak value of curve b and c in Figure 7. Extract the peak values of specific internal energy and speed at monitoring point 4 of each model and make Table 5.

From Table 5 , we can get the energy of the transmitted wave: , so the energy of the reflected wave: , so the confinement ability of energy from air, copper to lead increases sequentially. The three sets of simulated explosive JWL equations of state are the same, so the initial strength of the shock wave is the same, and the deformation rate of the medium is negligible compared with the shock wave speed. Suppose the wave impedance of the grain is and the wave impedance of the metal shell is ; when the shock wave propagates from the grain to the shell, due to the different wave impedances of the media on both sides of the interface, the incident compression wave will cause the reflected wave and the transmitted wave on the interface.

F represents the reflection coefficient and T represents the transmission coefficient, which is obtained by the conservation of momentum and boundary conditions on the one-dimensional wave surface [ 15 ]:. The wave impedance of copper is greater than that of lead, and the wave impedance of detonating cord is much smaller than that of lead and copper. Combined with formula 8 , it can be seen that the transmission coefficient of lead shell is smaller than that of copper shell, so the transmission energy of lead shell is smaller than that of copper shell.

This is consistent with the conclusion drawn from Figures 5 and 6. Therefore, when the initial wave speed and intensity are the same, the reflected energy of the lead shell is the largest, followed by the copper shell, and the unconstrained reflected energy is the smallest. It can be seen from formula 6 that the left side of the energy equation is formed by adding internal energy and kinetic energy. Now, select the center section of the model and integrate the internal energy in the shell at each time point grid by grid to get the total amount of kinetic energy at each time point.

Then, add the total amount of internal energy and kinetic energy at each time point to get the curve of total energy of the metal shell changing with time, as shown in Figure 8. After the explosion shock wave reaches the metal shell for the first time, the energy in the shell rises rapidly and reaches its peak value under the action of the first transmission shock wave.

At this time, the metal shell is in a high pressure state, and in the process of pressure propagation, the shock wave propagates outward when encountering the air interface and quickly takes away a large amount of energy.

From the phenomenon, the energy decreases step by step after its peak value. In the initial stage, the metal shell is reflected back to the internal energy of the explosive gas, which strengthens the pressure of the explosive gas, and the secondary transmitted compression wave reaches the inner shell again, which greatly slows down the rate of the shell energy decline; therefore, a stepped platform appears in the curve. After the cumulative integral comparison of the two cases of copper shell and lead shell, it can be found that the energy in the copper shell is about 1.

The test plan was designed according to the simulation plan. The charge structure is to process the metal shell into a C-shape and insert the detonating cord inside. The structure of the third group is shown in Figure 9 c , the lead shell of the second group is replaced with copper shell of the same size.

The total mass of the two detonating cord used in each group of tests is 4. In order to strictly control the simultaneous initiation of the detonating cord on both sides of plates, the ends of the two detonating cord are bound and connected with a detonator. The device structure is shown in Figure After the explosion reaction, collect the test plates and observe the results for comparison.

The test results are shown in Figure It can be seen from the test phenomenon that the test effect of 1 plate without any inertial constraint is the worst, and the composite plate has the least damage and is not separated; 2 plate and 3 plate are completely separated.

The tensile strength of the plate is less than the compressive strength; meanwhile, it can be seen from Figure 12 a that the side damage effect of 1 plate is significantly layered in the direction of thickness, so the damage mode of 1 plate is mainly tensile failure caused by stress wave. It can be seen from Figures 12 b and 12 c that the fracture damage effect of 2 and 3 plates is different from the side damage of 1 plate, the fracture surface of 2 and 3 plates is relatively flat, and there is no stratification of matrix fibers in the direction of fracture thickness, and it can be judged that the 3 plate is directly broken under the one-time compression with strong explosion load, and the plate was already broken before the shock wave reached the free surface and underwent reflection stretching, so the damage mode of the 2 and 3 plates is mainly the compression damage of the shock wave.

The failure mode is shown in Figure The surface of the 1 plate has a wider groove under the explosive load of the detonating cord.

This is due to the existence of the C-shaped metal shell opening, which makes the shock wave and detonation products have a large energy flow density and concentrates in a small area, and its impulse density is greater than the critical impulse density of the target medium, and when it acts on the surface of the plate, it will cause local compression and matrix cracking.

The shock wave propagates in the form of near spherical wave inside the composite plate; after the shock wave collides with the other side at the center, the wave front pressure increases, the fiber at the center is damaged first, and the shock wave continues to propagate to the other end of the plate to produce reflection stretching, and the tensile stress causes the fiber at the surface indentation crack to pull out, resulting in a wide groove on the surface of the plate, as shown in Figure 11 a.

At the same time, the residual stress wave pulse will reflect on the free surface formed by the central damage area; if the residual stress wave amplitude is high enough, tensile fracture will occur again near the damage surface [ 16 ], so as to form multiple spallation surfaces, as shown in Figure 12 a , and several obvious spallation surfaces appear along the direction from the center of the plate to both sides.

This tensile stress strength cannot further damage the plate and cannot make it completely fracture, but can make the matrix fiber delamination. In addition, the shock wave speed is much larger than the shell deformation rate; after the secondary compression wave is reflected on the shell interface, it will also propagate into the explosive gas; however, the pressure formed inside the explosive gas is relatively small at this time, and its strength can be ignored.

The wave energy matching is actually the wave impedance matching of the media on both sides of the interface [ 17 ]. If the wave impedance ratio of the two media is larger, the reflected energy will be greater.

The wave impedance ratio of detonating cord and lead is greater than that of detonating cord and copper, and the ductility of lead is better than that of copper; under the same impact load, the time for lead to maintain integrity is also stronger than that of copper, so it can be seen that lead has stronger inertial restraint ability on explosive energy and can better gather explosion energy. This is also consistent with the simulation results. This article focuses on the explosive separation of carbon fiber composite woven plates under inertial constraint and combines numerical simulation with experiments.

Explosive separation of the carbon fiber composite woven plate with a detonating cord wrapped in a metal shell successfully separated the composite plate that could not be separated without a shell, providing a reference plan for the explosive separation of the small charge structure in a narrow and complex environment.

The following conclusions were obtained: 1 The carbon fiber composite woven plate cannot be separated without the detonating cord wrapped by the metal shell, and the reason is that the shock waves on both sides collide at the center of the plate, although the wavefront pressure is increased and the inner center is damaged first, but the impact load strength cannot separate the plate, and the shock wave is reflected and stretched by the free surface, causing many layer cracks in the thickness direction of the plate center.

The charge structure of the detonating cord wrapped by the metal shell can effectively use its inertia to restrain the explosion energy and improve the separation ability during the explosion separation of the carbon fiber composite woven plate, and the effect of the lead shell to constraint the explosion energy is better than that of the copper shell. The authors declare that there are no conflicts of interest regarding the publication of this paper. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Amr A. Received 08 Dec Revised 27 Jun Accepted 07 Jul It can be seen that the thermocouple measurements at common depths vary between the three repeated specimens.

This is rather expected since, although pre-fixed, the thermocouples might have moved during casting and so their locations might vary; also, any concrete cracking could affect the thermocouple measurements, especially for those close to the heated surface. The temperature profiles obtained experimentally were compared with numerical predictions obtained using the Vulcan Thermal analysis software, developed at the University of Sheffield [ 36 ]. Vulcan Thermal has the ability to carry out thermal analysis on concrete, adopting a two-dimensional non-linear finite element procedure to predict the temperature distributions within the cross-sections of concrete members subjected to user-specified time—temperature fire curves [ 37 ].

The thermal properties of concrete vary with temperature, and the influence of moisture initially held within concrete is included in the model. These specimens were chosen since they did not spall, and the internal thermocouple readings are considered reasonably accurate. The fire curve used was taken from the surface thermocouple measurements obtained from each of the tests. A sensitivity analysis was carried out to investigate the effect of the variation of thermal parameters such as the emissivity of the concrete surface and the surface absorption factor.

The parameters used in the thermal analysis are presented in Table 6. The other thermal properties of concrete were taken according to EC2 [ 38 ]. The thermal analysis results are compared in Fig. The results show a good match between the time—temperature curves from the explosive spalling tests and Vulcan thermal analysis, which could be used as the basis for the future development of a thermos-hygro-mechanical spalling predictive model. Time-temperature curve of specimens at different depths numerical results vs.

The paper has shown promising initial experimental results, indicating the potential of using recycled tyre fibres to replace manufactured fibres for the development of more sustainable concretes which resist fire-spalling. It was found that recycled tyre polymer fibres have the potential to prevent fire-spalling.

The addition of RTPF had little influence on either the fresh or hardened properties of concrete but increased slightly the moisture loss during drying. The recycled tyre steel fibres could also contribute to a reduction of the risk of fire-induced spalling, possibly due to their unique dimensions and geometry.

RTSF could also prevent serious damage due to fire spalling by keeping the spalled concrete attached to the heated surface, and thus retaining thermal insulation to the steel re-bars. The above conclusions are drawn based on preliminary experiments subject to the testing conditions reported in this paper. Before more general conclusions can be drawn, further research is necessary and is currently being undertaken to confirm the effectiveness of RTSF and RTPF in preventing spalling, to quantify the optimum dosage of these fibres, to understand the mechanisms of spalling, to quantify spalling resistance, and eventually to develop design guidance for the use of RTSF and RTPF for spalling prevention.

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The authors also gratefully acknowledge the contribution of Grace Waterman and Shun Hey Dawn Hou to the experimental work. Fabio P. You can also search for this author in PubMed Google Scholar. Correspondence to Fabio P. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Reprints and Permissions. Figueiredo, F. Fire Technol 55, — Download citation. Received : 21 December Accepted : 25 January Published : 19 February Issue Date : 01 September Anyone you share the following link with will be able to read this content:.

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Skip to main content. Search SpringerLink Search. Download PDF. Abstract Modern high-performance concrete, increasingly used in tunnels and other important infrastructure, is susceptible to explosive fire-induced spalling. Introduction Despite the common perception that concrete is fireproof, it is prone to fire-induced spalling: the explosive loss of surface concrete when exposed to rapidly rising temperatures. Table 1 Specimen Specifications Full size table.

Table 2 Mix Design Full size table. Figure 1. Full size image. Figure 2. Figure 3. Test setup. Figure 4. Thermocouple locations. Results and Discussion Table 3 summarises the moisture content and compressive strength of each of the test specimens, as well as their spalling test results. Figure 5. Normalised moisture content profile of concrete slices of different thickness.

Figure 6. Load against time for specimen PF7. Figure 7. Figure 8. Surface temperature measured by thermal imaging camera. Figure 9. Maximum surface temperature against time of the slab for samples using the IR camera.

Figure Thermal Analysis The temperature profiles obtained experimentally were compared with numerical predictions obtained using the Vulcan Thermal analysis software, developed at the University of Sheffield [ 36 ]. Table 6 Parameters Used in the Analysis Full size table. Conclusions The paper has shown promising initial experimental results, indicating the potential of using recycled tyre fibres to replace manufactured fibres for the development of more sustainable concretes which resist fire-spalling.

References 1. Accessed 10 Sept 2. ACI —34 Google Scholar 6. Struct Surv 24 2 — Article Google Scholar Procedia Eng — Article Google Scholar Tunn Ouvrages Souterr — Google Scholar Figueiredo View author publications. View author publications. Additional information Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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