Explosive & Blastwall Simulation using LS-Dyna

Objective: To Perform Explosion and Blastwall Simulation and Calculate the blast wall Displacement.

Abstract:

Explosive tests were performed in the air to study the dynamic mechanical response of square honeycomb core sandwich panels made from a super-austenitic stainless steel alloy. Tests were conducted at three levels of impulse load on the sandwich panels and solid plates with the same areal density. The impulse was varied by changing the charge weight of the explosive at a constant standoff distance. At the lowest intensity load, significant front face bending and progressive cell wall buckling was observed at the canter of the panel closest to the explosion source. Cell wall buckling and core densification increased as the impulse increased. An air blast simulation code was used to determine the blast loads at the front surfaces of the test panels, and these were used as inputs to finite element calculations of the dynamic response of the sandwich structure. Very good agreement was observed between the finite element model predictions of the sandwich panel front and back faces displacements and the experimental observations. The model also captured many of the phenomenological details of the core deformation behavior. The honeycomb sandwich panels suffered significantly smaller back face deflections than solid plates of identical mass even though their design was far from optimal for such an application.

Introduction:

The need to protect structures from the high-intensity dynamic loads created by explosions has stimulated renewed interest in the mechanical response of metallic structures subjected to localized, high rate loading. One promising approach utilizes sandwich panel concepts to disperse the mechanical impulse transmitted into structures, thereby reducing the pressure applied to a protected structure located behind the panel. A schematic illustration of the basic concept is shown in Fig. 1.

Consider a sandwich panel consisting of a pair of solid metal faces and cellular metalcore that is rigidly edge supported and an explosive charge is detonated above the system. Several groups have examined the dynamic response of sandwich structures to impulse loading. Detailed finite element calculations using fully meshed geometries with a square honeycomb, prismatic corrugations and pyramidal truss topologies made from materials defined by their yield strength, strain hardening rate, and strain rate sensitivity have been conducted. These studies indicate a complex dynamic structural response. For near-field air blasts, a shock wave propagates from the source of the explosion to the front face and is reflected. The pressure resulting from the shock wave decays with distance (from the explosion source) and time. When the shock is incident on a rigid surface, the shock wave front undergoes a reflection. This requires the forward-moving air molecules comprising the shock wave to be brought to rest and further compressed, inducing a reflected overpressure on the wall that is of higher magnitude than the incident overpressure. An impulse is imparted to the front face of the structure (Fig. 2a),

causing it to acquire a velocity, Fig. 2b. In the acoustic limit, the pressure pulse applied to the sample front face during this process is twice that of the free-field shock (large stand-off distances and for weak explosions). In the near field where non-linear effects are present in the shock front, the pressure reflection coefficient can rise to a value of eight (under an ideal gas assumption). Even larger pressure reflection coefficients result when real gas effects (dissociation and ionization of the air molecules) occur in the free-field shock [6,7]. Deshpande and Fleck [9] refer to this initial phase of the blast shock–structure interaction as Stage I. For an ideal blast with no delayed (reflected) shock arrivals (e.g. due to the ground), a front face of mass mf will be moving at a velocity V1 towards the back face sheet and will have acquired its full momentum (mfV1) at the end of stage I. For sandwich panel structures, this front face motion is resisted by compression of the cellular core. A region of densified core is then created at the front face and this propagates at the core plastic wave speed towards the back face (Fig. 2b). This plastic wave speed Vp is given by,

`Vp = √ (Et)/ρ`

Where Et is the tangent modulus of the material used to make the core structure and r¯ is its relative density. Vp is typically 500 m/s for stainless steel alloys subjected to plastic strains of around 10%. It is about a tenth of the elastic wave speed of the materials used to make the structure. Core crushing occurs at a characteristic pressure and this crushing resists the front plate movement and slows the front face motion (Stage II). For weak explosive shocks, it is possible to arrest the densification front within the core [10]. The pressure that is transmitted to the support structure is controlled by the dynamic crush strength of cellular material during densification [11]. This crush strength depends on the core relative density, cell topology, and properties of the material used to make the cellular structure [12]. For large, spatially localized shock loadings, the impulse transmitted to the back face sheet can be sufficient to cause an edge-supported panel to bend. During this panel bending (Stage III), Fig. 2c, further mechanical energy dissipation occurs by a combination of core-collapse and core/face sheet stretching. In a well-designed system, the restraining forces accompanying this plastic dissipation are sufficient to arrest the motion of the panel before the loads applied to the support structure exceed design objectives, or tearing of the front faceplate occurs. It is important to recognize that core crushing continues to play an important role during Stage III because highly crush resistant cores maintain a larger face sheet separation and therefore a higher panel bend resistance [13]. Efforts to implement these blast shock wave protection concepts require a detailed understanding of the dynamic structural response and core-collapse mechanisms, the development of a design science that enables preferred core topologies, core relative densities and core materials to be identified, and manufacturing approaches for the materials/topologies of interest. Recent studies indicate that a square honeycomb topology with the webs aligned perpendicular to the face sheets has the highest crush resistance [14]. The dynamic response of this core to a shock wave has been simulated using the finite element method [14]. Significant quasi-static core strength enhancements can be achieved by constructing such cores from metals with a high yield strength and tangent modulus. This causes web buckling to control the core strength and the critical strength for this buckling mode can increase by increasing the web material’s tangent modulus. During dynamic loading, additional core strengthening has been predicted to occur by inertial buckling stabilization and strain rate hardening [14]. Materials with high strength, tangent modulus, and strain hardening rate are then best suited for blast wave mitigation applications. Many austenitic and super-austenitic stainless sheets of steel have a desirable combination of these properties [15]. Recent cellular manufacturing developments now enable the fabrication of many cellular metal core structures from stainless steel. These include the fabrication of triangular and square honeycombs [16], prismatic corrugations [17], lattice truss structures with pyramidal, tetrahedral, threedimensional Kagome architectures [17,18], and lattice structures with hollow truss or wire mesh lay-ups [19]. These cellular metal cores can be attached to face sheets using transient liquid phase bonding methods to create sandwich panel structures. Here, we describe a method for making square honeycomb sandwich cores from super-austenitic stainless steels and use it to construct large sandwich panels with a core relative density of around 5–6%. The panels were then exposed to shock waves created by close proximity air blasts and the resulting deformation and structural collapse mechanisms were characterized. The panel’s distribution of mass between the top face sheet, core, and bottom face sheet was around 2:1:2, somewhat different from distributions obtained from preliminary optimization studies [5]. Thicker panel faces than the optimized mass distributed design were used to deliberately avoid face sheet tearing so that the core-collapse behavior under very high-intensity loadings could be examined. We also tested and characterized solid plates of equivalent mass per unit area subjected to identical explosive loadings. The pressure fields applied to the panels were estimated using an air blast simulation code [8], and finite element simulations were then performed using LS-DYNA/Explicit [20] to investigate the dynamic deformation sequence and the core-collapse mechanisms controlling the overall response. The nonoptimized sandwich panels tested here suffered significantly smaller back face deflections than their equivalent areal density solid counterparts.

Methodology:

The simulation for blast wall is carried out by using international journal Paper ' Mechanical response for honeycomb sandwich panel structure to high-intensity dynamic loadings ' by Kumar P. Dharmasena.

Step 1:

The blast wall is created by using Shapemesher '4N shell' and defined P1, P2, P3 & P4 for nodes degrees of freedom. Each edge set to 100 elements for better accuracy. After creating a blast wall the boundary is fixed using Entity Criterion > Boundry > SPC >create new.

Step 2: Defined Section and Material

First, I can be defined as Section. The thickness of the wall as per journal Paper is 12.7mm and our Unit system is Kg-M-S. So, it can be converted into meter that is 0.0127m.

After Defining the section. I can be defined as Material. The Material is to be in this simulation is Stainless Steel. So, I choose the Mat_Piecewisw_Linear_Plasticity card because due to explosion wall is sustained high velocity. Due to High velocity, it is required to define the strain curve.

Strain rate is the change in strain (deformation) of a material with respect to time.

The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material change with time in the neighborhood of that point. It comprises both the rate at which the material is expanding or shrinking (expansion rate), and also the rate at which it is being deformed by progressive shearing without changing its volume (shear rate). It is zero if these distances do not change, as happens when all particles in some region are moving with the same velocity (same speed and direction) and/or rotating with the same angular velocity, as if that part of the medium were a rigid body.

The strain rate is a concept of materials science and continuum mechanics, that plays an essential role in the physics of fluids and deformable solids. In an isotropic Newtonian fluid, in particular, the viscous stress is a linear function of the rate of strain, defined by two coefficients, one relating to the expansion rate (the bulk viscosity coefficient) and one relating to the shear rate (the "ordinary" viscosity coefficient). In solids, higher strain rates can often cause normally ductile materials to fail in a brittle manner.

The Strain curve is defined using 0.0002, 0.02. 1, 100, 8000 Strain rate. The data is analyzed using an excel sheet. I can import excel sheet file for defining the curve. Once the defined all the curve I can merge into one table using Table card.

After Defining Section and Material. I can apply to Part. both sections and material.

Step 3: Defining Blast Load

The selection of an explosive charge mass (m) and/or standoff distance (r) enables a test panel to be subjected to a range of blast load intensities. We chose to fix the standoff distance, r, and vary the intensity of loading by varying the explosive charge weight. Three experiments with center detonated, TNT cylindrical charges of 1, 2 and 3 kg at a standoff distance of 10 cm were conducted with the sandwich panel test samples. An identical set of explosive charges was also used for three solid plate tests whose areal density was very close to that of the sandwich panels. For each test, a cylindrical charge with a length to diameter aspect ratio close to 1 was mounted on a platform with its axis aligned with the center of the test panel. Its front was 10cm from the front face of the sandwich plate, Each test sandwich panel or plate was attached to a calculated equivalent solid plate thickness (ts) was found to be 13.1 mm, and for the baseline solid plate experiments, a 12.7mm thick solid plate was used. The square honeycomb core and face sheet were fabricated from a high-ductility stainless steel alloy with an approximate composition of 49Fe–24Ni–21Cr–6Mo (wt%). A slotted metal sheet assembly approach was used for fabrication. Fig. 5 schematically illustrates the fabrication sequence. First, a two-dimensional profile was generated with a laser on a sheet metal strip incorporating the slots needed for the interlocking strip assembly and with allowances for bending the top and bottom flanges. The flanges were then bent at 90 degrees to the core web. Finally, the core was assembled by slip fitting the laser cut and bent strips to form a square grid pattern. The core consisted of an assembly of 38, 0.76mm thick (22 gauge) strips spaced 30mm apart to form an 18 cell_18 cell square grid. A brazing method was used for bonding the faceplates to the core. One side of each faceplate was sprayed with Wall Colmonoy Nicrobraz 31 braze alloy a 19mm thick steel plate that was bolted onto two I-beam vertical channels. The I-beam channels were restrained from movement by a heavy back support structure. The 19mm thick steel support plate had a 410_410mm square hole cut out at the center to allow open space for the sandwich panel to deform. The 610_610_60mm sandwich panel was placed vertically against the flat plate, centered on the flat plate opening. A square frame consisting of four flat bars and four 51_51mm square tubes were used to hold the test panel in position. The square tubes were used as spacers between the flat bar frame and the panel support plate. In the test arrangement used, the flat bar strips providing the picture frame effect in front of the test panel were bolted to the back support plate and the bolts tightened to a 34Nm torque level. The process of test panel assembly, explosive charge placement, and detonation was repeated for each sandwich panel and solid plate. A quadrant of each panel was wire EDM cut after the explosion tests to examine the deformation mechanisms at the center of each panel.

For Defining the load, First I can be defined The Blast using Blast_Segment card then applying using Blast_Segment_Set Card.

Step 4: Defined The Control Card

Now, Once the Defined all essential things for simulation. I can Define control time and output. The termination time is set to be 0.01 mili-second and to extraction for output using BINARY_D3PLOT for 0.00005 mili-second extracting the output from the simulation. It means 0.01/0.00005 = 200 animation files can be extracted from the Simulation.

Step 5: Solving

Post-Processing:

Displacement: 'Z' Directional

I Performed using 1 kg Blast load. In Fig(b), The curve for 21.5 Kpa is showing result of 1kg load explosion. The wall Displacement is almost 40mm and my Simulation result is Showing 37mm. They both result is almost the same.

Fig(a) Displacement result for Simulation

Fig(a) Displacement result for Journal Paper

Conclusion

In this Simulation, I can Successfully Perform Explosive and Blastwall Simulation Using Journal Paper. The Result of both is also accurate as per journal paper.

References:

https://www.seas.harvard.edu/hutchinson/papers/metallichoneycombs.pdf