1. Spall Fracture of Multi-Material Plates Under Explosive Loading Engineering Project Proposal Presentation By James Danyluk

2. Spall Fracture in Solids Shock waves traveling through a solid material is reflected at changes in material or free surfaces. These reflected shock waves are known as rarefaction waves or relief waves. When a free surface and rarefaction wave interact, a tensile stress can be generated in the solid material. ◦ This can also happen with two rarefaction waves interact. If this tensile stress exceeds the dynamic tensile strength, or spall strength, the material can fracture. This type of fracture is often seen in warhead applications, separation system and other energetic assemblies.

3. Examples of Rarefaction Waves t = t1t = t2 t = t3 Distance Pressure Incoming pressure wave Initial velocity = Vo Free Surface Zero initial velocity Distance Pressure Pressure wave reaches the free surface Free Surface Distance Pressure Pressure wave is reflected Velocity is reversed, V=-Vo After interaction from the pressure wave, the free surface now moves at Velocity V=Vo Tensile stress generated due to opposite moving waves

4. Proposed Modeling ANSYS AUTODYN, an explicit dynamics code, will be used to model the system. The Euler Multi-material solver will be used. The model will be setup as with an Explosive, Solid Material and Air layers. The analysis will model different materials and material combinations ◦ The tensile wave generated in the solid material(s) will be examined in each model. Solid Material SetupProposed Model HE (HMX)Air Selected Solid Materials Detonation front Single Layer Two Layers Three Layers

5. Example Results t = 0µs t = 2µs HMXAir Aluminum 6061-T6 Pressure Wave is generated by the explosive t = 5.4µs Pressure Wave has traveled through the solid, generating a rarefaction wave Rarefaction wave generates a tensile stress in the material. t = 9µs Tensile stress exceeds the spall strength, fracturing the material.

6. Expected Outcomes Materials under explosively induced loading may experience spallation due to the rarefaction waves. Stacking significantly different materials can either prevent spalling or accidentally cause it. The study will show how different materials being stacked can to induce or prevent spalling.

7. Schedule/Milestones 9/21/10:Submit Proposal 9/28/10:Complete Hand Calculations/Finish Research 10/5/10:Complete 1-D Elastic Hydrocode Model Results 10/12/10: Complete 1-D Elastic/Plastic Hydrocode Model Results 10/19/10:Submit First Progress Report 10/26/10:Complete 1-D Elastic/Plastic/Failure Hydrocode Model Results 11/9/10:Submit Second Progress Report 11/18/10:Complete 2-D Elastic/Plastic/Failure Hydrocode Model Results 11/30/10:Submit Final Draft 12/14/10:Submit Final Report