Spall Fracture of Multi-Spall Fracture of Multi-Material Plates Under Material Plates Under Explosive LoadingExplosive LoadingEngineering Project Proposal PresentationBy James Danyluk

Spall Fracture in SolidsSpall Fracture in SolidsShock 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.

Examples of Rarefaction Examples of Rarefaction WavesWavest = t1 t = t2

t = t3Distance

Pre

ssure

Incoming pressure waveInitial velocity = Vo

Free SurfaceZero initial velocity

Distance

Pre

ssure

Pressure wave reaches the free surface

Free Surface

Distance

Pre

ssure

Pressure wave is reflectedVelocity 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

Proposed ModelingProposed 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

Example ResultsExample Resultst = 0µs

t = 2µs

HMX Air

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.

Expected OutcomesExpected OutcomesMaterials 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.

Schedule/MilestonesSchedule/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