# Presentation: 400217

## Void Growth in Materials by Dislocation Mechanisms

**Void Growth in Materials by Dislocation Mechanisms**

**DOE NNSA Annual PI Meeting**
**San Antonio, Texas, 24 February 2005**

- ©2005 Board of Trustees of the University of Illinois

**D. C. Ahn, F. Xu, P. Sofronis**
**Center for Simulation of Advanced Rockets**
**University of Illinois at Urbana-Champaign**

**R. Minich**
**Lawrence Livermore National Laboratory**

## University of Illinois      Lawrence Livermore

**Collaboration:**** ASCI University Alliance Program Meeting in 1998**
**     ****Workshops on multiscale modeling organized by LLNL**
**The problem:**** ****void growth in materials**** **
**Illinois Rocket Center**
**solid propellants**
**continuum approach**
**Lawrence Livermore National Laboratory**
**metallic systems (e.g.  aluminum, copper****) **
**mechanism based approach by prismatic **
**    ****dislocation-loop emission**
**Objective:****  ****constitutive laws  and mechanical **
**     ****response accounting for void growth**** **
**Macroscopic dilatation and shear of voided materials**
**Fracture response**
**metallic systems under projectile impacts (spallation)**
**shear localization between ligaments (hot spot formation under dynamic impact)**
**Rate effects**
**Continuum vs atomistic: capabilities and limitations **

## Constitutive Law and Mechanical Behavior

**Three phases with different constitutive response**
**Binder: elastomeric rubber  (viscous and incompressible)**
**Fuel:     metal   (rigid)**
**Oxidizer: crystalline material (elastic in comparison to binder)**
**Dewetting**
**Fracture ****(void opening by dewetting, growth, and coalescence)**

- Two particle distributions of average sizes
- 30 microns and 200 microns

**profuse dewetting **
**at high temperatures**
**and low strain rates**

## Fracture: Multiscale Approach

-        **Crack tip **
**Fracture Process zone**

**Cohesive elements characterized by**
**a traction-separation law based on the void cell model**

## Dislocation Mechanism of Void Growth

**Dislocation Mechanism of Void Growth**

**Papkovich-Neuber representation**
**for the elasticity solution**

## Mechanics of Pile-up Formation

**Mechanics of Pile-up Formation**

## Macroscopic Volume Change: Size Effect

**Macroscopic Volume Change: Size Effect**

**Maximum Number of emitted loops**

## Conclusions

**Solid Propellants**
**Constitutive model accounting for void formation through state-of-the-art homogenization procedures**
**Study of void growth embedded in a solid propellant**
**Multiscale simulation of crack propagation for fracture toughness assessment**
**When coupled with chemical reaction theory, it can be used to investigate dynamic shear banding and hot-spot generation **
**collapse of a void**
**Metallic systems**
**Dislocation-loop emission mechanism**
**Length scale effect **
**Macroscopic constitutive model for void growth accounting for the **
**lattice resistance to dislocation motion**
**void surface energy effects**
**dynamic effects (viscous drag)**
**Multiscale simulation techniques and methodologies to address material response under extreme load and temperature conditions  (crack propagation-spallation)**
**Solid mechanics approach (MD simulations) **

## Quasi-Dynamic Loop Emission

**Quasi-Dynamic Loop Emission**

- Stress on a loop at position

- Dislocation-loop velocity

**N nonlinear first order equations**

- Loop nucleation site

-  It is assumed that the loop is nucleated at
-   10 Burger’s vector above the free surface of
-    the void when the glide shear stress is zero
-   Lattice friction is characterized by an intrinsic
-    drag coefficient (or damping ) *B*

## Dislocation-Loop Position vs Time

- Lower stress rate

**External stress does not increase rapidly. So repulsive**
** ****interaction between loops overrides the external stress**
** ****effect in pulling loops out.  So loops do not come out**
** ****easily.  Those that are out do sense the ones that are**
** ****punched out (curve jerk).**

- Higher stress rate

**External stress increases rapidly and therefore it **
**overrides the repulsive interaction between the loops.**
** ****So loops are coming out easily. Note that interaction**
** ****between loops does not facilitate loop emission.**

## Void-Volume Change vs Time

- Void growth model

## Solid Propellant Microstructure

**Particle dewetting under stress**
**polymer chain re-orientation, extension, debonding**** **

**pop-loose   or    tear-loose**

**profuse dewetting **
**at high temperatures**
**and low strain rates**

**oxidizer particles**

**Aluminum**
**particles (fuel)**

**Polymeric binder**
**(cushion material)**

- Two particle distributions of average sizes
- 30 microns and 200 microns

- Trumel et al. 2001

- Polyurethane
- Binder
- 49% KCl
- 32% Mg2SiO4

**void formation**
**or**
**localized shear**

**Coalescence and spall**

- At very large strains

## Void Cell Response  at  Constant Triaxiality T=3

- Oblate shape