Interference of Stress Waves (Spalling) simulated with FEM
This page has opened to public since 16 June 2006.
All Rights Reserved by Jun Shinozuka.
When an impact speed of a projectile toward a target is high (high speed or ultra high-speed), there is a possibility that the surface of the target in the opposite side of impacted surface is fractured (damaged).
This phenomenon is referred to as "Spalling". Spalling is induced by the interferences of stresses waves.
The follwing animation shows one of examples simulated. The simulation were performed by using of a FEA. The FEM is a dynamic nad thermo elastic plastic FEM (RdynFem) that I have developed. A projectile collides with a target at high speed (ultra high-speed). The material properties of both projectile and target are the same. When an impact speed is fast, a projectile is violently deformed plastically as shown below. A compressive stress wave propagates into both of projectile and target from the begining of the impact.
Let's look at the stress wave propagating in the target.
When the compressive stress wave reaches at the free surface opposite to the impacted surface, it reflects as tensile stress. The compressive stress traveling the impacted surface meets with the tensile stress reflected with the free surface. As seen in "Propagation of Elastic Stresses Waves", compressive or tensile stresses remain if the lengths of the input and output bars differ. The position that the tensile stress is generated by interferences of stresses first does not depend on the length of the output bar. The distance from the free surface to the position is equal to the length of the input bar.
Spalling (fracture) occurs when the tensile stress exceeds the tensile strength of the bar. Thus it is likely that the spalling occurs at that position (near the free surface). The stress propagates three dimensional in general cases. The situation of the contact surface changes due to the plastic deformation. Therefore, it may be difficult to detect the position where the spalling occurs and it may be difficult to detect the situation because it depends on stresses waves, if a complex shape is considered. We need a numerical simulation such as a finite element analysis.
Let's pay attention to the right hand side of the target material. Red color indicates a tensile stress, while blue color indicates a compressive stress. You can see the region that colored strong red appears in the right hand side of the target after the compressive stress reflected with the free surface first.
Left hand side shows a stress of horizontal component, while right hand side shows the mean normal stress (when the value of the mean normal stress is a negative, it is called the hydrostatic stress).
These results were simulated with FEM software "RDynFem" that has been developed by Dr.Jun Shinozuka.