Most of the ductile materials fail by dynamic failure modes due to the processes involves in material manufacture, crash events, explosive loading among others. It can be attributed that significant inertia effects take effects in the process of plastic flow, thus material properties are accelerated. High loading and changes in the plastic flow introduce macroscopic and microscopic deformation mechanisms in the materials. Literature indicates that material inertia affects the failure of ductile materials subjected to high rates of loading (Molinari, Jacques, Mercier, Leblond " Benzerga, 2015). This research is aimed at investing and analyzing how strain localization and fracture of ductile materials are affected by material inertia by using selected topics such as necking, adiabatic shear banding, fragmentation and dynamic damage by micro-voiding. Therefore, this research project proposes to obtain the results by using a spall fracture method. The method was chosen because it includes a microscale inertia. According to Molinari, Mercier and Jacques, (2014) the spalling fracture applications show that microscale inertia possess first order effects on the results (Molinari, Mercier " Jacques, 2014).
Schedule
Table 1. Project timeline and schedule
Task Name
Start
End
Duration (days)
Topic selection
6/16/2018
6/21/2018
5
Statement of objectives
6/22/2018
6/23/2018
1
Literature analysis
6/22/2018
6/28/2018
6
Methodology design
6/27/2018
6/30/2018
3
Recording the results
7/1/2018
7/4/2018
3
Analysis of results
7/5/2018
7/9/2018
4
Relation to Literature
7/9/2018
7/15/2018
6
Discussion
7/16/2018
7/20/2018
4
Conclusion
7/11/2018
7/14/2018
3
Recommendation
7/15/2018
7/22/2018
7
Report Writing
7/23/2018
8/2/2018
10
Proofreading and Submission
8/2/2018
8/7/2018
5
Fig 1. Project timeline and schedule
Research Statement
The project will be completed by using spall fracture technique which is based on the approach of semi-empirical law for damage rate. The method will be completed by using the law that describes that the generation of voids are inherent from increased pressure. The method assumes that a representative volume element (RVE) is free of voids due to the fact that a high purity tantalum if fully dense in its initial state. Besides, the method works under the assumption that the number of voids (Nc) nucleated per unit initial volume of representative volume element is a function of pressure that has been applied to the RVE expressed by the following formula for nucleation law (Molinari, Jacques, Mercier, Leblond " Benzerga, 2015).
Where, w(pc) is the Weibull probability density function with Poc, ß, and n
parameters. N is the maximum number of nucleation sites for void nucleation (Nc (P). At large pressure values, P, the void nucleation parameter changes to N. In this method, voids grow by maintaining a large spherical shape. The fracture takes place by impingement of the voids. When the material reaches a critical value fc which is the microscopic porosity associated with the RVE. However, according to Nengping, Yuan, Xiangyang and Yufan (2012), for high purity tantalum, the critical porosity is defined as fc
= 0.35 from metallography. Therefore, the study of Dynamic Damage and Fracture of Ductile Materials will be modelled by spall fracture because the method can characterize internal damage generated via micro-voiding. Conclusively, the method can control the growth-rate of voids by refraining large void with respect to small voids.
References
Molinari, A., Jacques, N., Mercier, S., Leblond, J. B., " Benzerga, A. A. (2015). A micromechanical model for the dynamic behavior of porous media in the void coalescence stage. International Journal of Solids and Structures, 71, 1-18.
Molinari, A., Mercier, S., " Jacques, N. (2014). Dynamic failure of ductile materials. Procedia IUTAM, 10, 201-220.
Nengping, G., Yuan, G., Xiangyang, J., " Yufan, L. (2012). Research on dynamic fracture toughness of granite and finite element analysis. Procedia Engineering, 37, 107-112.
