Conservative Formulation of Large Deformation Plasticity

1993 ◽  
Vol 46 (12) ◽  
pp. 519-526 ◽  
Author(s):  
James G. Glimm ◽  
Bradley J. Plohr ◽  
David H. Sharp
Keyword(s):  
High Resolution ◽  
Shear Band ◽  
Large Deformation ◽  
Large Deformations ◽  
Shear Bands ◽  
Shock Capturing ◽  
Jump Discontinuity ◽  
Governing Equations ◽  
Conservative Form ◽  
Deformation Plasticity

We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.

scholarly journals An Insight into Amorphous Shear Band in Magnetorheological Solid by Atomic Force Microscope

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4384
Author(s):  
Mohd Aidy Faizal Johari ◽  
Asmawan Mohd Sarman ◽  
Saiful Amri Mazlan ◽  
Ubaidillah U ◽  
Nur Azmah Nordin ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Shear Band ◽  
Shear Bands ◽  
Test Duration ◽  
Phase Imaging ◽  
Force Microscopy ◽  
Atomic Force ◽  
The Matrix ◽  
Relaxation Stress ◽  
Band Deformation

Micro mechanism consideration is critical for gaining a thorough understanding of amorphous shear band behavior in magnetorheological (MR) solids, particularly those with viscoelastic matrices. Heretofore, the characteristics of shear bands in terms of formation, physical evolution, and response to stress distribution at the localized region have gone largely unnoticed and unexplored. Notwithstanding these limitations, atomic force microscopy (AFM) has been used to explore the nature of shear band deformation in MR materials during stress relaxation. Stress relaxation at a constant low strain of 0.01% and an oscillatory shear of defined test duration played a major role in the creation of the shear band. In this analysis, the localized area of the study defined shear bands as varying in size and dominantly deformed in the matrix with no evidence of inhibition by embedded carbonyl iron particles (CIPs). The association between the shear band and the adjacent zone was further studied using in-phase imaging of AFM tapping mode and demonstrated the presence of localized affected zone around the shear band. Taken together, the results provide important insights into the proposed shear band deformation zone (SBDZ). This study sheds a contemporary light on the contentious issue of amorphous shear band deformation behavior and makes several contributions to the current literature.

Plastic Deformation-Induced Nanocrystalline Aluminum in Al-Based Amorphous Alloys

1993 ◽  
Vol 321 ◽  
Author(s):  
H. Chen ◽  
Y. He ◽  
G. J. Shiflet ◽  
S. J. Poon
Keyword(s):  
Plastic Deformation ◽  
Amorphous Alloy ◽  
Shear Band ◽  
Thin Layer ◽  
Ball Milling ◽  
Direct Observation ◽  
Amorphous Alloys ◽  
Shear Bands ◽  
Amorphous Ribbons ◽  
Nanocrystalline Aluminum

ABSTRACTWe report the first direct observation of crystallization induced in the slipped planes of aluminum based amorphous alloys by bending the amorphous ribbons. Nanometer-sized crystalline precipitates are found exclusively within a thin layer (shear band) in the slipped planes extending across the deformed amorphous alloy ribbons. It is also found that the nanocrystalline aluminum can be produced by ball-Milling. It is likely that local atomic rearrangements within the shear bands create the nanocrystals which appear after plastic deformation.

Dynamic Failure Mechanisms in Beryllium-Bearing Bulk Metallic Glasses

1998 ◽  
Vol 554 ◽  
Author(s):  
David M. Owen ◽  
Ares J. Rosakis ◽  
William L. Johnson
Keyword(s):  
Crack Initiation ◽  
Shear Band ◽  
Metallic Glasses ◽  
Impact Loading ◽  
High Speed ◽  
Failure Mechanisms ◽  
Shear Bands ◽  
Dynamic Crack ◽  
Dynamic Failure ◽  
Asymmetric Impact

AbstractThe understanding of dynamic failure mechanisms in bulk metallic glasses is important for the application of this class of materials to a variety of engineering problems. This is true not only for design environments in which components are subject to high loading rates, but also when components are subjected to quasi-static loading conditions where observations have been made of damage propagation occurring in an unstable, highly dynamic manner. This paper presents preliminary results of a study of the phenomena of dynamic crack initiation and growth as well as the phenomenon of dynamic localization (shear band formation) in a beryllium-bearing bulk metallic glass, Zr41.25Ti13.75Ni10Cu12.75Be22.5. Pre-notched and prefatigued plate specimens were subjected to quasi-static and dynamic three-point bend loading to investigate crack initiation and propagation. Asymmetric impact loading with a gas gun was used to induce dynamic shear band growth. The mechanical fields in the vicinity of the dynamically loaded crack or notch tip were characterized using high-speed optical diagnostic techniques. The results demonstrated a dramatic increase in the crack initiation toughness with loading rate and subsequent crack tip speeds approaching 1000 m s−1. Dynamic crack tip branching was also observed under certain conditions. Shear bands formed readily under asymmetric impact loading. The shear bands traveled at speeds of approximately 1300 m s−1 and were accompanied by intense localized heating measured using high-speed full-field infrared imaging. The maximum temperatures recorded across the shear bands were in excess of 1500 K.

The analytical solution of the Riemann problem in relativistic hydrodynamics

1994 ◽  
Vol 258 ◽  
pp. 317-333 ◽  
Author(s):  
José Ma Martí ◽  
Ewald Müller
Keyword(s):  
High Resolution ◽  
Analytical Solution ◽  
Riemann Problem ◽  
Shock Capturing ◽  
Relativistic Hydrodynamics ◽  
Minkowski Space Time ◽  
Intermediate States ◽  
Relativistic Flow ◽  
Initial Discontinuity ◽  
The Impact

We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space–time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we analyse the properties of the relativistic flow across shock waves and rarefactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which gives the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube problem in which the gas is initially at rest. Finally, we discuss the impact of this result on the development of high-resolution shock-capturing numerical codes to solve the equations of relativistic hydrodynamics.

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