Connecting shear localization with the long-range correlated polarized stress fields in granular materials

Martensite and bainite are the most complex structures being formed in steel in heat treatment including the quantitative interpretation. On frequent occasions, the application field of these steels includes the operation at high static and dynamic compression stresses. The thorough and comprehensive analysis of the materials’ structure after different types of treatment enables to use them competently for the manufacturing of the parts and structures providing them with the necessary complex of physical and mechanical properties. The factor determining the mechanical properties of the materials are the structure of solid solution, presence of nano-dimentional particles of the second phases, dislocation substructure, types and location of various boundaries and internal stress fields. For successful control of the formation of structural phase states and mechanical properties of the material it is necessary to know the quantitative laws and the cold hardening mechanisms of steels of different structural classes at active plastic deformation. By methods of transmission electron diffraction microscopy the analysis of cold hardening of 38CrNi3MoV steel with martensite and 30Cr2Ni-2MoV steel with bainite structures at active plastic compression deformation to 26 % and 36 %, respectively, was done in the research. The contributions caused by intraphase boundaries, dislocation substructure, carbide phases, atoms of alloying elements and long-range stress fields are considered. It is established that the substructural hardening (caused by the internal long-range stress fields) and solid solution strengthening (caused by carbon atoms) give largest contribution to cold hardening of 38CrNi3MoV hardened steel. For normalization of 30Cr2Ni2MoV steel hardening also takes place at the expense of the internal stress field’s action, at the penetration of carbon atoms to the ferrite crystal lattice as well as at the structural fragmentation with the deformation degree higher than 26 %. The dislocation substructure and the particles of carbide phase make comparatively small contribution to the hardening of these steels. It is shown that the cause of bainite steel softening at large (more than 15 %) degrees of deformation is connected with the activation of deformation microtwinning process.

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ON THE MECHANISM OF WORK HARDENING IN f.c.c. METALS

Canadian Journal of Physics ◽

10.1139/p67-053 ◽

1967 ◽

Vol 45 (2) ◽

pp. 631-661 ◽

Cited By ~ 67

Author(s):

Helmut Kronmüller

Keyword(s):

Flow Stress ◽

Single Crystals ◽

Long Range ◽

Work Hardening ◽

Slip Line ◽

Elastic Interaction ◽

Stress Fields ◽

Internal Stresses ◽

Transmission Microscopy ◽

Magnetic Methods

A review of the methods applied for the investigation of long-range stresses in deformed single crystals is given. The results found by magnetic methods are discussed in some detail; slip-line data and transmission microscopy are mentioned briefly. The effect of internal stresses on the flow stress is discussed and it is shown that the elastic interaction between the primary dislocations determines the flow stress almost completely. Secondary dislocations are found to be incapable of relaxing the stress fields of the primary dislocations appreciably.

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Coulomb–Mohr Granular Materials: Quasi-static Flows and the Highly Frictional Limit

Applied Mechanics Reviews ◽

10.1115/1.2987874 ◽

2008 ◽

Vol 61 (6) ◽

Cited By ~ 8

Author(s):

Grant M. Cox ◽

Ngamta Thamwattana ◽

Scott W. McCue ◽

James M. Hill

Keyword(s):

Granular Materials ◽

Soil Mechanics ◽

Yield Condition ◽

Stress Fields ◽

Flow Rule ◽

Axially Symmetric ◽

Governing Equations ◽

Frictional Materials ◽

Good Agreement ◽

Strong Agreement

One approach to modeling fully developed shear flow of frictional granular materials is to use a yield condition and a flow rule, in an analogous way to that commonly employed in the fields of metal plasticity and soil mechanics. Typically, the yield condition of choice for granular materials is the Coulomb–Mohr criterion, as this constraint is relatively simple to apply but at the same time is also known to predict stresses that are in good agreement with experimental observations. On the other hand, there is no strong agreement within the engineering and applied mechanics community as to which flow rule is most appropriate, and this subject is still very much open to debate. This paper provides a review of the governing equations used to describe the flow of granular materials subject to the Coulomb–Mohr yield condition, concentrating on the coaxial and double-shearing flow rules in both plane strain and axially symmetric geometries. Emphasis is given to highly frictional materials, which are defined as those granular materials that possess angles of internal friction whose trigonometric sine is close in value to unity. Furthermore, a discussion is provided on the practical problems of determining the stress and velocity distributions in a gravity flow hopper, as well as the stress fields beneath a standing stockpile and within a stable rat-hole.

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Explanation and Application of the Evolving Contact Traction Fields in Shallow Foundation Systems

Geotechnics ◽

10.3390/geotechnics2010004 ◽

2022 ◽

Vol 2 (1) ◽

pp. 91-113

Author(s):

Adam G. Taylor ◽

Jae H. Chung

Keyword(s):

Granular Materials ◽

Sensitivity Study ◽

Elastic Half Space ◽

Shallow Foundation ◽

Stress Fields ◽

Stress Distributions ◽

Modelling Method ◽

Semi Empirical ◽

Physical Phenomena ◽

Qualitative Discussion

The present paper provides a qualitative discussion of the evolution of contact traction fields beneath rigid shallow foundations resting on granular materials. A phenomenological similarity is recognized in the measured contact traction fields of rigid footings and at the bases of sandpiles. This observation leads to the hypothesis that the stress distributions are brought about by the same physical phenomena, namely the development of arching effects through force chains and mobilized intergranular friction. A set of semi-empirical equations are suggested for the normal and tangential components of this contact traction based on past experimental measurements and phenomenological assumptions of frictional behaviors at the foundation system scale. These equations are then applied to the prescribed boundary conditions for the analysis of the settlement, resistance, and stress fields in supporting granular materials beneath the footing. A parametric sensitivity study is performed on the proposed modelling method, highlighting solutions to the boundary-value problems in an isotropic, homogeneous elastic half-space.

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