Computational Aspects of Elasto-Plastic Deformation in Polycrystalline Solids

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Ronaldo I. Borja ◽  
Helia Rahmani
Keyword(s):  
Constitutive Equation ◽  
Slip System ◽  
Single Crystals ◽  
Plastic Behavior ◽  
Slip Systems ◽  
Exact Integration ◽  
Computational Aspects ◽  
System Activation ◽  
Crystallographic Planes ◽  
Return Algorithm

The overall elasto-plastic behavior of single crystals is governed by individual slips on crystallographic planes, which occur when the resolved shear stress on a critical slip system reaches a certain maximum value. The challenge lies in identifying the activated slip systems for a given load increment since the process involves selection from a pool of linearly dependent slip systems. In this paper, we use an “ultimate algorithm” for the numerical integration of the elasto-plastic constitutive equation for single crystals. The term ultimate indicates exact integration of the elasto-plastic constitutive equation and explicit tracking of the sequence of slip system activation. We implement the algorithm into a finite element code and report the performance for polycrystals subjected to complicated loading paths including non-proportional and reverse/cyclic loading at different crystal orientations. It is shown that the ultimate algorithm is comparable to the widely used radial return algorithm for J2 plasticity in terms of global numerical stability.

Plastic Behavior and Deformation Structure of Silicide Single Crystals with Transition Metals at High Temperatures

1993 ◽  
Vol 322 ◽  
Author(s):  
Y. Umakoshi ◽  
T. Nakashima ◽  
T. Nakano ◽  
E. Yanagisawa
Keyword(s):  
Brittle Fracture ◽  
Slip System ◽  
Single Crystals ◽  
Low Temperatures ◽  
Plastic Behavior ◽  
Deformation Structure ◽  
Secondary Slip ◽  
Ambient Temperatures ◽  
Brittle Transition ◽  
Increasing Temperature

AbstractThe mechanical and plastic behaviors of refractory silicide single crystals with Cllb (MoSi2), C40 (CrSi2, TaSi2 and NbSi2), D88 (Ti5Si3) and Cl (CoSi2 and (Co0.9Ni0.1)Si2) structures were investigated. The C40–type silicides were deformed by (0001)<1120> slip. Their yield stress decreased sharply with increasing temperature but NbSi2 and TaSi2 which were deformable even at low temperatures, exhibited anomalous strengthening around 1350°C. Deformation of Ti5Si3 whose ductile-brittle transition occurred around 1300°C was controlled by twins and the brittle fracture occurred on the basal plane. In CoSi2 the {001}<100> slip was only activated at ambient temperatures but addition of Ni activated {110}<110> slip as secondary slip system and improved the ductility. The creep behavior of MoSi2 and CrSi2 single crystals were also investigated and was found to be controlled by the viscous and glide motion of dislocations.

The slip modes of titanium and the effect of purity on their occurrence during tensile deformation of single crystals

1954 ◽  
Vol 226 (1165) ◽  
pp. 216-226 ◽  
Keyword(s):  
Shear Stress ◽  
Slip System ◽  
Single Crystals ◽  
Tensile Deformation ◽  
Interstitial Impurity ◽  
Slip Systems ◽  
Slip Planes ◽  
Critical Resolved Shear Stress ◽  
Interstitial Elements

Single-crystal test specimens of van Arkel titanium were obtained by a modification of the strain anneal technique.The modes of slip have been identified as (101̄0) [112̄0],(101̄1) [112̄0], and (0001) [112̄0]. It has been shown that not only does the interstitial impurity affect the magnitude of the critical resolved shear stress but also the relative values for the three slip systems. (101̄0) is the principal slip system and is favoured by increasing purity. A possible mechanism for the role of oxygen and nitrogen in this effect is put forward wherein it is shown that the interstitial sites occupied are such that interstitial elements render slip more difficult on two of the three slip planes in titanium.

Zone-axis ALCHEMI for the rapid assessment of site occupancies in garnets

1986 ◽  
Vol 44 ◽  
pp. 706-707
Author(s):  
M.T. Otten ◽  
P.R. Buseck
Keyword(s):  
Single Crystals ◽  
Rapid Assessment ◽  
Site Occupancy ◽  
Zone Axis ◽  
Synthetic Compounds ◽  
X Ray ◽  
Large Group ◽  
Crystallographic Planes

ALCHEMI (Atom Location by CHannelling-Enhanced Microanalysis) is a TEM technique for determining site occupancies in single crystals. The method uses the channelling of incident electrons along specific crystallographic planes. This channelling results in enhanced x-ray emission from the atoms on those planes, thereby providing the required site-occupancy information. ALCHEMI has been applied with success to spinel, olivine and feldspar. For the garnets, which form a large group of important minerals and synthetic compounds, the channelling effect is weaker, and significant results are more difficult to obtain. It was found, however, that the channelling effect is pronounced for low-index zone-axis orientations, yielding a method for assessing site occupancies that is rapid and easy to perform.

scholarly journals Room-temperature deformation of single crystals of ZrB2 and TiB2 with the hexagonal AlB2 structure investigated by micropillar compression

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhenghao Chen ◽  
Bhaskar Paul ◽  
Sanjib Majumdar ◽  
Norihiko L. Okamoto ◽  
Kyosuke Kishida ◽  
...  
Keyword(s):  
Single Crystals ◽  
Plastic Flow ◽  
Room Temperature ◽  
Resolve Shear Stress ◽  
Temperature Deformation ◽  
Slip Systems ◽  
Compression Tests ◽  
Plastic Deformation Behavior ◽  
Bulk Single Crystals ◽  
Micropillar Compression

AbstractThe plastic deformation behavior of single crystals of two transition-metal diborides, ZrB2 and TiB2 with the AlB2 structure has been investigated at room temperature as a function of crystal orientation and specimen size by micropillar compression tests. Although plastic flow is not observed at all for their bulk single crystals at room temperature, plastic flow is successfully observed at room temperature by the operation of slip on {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 3> in ZrB2 and by the operation of slip on {1$${\bar{1}}$$ 1 ¯ 00}<0001> and {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 0> in TiB2. Critical resolve shear stress values at room temperature are very high, exceeding 1 GPa for all observed slip systems; 3.01 GPa for {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 3> slip in ZrB2 and 1.72 GPa and 5.17 GPa, respectively for {1$${\bar{1}}$$ 1 ¯ 00}<0001> and {1$${\bar{1}}$$ 1 ¯ 00}<11$${\bar{2}}$$ 2 ¯ 0> slip in TiB2. The identified operative slip systems and their CRSS values are discussed in comparison with those identified in the corresponding bulk single crystals at high temperatures and those inferred from micro-hardness anisotropy in the early studies.

Anomaly of the Work Hardening of Zn-Cu Single Crystals Oriented for Slip in Secondary Systems

2011 ◽  
Vol 56 (4) ◽  
pp. 1021-1027
Author(s):  
K. Pieła
Keyword(s):  
Strain Hardening ◽  
Single Crystals ◽  
Yield Stress ◽  
Work Hardening ◽  
Temperature Anomaly ◽  
Strain Hardening Exponent ◽  
Plastic Behavior ◽  
Thermal Dependence ◽  
Copper Addition ◽  
Secondary Systems

Anomaly of the Work Hardening of Zn-Cu Single Crystals Oriented for Slip in Secondary SystemsThe copper alloyed (up to 1.5%) zinc single crystals oriented for slip in non-basal systems (orientation close to < 1120 >) were subjected to compression test within a range of temperatures of 77-293K. It has been stated, that Zn-Cu crystals exhibit characteristic anomalies of the thermal dependence of yield stress and of the strain hardening exponent. Both of them are related to the change in type and sequence of active non-basal slip systems: pyramidal of the 1storder {1011} < 1123 > (Py-1) and pyramidal of the 2ndorder {1122} < 1123 > (Py-2). The temperature anomaly of the yield stress results from the change of the slip from Py-2 systems to simultaneous slip in the Py-2 and Py-1 (Py-2 + Py-1) systems, occurring in the preyielding stage. On the other hand, sequential activation of pyramidal systems taking place in advanced plastic stage (i.e. the first Py-2 and next Py-2 + Py-1 systems) is responsible for temperature anomaly of strain hardening exponent. Increase in copper addition favors the activity of Py-2 systems at the expense of Py-1 slip, what leads to a drastic differences in plastic behavior of zinc single crystals.

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