Investigation of Three-Dimensional Stress Fields and Slip Systems for fcc Single-Crystal Superalloy Notched Specimens

2005 ◽  
Vol 127 (3) ◽  
pp. 629-637 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
Shadab Siddiqui ◽  
Shannon Magnan ◽  
Fereshteh Ebrahimi ◽  
Luis E. Forero
Keyword(s):  
Plastic Deformation ◽  
Plastic Zone ◽  
Single Crystal ◽  
Single Crystals ◽  
Crystallographic Orientation ◽  
Elastic Anisotropy ◽  
Three Dimensional ◽  
Stress Fields ◽  
Slip Systems ◽  
Zone Formation

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e., plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g., cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers [Rice, J. R., 1987, Mech. Mater. 6, pp. 317–335; Rice, J. R., and Saeedvafa, M., 1987, J. Mech. Phys. Solids 36, pp. 189–214; Saeedvafa, M., and Rice, J. R., 1988; ibid., 37, pp. 673–691; Rice, J. R., Hawk, D. E., Asaro, R. J., 1990, Int. J. Fract. 42, pp. 301–321; Saeedvafa, M., and Rice, J. R., 1992, Modell. Simul. Mater. Sci. Eng. 1, pp. 53–71] and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a fcc single-crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of three-dimensional (3D) stress fields and evolution of slip sector boundaries near notches in fcc single-crystal PWA1480 tension test specimens and demonstrate that a 3D linear elastic finite element model, which includes the effect of material anisotropy, is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near fcc single-crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single-crystal notches.

Investigation of Three-Dimensional Stress Fields and Slip Systems for FCC Single Crystal Superalloy Notched Specimens

2004 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
Shadab Siddiqui ◽  
Shannon Magnan ◽  
Fereshteh Ebrahimi ◽  
Luis E. Forero
Keyword(s):  
Plastic Deformation ◽  
Plastic Zone ◽  
Single Crystal ◽  
Single Crystals ◽  
Crystallographic Orientation ◽  
Elastic Anisotropy ◽  
Element Model ◽  
Stress Fields ◽  
Slip Systems ◽  
Zone Formation

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e. plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g. cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing, become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers [10–14] and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a FCC single crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of 3D stress fields and evolution of slip sector boundaries near notches in FCC single crystal PWA1480 tension test specimens, and demonstrate that a 3D linear elastic finite element model that includes the effect of material anisotropy is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near FCC single crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single crystal notches.

Influence of the Crystallographic Orientation of CuZn30 Single Crystal on the Portevin-Le Chatelier Effect

2013 ◽  
Vol 203-204 ◽  
pp. 406-410 ◽  
Author(s):  
Barbara Grzegorczyk ◽  
Wojciech Ozgowicz ◽  
Elżbieta Kalinowska-Ozgowicz
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Single Crystal ◽  
Single Crystals ◽  
Crystallographic Orientation ◽  
Stress And Strain ◽  
Complex Process ◽  
Orientation Axis ◽  
Chatelier Effect ◽  
Stress And Strain Rate

Plastic deformation of solid crystals is a complex process, mostly heterogeneous, due to the simultaneous effect of several deformation mechanisms. A dominating deformation mechanism depends on the properties of the material and external coefficients, viz. temperature, stress and strain rate. The applied Bridgman method permitted to obtain single crystal of the CuZn30 alloy adequate for plastic deformation investigations. Single crystal are characterized by selected crystallographic orientations from various areas of the basic triangle. In order to determine the influence of the crystallographic orientation on the Portevin-Le Chatelier effect selected single crystals were compressed at a temperature of 300°C at a strain rate of 10-3 s-1. Experiments confirmed the effect of the crystallographic orientation axis of CuZn30 single crystals on the observed differences in the intensity of stress oscillation on stress-strain curves.

Evolution of Slip Through the Thickness of a Single-Crystal Nickel-Base Superalloy Notched Specimen

2006 ◽  
Author(s):  
Shadab Siddiqui ◽  
Nagaraj K. Arakere ◽  
Fereshteh Ebrahimi
Keyword(s):  
Stress Concentration ◽  
Single Crystal ◽  
Normal Stress ◽  
Elastic Anisotropy ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Specimen Thickness ◽  
Face Centered Cubic ◽  
Slip Systems ◽  
Base Superalloy

Deformation mechanisms and failure modes of FCC (face centered cubic) single crystal components subjected to triaxial states of static and fatigue stress are very complicated to predict, because plasticity precedes fracture in regions of stress concentration, and the evolution of plasticity on the surface and through the thickness is influenced by elastic and plastic anisotropy. The triaxial stress state at regions of stress concentration results in the activation of many slip systems that otherwise would not be activated during uniaxial testing. We recently presented [1] results from a numerical and experimental investigation of evolution of slip systems at the surface of notched FCC single crystal specimens, as a function of secondary crystallographic orientation. Results showed that the slip sector boundaries have complex curved shapes with several slip systems active simultaneously near the notch. We extend our work on slip at the surface to investigating the evolution of slip or plastic deformation through the thickness of the specimen. A single crystal double-edge-notched rectangular specimen of a Ni-base superalloy, under the tensile loading ([001] load orientation and [110] notch direction) is considered. A three dimensional (3-D) finite element model (FEM) including elastic anisotropy is used for the numerical investigation. Results indicate that the stress distribution and slip fields are a strong function of axial location through the thickness. Numerical results are verified by comparing them with experimentally observed slip fields. We demonstrate that inclusion of three dimensional analysis and elastic anisotropy is important for predicting evolution of slip at the surface and through the specimen thickness. The resolved shear stresses (RSS) on the dominant slip systems and the normal stress on the dominant planes are shown to vary significantly from the surface to the midplane of the specimen. Based on the consideration of RSS, normal stress and the number of activated slip systems at each thickness level, it is concluded that fatigue cracks most likely start in the midplane, for the orientation reported here.

Sr4Pt10In21 – the first representative of the Ho4Ni10In21 type with a divalent cation

2019 ◽  
Vol 74 (5) ◽  
pp. 443-449 ◽  
Author(s):  
Birgit Heying ◽  
Jutta Kösters ◽  
Rainer Pöttgen
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Glassy Carbon ◽  
Divalent Cation ◽  
High Frequency ◽  
Three Dimensional ◽  
X Ray ◽  
Trigonal Prismatic Coordination ◽  
Trigonal Prismatic

AbstractRod-shaped single crystals of Sr4Pt10In21were prepared from the elements in glassy-carbon crucibles in a high-frequency furnace. The structure of Sr4Pt10In21was refined from single-crystal X-ray diffractometer data:C2/m, Ho4Ni10Ga21type,a = 2322.62(7),b = 450.27(2),c = 1958.09(7) pm,β = 133.191(3)°,wR = 0.0464, 3200F2values and 107 variables. The three-dimensional [Pt10In21]δ−polyanionic network is stabilized through substantial Pt–In (269–313 pm Pt–In) and In–In (294–362 pm In–In) bonding. All platinum atoms have slightly distorted tri-capped trigonal prismatic coordination and the two crystallographically independent strontium atoms are located in penta-capped pentagonal prisms.

A Continuum Model for Single Crystal Cyclic Plasticity

2003 ◽  
Vol 779 ◽  
Author(s):  
Biqiang Xu ◽  
Yanyao Jiang
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Kinematic Hardening ◽  
Strain Curve ◽  
Cyclic Behavior ◽  
Cyclic Plasticity ◽  
Amplitude Dependence ◽  
Slip Systems ◽  
Stress Strain ◽  
Copper Single Crystals

AbstractA constitutive model was developed to bridge the cyclic plasticity behavior of single crystals and the corresponding characteristic dislocation structures. Yield and flow were built on the individual slip systems. The Armstrong-Frederick kinematic hardening rule was invoked to capture the Bauschinger effect. A material memory parameter was introduced to consider the amplitude dependence of cyclic hardening. Latent hardening considering the interactions among the slip systems was used to describe the anisotropic cyclic behavior. The experimental results of copper single crystals were used to validate the model developed. It was found that the model was able to adequately describe the well-known three distinctive regions in the cyclic stress-strain curve of the FCC single crystal oriented for single slip and the associated dislocation substructures. The model was capable of capturing the enhanced hardening observed in copper single crystals in multi-slip orientations. For a given loading history, the model can predict not only the saturated stress-strain response but also the detailed evolution of the transient cyclic behavior. The characteristic dislocation structures can be featured with the slip evolution.

scholarly journals The critical shear stress of mercury single crystals

1937 ◽  
Vol 163 (912) ◽  
pp. 34-53 ◽  
Keyword(s):  
Plastic Deformation ◽  
Shear Stress ◽  
Melting Point ◽  
Single Crystal ◽  
Single Crystals ◽  
Critical Shear Stress ◽  
Impurity Content ◽  
Thermal Agitation ◽  
Plastic Yield ◽  
Metal Single Crystals

The influence of very small quantities of impurity on the critical shear stress of metal single crystals has an important bearing on the mechanism of their plastic deformation. For investigations in this field, mercury is a very suitable metal: its impurity content can easily be reduced to an extremely low level (Hulett 1911) and it contains no dissolved gases (Hulett 1911). Also, as first pointed out by Andrade (1914), single crystal wires of this metal can be prepared without difficulty. The low melting point of mercury (-38∙8° C.) is far from being a disadvantage. The crystals can be maintained at -60° C., and at a temperature so near the melting point the thermal agitation may be expected to accentuate phenomena not observable at lower temperatures, if such agitation plays the important part in the mechanism of glide ascribed to it (Taylor 1934; Polanyi 1934; Orowan 1934). As a possible instance of this, the experiments to be described have revealed the existence of a preliminary “set” preceding the true plastic yield. Widely differing forms of slip band have also been observed, and are described elsewhere (Greenland 1937). It is hoped that these results will throw further light on the mechanism of glide.

SIZE EFFECT ON DEFORMATION MODE IN MICRON-SIZED Ti-5Al SINGLE CRYSTAL LOADED ALONG $[2\,\overline 1 \,\overline 1 \,0]$ AND [0001]

2010 ◽  
Vol 24 (15n16) ◽  
pp. 2466-2471 ◽  
Author(s):  
LIN XIAO ◽  
QIAN YU ◽  
QIAOYAN SUN ◽  
JUN SUN
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Deformation Mode ◽  
Slip Systems ◽  
Free Standing ◽  
Physical Size ◽  
Specimen Width ◽  
Starvation Effects ◽  
Micro Pillars ◽  
Starvation Effect

Free-standing sub-micron Ti -5 Al single crystal square pillars were fabricated along [Formula: see text] double slip and [0001] twinning orientations using FIB fabrication processes. Samples in range of 0.4 to 2.0µm were compressed. The yield stress increases much higher than their bulk counterpart as the specimen width decreases. The tendency of "smaller is stronger" is displayed in Ti -5 Al single crystals loaded along [Formula: see text] and [0001] orientations. The number of slip systems is restricted by specimen physical size as it declines from 2µm to 0.5µm, when the specimens were subjected to double slip loading. Meanwhile, when sample size is less than 1.0µm, micro-pillars along twinning orientation have to compensate the incomplete twinning deformation via shearing due to geometrical restriction and dislocation starvation effects. This variation of deformation mode could be attributed to the starvation effect of dislocations.

The Stannides EuPdSn and EuPtSn

1996 ◽  
Vol 51 (6) ◽  
pp. 806-810 ◽  
Author(s):  
Rainer Pöttgen
Keyword(s):  
Single Crystal ◽  
Single Crystals ◽  
Crystal Chemistry ◽  
Three Dimensional ◽  
Type Structure ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray

Abstract EuPdSn and EuPtSn were prepared from the elements in tantalum tubes at 1070 K and investigated by X-ray diffraction on both powder as well as single crystals. They crystallize with the TiNiSi type structure of space group Pnma and with Z = 4 formula units per cell. Both structures were refined from single-crystal diffractometer data: a = 751.24(9), b = 469.15(6), c = 804.31(9) pm, V = 0.2835(1) nm3 for EuPdSn, and a = 753.38(7), b = 467.72(4), c = 793.08(7) pm, V = 0.2795(1) nnr for EuPtSn. The structures consist of three-dimensional [PdSn] and [PtSn] polyanionic networks in which the europium atoms are embedded. The crystal chemistry of these stannides is briefly discussed

Twinning in Ti-48%Ni-2%Fe Single Crystals under Rolling

2013 ◽  
Vol 738-739 ◽  
pp. 118-122
Author(s):  
Margarita Isaenkova ◽  
Yuriy Perlovich ◽  
Vladimir Fesenko ◽  
Tatyana Dementyeva
Keyword(s):  
Plastic Deformation ◽  
Single Crystal ◽  
Single Crystals ◽  
Stereographic Projection ◽  
Rolling Temperature ◽  
Main Mechanism ◽  
Geometrical Analysis ◽  
Pole Figures

Under rolling of Ti-48%Ni-2%Fe single crystals in the phase B2 at 350oC the twinning is the main mechanism of plastic deformation by many initial orientations of these single crystals, as texture data show clearly. Splitting of initial maxima in the stereographic projection of single crystal into several new ones is an evident manifestation of twinning. But this mode of reorientation is observed only at initial stages of rolling, when deformation degrees do not exceed ~10-15%. A geometrical analysis of pole figures for rolled single crystals showed, that at the used rolling temperature the preferable twinning planes there were {114} and {118}.

Mechanical and thermal properties of single crystals of ZrB2

2002 ◽  
Vol 753 ◽  
Author(s):  
N. L. Oka moto ◽  
M. Kusakari ◽  
K. Tanaka ◽  
H. Inui ◽  
M. Yamaguchi ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Thermal Expansion ◽  
Single Crystals ◽  
Elastic Constants ◽  
Layered Structure ◽  
Mechanical And Thermal Properties ◽  
Slip Systems ◽  
Compression Tests ◽  
Deformation Behaviors ◽  
Temperature Ranges

ABSTRACTCoefficients of thermal expansion (CTE), elastic constants and plastic deformation behaviors of single crystals of ZrB2, which possesses a hexagonal layered structure where pure Zr and pure B atomic planes stack alternatively along the c-axis, have been investigated in wide temperature ranges. While the observed elastic constants indicate highly anisotropic nature of atomic bonding being consistent with the layered structure, the observed CTE values are rather isotropic. Two operative slip systems, (0001)<1120> and on {1100}<1123>, are identified in compression tests. The observed plastic behaviors are discussed in the light of the deduced anisotropy in atomic bonding.

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