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.

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.

Reduction of Free-Edge Stress Concentration

1985 ◽  
Vol 52 (4) ◽  
pp. 801-805 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Free Edge ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Interlaminar Shear ◽  
Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

Effect of Temperature and Crystal Orientation on the Plasticity (SLIP) Evolution in Single Crystal Nickel Base Superalloy Notched Specimens

2007 ◽  
Author(s):  
Shadab Siddiqui ◽  
Nagaraj K. Arakere ◽  
Fereshteh Ebrahimi
Keyword(s):  
Shear Stress ◽  
Single Crystal ◽  
Element Model ◽  
Effect Of Temperature ◽  
Nickel Base Superalloy ◽  
Shear Stresses ◽  
Slip Systems ◽  
Slip Planes ◽  
Nickel Base ◽  
Critical Resolved Shear Stress

A comprehensive numerical investigation of plasticity (slip) evolution near notches was conducted at 28°C and 927°C, for two crystallographic orientations of double-notched single crystal nickel base superalloys (SCNBS) specimens. The two specimens have a common loading orientation of <001> and have notches parallel to the <010> (specimen I) and <110> (specimen II) orientation, respectively. A three dimensional anisotropic linear elastic finite element model was employed to calculate the stress field near the notch of these samples. Resolved shear stress values were obtained near the notch for the primary octahedral slip systems ({111} <110>) and cube slip systems ({100} <110>). The effect of temperature was incorporated in the model as changes in the elastic modulus values and the critical resolved shear stress (CRSS). The results suggest that the number of dominant slip systems (slip systems with the highest resolved shear stress) and the size and the shape of the plastic zones around the notch are both functions of the orientation as well as the test temperature. A comparison between the absolute values of resolved shear stresses near the notch at 28°C and 927°C on the {111} slip planes revealed that the plastic zone size and the number of activated dominant slip systems are not significantly affected by the temperature dependency of the elastic properties of the SCNBS, but rather by the change in critical resolved shear stress of this material with temperature. The load required to initiate slip was found to be lower in specimen II than in specimen I at both temperatures. Furthermore, at 927°C the maximum resolved shear stress (RSS) on the notch surface was found to be greater on the {100} slip planes as compared with the {111} slip planes in both specimens. The results from this study will be helpful in understanding the slip evolution in SCNBS at high temperatures.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Crack Problems

1981 ◽  
Vol 103 (3) ◽  
pp. 214-218 ◽  
Author(s):  
B. V. Kiefer ◽  
P. D. Hilton
Keyword(s):  
Finite Element ◽  
Normal Stress ◽  
Crack Front ◽  
Stress Component ◽  
Three Dimensional ◽  
Specimen Thickness ◽  
Element Analysis ◽  
Finite Element Program ◽  
Elastic Plastic ◽  
Crack Problems

A three-dimensional, elastic-plastic finite element program is developed and applied to analyze the stress field in a plate containing a through crack. The center cracked plate is subjected to uniform tensile loading which results in mode I opening of the crack surfaces. Transverse variations of the opening tensile stress component and of the effective stress (von Mises) in the vicinity of the crack front are presented. They clearly demonstrate the three-dimensional nature of this problem with distributions that depend on specimen thickness. For thinner plates, the plastic deformation concentrates near the plate surfaces while the normal stress is largest in the plate interior. In thicker plates the deformation and normal stress fields are more uniform in the plate interior near the crack front, but they develop a rapid boundary layer-type variation in the vicinity of the plate surfaces.

Subsurface Stress Fields in Face-Centered-Cubic Single-Crystal Anisotropic Contacts

2005 ◽  
Vol 128 (4) ◽  
pp. 879-888 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
Erik Knudsen ◽  
Gregory R. Swanson ◽  
Gregory Duke ◽  
Gilda Ham-Battista
Keyword(s):  
Finite Element ◽  
High Pressure ◽  
Fatigue Life ◽  
Crack Initiation ◽  
Single Crystal ◽  
Turbine Blades ◽  
Stress Fields ◽  
Shear Stresses ◽  
Face Centered Cubic ◽  
Subsurface Stress

Single-crystal superalloy turbine blades used in high-pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high-cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes and noncrystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single-crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two- and three-dimensional (3D) subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single-crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii (1963, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, Inc., San Francisco, pp. 1–40). Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis. Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single-crystal contact problems require extremely refined 3D finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses on the principal slip planes also involves considerable postprocessing work. For these reasons, it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Shear on the Flow Surface of Metallic Crystals

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Michel G. Darrieulat ◽  
Asdin Aoufi
Keyword(s):  
Three Dimensional ◽  
Shear Stresses ◽  
Slip Systems ◽  
Geometric Description ◽  
Cubic Metals ◽  
Maximum Value ◽  
Flow Surface ◽  
Kinematic Study ◽  
Principal Directions ◽  
Octahedral Slip

The present article addresses the following question: How is it that shears are so common in the plastic deformation of metallic alloys? An answer is sought in a geometric description of the shear flow when the deformation is produced by slip systems gliding according to the Schmid law. Such flows are represented schematically by what is called “simple shear” and a kinematic study is done of the way these shears can be produced by the joint activity of various slip systems. This implies specific conditions on the glide rates, which can be known analytically thanks to adequate parametrizations. All the possible shears have been calculated in the case of cubic metals deforming with identical critical resolved shear stresses (Bishop and Hill polyhedron). Three dimensional representations are given in the space of the Bunge angles associated with the principal directions of the shears. A special attention has been given to the number of slip systems involved. Most of the shears are not far from some combination of two or three systems. This is quantified by defining the misorientation ω between a shear taken at random and the set of shears produced by the glide on two or three octahedral slip systems. It is found that in most cases, ω<15 deg. The maximum value of ω (30.5 deg) is found for the orientations called Cube and U in rolled metals.

scholarly journals Plastic Deformation and Crystalline Texture in Equibiaxial Expansion

1979 ◽  
Vol 3 (3) ◽  
pp. 149-168 ◽  
Author(s):  
C. Gaspard ◽  
P. Messien ◽  
J. Mignon ◽  
T. Greday
Keyword(s):  
Plastic Deformation ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Deformation Model ◽  
Theoretical Treatment ◽  
Slip Systems ◽  
Factors Influencing ◽  
Experimental Behavior ◽  
Shear Planes

The classical three-dimensional analysis (O.D.F.) has been extended in such a manner as to obtain the representation of the texture, and, more precisely, the distribution of the slip systems <111> {hkℓ} in the planes where shear stresses induced in equibiaxial expansion are maximum.Quantification of the slip systems configuration allows the development of a deformation model which takes into account the factors influencing the degree of stretchability of the steels. From this model it is possible to define true hardening rates and equibiaxiality coefficients characterizing the ability of the steel to distribute the deformation in the macroscopic shear planes.In association with the resistance to thinning defined by the configuration of the slip systems, the theoretical treatment makes it possible to grade different steels according to their experimental behavior.

Crystal Plasticity Analysis of Thermal Deformation and Dislocation Accumulation in Gaas/Si Patterned Structure

1991 ◽  
Vol 226 ◽  
Author(s):  
Tetsuya Ohashi ◽  
Naoyuki Honda
Keyword(s):  
Thermal Deformation ◽  
Three Dimensional ◽  
Film Deposition ◽  
Shear Stresses ◽  
Slip Systems ◽  
Quantitative Expression ◽  
Plastic Slip ◽  
Dislocation Densities ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

AbstractPlastic slip deformation in patterned.GaAs films on Si substrate during cooling from film deposition temperature are numerically simulated under a continuum mechanics approximation. The plastic slip is assumed to take place on (111) <110> slip systems and activation condition of the slip systems is given by the Schmid's law. The critical resolved shear stresses for the activation of slip systems are expressed as a function of accumulated dislocation densities, which are evaluated by models for their movement and interaction. A three dimensional finite element computer program is developed, in which strain hardening behaviour is given a quantitative expression by the models for dislocations. Results of the simulation reveal process of plastic slip and dislocation accumulation in GaAs film. Residual stress evaluated by the simulation agreed well with results obtained by photo-luminescent experiments.

scholarly journals Estimate of theoretical shear strength of C60 single crystal by nanoindentation

2021 ◽  
Vol 56 (18) ◽  
pp. 10905-10914
Author(s):  
Sergey N. Dub ◽  
Cetin Haftaoglu ◽  
Vitaliy M. Kindrachuk
Keyword(s):  
Shear Strength ◽  
Single Crystal ◽  
Shear Stresses ◽  
Slip Systems ◽  
Berkovich Indenter ◽  
Element Analysis ◽  
Theoretical Shear Strength ◽  
Elastic Loading ◽  
Octahedral Slip ◽  
Realistic Geometry

AbstractThe onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems $$\langle{01}\overline{1}\rangle\left\{ {{111}} \right\}$$ ⟨ 01 1 ¯ ⟩ 111 , supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about $${1}/{11}$$ 1 / 11 of the shear modulus on {111} planes. Graphical abstract

Stresses in a bottoming stud assembly with chamfers at the ends of the threads

1983 ◽  
Vol 18 (1) ◽  
pp. 15-22 ◽  
Author(s):  
H Fessler ◽  
P K Jobson
Keyword(s):  
Stress Concentration ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Front End ◽  
Set Up

Three-dimensional, frozen-stress, photoelastic models of 1 in. BSW studs and tapped blocks have been loaded axially and in torsion. Detailed distributions of axial, principal, and shear stresses show that, as expected, the greatest stresses occur near the front end of engagement, but there are secondary peaks near the back end due to the stresses set up by ‘locking’ the stud at the bottom of the hole. Chamfering the first two turns of the thread of the block eliminates the stress concentration at the front of the block itself but does not reduce the stud stresses significantly. Similarly, the stresses at the back of engagement are reduced if the stud thread is chamfered.

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