Crystallographic Constitutive Models for Single Crystal Superalloys

2011 ◽  
Vol 197-198 ◽  
pp. 1381-1388 ◽  
Author(s):  
Qing Wu Wang ◽  
Mao Pang ◽  
Shi Hui Zhang
Keyword(s):  
Slip System ◽  
Single Crystal ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Slip Systems ◽  
Flow Equations ◽  
Hardening Law ◽  
Crystallographic Slip ◽  
Set Up ◽  
Octahedral Slip

Single crystal nickel base superalloys, such as Chinese material DD6 have been used in gas turbine blade in China more and more widely. In order to make better use of single crystal superalloys with many excellencies, constitutive models have been developed. In this paper, general method of crystallographic constitutive modeling was summarizes and a new constitutive model, based on crystallographic theory was proposed with phenomenological models' advantages. Based on crystallographic slip system principle, the basic slip-based viscoplasticity theory equations were set up on 12 octahedral slip systems and 6 cubic slip systems, total 18 slip systems. In micro-level slip system, the general unified constitutive formulations were used as the flow equations and hardening law. In the model, scalar forms were applied for constitutive equations on slip systems and the number and types of active slip systems were used to describe the material anisotropy, which was satisfied automatically by slip systems not anisotropic tensors and. The experimental and calculation results of two kind single crystal superalloys PWA1480 and DD6 were compared. The model had the capability to predict many mechanical response and analyze structure of single crystal superalloys. The modeling procedures and results showed that this crystallographic model had more clear physical meaning and was exact.

Multi-Resolution Material Hardening Law for CPFE Micro-Forming Analysis

2016 ◽  
Vol 716 ◽  
pp. 232-239
Author(s):  
Ji Ling Feng ◽  
Shi Wen Wang ◽  
Jian Guo Lin
Keyword(s):  
Slip System ◽  
Mechanical Response ◽  
Interaction Matrix ◽  
Micro Forming ◽  
Forming Simulation ◽  
Hardening Law ◽  
Forming Analysis ◽  
Factor C ◽  
Global And Local ◽  
Local Hardening

A new multi-resolution slip system-based material hardening law has been developed for micro-forming simulation using Crystal Plasticity Finite Element (CPFE) Approach. Material hardenings are formulated based on global and local hardening of dislocations for each slip system and defined with distinct physical meaning. Plasticity is assumed to arise solely from crystalline slip and the overall mechanical response with any crystallographic system, such as FCC, BCC, etc, can be addressed by a local hardening parameter, c, from 0 (pure anisotropic) to 1 (fully isotropic). No interaction matrix is necessary, since the latent hardening can be realized by the hardening factor , c , and the new dislocation density based hardening law can be implemented into existing FE software efficiently. The proposed equations are an extension of the existing hardening law from macro mechanics descriptions down to micro mechanics level, therefore unified constitutive equations had been established at multiscale resolution. Some features of the proposed hardening law will be demonstrated with a single cubic crystal under tension load.

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

scholarly journals Crystallographic Orientation Dependence of Mechanical Responses of FeCrAl Micropillars

Crystals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 943
Author(s):  
Dongyue Xie ◽  
Binqiang Wei ◽  
Wenqian Wu ◽  
Jian Wang
Keyword(s):  
Grain Boundary ◽  
Slip System ◽  
Single Crystal ◽  
Room Temperature ◽  
Orientation Dependence ◽  
Slip Systems ◽  
Flow Strength ◽  
Mechanical Responses ◽  
Fecral Alloy ◽  
Strain Hardening Rate

Iron-chromium-aluminum (FeCrAl) alloys are used in automobile exhaust gas purifying systems and nuclear reactors due to its superior high-temperature oxidation and excellent corrosion resistance. Single-phase FeCrAl alloys with a body centered cubic structure plastically deform through dislocation slips at room temperature. Here, we investigated the orientation dependence of mechanical responses of FeCrAl alloy through testing single-crystal and bi-crystal micropillars in a scanning electron microscopy at room temperature. Single-crystal micropillars were fabricated with specific orientations which favor the activity of single slip system or two slip systems or multiple slip systems. The strain hardening rate and flow strength increase with increasing the number of activated slip system in micropillars. Bi-crystal micropillars with respect to the continuity of slip systems across grain boundary were fabricated to study the effect of grain boundary on slip transmission. The high geometrical compatibility factor corresponds to a high flow strength and strain hardening rate. Experimental results provide insight into understanding mechanical response of FeCrAl alloy and developing the mechanisms-based constitutive laws for FeCrAl polycrystalline aggregates.

Slip systems and critical resolved shear stress in pyrite: an electron backscatter diffraction (EBSD) investigation

2008 ◽  
Vol 72 (6) ◽  
pp. 1181-1199 ◽  
Author(s):  
C. D. Barrie ◽  
A. P. Boyle ◽  
S. F. Cox ◽  
D. J. Prior
Keyword(s):  
Shear Stress ◽  
Slip System ◽  
Single Crystal ◽  
Electron Backscatter Diffraction ◽  
Lattice Rotation ◽  
Slip Systems ◽  
Boundary Trace ◽  
Electron Backscatter ◽  
Backscatter Diffraction ◽  
Critical Resolved Shear Stress

AbstractA suite of experimentally deformed single-crystal pyrite samples has been investigated using electron backscatter diffraction (EBSD). Single crystals were loaded parallel to <100> or <110> and deformed at a strain rate of 10-5s-1, confining pressure of 300 MPa and temperatures of 600°C and 700°C. Although geometrically (Schmid factor) the {001}<100> slip system should not be activated in <100> loaded samples, lattice rotation and boundary trace analyses of the distorted crystals indicate this slip system is easier to justify. Determination of 75 MPa as the critical resolved shear stress (CRSS) for {001}<100> activation, in the <110> loaded crystals, suggests a crystal misalignment of ~5—15° in the <100> loaded crystals would be sufficient to activate the {001}<100> slip system. Therefore, {001}<100> is considered the dominant slip system in all of the single-crystal pyrite samples studied. Slip-system analysis of the experimentally deformed polycrystalline pyrite aggregates is consistent with the single-crystal findings, with the exception that {001}<11̄> also appears to be important, although less common than the {001}<100> slip system. The lack of crystal preferred orientation (CPO) development in the polycrystalline pyrite aggregates can be accounted for by the presence of two independent symmetrically equivalent slip systems more than satisfying the von Mises criterion.

Electron Microscopy of Shock Loaded Polycrystalline Beryllium

1974 ◽  
Vol 32 ◽  
pp. 506-507 ◽  
Author(s):  
J. M. Galbraith ◽  
L. E. Murr ◽  
A. L. Stevens
Keyword(s):  
Electron Microscopy ◽  
Wave Propagation ◽  
Structural Change ◽  
Single Crystal ◽  
Diffraction Pattern ◽  
Shock Loading ◽  
Slip Systems ◽  
Compression Tests ◽  
X Ray Diffraction ◽  
X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

scholarly journals Understanding the Strain Path Effect on the Deformed Microstructure of Single Crystal Pure Aluminum

Metals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1189
Author(s):  
Yingjue Xiong ◽  
Qinmeng Luan ◽  
Kailun Zheng ◽  
Wei Wang ◽  
Jun Jiang
Keyword(s):  
Strain Rate ◽  
Single Crystal ◽  
Strain Path ◽  
Mechanical Response ◽  
Pure Aluminum ◽  
Lattice Rotation ◽  
Softening Behavior ◽  
Theoretical Support ◽  
Commercial Applications ◽  
Electron Back Scattered Diffraction

During plastic deformation, the change of structural states is known to be complicated and indeterminate, even in single crystals. This contributes to some enduring problems like the prediction of deformed texture and the commercial applications of such material. In this work, plane strain compression (PSC) tests were designed and implemented on single crystal pure aluminum to reveal the deformation mechanism. PSC tests were performed at different strain rates under strain control in either one-directional or two-directional compression. The deformed microstructures were analyzed according to the flow curve and the electron back-scattered diffraction (EBSD) mappings. The effects of grain orientation, strain rate, and strain path on the deformation and mechanical response were analyzed. Experimental results revealed that the degree of lattice rotation of one-dimensional compression mildly dependents on cube orientation, but it is profoundly sensitive to the strain rate. For two-dimensional compression, the softening behavior is found to be more pronounced in the case that provides greater dislocations gliding freeness in the first loading. Results presented in this work give new insights into aluminum deformation, which provides theoretical support for forming and manufacturing of aluminum.

scholarly journals Ability of Constitutive Models to Characterize the Temperature Dependence of Rubber Hyperelasticity and to Predict the Stress-Strain Behavior of Filled Rubber under Different Defor Mation States

Polymers ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 369
Author(s):  
Xintao Fu ◽  
Zepeng Wang ◽  
Lianxiang Ma
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Chain Model ◽  
Stress Strain ◽  
Filled Rubber ◽  
Yeoh Model

In this paper, some representative hyperelastic constitutive models of rubber materials were reviewed from the perspectives of molecular chain network statistical mechanics and continuum mechanics. Based on the advantages of existing models, an improved constitutive model was developed, and the stress–strain relationship was derived. Uniaxial tensile tests were performed on two types of filled tire compounds at different temperatures. The physical phenomena related to rubber deformation were analyzed, and the temperature dependence of the mechanical behavior of filled rubber in a larger deformation range (150% strain) was revealed from multiple angles. Based on the experimental data, the ability of several models to describe the stress–strain mechanical response of carbon black filled compound was studied, and the application limitations of some constitutive models were revealed. Combined with the experimental data, the ability of Yeoh model, Ogden model (n = 3), and improved eight-chain model to characterize the temperature dependence was studied, and the laws of temperature dependence of their parameters were revealed. By fitting the uniaxial tensile test data and comparing it with the Yeoh model, the improved eight-chain model was proved to have a better ability to predict the hyperelastic behavior of rubber materials under different deformation states. Finally, the improved eight-chain model was successfully applied to finite element analysis (FEA) and compared with the experimental data. It was found that the improved eight-chain model can accurately describe the stress–strain characteristics of filled rubber.

Evaluating the Mechanical Behavior of 316 Stainless Steel at the Microscale Using Finite Element Modelling and In-Situ Neutron Scattering

2010 ◽  
Author(s):  
Dong-Feng Li ◽  
Noel P. O’Dowd ◽  
Catrin M. Davies ◽  
Shu-Yan Zhang
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Finite Element Modelling ◽  
Mechanical Response ◽  
Fe Model ◽  
Lattice Strains ◽  
Crystallographic Slip ◽  
In Situ Neutron Diffraction ◽  
Elastic Lattice

In this study, the deformation behavior of an austenitic stainless steel is investigated at the microscale by means of in-situ neutron diffraction (ND) measurements in conjunction with finite-element (FE) simulations. Results are presented in terms of (elastic) lattice strains for selected grain (crystallite) families. The FE model is based on a crystallographic (slip system based) representation of the deformation at the microscale. The present study indicates that combined in-situ ND measurement and micromechanical modelling provides an enhanced understanding of the mechanical response at the microscale in engineering steels.

Analytical treatment of two-dimensional supersonic flow. II. Flow with weak shocks

1956 ◽  
Vol 248 (952) ◽  
pp. 499-515 ◽  
Keyword(s):  
Solution Process ◽  
Wave Interaction ◽  
Analytical Treatment ◽  
Plane Flow ◽  
Flow Equations ◽  
Interaction Regions ◽  
Steady Plane ◽  
Set Up ◽  
Downstream Flow ◽  
Weak Shocks

A scheme of approximate solution is presented for the treatment of shock waves in the steady, plane flow of a perfect gas. It is based on the neglect of any entropy variations produced by the shocks and hence is applicable only when the shocks are weak. The method provides an extension of Friedrichs’s (1948) results for simple waves to wave-interaction regions. By an examination of the solution of the continuous-flow equations in the neighbourhood of a known shock wave it is shown how the downstream flow may be calculated without reference to the particular shock shape (§2). There are certain cases in which this approach fails and they are discussed by means of a typical example in §3.3. Once the downstream flow has been calculated, it is possible to set up general equations for the determination of the shock (§ 2). Examples of the solution of these equations for typical problems are given in §3. In §4 there is a brief discussion of the validity of using homentropic theory and estimates of the errors involved in the solution process are obtained.

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