scholarly journals Regularized Yield Surfaces for Crystal Plasticity of Metals

Crystals ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 1076
Author(s):  
Bjørn Holmedal
Keyword(s):  
Yield Surface ◽  
Thermal Strain ◽  
Rate Sensitivity ◽  
Slip Systems ◽  
Large Yield ◽  
Latent Hardening ◽  
Yield Surfaces ◽  
Independent Behavior ◽  
Sharp Corners

The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of regularized yield surfaces are calibrated to exactly interpolate certain points on the facets of the perfect Schmid yield surface, while the different stress predictions in the corners are taken as the error estimate. Calibrations are discussed for slip systems commonly activated for bcc and fcc metals. It is found that the quality of calibrations of the ideal rate-independent behavior requires very large yield-surface exponents. However, the rounding of the corners of the yield surface can be regarded as an improved approximation accounting for the instant, thermal strain-rate sensitivity, which is directly related to the yield-surface exponent. Distortion of the crystal yield surface during latent hardening is also discussed, including Bauschinger behavior or pseudo slip systems for twinning, for which the forward and backward of the slip system are distinguished.

scholarly journals A novel p-harmonic descent approach applied to fluid dynamic shape optimization

2021 ◽  
Author(s):  
Peter Marvin Müller ◽  
Niklas Kühl ◽  
Martin Siebenborn ◽  
Klaus Deckelnick ◽  
Michael Hinze ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Large Deformations ◽  
Fluid Dynamic ◽  
Shape Optimisation ◽  
Shape Features ◽  
Floating Bodies ◽  
Novel Method ◽  
Sharp Corners ◽  
Dynamic Shape

AbstractWe introduce a novel method for the implementation of shape optimization for non-parameterized shapes in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $$p-$$ p - Laplacian for $$p > 2$$ p > 2 . This approach is closely related to the computation of steepest descent directions of the shape functional in the $$W^{1,\infty }-$$ W 1 , ∞ - topology and refers to the recent publication Deckelnick et al. (A novel $$W^{1,\infty}$$ W 1 , ∞ approach to shape optimisation with Lipschitz domains, 2021), where this idea is proposed. Our approach is demonstrated for shape optimization related to drag-minimal free floating bodies. The method is validated against existing approaches with respect to convergence of the optimization algorithm, the obtained shape, and regarding the quality of the computational grid after large deformations. Our numerical results strongly indicate that shape optimization related to the $$W^{1,\infty }$$ W 1 , ∞ -topology—though numerically more demanding—seems to be superior over the classical approaches invoking Hilbert space methods, concerning the convergence, the obtained shapes and the mesh quality after large deformations, in particular when the optimal shape features sharp corners.

Normality Structures With Thermodynamic Equilibrium Points

2007 ◽  
Vol 74 (5) ◽  
pp. 965-971 ◽  
Author(s):  
Q. Yang ◽  
R. K. Wang ◽  
L. J. Xue
Keyword(s):  
Thermodynamic Equilibrium ◽  
Equilibrium Points ◽  
Thermodynamic System ◽  
Internal Variables ◽  
System A ◽  
Plastic Dissipation ◽  
Flow Potential ◽  
Yield Surfaces ◽  
Intrinsic Dissipation ◽  
Independent Behavior

Enriched by the nonlinear Onsager reciprocal relations and thermodynamic equilibrium points (Onsager, Phys. Rev., 37, pp. 405–406; 38, pp. 2265–2279), an extended normality structure by Rice (1971, J. Mech. Phys. Solids, 19, pp. 433–455) is established in this paper as a unified nonlinear thermodynamic theory of solids. It is revealed that the normality structure stems from the microscale irrotational thermodynamic fluxes. Within the extended normality structure, this paper focuses on the microscale thermodynamic mechanisms and significance of the convexity of flow potentials and yield surfaces. It is shown that the flow potential is convex if the conjugate force increment cannot not oppose the increment of the rates of local internal variables. For the Rice fluxes, the convexity condition reduces to the local rates being monotonic increasing functions with respect to their conjugate forces. The convexity of the flow potential provides the thermodynamic system a capability against the disturbance of the thermodynamic equilibrium point. It is proposed for time-independent behavior that the set of plastically admissible stresses determined by yield conditions corresponds to the set of thermodynamic equilibrium points. Based on that viewpoint, the intrinsic dissipation inequality is just the thermodynamic counterpart of the principle of maximum plastic dissipation and requires the convexity of the yield surfaces.

scholarly journals Deformation Texture Evolution in Flat Profile AlMgSi Extrusions: Experiments, FEM, and Crystal Plasticity Modeling

2021 ◽  
Vol 8 ◽  
Author(s):  
Tomas Manik ◽  
Knut Marthinsen ◽  
Kai Zhang ◽  
Arash Imani Aria ◽  
Bjørn Holmedal
Keyword(s):  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Crystal Plasticity ◽  
Texture Evolution ◽  
Rate Sensitivity ◽  
Deformation Texture ◽  
Fiber Texture ◽  
Electron Back Scatter Diffraction ◽  
Slip Systems ◽  
Flat Profile

In the present work, the deformation textures during flat profile extrusion from round billets of an AA6063 and an AA6082 aluminium alloy have been numerically modeled by coupling FEM flow simulations and crystal plasticity simulations and compared to experimentally measured textures obtained by electron back-scatter diffraction (EBSD). The AA6063 alloy was extruded at a relatively low temperature (350°C), while the AA6082 alloy, containing dispersoids that prevent recrystallization, was extruded at a higher temperature (500°C). Both alloys were water quenched at the exit of the die, to maintain the deformation texture after extrusion. In the center of the profiles, both alloys exhibit a conventional β-fiber texture and the Cube component, which was significantly stronger at the highest extrusion temperature. The classical full-constraint (FC)-Taylor and the Alamel grain cluster model were employed for the texture predictions. Both models were implemented using the regularized single crystal yield surface. This approach enables activation of any number and type of slip systems, as well as accounting for strain rate sensitivity, which are important at 350°C and 500°C. The strength of the nonoctahedral slips and the strain-rate sensitivity were varied by a global optimization algorithm. At 350°C, a good fit could be obtained both with the FC Taylor and the Alamel model, although the Alamel model clearly performs the best. However, even with rate sensitivity and nonoctahedral slip systems invoked, none of the models are capable of predicting the strong Cube component observed experimentally at 500°C.

scholarly journals Incorporation of Load Induced Thermal Strain in Finite Element Models

10.14311/1079 ◽  
2009 ◽  
Vol 49 (1) ◽  
Author(s):  
A. Law ◽  
M. Gillie ◽  
P. Pankaj
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Thermal Strain ◽  
Finite Element Models ◽  
In Fire

Load induced thermal strains (LITS) are an integral part of the behaviour of concrete in fire; their existence has been well documented and modelled by different researchers. More thorough representation of LITS is needed to accurately represent their plastic constituents in finite element models. This paper develops a technique to allow the evolution of LITS in accordance with the rules developed in several academic models. The technique is implemented with a simple Drucker-Prager yield surface and the results assessed. 

Shear strength and yield surface of a partially saturated sandy silt under generalized stress states

2021 ◽  
Author(s):  
Rodrigo Carreira Weber ◽  
Enrique E. Romero Morales ◽  
Antonio Lloret
Keyword(s):  
Shear Strength ◽  
Yield Surface ◽  
Experimental Results ◽  
Model Parameters ◽  
Hollow Cylinder Apparatus ◽  
Clayey Silt ◽  
Lode Angle ◽  
Yield Surfaces ◽  
Stress States ◽  
Deviatoric Stresses

This paper studies the hydromechanical behavior of a slightly compacted mixture of sand and clayey silt (30%/70%) under a generalized stress state. The experimental study focused on analyzing the yielding response and shear strength behavior at different stress states (characterized by the intermediate principal stress parameter b, or Lode angle) and at different initial total suctions (as-compacted state). For the investigation, a hollow cylinder apparatus was used. The shear strength results allowed defining the variation of the critical state line with the Lode angle and the suction. Different models were proposed for isotropic and anisotropic yield surfaces, and their shape and rotation were calibrated with experimental results. The modeled yield surfaces fitted reasonably well the experimental results, considering their inclination and dependence on the suction, mean and deviatoric stresses and Lode angle. In addition, some relationships between the stresses and the model parameters were proposed to normalize the yield surface equation.

A simple mathematical theory of finite distortional latent hardening in single crystals

1977 ◽  
Vol 358 (1692) ◽  
pp. 47-70 ◽  
Keyword(s):  
Tensile Test ◽  
Single Crystals ◽  
Finite Deformation ◽  
Mathematical Theory ◽  
Slip Systems ◽  
Plastic Crystals ◽  
Hardening Law ◽  
Infinitesimal Strain ◽  
Latent Hardening ◽  
General Mathematical Theory

A simple (one-parameter) hardening law is proposed which accounts for the perpetuation of finite single slip, beyond the symmetry line, in the tensile test of f. c. c. crystals and reduces to Taylor’s rule at infinitesimal strain. This new law emerges as the simplest case of a general mathematical theory of finite deformation of elastic-plastic crystals. The fully anisotropic finite-distortional hardening of latent slip systems predicted by the simple theory is in qualitative agreement with experiment.

Deformation Behavior of Polycrystalline AZ31 Alloy at Room and Elevated Temperatures

2005 ◽  
Vol 488-489 ◽  
pp. 775-778
Author(s):  
Tsing Zhou ◽  
Goroh Itoh ◽  
Yohei Iseno ◽  
Yoshinobu Motohashi
Keyword(s):  
Deformation Behavior ◽  
Room Temperature ◽  
Elevated Temperatures ◽  
Rate Sensitivity ◽  
Tensile Tests ◽  
Az31 Alloy ◽  
Slip Systems ◽  
Type Specimens ◽  
Rolled Specimen ◽  
Hot Rolled

The hot-rolled and extruded AZ31 specimens are subjected to tensile tests at room and elevated temperatures. At room temperature, the yield stress of the hot-rolled specimen is significantly higher than that of the extruded, the reason for which is related to the different textures developed in the two type specimens, as well as the different slip systems activated. At elevated temperatures, the strain rate sensitivity and the activation energy are obtained to characterize the deformation mechanism of the alloy during the temperature range of 423~573K.

Effect of Cyclic Loading on the Yield Surface

1979 ◽  
Vol 101 (1) ◽  
pp. 59-63 ◽  
Author(s):  
F. Ellyin ◽  
K. W. Neale
Keyword(s):  
Aluminum Alloy ◽  
Steady State ◽  
Cyclic Loading ◽  
Yield Surface ◽  
Stress Ratio ◽  
Axial Stress ◽  
Repeated Loading ◽  
Plastic Response ◽  
Initial Yield ◽  
Yield Surfaces

The effect of repeated loading on the yield surface is investigated experimentally for an aluminum alloy. Initial yield surfaces under combined axial stress and torsion are first obtained, and yield surfaces subsequent to steady-state plastic response are then determined for various cyclic loading programs. The results suggest that the initial yield surface expands and translates under cyclic loading and that the form of the steady-state yield surface is independent of the stress ratio.

scholarly journals Computer-Aided Diagnosis of Speech Disorder Signal in Parkinson’s Disease

2016 ◽  
Vol 15 (9) ◽  
pp. 7117-7123
Author(s):  
Heba M. Afify ◽  
Basma Ahmed
Keyword(s):  
Speech Intelligibility ◽  
Rate Sensitivity ◽  
Speech Disorders ◽  
Computer Aided Diagnosis ◽  
Predictive Tool ◽  
Computer Aided ◽  
High Degree ◽  
Disordered Speech ◽  
Aided Diagnosis

Computer-aided diagnosis (CAD) can be used as a decision support system by physicians in the diagnosis and treatmentof disordered speech especially those who specialize in neurophysiology diseases. Parkinson's disease (PD) is aprogressive disorder of the nervous system that affects movement. It develops gradually, sometimes starting with a barelynoticeable tremor in speech. It has been found that 80% of persons with PD reported speech and voice disorders.Parkinson's disease symptoms worsen as the condition progresses over time. Therefore, Speech may become soft orslurred and these deficits in speech intelligibility impact on health status and quality of life. Different researchers arecurrently working in the analysis of speech signal of people with PD, including the study of different dimensions in speechsuch as phonation, articulation, prosody, and intelligibility. Here, we present the characteristics and features of normalspeech and speech disorders in people with PD and the types of classification for implementation of the efficacy oftreatment interventions. The results show that our classification algorithm using ANN is outperformed KNN and SVM. ANNis a practical and useful as a predictive tool for PD screening with a high degree of accuracy, approximately 96.1% of acorrect detection rate (sensitivity 94.7%, and specificity 96.6%). Based on the high levels of accuracy obtained by ourproposed algorithm, it can be used for enhancing the detection purpose to discriminate PD patients from healthy people.Our algorithm may be used by the clinicians as a tool to confirm their diagnosis.

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