Pressure Sensitive Nonassociative Plasticity Model for DRA Composites

2006 ◽  
Vol 129 (2) ◽  
pp. 255-264 ◽  
Author(s):  
Xin Lei ◽  
Cliff J. Lissenden
Keyword(s):  
Plastic Deformation ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Yield Function ◽  
Experimental Results ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Plasticity Model ◽  
Backward Euler ◽  
Model Predictions

Discontinuously reinforced aluminum (DRA) is currently used where design considerations include specific stiffness, tailorable coefficient of thermal expansion, or wear resistance. Plastic deformation plays a role in failures due to low cycle fatigue or simple ductile overload. DRA is known to exhibit pressure dependent yielding. Plastic deformation in metals is widely regarded to be incompressible, or very nearly so. A continuum plasticity model is developed that includes a Drucker–Prager pressure dependent yield function, plastic incompressibility via a nonassociative Prandtl–Reuss flow rule, and a generalized Armstrong–Frederick kinematic hardening law. The model is implemented using a return mapping algorithm with backward Euler integration for stability and the Newton method to determine the plastic multiplier. Material parameters are characterized from uniaxial tension and uniaxial compression experimental results. Model predictions are compared to experimental results for a nonproportional compression–shear load path. The tangent stiffness tensor is nonsymmetric because the flow rule is not associated with the yield function, which means that the commonly used algorithms that require symmetric matrices cannot be used with this material model. Model correlations with tension and compression loadings are excellent. Model predictions of shear and nonproportional compression–shear loadings are reasonably good. The nonassociative flow rule could not be validated by comparison of the plastic strain rate direction with the yield function and the flow potential due to scatter in the experimental results. The model is capable of predicting the material response obtained in the experiments, but additional validation is necessary for the condition of high hydrostatic pressure.

Stress update algorithm for non-associated flow metal plasticity

2012 ◽  
Vol 3 (2) ◽  
pp. 106-110
Author(s):  
Mohsen Safaei ◽  
Wim De Waele
Keyword(s):  
Plastic Strain ◽  
Yield Stress ◽  
Kinematic Hardening ◽  
Quadratic Function ◽  
Yield Function ◽  
Plastic Strain Rate ◽  
Isotropic Hardening ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

. In this paper we present the continuum plasticity model based on non-Associated Flow Rule (nonAFR) for Hill’s48 quadratic yield function. In case of non-AFR, Hill’s quadratic function used as plasticpotential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate.In addition, the yield function uses direction dependent yield stress data. Therefore more accuratepredictions are expected in terms of both yield stress and strain ratios at different orientations. Weimplemented a modified version of the non-associative flow rule originally developed by Stoughton [1] intothe commercial finite element code ABAQUS by means of a user material subroutine UMAT. The mainalgorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumesproportional loading cases and therefore only isotropic hardening effect is considered. In our model theincremental change of plastic strain rate tensor is not equal to the incremental change of the compliancefactor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finiteelement simulations with experimentally determined values for deep drawing steel DC06. A criticalcomparison is made between numerical results obtained from AFR and non-AFR based models.

A Crystal Visco-Plastic Model for Ni-Base Superalloys Under Low Cycle Fatigue

2019 ◽  
Author(s):  
Navindra Wijeyeratne ◽  
Firat Irmak ◽  
Grant Geiger ◽  
Jun-Young Jeon ◽  
Ali Gordon
Keyword(s):  
Gas Turbines ◽  
Internal State ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Turbine Blades ◽  
Material Behavior ◽  
Flow Rule ◽  
Loading Conditions ◽  
Analysis Model ◽  
Plastic Model

Abstract Components in gas turbines, specifically turbine blades are subjected to extreme loading conditions such as high temperatures and stresses over extended periods of time; therefore, predicting material behavior and life expectancy at these loading conditions are extremely important. The development of simulations that accurately predict monotonic response for these materials are highly desirable. Single crystal Ni-base superalloys used in the design of gas turbine blades exhibit anisotropic behavior resulting from texture development and dislocation substructures. A Crystal Visco-plastic (CVP) model has the capability of capturing both phenomena to accurately predict the deformation response of the material. The rate dependent crystal visco-plastic model consists of a flow rule and internal state variables. This model considers the inelastic mechanism of kinematic hardening which is captured using the Back stress. Crystal graphic slip is taken in to account by the incorporation of 12 Octahedral slip systems. An implicit integration structure that uses Newton Raphson iteration scheme is used to solve the desired solutions. The MATLAB model is developed in two parts, including a routine for the CVP constitutive model along with a separate routine which functions as an emulator. The emulator replicates a finite element analysis model and provides the initial calculations needed for the CVP. A significant advantage of the MATLAB model is its capability to optimize the modelling constants to increase accuracy. The CVP model has the capability to display material behavior for monotonic loading for a variety of material orientations and temperatures.

A Unified Viscoplastic Model for High Temperature Low Cycle Fatigue of Service-Aged P91 Steel

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
R. A. Barrett ◽  
T. P. Farragher ◽  
C. J. Hyde ◽  
N. P. O'Dowd ◽  
P. E. O'Donoghue ◽  
...  
Keyword(s):  
High Temperature ◽  
Power Plants ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Fatigue Behavior ◽  
Material Model ◽  
Cyclic Softening ◽  
Flow Rule ◽  
Cycle Fatigue ◽  
Hyperbolic Sine

The finite element (FE) implementation of a hyperbolic sine unified cyclic viscoplasticity model is presented. The hyperbolic sine flow rule facilitates the identification of strain-rate independent material parameters for high temperature applications. This is important for the thermo-mechanical fatigue of power plants where a significant stress range is experienced during operational cycles and at stress concentration features, such as welds and branched connections. The material model is successfully applied to the characterisation of the high temperature low cycle fatigue behavior of a service-aged P91 material, including isotropic (cyclic) softening and nonlinear kinematic hardening effects, across a range of temperatures and strain-rates.

scholarly journals Application of an Evolving Non-Associative Anisotropic-Asymmetric Plasticity Model for a Rare-Earth Magnesium Alloy

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1013 ◽  
Author(s):  
Armin Abedini ◽  
Cliff Butcher ◽  
Michael Worswick
Keyword(s):  
Plastic Deformation ◽  
Rare Earth ◽  
Magnesium Alloy ◽  
Constitutive Model ◽  
Magnesium Alloys ◽  
Yield Function ◽  
Flow Rule ◽  
Proportional Loading ◽  
Plastic Potential ◽  
Stress States

Magnesium sheet metal alloys have a hexagonal close packed (hcp) crystal structure that leads to severe evolving anisotropy and tension-compression asymmetry as a result of the activation of different deformation mechanisms (slip and twinning) that are extremely challenging to model numerically. The low density of magnesium alloys and their high specific strength relative to steel and aluminum alloys make them promising candidates for automotive light-weighting but standard phenomenological plasticity models cannot adequately capture the complex plastic response of these materials. In this study, the constitutive plastic behavior of a rare-earth magnesium alloy sheet, ZEK100 (O-temper), was considered at room temperature, under quasi-static conditions. The CPB06 yield criterion for hcp materials was employed along with a non-associative flow rule in which the yield function and plastic potential were calibrated for a range of plastic deformation levels to account for evolving anisotropy under proportional loading. The non-associative flow rule has not previously been applied to magnesium alloys which require the use of flexible constitutive models to capture the severe anisotropy and its evolution with plastic deformation. The non-associative flow rule can provide the required flexibility by decoupling the yield function and plastic potential. For the associative flow rule, such flexibility can only be achieved by multiple linear transformations of the stress tensor resulting in expensive models for calibration and simulations. The constitutive model was implemented as a user material subroutine (UMAT) within the commercial finite element software, LS-DYNA, for general 3-D stress states along with an interpolation technique to consider the evolution of anisotropy based upon the plastic work. To evaluate the accuracy of the implemented model, predictions of a single-element model were compared with the experimental results in terms of flow stresses and plastic flow directions under various proportional loading conditions and along different test directions. Finally, to assess the predictive capabilities of the model, full-scale simulations of coupon-level formability experiments were performed and compared with experimental results in terms of far-field load-displacement and local strain paths. Using these experiments, the constitutive model was evaluated across the full range of representative stress states for sheet metal forming operations. It was shown that the predictions of the model were in very good agreement with experimental data.

A strain rate dependent constitutive model for clays at residual strength

1998 ◽  
Vol 35 (2) ◽  
pp. 364-373 ◽  
Author(s):  
AMP Wedage ◽  
N R Morgenstern ◽  
D H Chan
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Residual Strength ◽  
Plasticity Theory ◽  
Constitutive Relationship ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Rate Dependent ◽  
Dependent Part ◽  
Rate Effects

Plasticity theory is extended to incorporate strain rate effects on the residual shear strength of clays. The clay is assumed to behave elastically before yielding and then in a perfectly plastic manner with no volume change during yielding. The Mohr-Coulomb failure criterion is used in the rate-dependent model in which the strain rate affects the mobilized effective friction angle of the material. During initial yielding and subsequent plastic deformation, the stress and strain states at a point will satisfy the rate-dependent yield function (loading function). When the effective plastic strain rate decreases to a threshold strain value, the loading surface moves, or collapses, to the static yield surface. A constant volume flow rule is used to calculate plastic deformation. The computed stress-strain relationship is formulated in two parts, namely a rate-independent part and a rate-dependent part. The rate-independent part is the same as that used in classical elastoplastic formulations, whereas the rate-dependent part is dependent on the current strain rate of the material. The use of the model is illustrated using a numerical example simulating a two-dimensional plane strain test.Key words: constitutive relationship, finite element, plasticity theory, pre-sheared clay, rate effects, residual strength.

scholarly journals Influences of Material Variations of Functionally Graded Pipe on the Bree Diagram

2020 ◽  
Vol 10 (8) ◽  
pp. 2936 ◽  
Author(s):  
Aref Mehditabar ◽  
Saeid Ansari Sadrabadi ◽  
Raffaele Sepe ◽  
Enrico Armentani ◽  
Jason Walker ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Bending Moment ◽  
Yield Function ◽  
Functionally Graded ◽  
Loading Conditions ◽  
Mapping Algorithm ◽  
First Case ◽  
Backward Euler

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram.

Gradient plasticity in isotropic solids

2021 ◽  
pp. 108128652110502
Author(s):  
D. J. Steigmann
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Plastic Deformation ◽  
Plastic Strain ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Order Partial Differential Equation ◽  
Riemannian Curvature ◽  
Gradient Plasticity ◽  
Isotropic Solids

We discuss a framework for the description of gradient plasticity in isotropic solids based on the Riemannian curvature derived from a metric induced by plastic deformation. This culminates in a flow rule in the form of a fourth-order partial differential equation for the plastic strain rate, in contrast to the second-order flow rules that have been proposed in alternative treatments of gradient plasticity in isotropic solids.

Evaluation of Associated and Non-Associated Flow Metal Plasticity; Application for DC06 Deep Drawing Steel

2012 ◽  
Vol 504-506 ◽  
pp. 661-666 ◽  
Author(s):  
Mohsen Safaei ◽  
Wim De Waele ◽  
Shun Lai Zang
Keyword(s):  
Finite Element ◽  
Plastic Strain ◽  
Strain Rate ◽  
Yield Stress ◽  
Deep Drawing ◽  
Kinematic Hardening ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Strain Rate Tensor ◽  
Incremental Change

In this paper the capabilities of Associated Flow Rule (AFR) and non-AFR based finite element models for sheet metal forming simulations is investigated. In case of non-AFR, Hill’s quadratic function used as plastic potential function, makes use of plastic strain ratios to determine the direction of effective plastic strain rate. In addition, the yield function uses direction dependent yield stress data. Therefore more accurate predictions are expected in terms of both yield stress and strain ratios at different orientations. We implemented a modified version of the non-associative flow rule originally developed by Stoughton [1] into the commercial finite element code ABAQUS by means of a user material subroutine UMAT. The main algorithm developed includes combined effects of isotropic and kinematic hardening [2]. This paper assumes proportional loading cases and therefore only isotropic hardening effect is considered. In our model the incremental change of plastic strain rate tensor is not equal to the incremental change of the compliance factor. The validity of the model is demonstrated by comparing stresses and strain ratios obtained from finite element simulations with experimentally determined values for deep drawing steel DC06. A critical comparison is made between numerical results obtained from AFR and non-AFR based models

Extension of Generalized Plasticity Model for Thermocyclic Loading

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
J. C. Sobotka ◽  
R. H. Dodds
Keyword(s):  
Large Scale ◽  
Energy Functional ◽  
Rate Equations ◽  
Plastic Strain Rate ◽  
Integration Scheme ◽  
Plasticity Model ◽  
Computationally Efficient ◽  
Flow Equations ◽  
Generalized Plasticity ◽  
Backward Euler

This work extends the generalized plasticity model for structural metals under cyclic loading proposed by Lubliner et al. (1993, “A New Model of Generalized Plasticity and its Numerical Implementation,” Int. J. Solids Struct., 22, pp. 3171–3184) to incorporate temperature-dependence into the elastic-plastic response. Proposed flow equations satisfy the Clausius–Duhem inequality through a thermodynamically consistent energy functional and retain key aspects of conventional plasticity models: Mises yield surface, normal plastic flow, and additive decomposition of strain. Uniaxial specialization of the 3D rate equations leads to a simple graphical method to estimate model properties. The 3D integration scheme based on backward Euler discretization leads to a scalar quadratic expression to determine the plastic strain rate multiplier and has a symmetric algorithmic tangent matrix. Both properties of the integration lead to a computationally efficient implementation especially suited to large-scale, finite element analyses. In comparison studies using experimental data from a Cottrell–Stokes test, the modified rate equations for the generalized plasticity model capture a thermally activated increase in the flow stress.

A Unified Viscoplastic Model for High Temperature Low Cycle Fatigue of Service-Aged P91 Steel

2013 ◽  
Author(s):  
R. A. Barrett ◽  
P. E. O’Donoghue ◽  
S. B. Leen
Keyword(s):  
High Temperature ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Material Model ◽  
Fatigue Behaviour ◽  
Cyclic Softening ◽  
Flow Rule ◽  
Strain Rates ◽  
Cycle Fatigue ◽  
Hyperbolic Sine

The finite element (FE) implementation of a hyperbolic sine unified cyclic viscoplasticity model is presented. The hyperbolic sine flow rule facilitates the identification of strain-rate independent material parameters for high temperature applications. This is important for the thermo-mechanical fatigue of power plant where a significant stress range is experienced during operational cycles and at stress concentration features, such as welds and branch connections. The material model is successfully applied to the characterisation of the high temperature low cycle fatigue behaviour of a service-aged P91 material, including isotropic (cyclic) softening and non-linear kinematic hardening effects, across a range of temperatures and strain-rates.

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