Adrian Willuweit

Use of the Elastic Predictor-Plastic Corrector Method for Integrating Finite Deformation Plasticity Laws

Classical plasticity theories are formulated by means of ordinary differential equations coupled with algebraic equations, so that the whole system of equations governing the material response is highly nonlinear. To integrate these equations, particular algorithms have been developed, the method of elastic predictor and plastic corrector being often used. This method has turned out to be a very efficient tool, when small deformation plasticity is considered. Especially, the usual constraint condition of plastic incompressibility is preserved exactly. However, when nonlinear geometry is involved, there are several possibilities to employ the method of elastic predictor and plastic corrector. Moreover, some effort has to be made, in order to ensure plastic incompressibility. The exponential map approach is one possibility to overcome the difficulties, but this approach is not suitable when deformation induced anisotropy is considered. The present work addresses the numerical integration of finite deformation plasticity models exhibiting both, isotropic and kinematic hardening. The integration of the evolution equations is based on the elastic predictor and plastic corrector procedure, appropriately adjusted to the structure of the adopted constitutive theory. Plastic incompressibility is preserved by introducing a further unknown into the system of equations to be solved numerically.

Using the Nonlinear Kinematic Hardening Material Model of Chaboche for Elastic–Plastic Ratcheting Analysis

Commonly used design codes for power plant components and pressure vessels include rules for ratcheting analysis that specify limits on accumulated strain. No guidance is provided on the use of the material model. The objective of the paper is to provide guidance that may be helpful to analysts. The Chaboche nonlinear kinematic (NLK) hardening material model is chosen as an appropriate model. Two methods are selected for its calibration that can determine the parameters for stainless steels. One is manual that requires no outside software and the other uses finite element software. Both are based on the monotonic stress–strain curve obtained from a tension specimen. The use of the Chaboche parameters for cases when ratcheting is caused by cyclic temperature fields is selected as the example of an application. The conclusion is that the number of allowable design cycles is far higher when using the parameters with temperature dependency than those at the constant maximum temperature that is being cycled.

Using Nonlinear Kinematic Hardening Material Models for Elastic-Plastic Ratcheting Analysis

Applicable design codes for power plant components and pressure vessels demand for a design check against progressive plastic deformation. In the simplest case, this demand is satisfied by compliance with shakedown rules in connection with elastic analyses. The possible non-compliance implicates the requirement of ratcheting analyses on elastic-plastic basis. In this case, criteria are specified on maximum allowable accumulated growth strain without clear guidance on what material models for cyclic plasticity are to be used. This is a considerable gap and a challenge for the practicing CAE (Computer Aided Engineering) engineer.As a follow-up to two independent previous papers PVP2013-98150 ASME [1] and PVP2014-28772 [2] it is the aim of this paper to close this gap by giving further detailed recommendation on the appropriate application of the nonlinear kinematic material model of Chaboche on an engineering scale and based on implementations already available within commercial finite element codes such as ANSYS® and ABAQUS®. Consistency of temperature-dependent runs in ANSYS® and ABAQUS® is to be checked. All three papers together constitute a comprehensive guideline for elasto-plastic ratcheting analysis.The following issues are examined and/or referenced:• Application of monotonic or cyclic material data for ratcheting analysis based on the Chaboche material model• Discussion of using monotonic and cyclic data for assessment of the (non-stabilized) cyclic deformation behavior• Number of backstress terms to be applied for consistent ratcheting results• Consideration of the temperature dependency of the relevant material parameters• Consistency of temperature-dependent runs in ANSYS® and ABAQUS®• Identification of material parameters dependent on the number of backstress terms• Identification of material data for different types of material (carbon steel, austenitic stainless steel) including the appropriate determination of the elastic limit• Quantification of conservatism of simple elastic-perfectly plastic behavior• Application of engineering versus true stress-strain data• Visual checks of data input consistency• Appropriate type of allowable accumulated growth strain.This way, a more accurate inelastic analysis methodology for direct practical application to real world examples in the framework of the design code conforming elasto-plastic ratcheting check is proposed.Copyright

Simulation of the Creep and Fatigue Damages in High-CR Steel Components Based on a Modified Becker-Hackenberg Model

Components of conventional power plants are subject to three potential damage mechanisms and their combination (accumulation) with impact on lifetime considerations: creep, fatigue and ratcheting. Currently, there is a growing need for advanced material models which are able to simulate these damage phenomena and can be implemented effectively within finite-element (FE) codes. This constitutes the basis of an advanced component design. In this work, a constitutive material model, named as the modified Becker-Hackenberg model, is proposed to simulate the thermo-mechanical behavior of high-Cr steel components subject to complex loading conditions. Both creep and viscoplasticity are taken into account in the model, which are viewed as two different kinds of inelastic mechanisms. The key features of the creep strain, i.e., the minimum creep rate and the average creep rupture time, are evaluated by using two Larson-Miller parameters. The cyclic viscoplastic strain is predicted through the conventional Chaboche-type modeling approach, where suitable constitutive evolution equations are adopted to capture the cyclic softening effect, ratcheting effect, time recovery effect and temperature rate effect. All the material parameters involved in this model are identified by using a strategy of stress-range separation. This constitutive model is further implemented in a commercial FE software to simulate the thermo-mechanical behaviors of high-Cr steel components with technologically relevant dimensions. The strain and stress evolution data obtained from the model can be further used for the fatigue damage assessment of high-Cr steel components subject to creep-fatigue interactions. Within an ongoing work, a multiaxial fatigue analyzer is developed to predict the fatigue lifetime of high-Cr steels subject to cyclic loading conditions respectively — in a further step — creep-fatigue interaction.Copyright

Using the Nonlinear Kinematic Hardening Material Model of Chaboche for Elastic-Plastic Ratcheting Analysis

Two calibration processes are selected for determining the parameters of the Chaboche nonlinear kinematic hardening (NLK) material model for stainless steel. One process is manual that requires no outside software and the other follows a finite element software. The basis of the calibration is the monotonic stress-strain curve obtained from a tension specimen subjected to unidirectional loading. The Chaboche model is meant for elastic-plastic ratcheting analysis that is included in commonly used design codes. It is chosen because it is known that it can represent realistically the materials that are used for power plant components and pressure vessels. To test the calibration results, a pressurized cylindrical shell subjected to thermal cycling is selected as an example. It was found that, for the example, no more than four Chaboche components should be used in the determination of its parameters.Copyright

Performance Study of the Simplified Theory of Plastic Zones for the Fatigue Check

As elastic-plastic fatigue analyses are still time consuming the simplified elastic-plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (Ke-factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with Ke correction, b) direct methods for the determination of stabilized elastic-plastic strain ranges and c) incremental elastic-plastic methods for the determination of stabilized elastic-plastic strain ranges.The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka’s method). Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed.Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic-plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic-plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication.Copyright