The restricted influence of kinematic hardening on shakedown loads pdfauthor (original) (raw)
Related papers
The restricted influence of kinematic hardening on shakedown loads
Structural design analyses are conducted with the aim of verifying the exclusion of ratcheting. To this end it is important to make a clear distinction between the shakedown range and the ratchetting range. In cyclic plasticity more sophisticated hardening models have been suggested in order to model the strain evolution observed in ratchetting experiments. The hardening models used in shakedown analysis are comparatively simple. It is shown that shakedown analysis can make quite stable predictions of admissible load ranges despite the simplicity of the underlying hardening models. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis. Both give identical or similar shakedown ranges. Structural shakedown analyses show that the loading may have a more pronounced effect than the hardening model.
Mechanics Research Communications, 2009
In this paper, shakedown analysis for plasticity models with hardening is considered by using the framework of implicit standard materials. It is shown that the concept of bipotential allows not only to retrieve some classical results in associated plasticity but also to consider non-associated laws e.g. the non-linear kinematic hardening rule. Furthermore, the comparison of the shakedown load for the three kinds of hardening on an example shows substantial differences and thus the importance of considering the non-linear kinematic hardening in shakedown analysis.
Shakedown and ratchetting under tension–torsion loadings: analysis and experiments
Nuclear Engineering and Design, 2003
Structural design analyses are conducted with the aim of verifying the exclusion of ratchetting. To this end it is important to make a clear distinction between the shakedown range and the ratchetting range. The performed experiment comprised a hollow tension specimen which was subjected to alternating axial forces, superimposed with constant moments. First, a series of uniaxial tests has been carried out in order to calibrate a bounded kinematic hardening rule. The load parameters have been selected on the basis of previous shakedown analyses with the PERMAS code using a kinematic hardening material model. It is shown that this shakedown analysis gives reasonable agreement between the experimental and the numerical results. A linear and a nonlinear kinematic hardening model of two-surface plasticity are compared in material shakedown analysis.
Shakedown Analysis Considering Limited Kinematic Hardening Materials
2016
In design or safety assessment of mechanical structures, the use of the Design by Analysis (DBA) route is a modern trend. However, for making possible to apply DBA to structures under variable loads, two basic failure modes considered by ASME or European Standards must be precluded. Those modes are the alternate plasticity and incremental collapse (with instantaneous plastic collapse as a particular case). Shakedown theory is a tool that permit us to assure that those kinds of failures will be avoided. However, in practical applications, very large nonlinear optimization problems are generated. Due to this facts, only in recent years have been possible to obtain algorithms sufficiently accurate, robust and efficient, for dealing with this class of problems. In this paper, one of these shakedown algorithms, developed for dealing with elastic ideally-plastic structures, is enhanced to include limited kinematic hardening, a more realistic material behavior. This is done in the continuo...
Shakedown analysis of engineering structures with limited kinematical hardening
International Journal of Solids and Structures
We present a numerical method for the computation of shakedown loads of engineering structures with limited kinematical hardening under thermo-mechanical loading. The method is based on Melan's statical shakedown theorem, which results in a nonlinear convex optimization problem. This is solved by an interior-point algorithm recently developed by the authors, specially designed for lower bound shakedown analysis of large-scale problems. Limited kinematical hardening is taken into account by use of a two-surface model, such that both alternating plasticity and incremental collapse can be captured. For the yield surface as well as for the bounding surface the von Mises criterion is used. The proposed method is validated by two examples, where numerical results are compared to those of literature where available.
European Journal of Mechanics - A/Solids, 2019
This paper presents a novel direct method for the structural shakedown analysis considering limited kinematic hardening and non-isothermal effect. The Melan's static shakedown theorem is extended to consider limited kinematic hardening material and implemented into the Linear Matching Method (LMM) shakedown module. Instead of using a specific kinematic hardening rule and an explicit back stress field, the general nonlinear hardening laws are considered by using a two-surface hardening model. A two-stage procedure is developed in the extended LMM algorithm, which can generate the limited hardening shakedown envelope and the unlimited hardening curve efficiently and accurately. Also, the material non-isothermal effect is considered during the computation process of the shakedown limit by proposing a temperature-dependent hardening factor, in place of a constant and fictitious one. To validate the extended LMM method, a numerical test on a thin cylinder pipe with temperature-independent material properties is performed, and the results match well with ones from literature. Then, a numerical study on a typical aero-engine turbine disk is conducted to investigate the influence of temperature-dependent material properties and operating conditions. Several shakedown curves considering kinematic hardening effect are derived and adequately discussed. As a result, the extended LMM shakedown module is proven to be a robust, efficient and versatile tool for practical industrial problems.
FEM-based shakedown analysis of hardening structures
Asia Pacific Journal on Computational Engineering, 2014
This paper develops a new finite element method (FEM)-based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple two-surface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the back-stress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
International Journal of Solids and Structures, 2006
The class of generalized standard materials is not relevant to model the nonassociative constitutive equations. The bipotential approach, based on a possible generalization of FenchelÕs inequality, allows the recovery of the flow rule normality in a weak form of an implicit relation. This defines the class of implicit standard materials. For such behaviours, this leads to a weak extension of the classical bound theorems of the shakedown analysis. In the present paper, we recall the relevant features of this theory. Considering an elastoplastic material with nonlinear kinematic hardening rule, we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain. The aim of the paper is to prove the exactness of the solution for this example by comparing it to step-by-step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level. A reliable criterion to stop the computations is proposed. The analytical and numerical solutions are compared and found to be closed one of each other. Moreover, the method allows uncovering an additional Ô2 cycle shakedown curveÕ that could be useful for the shakedown design of structure.
2011
This thesis develops a new FEM based algorithm for shakedown analysis of structures made of elastic plastic bounded linearly kinematic hardening material. Its concept can be briefly described as: Hardening law is simulated using a two-surface plastic model. One yield surface is the initial surface, defined by yield stress y , and the other one is the bounding surface, defined by ultimate strength u . The initial surface can translate inside the bounding surface without changing its shape and size. The subsequent yield surface is bounded by one of the two following conditions: (1) it always stays inside the bounding surface, or (2) its centre cannot move outside the back-stress surface, where the back-stress surface is defined by uy . Both ways of bounding are equivalent. The subsequent yield surface may touch the bounding surface, it means ratchetting occurs and benefit of hardening is quite clear, or it may not touch the bounding surface, it means alternating occurs, and there is no effect of hardening. If yu , the two-surface model becomes elastic perfectly plastic model, and if 2 uy , the model becomes unbounded kinematic hardening model. Since the two-surface model bases only on yield stress and ultimate strength, so it does not depend on the hardening curve, consequently it is linear kinematic hardening. Direct methods lead to plastic limit and shakedown bounds directly. They help to reduce considerably computing costs and numerical errors, and make the solution simpler. Mathematically, the shakedown problem is considered as a nonlinear programming problem. Starting from upper bound theorem, shakedown bound is the minimum of the plastic dissipation function, which is based on von Mises yield criterion, subjected to compatibility, incompressibility and normalized constraints. This constraint nonlinear optimization problem is solved by combined penalty function and Lagrange multiplier methods.