Shakedown Fatigue Limits for Materials With Minute Porosity

2009 ◽  
Vol 76 (3) ◽  
Author(s):  
Jehuda Tirosh ◽  
Sharon Peles
Keyword(s):  
Porous Materials ◽  
Endurance Limit ◽  
Stress Amplitude ◽  
Material Behavior ◽  
Space Industry ◽  
Pressure Dependency ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Gurson's Model ◽  
Dual Bounds

The intention of this study is to predict the fatigue-safe long life behavior of elastoplastic porous materials subjected to zero-tension fluctuating load. It is assumed that the materials contain a dilute amount of voids (less than 5%) and obey Gurson’s model of plastic yielding. The question to be answered is what would be the highest allowable stress amplitude that a porous material can endure (the “endurance limit”) when undergoing an infinite number of loading/unloading cycles. To reach the answer we employ the two shakedown theorems: (a) Melan’s static shakedown theorem (“elastic shakedown”) for establishing the lower bound to fatigue limit and (b) Koiter’s kinematic shakedown theorem (“plastic shakedown”) for establishing its upper bound. The two bounds are formulated rigorously but solved with some numerical assistance, mainly due to the nonlinear pressure dependency of the material behavior and the complex description of the plastic flow near stress-free voids. Both bounds (“dual bounds”) are adjusted to capture Gurson-like porous materials with noninteractive voids. General residual stresses (either real or virtual) are presented in the analysis. They are assumed to be time-independent as generated, say, by permanent temperature gradient between void surfaces and remote material boundaries. Such a situation is common, for instance, in ordinary porous sleeves (used in space industry and alike). A few experiments agree satisfactorily with the shakedown bounding concept.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Material Behavior ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavior, and demonstrates the connection to Melan's theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Local vs. Global Ratcheting in Cracked Structures

2014 ◽  
Author(s):  
R. Adibi-Asl ◽  
Wolf Reinhardt
Keyword(s):  
Cyclic Loading ◽  
Component Structure ◽  
Elastic Range ◽  
Cracked Structures ◽  
Elastic Shakedown ◽  
Plastic Shakedown ◽  
Time Invariant ◽  
Global And Local ◽  
Mean Time ◽  
Cracked Structure

The classical approaches in shakedown analysis are based on the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. The Non-Cyclic Method (NCM) has been proposed recently to determine both the elastic and the plastic ratchet boundary of a component or structure under cyclic loading by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. When a cracked structure is subjected to cyclic loading, the crack and its vicinity behave differently (local) than the rest of the structure (global). The crack may propagate during the application of cyclic loading. This will affect both local and global behavior of the cracked structure. This paper investigates global and local ratcheting of the cracked structures using the NCM and fracture mechanic parameters.

A Non-Cyclic Method for Plastic Shakedown Analysis

2003 ◽  
Author(s):  
W. Reinhardt
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Computing Time ◽  
Strain Accumulation ◽  
Analysis Method ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Cyclic Phenomenon ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Shakedown is a cyclic phenomenon, and for its analysis it seems natural to employ a cyclic analysis method. Two problems are associated when this direct approach is used in finite element analysis. Firstly, the analysis typically needs to be stabilized over several cycles, and the analysis of each individual cycle may need a considerable amount of computing time. Secondly, even in cases where a stable cycle is known to exist, the finite element analysis can show a small continuing amount of strain accumulation. For elastic shakedown, non-cyclic analysis methods that use Melan’s theorem have been proposed. The present paper extends non-cyclic lower bound methods to the analysis of plastic shakedown. The proposed method is demonstrated with several example problems.

scholarly journals Shakedown of a Thick Cylinder With a Radial Crosshole

2006 ◽  
Author(s):  
Duncan Camilleri ◽  
Donald Mackenzie ◽  
Robert Hamilton
Keyword(s):  
Thermal Loading ◽  
Constant Pressure ◽  
Element Analysis ◽  
Cyclic Thermal Loading ◽  
Interaction Diagram ◽  
Thin Cylinder ◽  
Structural Discontinuity ◽  
Thick Cylinder ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The shakedown behaviour of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behaviour of a thin cylinder, a thick cylinder and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree Diagram. Incorporating the radial crossbore in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole can therefore be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in Design by Analysis.

Direct Analysis of Post-Shakedown Quantities With the STPZ Considering Multi-Parameter Loading

2019 ◽  
Author(s):  
Bastian Vollrath ◽  
Hartwig Hübel
Keyword(s):  
Direct Method ◽  
Kinematic Hardening ◽  
Direct Analysis ◽  
Load Cycle ◽  
Material Behavior ◽  
Plastic Behavior ◽  
Method Effects ◽  
Plastic Shakedown ◽  
Initial Strains ◽  
Incremental Step

Abstract If a structure is subjected to cyclic loading, strain, displacements etc. may accumulate cycle by cycle due to a ratcheting mechanism. Design Codes frequently require strain limits to be satisfied at the end of the specified lifetime of the structure. Usually, this is requested to be done considering all load sets pairwise. However, this leads to the fact that ratcheting cannot be detected, if it occurs only because of multi-parameter loading. Ordinary incremental step-by-step calculations can easily exceed time and hardware resources. This is particularly true for travelling loads, where many load steps are required for one load cycle. As an alternative, the Simplified Theory of Plastic Zones (STPZ) is used in the present paper. Being a direct method, effects from load history are disregarded. The elastic-plastic behavior in the state of either elastic or plastic shakedown is estimated on the basis of purely elastic analyses. Two kinds of linear elastic analyses are to be performed, fictitious elastic analyses for each set of loading, and a number of modified elastic analyses. Few of these analyses are usually sufficient to obtain reasonable estimates of the post-shakedown quantities. Trilinear material behavior is adopted along with kinematic hardening, a Mises yield surface and an associated flow law. The modified elastic analyses are performed making use of modified elastic parameters (Young’s modulus and Poisson’s ratio) in the plastic zone and applying suitably defined initial strains. The results obtained can be improved iteratively. The theory of the method is briefly explained and its application is shown using an example with multi-parameter loading.

Finite Element Based Automated Analysis for Determining Ratchet, Shakedown and Elastic Limits

2011 ◽  
Author(s):  
Jeries Abou-Hanna ◽  
Michael Paluszkiewicz
Keyword(s):  
Finite Element ◽  
Cyclic Load ◽  
Complex Geometry ◽  
Limit Load ◽  
Automated Analysis ◽  
Numerical Approach ◽  
Material Behavior ◽  
Element Analysis ◽  
Daunting Task ◽  
Elastic Shakedown

In order to determine the ratchet and shakedown limit curves for even a simple component, such as a tube under a constant pressure load and cyclic thermal load, can be a daunting task when using conventional analysis methods (elasto-plastic cyclic finite element analysis) that require repeated iterative simulations to determine the state of the structure, elastic, shakedown, plastic or ratchet. In some cases, the process is further complicated by the difficulty in interpreting results of the cyclic loading to determine in which regime the structure is. Earlier work by Abou-Hanna and McGreevy was able to demonstrate limit load analysis of a structure whose yield strength is modified based on cyclic load, provided the ratchet limit [1]. The method, called Anisotropic Load Dependent Yield Modification (LDYM), was implemented by using a user subroutine with ABAQUS, a general commercial finite element code. The approach adopted provided ratchet limits for only one individual cyclic load value. The work presented here describes a process for analyzing the structure and determining the elastic, shakedown and ratchet boundaries all in one finite element simulation using only one analysis step. The approach manipulates the structure material behavior that enables the resetting of the material characteristics to their original values in order to be able to analyze the structure for different sets of cyclic and primary load combinations. The process was verified using problems available in the literature, such as the Bree tube and Ponter’s Holed Plate. Additionally, a tubular T-joint was used as an example of the effectiveness of the process for a three dimensional complex geometry. The tubular T-joint results are verified against baseline data from the iterative elastic-plastic simulations used to determine the elastic, shakedown, and ratchet limits. The work presented highlights the advantages and limitations of this numerical approach which requires little interaction with the analyst.

A Nonlinear Least Squares Logistic Fit Approach to Quantifying Uncertainty in Fatigue Stress-Life Models and an Application to Plain Concrete

2018 ◽  
Author(s):  
Jeffrey T. Fong ◽  
N. Alan Heckert ◽  
James J. Filliben ◽  
Paul H. Ziehl
Keyword(s):  
Least Squares ◽  
Endurance Limit ◽  
Stress Amplitude ◽  
Plain Concrete ◽  
Cyclic Stress ◽  
Logistic Function ◽  
Fatigue Stress ◽  
Least Squares Fit ◽  
Horizontal Asymptote ◽  
Number Of Cycles

A large number of fatigue life models for engineering materials such as concrete and steel are simply a linear or nonlinear relationship between the cyclic stress amplitude, σa, and the log of the number of cycles to failure, Nf. In the linear case, the relationship is a power-law relation between σa and Nf, with two constants determined by a linear least squares fit algorithm. The disadvantage of this simple linear fit of fatigue test data is that it fails to predict the existence of an endurance limit, which is defined as the cyclic stress amplitude at which the number of cycles is infinity. In this paper, we introduce a nonlinear least square fit based on a 4-parameter logistic function, where the curve of the y vs. x plot will have two horizontal asymptotes, namely, y0, at the left infinity, and y1, at the right infinity with y1 < y0 to simulate a fatigue model with a decreasing y for an increasing x. In addition, we need a third parameter, k, to denote the slope of the curve as it traverses from the left horizontal asymptote to the lower right horizontal asymptote, and a fourth parameter, x0, to denote the center of the curve where it crosses a horizontal line half-way between y0 and y1. In this paper, the 4-parameter logistic function is simplified to a 3-parameter function as we apply it to model a fatigue sress-life relationship, because in a stress-log (life) plot, the left upper horizontal asymptote, y0, can be assumed as a constant equal to the static ultimate strength of the material, U0. This simplification reduces the logistic function to the following form: y = U0 − (U0 − y1) / (1 + exp(−k (x − x0)), where y = σa, and x = log(Nf). The fit algorithm allows us to quantify the uncertainty of the model and the estimation of an endurance limit, which is the parameter, y1. An application of this nonlinear modeling technique is applied to fatigue data of plain concrete in the literature with excellent results. Significance and limitations of this new fit algorithm to the interpretation of fatigue stress-life data are presented and discussed.

On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load

1993 ◽  
Vol 60 (1) ◽  
pp. 20-25 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Limit State ◽  
Limit Load ◽  
Companion Paper ◽  
Material Structure ◽  
Perfectly Plastic ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.

Ratchet Limit Solution of a Beam With Arbitrary Cross Section

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt
Keyword(s):  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Fundamental Idea ◽  
Component Structure ◽  
Elastic Range ◽  
Limit Solution ◽  
Thin Walled Pipe ◽  
Bending Loads ◽  
Elastic Shakedown ◽  
Plastic Shakedown

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “noncyclic method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan's theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin-walled pipe are investigated.

Effect of Moisture Content on the Shakedown Limits of Base Course Materials

2020 ◽  
pp. 036119812095731
Author(s):  
Munir D. Nazzal ◽  
Louay N. Mohammad ◽  
Aaron Austin ◽  
Ahmad Al Hosainat
Keyword(s):  
Moisture Content ◽  
Triaxial Tests ◽  
Course Materials ◽  
Base Materials ◽  
Multi Stage ◽  
Base Course ◽  
Granular Base ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Plastic Shakedown

This paper summarizes the results of a laboratory testing program that was conducted to determine the effects of moisture content on the shakedown limits of unbound granular base materials. Two different types of granular base materials were investigated in this study, namely limestone and sandstone. Multi-stage repeated load triaxial tests were performed on these materials. The results of the tests were analyzed within the framework of the shakedown theory. The results indicate that the moisture content had an influence on the slope of the elastic and plastic shakedown limits lines. The effect of the moisture content was more pronounced on the slope of the elastic shakedown limit line, however. The moisture content affected the intercept of the elastic and plastic shakedown limits lines more significantly than the slope of these lines. The limestone material exhibited greater decrease in the intercept of the elastic and plastic shakedown limits with increase in moisture content compared with the sandstone material. This was explained by the limestone’s finer gradation.

Sign in / Sign up

Export Citation Format

Share Document