Hélder F. S. G. Pereira

Fatigue Damage Behavior of a Structural Component Made of P355NL1 Steel Under Block Loading

The common design practice of pressure vessels subjected to variable amplitude loading is based on the application of a linear damage summation rule, also known as the Palmgren-Miners rule. Even though damage induced by small stress cycles, below the fatigue limit, are often taken into account in design codes of practice by two-slope stress-life curves, the sequential effects of the load history have been neglected. Several studies have shown that linear damage summation rules can predict conservative as well as nonconservative lives depending on the loading sequence. This paper presents experimental results about the fatigue damage accumulation behavior of a structural component made of P355NL1 steel, which is a material usually applied for pressure vessel purposes. The structural component is a rectangular double notched plate, which was subjected to block loading. Each block is characterized by constant remote stress amplitude. Two-block sequences were applied for various combinations of remote stress ranges. Three stress ratios were considered, namely, R =0, R =0.15, and R =0.3. Also, constant amplitude fatigue data are generated for the investigated structural component. In general, the block loading illustrates that the fatigue damage evolves nonlinearly with the number of load cycles and is a function of the load sequence, stress levels, and stress ratios. In particular, a clear load sequence effect is verified for the two-block loading, with null stress ratio. For the other (higher) stress ratios, the load sequence effect is almost negligible; however the damage evolution still is nonlinear. This suggests an important effect of the stress ratio on fatigue damage accumulation.

Analysis of Constant and Variable Amplitude Strain-Life Data Using a Novel Probabilistic Weibull Regression Model

The relation between the total strain amplitude and the fatigue life measured in cycles is usually given as strain-life curves based on the former proposals of Basquin, for the elastic strain-life, and Coffin-Manson, for the plastic strain-life. In this paper, a novel Weibull regression model, based on an existing well established Weibull model for the statistical assessment of stress-life fatigue data, is proposed for the probabilistic definition of the strain-life field. This approach arises from sound statistical and physical assumptions and not from an empirical proposal insufficiently supported. It provides an analytical probabilistic definition of the whole strain-life field as quantile curves, both in the low-cycle and high-cycle fatigue regions. The proposed model deals directly with the total strain, without the need of separating its elastic and plastic strain components, permit dealing with run-outs, and can be applied for probabilistic lifetime prediction using damage accumulation. The parameters of the model can be estimated using different well established methods proposed in the fatigue literature, in particular, the maximum likelihood and the two-stage methods. In this work, the proposed model is applied to analyze fatigue data, available for a pressure vessel material—the P355NL1 steel— consisting of constant amplitude, block, and spectrum loading, applied to smooth specimens, previously obtained and published by authors. A new scheme to deal with variable amplitude loading in the background of the proposed regression strain-life Weibull model is described. The possibility to identify the model constants using both constant amplitude and two-block loading data is discussed. It is demonstrated that the proposed probabilistic model is able to correlate the constant amplitude strain-life data. Furthermore, it can be used to correlate the variable amplitude fatigue data if the model constants are derived from two-block loading data. The proposed probabilistic regression model is suitable for reliability analysis of notched details in the framework of the local approaches.

Cyclic and Fatigue Behavior of the P355NL1 Steel Under Block Loading

Current fatigue analyses of metallic structures undergoing variable amplitude loading, including pressure vessels, are mostly based on linear cumulative damage concepts, as proposed by Palmgren and Miner. This type of analysis neglects any sequential effects of the loading history. Several studies have shown that linear cumulative damage theories can produce inconsistent fatigue life predictions. In this paper, both fatigue damage accumulation and cyclic elastoplastic behaviors of the P355NL1 steel are characterized using block loading fatigue tests. The loading is composed of blocks of constant strain-controlled amplitudes, applied according to two and multiple alternate blocks sequences. Also, loading composed by blocks of variable strain-controlled amplitudes are investigated. The block loading illustrates that fatigue damage evolves nonlinearly with the number of load cycles, as a function of the block strain amplitudes. These observations suggest a nonlinear damage accumulation rule with load sequential effects for the P355NL1 steel. However, the damage accumulation nonlinearity and load sequential effects are more evident for the two block loading rather than for multiple alternate block sequences, which suggests that the linear Palmgren-Miner rule tends to produce better results for more irregular loading histories. Some phenomenological interpretations for the observed trends are discussed under a fracture mechanics framework.

Analysis of Variable Amplitude Fatigue Data of the P355NL1 Steel Using the Effective Strain Damage Model

This paper proposes an analysis of variable amplitude fatigue data obtained for the P355NL1 steel, using a strain-based cumulative damage model. The fatigue data consist of constant and variable amplitude block loading, which was applied to both smooth and notched specimens, previously published by the authors. The strain-based cumulative damage model, which has been proposed by D.L. DuQuesnay is based on the growth and closure mechanisms of microcracks. It incorporates a parameter termed net effective strain range, which is a function of the microcrack closure behavior and inherent ability to resist fatigue damage. A simplified version of the model is considered, which assumes crack closure at the lowest level for the entire spectrum and does not account for varying crack opening stresses. In general, the model produces conservative predictions within an accuracy range of two on lives, for both smooth and notched geometries, demonstrating the robustness of the model.

Cyclic Elastoplastic Analysis of Structures Concerning a Fatigue Assessment According to the Local Strain Approach: An Overview

This Technical Brief presents an overview about the current methodologies for elastoplastic calculation of structures undergoing cyclic loading, aiming a fatigue assessment according to the local strain approaches. The possibilities and limitations of the plasticity models available in most popular commercial finite element codes are discussed. Also, several methodologies for structural elastoplastic analysis, concerning the derivation of the stabilized material response, are also addressed highlighting their potentialities and drawbacks. The discussion proposed in this Technical Brief is intended as guidance for design engineers needing to ponder all calculation alternatives for assessing fatigue damage parameters before a rational decision is carried out, in the framework of local approaches to fatigue.

Fatigue Modeling of a Notched Flat Plate Under Variable Amplitude Loading Supported by Elastoplastic Finite Element Method Analyses

Although intensive research has been carried out to understand the fatigue behavior of steel notched components, under variable amplitude loading, no definite and general robust models have been derived so far. Therefore, every effort to augment the knowledge in this topic is welcomed. Within this context, existing variable amplitude data, derived by the authors for a notched low carbon pressure vessel steel (P355NL1) flat plate, is used to assess a local approach to fatigue. A linear damage summation framework, supported by elastoplastic finite element analyses, is used. Several variable amplitude loadings were selected and analyzed, using alternative configurations of kinematic hardening plasticity models (e.g., Chaboche’s model with distinct constants superposition). The predictions are assessed using available experimental data and data derived with simplified empirical elastoplastic tools. This paper highlights the difficulties of performing such elastoplastic analysis and compares the obtained results with those obtained using more classical tools for elastoplastic analysis (Glinka and Seeger–Heuler). It was found that fatigue predictions based on an elastoplastic finite element analysis, made using the Chaboche’s model, were significantly more accurate than predictions based on simplified elastoplastic analysis. These results have important practical relevance.

A Critical Analysis of the Plasticity Correction Factors Proposed in the EN13445 Standard for Fatigue Analysis of Unwelded Material

This paper presents a preliminary investigation about the plasticity correction factor, Ke , proposed in the Part 3–Clause 18 of the EN13445 standard, for correction of the elastic stress ranges exceeding twice the yield stress, resulting from mechanical loading. The plasticity correction factors are re-analyzed using a calculation strategy based on a comparison between results from fully-elastic and elastoplastic analyses. Several materials, elastoplastic models and geometries are considered in the study. The analyses revealed, for an important number of the situations, non-conservative results for Ke calculated according to the standard, which suggests the need for improvements in the standard procedures. However, more intensive research will be carried out to support these preliminary results. Nevertheless, authors recommend that a greater emphasis should be dedicated in the standard to the elastoplastic analysis, since the fatigue resistance data presented in the standard is strain-life type data. The elastoplastic analysis should be the preferred approach for evaluation of the strains/stresses for fatigue analysis.Copyright

Fatigue Modelling of a Notched Geometry Under Variable Amplitude Loading Supported on Elastoplastic FEM Analyses

Despite intensive research has been carried out to understand the fatigue behavior of steel notched geometries, under variable amplitude loading, no definite and general robust models have been derived so far. Therefore, any effort to increment the knowledge in the topic is welcome. Within this premise, it is proposed an assessment of existing variable amplitude data, which has been derived by authors for a notched geometry, made from a low carbon pressure vessel steel (P355NL1), within the local approaches and linear damage summation framework, and supported by elastoplastic finite element analyses. Several variable amplitude loading are selected and analyzed using alternative configurations of kinematic hardening plasticity models (e.g. Chaboche’s model with distinct constants superposition). The predictions are assessed using available experimental data as well as with predictions made with simplified empiric elastoplastic tools. This paper highlights the difficulties on performing such elastoplastic analysis and compares the obtained results with those obtained using more classical tools for elastoplastic analysis. Fatigue predictions based on elastoplastic analysis made using the Chaboche’s model, with a finite element model, were significantly more accurate than predictions based on simplified elastoplastic analysis. The proposed information has important practical relevance.Copyright

A Preliminary Assessment of the Ke Factor Proposed in the EN13445 Standard for Fatigue Analysis of Unwelded Material

This paper presents an investigation about the plasticity correction factor, K e , proposed in the Part 3-Clause 18 of the EN13445 standard, for correction of the elastic stress ranges exceeding twice the yield stress, resulting from mechanical loading. The plasticity correction factors are analyzed using a calculation strategy based on a comparison between results from linear elastic and elastoplastic analyses. Several materials, elastoplastic models, and geometries are considered in the study. The performed analyses revealed, for an important number of the situations, an underestimation of the K e factor when calculated according to the standard procedures. A greater emphasis should be dedicated in the standard to the elastoplastic analysis, since the fatigue resistance data presented in the standard are strain-life type data, overcoming the need for the plasticity correction factor. The elastoplastic analysis should be the preferred approach for evaluation of the strains/stresses for fatigue analysis.

A Discussion on the Performance of Continuum Plasticity Models for Fatigue Lifetime Assessment Based on the Local Strain Appraoch

This paper presents a discussion on the performance of continuum plasticity models for fatigue lifetime assessment according to the local strain approach. Several cyclic plasticity phenomena such as the cyclic hardening/softening, ratchetting, cyclic mean stress relaxation and non-proportional cyclic hardening require, in general, specialized continuum plasticity models. Continuum plasticity models, available in commercial finite element codes (e.g. ANSYS® ), with linear, multilinear and nonlinear kinematic hardening are identified using the experimental information available for a pressure vessel steel — the P355NL 1 steel. The potentialities of these plasticity models to describe the material cyclic behaviour are discussed, limiting the discussion to proportional loading. The plasticity models are applied to evaluate the strain ranges and mean stresses of a nozzle-to-plate connection. Two analysis strategies are applied to extract the strain ranges, namely the Twice Yield (TY) and the Cycle-by-Cycle (CBC) methods. The mean stress is only evaluated using the CBC method since the TY method has been proposed only for evaluation of the strain ranges. It is demonstrated that the TY and CBC methods gives similar results for the linear and multilinear kinematic hardening plasticity models. The plasticity model can have an important effect on the evaluation of the mean stresses and thus on predicted strain-life results, if mean stress effects are taken into account in the local strain approach. Finally, the calculated strain ranges and mean stresses are used in the evaluation of the fatigue life of the nozzle-to-plate connection using a local strain approach, and predictions are compared with available experimental results. The effect of the mean stress is important for long lives and is very dependent on the continuum plasticity model and on the number of cycles modelled in the CBC extraction method. Although differences are observed in the estimation of the strain ranges, using the several plasticity models, relatively small differences in fatigue life estimations were resulted.Copyright