Time-derivative equations for fatigue crack growth in metals

Pommier, Sylvie; Risbet, Marion

doi:10.1007/s10704-004-3633-9

Cited by 24 publications

(21 citation statements)

References 24 publications

(28 reference statements)

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“…[12][13][14][15][16] For the sake of clarity, the principles of the technique will be briefly explained for elastic-plastic pure mode I cracks, then the application to a railway steel and a turbine disk superalloy will be shown and finally the extension of the method to general mixed-mode (I þ II) conditions will be discussed. [3] …”

Section: Reviewmentioning

confidence: 99%

Fatigue Crack Propagation and History Effects Induced by Plasticity

Pommier

2009

Adv Eng Mater

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For security‐relevant components, a fracture mechanics assessment has to be carried out. When complex loading conditions are encountered, various problems arise. Among them the prediction of history effects induced by plasticity remains a difficult task and is the object of this paper. After an overload, for instance, plasticity‐induced crack closure is known to decelerate the crack growth. This effect is known to be related to residual stresses ahead of and behind the crack tip. Since residual stresses are related to the material stress–strain behavior, the overload effect may vary significantly from one material to another. Finite‐element (FE) methods are commonly employed to model plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modeled to predict the fatigue behavior of an industrial component, the method becomes computationally too expensive. By employing a multiscale approach, very precise analyses computed by FE methods can be brought to a global scale. The data generated using the FE method enables the identification of a global cyclic elastic‐plastic model for the crack tip region. Once this model is identified, it can be employed directly with no need of additional FE computations, resulting in fast computations. This method was employed so as to predict fatigue crack growth under variable amplitude fatigue in steels at room temperatures and correlates well with experimental data. It was also extended so as to model fatigue crack growth in a nickel base superalloy under non‐isothermal fatigue‐dwell conditions. At present, the method is being extended to mixed‐mode variable‐amplitude loading conditions.

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Section: Reviewmentioning

confidence: 99%

Fatigue Crack Propagation and History Effects Induced by Plasticity

Pommier

2009

Adv Eng Mater

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“…The local FE results are then brought to the global scale using a multiscale approach tailored for crack problems [25][26][27]. The global data generated by the post [25][26][27].…”

Section: The Multiscale Approachmentioning

confidence: 99%

“…The global data generated by the post [25][26][27]. In addition, a proportional growth law between the rate dt da of production of cracked area per unit length of the crack front and dt d I ρ , allows prediction of the crack growth rate.…”

Section: The Multiscale Approachmentioning

confidence: 99%

“…In order to model service conditions in engineering applications, the computations become even more expensive, because real components often have fatigue lives of millions cycles, and cracks do not generally remain planar. The objective of the proposed methodology is to combine the precision of local finite element computations with the rapidity of a global approach [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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History effect in fatigue crack growth under mixed-mode loading conditions

Decreuse¹,

Pommier²,

Gentot³

et al. 2009

International Journal of Fatigue

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Plastic deformation within the crack tip region introduces internal stresses that modify subsequent behaviour of the crack and are at the origin of history effects in fatigue crack growth.Consequently, fatigue crack growth models should include plasticity induced history effects. A model was developed and validated for mode I fatigue crack growth under variable amplitude loading conditions. The purpose of this study was to extend this model to mixed mode loading conditions. Finite element analyses are commonly employed to model crack tip plasticity and were shown to give very satisfactory results. However, if millions of cycles need to be modelled to predict the fatigue behaviour of an industrial component, the finite element method becomes computationally too expensive. By employing a multiscale approach, the local results of FE computations can be brought to the global scale. This approach consists of partitioning the velocity field at the crack tip into plastic and elastic parts. Each part is partitioned into mode I and mode II components, and finally each component is the product of a reference spatial field and an intensity factor. The intensity factor of the mode I and mode II plastic parts of the velocity fields, denoted by dρ I /dt and dρ II /dt, allow measuring mixed-mode plasticity in the crack tip region at the global scale.Evolutions of dρ I /dt and dρ II /dt, generated using the FE method for various loading histories, enable the identification of an empirical cyclic elastic-plastic constitutive model for the crack tip region at the global scale. Once identified, this empirical model can be employed, with no need of additional FE computations, resulting in faster computations. With the additional hypothesis that the fatigue crack growth rate and direction can be determined from mixed mode crack tip plasticity (dρ I /dt and dρ II /dt), it becomes possible to predict fatigue crack growth under I/II mixed mode and variable amplitude loading conditions. To compare the predictions of this model with experiments, an asymmetric four point bend test system was set-up. It allows applying any mixed mode loading case from a pure mode I condition to a pure mode II. Initial experimental results showed an increase of the mode I fatigue crack growth rate after the application of a set of mode II overload cycles.

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“…Trying to build a more general propagation law, and avoiding as much as possible empirical or experimentally fitted parameters, the Crack Tip Condensed Plasticity model (or CTCP model), was first introduced by Pommier et al [10] with only one single experimentally fitted material parameter α (see Equation (3)). Since then, it has been continually improved, in particular by taking into account the biaxiality state by means of the T-stress level, compressive loadings [11] and thermal effects [12].…”

Section: Introductionmentioning

confidence: 99%

A global/local model reduction approach dedicated to 3D fatigue crack growth with crack closure effect

Galland¹,

Gravouil²,

Rochette³

2010

IOP Conf. Ser.: Mater. Sci. Eng.

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Experimental and numerical study of fatigue crack propagation in a thick-walled cylinder under cyclic hoop stress I Salam, M A Malik, M Abid et al.Study on the relationship between stress intensity factor and J integral for mixed mode crack with arbitrary inclination based on SBFEM C L Zhu, J B Li, G Lin et al. Abstract. It has been known for decades that fatigue crack propagation in elastic-plastic media is very sensitive to load history since the nonlinear behavior of the material can have a great influence on propagation rates. However, raw computations of millions of nonlinear fatigue cycles on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose a global model reduction strategy, mixing both the a posteriori and a priori approaches in order to drastically decrease the computational cost of these types of problems. IntroductionThe accurate prediction of the fatigue lifetime of components or structures is of great interest for mechanical engineering applications. In this respect, it is now more and more needed to be able to simulate accurately 3D fatigue crack growth in complicated structures. Moreover, realistic problems are submitted to complicated spectrum loadings. In those cases, fatigue crack propagation in elastic-plastic media is particularly sensitive to the localized nonlinear phenomena that take place in the vicinity of the crack tip [1,2]. Indeed, contact and frictional effects along the crack faces as well as the confined plasticity are non-negligible issues in fatigue problems. As a consequence, numerical models for fatigue crack analysis need to be able to couple the characteristic lengths of the structure, the area of interest linked to the crack and its possible propagation, and the characteristic lengths of the confined nonlinearities close to the crack front. Obviously, such simulations are very challenging since raw computations of millions of nonlinear fatigue cycles on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose here to apply the so-called general idea of model reduction, in order to decrease this computational cost.The model reduction methods are used when many resolutions of similar problems are needed. They make use of the information contained in some solutions to make the other computations faster. Those methods can be put in two general categories: the a posteriori and a priori approaches. In the a posteriori approach, some preliminary computations are performed first to build a basis of a reduced subspace approximating the solution space associated with the considered problem. This is called the offline phase, it possibly has a high numerical cost, but it is performed only once. Then, the reduced model can be used in an online phase, many times,

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Time-derivative equations for fatigue crack growth in metals

Cited by 24 publications

References 24 publications

Fatigue Crack Propagation and History Effects Induced by Plasticity

Fatigue Crack Propagation and History Effects Induced by Plasticity

History effect in fatigue crack growth under mixed-mode loading conditions

A global/local model reduction approach dedicated to 3D fatigue crack growth with crack closure effect

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