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http://hdl.handle.net/10985/6796
Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads
ROBERT, Camille; SAINTIER, Nicolas; PALIN-LUC, Thierry; MOREL, Franck
An analysis of high cycle multiaxial fatigue behaviour is conducted through the numerical simulation of polycrystalline aggregates using the finite elementmethod. The metallicmaterial chosen for investigation is pure copper, which has a Face Centred Cubic (FCC) crystalline microstructure. The elementary volumes are modelled in 2D using an hypothesis of generalised plane strain and consist of 300 equi-probability, randomly oriented grains with equiaxed geometry. The aggregates are loaded at levels equivalent to the average macroscopic fatigue strength at 107 cycles. The goal is to compute the mechanical quantities at the mesoscopic scale (i.e. average within the grain) after stabilization of the local cyclic behaviour. The results show that the mesoscopic mechanical variables are characterised by high dispersion. A statistical analysis of the response of the aggregates is undertaken for different loading modes: fully reversed tensile loads, torsion and combined in-phase tension-torsion. Via the calculation of the local mechanical quantities for a sufficiently large number of different microstructures, a critical analysis of certain multiaxial endurance criteria (Crossland, Dang Van and Matake) is conducted. In terms of material behaviour models, it is shown that elastic anisotropy strongly affects the scatter of the mechanical parameters used in the different criteria and that its role is predominant compared to that of crystal plasticity. The analysis of multiaxial endurance criteria at both the macroscopic and mesoscopic scales clearly show that the critical plane type criteria (Dang Van and Matake) give an adequate estimation of the shear stress but badly reflect the scatter of the normal stress or the hydrostatic stress.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/67962012-01-01T00:00:00ZROBERT, CamilleSAINTIER, NicolasPALIN-LUC, ThierryMOREL, FranckAn analysis of high cycle multiaxial fatigue behaviour is conducted through the numerical simulation of polycrystalline aggregates using the finite elementmethod. The metallicmaterial chosen for investigation is pure copper, which has a Face Centred Cubic (FCC) crystalline microstructure. The elementary volumes are modelled in 2D using an hypothesis of generalised plane strain and consist of 300 equi-probability, randomly oriented grains with equiaxed geometry. The aggregates are loaded at levels equivalent to the average macroscopic fatigue strength at 107 cycles. The goal is to compute the mechanical quantities at the mesoscopic scale (i.e. average within the grain) after stabilization of the local cyclic behaviour. The results show that the mesoscopic mechanical variables are characterised by high dispersion. A statistical analysis of the response of the aggregates is undertaken for different loading modes: fully reversed tensile loads, torsion and combined in-phase tension-torsion. Via the calculation of the local mechanical quantities for a sufficiently large number of different microstructures, a critical analysis of certain multiaxial endurance criteria (Crossland, Dang Van and Matake) is conducted. In terms of material behaviour models, it is shown that elastic anisotropy strongly affects the scatter of the mechanical parameters used in the different criteria and that its role is predominant compared to that of crystal plasticity. The analysis of multiaxial endurance criteria at both the macroscopic and mesoscopic scales clearly show that the critical plane type criteria (Dang Van and Matake) give an adequate estimation of the shear stress but badly reflect the scatter of the normal stress or the hydrostatic stress.Effect of mean shear stress on the fatigue strength of notched components under multiaxial stress state
http://hdl.handle.net/10985/13395
Effect of mean shear stress on the fatigue strength of notched components under multiaxial stress state
BENNEBACH, Mohamed; PALIN-LUC, Thierry; MESSAGER, Alexandre
The effect of a static and intermittent shear stress on the HCF strength of two quenched and tempered steel grades used to produce shafts in crane industry was studied on notched specimens (Kt=1.7 and 2.7) for being representative of critical areas. Three main load cases were considered: C1=rotative bending (RB), C2=RB and static torsion and C3=RB and mean torsion fluctuating in blocks to simulated start and stop cycles. In this last case the first investigated mean shear stress, τm, was equal to the material yield stress in pure shear, τy. Additional C3 variants were investigated too where τm was equal to 0.3τy and 0.7τy. It has been shown that τm has little effect on the rotating bending HCF strength at 3×106 cycles. For both steel grades and notch geometries studied, the results of the fatigue tests confirm that the influence of a static torsion on the rotating bending HCF strength is negligible even when the static torsion level is equivalent to the yield strength of the material in torsion. However, in intermittent service conditions (C3), it has been shown that torsion cycles can affect significantly the HCF strength in RB, depending on the notch acuity and torsion level. Elastic-plastic cyclic FEA has been done for the two specimen geometries to assess the stabilized stress-strain state at the notch root and then to compute the fatigue life by using the multiaxial HCF life models proposed by: Fatemi-Socie, Smith-Watson-Topper, and Wang-Brown. The Palmgreen-Miner hypothesis was used to cumulate damage mainly because of its simplicity for design purposes. According to our simulations and with the chosen cumulative damage rule, none of the tested fatigue life calculation methods give good results for all the load cases. The efficiency of the tested methods is very dependent on both the material and the load cases. However, the Smith-Watson-Topper approach gives the best results whereas the Fatemi-Socie models leads to the more conservative ones except in one load case
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/133952018-01-01T00:00:00ZBENNEBACH, MohamedPALIN-LUC, ThierryMESSAGER, AlexandreThe effect of a static and intermittent shear stress on the HCF strength of two quenched and tempered steel grades used to produce shafts in crane industry was studied on notched specimens (Kt=1.7 and 2.7) for being representative of critical areas. Three main load cases were considered: C1=rotative bending (RB), C2=RB and static torsion and C3=RB and mean torsion fluctuating in blocks to simulated start and stop cycles. In this last case the first investigated mean shear stress, τm, was equal to the material yield stress in pure shear, τy. Additional C3 variants were investigated too where τm was equal to 0.3τy and 0.7τy. It has been shown that τm has little effect on the rotating bending HCF strength at 3×106 cycles. For both steel grades and notch geometries studied, the results of the fatigue tests confirm that the influence of a static torsion on the rotating bending HCF strength is negligible even when the static torsion level is equivalent to the yield strength of the material in torsion. However, in intermittent service conditions (C3), it has been shown that torsion cycles can affect significantly the HCF strength in RB, depending on the notch acuity and torsion level. Elastic-plastic cyclic FEA has been done for the two specimen geometries to assess the stabilized stress-strain state at the notch root and then to compute the fatigue life by using the multiaxial HCF life models proposed by: Fatemi-Socie, Smith-Watson-Topper, and Wang-Brown. The Palmgreen-Miner hypothesis was used to cumulate damage mainly because of its simplicity for design purposes. According to our simulations and with the chosen cumulative damage rule, none of the tested fatigue life calculation methods give good results for all the load cases. The efficiency of the tested methods is very dependent on both the material and the load cases. However, the Smith-Watson-Topper approach gives the best results whereas the Fatemi-Socie models leads to the more conservative ones except in one load caseStatistical assessment of multiaxial HCF criteria at the grain scale
http://hdl.handle.net/10985/8394
Statistical assessment of multiaxial HCF criteria at the grain scale
HOR, Anis; SAINTIER, Nicolas; ROBERT, Camille; PALIN-LUC, Thierry; MOREL, Franck
Multiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/83942014-01-01T00:00:00ZHOR, AnisSAINTIER, NicolasROBERT, CamillePALIN-LUC, ThierryMOREL, FranckMultiaxial high cycle fatigue modeling of materials is an issue that concerns many industrial domains (automotive, aerospace, nuclear, etc.) and in which many progress still remains to be achieved. Several approaches exist in the literature: invariants, energy, integral and critical plane approaches all of them having their advantages and drawbacks. These different formulations are usually based on mechanical quantities at the micro or mesoscales using localization schemes and strong assumptions to propose simple analytical forms. This study aims to revisit these formulations using a numerical approach based on crystal plasticity modeling coupled with explicit description of microstructure (morphology and texture) and proposes a statistical procedure for the analyses of numerical results in the HCF context. This work has three steps: First, 2.5D periodic digital microstructures based on a random grain sizes distribution are generated. Second, multiaxial cyclic loading conditions corresponding to the fatigue strength at 106 cycles are applied to these microstructures. Third, the mesoscopic Fatigue Indicator Parameters (FIPs), formulated from the different criteria existing in the literature, are identified using the finite element calculations of the mechanical fields. These mesoscopic FIP show the limits of the original criteria when it comes to applying them at the grain scale. A statistical method based on extreme value probability is used to redefine the thresholds of these criteria. These new thresholds contain the sensitivity of the HCF behavior to microstructure attributes. Finally, the biaxiality and phase shift effects are discussed at the grain scale and the loading paths of some critical grains are analyzed.High-Cycle Fatigue Behaviour of Pure Tantalum under Multiaxial and Variable Amplitude Loadings
http://hdl.handle.net/10985/8397
High-Cycle Fatigue Behaviour of Pure Tantalum under Multiaxial and Variable Amplitude Loadings
MARECHAL, David; SAINTIER, Nicolas; PALIN-LUC, Thierry; NADAL, François
Due to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High-cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood. This paper aims at better understanding the fatigue behaviour of tantalum and at clarifying the mechanisms of damage formation encountered under such loadings. HCF experiments performed at room temperature on commercially-pure tantalum are presented. Mean stress effects were investigated in the aim of clarifying the interaction between fatigue and creep. Fracture mechanisms were observed to vary from intergranular to transgranular depending on applied stress amplitude and mean stress. Damage mechanisms were investigated under tension and torsion. Results are analyzed in the light of existing fatigue criteria, the limitations of which are discussed. Finally, complex sequential loadings, representative of in-service loadings, were applied to tantalum smooth specimens. The contribution of each loading sequence to the overall damage was quantified and analyzed in terms of linear or non-linear cumulative damage rule
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/83972014-01-01T00:00:00ZMARECHAL, DavidSAINTIER, NicolasPALIN-LUC, ThierryNADAL, FrançoisDue to its specific mechanical properties, tantalum is often used in strength-demanding military applications. High-cycle fatigue (HCF) behaviour of pure tantalum, however, has been rarely reported and the mechanisms at stake to account for deformation under cyclic loadings are still badly understood. This paper aims at better understanding the fatigue behaviour of tantalum and at clarifying the mechanisms of damage formation encountered under such loadings. HCF experiments performed at room temperature on commercially-pure tantalum are presented. Mean stress effects were investigated in the aim of clarifying the interaction between fatigue and creep. Fracture mechanisms were observed to vary from intergranular to transgranular depending on applied stress amplitude and mean stress. Damage mechanisms were investigated under tension and torsion. Results are analyzed in the light of existing fatigue criteria, the limitations of which are discussed. Finally, complex sequential loadings, representative of in-service loadings, were applied to tantalum smooth specimens. The contribution of each loading sequence to the overall damage was quantified and analyzed in terms of linear or non-linear cumulative damage ruleHigh cycle multiaxial fatigue crack initiation : experimental observations and microstructure simulations
http://hdl.handle.net/10985/7497
High cycle multiaxial fatigue crack initiation : experimental observations and microstructure simulations
AGBESSI, Komlan; SAINTIER, Nicolas; PALIN-LUC, Thierry
This study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/74972013-01-01T00:00:00ZAGBESSI, KomlanSAINTIER, NicolasPALIN-LUC, ThierryThis study provides an analysis of high cycle multiaxial fatigue crack initiation modes based on SEM observations.The statistical study of crack initiation preferential sites shows that grains with multiple slip have a high probability of crack initiation. The application of Dang Van criterion at the grain scale using finite element analysis (cubic elasticity with / or without crystal plasticity) on 3D synthetic semi-periodic microstructures shows a strong heterogeneity of both the hydrostatic stress and shear. The evolution of this heterogeneity introduced by the material behavior is discussed. Finally, a method based on the extreme values statistics is proposed and applied to the fatigue indicative parameter associated to the Dang Van criterion. The effects of free surface and constitutive material model were analyzed.A review about the effects of structural and operational factors on the gigacycle fatigue of steels
http://hdl.handle.net/10985/13234
A review about the effects of structural and operational factors on the gigacycle fatigue of steels
JEDDI, Dalenda; PALIN-LUC, Thierry
It is well‐known that the high cycle fatigue (HCF) strength of steel components is influenced by a lot of factors depending on both material, loading (including environment), specimen or component geometry (design), and manufacturing process. Based on a literature review of a lot of experimental data, a synthesis is proposed in this paper to discuss the effect of the structural and operational factors on the very high cycle fatigue (VHCF) characteristics of steels. HCF and VHCF regimes are distinguished in terms of failure mechanisms and S‐N curve shapes for high and low strength steels. Then, the effect of the microstructural and mechanical features on the VHCF resistance is debated as different parameters (microstructure, inclusion size type and depth, hydrogen, environment, maximum tensile strength, and residual stresses). Next, the influence of the loading conditions is addressed by taking into account both the frequency effect, the highly stressed volume, the loading type, and loading ratio. Finally, the influence of the testing techniques used in VHCF experiments is discussed.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/132342018-01-01T00:00:00ZJEDDI, DalendaPALIN-LUC, ThierryIt is well‐known that the high cycle fatigue (HCF) strength of steel components is influenced by a lot of factors depending on both material, loading (including environment), specimen or component geometry (design), and manufacturing process. Based on a literature review of a lot of experimental data, a synthesis is proposed in this paper to discuss the effect of the structural and operational factors on the very high cycle fatigue (VHCF) characteristics of steels. HCF and VHCF regimes are distinguished in terms of failure mechanisms and S‐N curve shapes for high and low strength steels. Then, the effect of the microstructural and mechanical features on the VHCF resistance is debated as different parameters (microstructure, inclusion size type and depth, hydrogen, environment, maximum tensile strength, and residual stresses). Next, the influence of the loading conditions is addressed by taking into account both the frequency effect, the highly stressed volume, the loading type, and loading ratio. Finally, the influence of the testing techniques used in VHCF experiments is discussed.A new piezoelectric fatigue testing machine in pure torsion for ultrasonic gigacycle fatigue tests: application to forged and extruded titanium alloys
http://hdl.handle.net/10985/10017
A new piezoelectric fatigue testing machine in pure torsion for ultrasonic gigacycle fatigue tests: application to forged and extruded titanium alloys
NIKITIN, Alexander; BATHIAS, Claude; PALIN-LUC, Thierry
This article briefly discusses the history of the development of ultrasonic fatigue testing methods, with respect to industrial needs. The development of ultrasonic techniques and the progress made in the computer industry have led to improvements in ultrasonic testing techniques. It has been shown, that existing ultrasonic testing systems have limitations that lead to the need for a new ultrasonic fatigue testing machine operating in pure torsion. This paper introduces the development of a new piezoelectric machine working in the continuous regime (i.e. without pulse-pause). This machine has been used to investigate the Very High Cycle Fatigue (VHCF) properties of the VT3-1 alpha beta aeronautical titanium alloy (which is similar to Ti–6Al–4V) produced by two manufacturing processes: forging and extrusion. The extruded titanium alloy has a higher VHCF strength in torsion compared to the forged one. Despite the maximum shear stress occurring at the specimen surface under torsion loading, internal fatigue crack initiation can be observed in both the forged and extruded alloys.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100172015-01-01T00:00:00ZNIKITIN, AlexanderBATHIAS, ClaudePALIN-LUC, ThierryThis article briefly discusses the history of the development of ultrasonic fatigue testing methods, with respect to industrial needs. The development of ultrasonic techniques and the progress made in the computer industry have led to improvements in ultrasonic testing techniques. It has been shown, that existing ultrasonic testing systems have limitations that lead to the need for a new ultrasonic fatigue testing machine operating in pure torsion. This paper introduces the development of a new piezoelectric machine working in the continuous regime (i.e. without pulse-pause). This machine has been used to investigate the Very High Cycle Fatigue (VHCF) properties of the VT3-1 alpha beta aeronautical titanium alloy (which is similar to Ti–6Al–4V) produced by two manufacturing processes: forging and extrusion. The extruded titanium alloy has a higher VHCF strength in torsion compared to the forged one. Despite the maximum shear stress occurring at the specimen surface under torsion loading, internal fatigue crack initiation can be observed in both the forged and extruded alloys.Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings
http://hdl.handle.net/10985/7414
Non-local energy based fatigue life calculation method under multiaxial variable amplitude loadings
SAINTIER, Nicolas; PALIN-LUC, Thierry; BÉNABÈS, Jérôme; COCHETEUX, Francis
Reliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104 –107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previ- ously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude load- ings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/74142013-01-01T00:00:00ZSAINTIER, NicolasPALIN-LUC, ThierryBÉNABÈS, JérômeCOCHETEUX, FrancisReliable design of industrial components against high cycle multiaxial fatigue requires a model capable of predicting both stress gradient and load type effects. Indeed, taking into account gradient effects is of prior importance for the applicability of fatigue models to real structures. In this paper, a fatigue life assessment method is proposed for proportional and non-proportional multiaxial variable amplitude loadings in the range 104 –107 cycles. This method derives from the fatigue criterion initially proposed by Palin-Luc and Lasserre (1998) [2] and revisited by Banvillet et al. (2003) [16] for multiaxial constant amplitude loading. The new proposal consists of a complete reformulation and extension of the previ- ously cited energy based fatigue strength criteria. It includes two major improvements of the existing criteria. The first one consists in a fatigue criterion for multiaxial variable amplitude loadings while only constant amplitude loadings were considered in the above cited works. The second one is an extension to an incremental fatigue life assessment method for proportional and non-proportional multiaxial variable amplitude loadings. No cycle counting technique is needed whatever the variable amplitude load- ings type considered (uniaxial or multiaxial). The predictions of the method for constant and variable amplitude multiaxial loadings are compared with experimental results on specimens from literature and from new experiments on a ferrito-perlitic steel. The above mentioned method has been implemented as a post-processor of a finite element software. An application to a railway wheel is finally presented.A volumetric energy based high cycle multiaxial fatigue citerion
http://hdl.handle.net/10985/11218
A volumetric energy based high cycle multiaxial fatigue citerion
BANVILLET, ALexis; PALIN-LUC, Thierry; LASSERRE, Serge
A reliable design of industrial parts against high-cycle multiaxial fatigue requires a fatigue criterion capable of predicting both the stress gradient and the load-type effects. These effects are very important in the transfer of fatigue data from specimen to component. By using the concept of volume influencing fatigue crack initiation proposed by Palin-Luc and Lasserre with an energy based approach, a new criterion is presented. Based on the strain-work density given to the material, this proposal is usable whatever the constant amplitude loading is: in and out-of-phase combined loadings, with or without mean stress. Its predictions are compared both with a total of 38 experiments on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron) and with the predictions of local criteria (Crossland, Dang Van, Papadopoulos and Morel). The comparison shows that the predictions of the volumetric proposal are very good and less scattered than those of the local approaches, especially for loadings with mean stresses or under non-proportional loadings.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10985/112182003-01-01T00:00:00ZBANVILLET, ALexisPALIN-LUC, ThierryLASSERRE, SergeA reliable design of industrial parts against high-cycle multiaxial fatigue requires a fatigue criterion capable of predicting both the stress gradient and the load-type effects. These effects are very important in the transfer of fatigue data from specimen to component. By using the concept of volume influencing fatigue crack initiation proposed by Palin-Luc and Lasserre with an energy based approach, a new criterion is presented. Based on the strain-work density given to the material, this proposal is usable whatever the constant amplitude loading is: in and out-of-phase combined loadings, with or without mean stress. Its predictions are compared both with a total of 38 experiments on four materials (a mild steel, two high strength steels and a spheroidal graphite cast iron) and with the predictions of local criteria (Crossland, Dang Van, Papadopoulos and Morel). The comparison shows that the predictions of the volumetric proposal are very good and less scattered than those of the local approaches, especially for loadings with mean stresses or under non-proportional loadings.Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue
http://hdl.handle.net/10985/11221
Comparative study and link between mesoscopic and energetic approaches in high cycle multiaxial fatigue
MOREL, Franck; PALIN-LUC, Thierry; FROUSTEY, Catherine
Multiaxial fatigue analysis can be categorized into several viewpoints, i.e. empirical formulae, methods based on stress invariants, critical plane approaches, models using averages of stress quantities and energetic considerations. The aim of this paper is not to survey the current state of knowledge concerning multiaxial fatigue but to critically examine two endurance criteria so as to prove that a direct link can be established between them. The first of the two methods, proposed by Papadopoulos, has been built by exploring the fatigue of metals from the mesoscopic scale, that is from the scale of the metal grains of a metallic aggregate. The localized plastic strains developping in some less favourably oriented crystals is considered to be the main cause of fatigue crack nucleation. According to relationships between macroscopic and mesoscopic quantities, this model is finally expressed in terms of the usual macroscopic stresses relative to an elementary material volume. The second approach proposed by Froustey and Lasserre is an energetic based criterion. It has been deduced from experimental observations concerning multiaxial endurance limit and states that crack initiation occurs as soon as the total strain energy density exceeds a critical value. This paper shows that the critical value of the accumulated mesoscopic plastic strain used by Papadopoulos to characterize the endurance limit can be estimated with the global strain energy density at the macroscopic scale. Indeed, it is demonstrated that when dealing with in-phase or out-of-phase synchronous sinusoidal constant amplitude loadings, a single analytical formulation of these criteria can be written either with stress quantities or with energetic ones describing thus the same physical phenomenon. The mean stress influence is discussed; the predictions of the two approaches are similar when the material remains quasi elastic. Another important result concerns the phase difference of the stress tensor components. Very few approaches are able to predict the independence of the fatigue strength on the phase difference between normal and shear stresses. The two proposed criteria reflect this phenomenon which has been experimentally observed for many metals subjected to combined bending-torsion loading. Nevertheless, this independence with regard to the phase shift is no more effective when dealing with some biaxial stress systems with two normal stresses. In this case the two models are consistent with the experimental results since they show a marked influence of the phase difference.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10985/112212001-01-01T00:00:00ZMOREL, FranckPALIN-LUC, ThierryFROUSTEY, CatherineMultiaxial fatigue analysis can be categorized into several viewpoints, i.e. empirical formulae, methods based on stress invariants, critical plane approaches, models using averages of stress quantities and energetic considerations. The aim of this paper is not to survey the current state of knowledge concerning multiaxial fatigue but to critically examine two endurance criteria so as to prove that a direct link can be established between them. The first of the two methods, proposed by Papadopoulos, has been built by exploring the fatigue of metals from the mesoscopic scale, that is from the scale of the metal grains of a metallic aggregate. The localized plastic strains developping in some less favourably oriented crystals is considered to be the main cause of fatigue crack nucleation. According to relationships between macroscopic and mesoscopic quantities, this model is finally expressed in terms of the usual macroscopic stresses relative to an elementary material volume. The second approach proposed by Froustey and Lasserre is an energetic based criterion. It has been deduced from experimental observations concerning multiaxial endurance limit and states that crack initiation occurs as soon as the total strain energy density exceeds a critical value. This paper shows that the critical value of the accumulated mesoscopic plastic strain used by Papadopoulos to characterize the endurance limit can be estimated with the global strain energy density at the macroscopic scale. Indeed, it is demonstrated that when dealing with in-phase or out-of-phase synchronous sinusoidal constant amplitude loadings, a single analytical formulation of these criteria can be written either with stress quantities or with energetic ones describing thus the same physical phenomenon. The mean stress influence is discussed; the predictions of the two approaches are similar when the material remains quasi elastic. Another important result concerns the phase difference of the stress tensor components. Very few approaches are able to predict the independence of the fatigue strength on the phase difference between normal and shear stresses. The two proposed criteria reflect this phenomenon which has been experimentally observed for many metals subjected to combined bending-torsion loading. Nevertheless, this independence with regard to the phase shift is no more effective when dealing with some biaxial stress systems with two normal stresses. In this case the two models are consistent with the experimental results since they show a marked influence of the phase difference.