This paper presents the development of an anisotropic elastic damage theory. This is achieved by deriving a modified damage effect tensor M(D) for the effective stress equations capable of including the effect of anisotropic material damage. The modified tensor removes the restriction of a priori knowledge of the directions of principal stresses imposed by a damage effect tensor developed earlier and can now be made for general practical engineering applications of failure analysis. Reduction of the proposed tensor to a scalar for isotropic damage is shown to be possible when it is expressed not only in the principal directions but also in any arbitrary coordinate system, a necessary condition to verify the validity of the proposed tensor. Uniaxial tension and pure torsion are chosen to illustrate the application of the theory as well as associated damage variables that may be experimentally determined using laboratory size specimens. The measured damage variables confirm the presence of anisotropic damage from an initially isotropic material specimen and the magnitude is more pronounced at higher stresses and strains.

An anisotropic theory of elasticity for continuum damage mechanics

Fatigue crack initiation was studied in a bimodal TA6V titanium alloy. A ghost structure inherited from the forging process, the scale of which is roughly 100 times the apparent grain size, was found to govern the initiation process. In these macrograins, that we have labelled macrozones, most of the primary alpha grains (αp) are found to display the same crystallographic orientation. Fatigue cracks are initiated on the basal plane or, if basal slip is difficult, on the prismatic plane. Thus in macrozones, where basal or prismatic slip is easy, numerous neighbouring tiny cracks appear over the whole macrozone, which have the size of the primary αp grains. In these macrozones the contribution of crack coalescence to crack growth is consequently very significant. On the contrary, if basal and prismatic slips are both difficult in the macrozone, no crack can be found in the corresponding macrozone. The crack initiation process is thus highly heterogeneous at the scale of the macrozone. Furthermore, this microstructure is found to induce a large scatter in the fatigue life of notched samples.

Local texture and fatigue crack initiation in a Ti-6Al-4V titanium alloy

Within the thermodynamics of irreversible processes and the concept of in ternal state variables, a general phenomenological theory of coupled damage-elasto- (visco)plasticity at small strains is g...

On the Anelastic Flow with Damage

The effect of overloads, underloads and stress ratio on plasticity-induced crack opening level is examined for different ‘model’ materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results.

Bauschinger effect of alloys and plasticity-induced crack closure: a finite element analysis

After chemical, morphological, and mechanical characterization of ductile cast iron, the damage mechanisms were studied by tensile tests inside the scanning electron microscope (SEM). The evolutions of Young’s modulus and of Poisson’s ratio were measured in uniaxial tensile tests. Compression tests were used to measure the pressure sensitivity coefficient of the flow stress. The damage is produced by early initiation of cavities at the pole cap of graphite nodules by debonding of the interface, followed by the growth of cavities. The mechanical behavior was modeled in the elastic region by calculating the Hashin-Shtrickman bounds. This provided the elastic constants for the graphite nodules. The plastic behavior was modeled by considering that the graphite nodules were replaced by voids. The critical interfacial stress for debonding was determined by analytical as well as by finite-element calculations. The growth rate of cavities was deduced from the evolution of the Poisson’s ratio and was compared with predictions from Gurson’s potential. The stress-strain behavior could be modeled either by extension of the Mori-Tanaka analysis in the plastic range or by finite-element computations. This allowed a fair prediction of the observed behavior.

Damage Effect on the Fracture Toughness of Nodular Cast Iron: Part I. Damage Characterization and Plastic Flow Stress Modeling

— Crack growth rate measurements, performed on smooth specimens during creep-fatigue testing of the N18 nickel base superalloy at 650°C, reveal a strong detrimental effect of the compressive part of the loading cycle. This effect is attributed to the residual stresses in the wake of the crack, which promote early crack opening. A finite element analysis is conducted in order to predict the evolution of the opening stress level as a function of the stress ratio. Good agreement is found between numerical and experimental results. The influence of the constitutive equation of the material on the crack closure level is tested and the effects of kinematic hardening and viscosity are more specifically examined. An engineering simplified method is proposed to determine the opening stress intensity factor as a function of crack length, stress ratio and maximum stress. This method, developed for cracks in smooth specimens, is then applied to small cracks growing from a notch root. Good agreement is found between the results given by the engineering simplified method and the result of the finite element analysis.

Influence of a negative r ratio on the creep‐fatigue behaviour of the n18 nickel base superalloy

https://hal.archives-ouvertes.fr/hal-00771339/document

Polycrystal modelling of fatigue: Pre-hardening and surface roughness effects on damage initiation for 304L stainless steel

https://hal.archives-ouvertes.fr/docs/00/77/13/26/PDF/_LEP12b_Hal_.pdf

Thermo-mechanical FE model with memory effect for 304L austenitic stainless steel presenting microstructure gradient

Creep-fatigue tests were performed at 650°C in air on a N18 nickel base superalloy, using double notched and smooth specimens. The deformation mechanisms observed by TEM at the notch root are shown to be compatible with the constitutive set of equations used in the finite element analysis which is presented. For a given K max at the notch root, the crack growth rate is much higher in a notched specimen than in a smooth one. This effect can be explained by a variation of the crack closure stress level with the local R ratio and the local stress. A strong accelerating effect of the R ratio, especially for negative values, is found in smooth specimens. Introducing a K op correction in the experimental results leads to a good agreement between the measured crack growth rate plotted versus K eff in notched and smooth samples.

Ph. Bompard

Papers

Influence of a negative r ratio on the creep‐fatigue behaviour of the n18 nickel base superalloy

Polycrystal modelling of fatigue: Pre-hardening and surface roughness effects on damage initiation for 304L stainless steel

Thermo-mechanical FE model with memory effect for 304L austenitic stainless steel presenting microstructure gradient

Crack closure effect on crack growth rate at 650°c in double notched specimens of a nickel base superalloy

Mechanical and fracture behaviour of porous materials