Mechanics of Growth and Coalescence of Pre-existing Voids in a Ductile Matrix

This research project experimentally and numerically investigates the growth and coalescence of pre-existing voids for a wide range of stress states in a ductile matrix with a special focus on shear dominated loading conditions and presents quantitative kinetics data for these processes. The results obtained contribute to further development of current fracture models by generating reliable experimental data for void growth and coalescence, which can be used to evaluate the existing fracture models. A lead-containing copper alloy has been selected as model material, in which lead inclusions act as pre-existing voids – as demonstrated by unit cell numerical simulations for a wide range of stress states. A second copper alloy of similar composition, but without lead allows us to obtain mechanical properties of the matrix. By comparing the behavior of the two alloys it is possible to evaluate the effect of the voids on the macroscopic mechanical behavior. The model materials are deformed and fractured in combined torsion / tension tests and notched tensile tests to subject them to the desired wide range of stress triaxialities. Quantitative fractography and metallography provide the desired kinetics data on void shape, size and orientation, that can be correlated with numerical simulations, as well as existing void growth and coalescence models. The influence of stress-state and micro-structural characteristics on void growth and void coalescence – particularly for zero nominal stress triaxiality conditions – is illustrated at the hand of the results of the investigation. Contrary to the predictions of current micromechanical models, significant growth of small voids resulting in moderate increases in the total void volume is observed in torsion specimens. This growth may be triggered by the developing texture of the matrix material and particularly by twinning. By means of FEM computations with 3D single cell simulations comprising initially ellipsoidal voids, the effect of the initial texture and texture evolution is emphasized. The numerical results showed that the experimentally observed texture of the material accelerates void growth under relatively high stress triaxialities, and possibly allows growth of small voids under low and zero stress triaxialities. The initial shape of the lead inclusions and possibly their growth, was found to be dependent on their initial size. These results emphasize the need for a complete and rather detailed modeling of microstructural and deformation features in order to model damage process correctly. The presented work contributes to a better understanding of void growth and coalescence fracture processes, particularly under shear dominated loading conditions.

Analyse de l'état de contrainte et de l'endommagement d'assemblages sertis en matériau mixte métal-composite sollicités en traction ou en flexion

Alain Michel Prenleloup

The constant improvement of polymer composite materials has allowed their integration in many industrial fields where their mechanical and chemical properties are apparently attractive. Mixed metal-composite insulators are now increasingly used for high voltage networks instead of conventional porcelain structures because of their high strength and reduced maintenance requirements due to their strong resistance against chemical degradation and dynamic loading. The composite insulators investigated in this study are made of an epoxy rod reinforced with glass fibres, two steel fittings being strongly crimped to both ends of the rod to transfer loads between the suspended electrical components and the fixation points. Due to the plastic deformation of the steel induced by the crimping process, a purely mechanical link results from the residual radial stresses at the interface between the composite rod and the metallic fitting. The strength of the joints plays an important role during the tensile and bending loading of the assemblies (clamping of the high-voltage line on the electrical tower and guiding of the electrical transformation substation). Experimental and numerical studies on the crimped joints are performed simultaneously in order to determine the strength of the structures and to characterise the damage and fracture mechanisms. The traction and bending tests are achieved to highlight the failure modes appearing for very high loads. In parallel, the numerical analysis provides complementary information on the stress state and the sensitivity of some influent parameters. The proposed dual approach allows the identification of the critical loads corresponding to the failure initiation and the possible mechanisms associated. The results for the tensile tests performed on structures subjected to a crimping load between 290 and 460 kN exhibit a nonlinear increase from 110 to 160 kN of the maximum pull-out load, and a transition of the failure mode of the link from a sliding of the rod out of the end-fitting for weakly crimped insulators and a delamination of the composite for strongly crimped ones. For still higher crimping conditions, the maximum tensile load decreases due to the damage introduced before tensile loading. In parallel to the experimental study, the numerical model developed for the crimping and traction steps provides the stress state in the joint during the solicitations. The comparison between the numerical predictions and the experimental observations highlights the strength limit of the bond by delamination of the outer layers of the composite. The use in the numerical model of a tensor damage factor depending on the stress state in the composite provides additional information on the failure initiation resulting from the stress combination and allows the characterisation of the critical crimping and loading conditions. The analysis of the crimped joints under tensile loading is extended to the study of insulators subjected to bending loading. Experimental tests are performed for two different sizes of insulators showing different final failure modes. For 51mm-thick insulators, a collapse of the compressive part of the rod occurs while for the 63mm-thick assemblies a shear crack propagation on the mid-plane of the rod can be observed. In addition to the fracture behaviour, the tests show a progressive embrittlement of the joint due to the damage onset appearing at 60 and 50% of the maximum mechanical loading of 15.7 and 21 kN found for the 51mm- and 63mm-thick rods respectively. Moreover, the numerical simulations contribute to the understanding of the failure zones and allow the identification of the critical loads and the stress state associated with the damage observed. Owing to the numerical and experimental analysis, structural modifications are proposed for improving the current bearing capacities of the crimped structures in order to shift the damage initiation and to increase the maximal strength of these assemblies under industrial use. In the tensile loading case, an optimal contact area between the rod and the end-fitting ensures an increase of 50% of the maximum mechanical load for the 18.7mm-thick insulator. For the bending case, the damage initiation at loading rates which are much lower than the bearing capacity can be postponed by changing the conical form of the metal end-fitting. However, the maximum bending load cannot be improved since it is directly limited by the diameter of the rod.

EPFL2008

Microstructure and embrittlement of leaded copper alloys

Laurent Felberbaum

Mechanisms responsible for the embrittlement of leaded "free-machining" copper alloys at intermediate temperatures (i.e. around 400 °C) are examined using a combination of microstructural and mechanical characterization. Tensile tests are conducted on pure copper and on industrial high-strength Cu-Ni-Sn alloys, comparing leaded and unleaded versions, at strain rates ranging from 10-4 to 10 s-1, and various temperatures between 25 °C and 800 °C. It is found that, in the leaded samples, both liquid metal embrittlement and grain boundary embrittlement operate at intermediate temperature,i.e., near the melting point of lead. Their respective importance depends mainly on the strain rate: fracture at high strain rate (10 s-1) displays characteristic signatures of liquid metal embrittlement, while at low strain rate (10-4 s-1) the ductility trough behaviour can be attributed to grain boundary embrittlement. In leaded copper and copper alloys, lead is mostly present as discrete inclusions, frequently located along grain boundaries. The dihedral angle of intergranular lead inclusions is then the main microstructural parameter besides their size. A new technique is proposed and demonstrated for the measurement of inclusion dihedral angle in a high-purity Cu-1 wt.% Pb alloy, based on room temperature characterization of samples that were held at elevated temperature at times sufficiently long for shape equilibration of the inclusions and then rapidly quenched. Quantitative scanning electron microscopic analysis of metallographic surfaces along which individual inclusions have been dissolved is used to deduce the dihedral angle using a mathematical fit of their solid/liquid interface. For a specific temperature, we show that the dihedral angle is not unique; this reflects the fact that high-angle grain boundary energies are not constant in copper. Existing micromechanical analyses of shape equilibrium for intergranular inclusions in the presence of external stress are adapted to produce an improved description at low stress and to take into account the inclusion bulk compressibility. The derivation is based on minimization of the global capillary and elastic strain energy associated with such inclusions. An adimensional parameter that depends on the applied stress, the inclusion volume, the elastic properties of the solid, and the relevant interfacial energies emerges from the analysis as the sole factor governing the shape of the inclusion. If void nucleation occurs easily within the inclusion, such that its apparent bulk modulus is nil, the inclusion become unstable, degenerating to a crack when this adimensional parameter exceeds a critical value. Measurements of the dihedral angle on samples previously subjected to a remote stress at 400 °C show that applied stress causes a reduction in the apparent dihedral angle of liquid lead inclusions. Calculated critical stresses for both leaded pure copper and leaded copper-nickel-tin alloys that fail at high strain rate by liquid metal embrittlement are calculated for individual inclusions in the metal. These calculated critical stresses correlate relatively well with the measured fracture stress, suggesting that shape instability of the inclusions cause fracture of the alloys. This result is applied towards the suggestion of general strategies for reduction of the susceptibility of leaded copper alloys to liquid metal embrittlement. A case study addressing the problem of quench cracking of leaded Cu-Ni-Sn alloys on the basis of experimentation and finite element thermomechanical simulation, showing how the problem can be alleviated in production, concludes the thesis.

EPFL2005

Thermo mechanical effects in Ultra-High Performance Fibre Reinforced Concretes (UHPFRC) at early age

Eugen Brühwiler, Emmanuel Denarié, Aicha Kamen, Hamid Sadouki

The extremely low permeability of Ultra-High Performance Fibre Reinforced Concretes (UHPFRC)associated to their outstanding mechanical properties make them especially suitable to locally "harden" reinforced concrete structures in critical zones subjected to an aggressive environment and to significant mechanical stresses. Composite UHPFRC-concrete structures promise a long-term durability which helps avoid multiple interventions on structures during their service life. Temperature Stress Testing Machines (TSTM) are very well suited to "experimentally simulate" the conditions encountered in composite structures in a new layer, at early age, subjected to restrained shrinkage under complex environmental conditions. They can also be used to determine intrinsic properties such as free shrinkage and creep response under well defined conditions of restraint and temperature. A new TSTM testing setup has been used to characterize the response of two types of strain hardening UHPFRC, with different binders (CEM I and CEM III), under various thermo mechanical conditions. Isotherm tests as well as test under realistic temperature conditions have been performed. Current numerical models have been applied to simulate the tests and the range of their applicability has been determined for temperatures between 10 and 30 °C. Moreover, the significant influence of non linearity in the creep response of UHPFRC, at early age, under moderate to high tensile load levels has been demonstrated. The test results showed a significant creep potential due to the high volume of paste. This beneficial effect was reflected by the linearly increasing -relationship between tensile creep and shrinkage. As expected, UHPFRC tensile creep behaviour was also sensitive to the loading level. Above 35 % of the tensile strength at the loading age, the material exhibited a non linear behaviour. A Maxwell chain model was applied to predict the early age UHPFRC tensile creep and confirmed the observed non-linear response.

2008