Void Growth Rate Research Articles

Ductile tearing in part-through cracks: experiments and cell-model predictions

This study describes an application of the computational cell model to predict ductile crack growth measured in experiments performed on surface-cracked, thick plates fabricated from a ferritic pressure vessel steel. The cell model limits void growth and coalescence to within a thin layer of material over the crack plane. Outside this layer, the material deforms plastically but remains void free. The Gurson–Tvergaard dilatant plasticity model describes the evolution of void growth and the associated macroscopic softening within the cells. Material-specific, cell parameters readily separate into two categories: those describing the micromechanics of void growth rate and those describing the local fracture process of the cell. Calibration of these parameters utilizes both discrete (3-D) cell models and R-curves measured using standard deep-notch bend or compact tension specimens. The cell model is applied here to surface-cracked plates subjected to different loading histories of tension and bending. The calibrated cell model reproduces accurately full details of the load-deformation records and the crack growth profiles for all the cases. These numerical studies suggest that the computational approach based on the cell model provides an engineering tool to predict ductile crack growth behavior in flawed structural components.

Estimation of the lifetime of Al/Ni-plated material for wet-seal area in molten carbonate fuel cells

Al/Ni-plated material, which is produced by electroplating of Ni and Al on a stainless-steel substrate followed by heat-treating at 750°C, has been investigated for the wet-seal material. In order to estimate the lifetime of the material, Type A and Type B were prepared, and immersion test in molten carbonate and heating test in air at various temperatures were carried out. Results of this study are summarized as follows. Two types of Al/Ni-plated material showed a good corrosion resistance against the molten carbonate at 650°C in 70% air/30% CO2 for 14 500 h. In the accelerated heating test, Al concentration in the Al–Ni layer kept nearly constant after 10 000 h, but voids were observed at the Al–Ni layer/the substrate interface. It was found that the growth rate of void, which was calculated from the area fraction of voids observed at each temperature, was proportional to temperature. The log k decreased linearly with 1/T, where k was a constant of the growth rate of voids. It was suggested that the lifetime of the Al/Ni-plated material is expected to be more than 40 000 h at 650°C in molten carbonate.

Evaluation of the rate of diffusion growth of voids with regard for the concentration of stresses in their vicinity

We study the effect of concentration of stresses near grain-boundary voids on their growth rate for the diffusion mechanism of growth. For this purpose, we use the boundary-value problem of diffusion posed earlier on the basis of the thermodynamic analysis of a two-phase metal-void system with vacancies. To obtain its solution in the analytic form, we apply a simplified geometric scheme in which the voids are regarded as infinite tubes in the planes of grain boundaries. The results of numerical calculations demonstrate that if we ignore the effect of concentration of stresses, then we obtain (1.5–2)-times underestimated values both of the void growth rate and of the time to fracture of the grain boundary.

Modelling the flow processes of a particle reinforced metal matrix composite during machining

Abstract This paper reports on a numerical test program to model the micromechanics associated with the machining of a particle-reinforced metal matrix composite (PRMMC) The composite material modelled was a 35% by volume SiC particle-reinforced A356 aluminium alloy. A submodelling approach was adopted in order to analyse the micromechanical problem. Simulation of the metal cutting process was performed using FORGE2, an elasto-visco plastic FEA code. The micromechanical submodelling was performed using ANSYS 5.2, an elastoplastic FEA code. The machining model of the aluminium alloy without the reinforcement and the resulting hydrostatic pressure istribution were used as inputs for the ANSYS micromechanical submodels of the composite. The regions modelled included the primary shear zone, the machined surface, and the chip-tool contact region, in both the sticking and sliding regions along the rake face. All FE models were assumed to be plane strain. The results of the FE submodelling agree favourably with those obtained from machined test pieces when observed under a scanning electron microscope (SEM). Particle clustering has a detrimental effect on the rate of void growth. It was observed that SiC particles under the action of normal loads cause intense normal stresses at the point of contact between the aluminium matrix and the tungsten-carbide particles within the cutting tool. Overstraining of the matrix envelopes the SiC particle in contact with the cutting tool. A coarse grade of diamond tool had a superior wear resistance compared to a fine grade.

GROWTH OF SPHEROIDAL VOIDS IN ELASTIC‐PLASTIC SOLIDS

Abstract— The effect of void shape on the mechanical behaviour of an elastic‐plastic solid containing an isotropic array of aligned axisymmetric voids is examined. The mechanical response of such a material is studied by means of finite element (FE) analyses of an elementary unit cell containing an isolated void. The void shape is found to have a strong influence on both void growth rate and coalescence strain. This effect is strongest for low stress triaxialities. The numerical results are compared with analytical models of void growth, but none of the examined models give any good predictions of the results obtained numerically. A simple modification of the classical Gurson model is suggested so as to give reasonable correspondence with numerical results. Finally, some practical considerations of void shape effects are given.

Measurement of cavitation damage in isothermally crept Al/SiC p composites using small-angle neutron scattering

Small-angle neutron scattering is shown to enable the detection of cavities in strained Al/SiC p composites. An iterative method based upon analytically calculated scatterer size distribution functions is introduced. Generally, this method allowed the determination of scatterer shapes with little initial knowledge of their exact geometry. It is suggested that fewer cavities are nucleated during tensile testing than during creep tests. Larger reinforcement sizes are demonstrated to raise the rate of void growth, but to lower the overall number of generated cavities. Composite pre-fatiguing is shown to increase significantly the number of nucleated voids.

Modelling void nucleation and growth in axisymmetric extrusion

Elastic-viscoplastic constitutive equations, with kinematic and isotropic hardening, are employed to model the deformation behaviour of an aluminium alloy in extrusion. Constitutive equations are also employed for void nucleation and growth, which are fully coupled with the deformation behaviour. The material model is employed to investigate the roles of void nucleation and growth in extrusion defect formation. It has been shown that central bursting is a void growth controlled process. The existence of nucleated voids only leads to central burst formation with the existence of appropriate stress states which lead to void growth. The results obtained show excellent agreement with well-established limit diagrams, obtained analytically and experimentally. The results also show that for a given combination of area reduction and semi-cone die angle, the introduction of friction tends to inhibit the formation of central bursting, but increases the likelihood of surface tearing/cracking. The tendency to inhibit central burst formation with increasing friction results from the reduction in the levels of tensile hydrostatic stress, which therefore reduce the rate of void growth. A comparison of the results obtained using kinematic and isotropic hardening in the extrusion process showed that significantly different residual stress fields are obtained for the two cases. This is of importance, for example, in the case of multipass extrusion or where the residual stress field is to be used subsequently in design analysis.

The effect of hydrogen on the fracture toughness of alloy X-750

The effect of hydrogen on the fracture toughness behavior of a nickel-base superalloy, Alloy X-750, in the solutionized and aged condition was investigated. Notched bend specimens were tested to determine if the fracture process was stress or strain controlled. The fracture was observed to initiate at a distance between the location of maximum stress and maximum strain, suggesting that fracture required both a critical stress and strain. The effect of hydrogen was further investigated and modeled using fracture toughness testing and fractographic examination. The fracture toughness of the non-charged specimen was 147 \(MPa\sqrt m \). Charging with hydrogen decreased the fracture toughness, Klc, to 52 \(MPa\sqrt m \) at a rapid loading rate and further decreased the toughness to 42 \(MPa\sqrt m \) for a slow loading rate. This is consistent with the rate-limiting step forthe embrittlement process being hydrogen diffusion. The fracture morphology for the hydrogen-charged specimens was intergranular ductile dimple, while the fracture morphology of noncharged specimens was a mixture of large transgranular dimples and fine intergranular dimples. The intergranular failure mechanism in Alloy X-750 was a microvoid initiation process at grain boundary carbides followed by void growth and coalescence. One role of hydrogen was to reduce the void initiation strain for the fine intergranular carbides. Hydrogen may have also increased the rate of void growth. The conditions ahead of a crack satisfy the critical stress criterion at a much lower applied stress intensity factor than for the critical fracture strain criterion. A model based on a critical fracture strain criterion is shown to predict the fracture behavior.

Application of Local Damage and Fracture Models to Notched Round Copper Bars

The Rice & Tracey, damage work, and Lemaitre & Chaboche models were investigated on cylindrical notched extruded copper bars. The values of the two constant factors appearing in the expression of the void growth rate in the Rice & Tracey model were reevaluated by combining experiments (porosity measurements and tensile tests) and numerical computations of uniaxial tensile tests and of tensile tests on notched round bars. The values of the critical void growth rates (Beremin approach) and critical damage works were found to be independent on triaxiality. The application of the Lemaitre & Chaboche model allows to predict the softening appearing at initiation for lower triaxialities. Difficulties were encountered to physically identify the parameters of the model.

A Numerical Study of the Ductile Tearing in Welded Joints Using the Rice-Tracey Void Growth Model

A finite element (FE) analysis of a CT25 specimen has been achieved for three configurations of a welded structure : monometallic (base metal), bimetallic (base metal and weld metal) and trimetallic (BM+WM+HAZ). Using the RICE-TRACEY model, a void growth parameter R/Ro has been computed for each case. The evolution of this parameter indicates clearly that the bimetallic specimen is the most harmful while the monometallic case leads to conservative results. Furthermore, a crack propagation analysis, based upon a critical value of the void growth rate, has been performed. Numerical and experimental tearing rates dJ/da are in good agreement but numerical J values are clearly underestimated. Concerning the trimetallic specimen, when analysing the void growth rate distribution around the crack tip, a prediction of crack propagation direction may be possible.

Analysis of growth rates of voids in the matrix and at precipitates in irradiated alloys

A characteristic feature of irradiated complex alloys is the correlated evolution of voids, dislocations and seconday phase precipitates, with the largest voids often adjacent to precipitates. Two mechanisms can be responsible for enhanced growth of voids at precipitates. The collector mechanism considers the whole surface of the pair void—precipitate as a point defect sink. The segregation mechanism accounts for the difference in radiation-induced segregation near free voids and voids at precipitates and corresponding difference in segregation-induced biases. In this paper a kinetic model for size distribution functions of isolated voids and voids adjacent to precipitates is developed. By fitting the model calculations to experimental data, the effective bias of voids at G-phase precipitates in neutron-irradiated 12Cr 15Ni steel is calculated and compared with predictions of collector and segregation mechanisms. The effect of precipitates on swelling rate of alloys is analysed.

Influence of Strain History on Ductile Failure of Steel

Notched tensile bars of a high strength structural steel were loaded to void coalescense. The results show that the damage curve determined using radially loaded specimens is not valid for specimens under non-radial loading. The results of the experiments with different load histories of notched tensile bars show, that a single parameter criterion like a damage parameter is not sufficient to describe the initiation process of void coalescense. The shape of the voids and the triaxiality at initiation exhibit a strong influence on the initation values. There are two ways to describe the initiation. A simple one considers a critical combination of void growth rate, triaxiality and plastic strain at initiation. The other one uses a shape factor to describe the shape of the voids and calculates the initiation values. Both models work with an accuracy in the order of the experimental scatter.

Modeling Ductile Fracture of Al Alloys in Relation with Statistical Distribution of Second Phase Particles

Fracture toughness tests have been carried out on two Al alloys (7075 and 7475) containing different amounts of Fe and Si. These materials were tested in T3, T6 and T7 conditions, along six orientations (LT, LS, TL, TS, SL and ST). Large variations in the fracture toughness (20-60 MPa√m) were measured. Mechanical tests on notched specimens were also performed to determine the influence of stress triaxiality ratio on ductility. These specimens were calculated by finite element method. Quantitative metallography was largely used to measure the volume fraction of intermetallic particles (Mg 2 Si and Fe-rich precipitates) and the statistical distribution of these particles. The Gurson potential is used to interpret these test resulls carried out on volume elements and on cracked specimens. It is shown that the ductility of notched specimens and the measured variations in fracture toughness can be interpreted with the Gurson potential provided that the non homogeneous distribution of intermetallic particles is taken into account. A model has been developed to relate the toughness of the alloys to the field strength, the critical void growth rate calculated on notched specimen from Rice and Tracey equation and to the mean distance between the clusters of second phase particles.

An analysis of the extrusion of bimetallic tubes by numerical simulation

This paper presents a numerical analysis of a high temperature extrusion process applied to bimaterial tubes made of two pre-bonded metallic materials with different plastic properties. The analysis has been carried out for different geometries and material combinations by using a FE code. An elasto-plastic behaviour with strain rate dependence has been assumed. A parameter related to the void growth rate at the bimaterial interface has been considered for fracture prediction during the extrusion operation. The influence of the different extrusion variables, namely the yield stress ratio, the location and relative thickness of the layers and the die angle, has been assessed. As a conclusion of the analysis, the yield stress ratio between the two materials turns out to be the most critical parameter of the process. Besides, the thickness fluctuations of the harder layer in the final product have been analysed for several material combinations. Those fluctuations can lead to an unacceptable geometrical heterogeneity under certain conditions. The results of the FE calculations are in reasonable agreement with the scarce data available from similar industrial operations. In short, the paper shows that use of FE calculations can be a pre-screening tool for the selection of material couples and extrusion conditions for the production of sound bimetallic tubes, before being engaged in very costly full-scaled trials.

Electromigration and Diffusion in Pure Cu And Cu(Sn) Alloys

AbstractAtom movements of Cu in pure Cu and Cu(0.5 to 2 wt.% Sn) alloys have been investigated using drift velocity and radioactive tracer techniques. The void growth rate in pure Cu at the cathode end, as a result of electromigration driving force, linearly increases with the applied current density. A marked decrease in the Cu grain boundary diffusivity and electromigration drift velocity is attributed to Sn trapping of Cu atoms and/or binding defects at grain boundaries. The effect is more pronounced at lower temperatures. The activation energies for electromigration and diffusion of Cu in pure Cu grain boundaries were found to be in the range of 0.7 – 0.9 eV. Addition of about 0.5 to 2 wt.% Sn increased these energies to 1.1 – 1.3 eV, respectively which resulted in enhancement of electromigration resistance by several orders of magnitude over that in pure Cu at the field operation temperature.

Electromigration and Diffusion in Pure Cu and Cu(Sn) Alloys

AbstractAtom movements of Cu in pure Cu and Cu(0.5 to 2 wt.% Sn) alloys have been investigated using drift velocity and radioactive tracer techniques. The void growth rate in pure Cu at the cathode end, as a result of electromigration driving force, linearly increases with the applied current density. A marked decrease in the Cu grain boundary diffusivity and electromigration drift velocity is attributed to Sn trapping of Cu atoms and/or binding defects at grain boundaries. The effect is more pronounced at lower temperatures. The activation energies for electromigration and diffusion of Cu in pure Cu grain boundaries were found to be in the range of 0.7 - 0.9 eV. Addition of about 0.5 to 2 wt.% Sn increased these energies to 1.1 - 1.3 eV, respectively which resulted in enhancement of electromigration resistance by several orders of magnitude over that in pure Cu at the field operation temperature.

Elliptical void growth in shear

An approximate upper bound approach is developed to analyse the growth of an el­liptical void contained in a finite unit cell undergoing simple shearing combined with superimposed hydrostatic tension. The matrix is assumed to be an incompressible nonlinear power-law viscous solid. For a void in an infinite linearly viscous matrix material, the present result is in good agreement with Eshelby’s solution. For a non-linearly viscous matrix material, to calculate the constitutive potential, an accurate numerical method is developed. Comparisons of the upper bound solution of the potential and its first-order approximation with the accurate one are made. It is found that the potential values from the first-order approximation are closer to the accurate values than those from the upper bound solution. Therefore, the first-order approximation of the upper bound for the constitutive relations is used to give the relations of the stress triaxiality and the void growth rate. For both Newtonian materials and perfectly plastic materials, the suggested method gives closed forms for the void growth rate as an implicit function of the stress triaxiality, the void volume fraction, the void aspect ratio and the strain rate sensitivity exponent. For other cases, the void growth is investigated numerically.

Analysis of electromigration-induced failures in high-temperature sputtered Al-alloy metallization

Electromigration-induced failures in high-temperature sputtered Al-alloy metallization have been studied in terms of Al-alloy microstructure, Si nodules, and reaction products between the Al alloy and the underlayer material. Highly reliable interconnects can be realized by high-temperature sputtered Al–Si–Cu-alloy metallization utilizing a Ti underlayer. The interfacial reaction between the growing Al–Si–Cu film and the Ti underlayer during high-temperature sputtering produces an Al3Ti-alloy layer having a resistivity of about 40 μΩ cm, and Si in Al alloy is absorbed in the Al3Ti layer without forming Si nodules. As the result, a bilayer structure of Al alloy/Al–Ti–Si alloy is formed. The electromigration resistance of the resultant TiN/Al alloy/Al–Ti–Si/TiN structure is drastically improved. It is speculated from the experimental results that this is because of the high quality of the Al-alloy film microstructure, i.e., an increase in (111) orientation, a decrease in the standard deviation of the grain distribution, and the superior current bypass effect through the Al–Ti–Si alloy and underlying TiN layer. In particular, an electrical current easily flows through the Al–Ti–Si alloy and TiN layer before a void completely crosses the upper Al alloy part of the metal line because the formation of the AlN high-resistance layer is suppressed by laying the Ti film between the Al–Si–Cu film and the underlying TiN film. Accordingly, the local temperature increase in the vicinity of the void is not essential to the subsequent void growth due to the lower resistivity of the Al–Ti–Si-alloy layer, resulting in the low void growth rate.

Evolution of Void Shape and Size in Creeping Solids

A boundary value problem for a periodic array of initially spherical voids in a power law creeping solid is analyzed. An axisymmetric cell model relevant for simulating grain boundary void growth is used. The rate boundary value problem is solved by means of a finite element method. Void growth histories accounting for void shape changes and, within the cell model context, void interaction effects are computed for various remote stress triaxiality states. An automatic remeshing algorithm permits computations for large changes in void size and shape. The computed void growth rates are compared with predictions from available analytical formulas that neglect shape change effects.

Ductile fracture processes in 7075 aluminum

The ductile fracture of 7075 aluminum was examined as a function of aging condition, from underaged to overaged. Notched specimens allowed the triaxiality of stress to be varied. In-creasing triaxiality, which was due to increasing notch acuity, decreased ductility and increased nucleation of voids, in accord with expectations from ductile fracture models. Overaged ma-terial, which is generally resistant to environmental damage, was not susceptible to hydrogen embrittlement even with high triaxiality, but void sizes were increased by hydrogen. That in-crease suggested that void growth rates may be assisted by hydrogen in overaged 7075 aluminum.