A microscopic model for the void growth behavior

A model for void growth behavior is developed on the basis of a dislocation theory. In order to model many uniformly distributed voids, a spherical unit cell with a growing void is considered to be subjected to a hydrostatic tensile stress under the condition of a constant applied strain rate. In the spherical unit cell, the relationships between several deformation parameters characterizing the void growth behavior are determined. It is assumed that as a void grows, it maintains the spherical shape and a constant average density of mobile dislocations in the intervoid matrix. A microscopic constitutive equation related to the void growth is established by correlating the mobility of dislocations to the thermally activated shear stress. Taking into account a mechanical condition that the applied energy rate is dissipated by the plastic work rate expended for the motion of dislocations, an equation controlling the void growth is developed. The relationship of the void growth rate to the hydrostatic tensile stress and the void fraction is derived as a function of the product of the thermally activated shear stress and the activation volume for dislocation motion for two limiting cases of the mobile dislocation distribution. The effect of localized deformation behavior on the void growth is discussed compared with a continuum plasticity theory.     

The influence of multiaxial states of stress on the hydrogen embrittlement of zirconium alloy sheet

The ductility of ZIRCALOY *-2 sheets containing 21-615 wt ppm hydrogen has been investigated at room temperature over a range of stress states from uniaxial to equibiaxial tension. Data based on locally determined fracture strains show a decrease in ductility with both increasing hydrogen content and increasing degree of biaxiality of the stress state. Metallographic and fractographic examinations indicate that the embrittlement is a consequence of void nucleation (due to hydride fracture), void growth, and void link-up. The influence of hydrogen content and stress state on each of the sequential stages of ductile fracture is determined. These results indicate that the primary cause for the influence of stress state on the hydrogen embrittlement of the ZIRCALOY sheet is that void link-up is initiated at a much lower critical void density in equibiaxial tension than in uniaxial tension. This appears to be a result of equibiaxial deformation enhancing (a) direct participation of previously unfractured hydrides in providing a fracture path linking up voids and (b) a localized shear instability process which is triggered by the nucleation of voids.     

The influence of tensile stress states on the failure of HY-100 steel

The failure of an HY-100 steel plate has been examined as a function of stress state using notched and un-notched axisymmetric tensile specimens. The results show that increasing stress triaxiality leads to a rapid decrease in failure strains in a manner that is exponentially dependent on the degree of triaxiality. Two ductile failure mechanisms are identified: a void coalescence process, in which relatively equiaxed voids grow to impingement, and a void-sheet process, which links by a shear instability process large, elongated inclusion-initiated voids. The void-sheet mechanism intervenes and limits ductility at high-stress triaxialities in transversely oriented HY steel plate material, whereas the former process controls failure in longitudinally oriented material. These orientation effects are related to the morphology and alignment of the nonmetallic inclusion stringers that act as the primary void nucleation sites. Calcium treatments for inclusion-shape control improve ductility, especially at intermediate-stress triaxialities, primarily by suppressing the local conditions which give rise to the void-sheet instability process.     

Temperature-Induced transition

A nitrogen-strengthened austenitic stainless steel was tested in uniaxial tension at room temperature (295 K) and in liquid nitrogen (76 K). A transition in ductile fracture appearance from a cup-cone fracture at room temperature to shear fracture at cryogenic temperature is observed and correlated to deformation behavior and micromechanisms (void nucleation and strain localization) of fracture. The flow stresses, fracture stresses, and strain hardening rates are all higher at liquid nitrogen temperature compared to those at room temperature, and the significant increases in plastic flow stresses are accompanied by planar deformation mechanisms. At both temperatures, primary void nucleation is observed mainly at scattered, large patches of sigma phase, and initial primary void growth is associated with tensile instability (necking) in the specimen. Postuniform elongation at 295 K leads to secondary void nucleation from small, less than 1 μm in diameter, microalloy particles, leading directly to failure; the strain required for secondary void growth and coalescence is highly localized and does not contribute to macroscopic elongation. At 76 K, uniform strain increases, total strain decreases, and strain localization into shear bands between the primary voids and the surface of the neck leads directly to failure. Secondary void nucleation, growth, and coalescence are limited to shear bands and also do not contribute to the macroscopic elongation. The observations of void nucleation are characterized in terms of a continuum analysis for the interfacial stress at voidnucleating particles. The critical interfacial stress for void nucleation at the lower temperature correlates with the increased flow properties of the matrix.     

The mechanism of void formation,void growth,and tensile fracture in an alloy consisting of two ductile phases

An investigation has shown that it is possible to relate void formation, void growth, and tensile ductility to microstructural features in an α-β titanium alloy, Ti-5.25A1-5.5V-0.9Fe-0.5Cu, heat treated to a constant yield strength. Equations relating tensile void growth rates to microstructure for both equiaxed,E, and Widmanstätten plus grain boundaryα, W + ITG. B.,in aged β morphologies have been derived. A mechanism for void formation at α-β interfaces is presented which accounts for the observed fact that voids do not form at Widmanstätten α platelets. Tensile fracture is shown to be intergranular in nature and occurs when a critical crack length-stress relationship is satisfied. The amount of ductility achievable in a specimen depends upon the rate of void growth. If the rate is large, the void reaches a critical size for fracture at a lower applied stress and strain and hence the ductility is less.     

An investigation of the plastic fracture of AISI 4340 and 18 Nickel-200 grade maraging steels

The mechanisms of plastic fracture (dimpled rupture) in high-purity and commercial 18 Ni, 200 grade maraging steels and quenched and tempered AISI 4340 steels have been studied. Plastic fracture takes place in the maraging alloys through void initiation by fracture of titanium carbo-nitride inclusions and the growth of these voids until impingement results in coalescence and final fracture. The fracture of AISI 4340 steel at a yield strength of 200 ksi (1378 MN/mm²) occurs by nucleation and subsequent growth of voids formed by fracture of the interface between manganese sulfide inclusions and the matrix. The growth of these inclusion-nucleated voids is interrupted long before coalescence by impingement, by the formation of void sheets which connect neighboring sulfide-nucleated voids. These sheets are composed of small voids nucleated by the cementite precipitates in the quenched and tempered structures. The sizes of non-metallic inclusions are an important aspect of the fracture resistance of these alloys since the investigation demonstrates that void nuclea-tion occurs more readily at the larger inclusions and that void growth also proceeds more rapidly from the larger inclusions. Using both notched and smooth round tensile specimens, it was demonstrated that the level of tensile stress triaxiality does not effect the void nu-cleation process in these alloys but that increased levels of triaxial tension do result in greatly increased rates of void growth and a concomitant reduction in the resistance to plastic fracture.     

The effects of triaxial stress on void growth and yield equations of power-hardening porous materials

In engineering applications, especially for ductile fracture of materials, nucleation, growth and coalescence of voids have often been observed. Currently there is an increase in interest for the effects of voids on the behaviour of engineering materials. In this paper, by the method of combining micro- and macro-parameters, the effects of triaxial stress on the rates of void growth and yield equations are presented for porous materials with power-hardening. The relations between triaxial stress and the rates of void growth for different n-values and yield equations with different n-values and void volume fractions are discussed. Following results have been obtained: For a porous material with power-hardening, the yield equation can be approximately expressed by an elliptical equation in equivalent stress and triaxial stress. Both the long half-axis and the short half-axis of the elliptical equation are functions of the void volume fraction for a given hardening exponent. The triaxial stress has a strong effect on the growth rates of voids. For linear hardening materials, the relation between the growth rate of voids and the triaxial stress is linear. For elastic/perfectly plastic materials with a small void volume fraction, the growth rate of voids can be described in relation to the triaxial stress with an exponential function. The results from this paper are compared with theoretical results from other researchers for elastic/perfectly plastic materials. A good agreement is shown.     

Creep and intergranular cracking of Ni-Cr-Fe-C in 360 °C argon

The influence of carbon and chromium on the creep and intergranular (IG) cracking behavior of controlled-purity Ni-xCr-9Fe-yC alloys in 360 °C argon was investigated using constant extension rate tension (CERT) and constant load tension (CLT) testing. The CERT test results at 360 °C show that the degree of IG cracking increases with decreasing bulk chromium or carbon content. The CLT test results at 360 °C and 430 °C reveal that, as the amounts of chromium and carbon in solution decrease, the steady-state creep rate increases. The occurrence of severe IG cracking correlates with a high steady-state creep rate, suggesting that creep plays a role in the IG cracking behavior in argon at 360 °C. The failure mode of IG cracking and the deformation mode of creep are coupled through the formation of grain boundary voids that interlink to form grain boundary cavities, resulting in eventual failure by IG cavitation and ductile overload of the remaining ligaments. Grain boundary sliding may be enhancing grain boundary cavitation by redistributing the stress from inclined to more perpendicular boundaries and concentrating stress at discontinuities for the boundaries oriented 45 deg with respect to the tensile axis. Additions of carbon or chromium, which reduce the creep rate over all stress levels, also reduce the amount of IG fracture in CERT experiments. A damage accumulation model was formulated and applied to CERT tests to determine whether creep damage during a CERT test controls failure. Results show that, while creep plays a significant role in CERT experiments, failure is likely controlled by ductile overload caused by reduction in area resulting from grain boundary void formation and interlinkage. Thomas M. Angeliu, formerly Graduate Student Research Assistant, Department of Materials Science and Engineering, the University of Michigan, Ann Arbor, MI,.     

Hydrogen embrittlement of titanium sheet under multiaxial states of stress

The influence of hydrogen on the ductility of commercially pure titanium sheet has been investigated over a range of stress states from uniaxial to equibiaxial tension. The data show that hydrogen embrittlement of plastically anisotropic Ti sheet depends on stress state, being the most severe in equibiaxial tension. Quantitative metallography indicates that the effect of stress state is primarily a result of two factors: (1) plane strain and equibiaxial tensile deformation are especially effective in causing the strain-induced fracture of hydrides and consequently void formation, and (2) the void link-up process in plane strain and equibiaxial tension initiates at a comparatively low bulk void density. The results are analyzed in terms of the influence of stress state on both hydride fracture and the occurrence of shear instabilities triggered by hydride fracture/void nucleation.     

A study of void nucleation,growth, and coalescence in spheroidized 1518 steel

The ductile fracture of a spheroidized 1518 steel has been investigated using three types of tensile specimens — smooth tensile, notched tensile, and plane-strain tensile. It was found that void nucleation has two different modes (Type I and Type II) depending on local conditions, the most important of which are the size, shape, and distribution of the particles. By identifying the low-strain-range nucleation behavior (Type I), it was possible to determine the value of plastic strain, ε_N, after which void nucleation at average-sized carbide particles (Type II) begins; ε_N is 0.45 for the smooth tensile case, 0.30 for the notched, and 0.25 for the plane strain. The critical stress for Type II void nucleation, σ_c, is of the order of 1200 MPa. Void growth depends on the macroscopic stress-strain state: longitudinal growth is given by a linear function of applied plastic strain, ε_p, whereas lateral growth shows a linear dependence on the triaxial stress, σ_T. When the local value ofV _f reaches a critical volume fraction of voids (V _f ^cri = 5 ± 0.5 pct), void coalescence occurs in a catastrophic manner, leading to final separation within a highly localized zone. The stress concentration caused by the notched tensile specimen geometry and the localized mode of plastic flow caused by the constraint of the plane-strain state in a Clausing-type specimen were found to affect the substeps of void nucleation, growth, and coalescence. Formerly Graduate Research Assistant, Division of Engineering, Brown University. Formerly Professor, Division of Engineering, Brown University, Providence, RI.     

On void nucleation and growth in metal interconnect lines under electromigration conditions

Electromigration failure in rigidly passivated metal interconnect lines is studied with particular reference to the vacancy supersaturations and hydrostatic stresses that can be developed at blocking grain boundaries under electromigration conditions. It is shown that the high stresses needed for homogeneous void nucleation to occur are probably too high to be developed by electromigration and that failure is more likely to involve the growth of pre-existing voids. We also show that the amount of void growth that can occur at a blocking grain boundary by electromigration of vacancies down the adjoining grain boundaries is small relative to the dimensions of the line unless the adjoining grain boundaries are continuous in a very long section of the line. This suggests that other mechanisms of void growth are responsible for electromigration failure. An analysis of the electromigration of small pre-existing voids shows that above a critical size, large voids migrate faster than smaller ones. This leads to a catastrophic process in which large voids can catch up with and coalesce with smaller ones, growing in size and migrating more rapidly as they do so. We conclude that the migration and coalescence of preexisting voids is a more likely mechanism of electromigration failure. This paper is based on a presentation made in the “G. Marshall Pound Memorial Symposium on the Kinetics of Phase Transformations” presented as part of the 1990 fall meeting of TMS, October 8–12, 1990, in Detroit, MI, under the auspices of the ASM/MSD Phase Transformations Committee.     

Failure behavior of heat-affected zones within HSLA-100 and HY-100 steel weldments

The deformation and fracture behavior of simulated heat-affected zones (HAZ) within HSLA-100 and HY-100 steel weldments has been studied as a function of stress state using notched and unnotched axisymmetric tensile specimens. For the case of the HSLA-100 steel, the results for fine-grained, as well as coarse-grain HAZ (CGHAZ) material, show that, despite large differences in the deformation behavior when compared to base plate or weld metal, the failure strains are only weakly dependent on the thermal history or microstructure. Ductile microvoid fracture dominates the failure of the HSLA-100 steel with small losses of ductility occurring in the HAZ conditions only at high stress triaxialities. In contrast, the HY-100 steel is susceptible to a large loss of ductility over all of the stress states when subjected to a severe, single-pass simulation of a CGHAZ. The ductility loss is greatest at the high stress triaxiality ratio in which case failure initiation occurs by a combination of localized cleavage and ductile microvoid fracture.     

Synchrotron Tomographic Characterization of Damage Evolution During Aluminum Alloy Solidification

Fast synchrotron X-ray microtomography was used to directly observe damage accumulation in a semi-solid Al-15 wt pct Cu alloy with a solid fraction of ~0.75 during isothermal tensile deformation. The evolution of damage was quantified in terms of size distribution of internal and surface-connected damage, strain mapping, and volume change to provide an insight into hot tear formation. A combination of existing void growth, void nucleation, and void coalescence all contribute to the final failure, although each dominates during different stages of deformation. Specifically, internal voids are shown to grow and coalesce from the region of high triaxiality at the center of the gage length outward and prove to be the contributing factor to final failure caused by insufficient liquid feeding.     

High-temperature rupture of microstructurally unstable 304 stainless steel under uniaxial and triaxial stress states

Specimens of 304 stainless steel were tested to failure under two different stress states, uniaxial tension using smooth bar specimens and triaxial tension using notched bar specimens. The tests were conducted at a temperature that gives rise to carbide particle growth which, in turn, leads to microstructural softening. Rupture times are compared for uniaxial and triaxial stress states with respect to multiaxial stress parameters that are directly related to physical mechanisms. The success of the parameters is judged according to how well the rupture times of notched specimens can be predicted using the rupture data for specimens under uniaxial tension. The data indicate that the rupture time is not governed by deformation processes, despite evidence for substantial softening by particle coarsening. The results further suggest that the creep rupture process is dominated by cavitation that is coupled with localized shear deformation along the inclined grain boundaries.     

Void growth and coalescence in Constrained Silver Interlayers

The mechanisms of void growth and coalescence during fracture of thin Ag interlayers were studied by tensile testing and metallographic examination. No measurable void growth was observed in the deformed interlayers prior to fracture. The fracture surface dimple size, how- ever, increased with increasing interlayer diameter-to-thickness ratio(D/T). The experimental results suggest that fracture in the constrained Ag interlayers occurred by void initiation at sil- icon oxide inclusions followed immediately by void coalescence. The highly triaxial stress state in the interlayer promoted void coalescence by plastic instability and accounts for the observed change in fracture surface dimple size withD/T. An expression, based upon a slip-line field model of the deformation zone between neighboring voids, is presented which relates the dimple size to the average inclusion diameter and the stress state in the interlayer. The predictions of the expression are in broad agreement with the experimental data.     

Influence of Grain Boundary Character on Creep Void Formation in Alloy 617

Alloy 617, a high-temperature creep-resistant, nickel-based alloy, is being considered for the primary heat exchanger for the Next Generation Nuclear Plant (NGNP), which will operate at temperatures exceeding 760 °C and a helium pressure of approximately 7 MPa. Observations of the crept microstructure using optical microscopy indicate creep stress does not significantly influence the creep void fraction at a given creep strain over the relatively narrow set of creep conditions studied. Void formation was found to occur only after significant creep in the tertiary regime (>5 pct total creep strain) had occurred. Also, orientation imaging microscopy (OIM) was used to characterize the grain boundaries in the vicinity of creep voids that develop during high-temperature creep tests (900 °C to 1000 °C at creep stresses ranging from 20 to 40 MPa) terminated at creep strains ranging from 5 to 40 pct. Preliminary analysis of the OIM data indicates voids tend to form on grain boundaries parallel, perpendicular, or 45 deg to the tensile axis, while few voids are found at intermediate inclinations to the tensile axis. Random grain boundaries intersect most voids, while coincident site lattice (CSL)–related grain boundaries did not appear to be consistently associated with void development. Similar results were found in oxygen-free, high-conductivity (OFHC) copper, severely deformed using equal channel angular extrusion, and creep tested at 450 °C and 14 MPa.     

A three-dimensional model for ductile fracture by the growth and coalescence of microvoids

A general three-dimensional model of the ductile fracture process in metals is developed for the case of a rigid non-hardening plastic solid, containing a regular distribution of spherical microvoids. The model takes full account of the effects of volumetric growth and shape change of the individual voids, in triaxial stress fields and defines the condition of plastic limit-load failure of the intervoid matrix at incipient void coalescence. The results suggest that the primary influence of the mean-normal stress on ductile fracture is in promoting plastic-limit load failure of the intervoid matrix, rather than in promoting dilational growth of the voids. The theoretical ductile fracture strains are found to be in good agreement with experimental results.     

Assessment of void growth models from porosity measurements in cold-drawn copper bars

This work investigates void growth in cold-drawn copper bars containing a fine dispersion of small inclusions at which voids nucleate. Using the Rice and Tracey (RT), the Gurson-Tvergaard (GT), and the Gurson-Leblond-Perrin (GLP) void growth models, a procedure is proposed for deriving the porosity distribution from density measurements on specimens sectioned from the neck of a tensile bar. This procedure allows identification of the parameters of the models. The effect of strain hardening on porosity evolution is analyzed by comparing the behavior of the material in the cold-drawn state (n≈0.1) and in the recrystallized state (n≈0.4). Inclusion dimensions and distributions were found to be identical in these two states. The parameter α of the RT model is found to depend on n, whereas the parameter q of the Gurson-type models does not vary with n. Numerical modeling of porosity variations in notched, round copper bars shows that both the parameter α and the parameter q in the GT model depend on the stress triaxiality in the recrystallized material, whereas the parameter q remains a constant in the GLP model. Accounting for the ellipsoidal void shapes and for the presence of the inclusion significantly affects the prediction of porosity variations.     

Void growth and coalescence in constrained silver interlayers

The mechanisms of void growth and coalescence during fracture of thin Ag interlayers were studied by tensile testing and metallographic examination. No measurable void growth was observed in the deformed interlayers prior to fracture. The fracture surface dimple size, however, increased with increasing interlayer diameter-to-thickness ratio(D/T). The experimental results suggest that fracture in the constrained Ag interlayers occurred by void initiation at silicon oxide inclusions followed immediately by void coalescence. The highly triaxial stress state in the interlayer promoted void coalescence by plastic instability and accounts for the observed change in fracture surface dimple size withD/T. An expression, based upon a slip-line field model of the deformation zone between neighboring voids, is presented which relates the dimple size to the average inclusion diameter and the stress state in the interlayer. The predictions of the expression are in broad agreement with the experimental data. R.J. KLASSEN, formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto. G.C. WEATHERLY, formerly with the Department of Metallurgy and Materials Science, University of Toronto.