Cavity formation from inclusions in ductile fracture

The previously proposed conditions for cavity formation from equiaxed inclusions in ductile fracture have been examined. Critical local elastic energy conditions are found to be necessary but not sufficient for cavity formation. The interfacial strength must also be reached on part of the boundary. For inclusions larger than about 100Å the energy condition is always satisfied when the interfacial strength is reached and cavities form by a critical interfacial stress condition. For smaller cavities the stored elastic energy is insufficient to open up interfacial cavities spontaneously. Approximate continuum analyses for extreme idealizations of matrix behavior furnish relatively close limits for the interfacial stress concentration for strain hardening matrices flowing around rigid non-yielding equiaxed inclusions. Such analyses give that in pure shear loading the maximum interfacial stress is very nearly equal to the equivalent flow stress in tension for the given state of plastic strain. Previously proposed models based on a local dissipation of deformation incompatibilities by the punching of dislocation loops lead to rather similar results for interfacial stress concentration when local plastic relaxation is allowed inside the loops. At very small volume fractions of second phase the inclusions do not interact for very substantial amounts of plastic strain. In this regime the interfacial stress is independent of inclusion size. At larger volume fractions of second phase, inclusions begin to interact after moderate amounts of plastic strain, and the interfacial stress concentration becomes dependent on second phase volume fraction. Some of the many reported instances of inclusion size effect in cavity formation can thus be satisfactorily explained by variations of volume fraction of second phase from point to point.     

Cavity formation from inclusions in ductile fracture of A508 steel

Experiments were performed on A508 class 3 steel in order to determine the conditions for cavity formation from elongated MnS inclusions. Circumferentially notched tensile specimens were employed in order to investigate the effect of negative hydrostatic pressure. The results of finite element calculations and metallographic observations on polished sections were used to evaluate the conditions required for cavity initiation. Tests were performed at different temperatures in both longitudinal and short transverse direction. The results can be explained in terms of a local critical stress independent of temperature. This local stress is tentatively calculated using an extension of Eshelby’s theory for inclusions proposed by Berveiller and Zaoui.     

The shear mode of ductile fracture in materials with few inclusions

The mechanism of the shear mode of ductile fracture has been investigated in sheet tensile specimens of an α brass containing few inclusions. The techniques of optical metallography, scanning electron microscopy and transmission electron microscopy of both thin foils and replicas were all used in order to obtain as complete a picture of the fracture mechanism as possible. It was found that a zone of shear deformation, made up of many intense shear bands, developed across the specimen neck and fracture occurred within this zone along the shear bands. These shear bands consisted of material with a fine subgrain structure. No voids were found in the necked region of either deformed or fractured specimens yet the fracture surfaces were covered with elongated dimples. It is therefore suggested that the dimples on the fracture surface are not a precursor of the fracture but form only during the final process of separation.     

The shear mode of ductile fracture in materials with few inclusions

The mechanism of the shear mode of ductile fracture has been investigated in sheet tensile specimens of an α brass containing few inclusions. The techniques of optical metallography, scanning electron microscopy and transmission electron microscopy of both thin foils and replicas were all used in order to obtain as complete a picture of the fracture mechanism as possible. It was found that a zone of shear deformation, made up of many intense shear bands, developed across the specimen neck and fracture occurred within this zone along the shear bands. These shear bands consisted of material with a fine subgrain structure. No voids were found in the necked region of either deformed or fractured specimens yet the fracture surfaces were covered with elongated dimples. It is therefore suggested that the dimples on the fracture surface are not a precursor of the fracture but form only during the final process of separation.     

Hydrogen-assisted ductile fracture in porous iron

The present paper has studied the effect of porosity and hydrogen on the deformation and fracture properties in porous iron using double notched specimen tests and quantitative metallography analyses to characterize void growth. The presence of hydrogen produced the greatest hardening effect in the sample with a porosity of 0.037. It was found that while the effect of hydrogen on the reduction in area was greatest in the specimen with a porosity of 0.037, its effect on the fracture energy did not depend on the porosity. The ductile fracture surface morphology remained the same in all the specimens without and with hydrogen except for the sample with porosity of 0.003 where hydrogen induced some quasi-cleavage fracture. The quantitative metallography analysis of voids in the region near the fracture surface and below the unfractured notch has demonstrated that hydrogen causes the void growth to increase prior to plastic instability. The effect of hydrogen on the void growth was found to be slightly enhanced as the porosity was increased. The microscopic process of hardening induced by hydrogen is presented. The mechanism for hydrogen-assisted void growth is discussed in light of a recently developed model using a dislocation theory.     

Modeling of local strains in ductile fracture

The concept of dividing microvoid coalescence (MVC) ductile fracture into three constituent processes, nucleation, growth, and coalescence, is discussed, with emphasis on needs for additional analytical and experimental work. Statistical and stochastic aspects of the problem are presented. Recent work on modeling of local strains during ductile fracture, and particularly as components of fracture toughness, is summarized and discussed in light of current knowledge of ductile fracture. Such local strain modeling is especially attractive because it permits micromechanisms of fracture to be explicitly included in the fracture model. This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.     

Brittle to ductile transition in cleavage fracture

In many cleavable solids, cleavage cracks can propagate at steady state by laying down a trail of dislocations emanating from the crack tip and lying on planes inclined to the crack front. These crack-tip initiated dislocations produce shielding at the crack tip that reduces both the crack tip tensile stresses and the shear stresses on the inclined planes. They also blunt the crack. Cleavage cracks, can nevertheless, still propagate under appropriately increased stress intensity conditions to keep the crack tip tensile stress constant. A condition is reached in the propagation of such slightly blunted cracks where a small increment in temperature or a decrement in the crack velocity permits the nucleation of a new set of dislocations that produce additional shielding and blunting which tip the balance against the crack-tip tensile stresses. This results in a transition from brittle cleavage to ductile behavior. The steady state specific plastic work that can just be tolerated by a propagating cleavage crack before it catastrophically blunts is calculated to be only of the order of 10% of the specific surface energy. Although most geometrical details of the dislocation emission process are adequately modeled, the calculated brittle to ductile transition temperatures are found to be more than an order of magnitude higher than those that have been experimentally measured. This discrepancy is a result of the present inadequate methods of modeling activation configurations by considering the dislocation loop radius as the only activation parameter, while proper modeling of such configurations must consider also the Burgers shear displacement of the loop as an activation parameter. Such two parameter analyses, however, require accurate information on interlayer atomic shear resistance profiles for specific crystals which are presently not available. The analysis furnishes ready explanations of the toughening effects of so-called “ductilization” treatments and embrittling effect of aging and dislocation locking, as well as the relatively large difference between the lowest levels of toughness between fracture in polycrystals and in single crystals.     

Hydrogen-assisted ductile fracture in spheroidized 1518 steel

Hydrogen was introduced into smooth and notched tensile specimens of spheroidized 1518 steel by electrocharging under controlled galvanostatic conditions. The role of hydrogen during void nucleation and growth was investigated by identifying two different void nucleation modes. Hydrogen promoted void nucleation at average-sized carbide particles by reducing the critical interfacial strength, σ_C, from 1200 to 1000 MPa (using a dislocation model). The stress-induced hydrogen segregation to the particle interfaces during deformation was estimated to explain the hydrogen-reduced σ_C. Void growth in both longitudinal and lateral directions was enhanced by internal pressurization of hydrogen. In order to better quantify such hydrogen-enhanced void growth, the internal hydrogen pressure inside a void was calculated on the basis of thermodynamics. The final void coalescence stage was analyzed by assuming that the void nucleation rate follows a normal distribution.     

Effect of prestrain on stretch-zone formation during ductile fracture of Cu-strengthened high-strength low-alloy steels

The effects of prestrain on the ductile fracture behavior of two varieties of Cu-strengthened high-strength low-alloy (HSLA) steels have been investigated through stretch-zone geometry measurements. It is noted that the ductile fracture-initiation toughness of both the steels remained unaltered up to prestrains of ∼2 pct, beyond which the toughness decreased sharply. A methodology for estimating the stretch-zone dimensions is proposed. Fracture-toughness estimations through stretch-zone width (SZW) and stretch-zone depth (SZD) measurements revealed that the nature of the variation of ductile fracture toughness with prestrain can be better predicted through SZD rather than the SZW measurements. However, for the specimen geometries and prestrain levels that were investigated, none of these methods were found suitable for quantifying the initiation fracture toughness.     

Layer thickness effect on ductile tensile fracture

Laminated metal composites containing equal volume percentage of ultrahigh carbon steel (UHCS) and brass were prepared in three different layer thicknesses (750, 200, and 50 μm) by press- bonding and rolling at elevated temperature and were tensile tested at ambient temperature. A dramatic increase in tensile ductility (from 13 to 21 to 60 pct) and a decrease in delamination tendency at the UHCS-brass interfaces were observed as the layer thickness was decreased. The layer thickness effect on ductility is attributed to residual stress whose influence on delamination is decreased as the layer thickness is decreased. Suppression of delamination inhibits neck for- mation in the UHCS layers, allowing for extended uniform plasticity. For a given layer thick- ness, the tensile ductility decreases as the ratio of hardness of component layers is increased.     

Void/pore distributions and ductile fracture

The dependence of ductile, microvoid fracture on the size and distribution of voids or pores has been modeled experimentally. Pores or voids have been physically modeled in two dimensions by both random and regular arrays of equi-sized holes drilled through the thickness of tensile specimens of 1100-0 Al sheet and 7075-T6 Al plate and sheet. Fracture strains as well as failure paths have been determined for different hole sizes, spacings, and area fractions. A statistical analysis of the data indicates that increasing the minimum hole spacing, which decreases the degree of hole clustering, increases both strength and ductility. Conversely, decreasing the hole size causes a minor increase in both strength and ductility. Increasing the rate of work hardening is beneficial to ductility in that a high strain hardening rate appears to increase the resistance to flow localization between holes. The results are discussed in terms of a fracture process which depends on shear localization between holes/voids and which is very sensitive to void/pore distributions. This paper is based on a presentation made at the symposium “Stochastic Aspects of Fracture” held at the 1986 annual AIME meeting in New Orleans, LA, on March 2-6, 1986, under the auspices of the ASM/MSD Flow and Fracture Committee.     

Grain boundary ductile fracture in precipitation hardened aluminum alloys

Published microstructural studies of grain boundary (gb) fracture in precipitation hardened aluminum alloys are reviewed with respect to the three main ideas that have been developed to explain the gb fracture surfaces. The ideas are

• 1.(1) microvoid growth at large gb precipitates,
• 2.(2) strain localization in the soft, and sometimes solute-free, gb precipitate free zones (pfz) and
• 3.(3) the influence of matrix precipitate shear giving rise to inhomogeneous “planar” slip that may apply large stress concentrations to the gb at the end of slip bands. Although the last two processes have a supporting role in many cases, the published evidence strongly suggests that the first process is of overwhelming importance. This conclusion has been tested by reversion experiments in model Al-Li alloys in which microstructures with increasing area fractions, A_f, of large stable δ precipitates (Al-Li) were produced, but with equivalent matrix structures and yield strengths. The materials show marked falls of toughness and of fracture strain as A_f was increased. Studies of surface slip markings in the Al-Li alloys suggested that slip was initiated at the large gb δ precipitates. Only very limited evidence for a role of planar slip in the fracture of the Al-Li alloys was found in contrast to observations on high purity Al-Zn-Mg-Cu alloys where planar slip seemed to show more importance. Brief studies on a nickel based alloy, MAR-M200, suggested that even in the absence of a pfz, strong room temperature embrittlement by gb precipitates was produced. The results of this study suggest that the marked problems of gb fracture in Al-Li alloys are associated with large gb δ precipitates. Jensrud and Ryum [Mater. Sci. Engng64, 229 (1984)] have shown how gb precipitate growth is facilitated in this system as the gb δ phase is very much less soluble than the strengthening δ′ (Al₃Li) phase.

     

A model for the graphite formation in ductile

In the present investigation, mathematical models have been developed to quantify the extent of carbon diffusion occurring in ductile cast iron during cooling from the eutectic temperature. Computer calculations show that small variations in the cooling conditions may significantly alter the number density and size distribution of graphite nodules in the iron matrix, in agreement with experimental observations. This makes it difficult to compare microstructure data from various section size materials without allowing for differences in the kinetic strength of the thermal cycles with respect to carbon diffusion. formerly Ph.D. Graduate Student, Division of formerly Ph.D. Graduate Student, Division of     

An acoustic emission investigation of microscopic ductile fracture

A high-strength 4340 steel fracture-toughness specimen was heat treated to give a ductile-rupture type of slow crack growth under rising load. For evaluation of the step-wise growth process, the specimen was instrumented with acoustic stress wave emission (SWE) detection equipment. The resulting crack area swept out by the advancing crack was correlated to the magnitude and number of the acoustic emission pulses. A crack growth model was developed which accounts for the direct relationship between crack area swept out and the sum of the individual SWE amplitudes, and for the experimentally observed bimodal distribution of the SWE amplitudes. The model postulates that slow crack growth takes place in a step-wise mechanism. This involves a repeated two-step process where the first step is the formation of a multitude of individual thumbnail cracks and the second step is the simultaneous interconnection of these thumbnail cracks to form a new continuous crack front. Formerly , Postdoctorate Associate, Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minn.     

Hydrogen assisted ductile fracture of spheroidized carbon steels

The effects of hydrogen on ductile fracture were studied in two spheroidized plain carbon steels, containing 0.16 and 0.79 pct C. A combination of fractography and quantitative metallography on sectioned, deformed specimens permitted separation of the effects of hydrogen on the initiation, growth, and link-up of voids. In both steels, hydrogen was found to have no significant effect on either the initiation of voids at carbides, or early growth of voids, prior to link-up. In the higher carbon steel the fracture surface dimple size increased after hydrogen exposure with no other evident change in the fracture surface appearance; it is therefore inferred that hydrogen primarily assists void growth during link-up in this steel. In the lower carbon steel the fracture appearance changed and a decrease in void size due to hydrogen was found fractographically; thus, both initiation and growth of voids are apparently enhanced during the link-up phase of fracture in this steel. It is hypothesized that these effects may be due largely to a void pressure mechanism if hydrogen is transported by mobile dislocations. Formaly Graduate Student, Department of Metallurgy and Materials Science, Carnegie-Mellon University     

An acoustic emission investigation of microscopic ductile fracture

A high-strength 4340 steel fracture-toughness specimen was heat treated to give a ductile-rupture type of slow crack growth under rising load. For evaluation of the step-wise growth process, the specimen was instrumented with acoustic stress wave emission (SWE) detection equipment. The resulting crack area swept out by the advancing crack was correlated to the magnitude and number of the acoustic emission pulses. A crack growth model was developed which accounts for the direct relationship between crack area swept out and the sum of the individual SWE amplitudes, and for the experimentally observed bimodal distribution of the SWE amplitudes. The model postulates that slow crack growth takes place in a step-wise mechanism. This involves a repeated two-step process where the first step is the formation of a multitude of individual thumbnail cracks and the second step is the simultaneous interconnection of these thumbnail cracks to form a new continuous crack front.     

The role of plasticity in bimaterial fracture with ductile interlayers

Evaluation of the plasticity effects in fracture along ductile/brittle interfaces requires appropriate models for plastic dissipation in a ductile component. For thin ductile films, constitutive properties appropriate to the small volumes involved are essential for adequate modeling. Here, yield stress is of primary importance. With nanoindentation, one can obtain both a large strain flow stress as well as the far field yield stress representing the small strain elastic-plastic boundary. Using these to estimate an appropriate plastic strain energy density, the crack tip plastic energy dissipation rates associated with the interfacial crack extension can be estimated for a ductile film. With the preceding analysis, plasticity effects on the interfacial toughness have been evaluated for external measures of strain energy release rates as obtained from indentation tests using the axisymmetric bilayer theory. Comparison involved RF sputtered 200-to 2000-nm-thick Cu interlayers between oxidized silicon and sputtered tungsten. Experimental values for the Cu/SiO₂ interface increased with Cu film thickness from 1 to 15 J/m². This was in qualitative agreement with the theoretical predictions for plastic energy dissipation rates. In contrast, first-order estimates suggest that the observed interfacial toughness increases cannot be attributed to either mode mixity effects or increased intrinsic interfacial fracture energies. As such, crack tip plasticity is identified as the dominant mechanism for increasing interfacial toughness. This article is based on a presentation made in the Symposium “Mechanisms and Mechanics of Composites Fracture” held October 11–15, 1998, at the TMS Fall Meeting in Rosemont, Illinois, under the auspices of the TMS-SMD/ASM-MSCTS Composite Materials Committee.