Analysis of the cup-cone fracture in a round tensile bar

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The localization of plastic deformation

Publisher Summary This chapter describes the material failure by coalescence of microscopic voids. The voids nucleate mainly at second phase particles, by decohesion of the particle-matrix interface or by particle fracture, and subsequently the voids grow because of plastic straining of the surrounding material. The growth of voids to coalescence by plastic yielding of the surrounding material involves so large geometry changes that finite strain formulations of the field equations are a necessary tool. A convected coordinate formulation of the governing equations is used. Convected coordinates are introduced, which serve as particle labels. The convected coordinate net can be visualized as being inscribed on the body in the reference state and deforming with the material. It is found that after nucleation, cavities elongate along the major tensile axis and that two neighboring cavities coalesce when their length has grown to the order of magnitude of their spacing. This local failure occurs by the development of slip planes between the cavities or simply necking of the ligament. A detailed micromechanical study of shear band bifurcation that accounts for the interaction between neighboring voids and the strongly nonhomogeneous stress distributions around each void has been carried out, and are also elaborated in this chapter.

Material Failure by Void Growth to Coalescence

A nalyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J -integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J -integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for 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 100A 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

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.

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

Effects of microstructure on fracture toughness of high strength alloys

Grain boundary segregation during temper embrittlement of an Sb-containing, Ni-Cr steel has been examined both by Auger electron analysis and by chemical analysis by neutron activation of residues of surface layers dissolved by etching intercrystalline fracture surfaces. No grain boundary segregation of either alloying additions or impurities was detected during austenitization or tempering. Redistribution of Cr, Ni, and Sb between carbide and ferrite was observed during tempering, but no grain boundary segregation was noted. Both Ni and Sb were observed to segregate to the boundaries during embrittling. The segregated Sb was shown to be uniformly distributed along the prior austenitic grain boundaries and to control the ductile brittle transition temperature of the alloy studied. Ni segregating to the prior austenitic boundaries during embrittling was shown to be localized in a phase other than the ferritic portions of the boundaries. A possible location was shown to be the ferritecarbide interfaces in the grain boundaries. Weakening of these normally tenacious carbide and ferrite interfaces could account for the change in mode of brittle failure from transcrystalline cleavage to intercrystalline along the prior austenitic grain boundaries that is observed in temper brittle steels.

Effect of prior austenitic grain boundary composition on temper brittleness in a Ni-Cr-Sb steel

Crack propagation rates for the intergranular fracture of an Al-15 wt pct Zn alloy tested in air, distilled H2O, and 0.5M NaCl have been studied using a double cantilever beam specimen. This technique has been applied to two different types of specimens: polycrystals with large equiaxed grains and bicrystals. The susceptibility to intergranular fracture in air and 0.5M NaCl increases as the volume fraction of G.P. zones in the matrix increases. The microstructure which is most susceptible to fracture exhibits intense planar slip traces while the more resistant microstructures have a more diffuse surface slip pattern. The dependence of cracking rates on the microstructure is explained in terms of the blocking of inhomogeneous plastic flow in the matrix by grain boundaries, resulting in locally severe stress concentrations at the boundaries. Bicrystal tests substantiate these results and show that orientations favoring partial continuity of slip bands across grain boundaries are less susceptible to stress corrosion cracking than arbitrarily oriented boundaries with no slip continuity.

Intergranular fracture in an Al-15 Wt Pct Zn alloy

: Cracking kinetics involved in the intergranular fracture of an A1- 15wt% Zn alloy tested in air, distilled H2O, and 0.5M NaCl have been studied by means of the elastic strain energy released during crack propagation in a double cantilever beam specimen. This technique has been applied to two different types of specimens: polycrystals with equi-axed grains and bi-crystals with crack propagation confined to the grain boundary. By varying the microstructure through selective aging treatments, a wide range of cracking susceptibility has been observed. The results show that the fracture toughness of this alloy increases with a decreasing volume fraction of G. P. zones in the matrix. A similar trend in the stress-corrosion cracking tests in 0.5M NaCl is noted, and the susceptibility to fracture increases as the volume fraction of G.P. zones in the matrix increases. The microstructure highly susceptible to fracture exhibits planar slip traces while the more resistant microstructures show a dispersed type surface slip pattern. The dependence of cracking rates on the microstructure is explained in terms of inhomogeneous plastic flow in the matrix being blocked by grain boundaries and leading to severe stress concentrations at the boundaries. The bi-crystal tests substantiate these results and show that orientations favoring partial continuity of slip bands across grain boundaries are less susceptible to stress corrosion cracking than arbitrarily oriented boundaries with no slip continuity.

John R. Low

Papers

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

Effects of microstructure on fracture toughness of high strength alloys

Effect of prior austenitic grain boundary composition on temper brittleness in a Ni-Cr-Sb steel

Intergranular fracture in an Al-15 Wt Pct Zn alloy

INTERGRANULAR FRACTURE IN AN A1-15 WT. % Zn ALLOY