A cohesive zone model, taking full account of finite geometry changes, is used to provide a unified framework for describing the process of void nucleation from in­itial debonding through complete decohesion. A boundary value problem simulating a periodic array of rigid spherical inclusions in an isotropically hardening elastic-viscoplastic matrix is analyzed. Dimensional considerations introduce a characteristic length into the formulation and, depending on the ratio of this characteristic length to the inclusion radius, decohesion occurs either in a "ductile" or "brittle" manner. The effect of the triaxiality of the imposed stress state on nucleation is studied and the numerical results are related to the description of void nucleation within a phenomenological constitutive framework for progressively cavitating solids. 1 Introduction The nucleation of voids from inclusions and second phase particles plays a key role in limiting the ductility and toughness of plastically deforming solids, including structural metals and composites. The voids initiate either by inclusion cracking or by decohesion of the interface, but here attention is confined to consideration of void nucleation by interfacial decohesion. Theoretical descriptions of void nucleation from second phase particles have been developed based on both continuum and dislocation concepts, e.g., Brown and Stobbs (1971), Argon et al. (1975), Chang and Asaro (1978), Goods and Brown (1979), and Fisher and Gurland (1981). These models have focussed on critical conditions for separation and have not explicitly treated propagation of the debonded zone along the interface. Interface debonding problems have been treated within the context of continuum linear elasticity theory; for example, the problem of separation of a circular cylindrical in­clusion from a matrix has been solved for an interface that supports neither shearing nor tensile normal tractions (Keer et al., 1973). The growth of a void at a rigid inclusion has been analyzed by Taya and Patterson (1982), for a nonlinear viscous solid subject to overall uniaxial straining and with the strength of the interface neglected. The model introduced in this investigation is aimed at describing the evolution from initial debonding through com­plete separation and subsequent void growth within a unified framework. The formulation is a purely continuum one using a cohesive zone (Barenblatt, 1962; Dugdale, 1960) type model for the interface but with full account taken of finite geometry

A continuum model for void nucleation by inclusion debonding

The effects of hydrogen on the physical and mechanical properties of iron and steel are reviewed. A new mechanism for the cold work peak for hydrogen in iron is considered. Together, internal friction and mechanical properties indicate that hydrogen softens iron by enhancing screw dislocation mobility at room temperature but hardens iron by core interactions at low temperatures. No single mechanism exists for the degradation of the properties of steel by hydrogen. Instead a complex process involving many of the proposed mechanisms as contributing factors is shown to account for most degradation phenomena.

Effects of hydrogen on the properties of iron and steel

The effect of hydrogen on dislocation dynamics

The relative amount of trapped hydrogen and the activation energy for its evolution from various lattice defects in iron were calculated by monitoring the pressure change caused by release of hydrogen from charged specimens heated at uniform heating rates. Hydrogen release peaks were observed at 385 K, 488 K, and 578 K, respectively, when the hydrogen charged specimen were heated at 2.6 K per minute. Analysis suggests that the peak at 385 K corresponds to hydrogen release from grain boundaries, and the peak at 488 K corresponds to release from dislocations, while the peak at 578 K results from release from micro voids. The activation energies for evolution of trapped hydrogen were determined experimentally from measured peak temperatures at different heating rates and were found to be 17.2 KJ/mol, 26.8 KJ/mol, and 35.2 KJ/mol, respectively, in grain boundaries, dislocations, and microvoids. It was also observed that most of hydrogen is trapped on dislocations if the density of specimen is greater than 98.95 pct, and in microvoids if less than 98.95 pct.

Thermal analysis of trapped hydrogen in pure iron

T he hydrogen transport problem is studied in conjunction with large deformation elastic—plastic behavior of a material. Oriani's equilibrium theory is used to relate the hydrogen in traps (micro-structural defects) to concentration in normal interstitial lattice sites (NILS). The resulting non-linear transient hydrogen diffusion equations are integrated using a modified backward Euler method. Coupled diffusion and plastic straining is analysed with this numerical procedure in the area around a blunting crack tip. A uniform NILS concentration as dictated by Sievert's law at the pressure and temperature of interest is used as initial condition throughout the body. The crack is initially blunted by plane strain mode I (tensile) loading. The finite element results show that hydrogen residing at NILS is generally very small in comparison with the population that develops in trapping sites near the crack surface. That is, lattice diffusion delivers the hydrogen but it is predominantly the trapping that determines its distribution at temperatures of interest. The predominance of trapped hydrogen over lattice concentration prevails even in the case when hydrogen migrates under steady state conditions. Hence, the hydrostatic stress effect is less important than traps created by plastic straining as far as the creation of high total hydrogen concentration is concerned. The trapping site locations and the temperature determine the amounts and locations of high hydrogen concentrations. Consequently, ahead of a blunting crack tip, the total hydrogen concentration and plastic strain diminish with distance from the crack tip whereas the hydrostatic stress rises. This would seem to have significant consequences for fractures induced by the presence of hydrogen.

Numerical analysis of hydrogen transport near a blunting crack tip

A kinetic model is presented for the transport of hydrogen, as Cottrell atmospheres on dislocation, at a rate appreciably in excess of that for lattice diffusion. The particular destinations for the hydrogen which are modeled here are ductile fracture initiation sites such as inclusions and microvoids. The functional predictions of the mechanism are shown to be consistent with available experimental evidence on ductile fracture behavior in the presence of hydrogen.

Hydrogen transport by dislocations

The complex hydrogen trapping characteristics of iron-titanium-carbon alloys, contain-ing both reversible and irreversible traps have been fully analyzed. The key to this quantitative analysis is a complete identification of the type and number of each operating trap. The trapping parameters were obtained from an analysis of the relevant hydrogen permeation transients. Titanium substitutional atoms have been shown to be reversible, low occupancy traps with an interaction energy with hydrogen,E (Ti-H), of 0.27 eV. Typi-cal rate constants for these alloys are; a hydrogen capture rate constant of approximately 10-24 cm3/atom .s a release rate constant of approximately 10-3 s-1 and a trapping rate of the order of 1015 atoms, H/cm3 .s. TiC particles are irreversible traps with a large oc-cupancy and an interaction energy, .E(TiC-H), of 0.98 eV. The irreversible trapping parameters are calculated from the first permeation transient, where mixed trapping oc-curs. The trapping kinetics are about an order of magnitude faster than when only rever-sible trapping exists. The role of trapping on the effective diffusivity of hydrogen is dis-cussed as is, briefly, its role in affecting hydrogen-induced damage. Finally, guidelines are given to permit the trapping behavior of more general alloys to be analyzed.

A quantitative analysis of hydrogen trapping

An experimental program was carried out to clarify the structure-property relationships in fully-pearlitic steels of moderately high strength levels, and to identify the critical microstructural features that control the deformation and fracture processes. Specifically, the yield strength was shown to be controlled primarily by the interlamellar pearlite spacing, which itself was a function of the isothermal transformation temperature and to a limited degree the prior-austenite grain size. Charpy tests on standard and fatigue precracked samples revealed that variations in the impact energy and dynamic fracture toughness were dependent primarily on the prior-austenite grain size, increasing with decreasing grain size, and to a lesser extent with decreasing pearlite colony size. These trends were substantiated by a statistical analysis of the data, that identified the relative contribution of each of the dependent variables on the value of the independent variable of interest. The results were examined in terms of the deformation behavior being controlled by the interaction of slip dislocations with the ferrite- cementite interface, and the fracture behavior being controlled by a structural subunit of constant ferrite orientation. Preliminary data suggests that the size of such units are controlled by, but are not identical to, the prior-austenite grain size. Possible origins of this fracture unit are considered.

The role of microstructure on the strength and toughness of fully pearlitic steels

The process of cleavage crack initiation and the character of the effective grain size which controls the fracture toughness of pearlitic eutectoid steel has been investigated using smooth tensile and precracked Charpy impact specimens. The results demonstrated that initial cracking in both specimens was largely the result of shear cracking of pearlite;i.e., localized slip bands in ferrite promoted cracking of the cementite plates, which was then followed by tearing of the adjacent ferrite laths. Such behavior initially results in a fibrous crack. In the tensile specimen, the initiation site was identified as a fibrous region which grew under the applied stress, eventually initiating an unstable cleavage crack. In precracked impact specimens, this critical crack size was much smaller due to the high state of stress near the precrack tip. Fracture mechanics analysis showed that the first one or two dimples formed by the shear cracking process can initiate a cleavage crack. Using thin foil transmission electron microscopy, a cleavage facet was found to be an orientation unit where the ferrites (and the cementites) of contiguous colonies share a common orientation. The size of this orientation unit, which is equal to the cleavage facet size, is controlled by the prior austenite grain size. The influence of austenite grain size on toughness is thus explained by the fact that the austenite grain structure can control the resultant orientation of ferrite and cementite in pearlitic structures.

The process of crack initiation and effective grain size for cleavage fracture in pearlitic eutectoid steel

Crystallographic and fractographic studies have been carried out on hydrogen charged purified iron and on iron-silicon alloys with silicon contents up to 3 pct. The specimens could be cracked by cathodically charging with hydrogen even without the application of an external stress. An experimental technique was developed which enabled the exposure of the fracture surface formed purely by hydrogen charging, and to contrast this with an adjacent mechanically induced fracture surface. In the case of purified iron, hydrogen induced cracks are found to occur on potential slip planes whereas in the case of iron-3 pct silicon, the crack follows the observed cleavage plane. Intermediate silicon content alloys showed transitional behavior. In agreement with the variation of crack plane in the alloys, the fracture surface appearances was also drastically different, reflecting the change in intrinsic toughness with alloy content. The observed transition from slip plane cracking to cleavage plane cracking was found to occur near a silicon content of 0.7 pct. The observed behavior is discussed in terms of how the intrinsic toughness of the ironbased lattice affects how hydrogen-induced cracks are formed.

I. M. Bernstein

Papers

Hydrogen transport by dislocations

A quantitative analysis of hydrogen trapping

The role of microstructure on the strength and toughness of fully pearlitic steels

The process of crack initiation and effective grain size for cleavage fracture in pearlitic eutectoid steel

Crystallographic and fractographic studies of hydrogen- induced cracking in purified iron and iron- silicon alloys