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 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

The solubility and diffusivity of hydrogen in well-annealed and deformed iron

Deep trapping states for hydrogen in deformed iron

Hydrogen and deuterium in iron, 49–506°C

Hydrogen and deuterium in iron, 9–73°C

Diffusion of light interstitials through nonuniformly distributed traps

A theoretical study has been made of the effect of nonuniformly distributed saturable and nonsaturable (void) traps on the permeation behavior of a mobile interstitial through a metal. Analytic time lag equations for trap distributions represented by a step function, an error function and a thin film solution have been derived using Frisch's method. Time lags for nonuniform distributions of traps were also evaluated numerically. Consistent results were obtained from time lag and transient calculations. Permeation transient and time lag were found to depend strongly on the average trap density of a distribution. At constant average trap density, the delaying effect of a nonuniform trap distribution can be larger or smaller than that of a uniform distribution. Traps concentrated near the exit surface in general are more effective in delaying the overall transport behavior than near the input surface. Asymmetric behavior was observed in both the transient and the time lag calculations, which can be used to detect the nonuniformity of the trap distribution. An analog between diffusion through nonuniformly distributed traps and diffusion through a laminate was examined.

H.H. Johnson

Papers

Deep trapping states for hydrogen in deformed iron

Hydrogen and deuterium in iron, 49–506°C

Hydrogen and deuterium in iron, 9–73°C

Diffusion of light interstitials through nonuniformly distributed traps

Diffusion of light interstitials through nonuniformly distributed traps