A. Toshimitsu Yokobori

Numerical analysis on hydrogen diffusion and concentration in solid with emission around the crack tip

Abstract Construction of a physical model and numerical analysis were carried out concerning hydrogen diffusion in solid under elastic-plastic local stress field with hydrogen emission around the crack tip due to the dissolvent anodic reaction. These analyses showed that hydrogen diffuses and concentrates at the site of the elastic-plastic boundary in the direction of crack length when several mechanical conditions are satisfied. Hydrogen accumulation becomes much more remarkable with increase of yield stress. The effect of the diffusion constant is found to correspond to the rate of hydrogen diffusion. It accelerates the rate of increase of hydrogen accumulation at the elastic-plastic boundary, although the maximum saturated value of the concentration is not affected. This analysis shows that a high strength steel is liable to cause the microcrack initiation and coalescence with the main crack due to the hydrogen accumulation and embrittlement at the elastic-plastic boundary. This gives the theoretical foundation to the mechanism on the stress corrosion cracking accompanied with subcritical crack growth for high strength steels.

The characteristics of hydrogen diffusion and concentration around a crack tip concerned with hydrogen embrittlement

Abstract Previously, we proposed a physical model for hydrogen diffusion and accumulation around the crack tip and performed accurate numerical analysis which takes account of the effects of both hydrogen diffusion and accumulation due to the stress gradient. Based on this analysis, the characteristics of hydrogen accumulation around the crack tip were clarified. Since the characteristics of stress corrosion cracking and corrosion fatigue are dominated by chemical anodic reaction, hydrogen embrittlement and dislocation mechanism, to perform the analysis on the competitive phenomenon by these mechanism and to relate the sensitivity of hydrogen embrittlement to the characteristics of corrosion fatigue, it is necessary to construct a exact physical law on the characteristics of hydrogen diffusion and concentration and to formulate the characteristics as a simple function such as diffusion constant, D, yield stress σys, and stress intensity factor, K. The effect of stress field such as plane strain and plane stress on the hydrogen embrittlement is necessary to be clarified as the effect of specimen thickness on the hydrogen embrittlement. In this paper, based on this view point, the effect of D, σys, and K on hydrogen embrittlement were investigated and formulated. A quantitative parameter which characterize hydrogen embrittlement was proposed for both cases of plane strain and plane stress conditions as the effect of specimen thickness on the hydrogen embrittlement.

An alternative correlating parameter for creep crack growth rate and its application: derivation of the parameter Q*

The parameter Q* has been proposed for correlating or characterizing creep crack growth rate. The creep crack growth rate has been expressed in terms of an activation process equation, and the parameter Q* was defined as the exponent of the exponential in the thermal activation process equation for da/dt, in which the activation energy is expressed in terms of free energy. CrMoV steel was used for VAMAS round-robin tests, and other materials such as SUS 304 and the Nl-base alloy of Hastelloy-XR were used. For these materials good correlations are obtained. An analytical conclusion about the effect of thickness on crack growth is described.

The crack initiation and growth under high temperature creep, fatigue and creep-fatigue multiplication☆

Abstract This article concerns some of our recent studies on the crack initiation, early stage crack growth and its subsequent crack growth under high temperature creep, fatigue and creep-fatigue multiplication. The criteria for these and some new ideas are proposed. For instance, the relative notch opening displacement (RNOD) criterion for the crack initiation and the Q ∗ parameter for the crack growth are critically reviewed. Early stage crack growth and its subsequent crack growth as affected by notch tip acuity were studied. The behaviour of the tail part in the log da dN vs log C ∗ curve has been attempted to explain in terms of the curve of the creep behaviour and of the crack length against time. Furthermore it was proposed that early stage crack growth, say, the so-called first stage crack growth in terms of log da dN vs log K curve may be characterized by the parameter different from those for the so-called second stage crack growth.

DIFFERENCE IN THE CREEP AND CREEP CRACK GROWTH BEHAVIOUR BETWEEN CREEP DUCTILE AND BRITTLE MATERIALS

Abstract By relating the creep crack growth versus time curve to the creep displacement curve, different characteristics have been observed between creep-ductile and creep-brittle materials in a precracked or a notched specimen. In the present paper, an attempt has been made to further clarify these differences by including the microstructural mechanism, the damage mechanics and continuum mechanical analysis. Based on the results, new ideas have been proposed for explaining the difference between the behaviour of creep-ductile and creep-brittle materials in a precracked or a notched specimen.

Evaluation of creep crack growth properties using circular notched specimens

It is important to evaluate the effect of multiaxial stress conditions on initiation and growth of creep cracks, when the laboratory data are subsequently applied to structural components under the same or similar stress state. The round robin tests of creep crack growth using circular notched specimens of 1CrMoV steel at 538 and 594 °C and 12CrWCoB steel at 650 °C were conducted by the Japanese VAMAS TWA25 group. The effect of notch depth and specimen size, i.e. stress multiaxiality on crack growth properties was investigated. The test procedure including criteria for crack length measurement by electric potential drop was established. The circular notched specimens fractured intergranularly and showed different crack growth behaviour from that of a CT specimen due to the multiaxial stress field. The creep crack growth rate for the same C* value increased as the ratio of the notch depth to specimen diameter, i.e. stress multiaxiality increased. The Q* evaluation method based on the thermally activated process can also be applied to the circular notched specimen.

Comparative study on characterization parameters for high temperature creep crack growth with special emphasis on dual value behaviour of crack growth rate

Abstract If the logarithms of experimental values of high temperature creep crack growth rate, log d a d t are plotted against the logarithm of C ∗ or δ (creep displacement rate), the relation or curve reveals in many cases the dual value or the nose part. This dual behaviour appears in terms of various patterns according to the materials or its processing. An analytical model has been proposed for dual behaviour of crack growth rate plotted against C ∗ or δ dot . The methodology is to analyse the relation of creep displacement rate curve and crack growth length curve with respect to applied load time. Q ∗ parameter projection for d a d t predicts that log d a d t is a simple monotonical increasing linear function of Q ∗ , does not reveal dual values, and shows threshold behaviour at an early stage of crack growth.

The variation of the stress singularity at the notch tip as notch angle and radius of curvature

Abstract This paper concerns itself with the analysis of the deviations of the stress singularity at the blunted notch tip from the square root singularity which is associated with an ideal crack. The stress distributions and the stress intensity factors for V and U notches were analyzed for several blunting angles and the radii of curvature, using finite element method. The results showed that the differences of the stress intensity factors between V notch tip and an ideal crack were quite little in the region of that the notch angle is from 0 to 80°.

The mechanical behavior and morphological structure of callus in experimental callotasis.

Experimental callotasis was made in rabbit femurs. In order to compare mechanical behaviors and morphological structure of callus in callotasis, mechanical tests and histological examination were performed. Twenty Japanese white male rabbits were used. The right femurs were osteotomized at the level of the midshaft with a rotary cutter and fixed with a mini-model external fixator. After a 5-day waiting period, bone lengthening was started at the rate of 0.25 mm two times a day. Animals were divided into four groups. Group 1 and Group 2 were continual distraction group, Group 3 and Group 4 discontinued distraction group. The viscoelastic property was demonstrated in continual distraction group irrespective of distraction period, we thought the central undifferentiated connective tissue in callus was mainly responsible for the mechanical behavior. On the other hand, in discontinued distraction group, viscoelastic property shifted to elastic property corresponding to the rest period, we thought this change of mechanical behavior was histologically owing to the replacement of undifferentiated connective tissue by cartilage and the partial union of bone in callus.

Characterization of high temperature creep crack growth and creep life from high temperature ductile through to high temperature brittle materials

Abstract Yokobori and colleagues have treated time-dependent fracture, such as fatigue and creep fracture, as a stochastic process and a thermally activated process, extended the studies, and proposed the crack growth rate equations for fracture of various kinds. Among those for high temperature creep, fatigue and creep-fatigue multiplications, the following equation has been proposed for crack growth rate based on stochastic and thermally activated processes: d a d t =A e Q∗ where Q ∗ = −[(ΔH g − θ(σ))]/RT + constant. It has been found that, using the Q ∗ parameter, the high temperature creep crack growth rate is very well characterized. In smooth specimens, final fracture of two types may be realistic. One is where one crack which started from the small original defect extends and the final fracture is caused: by the stress intensity factor for the critical length of the crack attained due to this one-crack extension. The other may be the case where multi-site cracks, say a number of cracks initiated from a number of small defects, grow and join together. In the latter case it was shown previously that the fracture time is determined by the time when each growing crack attains the critical length depending on the distance between each tip of the originally initiated small cracks. Thus, for the final fracture of both types mentioned above, creep fracture time t ƒ can be obtained by integrating da/dt expressed in terms of Q ∗ mentioned above. Using creep strain rate (for steady creep or minimum creep) expressed for a thermally activated process, and calculating t ƒ ϵ , then the equation t ƒ ϵ is found to be given as the equation of activation type. This equation thus obtained for smooth specimen includes, as a special case, the formula experimentally obtained by Monkman and Grant, and nearly coincides with the formula modified experimentally by Wiederhorn et al. for alumina ceramics. For notched or cracked specimens, it has not been found whether the Larson-Miller formula is valid or not. By integrating the equation expressed in terms of Q ∗ , it was found that the master curve for creep fracture time t ƒ was obtained in terms of applied stress and temperature. In conclusion, it may be possible to predict or characterize the creep crack growth rate and the creep life throughout, from high temperature ductile materials such as Cr-Mo—V steel and SUS 304 stainless steel to high temperature brittle materials such as alumina ceramics, using the unified formula based on the Q ∗ parameter concept. The effect of creep ductility on creep life can be discriminated by the material constants.