The strain required to initiate ductile failure in three low-alloy, quenched and tempered steels has been determined in multi-axial stress-states. The ductility was found to depend markedly both on the orientation of the stress system with respect to the rolling direction and on the tri-axiality of the stress-state. In some cases, ductile failure occurred at plastic strains which were only a few times the yield strain. Metallographic studies have been used to compare the size, shape and orientation of the holes which cause failure initiation with the isotropic continuum analysis of F.A. Mc Clintock (1968). The application of ductile-fracture models to directional steels is discussed with particular reference to the effects of directionality and stress-state on the condition for flow localization to occur between holes.

On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states

Experiments were performed on three heats of A508 class 3 steel in order to determine the mechanical conditions for cleavage fracture. These tests were carried out on various geometries including 4-point bend specimens and axisymmetric notched tensile bars with different notch radii which have been modelized using the finite element method. In one heat, the temperature range investigated was from 77 K to 233 K. It is shown that the cleavage resistance is increased by tensile straining. Moreover, the probability of fracture obeys the Weibull statistical distribution. All the results can be accounted for in terms of a local criterion based on Weibull theory and which takes into account the effect of plastic strain. In this criterion, the parameters which were experimentally determined are found to be temperature independent over the range 77 K to 170 K. The applicability of the approach proposed for cleavage fracture at the crack tip is also examined. It is shown that the experimental results published in the literature giving the variation of fracture toughness with temperature can be explained by the proposed criterion which predicts reasonably well both the scatter in the experimental results and theKICtemperature dependence.

A Local Criterion for Cleavage Fracture of a Nuclear Pressure Vessel Steel

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

Assessment of the integrity of structures containing defects

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

SUMMARY AN ANALYSIS is presented which relates the critical value of tensile stress (a,) for unstable cleavage fracture to the fracture toughness (K,,) for a high-nitrogen mild steel under plane strain conditions. The correlation is based on (i) the model for cleavage cracking developed by E. Smith and (ii) accurate plastic*lastic solutions for the stress distributions ahead of a sharp crack derived by J. R. Rice and co-workers. Unstable fracture is found to be consistent with the attainment of a stress intensification close to the tip such that the maximum principal stress a,, exceeds a, over a characteristic distance, determined as twice the grain size. The model is seen to predict the experimentally determined variation of K,, with temperature over the range -150 to -75°C from a knowledge of the yield stress and hardening properties. It is further shown that the onset of fibrous fracture ahead of the tip can be deduced from the position of the maximum achievable stress intensiiication. The relationship between the model for fracture ahead of a sharp crack, and that ahead of a rounded notch, is discussed in detail.

On the relationship between critical tensile stress and fracture toughness in mild steel

C ritical crack opening displacement (COD) values have been examined for a range of specimen thicknesses. The COD at the initiation of fracture δ1 is found to be constant, given a plane-strain crack-tip stress-state, whereas the COD at maximum load δmax decreases with increasing thickness. The loads required to produce instability are found to vary with thickness, in a way analogous to behaviour observed under linear elastic conditions. Crack growth under constant load for a range of specimen thicknesses has been examined, and failure has been found to occur at loads below that associated with Δmax,; the minimum load per unit thickness required to cause failure decreasing with specimen thickness.

On effects of thickness on ductile crack growth in mild steel

The use of conformal mapping techniques in the determination of calibration curves for electrical- potential crack-monitoring systems is discussed, and calibrations are produced for cracks growing from notches of various geometries, including the important case of the V-notch. The sensitivity of the system to the positioning of potential probes is determined from these calibrations.

Measurement of fatigue cracks in notched specimens by means of theoretical electrical potential calibrations

The first part of this paper deals with the fracture behaviour of material that is sensibly homogeneous. The statistical distributions of toughness and fracture stress for this case are determined, and the accuracies of the methods used of measuring toughness and fracture stress are assessed. Subsequently, the second part deals with the fracture of microstructurally inhomogeneous (two-phase) materials. The statistical distributions obtained for fracture stress, fracture toughness and critical crack opening displacement are assessed, and the relationships between them for inhomogeneous materials are discussed. A model is developed which explains the shapes of the distributions obtained in terms of a sampling argument. In Part III the model is applied to data for metallurgically inhomogeneous material. This is material which has a homogeneous microstructure but has chemical inhomogeneity due to segregation of alloy elements. These data are from the transition region and the lower shelf and the model predicts accurately the effect of specimen size. The model is also faithful to the change of distribution shape with proximity to the sharp transition in toughness and this too is explainable by the sampling argument.

Statistical distributions of toughness and fracture stress for homogeneous and inhomogeneous materials

The results of fracture toughness tests on a high strength steel 300m are presented. These results show (i) that in the presence of through-thickness cracks the toughness remains constant down to (a/W)-ratios as low as 0.01 and failure loads up to 0.85σy, and (ii) that the material is more resistant to crack growth when the cracks are semi-elliptical in shape, giving a toughness value which is almost 25 per cent higher than the through-thickness one. Three independent stress analyses are used to obtain stress intensity values for the semi-elliptical cracks and additional confirmation of the increase in toughness comes from stretch zone measurements.

J.F. Knott

Papers

On the relationship between critical tensile stress and fracture toughness in mild steel

On effects of thickness on ductile crack growth in mild steel

Measurement of fatigue cracks in notched specimens by means of theoretical electrical potential calibrations

Statistical distributions of toughness and fracture stress for homogeneous and inhomogeneous materials

The effects of crack length and shape on the fracture toughness of a high strength steel 300m