Shang-Xian Wu

A model of fatigue crack growth based on dugdale model and damage accumulation

The modified Dugdale model given by Budiansky-Hutchinson and a Coffin-Manson type damage law are used to calculate the cumulative fatigue damage of material elements at the tip of a fatigue crack. From this analysis a fatigue crack growth equation is obtained which gives predicted crack growth rates in reasonable agreement with experimental data for two aluminium alloys 7075-T6 and 2024-T81, two titanium alloys Ti-8A1-1Mo-1V and Ti-6A1-6V and a PH13-8Mo stainless steel. Limitations of this new fatigue crack growth model are also discussed.

Slip-line field solutions of three-point bend specimens with deep notches

Abstract Slip-line field solutions of three-point bend specimens with different notch depths, notch angles and notch root radii are presented. For notch angles less than the critical value the plastic region is localized at the ligament but for larger notch angles the plastic region spreads to the flanks of the notch. It is shown that the critical angle decreases with increasing notch depth and decreasing root radius. Solutions for the constraint factor and maximum hydrostatic stress beneath the notch tip are also obtained as a function of both notch depth and root radius for notch angles above and below the critical value.

Prediction of the initiation of ductile fracture

Abstract The initiation of a ductile tear at a sharp notch is modelled by the growth of an isolated void embedded in a J - Q stress field. This model gives the predicted value of J at the initiation of a ductile tear, for any geometry and size, in terms of its value for a standard test specimen. Experimental data from a wide range of specimen geometries, both new and previously published data, are presented in support of the new model.

Finite element analysis and experimental evaluation of ductile-brittle transition in compact tension specimen

Using finite element analysis, metallographic observations and statistical analysis, the stress field ahead of stationary and growing cracks and the ductile-brittle transition mechanism in compact tension (CT) specimens have been evaluated. Compared to a stationary crack, a growing crack elevates the opening stress on the remaining ligament and this may be partially attributed to the re-sharpening of the crack tip after ductile growth. The area of material covered by the high opening stress of the same magnitude also increases with ductile crack growth. In this study, no significant difference for measured cleavage stress can be found for the specimens fractured with and without ductile crack growth. There is a large scatter for the distance between the cleavage initiation site and the stationary or growing crack tip. Cleavage fracture after some amount of ductile crack growth is attributed to the increase of both the opening stress and the area of material under high opening stresses. Finally, the lower bound toughness is predicted using a small data set statistical model in connection with constraint correction. The predicted values give the same trend as the lower bound of the experimental measurements from the lower-shelf to the temperature at which ductile crack growth occurs.

On the relationship between crack tip opening displacement at the initiation of a ductile tear in low carbon steel, hydrostatic stress, and void growth

The effect of hydrostatic stress on the growth of voids from inclusions located near the tips of deep and shallow notches in three-point bend specimens is analysed using slip-line field theory and the Rice-Tracey void growth model. The analysis explains qualitatively the observed dependence of the crack tip opening displacement δi at the initiation of a ductile tear in low carbon steel on the hydrostatic stress. Although a plot of the experimental values of δi normalised by the inclusion spacing against the inclusion spacing/size ratio do not agree well with the theory, the plot is a promising means of determining experimentally the dependence of δi on hydrostatic stress for any particular steel.

Plastic Rotation Factors of Three-Point Bend and Compact Tension Specimens

Plastic rotation factors (rp) for three-point bend and compact tension specimens were obtained for a range of normalized crack depths (a/W) from 0.25 to 0.88 and power law hardening materials. The theoretical slip-line field solutions were used for non-strain hardening materials (i.e., n = ∞) and the Kumar-German-Shih finite element plastic displacement solutions for strain hardening materials (i.e., n 5 and are in reasonable agreement with those values recommended by ASTM Subcommittee E24.08 for calculation of crack tip opening displacements in these two types of specimens. For n ≤ 5 the error in rp becomes appreciably large.

Application of J-Q theory to the local approach statistical model of cleavage fracture

A statistical model has been established to predict the fracture toughness in the lower-shelf and lower transition regions. It considers the in-plane constraint effect in terms of the two-parameter J-Q stress field. This model has been applied to predict the effect of crack depth and specimen geometry on fracture toughness and there is good agreement with experimental data. The specimens with lower in-plane constraints have a large toughness scatter due to the significant constraint loss during the loading process. The lower-bound toughness is not sensitive to crack depth and specimen geometry and this is attributed to the fact that all specimens have a similar in-plane constraint at small loads.

The effect of constraint on fracture of carbon and low alloy steel

The constraint at a crack tip has an effect on the fracture of all but the most brittle materials unless the specimen size is very large. Standard fracture toughness tests are designed so that constraint is high and the fracture parameters obtained from such tests can be conservative when applied to shallow cracks of low constraint in carbon and low alloy steels. Low constraint has two effects. It can greatly increase the critical CTOD or J Ic for ductile tearing or cleavage fracture and also, because low constraint limits the stress, it can cause a change in the mode of fracture from cleavage to ductile tearing. For ductile tearing it is suggested that the effects of constraint can be predicted if the stress-strain relationship for the fracture process zone is known. For cleavage fracture and fracture transition it is shown that the critical stress over a characteristic distance is applicable.