Three-dimensional T-stresses for three-point-bend specimens with large thickness variation

Three-point-bend (3PB) test specimens are useful for the systematic investigation of the influence of statistical and constraint loss size effects on the cleavage fracture toughness of a material in the ductile-to-brittle transition temperature range. Because the in- and out-of-plane elastic T-stresses (T11 and T33) are a measure of the crack-tip constraint and even the in-plane T11 exhibits three-dimensional (3D) effects, the 3D T-stresses solutions were obtained by running finite element analyses (FEA) for 3PB specimens with wide ranges of the crack depth-to-width ratio (a/W = 0.2 to 0.8) and the specimen thickness-to-width ratio (B/W = 0.1 to 40). The results show that the 3D T11 at the specimen mid-plane tended to deviate from the 2D T11 as B/W increased, with the deviation saturating for B/W ≥ 2. The mid-plane T33 increased with B/W and was close to the plane strain value νT11 for B/W ≥ 2

Stress Intensity Factor for a Circumferential Crack in a Finite-Length Thin to Thick Walled Cylinder under an Arbitrary Biquadratic Stress Distribution on the Crack Surfaces

This paper presents the development of a practical method, by using prepared tabulated data, to calculate the mode I stress intensity factor (SIF) for an inner surface circumferential crack in a finite length cylinder. The crack surfaces are subjected to an axisymmetric stress with an arbitrary biquadratic radial distribution. The method was derived by applying the authors’ weight function for the crack. This work is based on the thin shell theory and the Petroski-Achenbach method. Our method is valid over a wide range of mean radius to wall thickness ratio, Rm/W ≥ 1, and for relatively short cracks with a/W ≤ 0.5. The difference between the SIF obtained by our method for the geometry and that from finite element analysis is within 5%. The method we developed describes the effect that cylinder length gives on the SIF. This effect needs to be considered for cylinders shorter than non-dimensional cylinder length βH≤ 5

Engineering Framework to Transfer the Lower Bound Fracture Toughness between Different Temperatures in the DBTT Region

AbstractIn this paper, an engineering framework to transfer the lower bound fracture toughness between different temperatures in the ductile–to–brittle (DBTT) temperature region is proposed and validated for 0.55% carbon steel using 0.5TSE(B) specimens. The framework requires only stress–strain curve for different temperatures as experimental data. The approach was based on the authors’ finding that the critical stress σ22c of the modified Ritchie–Knott–Rice criterion (the criterion predicts onset of cleavage fracture of a material in the DBTT transition temperature region, when the mid-plane crack-opening stress σ22 measured at a distance from the crack-tip equal to four times the crack-tip opening displacement δt, denoted as σ22d, exceeds a critical value σ22c) seems to be correlated with the lower bound fracture toughness for a specific specimen configuration. The proposed approach is expected to overcome some inconveniences which recent studies have reported to the Master Curve Local approaches to cleavage fracture that the Weibull parameters vary with size and temperature and are different from those stated in the Master Curve

Stress Intensity Factor Evaluation of a Circumferential Crack in a Finite Length Thin-Walled Cylinder for Arbitrarily Distributed Stress on Crack Surface by Weight Function Method

A weight function to evaluate the stress intensity factor (SIF) of a circumferential crack, subjected to arbitrarily distributed stress on the crack surfaces, in a finite length thin-walled cylinder was derived based on the closed form SIF equation previously developed by the authors. It is easy to evaluate the effects of structural parameters and stress distribution on the SIF with this weight function. Numerical examples confirmed the validity of the weight function. These examples showed that the effect of cylinder length on the SIF is quite large

Influence of Circumferential Flaw Length on Internal Burst Pressure of a Wall-Thinned Pipe

This paper examines the effect of the circumferential angle of a flaw θ on the internal burst pressure pf of pipes with artificial wall-thinned flaws. The effect of θ has conventionally been regarded as unimportant in the evaluation of the pf of wall-thinned straight pipes. Therefore, a burst pressure equation for an axial crack inside a cylinder (Fig. 1, left), such as Kiefner’s equation (Kiefner et al., 1973), has been widely applied (ANSI/ASME B31.G., 1991; Hasegawa et al., 2011). However, the following implicit assumptions notably exist when applying the equation to planar flaws in situations with non-planar flaws. 1) The fracture mode of the non-planar flaw under consideration is identical to that of the crack. 2) The effect of θ on pf, which is not considered for an axial crack, is small or negligible. However, the experimental results from the systematic burst tests for carbon steel pipes with artificial wall-thinned flaws examined in this paper showed that these implicit assumptions may be incorrect. In this paper the experimental results are evaluated in further detail. The purpose of the evaluation was to clarify the effect of θ on pf. Specifically, the significance of the flaw configuration (axial length δz and wall-thinning ratio t1/t) was studied for its effects on θ　and pf. In addition, a simulation of this effect was conducted using a large strain elastic-plastic Finite Element Analysis (FEA) model. As observed from the experimental results, θ　tended to affect pf in cases with large δz, and t1/t was also correlated with a decrease in pf with an increase in θ. These tendencies were successfully simulated by the large strain elastic-plastic FEA model. The observed effects demonstrate that the burst pressure predicted for a crack with identical ligament thickness decreases with an increase in θ, so that the effect of θ on pf should be taken into consideration when evaluating pf

Stress Intensity Factor Evaluation of a Circumferential Crack in a Finite Length Thin-Walled Cylinder for Arbitrarily Distributed Stress on Crack Surface by Weight Function Method

A weight function to evaluate the stress intensity factor (SIF) of a circumferential crack, subjected to arbitrarily distributed stress on the crack surfaces, in a finite length thin-walled cylinder was derived based on the closed form SIF equation previously developed by the authors. It is easy to evaluate the effects of structural parameters and stress distribution on the SIF with this weight function. Numerical examples confirmed the validity of the weight function. These examples showed that the effect of cylinder length on the SIF is quite large

Experimental T33-stress Formulation of Test Specimen Thickness Effect on Fracture Toughness in the Transition Temperature Region

This paper describes a study of the test specimen thickness effect on fracture toughness of a material, in the transition temperature region, for CT specimens. In addition we studied the specimen thickness effect on the T33-stress (the out-of-plane non-singular term in the series of elastic crack-tip stress fields), expecting that T33-stress affected the crack-tip triaxiality and thus constraint in the out-of-plane direction. Finally, an experimental expression for the thickness effect on the fracture toughness using T33-stress is proposed for 0.55% carbon steel S55C. In addition to the fact that T33 (which was negative) seemed to show an upper bound for large B/W, these results indicate the possibility of improving the existing methods for correlating fracture toughness obtained by test specimen with the toughness of actual cracks found in the structure, using T33–stress

Influence of Circumferential Flaw Length on Internal Burst Pressure of a Wall-Thinned Pipe

This paper examines the effect of the circumferential angle of a flaw θ on the internal burst pressure pf of pipes with artificial wall-thinned flaws. The effect of θ has conventionally been regarded as unimportant in the evaluation of the pf of wall-thinned straight pipes. Therefore, a burst pressure equation for an axial crack inside a cylinder (Fig. 1, left), such as Kiefner’s equation (Kiefner et al., 1973), has been widely applied (ANSI/ASME B31.G., 1991; Hasegawa et al., 2011). However, the following implicit assumptions notably exist when applying the equation to planar flaws in situations with non-planar flaws. 1) The fracture mode of the non-planar flaw under consideration is identical to that of the crack. 2) The effect of θ on pf, which is not considered for an axial crack, is small or negligible. However, the experimental results from the systematic burst tests for carbon steel pipes with artificial wall-thinned flaws examined in this paper showed that these implicit assumptions may be incorrect. In this paper the experimental results are evaluated in further detail. The purpose of the evaluation was to clarify the effect of θ on pf. Specifically, the significance of the flaw configuration (axial length δz and wall-thinning ratio t1/t) was studied for its effects on θ　and pf. In addition, a simulation of this effect was conducted using a large strain elastic-plastic Finite Element Analysis (FEA) model. As observed from the experimental results, θ　tended to affect pf in cases with large δz, and t1/t was also correlated with a decrease in pf with an increase in θ. These tendencies were successfully simulated by the large strain elastic-plastic FEA model. The observed effects demonstrate that the burst pressure predicted for a crack with identical ligament thickness decreases with an increase in θ, so that the effect of θ on pf should be taken into consideration when evaluating pf

Simplified Method to Evaluate Upper Limit Stress Intensity Factor Range of an Inner-Surface Circumferential Crack under Steady State Thermal Striping

Simplified method to evaluate the upper limit stress intensity factor (SIF) range of an inner-surface circumferential crack in a thin- to thick-walled cylinder under steady state thermal striping was considered in this paper. The edges of the cylinder were rotation-restrained and the outer surface was adiabatically insulated. The inner surface of the cylinder was heated by a fluid with constant heat transfer coefficient whose temperature fluctuated sinusoidally at constant amplitude ΔT. By combining our analytical temperature solution for the problem and our semianalytical numerical SIF evaluation method for the crack, we showed that the desired maximum steady state SIF range can be evaluated with an engineering accuracy after ΔT, the mean radius to wall thickness ratio rm/W of the cylinder, the thermal expansion coefficient and Poisson’s ratio are specified. By applying are method, no transient SIF analysis nor sensitivity analysis of the striping frequency on the SIF range is necessary. Numerical results showed that our method is valid for cylinders in a range of rm/W = 10 to 1