Autofrettaged Thick-walled Cylinder Research Articles

Numerical evaluation of an autofrettaged thick-walled cylinder under dynamically applied axially non-uniform internal service pressure distribution

Abstract A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasi-internal ballistics structural model was checked. The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared. The difference for the worse case was 20% and for the best case was 0.1%. Furthermore, the model gave better agreement for the higher charge masses. The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.

Experimental assessment of residual stresses induced by the thermal autofrettage of thick-walled cylinders

In this work, an experimental study of the residual stresses present in the thermally autofrettaged thick-walled cylinders is carried out. The idea of thermal autofrettage has been conceived recently, and due to its simplicity, it has the potential to be competitive with the existing hydraulic and swage autofrettage processes. In thermal autofrettage, the beneficial compressive residual stresses at the inner wall are produced by means of thermal gradient across the wall thickness. In this work, the residual stresses setup in the cylinders are determined experimentally using Sachs boring method. The experimental results are compared with the analytically determined residual stresses and found to be in good agreement. In addition to the Sachs boring method, two other methods, namely, microhardness test and the measurement of opening angle as a result of cutting through the wall of the cylinders, are also carried out in order to infer the generation of residual stresses in the autofrettaged cylinders. All three experimental methods advocate the feasibility of thermal autofrettage for producing beneficial compressive residual stresses at the inner wall.

Fatigue Evaluation of Autofrettaged Thick-Walled Cylinders with a Radial Cross-Bore

The fatigue life of autofrettaged thick-walled cylinders with a radial cross-bore is investigated by applying inelastic finite element analysis with cyclic pressure loading. A non-linear kinematic hardening model considering bauschinger effect is used for determining cyclic plastic strain ranges in fatigue evaluations. A macro is written in ANSYS to calculate the equivalent alternating stress intensity, based on the ASME Boiler and Pressure Vessel Code. For a specific cyclic load level, a distinct optimum autofrettage pressure is identified by plotting autofrettage pressure against the equivalent alternating stress intensity and the number of cycles from design fatigue data. The optimum autofrettage pressure was found in the range of 80.5%-92.5% of limit pressure. The hydrotest had little influence on the fatigue life when the thick-walled cylinder was autofrettaged with an optimum autofrettage pressure.

Effect of Material Damage on Autofrettage of Thick-Walled Cylinder

Continuum damage mechanics approach has been used for analysis of the autofrettage process. General set of government equations of elastic-plastic bodies is derived by using the effective stress concept. Strain - damage coupling constitutive equations are developed on the base of plasticity relationships with bilinear kinematic hardening and kinetic law of ductile damage evolution. Damage of the material leads to decrease of Young's modulus after plastic deforming that affects on the unloading stage of autofrettage. Influence of material damage on residual hoop stress was considered by the example of autofrettaged thick-walled cylinder. Numerical results were obtained by finite-element method for plane-strain case. These results showed that material damage modifies the residual stress distributions and reduced residual hoop stress value on bore area.

Research on Fatigue Life of Autofrettaged Thick-Walled Cylinder in Probabilistic Fracture Mechanics

Based on the theory of probabilistic fracture mechanics and Monte Carlo simulation, reliability analysis method for fatigue life of autofrettaged thick-walled cylinder was given. The forms of fatigue cracks in bore of autofrettaged thick-walled cylinder were considered as semi-elliptical cracks. The autofrettage residual stress solution was suitable for the thick-walled cylinder made of steel with strain hardening and Bauschinger effect. The stress intensity factors of thick-walled cylinder were calculated according to weight function method. The analysis of the examples showed that lognormal distribution is the best fit for fatigue life. Finally, the fatigue life of autofrettaged thick-walled on the condition of different reliabilities and confidences were presented.

A Study of the Residual Stress Distribution in an Autofrettaged, Thick-Walled Cylinder With Cross-Bore

It may be necessary to provide a radial opening such as gas evacuator holes, or an opening to operate the unlocking of the bolt mechanism by means of exhaust gases, in a gun barrel, which is a thick walled cylinder. A three dimensional finite element analysis has been performed to evaluate the effect of introducing a radial cross-bore in an autofrettaged thick-walled cylinder. From the analysis of the cross-bored autofrettaged cylinder, it was observed that there is a severe localized change in the residual stress profile in the vicinity of the cross-bore. The residual circumferential stress increases in compression at the bore. Similarly it increases in tension at the outer diameter, thus making the outer diameter more vulnerable to fatigue failure or crack initiation under stresses arising as a result of firing. Analyses were also performed by varying the cross-bore diameter and it was observed that, by increasing the diameter of the radial hole, the residual circumferential stress at the bore reduces, while it increases at the outer diameter, with an increase in the cross bore diameter. The re-pressurization pressure of an autofrettaged cylinder with radial cross-bore was found to be approximately 65 percent less than the actual autofrettage pressure in a particular case discussed in this paper. A comparison is also made with the residual stress field which would result if the cross-bore was machined before autofrettage.

Comparative measurements on autofrettaged cylinders with large Bauschinger reverse yielding zones

A comparative study to map the residual strain/stress states through the walls of autofrettaged thick-walled steel cylinders has been conducted with neutron diffraction, Sachs boring and the compliance methods. Test samples with different wall thickness ratios were prepared to have significant amounts of reverse yielding due to the Bauschinger effect. All three methods indicate that the autofrettage action primarily influenced the hoop stresses, which varied rapidly close to the bores from compressive to tensile within the first half of the wall thickness. Quantitatively, results from the neutron diffraction and Sachs boring techniques compare favourably across large regions of the cylinder walls, while the compliance results showed different features. The existence of reverse yielding close to the cylinder bores has been sensed to different magnitudes and distances from the bores. Plastically yielded material regions identified from the neutron diffraction results correlated well with theoretical modelling.

3-D Stress Intensity Factors for Internal Cracks in an Overstrained Cylindrical Pressure Vessel—Part I: The Effect of Autofrettage Level

Three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of internal surface cracks emanating from the bore of an autofrettaged thick-walled cylinder are evaluated in Part I of this paper. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent temperature field. More than 200 different crack configurations were analyzed. SIFs for numerous crack arrays (n=1–180 cracks), a wide range of crack-depth-to-wall-thickness ratios a/t=0.05-0.6, various ellipticities a/c=0.2-1.5, and different levels of autofrettage (e=10–100 percent) were evaluated. The results clearly indicate the importance of autofrettage in reducing the effective stress intensity factor, and thus, slowing the crack growth rate. The sensitivity of this favorable effect to the number of cracks in the array as well as to the level of autofrettage are also discussed. The combined effect of pressure and autofrettage is discussed in detail in Part II of this paper. [S0094-9930(00)00604-1]

3-D Stress Intensity Factors for Internal Cracks in an Overstrained Cylindrical Pressure Vessel—Part II: The Combined Effect of Pressure and Autofrettage

K IA and KIP stress intensity factors (SIF) for three-dimensional semi-elliptical, surface, radial cracks prevailing in a pressurized or autofrettaged thick-walled cylinder were evaluated and discussed in Part I of this paper and in Perl et al. 1996, “Three-Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder—Part I: Radial Surface Cracks,” AMSE J. Pressure Vessel Technol. 118, pp. 357–363), respectively. These SIFs were calculated for a wide range of configurations: for cracks pertaining to large arrays of up to 180 cracks, with ellipticities of a/c=0.2, 0.5, 1, 1.5, depth ratios of a/t=0.05−0.6, and for various levels of autofrettage. In Part II of this paper, the effect of the combined SIF KIN=KIP+KIA is considered, which enables the prediction of fracture endurance, crack growth rate, and the total fatigue life for a modern gun barrel. The results reconfirm the impact autofrettage has on delaying crack initiation and propagation. This favorable effect is found to be governed by ψ=σ0/p—the ratio of the vessel’s material yield stress to its internal pressure. The higher ψ is, the more effective autofrettage becomes. While KIA and KIP reach their maximum absolute values, usually, for an array of n=2 cracks, the largest combined SIF-KIN occurs for arrays of 2–16 cracks. Finally, the similarity in the behavior of KIA and KIP along the crack front is studied as well as its relation to the respective stress fields.

Cracks Emanating From an Erosion in a Pressurized Autofrettaged Thick-Walled Cylinder—Part II: Erosion Depth and Ellipticity Effects

In Part I of this paper, the effects of constant depth erosion on the mode I stress intensity factor (SIF) were determined for a crack emanating from the erosion deepest point in a pressurized, autofrettaged, thick-walled cylinder. The erosion geometries investigated included semi-circular erosions and several arc erosions of various radii of curvature. Due to the trends found in that portion of the study, erosion depth and ellipticity are believed to have equally important impact on the SIFs. The present paper delves further into these two parameters using the following configurations: (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, W; and (b) semi-elliptical erosions with ellipticities of d/h = 0.3 – 2.0. Deep cracks are found to be practically unaffected by the erosion, similar to the results presented in Part I of the paper. The effective SIF for relatively short cracks is found to be dramatically enhanced by the stress concentration factor (SCF), which encompasses the depth of the erosion as well as its radius of curvature at the tip. As a result of the increased effective SIF, a significant decrease in the vessel’s fatigue life of up to an order of magnitude may occur.

Cracks Emanating From an Erosion in a Pressurized Autofrettaged Thick-Walled Cylinder—Part I: Semi-Circular and Arc Erosions

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from the erosion’s deepest point in an autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is solved via the FEM method and knowledge of the asymptotic behavior of short cracks. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack lengths, a0/W = 0.01 – 0.45, emanating from the tip of erosions of different geometries. In Part I of this paper, two configurations are considered: (a) semi-circular erosions of relative depths of 5 percent of the cylinder’s wall thickness, W; and (b) arc erosions for several dimensionless radii of curvature, r′/W = 0.05 – 0.4. While deep cracks are almost unaffected by the erosion, the effective SIF for relatively short cracks is found to be significantly enhanced by the presence and geometry of the erosion and might reduce the vessel’s fatigue life.

Fatigue crack propagation life evaluation of an autofrettaged thick-walled cylinder

To ensure the structural integrity of the autofrettaged thick-walled cylinder subjected to cyclic internal pressure loading, the fatigue crack propagation life of the cylinder was evaluated. Stress intensity factors of the external cracked cylinder due to internal pressure and autofrettage loadings were calculated using the finite element method. The fatigue crack propagation lives of the cylinder based on the fracture mechanics concepts were predicted and compared to the experimental fatigue lives evaluated from the C-shaped simulation specimens. There were good correlations between the predicted and experimental fatigue lives within a factor of 3 for the single and double grooved C-shaped simulation specimens. Predicted fatigue crack propagation lives of the double grooved cylinders were about 1.5-5 times longer than those of the single grooved cylinders depending on the levels of autofrettage.

Stress intensity factors for semi-elliptical internal surface cracks in autofrettaged thick-walled cylinders

Stress intensity factors for internal semi-elliptical surface cracks in autofrettaged cylinders with and without internal pressures applied are presented. The three-dimensional finite element based displacement method with the crack tip square-root singularity of stresses and strains simulated is used to evaluate the stress intensity factors along the crack front. Both allowing and disallowing the overlapping of crack faces are considered in this investigation, the latter being simulated by considering crack surface contact through a kind of interface element introduced into the cracked area. The residual stress distribution assumed to act on the crack face is obtained according to Tresca's yield criterion with the material assumed to be elastic-perfectly plastic. Three different overstrains of autofrettage are chosen. The results show that the stress intensity factor is generally underestimated if the crack contact that has actually occurred is ignored, which may lead to a danger in the assessment of either fracture strength or fatigue life. Implications of the stress intensity factor results are also briefly discussed, particularly for the prediction of fatigue lives, and it is shown that the full autofrettage treatment might be the most beneficial for increasing the fatigue life of cracks initiated from the inner core.

Different solutions for stress and strain fields in autofrettaged thick-walled cylinders

In the first part of the paper we will present an analytical solution to the plastic stress and strain distribution induced by a single over-pressure cycle in a cylindrical vessel. The solution is valid for materials which, during the loading phase, can be described by a linear hardening law as well as by the modified Ramberg-Osgood law. We will clarify the conditions for which the stress field expressions can be simplified, thus facilitating a parametric analysis of their increase with respect to the values one would obtain when considering an ideal elastic-perfectly plastic behaviour of the material. In the second part of the paper, residual stress fields will be numerically evaluated, taking into account, during the unloading phase, both the variability of the stress flow and the Bauschinger effect factor as a function of pre-strains.

A numerical approach for nonclassical plasticity

A new incremental form of constitutive equation and the corresponding nonlinear FEM approach are developed based on an endochronic constitutive equation without using a yield surface; a kind of nonclassical theory of plasticity. Compared with the numerical method proposed elsewhere, the new algorithm greatly reduces the error induced in the numerical process, especially in the region of initial extremely small inelastic strain with its slope of stress-plastic strain curve being sufficiently large. The residual stress field of an autofrettaged thick-walled cylinder and the cyclic stress responses of a notched plate are then analyzed.

Prediction of Residual Stresses in an Autofrettaged Thick–Walled Cylinder

ABSTRACTMost of the earlier results for residual stresses are based on the assumption of elastic unloading. In this paper, the prediction of residual stresses for the case of reverse yielding including the combined Bauschinger and hardening effect will be reported for an autofrettaged thick-walled cylinder. The Bauschinger effect factor is varying as a function of overstrain. The strain-hardening effect is considered with different parameters used for loading and unloading process. The new results indicate that the influence of the combined Bauschinger and hardening effect on residual stress distribution is significant.