Parametric study on the effect of the material hardening parameter on the predicted tension-pressure collapse coils (T→ P, Do!t= 18.2. Stress-strain curves represented by Ramberg-Osgood Fit for three different stress values of Parametric study on the yield stress in coils predicted tension-pressure collapse (T → P, Do!t= 18.2).
Motivation
Based on the configuration of the pipe string, certain locations are also subjected to high bending moments. The movement of the sea level installation with the winds, currents and waves further causes a small amplitude cycle of the load conditions on the pipeline, which accelerates its deterioration. In such environments, a local collapse pattern may develop at the weakest point on the line if the loads are large enough.
Definition of Collapse
It can be clearly seen that the weight of the pipe string results in an axial load distribution in which it is a maximum at the surface level going to a minimum at the bottom. The propagating nature [3-6] of collapse at ambient pressures much lower than the onset pressure makes the problem more challenging. Collapse results in flattening of the pipe and high circumferential stresses develop along the sides of the pipe.
Research Background
These figures represent the limit point load-displacement behavior of an initially imperfect tube, characterized by an atypical set of geometric and material parameters observed in the experiments. This can only be considered useful in the limited cases where the failure strength is proportional to the yield strength. Later, Pattillo [27] reported a new formulation that incorporated the effect of initial geometric imperfections in the shape of an ovality.
Objective and Scope
In this chapter, the details of the experimental procedure are described, and the results obtained are illustrated with tables and figures. Thick-walled tubes of small diameter were used to prepare the specimens in the collapse tests. The experimental facility developed for these tests had a pressure rating of 10,000 psi and a tensile strength of 20,000 lbs.
Description of Experiments
Referring to Figure 2.2, the data obtained from each circumferential scan could be interpreted to give the outer tube radius R (θ) as a function of angular position θ. The variation of the imperfection and ovality profile along the length of the specimen as observed in a typical case is given in Figure 2.4. The annealed 304 stainless steel used exhibited very high ductility and was found to yield at high stress levels. The aluminum material 6061-0 was chosen because of its relatively low creep tendency and its better isotropic yielding properties. These tests provided a database for correlation with the collapse analysis of thick-walled pipes under combined loading.
Experimental Results and Discussion
Using strain gauges, the strain response of the specimen at different locations of interest could be measured until collapse. It shows how material parameters for cold drawn tubes of the same material and heat treatment can vary. This effort is an extension of the previous work done on the problem of inelastic collapse under external pressure [8,16,30].
Problem Formulation
In general, the load paths followed by the material points in the tube cross-section under biaxial loading are not uniform. Very often tube manufacturing processes, such as rolling and drawing, introduce anisotropies into the tube. Some of the details about the experimental procedure and the interpretation of the data are given in Appendix B.
Numerical Results
The predicted stress-compression collapse envelope based on the measured anisotropies is in better agreement with the experiments (see Figure 4.5a). The initial ovality, measured at each of the axial locations, is also shown in Figure 4.12b. The agreement between the measured hoop strain-compression response at different axial locations is good (see Figure 4.12b).
Initial Ovality
While for a pipe of Dolt=18.2 and the same material properties, the collapse pressure is only reduced by 40%.
Material Parameters
Collapse pressures for a string Dit, for three sets of Sθ = Sr values are given in figure 5.10. These results suggest that changing the anisotropic parameters which effectively change the yield stress collapse strength of thicker pipes are more affected. The predicted stress-pressure collapse envelopes for three sets of Sθ= Sr values are shown in Figure 5.11.
Residual Stresses
By giving a value of unity to Se and Sr, the above plasticity model reduces to the classical Jr2 theory with isotropic hardening. They (see Figures) show that the effect of including residual stresses becomes negligible at higher tensile loads.
Loading Path
Other Parameters
This chapter deals with the failure of a long, thick-walled pipe, subjected to external pressure and axial tension, made of a material that exhibits elastic-plastic and primary creep behavior.
Introduction
Many of the studies in the literature on creep buckling focus on the problem of columns, plates and shells under axial compressive loading. By modeling only the secondary (steady state) creep behavior, a relatively simple scheme is obtained to obtain the critical time. Bushnell [40] implemented a scheme in a computer program called BOSOR to analyze shells of revolution involving plasticity and creep behavior.
Creep Formulation
Extensive studies of creep behavior in metals [36] have led to the development of the two simple hardening models, namely the strain hardening model and the time hardening model. In the strain hardening model, for isothermal cases, the creep strain rate at any time is given by a function of the stress, σe, and the accumulated creep strain, εec. In the time-hardening model, the creep strain rate is given by a function of the stress, σe, and the time, t.
In this formulation, the strain-hardening model modified [40] with an element of the time-hardening method is used. This modification made the numerical implementation more convenient and its effect on the accuracy of the strain hardening model can be made minimal. In Figure 6.3, the graphical presentation of the equilibrium load-displacement curves with limit points is given.
If the pipe exhibits creep behavior when subjected to a load time history as described above, then the O Ao Bo curve represents the instantaneous response (time t=0) of the structure. This curve O Ac Bc is interpreted as the load-displacement equilibrium behavior of the pipe corresponding to the time tc. For a load λ (see Figure 6.3), the pipe will collapse at time tc if the point Ac happens to be a limit point characterized by the slope of the load-displacement curve going to zero.
The load λc is defined as the failure load of the pipe corresponding to the time tc.
Numerical Predictions
The extent of this reduction in collapse pressure from tension is strongly dependent on the stress-strain behavior of the pipe material. E., "The Propagating Buckle", Proceedings of the International Conference on the Behavior of Offshore Structures (BOSS), Vol. D., "On the Dynamics and Arrest of Buckle Propagation in Offshore Pipelines," OTC 3479, Proceedings of the 11th Offshore Technology Conference,"pp.
10] Tvergaard, Vol., "Bending of Elastic-Plastic Cylindrical Plates under Axial Compression," InternationalJournal of Solids and Structures, Vol. H., "Application of the Energy Test to the Collapse of a Long Thin Tube under External Pressure", Proceedingsofthe Cambridge Philosophical Society, Vol. 20] Lubinski, A., "Effect of Neutral Axial Stress on Pipe Yield and Fracture," ASME Journal of Engineering for Industry, Vol.
21] Fabian, O., "Collapse of cylindrical elastic tubes under combined bending, compressive and axial loads", International Journal of Solids and Structures, Vol. 24] Tamano,T., Mimura,H., Yanagimoto,S., "Investigation of the Collapse Strength of Commercial Enclosures under Axial Load", Proceedings of the First Offshore Mechanics!Artie Engineering!Deep SeaSystemsSymposium, ASME 1, pp. 40] Bushnell , D., "A strategy for the solution of problems involving large deflections, plasticity and creep", International Journal for Numerical Methods in Engineering, Vol.
41] Krempl, E., "Experimental Study of Room Temperature Rate Sensitivity, Creep and Relaxation of AISI Type 304 Stainless Steel," Journal of Mechanics and Physics of Solids, Vol.
Principle of Virtual Work
The first term, which is an integrated cross section over the pipe, represents the increase in strain energy. For the problem of a long pipe subjected to external pressure and axial load, this equation reduces to the following expression. Therefore, for a segment of unit length using the symmetry about the line through θ = 0 and θ = π (see Figure 3.lb).
In this equation, the first term stands for the increase in the strain energy obtained from the biaxial state of stress in the tube cross-section, the second term gives the incremental work performed by the external pressure [42], and the third term defines the incremental work which is done by the axial tension.
Numerical Solution Procedure
Therefore, the measured stress-strain relationship may depend on the orientation of the uniaxial test specimen with respect to the direction of rotation or traction. In cold or hot drawn tubes, these anisotropies will appear as different yield behaviors in the axial and circumferential directions. The collapse strength of thick-walled pipe is strongly influenced by the yield behavior of the pipe material.
If anisotropies exist in the yield, it becomes important to characterize them for better prediction of failure strength. The yield function in Hill's theory reduces to the following form (see Chapter 3) for the biaxial stress state in the pipe cross-section.
Deriving the Anisotropic Parameters
From the uniaxial test results, σox is obtained, which is the initial yield stress in the axial direction. The initial yield stress in the hoop directionσoθ is obtained from the measured hoop stress-strain behavior. The results from the hydrostatic pressure test are used to derive an equivalent stress-strain relationship.
Once dεlpj is known, the equivalent plastic strain is obtained from the work equation aijdε[j = σedεξ. From this working equality, the definition for the corresponding plastic strain increment (after some algebraic manipulations) becomes. Once the parameters Sθ and Sr are known, using equations (B.4) and (B.5), the compressive stress data from the hydrostatic pressure test are reduced to obtain the equivalent stress-strain behavior (σe - εf ).
The iterative procedure through which the Sθand Sr parameters are obtained is illustrated in Figure B.2b. The axial and circumferential stress-strain curves are also reduced to obtain the corresponding σe-ε relations (see Figure B.2a). If the material is not isotropic, then the anisotropic parameter Sθ is obtained from the axial curve and stress-strain curves as described above.
Once Sθ is known, the value for Sr is varied until for a value of Sr the resulting σe -εf curve derived from the hydrostatic test data matches the σe -εf relation in the axial direction. In the given sample results (see Figures B.2b), the values for S θ and Sr are found to be 0.77 and 0.85, respectively. Schematic of the hydraulic flat plate press used to induce initial ovality in the test specimen.
Schematic of the setup used to measure the frictional resistance of the seals at different pressures.
