Evaluation Of Limit Load Research Articles

Limit load evaluation for healthy elbows and elbows with notch at intrados under in-plane bending moment

Elbows are critical parts of any piping system used in nuclear power plant industry. These elbows experience internal pressure and also undergoes in-plane bending due to external loading. In the present study, limit load for two types of elbows, viz., healthy elbow and elbow having circumferential through-wall notch at intrados, with and without internal pressure subjected to in-plane bending moment is determined. Limit load is dependent on the parameters, namely, thickness, mean radius, bent radius, internal pressure, yield stress, notch size and deformed diameter of the elbow. Based on the experimental and numerical studies, the expressions for limit load evaluation were proposed by various researchers. In the present study, the limit load evaluation expressions proposed by Chattopadhyay and Tomar (2006), Chang-Sik and Kim (2006) and Hong et al. (2010) are considered. The general approach followed is to arrive at a weakening factor for considering the effects of bend geometry, internal pressure and presence of notch. Limit load obtained by using the above expressions have been compared with the twice elastic slope (TES) method and experimental measured maximum load (EMML) values. For elbows without any defect, limit load of TES method are about one-third approximately compared to EMML values. But for elbows with defect, it is lesser than EMML values by 20%. Predicted limit load for healthy elbows with and without internal pressure using the different expressions, found to vary less than 10% compared to TES method. For the elbows with circumferential through-wall crack at intrados without internal pressure, limit load obtained using TES method is around 15% more compared to the values obtained using the expressions.

Limit load evaluation of inlet pigtail pipe bends with ovality under in-plane bending

AbstractThe prediction of limit load on inlet pigtail pipe bends employed in a hydrogen reformer is one of the unresolved engineering tasks in chemical industries. This is because of the uncertainty and required extrapolation of the applicable data. In practice, the cross section of the inlet pigtail pipe bend becomes non-circular due to the bending process. This irregularity in shape extends when pipes are subjected to in-plane bending moment during plant operation. Ovality is the shape imperfection in a pipe bend considered for the present study. It affects the load carrying capacity and life cycle of the pipe bend. A three-dimensional finite element method is used to model and analyze a stand-alone, long radius inlet pigtail pipe bend. The pipe bend is modeled with a shape irregularity for which the percent ovality varies from 0 to 20. By considering ovality, it is shown that there is a significant effect in limit load due to in-plane bending moment. Also, the stress induced in the pipe bend geometry increases with the percentage of ovality. The allowable levels are obtained from finite elements analysis, considering various bend factors, and the closed form limit load solution is proposed, including the effect of ovality in pipe bend.

Imperfection sensitivity analysis of composite cylindrical shells using Koiter’s method

ABSTRACTThe novel methodology for imperfection sensitivity analysis, presented in Barbero et al. [1], is here applied for the evaluation of limit load of composite cylindrical shells. Koiter’s perturbation method is used to calculate the imperfection paths emanating from mode interaction bifurcations, and the Monte Carlo method is used to test a large number of modes and all possible interactions among them. The computational cost is low because of the efficiency of Koiter’s method. The demands of Koiter’s method for accurate evaluations of higher order derivatives of the potential energy are met by a mixed, corotational element.

Incorporated Strength Capacity Technique for Limit Load Evaluation of Trusses and Framed Structures under Constant Loading

AbstractTo overcome the difficulties encountered by the elastic modulus adjustment procedures applied to the ultimate bearing capacity analysis of framed structures under combined action of both constant and varying live loads, an efficient incorporated strength capacity technique is proposed in this work. A new structural analysis model is developed with totally different distributions of loads and resistance from the original model by incorporating the constant load effects into the sectional strength capacity of components in framed structures. The element bearing ratio (EBR) is defined according to the modified structural model on the basis of the generalized yield function of spatial beam element. The uniformity of the EBR is presented in terms of the EBR distribution characteristics, on the basis of which the reference EBR (REBR) is defined as a dynamic threshold to identify the highly stressed elements with the EBR greater than the REBR. Subsequently, an adaptive strategy of elastic modulus adjustm...

Limit Load Evaluation Using the mα-Tangent Multiplier in Conjunction With Elastic Modulus Adjustment Procedure

In this paper, the mα-tangent multiplier is used in conjunction with the elastic modulus adjustment procedure (EMAP) for limit load determination. This technique is applied to a number of mechanical components possessing different kinematic redundancies. By specifying spatial variations in the elastic modulus, numerous sets of statically admissible and kinematically admissible stress and strain distributions are generated, and limit loads for practical components are then determined using the mα-tangent method. The procedure ensures sufficiently accurate limit loads within a reasonable number of iterations. Results are compared with the inelastic finite element results and are found to be in satisfactory agreement.

An FE-MPEC approach for limit load evaluation in the presence of contact and displacement constraints

This paper describes a mathematical programing based approach for the direct limit load evaluation of a structural system under simultaneous contact and limited displacement conditions. The contact model we adopt can simulate either a classical unilateral (nonassociative) Coulomb friction situation or a cohesive fracture idealization at the potential discontinuity interface between contacting bodies. The discrete FE model is constructed using locking free mixed finite elements. The main feature and novelty of our proposed approach is to compute in a single step the maximum load capacity of the structure, such that both the imposed displacement limitations and the contact conditions are satisfied. In essence, the formulation is a nontrivial extension of classical limit analysis. The analysis is cast in its most natural form, namely in mixed static-kinematic variables, and leads to, what is known in the mathematical programing literature, as a mathematical program with equilibrium constraints or MPEC. A nonlinear programing (NLP) based algorithm is proposed to solve the MPEC. Two examples are provided to illustrate application of the proposed scheme, and some comments regarding the various advantages of the adopted mathematical programing framework are made.

1006 Ni基合金円筒溶接継手の破壊強度評価(OS10-2 供用エネルギー機器の経年変化と健全性評価-破壊評価-)

For the purpose of establishing fracture evaluation method of Alloy 600 weld of nuclear power plants, fracture tests using pipe model(8B and 14B) with alloy 600 weld joint have been perfonned at RT and 325℃. Predicted loads calculated by limit load evaluation method using measured and code regulated flow stresses were compared with the maximum test loads. And the predicted loads of the pipe at 325℃(8B and 14B) and at RT(8B), the initial crack depth of which is 75% of the pipe thickness, were in good agreement with the maximum test loads.

1019 エルボ配管の面内曲げに対する梁理論の適用限界(OS10-5 供用エネルギー機器の経年変化と健全性評価-配管・エルボー強度-)

The beam theory has been used for the limit load evaluation for straight pipes with surface flaws. In case of elbow pipe, however, the beam theory gives just an approximated solution because of the three-dimensional defomiation combining the beam bending and plate bending. In this study, we searched for the boundary, within which the approximation based on the beam theory was applicable. To determine the boundary, the bend radius and wall thickness was systematically changed, and the reasonable solutions were obtained by the fmite element analysis using the solid element with the reduced integration to avoid the numerical locking. The variation of error in the extrados and intrados surface stress with respect to the pipe dimensions was numerically clarified and 10%-error bound was fixed as the applicability boundary. The explicit formulation of the boundary was found to judge the applicability of beam theory to the elbow pipes.

Elastic modulus reduction method for limit load evaluation of frame structures

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio (EBR), and the elastic modulus reduction method (EMRM) is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion, and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility, accuracy and efficiency of the proposed method.

On the equivalence of slip-line fields and work principles for rigid–plastic body in plane strain

Extremum/work principles for a rigid–plastic body have been discussed in classical theory of plasticity to be of immense significance. Unfortunately, till now, these extremum theorems have been used only as a crude method of obtaining the limit load of a rigid–plastic body, using successive approximations by upper and lower bound estimates. On the other hand slip-line fields (SLF) have been extensively used not only for evaluation of limit load but also for obtaining sufficiently accurate estimates of stresses in the plastic region as well as in the vicinity of crack tip. Till now, these two methods of plastic analyses, that is, the work principles and SLF have remained more or less independent apart from the fact that both are upper bounds as they use kinematically admissible velocity fields. Recently, a new load bounding technique, modified upper bound (MUB) Approach, was proposed by Khan and Ghosh [Khan, I.A., Ghosh, A.K., 2007. A modified upper bound approach to limit analysis for plane strain deeply cracked specimens. International Journal of Solids and Structures 44 (10), 3114–3135]. In this article, a rigorous mathematical basis of this load bounding technique is presented and it is demonstrated that the method is actually a new form of the general extremum/work principles. The equivalence of this new form of work principle, that is, MUB with the classical SLF analysis, for a rigid–plastic material in plane strain, has been discussed in detail. Since plastic deformation fields depend on specimen geometry and type of loading specific cases have been considered. Both cracked and uncracked configurations have been analysed to establish this equivalence in general. Various simplifications resulting from the use of this new load bounding technique over SLF method has been demonstrated. Several standard problems of plane strain analysed by SLF method and validated by experiments in past have been considered in this article. As a novel application of the proposed method, single-edge-cracked plate under combined bending and tensile load has been analysed. For this specimen SLF solutions are available only for bending with small tensile load (defined in Section 3.2.4) while classical upper bound solutions are valid for bending with large tensile load. In this work a completely analytical formulation for yield locus for the entire range of tensile and bending load has been obtained. Apart from accurate evaluation of limit load, detailed evaluation of crack tip stresses and hence constraint near the crack tip has been performed using this new form of work principles.

Fatigue‐creep and plastic collapse of notched bars

ABSTRACTThe paper describes a study of the application of a new assessment method, based on the linear matching method (LMM), to the creep fatigue of notched bars of Udimet 720Li at 650 °C. This high strength nickel based alloy is taken as typical of alloys used in high temperature gas turbine applications. The primary purpose of the study is to see whether it is possible to predict the failure modes for such alloys in terms of standard materials data by the evaluation of a sequence of simplified calculations corresponding to the steady state cyclic stress history. These calculations involve the evaluation of limit load, shakedown limit and ratchet limit for perfect plasticity, rapid cycle creep solutions and the evaluation of an elastic follow‐up factor. Within the limitations of the tests, the correlation between predicted failure mode and observed mode is very good and the calculations clearly show up the differences between the two types of notched bars discussed. This implies that LM methods are well suited to the evaluation of failure modes in materials of this type.

Consistent shakedown theorems for materials with temperature dependent yield functions

The (elastic) shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic–plastic rate-independent associative material models with temperature-dependent yield functions. Assuming the yield functions convex in the stress/temperature space, a thermodynamically consistent small-deformation thermo-plasticity theory is provided, in which the set of state and evolutive variables includes the temperature and the plastic entropy rate. Within the latter theory the known static (Prager's) and kinematic (König's) shakedown theorems — which hold for yield functions convex in the stress space — are restated in an appropriate consistent format. In contrast with the above known theorems, the restated theorems provide dual lower and upper bound statements for the shakedown limit loads; additionally, the latter theorems can be expressed in terms of only dominant thermo-mechanical loads (generally the vertices of a polyhedral load domain in which the loadings are allowed to range). The shakedown limit load evaluation problem is discussed together with the related shakedown limit state of the structure. A few numerical applications are presented.

On the solution of limit load and reference stress of 3-D structures under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially considering multi-loading systems. The limit analysis of structures and the reference stress method (RSM) have been proven to be successful in problems pertaining to two-criteria failure assessment, creep growth, rupture damage, and more recently, elastic-plastic fracture toughness. However, the determination of limit load and reference stress of 3-D structures under multi-loading systems is not a simple task. In the present paper, a solution method for radial loading is presented, the mathematical programming formulation is derived for the upper bound limit analysis of 3-D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The penalty function method is used to deal with the plastic incompressibility condition. All the numerical examples show that the proposed radial loading path scheme is reasonable and effective. The mathematical programming method without search used here can overcome the difficulties caused by the nonlinearity and nonsmoothness of the objective function and avoid the complicated computations of incremental elastic-plastic analysis.

Numerical analysis of limit load and reference stress of defective pipelines under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially in Nuclear Electric's (formerly CEGB) R5 and R6 procedures. The reference stress method has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and more recently, elastic–plastic fracture toughness. An approximate method of reference stress determination relies on prior knowledge of limit loads for various configurations and loadings. However, determination of the limit loads for the problems with complicated geometric forms and loading conditions is not a simple task. In the present paper, a numerical solution method for radial loading is presented, the mathematical programming formulation is derived for the kinematic limit analysis of 3D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The numerical procedure is applied to determine the limit load and reference stress of defective pipelines under multi-loading systems. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated in detail. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.