Plastic Limit Load Research Articles

Exclusion of rupture for welded piping systems of power stations by component tests and failure approaches

High temperature seamless pipes of dimensions O.D. × T × L = 457 × 15 × 5500 mm 3 made from 15 NiCuMoNb 5 material were loaded by internal pressure and a superimposed external bending moment. 27 tests with different geometries and positions of circumferential flaws in the base metal or in circumferential welds were performed at room temperature. Depending on the geometric conditions, the load bearing and failure behaviour of the investigated pipes could clearly be represented in a common failure diagram. Significant differences in maximum loads due to the position of the flaws in the structure, or whether inside or outside, could not be detected. Maximum loads were compared with calculations using applied engineering failure approaches, based on concepts of local flow stress and plastic limit load. Elastic-plastic fracture mechanics was applied to some of the component tests and the initiation and instability criteria verified.

Cone‐Cylinder Intersection under Pressure: Axisymmetric Failure

This paper presents a detailed finite‐element investigation into the axisymmetric failure behavior and strength of intersections of the large end of a cone and a cylinder subject to uniform internal pressure. The study considers shells of uniform thickness with cone‐apex half angles ranging from 10° to 85° and cylinder radius‐to‐thickness ratios from 10 to 1,000. Plastic limit loads from a small‐deflection elastic‐plastic analysis are first presented. A rationally based simple equation is then established, which approximates the finite‐element limit loads very closely and is suitable for future incorporation in pressure‐vessel design codes. The effect of large deflections on the load‐deflection behavior is examined extensively for the covered geometric parameters for three different yield stresses. An approximate equation to assess the beneficial effect of large deflections on failure strength is also developed.

A simple model to explain the geometry dependence of J??a-curves

Very different patterns of geometry effects may occur if in a bend type specimen the ligament length is increased at constant specimen thickness. These geometry effects can be explained by a model of the total crack growth resistance R which is defined as the sum of the non-reversible energy which must be put into a body to produce an increment of crack area. The relationship between R and the commonly used J−Δa-curves is worked out. The model shows that a ‘wider-lower’ pattern, i.e. the case where an increase of the ligament length causes a flatter J−Δa-curve, appears for fracture under lefm conditions or for contained yielding where R is independent of the geometry. A ‘wider-no effect’ or a ‘wider-higher’ pattern may be observed if the crack extension occurs at the plastic limit load and if either plane strain or plane stress conditions prevail.

Incompatible numerical simulation of the axisymmetric cracked body made of ideally elastic-plastic material

It is well known that isoparametric axisymmetric elements always encounter various numerical difficulties in computational plasticity. An incompatible axisymmetric element which can avoid the above-mentioned difficulties is presented and then used to solve axisymmetric ductile fracture problems. As an example a stretched cylinder with a circumferential crack is investigated, and elastic, elastic-plastic solutions and plastic limit loads of the cracked cylinders are given and examined. In addition, the path-independence of the J integral is inspected, and the limits for use of the axisymmetric J integral are suggested.

Influence of specimen thickness on the deformation and fracture behaviour of wide plates

The influence of specimen thickness on the deformation behaviour and the load bearing capacity has been investigated with large scale double edge notched tension specimens (DENT). The difference of the state of stress can be modelled by simplifications (plain strain, plain stress). Equations for the calculation of plastic limit loads taking into account the defect ratio a/W have been derived based on analytical, numerical and experimental investigations. Already existing equations may lead to unsafe prediction in special situations. The difference between plastic limit and maximum load is smaller for the thicker specimens due to higher toughness requirements. The toughness requirements have been quantified for the DENT specimens using the J-integral analysis. The requirements mainly depend on the overall dimensions ( W, B), the thickness ratio ( B/W) and the defect ratio ( a/W).

Experiments on the transferability of creep crack growth laws to tubes

The present study served to investigate creep crack growth experiments for a tube with a 180° surface crack in circumferential direction. The tube had an outer diameter of 197 mm and a wall thickness of 23.5 mm. It was loaded with four-point bending at 700°C. No solutions for calculation of the C ∗- integral were available in the literature for this testing geometry, so new approaches had to be found. An approximation method, the so-called limit analysis technique was used for this purpose. It requires the plastic limit load of a specimen and the displacement rate of the load application points as the experimental input parameters. Before the limit analysis technique was applied to the tube under bending, results from earlier creep crack growth experiments were used to verify this technique. The C ∗ values determined from the limit analysis were compared with values based on the numerical calculations of the EPRI handbook. A good agreement was found for both calculation methods. It therefore seems justified to apply the limit load procedure also to the tube loaded in bending. The calculation on the basis of the limit analysis was performed in two ways, which differed by the type of crack front modelling. The simpler model yielded results that were too conservative in comparison with the experimental results of CT specimens. The application of the second model, which better covers the true crack front, provides values for da/ dt versus C ∗ which are actually within the scatter band of CT specimen results. This procedure therefore permits the transfer of standard specimen results to components.

Extended bounding theorems for nonlinear limit analysis

A stability criterion for rigid-perfectly plastic structural analysis for structures undergoing large deformation is formulated, which plays a key role in nonlinear limit analysis. Based on the property of the superpotential in this theory, various variational techniques are suggested for optimal bounds of the plastic limit load factor. An application is illustrated.

Plastic limit analysis of incompatible finite element method

This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.

The plastic zone and limit load of centre-cracked plate by the weighted residual method and elasto-viscoplastic theory

A combination of the weighted residual method and elasto-viscoplastic theory is used to study the plastic zone and the limit load of centre-cracked plate. A new set of displacement functions has been assumed, and a series of governing equations for elasto-plastic analysis are derived. Numerical examples show that this method offers good accuracy but requires very little computer time.

Untersuchungen zum Einfluß der Probendicke auf das Verformungs‐ und Bruchverhalten bauteilähnlicher Großzugproben

AbstractInfluence of specimen thickness on the deformation and fracture behaviour of wide platesThe influence of specimen thickness on the deformation behaviour and the load bearing capacity has been investigated with large scale double‐edge‐notched‐tension‐specimens (DENT). The difference of the state of stress can be modelled by simplifications (plain strain, plain stress). Equations for the calculation of plastic limit loads taking into account the defect ratio a/W have been derived based on analytical, numerical and experimental investigations. Already existing equations may lead to unsafe prediction in special situations. The difference between plastic limit and maximum load is smaller for the thicker specimens due to higher toughness requirements. The toughness requirements have been quantified for the DENT‐specimens using the J‐integral analysis. The requirements mainly depend on the overall dimensions (W, B), the thickness ratio (B/W) and the defect ratio (a/W).

Assessment of large scale pipe tests by fracture mechanics approximation procedures with regard to leak-before-break

On the basis of numerous tests which were performed to demonstrate the “Leak-Before-Break” (LBB) behaviour predictions based on analyses could be further developed and substantiated. The methods applied (local flow stress concept, plastic limit load concept and two criteria approach) for the calculation of failure loads in pipes with circumferential cracks subjected to bending moment and internal pressure loading are evaluated and compared to the results gained by experiments. LBB predictions on the basis of the methods described show that reliable statements can be made. This has been confirmed by the experiments performed.

Moment loads on branch-pipe junctions: The effect of run-pipe fixing on elastic stress levels and its implications on plastic limit loads

Experimental stress analysis results on a series of eight branch-pipe intersections, and finite element results on a series of four branch junctions, have been used to assess the effect on elastic stress levels, arising from branch moment loading, of varying the run-pipe boundary conditions. It is shown that for branch/run-pipe diameter ratios of 0·5 or less boundary condition effects are not significant. Conversely, for junctions with larger diameter ratios, there are significant differences, depending on whether one or both run-pipe limbs are clamped. The implications of the results on plastic limit loads for branch-pipe junctions are discussed.

Evaluation of tests of pipes with circumferential cracks based on the limit load concept

Circumferentially cracked pipes of an austentic stainless steel were tested in four-point bending. The test results are evaluated using the plastic limit load concept. A simple equation is derived for the limit moment of an ovalized pipe. The test results agree only qualitatively with the limit moments predicted which tend to be non-conservative because the hardening effects are not taken into account properly. The CEGB-R6 approach is shown to give conservative estimates of the maximum moment observed.

Influence of material properties and geometry on the limit load behaviour of flawed structures

On the basis of previous results, 1 two effects are discussed which may raise the actual plastic limit load of a structure above a lower bound limit load estimated according to plasticity theory. A database has been used that includes more than 1200 fracture mechanics experiments performed by many industrial companies and research institutions. A wide variety of specimen shapes, as well as pressure vessel and piping components, which were made of ferritic and austenitic steels common to nuclear power plant applications, have been evaluated. Firstly, finite element calculations as well as simple plastic limit load evaluations show that the strain hardening capacity of the material does not in general raise the flawed structure's ultimate load such as to reach a net section stress equal to the mean of yield and ultimate tensile strength. Secondly, many of the tests reveal that the anticipated gain due to increasing triaxiality of stress state with bigger structures (stress hardening), which has sound theoretical backing, is actually zero. Hence, upon applying the method of plastic limit loads to assess the integrity of flawed structures, the analyst is well advised to consider only the yield strength and the state of plane stress.

Ductility, Snapback, Size Effect, and Redistribution in Softening Beams or Frames

A layered finite element model with strain‐softening material properties, whose applicability to reinforced concrete was corroborated by comparisons with experimental data in the preceding paper, is used in a parametric study aimed at the effect of several factors: structure size, finite element size, downward slope of strain‐softening stress‐strain relation, length of the plastic yield plateau before the onset of strain softening (if any), and end‐restraint stiffness. To quantify the response, several new response characteristics are introduced: the ductile strengthening factor, characterizing how strain softening reduces the maximum load compared to the plastic limit load; the redistribution ratio, characterizing the degree of bending moment redistribution in comparison to that in plastic limit analysis; the energy safety factor, describing the energy to deform the structure to the peak load; and the ductility factor, characterizing the deflection increase at maximum load relative to the deflection from elastic analysis. The condition of snapback instability, which determines the ductility factor, is derived analytically for an elastically restrained beam. Finally, it is shown that strain‐softening segments in beams cannot be modeled as softening hinges except for sufficiently slender beams.

Ductility minimum for application of plastic limit load concept to failure analysis of structures with imperfections

When using the plastic limit load concept for structure failure analysis, the stress analyst must confirm that the material of the structure possesses adequate ductility to deform in the plastic domain without instability, even in the presence of known or assumed manufacturing defects. The work reported in this paper has determined that, for use with a lower-bound plastic limit load method, this minimum adequate ductility is 45 J, expressed in terms of Charpy-V-notch energy ( C v-energy ) as measured by standard material tests. The lower-bound method uses plane stress formulae and the yield strength in simple tension σ y instead of the flow stress σ∗ (i.e. no accounting for strain hardening) to yield results on the safe side. This determination is based on an evaluation of more than 400 burst and fracture mechanics tests on components (shell type structures) and specimens (various tensile and bend specimens) made of ferritic and austenitic steels of nuclear grades as well as conventional structural steels, and including some intentionally degraded melts. Another proposed criterion, namely that the C v-energy to yield strength ratio should be equal to or greater than 0·12 J MPa −1 for the application of the plastic limit load concept, was found to result in an unnecessarily stringent limit for materials above 375 MPa yield strength. In addition, the reduction in area measured in tensile tests has been investigated as an alternative index of toughness. This property, however, was found to be unsuitable for defining a ductility limit for use with the plastic limit load concept. Therefore, the aforementioned easy-to-use engineering rule, which requires only geometrical data and two material properties, C v-energy and the yield strength in simple tension, is recommended for failure analysis of cracked structures.

A numerical procedure for evaluating the plastic limit load of a circular plate using mises yield criterion

The problem of evaluating the plastic limit load of a circular plate using Mises yield criterion is reduced to a special problem of finding the eigenvalue of an ordinary differential equation. The proposed problem can be solved easily by using a trying technique.

On the required toughness for the application of the net section yield criterion on nuclear power plant components

Abstract The principles of plastic limit load are recaptured. A method is developed to calculate lower bound estimates of critical crack sizes for nuclear plant components. More than 250 fracture mechanics experiments on specimen and component geometries have been evaluated focussing on the material toughness in terms of Charpy-V energy. The thus determined Charpy threshold value for the application of the aforementioned method is 45 J regardless whether the material has already reached the upper shelf toughness or is still within the transition region. The method is not able to cope with the phenomenon of “ductile tearing”. However when predicting critical crack sizes the method yields conservative results even when ductile tearing must be expected.

Materials for LWRs in the light of new developments

One of the pillars of the outstanding safety level and high availability of KWU nuclear power plants is the quality of the materials used. Base material toughness, weld quality and new fabrication methods for piping components are used as examples to describe this high quality. Plastic limit load theory is applied to define the relationship between attainable and specified toughness. The conclusions already drawn and the developments which may conceivably be derived from them are discussed on the basis of the aforementioned facts.

Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids

Upper-bound methods are used to obtain close approximations to the constraint factor in a three-dimensional model of the intervoid matrix at incipient plastic limit-load failure. This is the condition where homogeneous deformation can no longer continue throughout a ductile porous solid and all subsequent plastic deformation becomes concentrated in the intervoid matrix over a single sheet of microvoids; thus producing a ductile-fracture surface. The results are obtained for square-prismatic unit cells, which can be assembled to give a continuous intervoid matrix and a simple empirical expression is fitted to the results to give a closed-form expression for the constraint factor, for use in subsequent work on the mechanics of ductile fracture. The upper-bound results for the plastic limit-loads are used to illustrate, on a quantitative basis, the truncation of the Berg-Gurson dilational-plastic yield locus, which was illustrated in previous work only on a qualitative basis.