J J Webster

Elasto-plastic and creep behaviour of axially loaded, shouldered tubes

Abstract This paper compares the finite element predictions of elasto-plastic and creep behaviour with experimental data for axially loaded, shouldered tube models. Four shouldered tube models were made of a lead alloy and tested at 61°C, using strain gauges to measure the elasto-plastic and creep strains in the plain tube and fillet regions of the models. Instantaneous stress-strain and creep data were obtained from strain-gauged, uniaxial tensile specimens. The finite element solutions are based on the incremental Prandtl-Reuss equations. The elasto-plastic iterative solutions use a ‘negative gradient’ from the calculated point to the equivalent stress-equivalent strain curve to get the next estimate of the plastic strain increment. A time incremental method is used to obtain the creep solutions. Tests with the mean tube stress below, at and above the yield stress showed very good agreement between prediction and measurement of initial strains in the fillets. Differences between predictions and measurements of creep strains are attributable to cast-to-cast variations.

Stationary creep prediction from model tests using reference stresses

Abstract The theoretical basis of the experimental determination of reference stresses from model tests is established for one-dimensional and complex stress systems. A graphical method of obtaining the experimental reference stress is presented and used to determine reference stresses for the strain in beams in pure bending and the tip deflection of cantilever beams from room-temperature tests of lead-antimony-arsenic models. The results are compared with theoretical values. It is shown how prototype deformation can be predicted from a test of a model of the component, model material creep data and the strain of a uniaxial prototype material specimen tested at the reference stress. Errors in the prediction of prototype deformations are considered.

Experimental investigation of creep crack growth in a lead alloy

Abstract The results of 27 creep crack growth tests performed on four different specimen types (CT, 3PB, ECP, and CCP) are reported. A lead alloy, previously used as a creep ‘model material’ was used. Of the parameters commonly used to correlate creep crack growth data, the C∗ parameter was found to be the best for the lead alloy data. It is concluded that the lead alloy may be useful for ‘modelling’ the creep crack growth rates in components made of other materials with similar creep ductilities.

Thermal ratchetting of axially loaded tubes operating in the creep range

Abstract Finite element predictions of ratchetting and creep behaviour are compared with experimental data for axially loaded tubes subjected to axisymmetric cyclic temperature variations. Eleven tubes made of a lead alloy model material which creeps at ambient temperature were tested. Strain gauges were used to measure the ratchet and creep strains. In the finite element calculations it was assumed that no plasticity-creep interactions occur. Reasonably good predictions of ratchet strains were obtained, particularly in the range of most practical interest. Some of the discrepancies between ratchet and creep results can be accounted for by considering the results from a small number of uniaxial plasticity-creep interaction tests.

A rig for creep and thermal ratchet testing of lead alloy models

Abstract The development and calibration of a rig and an axisymmetric lead alloy component for isothermal creep, non-isothermal creep, and thermal ratchetting testing is described. Steady and variable, axial mechanical loads are applied by a dead weight and lever system. Thermal loads are applied by controlled variations of the temperature of water flowing through the bore and along the outside of the component. Strains and temperature are measured with electrical resistance strain gauges and thermocouples, respectively.

Comparison of finite element predictions of creep crack growth with experimental data

Abstract Five, pre-fatigued, compact tension specimens made from a model material, which exhibits similar macroscopic behaviour to some high temperature materials, have been subjected to steady loads. The results of these tests indicate that the ‘crack tip opening displacement’ governs the intiation of crack propagation. The subsequent creep crack growth rates are accurately predicted by the C∗ parameter. ‘Moving crack’ finite element calculations have shown that accurate predictions of creep crack growth rates are possible even with relatively coarse meshes. However, the predictions are very sensitive to both the critical crack tip opening displacement used for initiation and to the magnitude of the load. Also, although the C∗ parameter is strictly only applicable to stationary state stresses at stationary cracks, predictions of crack growth were found to be accurate when using C∗ under non-stationary stress and moving crack situations.

Elastic-plastic-creep behaviour of a compact-tension specimen

Abstract Elastic, elastic-plastic, elastic-creep, and elastic-plastic-creep finite element calculations have been performed for a compact-tension specimen under plane-stress conditions. The von-Mises effective stress criterion and the Prandtl-Reuss flow rule were assumed for both the plastic and creep deformations. A 4-line stress-strain relationship with a UTS value 1.48 times greater than the yield stress was used. A strain hardening, Norton-Bailey creep law was assumed. A fairly course mesh of 8 noded, isoparametric elements was found to be adequate for determining reference stress, crack tip opening displacement, J-contour integral, and C∗-contour integral values. The UTS zone, rather than the yield zone, was found to have a significant effect on the C∗-contour integrals and CTOD rates. An approximate method of determining C∗ values was found to give reasonable results, particularly for low load cases, i.e., when the UTS zones are small. Hence, provided care is taken not to perform tests at very high loads, accurate C∗ values can be determined from experimentally determined pin displacement rates.

Predicting the thermal ratchetting and creep behaviour of a component with a stress concentration

Abstract Finite element and ‘upper bound’ predictions of ratchetting and creep are compared with experimental data from two axially loaded shouldered tubes subjected to axisymmetric cyclic temperature variations. The shouldered tubes were machined from chill-cast bars of a lead alloy material. Electrical resistance strain gauges were used to measure the ratchet and creep strain. The results show that ratchet strains can accumulate significantly faster in stress concentration regions when compared with plain tube regions. Acceptable predictions were obtained for the ratchet strains. The discrepancies between the predicted and measured dwell period strains were due to neglecting the material plasticity-creep interactions. Some simple methods for estimating the strains are suggested.

Experimental theramal ratchetting data for a component with a stres concentration

Abstract The result from eleven tests of lead alloy model shouldered tubes, subjected to constant axial mechanical loads and cyclic, axisymmetric thermal shocks are described. Dwell periods between 0.5 h and 24 h allowed creep to occur between the thermal shocks. Electrical resistance strain gauges were used to measure ratchet and creep strains. At low mean axial stresses (< 0.94σy), it was found that the ratchet strains increased with load and dwell period. It was also found that the ratchet strains in the fillet region were significantly larger than those in the shank and are induced at lower mechanical loads than those in the shank. For higher stresses, the ratchet strains were found to be relatively insensitive to both load and dwell period. Also, the ratchet strains in the fillet and shank were found to be of the same magnitude.

An assessment of simple material behaviour models for predicting the mechanical ratchetting of a stepped beam

Abstract Finite element programs are often used, without experimental verification, to predict the elastic-plastic behaviour of components, but most programs only contain simple material behaviour models. In this paper, the results from three lead alloy stepped beam components, subjected to steady axial load and cyclic bending, are compared with predictions based on elastic-perfectly plastic, isotropic hardening, and kinematic hardening material behaviour models. These comparsions show that under severe load conditions, in which cyclic plasticity occurs, none of these simple models provides good predictions for the ratchetting behaviour of the beams. This is because the models do not accurately describe the cyclic elastic-plastic behaviour of the lead alloy which is similar to that of many engineering materials. It is concluded that the simple elastic-plastic material behaviour models included in most finite element packages will have to be extended to include more accurate models of material cyclic behaviour if they are to provide accurate predictions for component behaviour.