SUMMARY REPORT ON GRANT GR/K76832

Plastic Strain Estimation in Metals

G. M. Swallowe, Loughborough University, LEl1 3TU

The use of neutrons as a tool in engineering residual strain measurements has been well established in recent years. Strain at an array of points within the material is investigated by scanning the sample using suitable translation stages and a sampling volume defined by input and output slits. The small sampling volumes used and the need to investigate a large number of points within the material in order to determine strain distributions leads to severe restrictions on the time that can be spent investigating any one point. The usual result is that, at reactor sources, frequently only one Bragg reflection peak is investigated. It is usual also to only study peak position shifts and hence deduce the state of elastic strain in the material. Plastic deformation introduces defects into the material and these give rise to microstrains which result in a broadening of the diffraction peak. At higher plastic strains dislocations form cell structures which effectively divide the material into small coherent scattering volumes, these also cause peak broadening. Coherent size broadening is independent of diffraction order but strain broadening is dependent on diffracting angle and hence diffraction order. In principle it is therefore possible to distinguish between broadening contributions due to size and strain. This is carried out by examining a complete diffraction pattern and studying the comparative broadening of different diffraction peaks. However this traditional method is impossible when only one diffraction order is available, as is the usual case in reactor based neutron residual stress studies. The purpose of this grant was to provide funds to carry out experiments and use single peak analysis techniques to see if further analysis of the data already routinely gathered in neutron residual stress experiments could be used to provide estimates of both elastic and plastic strains. Estimates of plastic strain are potentially valuable to the engineer since the variations in plastic strain at points within a sample will be mirrored in variations of yield stress.

Experiments were carried out at the reactor of the Czech Nuclear Physics Institute in Rez (near Prague) since the strain measuring instrument at this reactor has a very small intrinsic peak width and is therefore an ideal instrument on which to study peak widths/shapes as a function of plastic strain. Two types of measurement were carried out on the instrument. In the first high purity annealed samples of iron, copper and nickel with known plastic strains were studied and the single peak method of de Keijser et al. was used to separate size and strain effects. The derived microstrains scaled with the known applied bulk plastic strains and the predicted coherent size behaved in accordance with the observations of dislocation cell structure reported by Gracio et al.

These results demonstrate that careful data gathering and analysis can indeed lead to the elucidation of a great deal of information about the materials microstructure even in single peak measurements. The first series of experiments were carried out using well annealed high purity samples. These are not representative of typical engineering residual stress measurements. Therefore a second set of experiments to provide data more typical of that of routine engineering experiments was carried out in which compressed discs of low carbon steel were studied to produce a calibration curve of Gaussian peak width against plastic strain. This curve was then used to estimate the plastic strain in another compressed steel sample made with the same material but inducing a complex stress state but compressing between unlubricated platens. The range of values of plastic strain obtained at different points within the disc were typical of what would be expected from the complex deformation state from such a sample. The results of this work demonstrate that application of simple techniques of single peak analysis could greatly increase the use that can be made of data gathered in standard neutron residual strain measurement experiments.

SUMMARY REPORT Grant GR/L14220

Investigation of high strain rate induced crystallisation in semi-crystalline polymers.

G. M. Swallowe, Loughborough University.

The purpose of the research undertaken with funding from this grant was to further investigate the previously observed increases in crystallinity of polymers which is associated with the rapid increase in the yield stress when strain rate reaches values in excess of 10² sec^-1. It had been proposed that crystallinity changes may be the cause of the flow stress increase and the main purpose of the research was to investigate this link. It was also hoped to help clear up disputes in the literature arising from some experimental work showing drops or little change in yield stress while the majority of workers reported an increase at high strain rates.

Experiments at strain rates in the range 10^-3 to 10³ sec^-1 on PEEK and Nylatron using both compressive and tensile tests clearly showed a peak in the flow stress at strain rates in the region of 10³ sec^-1. At strain rates of ~ 10⁴ sec^-1 the flow stress had returned to values only slightly larger that those observed at 10² sec^-1. These comprehensive sets of observations explain the variations found in the literature. The rapid increase in flow stress takes place over only 1 decade of strain rate and then falls just as rapidly back to lower values, the peak being at slightly different strain rates for different polymers. Most high strain rate experimental work is carried out only at one or two specific high strain rates and therefore will show an increase, no change or a decrease depending on the precise position of the strain rate used in relation to the position of the peak. The values of crystallinity of samples measured after testing showed a close association with flow stress, high crystallinity being associated with high flow stress. Further experiments on PET and Nylon 11 also showed a large flow stress increase at strain rates ~ 10³ which was also associated with crystallinity increases.

Differential Scanning Calorimetry (DSC) was used to evaluate the kinetics of the cold crystallisation process in the polymers investigated and temperature-time histories of polymer samples during the course of a high rate test were evaluated from the stress-strain curves. This work leads to the conclusion that cold crystallisation could not be the cause of yield stress increases although it could be partly responsible for crystallinity increases during the latter part of a high strain rate test (at strains ~ 100% +). Strain limited measurements in which high rates tests were stopped at a range of strains showed that the degree of crystallinity did not increase substantially until strains in excess of 70% were achieved thus confirming that crystallinity increases cannot be the reason for flow stress increases.

Wide angle x-ray diffraction of tested samples complimented and confirmed the DSC based crystallinity measurements. They lead also to the conclusion that the strain induced crystallisation process is different in tensile and compressive tests since the results contradict those of previous workers who had carried out exclusively tensile tests of the relationship between crystallinity and strain. The x-ray data also indicates that Nylon samples undergo a phase transition from the triclinic to the pseudohexagonal form in the region of flow stress peak.

In conclusion the work has established the generality of the link between crystallinity increases and rapid flow stress increases at high strain rates. It has explained the contradictions in data reported by other workers on the reality of the flow stress increase and it has also eliminated increased crystallinity as the source of the yield stress increase whilst still leaving open the possibility of crystallinity as a contributor to the increased flow stress at large strains.