Elastoplastic deformation of ferritic steel and cementite studied by neutron diffraction and self-consistent modelling

Abstract

A tensile specimen was machined from heat treated ferritic steel, with a small volume fraction of carbon in the form of cementite. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction, to macroscopic plastic strains of around 3%. The experimental results are compared with predictions from a self-consistent Hill–Hutchinson model modified to take into account the presence of the second phase. Good agreement was obtained between model and experimental data. The interpretation of residual stress measurements, for both single peak and Rietveld measurements is considered in light of these results.

Introduction

Internal and residual stresses in materials have a considerable effect on material properties, including fatigue resistance, fracture toughness and strength. These stresses can vary greatly as a function of position within engineering components, due to manufacturing processes during the production route. Their measurement and interpretation is thus of considerable interest to the engineer. This paper will address a number of issues relating to mechanisms of materials deformation, and to the practical measurement of stress in components by diffraction from the Fe/Fe₃C system. The paper also describes the new in situ loading facilities on the ENGIN diffractometer at ISIS.

The strength of a two phase material depends both on the level of in-situ matrix strengthening (for example due to an increased dislocation density from the presence of the reinforcing phase), as well as on the efficiency of load transfer between the matrix and reinforcing phase. If a high proportion of the applied load is carried by the reinforcing phase, the composite is efficient. The level of load sharing is dependent on reinforcement volume fraction, shape and orientation and on the relative elastic properties of the phases [1]. The partitioning ratio of an applied load between matrix and reinforcement will remain constant with increasing applied load provided that both phases remain elastic. However, once the stress levels in one of the phases are high enough for relaxation or inelastic deformation processes to occur, the load partitioning ratio changes.

One experimental technique ideal both for profiling macro-strain variations as a function of position, and for measuring phase specific load transfer, is neutron diffraction. Relying on the same physics describing the analagous measurement of stress using X-ray diffraction [2], neutrons have one principal benefit compared to traditional X-rays for the engineer or materials scientist. Since neutrons interact primarily with the nucleus, rather than the electron cloud as X-rays do, the penetration depth of neutrons is very large compared to X-rays. For example, the penetration depth (1/e) for steel is ∼1 cm for thermal neutrons, but less than 10 μm for X-rays of comparable wavelength [3]. This results in neutrons being a probe suitable for bulk average measurements of material properties. For many practical applications, it is bulk averaged properties that the engineer or material scientist is primarily interested in.

Diffraction measurement of strain involves the monitoring of changes in separation of one or more suitably orientated crystallographic lattice planes. It is thus a direct measure of the elastic strain in the material. In a polycrystal a diffraction peak represents the average lattice separation over all the grains in the irradiated volume which are suitably oriented to diffract. In the presence of an applied stress, the responses of individual diffraction peaks may differ in magnitude with respect to each other, and to the continuum macrostrain (e.g. [4]). The importance of understanding the mechanisms of interaction between differently orientated crystallites is highlighted when one considers that not only do individual grains exhibit elastic stiffness anisotropy, but also that plastic relaxation occurs preferentially on certain slip systems (plastic anisotropy). Despite increasingly sophisticated models (e.g. [5]) the current state of the art is far from quantitatively predicting the evolution of hkl dependent strains or the implications of their spread on failure. The use of self-consistent models does however give a direct insight into plasticity in polycrystals; the onset of deformation in differently oriented crystallites and the importance of hardening mechanisms. Systems where an elastic phase interacts with a ductile phase have been treated extensively using continuum mechanics arguments [1], but are relatively unexplored using crystal plasticity arguments. This paper applies a self consistent model to the deformation of bcc iron with a small volume fraction of cementite (Fe₃C) present, and compares the results with lattice reflection data from neutron diffraction experiments. Wilson and Konnan [6] first measured lattice strains in the phases of a spheroidised high carbon steel using X-ray diffraction in 1964; such results however suffer from near surface effects due to the low penetration depth of traditional X-rays. More recently, residual stresses have been studied in both phases of a similar material in studies on fatigue crack propagation [7]. Oliver et al. [8] have reported interphase and intergranular measurements on a high carbon steel (19% cementite); these measurements were complicated by the presence of significant Lüders straining which caused very rapid transfer of load from the ferrite to cementite phases.

In the interpretation of many strain mapping measurements the assumption is made that macrostrain effects outweigh microstrain effects in importance, at least as far the stress measurement engineer is concerned, and despite the atypical responses for specific reflections associated with intergranular effects. The practical outcome of this assumption is that a suitable (individual) plane for macrostrain profiling is defined as one that is little affected by intergranular strains. More specifically it is one whose response is linear with applied or with residual stress. Indeed, it is on the selection of a suitable reflection that the efficiency of measurements at constant wavelength sources relies since it is often impractical to measure multiple reflections. At pulsed neutron or energy dispersive X-ray sources however, a diffraction pattern is recorded over a range of lattice spacings (or wavelengths) and thus many diffraction peaks are recorded (in the same sample direction). This has been used to provide information about intergranular interactions, which are fundamental to an understanding of polycrystalline plasticity [9], [10], [11], [12]. However we can also analyse the data from the viewpoint of identifying a suitable parameter for macrostrain profiling. In previous papers [13], [14] we analysed diffraction data obtained during a uniaxial loading test on face centred cubic steel and hexagonal close packed beryllium by Rietveld refinement. In those cases a “macrostrain” response was obtained from the lattice parameters which was comparable in linearity with the “best” single peak fits, with stiffness very close to the macroscopic modulus. The result was obtained despite the imperfection of the Rietveld fit, which assumed an “undeformed” crystal structure. This paper extends the discussion to a body centred cubic crystal structure.