Mahmoud Mostafavi

3D Studies of Indentation by Combined X-Ray Tomography and Digital Volume Correlation

Hardness testing obtains material properties from small specimens via measurement of load-displacement response to an imposed indentation; it is a surface characterisation technique so, except in optically transparent materials, there is no direct observation of the assumed damage and deformation processes within the material. Three-dimensional digital image correlation (digital volume correlation) is applied to study deformation beneath indentations, mapping the relative displacements between high-resolution synchrotron X-ray computed tomographs (0.9 μm voxel size). Two classes of material are examined: ductile aluminium-silicon carbide composite (Al-SiC) and brittle alumina (Al2O3). The measured displacements for Hertzian indentation in Al-SiC are in good agreement with an elastic-plastic finite element simulation. In alumina, radial cracking is observed beneath a Vickers indentation and the crack opening displacements are measured, in situ under load, for the first time. Potential applications are discussed of this characterization technique, which does not require resolution of microstructural features.

Quantifying yield behaviour in metals by X-ray nanotomography

Nanoindentation of engineering materials is commonly used to study, at small length scales, the continuum mechanical properties of elastic modulus and yield strength. However, it is difficult to measure strain hardening via nanoindentation. Strain hardening, which describes the increase in strength with plastic deformation, affects fracture toughness and ductility, and is an important engineering material property. The problem is that the load-displacement data of a single nanoindentation do not provide a unique solution for the material’s plastic properties, which can be described by its stress-strain behaviour. Three-dimensional mapping of the displacement field beneath the indentation provides additional information that can overcome this difficulty. We have applied digital volume correlation of X-ray nano-tomographs of a nanoindentation to measure the sub-surface displacement field and so obtain the plastic properties of a nano-structured oxide dispersion strengthened steel. This steel has potential applications in advanced nuclear energy systems, and this novel method could characterise samples where proton irradiation of the surface simulates the effects of fast neutron damage, since facilities do not yet exist that can replicate this damage in bulk materials.

2D mapping of plane stress crack-tip fields following an overload

The evolution of crack-tip strain fields in a thin (plane stress) compact tension sample following an overload (OL) event has been studied using two different experimental techniques. Surface behaviour has been characterised by Digital Image Correlation (DIC), while the bulk behaviour has been characterised by means of synchrotron X-ray diffraction (XRD). The combination of both surface and bulk information allowed us to visualise the through-thickness evolution of the strain fields before the OL event, during the overload event, just after OL and at various stages after it. Unlike previous work, complete 2D maps of strains around the crack-tip were acquired at 60m spatial resolution by XRD. The DIC shows less crack opening after overload and the XRD a lower crack-tip peak stress after OL until the crack has grown past the compressive crack-tip residual stress introduced by the overload after which the behaviour returned to that for the baseline fatigue response. While the peak crack-tip stress is supressed by the compressive residual stress, the crack-tip stress field changes over each cycle are nevertheless the same for all Kmax cycles except at OL.

Development of Residual Stresses During Laser Cladding

Laser cladding rail steel with a hard-wearing martensitic stainless-steel coating is a possible technique for improving the track durability of rail networks. However, the cladding process induces significant residual stresses in the clad material, due to the thermal mismatch between the two materials and the shape changes during the martensitic phase transformation. Predictions of the residual stress remain poorly verified as the process is complex and measurements made on final clad parts can be influenced by multiple parameters. A cladded and heat-treated rail section was subject to sequential laser-pulses representative of the actual cladding process. The thermal cycle of these pulses is much simpler than real clads, easing the task of validating the component parts of simulations. Synchrotron X-ray diffraction was used to determine the phase selective residual stresses around the heated region before and after each pulse. In this manner it was possible to determine the change in stress due to a pulse and the degree of relaxation that is possible due to a neighbouring thermal cycle. Introduction A typical piece of rail sees many train wheels passing over it each day. The contact forces involved are high, and involve a mixture of dynamic and static loading, the combination of which can precipitate crack formation and wear towards the surface of the rail. To mitigate against this, it is possible to coat a section of generic rail steel (the substrate material) with a thin layer of a harder, more damage resistant alloy (the clad material) using laser cladding. This involves depositing a powdered form of the clad material onto the surface of the substrate and using a laser to melt it and form a coating. The process involves high, localized thermal gradients occurring over a short time-span and can therefore induce residual stresses in the clad-substrate system. Residual stresses interact with the applied loads to create more complex stress states, the result of which can cause damage at loads that would normally be considered to be within safe limits [1,2] and it is important to be able to understand and predict this interaction. Martensitic stainless steel is a potential clad but stress development during cooling is complicated by the volumetric and shear strains that occur during the martensitic phase transformation. These can be difficult to account for in simulations [3–5], particularly when the transient temperatures are themselves hard to model. The thermal excursion has been simplified by using a single, tightly-controlled, laser pulse and then measured the residual stresses between pulses. This has been performed to provide a simple analogue of the heat input to the material while minimising the practical difficulties of powder deposition in an X-Ray beamline. If later finite element analysis (FEA) can predict the stress state accurately while incorporating effects of phase transformations, it can be extended for the full laser cladding simulations. Synchrotron Xray diffraction using 2D imaging provides excellent spatial resolution, far in excess of lab X-ray and neutron diffraction, and simultaneous measurement of multiple phases. Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 45-50 doi: http://dx.doi.org/10.21741/9781945291890-8 46 Materials and Methods Clad samples were cut from a previously clad rail, 250 mm in length, resulting in 2mm thick slices with the dimensions shown in Figure 1. The clad had been applied by laser cladding in two layers to a depth of 2 mm, before being ground down to provide a smooth surface finish with a clad approximately 1.2 mm thick. The clad consists of a martensitic stainless steel (hereafter referred to as MSS, and whose composition is detailed in Table 1), while the substrate was rail steel grade 260 (also known as UIC 900A) [6]. The use of pre-clad rail ensured the microstructure of the martensite was typical of laser-deposited material. Pre-existing residual stresses were relieved, so far as possible, by tempering the samples at 600°C for two hours. Figure 1. Illustrations of the sample and setup. The orientation of the sample (left) with respect the incoming beam and detector with the diffraction angle 2θ and azimuthal angle φ defined. The sample (right) is cut from a larger rail and was positioned with the laser above it so that the hot zone lies within the clad. The nominal heat affected zone (HAZ) is shown but is only a guide. Table 1 Composition of MSS clad material including main alloying elements Element C Mn Si Cr Ni Mo Fe Wt % 0.04 0.8 0.6 13.0 4.1 0.5 Balance The experiment was performed by positioning a 500 W laser above the specimen and focusing it on the clad surface. The laser produced a pulse of set dimensions of 1.4 mm diameter with a set duration of 0.015 s. This would theoretically generate an axisymmetric molten zone on the upper surface, inducing austenitisation to a greater depth followed by martensite formation during the rapid cool. The width of the hot zone was approximately equal to the thickness of the clad slice and about half the depth of the clad (Figure 1). The temperature of the rear surface (facing beam) was measured using a FLIR T650sc thermal imaging camera operating at 30 Hz. Stresses were measured using synchrotron X-rays on the ID31a beamline at the European Synchrotron Radiation Facility (ESRF). A monochromatic beam of wavelength 0.0173 nm was focussed onto the sample with a spot size of 40 x 15 μm. The interaction volume covered the full thickness of the sample. Due to the wide laser spot size it is assumed the temperature is uniform throughout this volume. The detector was a Pilatus Cadmium-Tellurium (CdTe) 2D detector that allowed for individual photon counting, resulting in patterns with very low noise and high sensitivity to small phase fractions. Tilts were corrected using an image from a Ceria powder sample. Each image was integrated azimuthally into 36 patterns (See Figure 2). It is notable that blank regions between detector sections mean that some reflections are missing or distorted. The Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 45-50 doi: http://dx.doi.org/10.21741/9781945291890-8 47 measurement was from the initial clad and α (i.e. martensite) dominates with only small amounts of retained γ phases. The number of counts away from peaks (i.e. the background) is extremely low and even small peaks are easily resolved and fittable. Peaks were fitted using a pseudovoigt function, which was found to accurately match the peak shape. Fitting has been limited to nonoverlapping peaks i.e. ferritic (martensite): (200), (211), (220) and austenite: (220), (222), (311). Figure 2. A sample image obtained using the Pilatus detector (left) and the patterns derived from the results (right) with the peaks families labelled. The patterns show the sqrt(I) to emphasise smaller peaks. The sample had three pulses applied to it sequentially and separated laterally (centre-tocentre, y-direction) by 1 mm. The purpose of this was to mimic the effect of creating a continuous clad. The residual stress field before and after each pulse was measured over a 4 x 1 mm region, entirely within the clad, with a grid spacing of around 100 μm in the z-direction and 140 μm in the y-direction. The low diffraction angle (<10o) means the scattering vectors for all peaks lie close to the plane of the clad slice. The strain from the peak shift Δq for any (hkl) peak is given by εφ = Δq q0 = p11σ11 + p12σ12 + p22σ22 where q0is the peak position in the absence of a stress and piiare the stress factors. These incorporate both the direction (i.e. azimuthal angle, φ) and the (hkl) dependent diffraction elastic constants (S1, 1/2S2). Ignoring the slight out-of-plane component of the scattering vector, assuming alignment of the lab and sample coordinate systems, and setting φ=0 for the vertical detector element gives pii = � 1 2 S2hi + S1 ii i = j 2. 1 2 S2hihi ii i ≠ j where h = � cosφ sinφ� The diffraction elastic constants were obtained using the Isodec software without texture [7]. For each measurement and each phase there are 3 (hkl) per spectra and 36 spectra at different φ angles. The stress components can be determined by solving the resulting set of linear equations. Residual Stresses 2018 – ECRS-10 Materials Research Forum LLC Materials Research Proceedings 6 (2018) 45-50 doi: http://dx.doi.org/10.21741/9781945291890-8 48 Figure 3 The lattice parameter of the martensite and austenite measured as a function of depth below the clad surface near to the edge of the sample. The clad finishes about 1.2. The low volume fraction of austenite in the substrate (>1.5 mm) makes values beyond this depth unreliable.

1Constraint influence on the micromechanics of the Al2024 fracture behaviour

A clear understanding of the fracture behaviour of materials is of great importance in assessing the safety of cracked components. Despite this fact, there is considerable uncertainty in the effect of plastic constraint in the fracture of metallic materials. It is rare that good fracture predictions can be obtained, particularly in the case of combined in and out of plane constraint. Hence, the purpose of this paper is to explore this combined effect in one of the most frequently used materials in the aerospace industry: Aluminium alloy 2024. To this end, a numerical simulation is performed which includes the interaction between voids which form in the early stages of the loading and a pre-existing crack. It is shown that good predictions can be obtained for different levels of in and out of plane constraint using a local fracture criterion. This is confirmed by comparing the finite element predictions and the results of experimental studies.