Elsevier

Carbon

Volume 59, August 2013, Pages 325-336
Carbon

Flexural strength and defect behaviour of polygranular graphite under different states of stress

https://doi.org/10.1016/j.carbon.2013.03.025Get rights and content

Abstract

The effect of stress state on the fracture behaviour of Gilsocarbon, an isotropic nuclear grade polygranular graphite, has been studied by employing four-point bend and ring-on-ring loading configurations to achieve uniaxial and equi-biaxial flexural stress states, respectively. Optical images of the specimens’ tensile surface were analysed by digital image correlation to measure the full-field displacements: these were used to identify the fracture initiation sites, analyse crack geometry (surface length and opening displacements) and also to calculate the J-integral strain energy release rate associated with surface crack propagation. Surface cracks that did not propagate to failure were identified and subsequently examined by X-ray computed tomography combined with digital volume correlation: measurements were made of their three-dimensional displacement fields when subjected to an opening tensile stress using a modified (flat) Brazilian Disk test geometry. The crack opening behaviour is explained by an effect of stress state on the development of the crack tip fracture process zone, which is in agreement with the effect of stress state on the measured strain energy release rates of sub-critical crack propagation. Both are attributed to the plastic constraint effect, which varies with the stress state in materials that can undergo inelastic deformation.

Introduction

Polygranular graphite is a quasi-brittle material. Its unique physical properties lead to use in various structural applications, including neutron moderation in fission reactors such as the UK’s gas cooled reactors [1], muon generating targets for high intensity accelerated proton beams [2] and also thermal-shock resistant moulds for continuous casting systems [3]. In such applications, an understanding of the conditions for component failure is needed for design and safe operation. There have been many studies of graphite’s fracture properties under uniaxial loading (e.g. [4], [5]), but fewer studies on the effects of stress state (e.g. [6], [7]), despite the fact that many applications impose multi-axial stresses. For example, in graphite components in nuclear reactors the multi-axial stress-state can be either internal stresses due to irradiation-induced dimensional change or external loads from component interactions [8]; stress concentrators such as keyways that act as notches further affect the multiaxiality of stresses [9], [10]). The effect of multi-axial stress can be significant: for graphite with isotropic properties, equi-biaxial loading causes an approximate 20% reduction in flexural strength compared to uniaxial loading [11]. The mechanism for this has not been investigated deeply, in contrast to the well-documented stress biaxiality effect on the fracture of ductile metals that is explained by plastic constraint (e.g. [12]).

The constraint effect on fracture of ductile materials is a significant element in structural integrity assessments, since accounting for constraint may better define the margin between conservative and realistic behaviour [13]. The plastic constraint effect may be explained briefly as follows: fracture toughness can be expressed in terms of a critical strain energy release rate, which is generally considered a material parameter. However, the measured fracture toughness may be geometry dependent in materials that are capable of dissipating energy through permanent (i.e. plastic or more generally inelastic) deformation. Plastic constraint, defined as the resistance of the specimen against inelastic deformation [14], is employed to explain this phenomenon. The energy release rate required to propagate fracture includes energy dissipated through the inelastic deformation processes that accompany the creation of new surfaces. For metallic materials, the inelastic processes include deformation to nucleate voids for ductile rupture or to debond particles (such as carbides in steel) from the matrix for brittle cleavage. For quasi-brittle materials, of which graphite, concrete, ceramic matrix composites and artificial bone replacements are examples, the equivalent inelastic energy can be due to distributed micro-cracking [15]. These energy dissipation processes occur within the enclave of an inelastic crack tip zone: in metals this is commonly described as the crack tip plastic zone. This inelastic zone mediates between the crack tip and the surrounding elastic strain field, and may thereby affect the condition for fracture propagation in a test specimen or component. A root cause of geometry dependent fracture toughness is neglect of the effect of constraint on inelastic deformation within the calculation of the strain energy release rate for crack propagation in test specimens and components. In ductile metals, a relation between the development of the inelastic zone (i.e. crack tip plastic zone) and constraint may be established [12], and this has been shown to account for the effect of constraint on measured fracture toughness [16]. For materials that are in a condition of small scale yielding, the most commonly used parameter to quantify in-plane constraint is the non-singular term of the asymptotic stress distribution; the T-stress [17].

Fracture assessment codes for metallic materials (such as R6 [13]) therefore include correction factors, applied to linear elastic calculations, to account for plastic constraint in structural components. This allows data from high constraint test specimens to be applied to lower constraint components: high constraint reduces the measured toughness in ductile metals, so this approach improves confidence in the safety margin of the assessment. The potential effect of plastic constraint is not considered in structural integrity codes for quasi-brittle materials such as graphite [18]; physically-based models for the effects of constraint on inelastic deformation are required for this to be achieved. In addition to improving confidence in the structural integrity assessment of graphite, the development of an approach that addresses constraint effects will benefit the application of other quasi-brittle materials in engineering structures.

The focus of this paper is therefore on an isotropic, nuclear-grade, polygranular graphite: Gilsocarbon; in addition to being technologically important, it is a good model material for quasi-brittle behaviour. This grade of graphite is primarily used as reflector and moderator in UK’s Advanced Gas Reactors (AGR). Its porous structure comprises approximately spherical filler particles order of about 0.5 mm in size [19] within a matrix of graphitised pitch and finer filler particles.

This paper reports an experimental study of strength and defects in Gilsocarbon under uniaxial (four-point bend) and equi-biaxial (ring-on-ring) loading. The work contributes to a research programme that aims to understand the effects of component geometries such as stress concentrating notches on their strength: this requires a knowledge of defect behaviour under different states of stress that may be described in terms of constraint. In this work, digital image correlation (DIC) of optical images has been used to measure the full-field displacements on the specimen tensile surface up to the point of fracture, and thereby the surface lengths and opening displacements of the identified crack nuclei. A method to obtain the strain energy release rate from the experimentally measured displacement fields [20] has been applied to calculate the J-integral associated with the surface propagation of the crack nuclei. Three-dimensional examination of non-critical cracks that did not propagate to failure has been performed using in situ X-ray computed tomography (XCT) and the digital volume correlation (DVC) to investigate the opening of such non-critical cracks under load and hence their dimensions. The behaviours of crack nuclei in a quasi-brittle material were thereby investigated on their first and subsequent exposure to stresses that were close to fracture. The objectives were to determine whether the stress state affected the development of crack tip deformation and the corresponding energy required for crack propagation, and to consider whether this might be understood in terms of constraint in a manner analogous to ductile materials.

Section snippets

In-situ 2D optical observation

To obtain statistically significant data, 62 four-point bend and 26 ring-on-ring specimens were tested. The surfaces of the specimens were monitored during loading; the majority of tests (35 uniaxial and 17 biaxial specimens) used a 4 MPixel 14 bit camera recording images at 1 frame per second. The remainder (21 uniaxial and 9 biaxial samples) were observed by a high-speed Photoron Fastcam 1024 LRT DVR system (1 MPixel, 10 bit camera) recording images at 125–1000 frames per second (fps). The

In-situ computed X-ray tomography observation

In some test specimens several sub-critical crack nuclei were observed prior to failure (e.g. crack 3 in Fig. 3a and crack 2 in Fig. 3b), of which only one subsequently propagated as the critical crack. Preliminary examinations showed that non-critical nuclei could not be observed reliably by post-test microscopy due to the complex microstructure of nuclear graphite and the narrow crack openings. To characterise the crack dimensions, the three-dimensional displacements in response to applied

Discussion

The flexural strength of Gilsocarbon nuclear-grade isotropic polygranular graphite has been measured under uniaxial (four-point bend) and equi-biaxial (ring-on-ring) loading. The average bending stress for unstable fracture is reduced by approximately 18% under equi-biaxial stress compared to uniaxial stress. This is consistent with previous observations in isotropic polygranular graphite [11]. The measured strengths fit a Weibull distribution for both conditions, with no significant effect of

Conclusions

  • The flexural strength in slender specimens of Gilsocarbon polygranular graphite decreases by 17.8% under equi-biaxial loading compared to the uniaxial loading.

  • Digital image correlation, applied to optical observations of the tensile surface, shows that unstable fracture is preceded by the sub-critical propagation of surface cracks: their opening compliance (the ratio of crack mouth opening displacement to stress) was measured to be greatest under equi-biaxial loading. Digital volume correlation

Acknowledgement

T.J. Marrow and M. Mostafavi acknowledge the support of the Oxford Martin School and EDF Energy (GRA/GNSR/6041). The opinions expressed are those of the authors and not necessarily those of EDF Energy. We acknowledge funding from the EPSRC for the X-ray imaging facility under EP/F007906/1 and EP/F028431/1. M. Mostafavi also acknowledges the support of Linacre College, Oxford, through a Junior Research Fellowship. H. Cetinel thanks Higher Education Council of Turkey (YÖK) for the financial

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