AN ANALYSIS OF IRRADIATION AN ANALYSIS OF IRRADIATION CREEP IN NUCLEAR GRAPHITE CREEP IN NUCLEAR GRAPHITE G. B. Neighbour 1 and P. J. Hacker 2 1. Department of Engineering, University of Hull, UK. 2. British Energy Generation Ltd, Barnwood, Gloucester, UK.
INTRODUCTION Irradiation • Nuclear Graphite Irradiation Creep Dimensional Change – High creep ductility under load with neutron fluence – Additional to dimensional changes Elastic Properties Thermal Properties – Important property - compensates other irradiation effects Mechanical Properties, e.g . strength – Complex and often neglected Department of Department of Engineering Engineering
OBJECTIVES • Review the UK Creep Law – High neutron fluence, applied stress and radiolytic oxidation • Better understanding of creep data – Historically, data obtained under very different conditions – Improved predictions of irradiation creep, particularly for simultaneous neutron fluence and radiolytic oxidation • The output! – Alternative analysis of irradiation creep applicable to most situations, including HTR systems, using AGR moderator graphite as an example. Department of Department of Engineering Engineering
EARLY CREEP EXPERIMENTS (1) • First “real” irradiation creep experiments undertaken in 1963 by C. R. Kennedy – cantilever beams under constant load – transient creep and steady-state creep detected • Three main experimental methods • “Real” creep experiment where samples are subjected to a constant stress under irradiation with continuous strain measurement – High complexity and cost – Large number of specimens impractical Department of Department of Engineering Engineering
EARLY CREEP EXPERIMENTS (2) • “Restrained Shrinkage” experiments – Dimensional change rates differ markedly between graphites – E.G. graphite tensile specimen restrained by split sleeves made of a graphite that exhibits a smaller shrinkage rate – Induced creep strain calculated knowing the various differences in shrinkage rates of the various components (stress deduced from established creep laws) – Disadvantage - no measurements during the irradiation. – Advantage - many results (less accurate) Department of Department of Engineering Engineering
EARLY CREEP EXPERIMENTS (3) • Combination of stress relaxation and restrained shrinkage experiment – Large block of graphite irradiated under a temperature and neutron flux density gradient – Strips cut from block and their curvatures measured – Results only meaningful if a stress calculation can be performed (used in Dragon experiments) Department of Department of Engineering Engineering
A SUITE OF TECHNIQUES? • Complementary • Real irradiation experiments derive the creep laws • Restrained shrinkage experiments provide information on different material, temperatures and flux gradients • Larger block experiments provides a test of the data and stress models under more realistic conditions Department of Department of Engineering Engineering
IRRADIATION CREEP DATA • All studies support the view that any nuclear graphite irradiated under constant stress, the tensile and compressive creep strains, plotted as creep strain/initial elastic strain ( ε c E 0 / σ ) are directly proportional to the fluence and independent of temperature in the range 140-650 ° C • At >600 °C, creep strain/initial elastic strain is the same for all graphites over a wide range of stresses, but the gradient of the line is proportional to irradiation temperature. Only at very high stresses (~30 MN/m 2 ) is there a deviation from linearity Department of Department of Engineering Engineering
UK Creep Law Creep strain/initial elastic strain (E 0 ε c / σ ) Fast neutron fluence ( γ ) Department of Department of Engineering Engineering
IRRADIATION CREEP OF GRAPHITE UK Creep Law σ σ 20 20 0 . 23 10 = E [ 1 exp( 4 10 )] − − ε = × γ + ε ε − − × γ C CT CT E 0 0 • At fluence > 60 x 10 20 n cm -2 EDN – Steady state creep rate deviates from linearity (decreases with increasing fluence – Often attributed to structural changes, i.e. E 0 replaced by SE 0 (ignoring any weight loss term) γ 1 d k ' ε = σ γ II � S Department of Department of 0 Engineering Engineering
RECENT DEVELOPMENTS • UK Creep Model – Assumes that the properties measured on a control sample exposed unstressed apply to the stressed sample. – CTE is known to change with irradiation creep and so other properties may also be affected. Department of Department of Engineering Engineering
3 2.5 Changes in CTE (20-120 degC) 2 α x ) (x 10 -6 K -1 ) 1.5 1 0.5 α ' x - α α α 0 ( α α α -5 -4 -3 -2 -1 0 1 -0.5 -1 -1.5 Apparent Irradiation Creep Strain (%) Department of Department of Engineering Engineering Data taken from Kelly and Brocklehurst, 1994
5 Changes in CTE (20-120 degC) 4 y = -0.6101x R 2 = 0.7116 α x )(x 10 -6 K -1 ) 3 2 1 α ' x - α α α 0 ( α α α -6 -5 -4 -3 -2 -1 0 1 2 -1 -2 Apparent Irradiation Creep Strain (%) AGR Graphite Price Mobasheran Linear (AGR Graphite) Department of Department of Engineering Engineering Data points taken from Kelly and Brocklehurst, 1994
RECAP • UK Creep Law represents data well up to ~60 x 10 20 n.cm -2 EDN • At higher fluence, the UK creep law progressively underestimates the measured creep strain, ε c ’, i.e. mismatch between the true creep strain ε c and the measured creep strain ε c ’ • Structure term added to account for any discrepancy between the measured and predicted creep strain, however this term has limited success, no real physical meaning and cannot be measured directly Department of Department of Engineering Engineering
A NEW ANALYSIS • Without reference to a structure term • Generate a relationship between the apparent creep strain ε c ’ and fluence γ • Evidence to suggest that CTE variance with irradiation creep is LINEAR • For UK AGR graphite ( α x '- α x ) = -0.6106 ε c ' Department of Department of Engineering Engineering
IRRADIATION CREEP OF GRAPHITE γ 1 dX α − α � � � � 1 e e x x T d = − ⋅ γ � � � � � c c d � � � � α − α γ c a 0 � � � � dX T - crystal shape change parameter (HAPG data) e c is true creep strain e c ’ is apparent creep strain 1 α − α � � [ ] 2 6 2 C x x 0 . 1864 10 2 . 7803 10 − − = × γ + × γ � � ε � � α − α c a � � ( ) ' ' 0 . 6106 α − α = − ε x x c ( 1 exp ( 4 ) ) 0 . 23 − − γ + γ ' ( ) esu ε = ( ( ) ) c Department of Department of 2 6 2 1 0 . 4043 10 6 . 0316 10 − − + × γ + × γ Engineering Engineering
50.00 45.00 Irradiation Creep Strain (esu) 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 0 50 100 150 200 Neutron Fluence (x10 20 n cm -2 EDN) UK Creep Law Expected Apparent Creep Strain Department of Department of Engineering Engineering
STRESS • Deviation from linear creep rate does not become apparent until samples experience stress above ~30MN/m2 Effect of applied stress on compressive creep strain of different graphites after ~10 21 n/cm 2 (EDN) (taken from Kelly and Brocklehurst, 1977). Department of Department of Engineering Engineering
WEIGHT LOSS(1) • Young’s modulus is known to decrease exponentially with thermal or radiolytic oxidation to high levels of weight loss (E ox = E 0 exp(-bx) where b=3.4). • It seems intuitive that irradiation creep can continue to be predicted by correcting E c by E ox . At present, there is no evidence to suggest that these relationships will not continue to hold at high weight losses. • Effects of simultaneous oxidation and irradiation appear not to have been addressed either experimentally or theoretically. Department of Department of Engineering Engineering
WEIGHT LOSS(2) γ σ 0 . 23 d ' ε = γ � II E C 0 If the relationship to include simultaneous weight loss is considered it can be shown that E exp( ab ) 1 ε γ − � � 0 II 0 . 23 = ab � � σ � � Department of Department of Engineering Engineering
80 Irradiation (True) Creep (esu) 70 60 50 40 30 20 10 0 0 50 100 150 200 Neutron Fluence (x10 20 n cm -2 EDN) Simultaneous Ox and Irr Irradiation only Pre-oxidation (15%) Simultaneous Ox and Irr (x1.5) Department of Department of Engineering Engineering
80 Irradiation (Apparent) Creep 70 60 50 (esu) 40 30 20 10 0 0 50 100 150 200 Neutron Fluence (x10 20 n cm -2 EDN) Simultaneous Ox and Irr Irradiation only Pre-oxidation (15%) Simultaneous Ox and Irr (x1.5) Department of Department of Engineering Engineering
SUMMARY AND CONCLUSIONS (1) • The UK Creep Law is semi-empirical and indicates Young’s modulus is the controlling parameter. • Steady-state creep progressively deviates from linearity and an apparent reduction in creep strain is observed. • The “Structure” term does not this explain this phenomenon satisfactorily. • The effects of radiolytic oxidation on creep strain is predictable, BUT simultaneous oxidation and irradiation does not appear to have been addressed. Department of Department of Engineering Engineering
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