1. CEA/DEN/DM2S/SEMT/LISN
ASME PROJECT TEAM ON GRAPHITE CORE COMPONENTSFAILURE ASSESSMENT VALIDATION EXERCISE : Application of stress-based criteria for brittle fracture in graphite
S. Chapuliot
CEA/DEN/DM2S/SEMT/LISN
Saclay - France

2. Problematic of the design of graphite components
Major difficulty for graphite material is to prevent cracking
This material is brittle at room temperature (i.e. at normal operation)
Large difficulty for safety demonstration :
Our culture and experience is mainly based on ductile materials (metallic)
Brittle fracture is probabilistic :
How evaluate the probability of failure with a good confidence for a very large structure ? What is the acceptable one ?
Two main families of criteria :
Deterministic assessment methodologies, primarily comparing the stress to a strength value
Probabilistic assessment methodologies, mainly based on the Weibull weakest link theory

3. General objectives of stress based criteria
Major difficulty in deterministic approaches is to define a ‘reasonable strength’ (with a good confidence but not so low !)
From our experience, confidence in classical Weibull models is not sufficient to demonstrate safety of components:
Difficulties in the transposition from specimen to specimen and then specimen to structures
Major difficulty due to threshold definition : Pr = 0  s = 0 !
Pr = 0 demonstration is however a major goal for safety demonstration :
Therefore, tentative of application on graphite material of the stress based criteria in development for metals and based on two hypothesis:
1 – There exists a critical stress under which brittle fracture is not possible
2 – In case of stress concentration, when this stress is exceeded, the probability of failure is proportional to the volume concerned

4. First developments performed in 2005 - 2006
Objective to understand the graphite behavior and the influence of specimen geometry on fracture level
New testing on two different loading devices: 3 points (3P) and 4 points (4P) bending on graphite bars
NBG17 (SGL) graphite
Precise measurements to understand the material behavior: precise determination of the load-deflection curve

5. First developments performed in 2005 - 2006
Evidence of a non-linear behavior:
Non-linearity starts for a low level of loading (in comparison to fracture)
Apparent linear limit is higher for 3P bending
No particular correlation between linear limit and elastic fracture stress

6. Analysis of these tests results
This nonlinear behavior is explained by micro-cracking inside the material
More brittle or best orientation for first grains
Increase of this number of micro-cracks with increasing loading
Coalescence and instability at fracture
Proposition of a simple bilinear model to represent this behavior
Damage of the material only under tensile stress

7. Analysis of these tests results
This simple model allows to reproduce the specimen behavior with a good accuracy:
With the same two parameters:
sy = 10MPa – H/E = 0.54
Nonlinear limit obtained is in accordance with the mean value determined on 4P specimen
Consequent reduction of the real stress at fracture:
4P mean stress : 22.4 MPa (28.0 in elastic)
3P mean stress : 23.5 MPa (29.5 in elastic)
The calculation of the real imposed stress is a key issue for the possibility to transpose criteria from specimen to specimen and specimen to structures
3P tests
4P tests

8. Application to the benchmark study
Major difficulty in the benchmark study is the lack of information:
In most cases, only the elastic stress at failure is given (without precision on the model used to determine it)
In some cases, small number of results making it difficult to investigate the probabilistic problem
Sometimes, results seems to be irrelevant (for coarse grain in VP-05 for example)
In our case, no information on the non linear behavior of the material !
Some aspects of the benchmark have however some interest:
It constitutes a first step !
Some geometrical configurations are pertinent : Notch tensile specimen, beams with holes, L-shaped specimen…
Prospective analyses for the V483T material (where a large number of tests exist)

9. Application to the benchmark study
The different cases studied for this material: (V483T graphite)
Four-point bending tests on beams with holes (VP-05)
Rectangular Notched Beam Specimen (VP-02)
Three-point bending tests on small cylindrical specimens (VP-05)

10. Application to the benchmark study
Parametric study for different material behavior:
Arbitrary choice of 4 configurations
Application to the ‘notch tensile’ case
Stress reduction due to plasticity is not so important in this case (small stress redistribution)
Same application to the beam with holes :
In this case with stress singularity, stress concentration varies from 1.61 (elastic case) to 1.4 (H/E = 0.4, Sy = 20 Mpa) (15% of reduction)
For 3P bending on small specimen reduction factor comes to 1.32

11. Synthesis results
Application of this kind of model on the hole experimental data set shows for (H/E = 0.4, Sy = 15):
Reasonable accordance between results, in particular the lowest values (which at not depending on specimen size)
Correct position in comparison to data given for Weibull model (obtained with tensile tests)
Elastic analysis
Bi-linear analysis

12. Conclusions and perspectives
Large difficulties to apply criteria to the selected cases, principally because of the lack of information
Parametric application of the critical stress concept to V483T material
Large number of tests for this configuration
Possibility to compare the different stresses at failure – a reasonable accordance between the different specimen is obtained, but more information are needed
Next steps:
We need to have more accurate and precise experimental data to progress in the criteria development and validation: larger tests series, precise measurements…
From our side two main points to investigate (in a probabilistic frame): transposition from bending to tensile, from smooth specimen to geometrical singularities (notches or cracks), …
We are ready to discuss the pertinence and the results of our new tests series in the frame of the ASME group: the first benchmark step is a good starting point, giving us ideas for testing configuration, interpretations, first selection of criteria…