Advantages of code_aster for integrity assessments on large-scale structures featuring cracks within a residual stress field

J. Draup (EDF Energy R&D UK Centre)

Background Context

In the UK, the lifetime extension programme for its ageing nuclear infrastructure is necessary to ensure the security of the national energy supply. EDF Energy R&D UK Centre is contributing to this programme through improving of existing engineering methodologies for assessing the fatigue life of welded components, with particular relevance to the AGR pod boiler spine structure (Figure 1). With respect to welded components, this can be done through estimation of the strain energy release rate, G, around the crack. For large structures with residual stress fields, assessments with existing methodologies are complicated as they push the limit of validity of the fundamental theory, which is a problem for the wider engineering community.

Figure 1

Numerical Study

In an attempt to better understand the in-service boiler spine fracture behaviour, EDF Energy participated in a European research project (STYLE). A large scale (7m length) girth welded steel pipe structure was manufactured, whose features include a repair weld (Figure 2) and a machined crack (Figure 3). This structure was loaded in four-point bending and the experimental data was used to validate numerical simulations to assess G around the crack.

Figure 2
Figure 3

code_aster was used to simulate the experiment and benchmarked against commercial tools using the following setup :

  • Mesh The pipe structure containing a structural girth weld, a repair weld and a circumferential crack was meshed using quadratic 20-node hexahedron elements ; following a mesh sensitivity study, the elements were refined in the regions of the welds and had a size of 35μm at the crack tip (Figures 4 and 5). The crack was modelled as a sharp crack for elasticity and as a notch for plasticity.
Figure 4
Figure 5
  • Boundary Conditions The pipe was modelled in half symmetry about the long axis with fixed boundary conditions at the clamped locations. A prescribed ramped displacement was applied to the nodes to simulate loading.
  • Material Properties Elastic parameters, Young’s modulus and Poisson’s ratio are defined using DEFI_MATERIAU and isotropic plastic hardening defined as a function of plastic strain.
  • Residual Stress A residual stress field measured using incremental deep hole drilling was projected to the mesh structure using PROJ_CHAMP. The input stress distribution was adjusted iteratively until the equilibrium stress distribution matched the experimental measurements, verified using STAT_NON_LINE to ensure equilibrium.
  • Solver The solver STAT_NON_LINE was used to compute the global stress and strain within the structure using RELATION=’ELAS’ for elasticity and RELATION=’VMIS_ISOT_TRAC’ for small deformations in plasticity.
  • Model Verification The predicted load and crack mouth opening displacement were validated against the experimental measurements. These values were found to be in good agreement, hence, the predicted conditions in the pipe were assumed to be representative of the problem.
  • Post-processing The energy release rate was computed ahead of the crack tip using the CALC_G operator with option CALC_G for elasticity and option CALC_GTP for plasticity. A sensitivity study was performed and the optimal smoothing function for this problem was found to be the default LEGENDRE (degree 5 polynomial).
  • Benchmarking The prediction of energy release rate calculated in code_aster for the case of elasticity and plasticity were compared to the J-integral values calculated using ABAQUS. The comparisons were repeated for the case of primary load both with and without residual stresses.


The results (Figure 6) show that code_aster can be used to assess the stability of defects in large scale complex geometries and loading conditions. Indeed, the predictions are in good agreement with known analytical solutions, particularly when assuming the framework of elasticity. The predictions are also seen to be comparable to predictions using commercial finite element software. However, the effect of residual stresses are to induce some uncertainty in the computations. In the case of plasticity, the predictions in code_aster are still comparable with commercial software but there is more uncertainty in predictions, which is exacerbated by the presence of residual stresses. Examination of the fundamental theory of G indicates that the formulation within code_aster is well suited for modification to incorporate residual stresses. Moreover, the present study has led to a follow-on project to develop an operator featuring these modifications.

Figure 6