Continuum damage FEA implementation in HTHA model
Using the power of finite element analysis to accurately capture high-temperature hydrogen attack damage through the use of a custom creep user subroutine.
Dan Drabble, Scott Leakey and Dave Dewees
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It’s approaching three years since we demonstrated a mechanistic model for high-temperature hydrogen attack (HTHA). The model is fundamentally based on void growth and captures both mass-diffusion as well as power-law creep mechanisms which are responsible for the growth and eventual linking of internal cavities.
A six-part series on the mechanics of the model has already been presented. More recent enhancements, including the inclusion of weld residual stresses, nucleation effects, C-0.5Mo material, and validation of through-wall damage predictions over close to 100 case histories has also been developed.
Modelling HTHA requires several inputs, some of which are not always known or easily calculated by hand. Temperature, hydrogen partial pressure, applied (and residual) stress, for example, all affect damage rate and often vary with position and (especially in the case of stress) even time. In all but the simplest component geometries, these spatial and temporal variations become increasingly difficult to predict with closed-form solutions.
Assessment of more complex three-dimensional components lends itself perfectly to finite element analysis (FEA), where the thermal, hydrogen partial pressure, and stress distributions within the component are readily obtained through heat transfer, mass diffusion, and viscoelastic stress analyses, respectively.
Since development on the HTHA modelling began, it has always been the intent to use the power of FEA to accurately capture HTHA damage in conditional assessments of in-service equipment where geometric complexities were previously limited to simplifying 1D assumptions.
For the first time, the Becht HTHA model has been applied within the sequential coupled multi-physics FEA methodology described above, through the use of a custom creep user subroutine developed for the commercial analysis software package, ABAQUS.
The subroutine calculates HTHA damage accumulation throughout a quasi-static stress analysis resulting in a three-dimensional progression of the damage field that may be used to inform risk calculations, remaining life assessments, and inspection recommendations.
The analysis has been conducted as a benchmarking study against a seminal paper1 in the field, in which damage accumulation in a pressure vessel nozzle was simulated and later verified through destructive examination.
The HTHA model uses the CREEP user subroutine available in ABAQUS. State-dependent variables (SDVs) are used to track the HTHA damage fraction element integration points, along with other variables such as methane pressure, diffusion rates, local creep rates, hydrogen partial pressure, and principal stresses.
Hydrogen partial pressure distribution through the component wall is not specified but rather solved for directly through a mass-diffusion analysis and application of the Sievert Law. This is particularly important for configurations that involve regions of complex geometry which promote three-dimensional diffusion effects.
Temperature and partial pressure variation over time can be captured directly, which is a valuable technique for complex time histories. The approach may also be combined with a transient assessment in Becht’s 1D HTHA tool to generate an estimate of the ‘damage equivalent’ steady-state operating conditions which can then be adopted as a single analysis case in the FEA.
At this time, coupling of the damage field with the diffused hydrogen and temperature fields is only possible on a sequential basis, meaning that changes to the underlying pressure distribution as material becomes fully damaged – with higher partial pressures allowed to penetrate through the damaged material – are currently not accounted for without sequential iteration. Exploration into coupling these fields together is planned in the future.
Comparison and verification
In a paper presented at the ASME Pressure Vessels & Piping Conference in 20201, Bagnoli et al., of EMRE described a continuum damage mechanics (CDM) approach to HTHA modelling based on ductility exhaustion. The model included strain effects due to both HTHA as well as traditional creep phenomena.
The strain rate based on HTHA damage was essentially an empirical relationship based on published dilatometry experiments2,3,4,5. As verification, the authors modelled HTHA damage progression in an inlet nozzle of a hydroprocessing unit, which was then destructively examined. Good agreement was found between the modelled and detected HTHA damage.
Some significant differences are observed between the Becht and EMRE models. Although the HTHA creep strains are used in the calculation of the damage measure, the Becht model does not use ductility exhaustion as a means of quantifying failure.
Becht’s failure criterion is based on correlation between macroscopic structural damage and toughness loss in comparison to a grain boundary void growth damage parameter. The way damaged material reacts is also different – in the Becht model, damaged material observes a corresponding reduction to elastic modulus, which is common to the EMRE work, but is significantly less severe by comparison.
Given these differences in approach, it was expected that some differences in results would be observed, but given the good experimental validation, we decided to analyse the exact same nozzle under the same conditions to see how the Becht model would perform.
The nozzle in question is shown in Figure 1 and the geometry was extracted from the original analysis with the generous assistance of EMRE. The 2D axisymmetric model includes the nozzle itself along with a sufficient portion of the vessel head to limit boundary effects. The model also includes a type-347 weld overlay along the internal wetted surface.
A constant isothermal temperature distribution of 400°C (752°F) was assumed in the EMRE model and replicated in our analysis. For establishing the thru-wall hydrogen partial pressure distribution, both approaches included a mass-diffusion analysis. Given that the operating conditions (PH2 = 4.3 MPa) were identical, the geometry was identical, and the material solubility and diffusivity was derived from the same source6, the results were unsurprisingly also identical, as demonstrated in Figure 2.
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