Review of current status of the LICON methodology

Abstract

Since the LICON methodology was first developed in the late 1990s to predict the long term creep rupture behaviour of new generation martensitic 9% Cr steels from the results of relatively short duration multi-axial specimen tests, there have been a number of necessary refinements to this originally simple concept. These are reviewed.

Keywords

LICON multi-axial creep damage enhancement

Nomenclature

a, a_o

crack length; initial crack size

Δ a_{c}

creep crack extension

A, A′, A″, A_CT

constants in $t (\bar{σ})$ formulation; A in Regime-1; A in Regime-2; A for CT testpiece

CCI

creep crack incubation

compact tension (testpiece)

DCPD

direct current potential drop (crack monitoring voltage)

DMW

dissimilar metal weld

FE(A)

finite element (analysis)

fusion line

H, H_z

multi-axiality factor ( $σ_{1} / {\bar{σ}}_{VM}$ ); H for a given multi-axial geometry/feature defined by z (e.g. CT)

HAZ, ICHAZ

heat affected zone; inter-critical heat affected zone

HCS

high creep strength

LPD

load point displacement (in CCI test)

stress exponent in uniaxial creep strain rate model

parent material

Rp_0.01, Rp_0.2

limit of proportionality; 0.2% proof strength

t, t_r

time; time to rupture in uniaxial testpiece

t_i,x, t_i,0.5

time to initiate a crack in a multi-axial testpiece (with crack initiation criterion, $x = Δ a_{c} = 0.5 mm$ )

t _SS

time to steady state creep conditions

temperature

von Mises (stress)

designation for multi-axial geometry/feature, e.g. $z = CT$

strain

{\dot{ε}}_{SS}

steady-state creep strain rate

γ, γ′, γ″

multi-axial rupture exponent; γ in Regime-1; γ in Regime-2

ν, ν′, ν″

stress exponent in time to rupture model; ν in Regime-1; ν in Regime-2

σ, σ_o

stress, initial stress (in constant load uniaxial test; all parent material)

σ ₁

maximum principal stress

\bar{σ}

{\bar{σ}}_{z}

effective stress; representative effective stress associated with multi-axial geometry/feature

σ ^∗

stress marking transition between power law creep and power law breakdown regimes

1 Introduction

The LICON approach was originally developed in the late 1990s to predict the long term creep rupture behaviour of new generation martensitic 9% Cr steels (including their welded joints) from the results of relatively short duration multi-axial specimen tests [1,2]. The creep life and condition assessment methodology relied on the acceleration of creep damage development under multi-axial loading conditions to enable extended extrapolation of rupture strength into the long time fracture regime. In its original form, the methodology did not account for the long term ageing effects which could occur during the service duty lifetime of certain materials, and this is still a topic of current research. Nevertheless, the approach provided similarity with the loading conditions experienced in real structures and enabled a more accurate evaluation of the future in-service performance of welded components for which no long term operating experience existed. Other potential applications included the heat-specific remaining life prediction of high temperature components with multi-axial features.

Subsequent development of the concept was mainly limited to activity by some of the original project team in Switzerland [3–7] and Finland [8], although some independent activity in Germany had been reported in [9]. As the effectiveness of the methodology was evaluated for an increasing scope of materials, a number of new issues had to be addressed, and the following paper examines these more recent developments.

2 LICON methodology

2.1 The concept

The original LICON development was based on the time to crack initiation formulation: $t_{i, x} = A (T) \cdot {(\bar{σ})}^{- ν} \cdot {(H)}^{- γ}$ (1) with $H = σ_{1} / \bar{σ}$ , where $σ_{1}$ is the maximum principal stress, $\bar{σ}$ is the relevant representative effective stress, ν is the stress exponent, and where γ varies with material and conditions of temperature and stress (and is the significant parameter defining the material’s multi-axial creep-rupture response) [10]. In Eq. (1) and below, subscript ‘x’ relates to the crack initiation criterion adopted to indicate the equivalent rupture life in the multi-axial feature under consideration (e.g. $Δ a_{c} = 0.5 mm$ ). Typically, γ varies between zero for $\bar{σ}$ controlled rupture and ν for $σ_{1}$ controlled rupture. In the original development, ${\bar{σ}}_{VM}$ was adopted as the effective stress [1,2]. The LICON approach is not limited to this formulation. While the use of H has been demonstrated to work for a number of steels, it is acknowledged that other multi-axiality factors may be more appropriate for different material classes in specific $t_{r} (T, σ)$ application ranges. In its original formulation, the LICON model equations characterised the rupture behaviour of advanced 9% Cr steels in two mechanism regimes (Fig. 1), i.e.

Fig. 1.

Schematic representation of the LICON concept (typically, $x = Δ a_{c} = 0.5 mm$ and $z = CT$ ) [2].

2.1.1 Mechanism Regime-1

$\begin{array}{rclr} t_{r} = A^{'} \cdot {(σ_{o})}^{- ν^{'}} uniaxial, & (2a) \\ t_{i, x}^{z} = A_{z} \cdot {({\bar{σ}}_{z})}^{- ν^{'}} \cdot {(H_{z})}^{- γ} e.g. with γ^{'} \to 0 multi-axial . & (2b) \end{array}$

Typically for ferritic steels in Regime-1, the damage mechanism is predominantly void nucleation due to particle/matrix decohesion, rupture is $\bar{σ}$ controlled, and $γ^{'} \to 0$ . The designation ‘z’ provides a reference to the multi-axial testpiece configuration used to establish the short time experimental data forming the basis of life prediction or the geometry of the feature whose life is to be predicted (e.g. $z = CT$ for a compact tension testpiece). Typically, multi-axial laboratory data is collected for the LICON method using the CT testpiece geometry, and ‘z’ is set to CT when appropriate in the following text.

2.1.2 Mechanism Regime-2

$\begin{array}{rclr} t_{i, x}^{CT} = A_{CT} \cdot {({\bar{σ}}_{CT})}^{- ν^{″}} short time multi-axial, & (3a) \\ t_{i, x}^{z} = A_{CT} \cdot {({\bar{σ}}_{CT})}^{- ν^{″}} \cdot {(H_{z} / H_{CT})}^{- γ^{″}} e.g. with γ^{″} \to ν^{″} long time multi-axial, & (3b) \\ t_{r} = A^{″} \cdot {(σ_{o})}^{- ν^{″}} long time uniaxial, & (3c) \end{array}$ and $\begin{array}{rclr} A_{CT} = A^{″} \cdot {(H_{CT})}^{- γ^{″}} e.g. with γ^{″} \to ν^{″} . & (3d) \end{array}$

In Mechanism Regime-2 in ferritic steels, damage typically nucleates and develops at grain/lath boundaries, rupture is $σ_{1}$ controlled, and $γ^{″} \to ν^{″}$ . The methodology is not limited to materials exhibiting regimes involving only these mechanisms.

The Regime-2 equation set (i.e. Eqs (3a)–(3d)) may be used for different purposes. For example, having determined the parameters for Eq. (3a) from the results of a series of tests using a multi-axial specimen geometry such as a CT-testpiece, these may be used to predict either long term uniaxial rupture behaviour using Eqs (3c), (3d) or the life of a component with a multi-axial feature or a uniaxial x-weld specimen (e.g. [7]) using Eq. (3b). In this case, for example, $H_{CT}$ is the steady-state triaxiality factor for the adopted CT multi-axial testpiece geometry and $H_{z}$ is the steady-state triaxiality factor relating to the stress state at a component critical feature. $H_{z}$ on the attainment of steady-state creep conditions is determined by finite element analysis. Implementation of the LICON methodology is not limited to the use of CT specimens. The original concept was developed using a range of multi-axial geometries [1,2]. Indeed, for a more precise determination of γ, observations from more than one geometry are necessary [3,11].

In order to implement this methodology it is necessary to determine experimental $t_{i, x}^{z} ({\bar{σ}}_{z}, H_{z})$ creep crack initiation time (incubation) data using a multi-axial specimen (e.g. [4,12,13]). It is also necessary to know the representative stress, ${\bar{σ}}_{z}$ , and $H_{z}$ .

Fig. 2.

Example of variation of load point displacement and creep crack extension with time during a creep crack incubation test of HCS 1% CrMoV steel at 550°C [3]. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/SFC-150179.)

2.2 Experimental procedure

A series of creep crack incubation tests (e.g. Fig. 2) are performed to provide the $t_{i, x}^{z} ({\bar{σ}}_{z}, H_{z})$ co-ordinates to define the Regime-1 and Regime-2 multi-axial data lines shown schematically in Fig. 1, i.e. to determine the $A^{'}$ and $ν^{'}$ , and $A^{″}$ and $ν^{″}$ parameters, e.g. [3–7]. These involve the continuous monitoring of creep crack development using electrical DCPD instrumentation to determine the formation of 0.5 mm crack extension (i.e. the adopted crack initiation criterion for the LICON procedure, $x = Δ a_{c} = 0.5 mm$ ). The results of a small number of uniaxial creep-rupture results are also required to give the $t_{r} (σ_{o})$ co-ordinates to form the basis of the uniaxial data line in Fig. 1, and to provide added evidence to substantiate the values of $A^{'}$ and $ν^{'}$ . The creep strain data from the uniaxial tests also provide the basis of the high stress regime component of the creep model for the material under investigation.

In the original LICON procedure [2], rationalisation of the Regime-1 multi-axial and uniaxial data lines led to identification of the most appropriate representative stress for the material (e.g. from the solutions given in [14]).

2.3 Mechanical analysis

On the basis of the original development with results for the advanced martensitic 9% Cr P91, P92 and E911 steels [2], it was concluded that $\bar{σ}$ could be represented by a standard equivalent reference stress solution (e.g. [14]) which was material dependent, and which could be identified by a small number of short duration uniaxial and multi-axial tests (Section 2.2). It was also concluded that $H_{z}$ was geometry dependent, but would only have to be determined once by FEA for a given geometry. It then became apparent that both parameters were apparently sensitive to material and to the type of creep model used [5]. In particular, in circumstances for which there was not full stress redistribution prior to the onset of cracking at the multi-axial feature, even $H_{z}$ , values could be sensitive to whether components of primary and/or tertiary creep deformation were represented in the creep model employed.

Fig. 3.

Stress redistribution characteristics of ‘reference stress’ and ‘non-reference stress’ materials.

3 Refinements to analytical procedure

3.1 Stress state

An important feature of the 9% Cr steels with which the LICON concept was originally developed was that the stress state ahead of the specimen multi-axial feature fully redistributed prior to the onset of creep crack extension, Fig. 3. Such materials may be referred to as ‘reference stress’ materials [15], and typically exhibit high creep rupture ductility and are notch insensitive. Subsequent difficulties with applying the methodology to different alloys arose because for some of these (e.g. high creep strength (HCS) 1% CrMoV steel), the onset of cracking occurred before full stress redistribution [6], Fig. 3. In such circumstances it was shown to be necessary to know the stress state at the time of crack initiation rather than simply after full redistribution. In addition, the stress could vary widely in magnitude with position ahead of the multi-axial crack starter at the onset of cracking. This made the mechanical analysis part of the methodology more demanding, in particular for low creep ductility, notch sensitive materials. Moreover, as the results of more multi-axial specimen reference tests were analysed, it also became apparent that $H_{z}$ could be stress dependent (i.e. $H_{z} (σ)$ ). In order to account for both effects, it was necessary to characterise the state of stress-ahead of multi-axial features, on a case-by-case basis, and continually to the onset of crack development. The most effective way to achieve this was by full non-linear FE simulation with an appropriate multi-stress regime creep model [5–7].

3.2 Creep model

An important development was the recognition that, in some circumstances prior to full stress redistribution, the determined stress state could depend on whether components of primary and/or tertiary creep deformation were represented in the creep model employed. This meant that the originally determined $H_{z}$ values using a Norton secondary creep law [1,2] would not necessarily be the same when an alternative model was adopted (e.g. the Bartsch primary/secondary model used in [3] or the logistic creep strain prediction (LCSP) primary/secondary/tertiary model adopted in [8]).

It was also realised that much greater numerical precision could be achieved by adopting a multi-stress regime creep model which acknowledged the differences in deformation response associated with different mechanism regimes, e.g. Fig. 4.

Fig. 4.

Schematic representation of steady-state creep rate versus stress.

Within the application temperature range of many creep resistant engineering alloys, the influence of stress on creep strain rate may simply be represented as shown in Fig. 4. At high stresses above $σ^{*}$ , the ${\dot{ε}}_{SS} (σ^{n})$ stress exponent is relatively high, but can be determined from the results of relatively short duration (Regime-1) creep-rupture tests. Typically, there is an intermediate regime (coinciding with Regime-2), below $σ^{*}$ , for which stress exponents are similar for a number of engineering alloys. At low stresses, typically below the practical application range, creep is diffusion controlled and the stress exponent approaches ∼1.

One difficulty with the necessity to have a multi-stress regime creep model is that in principle it requires long duration experimental data to underpin the lower stress regime parts of the model. If long duration tests had actually to be performed for this purpose, it negated the need for a concept to predict long duration creep properties from short time tests. This problem was overcome when it was demonstrated that $σ^{*}$ for many engineering alloys was typically 63% of the monotonic limit of proportionality, and that the stress exponent for the intermediate strain rate regime was typically ∼3 [6], e.g. Fig. 5 (with data originating from [16]).

Fig. 5.

Variation of steady state creep rate with $σ / R p_{0.01}$ [6] (data courtesy of NIMS [16]).

3.3 Creep-rupture life prediction

The development work conducted on HCS 1% CrMoV benefitted from the fact that the heat of the steel evaluated was already well characterised in terms of its creep properties for rupture durations out to 35 kh [3]. By adopting the described refinements to the analytical procedure, it was possible to significantly improve the predictive capability of the LICON procedure when applied to this ‘non-reference stress’ (low creep ductility, notch sensitive) material (Fig. 6).

Fig. 6.

LICON prediction of long time (Regime-2) uniaxial creep-rupture strength of HCS 1% CrMoV at 550°C (solid line) compared with actual experimental data for same heat of steel (dashed line) [6].

4 Application to welds

It had been recognised for some time that the main application of the LICON methodology was likely to be for prediction of the long time creep-rupture strength of weldments. What probably was not originally appreciated was that it would be necessary to consider the uniaxial cross weld specimen, whose properties were to be predicted, as a multi-axial structure in its own right. This was demonstrated with specimens taken from a 1% CrMoV/Ni-base alloy dissimilar metal weld (DMW), with Alloy-617 weld metal, in [7].

Assessment of the DMW was a particularly demanding challenge. In tests conducted at 550°C, it was predictable that creep-rupture would occur on the 1% CrMoV side of the joint. Had the joint been a similar welded joint (e.g. between 1% CrMoV and 1% CrMoV parent materials, with a CrMoV weld metal), creep-rupture would have occurred in the inter-critical heat affected zone (ICHAZ) of the low alloy ferritic steel in the form of Type IV cracking. In the case of the 1% CrMoV/Alloy-617 DMW, cracking developed not only in the ICHAZ, but also in the 1% CrMoV at the fusion boundary (e.g. [17]).

A good test of the effectiveness of the FEA model adopted for the mechanical analysis part of the LICON procedure when applied to the target weldment is to extend it to the prediction of damage development in the uniaxial and CT cross-weld specimens being used to form the basis of the analysis. An example of this is shown in Fig. 7 where it is evident that there is good agreement between the analytical prediction of H distribution and the experimental observation of damage accumulated in both specimen types.

Fig. 7.

Comparison of FEA predicted H distribution and actually observed damage development in (a) uniaxial and (b) CT cross-weld specimen tests [7]. (Colors are visible in the online version of the article; https://dx-doi-org.web.bisu.edu.cn/10.3233/SFC-150179.)

Fig. 8.

Effective LICON prediction of long time (Regime-2) uniaxial creep-rupture strength of 1% CrMoV/Ni-base DMW at 550°C using $H_{z} = H_{DMW}$ in Eq. (3b) (shaded squares are CT x-weld specimen test data co-ordinates, open circles are uniaxial x-weld specimen test data co-ordinates [7]).

For the prediction of Regime-2 cross-weld specimen creep-rupture lives it is necessary to use Eq. (3b) with $H_{CT}$ being the multi-axiality factor for the cross-weld CT specimen geometry at crack initiation and $H_{z}$ being the multi-axiality factor for the cross-weld uniaxial specimen geometry (and not simply equal to unity, as for PM uniaxial specimens), Fig. 8, i.e. $t_{i, x}^{DMW} = A_{CT}^{DMW} \cdot {({\bar{σ}}_{CT}^{DMW})}^{- ν^{″}} \cdot {(H_{o}^{DMW} (σ) / H_{CT}^{DMW} (σ))}^{- γ^{″}} with γ^{″} \to ν^{″} .$ (4)

5 Concluding remarks

An important development has been refinement of the method to be also applicable to so-called ‘non-reference stress’ (creep brittle, notch sensitive) materials, which is an essential feature when the procedure is to be used to predict the long time creep-rupture properties of a new material (for which the multi-axial creep rupture response is unknown). Changes to the methodology for this purpose have involved the adoption of: (i) more advanced non-linear FE stress analysis instead of approximate solutions, as a routine, and (ii) multi-stress regime creep constitutive modelling.

Application of the refined procedure, and treatment of cross-weld uniaxial specimens as multi-axial structures enables the LICON methodology to be used to predict the long term creep-rupture behaviour of both similar and dissimilar metal welds.

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