An Integrated Creep Model Based on Internal Stress Evolution

Author(s):  
Nicola Bonora ◽  
Luca Esposito

In creep design, not only secondary creep but also primary and tertiary creep regimes become important for an accurate creep life prediction and need to be accounted for in more sophisticated models. Mechanism-based theories showed a better potential since they usually leads to more accurate prediction over wider range of stress and temperature. It has long been recognized that the mechanics and kinetics of the deformation and recovery processes occurring at the microscale are determined by, amongst other things, the local effective stress while, at macroscopic level, it may still possible to discern an effective stress, which is different from the applied stress that drives the creep strain accumulation, [1]. Recently, the authors proposed an internal stress based model for primary creep, which is independent on the creep rate formulation at the steady state, ensuring the continuity of the creep curve at the transition between primary and secondary creep stages, [2]. In this work, in order to account for all creep stages, this modeling framework is extended further. In particular, for tertiary creep stage, it is assumed that the occurrence of microstructural modifications (such as fine particle dissolution, secondary phase precipitations, etc.) is the process responsible for the reduction of the internal stress and consequent increase of the creep rate as result of the increment of the effective stress. The possibility to derive the internal stress decay function from tertiary creep data is discussed. The proposed model has been applied to P91 high chromium steel and preliminary results are presented in this work.

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Luca Esposito ◽  
Nicola Bonora

In high temperature design, the accumulation of creep strain during the primary stage has to be considered since most of the allowable design strain occurs in this stage. In this work, assuming that the creep rate in the transient regime can be given as a fraction of the steady state creep rate and function of the internal stress, a mechanism based model for primary creep has been derived. Taking into account that the apparent activation energy varies with the internal stress, which evolves with creep strain, an exponential form of the creep rate versus creep strain has been obtained. The proposed model for primary creep requires the identification of two material parameters only which are shown to be function of the applied stress and independent of temperature. The proposed model has been validated for high chromium steel P91.


2018 ◽  
Vol 140 (5) ◽  
Author(s):  
J. Christopher ◽  
B. K. Choudhary

Additive creep rate model has been developed to predict creep strain-time behavior of materials important to engineering creep design of components for high temperature applications. The model has two additive formulations: the first one is related to sine hyperbolic rate equation describing primary and secondary creep deformation based on the evolution of internal stress with strain/time, and the second defines the tertiary creep rate as a function of tertiary creep strain. In order to describe creep data accurately, tertiary creep rate relation based on MPC-Omega methodology has been appropriately modified. The applicability of the model has been demonstrated for tempered martensitic plain 9Cr-1Mo steel for different applied stresses at 873 K. Based on the observations, a power law relationship between internal stress and applied stress has been established for the steel. Further, a higher creep damage accumulation with increasing life fraction has been observed at low stresses than those obtained at high stresses.


Author(s):  
W. David Day ◽  
Ali P. Gordon

Accurate prediction of creep deformation is critical to assuring the mechanical integrity of heavy-duty, industrial gas turbine (IGT) hardware. The classical description of the creep deformation curve consists of a brief primary, followed by a longer secondary, and then a brief tertiary creep phase. An examination of creep tests at four temperatures for a proprietary, nickel-based, equiaxed, super-alloy revealed many occasions where there is no clear transition from secondary to tertiary creep. This paper presents a new creep model for a Nickel-based super-alloy, with some similarities to the Theta Projection (TP) creep model by Evans and all [1]. The alternative creep equation presented here was developed using meaningful parameters, or θ’s, such as: the primary creep strain, time at primary creep strain, minimum (or secondary) creep rate, and time that tertiary creep begins. By plotting the first and second derivative of creep, the authors were able to develop a creep equation that accurately matches tests. This creep equation is identical to the primary creep portion of the theta projection model, but has a modified second term. An additional term is included to simulate tertiary creep. An overall scaling factor is used to satisfy physical constraints and ensure solution stability. The new model allows a constant creep rate phase to be maintained, captures tertiary creep, and satisfies physical constraints. The coefficients of the creep equations were developed using results from 27 creep tests performed at 4 temperatures. An automated routine was developed to directly fit the θ coefficients for each phase, resulting in a close overall fit for the material. The resultant constitutive creep model can be applied to components which are subjected to a wide range of temperatures and stresses. Useful information is provided to designers in the form of time to secondary and tertiary creep for a given stress and temperature. More accurate creep predictions allow PSM to improve the structural integrity of its turbine blades and vanes.


1969 ◽  
Vol 4 (2) ◽  
pp. 95-104 ◽  
Author(s):  
J M Clarke

The changes of creep-strain rate associated with primary and tertiary creep are attributed to a process of internal-stress redistribution between the strong and weak portions of material while for each portion the creep rate depends only on its stress. An expression for the primary-creep curve is derived which is shown to be in substantial agreement with the usual empirical (time)1/3 power law. The model describes the changes in creep rate when the stress is constant and implies as a natural extension a method of calculating creep rate when the stress changes because memory effects are attributed solely to changes of internal stress. The calculated rates obtained according to the method show the creep-recovery phenomenon and in this respect are superior to the ‘hardening hypotheses’ which fail to simulate creep recovery but are normally used for stress-redistribution calculations. According to the model the strain during primary creep is dependent on the stress derivative of the secondary creep rate. Analysis of results for the aluminium alloy DTD 5070A has helped confirm the model by showing a correlation between these quantities.


Author(s):  
Luca Esposito ◽  
Nicola Bonora

In the high temperature component design the accumulation of creep strain during the primary stage cannot be ignored, since most the allowable design strain occurs in this stage, for which appropriate modelling is needed. In this work a mechanism based model for primary creep has been derived assuming that the creep rate in the transient regime can be given as a fraction of the steady state creep rate and as a function of the internal stress. Taking into account that the apparent activation energy varies with the internal stress and that the internal stress kinetic can be given as a function of strain, an exponential form of the creep rate vs creep strain has been obtained. The proposed model has been applied to high chromium steel P91 and the evolution of the decay constant and scaled activation volume with the applied stress has been determined.


10.30544/745 ◽  
2021 ◽  
Vol 27 (4) ◽  
pp. 531-539
Author(s):  
P. Bharath Sreevatsava ◽  
E. Vara Prasad ◽  
A. Sai Deepak Kumar ◽  
Mohammad Fayaz Anwar ◽  
Vadapally Rama Rao ◽  
...  

Austenitic Stainless steels are majorly used because of their high resistance to aqueous corrosion and high temperature properties. Some major applications of stainless steels at high temperatures include engine and exhaust components in aircrafts, recuperators in steel mills, and pulverized coal injection lances for blast furnaces. In all the above said applications, the components are constantly subjected to loads and high temperatures. This makes the study of their creep behavior very important to decide the life of the component. Cr-Ni stainless steel was used as a starting material, and hot impression creep test was performed on cylindrical samples of 10 mm height and 15 mm diameter for a dwell time of 150 min at two different loads of 84 and 98 MPa and at two different temperatures 450 and 500 °C. The time vs. indentation depth was plotted, and creep rate was calculated in each case. It was observed that with an increase in time, creep rate increased in the primary creep region and remained almost constant in the secondary creep region irrespective of temperature and load. The indentation depth and creep rate increased with an increase in load and temperature.


1949 ◽  
Vol 16 (3) ◽  
pp. 229-241
Author(s):  
L. F. Coffin ◽  
P. R. Shepler ◽  
G. S. Cherniak

Abstract The paper evaluates the stresses and the permanent strains at a particular time, resulting from loading a thick-walled cylinder under constant internal pressure and elevated temperature when account is taken of the primary creep characteristics of a given material. The results are compared with permanent strains obtained by considering secondary creep as the general basis for pressure-vessel design. For a thick-walled cylinder of wall ratio of R1/R0 = 2 and of 12 per cent chromium steel, operating under 12,000 psi at 850 F, the permanent strain at the end of 25 hr by the primary-creep analysis was found to be equal to the strain at the end of 2000 hr, considering only secondary creep. The methods formulated are shown to be suitable for design of pressure vessels intended for short life.


Author(s):  
Sinisa Dj. Mesarovic

Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro–Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro–Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.


Author(s):  
Subhasis Mukherjee ◽  
Bite Zhou ◽  
Abhijit Dasgupta ◽  
Thomas R. Bieler

A multiscale modeling framework is proposed in this study to capture the influence of the inherent elastic anisotropy of single crystal Sn and the inherent heterogeneous microstructure of a single crystal SnAgCu (SAC) solder grain on the secondary creep response of the grain. The modeling framework treats the SAC microstructure as having several distinct length scales. The smallest length scale (Tier 0) consists of the Sn BCT lattice. The eutectic Sn-Ag micro-constituent, consisting of nanoscale Ag3Sn IMC particles embedded in the single crystal BCT Sn matrix, is termed Tier 1. The single-crystal SAC microstructure, consisting of Sn dendrites and surrounding eutectic Sn-Ag phase, is termed Tier 2. Dislocation recovery mechanisms, such as Orowan climb and detachment from nanoscale Ag3Sn particles, are found to be the rate controlling mechanisms for creep deformation in the eutectic Sn-Ag phase (Tier 1) of a SAC single crystal. The anisotropic secondary creep rate of eutectic Sn-Ag phase (Tier 1), is then modeled using the above inputs and the saturated dislocation density calculated for dominant glide systems during secondary stage of creep. Saturated dislocation density is estimated as the equilibrium saturation between three competing processes: (1) dislocation generation; (2) dislocation impediment caused by back stress from pinning of dislocations at IMCs; and (3) dislocation recovery due to climb/detachment from IMCs. Secondary creep strain rate of eutectic Sn-Ag phase in three most facile slip systems is calculated and compared against the isotropic prediction. At low stress level secondary steady state creep rate along (110)[001] system is predicted to be ten times the creep rate along (100)[0-11] system. However, at high stress level, secondary steady state creep rate along (110)[001] system is predicted to be ten thousand times the creep rate along (100)[0-11] system. The above predictions are in strong agreement with (1–4) orders of magnitude of anisotropy observed in steady state secondary creep response in SAC305 solder joints tested under identical loading conditions in experiments conducted by several authors. The above model is then combined with Eigen-strain methods and average matrix stress concepts to homogenize the load sharing between the Sn dendrites and the surrounding eutectic Ag-Sn matrix. The resulting steady state creep rates are predicted for a few discrete single crystal SAC305 specimens. Very good agreement is observed between the predicted steady state creep rate and the measured creep rates for two SAC305 single crystal specimens.


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