Tertiary Creep Research Articles

Creep Damage Evaluation of DS CM247 Nickel Base Superalloy Using Alternate Current Potential Drop Technique

The evolution of creep damage in a directionally solidified DS CM247 alloy during creep at 950 °C/250 MPa has been evaluated using alternate current potential drop (ACPD) technique in which a constant alternating current was passed through the specimen and corresponding potential drop was measured. Creep tests were interrupted at different strain levels in order to examine the microstructural degradation of the alloy during creep. The creep curve of the alloy exhibited limited primary and secondary creep regimes, but extended tertiary creep regime. Microstructural examination revealed the progressive directional coarsening of γ′ precipitates i.e., rafting and widening of γ matrix channel with accumulation of creep strain. The specimen exhibited a considerable amount of creep strain prior to fracture. Further, creep cavitation was observed only close to the fractured end of the specimens. Various factors responsible for the extended tertiary creep regime of the alloy are discussed. The potential of ACPD technique to be used as a NDE tool to monitor in service/online creep damage evaluation, has been established/demonstrated.

Characterization of creep behavior of TiAl alloy with high Nb content at elevated temperatures

Creep experiments of the TiAl alloy with high Nb content were conducted to consider both the temperature dependence and stress dependence of its creep behavior. The creep curves were characterized by Theta constitutive model, and Newton–Gauss method was applied to obtain the material parameters. Based on the rupture strain, the rupture life of the TiAl alloy was able to be predicted by Theta constitutive model. The results show that the creep curves of the TiAl alloy contain primary creep, secondary creep and tertiary creep stages, especially for the lower stress. The rupture life of the TiAl alloy decreases with the increase in either applied stress or temperature. Theta constitutive model is able to describe the creep deformation of the TiAl alloy accurately, and the predicted life agrees well with the experimental result.

Comparison of voiding mechanisms in semi-crystalline polyamide 6 during tensile and creep tests

Behaviour of a semi-crystalline polymer, polyamide 6, described by loading curves, as well as necking and whitening phenomena, is related to its micro-structural evolution in terms of void morphology and distribution during both tensile and creep tests. Notched bars have been subjected to creep tests interrupted at the onset of the tertiary creep stage and at the onset of final rupture. Inspections of these specimens using Synchrotron Radiation Tomography have been coupled with statistical image analysis treatment to obtain spatial distributions of void length and void volume fraction. Cavitation mechanisms observed and quantified during creep and tensile tests were similar: from penny shaped voids (diameter larger than height) perpendicular to the drawing direction to cylindrical voids (diameter equal to the height) arranged in columns during the neck extension. The void volume fraction distributions along radial and axial directions presented an inverted parabolic profile with a maximum located at the centre of the sample.

The peridynamic model of viscoelastic creep and recovery

Purpose – The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method. Design/methodology/approach – A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data. Findings – The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters. Research limitations/implications – The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper. Practical implications – The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss. Originality/value – The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Experimental investigations on the short- and long-term behaviour of Jinping marble in deep tunnels

The tunnels of Jinping II hydropower station are characterised by its ultra-long and deep-buried properties. For the stability of the tunnels, it is of great important to investigate the short-term and time-dependent mechanical behaviour of surrounding rocks. The triaxial compression tests with confining stress up to 100 MPa were performed in order to complete the short-term mechanical behaviour of Jinping marble. Typical characteristics of brittle rock, such as volumetric compaction–dilatancy transition, degradation of elastic modulus, dependence of strength and failure mode on confining stress were observed. Two constant axial stresses were applied in the uniaxial compressive creep tests, and tertiary creep phases were realised. The evolutions of creep strain of the uniaxial compressive creep tests presented obvious anisotropy. One triaxial compressive creep test was also performed under confining stress of 10 MPa. The creep strain rates in both axial and lateral directions of triaxial compressive creep tests were significantly lower than those of uniaxial compressive creep tests. The significant anisotropy of creep strain in uniaxial compressive creep tests was attenuated in triaxial compressive creep tests. Immediate support is thus of great important to provide an effect as confining stress after the excavation of the tunnel under high in situ stress.

Micro-Macro Analysis and Phenomenological Modelling of Salt Viscous Damage and Application to Salt Caverns

This paper aims to gain fundamental understanding of the microscopic mechanisms that control the transition between secondary and tertiary creep around salt caverns in typical geological storage conditions. We use a self-consistent inclusion-matrix model to homogenize the viscoplastic deformation of halite polycrystals and predict the number of broken grains in a Representative Elementary Volume of salt. We use this micro-macro modeling framework to simulate creep tests under various axial stresses, which gives us the critical viscoplastic strain at which grain breakage (i.e., tertiary creep) is expected to occur. The comparison of simulation results for short-term and long-term creep indicates that the initiation of tertiary creep depends on the stress and the viscoplastic strain. We use the critical viscoplastic deformation as a yield criterion to control the transition between secondary and tertiary creep in a phenomenological viscoplastic model, which we implement into the Finite Element Method program POROFIS. We model a 850-m-deep salt cavern of irregular shape, in axis-symmetric conditions. Simulations of cavern depressurization indicate that a strain-dependent damage evolution law is more suitable than a stress-dependent damage evolution law, because it avoids high damage concentrations and allows capturing the formation of a damaged zone around the cavity. The modeling framework explained in this paper is expected to provide new insights to link grain breakage to phenomenological damage variables used in Continuum Damage Mechanics.

Creep in Interlaminar Shear of an Oxide/Oxide Ceramic-Matrix Composite at Elevated Temperature1

Creep behavior in interlaminar shear of an oxide–oxide ceramic composite was evaluated at 1100 °C in laboratory air and in steam environment. The composite (N720/AS) consists of a porous aluminosilicate matrix reinforced with laminated, woven mullite/alumina (Nextel™720) fibers, has no interface between the fiber and matrix, and relies on the porous matrix for flaw tolerance. The interlaminar shear properties were measured. The interlaminar shear strength (ILSS) was determined as 7.6 MPa. The creep behavior was examined for interlaminar shear stresses in the 2–6 MPa range. Primary and secondary creep regimes were observed in all tests conducted in air and in steam. Tertiary creep was noted in tests performed at 6 MPa. Creep run-out defined as 100 hrs at creep stress was not achieved in any of the tests. Larger creep strains and higher creep strain rates were produced in steam. However, the presence of steam had a beneficial effect on creep lifetimes. Composite microstructure, as well as damage and failure mechanisms, was investigated.

Creep ruptures of AISI 347 austenitic stainless steel foils at elevated temperature of 750 ℃

The creep rupture properties of AISI 347 austenitic stainless steel foil used in compact recuperators have been evaluated at 750 ℃ in the stress range of 54–221 MPa to establish baseline behavior for its extended use. The creep curve of the foil shows that the primary creep stage is brief and creep life is dominated by tertiary creep deformation with rupture lives in the range 3–433 h. Power law relationship was obtained between the minimum creep rate and the applied stress with stress exponent value of n = 4.25. The creep damage tolerance parameter for specimen tested at 750 ℃ and 54 MPa indicates that creep fracture takes place by precipitate coarsening mechanism. Nucleation of voids mainly occurs at second-phase particles (Cr23C6 carbides). The improvement in strength is attributed to the precipitation of fine niobium carbides in the matrix which prevents dislocation movement of the microstructure.

Stochastic model prediction of nonlinear creep in glassy polymers

Nonlinear creep is one of the generic features of deformation response of glassy polymers, where a rich set of strain vs time responses is observed that depend upon the applied stress and the thermal history used to form the glass. Although existing constitutive models may be able to describe some aspects of nonlinear creep, these models are unable to provide a unified description of the diverse nonlinear creep behaviors exhibited by glassy polymers, where predicting the effects of thermal history has proved especially challenging. In this paper the ability of a recently developed Stochastic Constitutive Model (SCM) to describe nonlinear creep is critically examined, where it is demonstrated that the SCM qualitatively captures all of the major features of nonlinear creep of glassy polymers, including the tertiary creep. In particular the SCM predicts how the duration of the secondary creep and the range of the tertiary creep depend on the aging time prior to deformation. The SCM predicts the existence of Stage IV creep, which comes after the tertiary creep – where examination of nonlinear creep data clearly indicate the presence of Stage IV creep, although heretofore not recognized, in the experimental data. The SCM unifies the description of nonlinear creep, and provides a detailed mesoscopic picture of the processes that underlie both strain controlled and stress controlled experiments.

Modification of creep and low cycle fatigue behavior induced by welding

In this work, the mechanical properties of Waspaloy superalloy have been evaluated in case of welded repaired material and compared to base material. Test program considered flat specimens on base and TIG welded material subjected to static, low-cycle fatigue and creep test at different temperatures.Results of uniaxial tensile tests showed that the presence of welded material in the gage length specimen does not have a relevant influence on yield strength and UTS. However, elongation at failure of TIG material was reduced with respect to the base material.Moreover, low-cycle fatigue properties have been determined carrying out tests at different temperature (room temperature RT, 538°C and 760°C) in both base and TIG welded material. Welded material showed an increase of the data scatter. Fatigue strength was reduced, with respect to the base material. During test, all the hysteresis cycles were recorded in order to evaluate the trend of elastic modulus and hysteresis area against the number of cycles. A clear correlation between hysteresis and fatigue life was found.Finally, creep test carried out on a limited number of specimens allowed establishing some changes about the creep rate and time to failure of base and welded material. TIG welded specimen showed a lower time to reach a fixed strain or failure when a low stress level is applied. In all cases, creep behavior of welded material is characterized by the absence of the tertiary creep.

Assessment of Tungsten Content on Tertiary Creep Deformation Behavior of Reduced Activation Ferritic–Martensitic Steel

Tertiary creep deformation behavior of reduced activation ferritic–martensitic (RAFM) steels having different tungsten contents has been assessed. Creep tests were carried out at 823 K (550 °C) over a stress range of 180 to 260 MPa on three heats of the RAFM steel (9Cr-W-0.06Ta-0.22V) with tungsten content of 1, 1.4, and 2.0 wt pct. With creep exposure, the steels exhibited minimum in creep rate followed by progressive increase in creep rate until fracture. The minimum creep rate decreased, rupture life increased, and the onset of tertiary stage of creep deformation delayed with the increase in tungsten content. The tertiary creep behavior has been assessed based on the relationship, $$ \varepsilon = \varepsilon_{\text{o}} + \dot{\varepsilon }_{\text{m}} t + \varepsilon_3{\exp }\left[ {p\left( {t - t_{\text{t}} } \right)} \right] $$ , considering minimum creep rate ( $$ \dot{\varepsilon }_{\text{m}} $$ ) instead of steady-state creep rate. The increase in tungsten content was found to decrease the rate of acceleration of tertiary parameter ‘p.’ The relationships between (1) tertiary parameter ‘p’ with minimum creep rate and time spent in tertiary creep deformation and (2) the final creep rate $$ \dot{\varepsilon }_{\text{f}} $$ with minimum creep rate revealed that the same first-order reaction rate theory prevailed in the minimum creep rate as well as throughout the tertiary creep deformation behavior of the steel. A master tertiary creep curve of the steels has been developed. Scanning electron microscopic investigation revealed enhanced coarsening resistance of carbides in the steel on creep exposure with increase in tungsten content. The decrease in tertiary parameter ‘p’ with tungsten content with the consequent decrease in minimum creep rate and increase in rupture life has been attributed to the enhanced microstructural stability of the steel.

Microstructural evolution and creep-rupture life estimation of high-Cr martensitic heat-resistant steels

The creep behavior of high-Cr martensitic heat-resistant steels was investigated to discuss the dominant factors determining the creep-rupture life in the temperature range from 839 to 894K. Variation in the content of Nb, a carbide former, induced a difference in creep-degradation at the long-term creep condition, which was attributed to the formation of a Z-phase at the expense of M2N precipitates. Due to the continuous evolution of the microstructure during creep service, a simple form of the Monkman–Grant equation could not properly describe the creep-rupture life of the alloys; however, the modified Monkman–Grant equation, which incorporates the creep rate at the tertiary creep region, resulted in a reasonable estimation of creep-rupture life.

Overview of aluminum alloy mechanical properties during and after fires

AbstractAluminum alloys are increasingly being used in a broad spectrum of load-bearing applications such as lightweight structures, light rail, bridge decks, marine crafts, and off-shore platforms. A major concern in the design of land-based and marine aluminum structures is fire safety, at least in part due to mechanical property reduction at temperatures significantly lower than that for steel. A substantial concern also exists regarding the integrity and stability of an aluminum structure following a fire; however, little research has been reported on this topic. This paper provides a broad overview of the mechanical behavior of aluminum alloys both during and following fire. The two aluminum alloys discussed in this work, 5083-H116 and 6061-T651, were selected due to their prevalence as lightweight structural alloys and their differing strengthening mechanisms (5083 – strain hardened, 6061 – precipitation hardened). The high temperature quasi-static mechanical and creep behavior are discussed. A creep model is presented to predict the secondary and tertiary creep strains followed by creep rupture. The residual mechanical behavior following fire (with and without applied stress) is elucidated in terms of the governing kinetically-dependent microstructural mechanisms. A review is provided on modeling techniques for residual mechanical behavior following fire including empirical relations, physically-based constitutive models, and finite element implementations. The principal objective is to provide a comprehensive description of select aluminum alloys, 5083-H116 and 6061-T651, to aid design and analysis of aluminum structures during and after fire.

Creep behavior of boom clay

Several creep tests (lasting more than one year) were performed to study the delayed mechanical behavior of Boom clay under the hydro-mechanical coupling effect. To prevent the soil from swelling as much as possible during re-saturation, the samples were submitted to a confining pressure close to the in situ effective mean stress (2.5MPa) at a room temperature of 21°C. However, certain swelling still exists at the beginning of the saturation. Creep tests further highlight the creep potential of Boom clay. Delayed behavior became more and more significant as the deviatoric stress increased. A deviatoric stress threshold (approximately 1.0MPa), below which only primary creep occurred, was proved to exist from the development of secondary and tertiary creep phases during the creep tests. If we introduce a quasi-steady state creep rate, i.e., the average creep rate after the creep deformation becoming stable, it can be found that the quasi-steady state creep rate of Boom clay is on the order of 10−6ε/h under low deviatoric stress (1.5MPa) in the laboratory, which is on the same order as the average creep rate of the in situ measurements in the second year (1988). However, in situ measurements show that steady creep state of the host rock was not reached even after five years. The in situ quasi-steady state diameter reduction rate calculated from the average of 10 years (1996–2006) of stable deformation of the tunnel linings is on the order of 10−8ε/h.

Creep of outlet pigtail tubes of steam reformer and grain size effect on Creep of an Incoloy 800H material

During the inspection of a scheduled turnaround of one of the Steam Reformers in a Methanol Plant, a diameter increase was observed on the outlet pigtail tubes. Original dimension of the outlet pigtail tubes is; 1¼ × 0.2 inch wall thickness & Sch. 80 (42.2 mm OD). The material of the tubes was Incoloy 800H. The outlet pigtail tubes of the steam reformer are connected to a manifold header which used to transport the process fluid. It was requested to conduct a failure analysis on damages in the outlet pigtail tubes that occurred in the form of a diametral expansion. The failure analysis study is described in details and the mechanism of the diametral expansion damage is identified. The grain size effect of different increases in the strain of the tube OD was studied to correlate its effect on the material’s creep. It was also concluded that the tertiary creep phase (instable behaviour) starts around 7% increase in the strain of the tube OD. The 7% is set as the creep limit and the criterion of end-of-safe life.

Progressive failure leading to the 3 December 2013 rockfall at Puigcercós scarp (Catalonia, Spain)

A detailed analysis of the pre-failure behavior of the 3 December 2013 rockfall (1,012 m3) occurred on Puigcercos pilot study area (Catalonia, Spain) is presented. The exact date of failure was obtained based on a photographic monitoring performed every 4 h. The long-term monitoring (2,217 days) of the rock slope carried out by a Terrestrial LiDAR allowed the early detection of both pre-failure deformation and precursory rockfalls preceding the final failure. By means of the analysis of the pre-failure deformation, four different deformed areas were detected and the tertiary creep phase was observed in three of them. An attempt to predict the time to failure was performed using the Fukuzono’s (1985) method. Furthermore, the temporal evolution of the precursory rockfalls occurred in those four areas during the progressive failure showed a close resemblance with the exponential pattern of the cumulated displacements at tertiary creep stage. Finally, the study of the meteorological conditions did not show any single triggering factor associated with the final failure. Reversely, the increase in the occurrence of precursory rockfalls on several areas of the slope together with the observed acceleration on the deformation pattern reinforce the role of a progressive degradation of the stability conditions, which ultimately leaded to the 3 December rockfall event.

A micromechanical model of the viscoplastic behaviour of titanium accounting for its anisotropic and strain-rate-dependent viscosity

The viscoplastic behaviour of two batches of commercially pure titanium with different oxygen contents was characterized at room temperature through tension, creep, relaxation, and strain-rate jump tests along the rolling and transverse directions. Depending on the applied stress, creep saturated, or the primary creep stage was followed by secondary and even tertiary creep leading to fracture within a few hours. 33 % to 40 % of the flow stress was relaxed within 20 hours. The strain-rate sensitivity was found to increase with the oxygen content and when the strain rate decreased. It was up to 25 % higher along the transverse direction than along the rolling direction. The experimental data were used to identify a simple mean field crystal viscoplasticity model. Assuming different viscosities on prismatic and nonprismatic slip systems, the anisotropy and strain-rate dependence of the strain-rate sensitivity were captured. As a consequence of these different viscosities, the relative contributions of each type of slip system to the overall deformation are predicted to vary with the strain rate, in accordance with some data from the literature.

Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

AbstractAn experimental work is presented that aimed at improving our understanding of the mechanical evolution of cracks under brittle creep conditions. Brittle creep may be an important slow deformation process in the Earth's crust. Synthetic glass samples have been used to observe and document brittle creep due to slow crack‐propagation. A crack density of 0.05 was introduced in intact synthetic glass samples by thermal shock. Creep tests were performed at constant confining pressure (15 MPa) for water saturated conditions. Data were obtained by maintaining the differential‐stress constant in steps of 24 h duration. A set of sensors allowed us to record strains and acoustic emissions during creep. The effect of temperature on creep was investigated from ambient temperature to 70°C. The activation energy for crack growth was found to be 32 kJ/mol. In secondary creep, a large dilatancy was observed that did not occur in constant strain rate tests. This is correlated to acoustic emission activity associated with crack growth. As a consequence, slow crack growth has been evidenced in glass. Beyond secondary creep, failure in tertiary creep was found to be a progressive process. The data are interpreted through a previously developed micromechanical damage model that describes crack propagation. This model allows one to predict the secondary brittle creep phase and also to give an analytical expression for the time to rupture. Comparison between glass and crystalline rock indicates that the brittle creep behavior is probably controlled by the same process even if stress sensitivity for glass is lower than for rocks.

Brittle Creep Failure, Critical Behavior, and Time-to-Failure Prediction of Concrete under Uniaxial Compression

Understanding the time-dependent brittle deformation behavior of concrete as a main building material is fundamental for the lifetime prediction and engineering design. Herein, we present the experimental measures of brittle creep failure, critical behavior, and the dependence of time-to-failure, on the secondary creep rate of concrete under sustained uniaxial compression. A complete evolution process of creep failure is achieved. Three typical creep stages are observed, including the primary (decelerating), secondary (steady state creep regime), and tertiary creep (accelerating creep) stages. The time-to-failure shows sample-specificity although all samples exhibit a similar creep process. All specimens exhibit a critical power-law behavior with an exponent of −0.51 ± 0.06, approximately equal to the theoretical value of −1/2. All samples have a long-term secondary stage characterized by a constant strain rate that dominates the lifetime of a sample. The average creep rate expressed by the total creep strain over the lifetime (tf-t0) for each specimen shows a power-law dependence on the secondary creep rate with an exponent of −1. This could provide a clue to the prediction of the time-to-failure of concrete, based on the monitoring of the creep behavior at the steady stage.

Modelled stress distributions at the Dome Summit South borehole, Law Dome, East Antarctica: a comparison of anisotropic ice flow relations

AbstractIn this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized.