Improved relaxation time coverage in ramp-strain histories

Standard methods for deriving relaxation data from measurements invariably involve some form of ramp-type deformation history, the initial portion of which is typically not employed for modulus evaluation. In fact, the “ten-times-rule” or a variant thereof is widely used at the expense of short term data acquisition. This paper suggests a simple if (not) obvious method to extend the range of relaxation data that can be acquired from a single test at a single temperature. The method draws on new computational developments for inverting ill-conditioned systems of equations which allows the determination of relaxation parameters nearly routinely and trouble-free. We demonstrate this process for extraction of relaxation characterization from ramp strain histories through (a) numerical evaluation with a virtual test sequence, as well as through (b) data measured in the laboratory. Limitations regarding the time range over which the relaxation modulus can be extracted from laboratory measurements in terms of equipment resolution and stability are discussed. With these constraints in mind it appears feasible to extend the time range by three to four decades towards shorter times when compared with the application of the “ten-times-rule”. Similar treatments apply to the acquisition of creep compliance data.     

Determination of the relaxation modulus of a linearly viscoelastic material

In this paper, a numerical method for computing the relaxation modulus of a linearly viscoelastic material is presented. The method is valid for relaxation tests where a constant strain rate is followed by a constant strain. The method is similar to the procedure suggested by Zapas and Phillips. Unlike Zapas-Phillips approach, this new method can be also applied for times shorter than t ₁/2, where t ₁ denotes time when the maximum strain is achieved. Therefore this method is very suitable for materials that experiences fast relaxation. The method is verified with numerical simulations. Results from the simulations are compared with analytical solution and Zapas-Phillips method. Results indicate that the presented approach is suitable for estimating the relaxation modulus.     

Higher-order fractional constitutive equations of viscoelastic materials involving three different parameters and their relaxation and creep functions

Two higher-order fractional viscoelastic material models consisting of the fractional Voigt model (FVM) and the fractional Maxwell model (FMM) are considered. Their higher-order fractional constitutive equations are derived due to the models’ constructions. We call them the higher-order fractional constitutive equations because they contain three different fractional parameters and the maximum order of equations is more than one. The relaxation and creep functions of the higher-order fractional constitutive equations are obtained by Laplace transform method. As particular cases, the analytical solutions of standard (integer-order) quadratic constitutive equations are contained. The generalized Mittag–Leffler function and H-Fox function play an important role in the solutions of the higher-order fractional constitutive equations. Finally, experimental data of human cranial bone are used to fit with the models given by this paper. The fitting plots show that the models given in the paper are efficient in describing the property of viscoelastic materials.     

Creep and relaxation functions of a heterogeneous viscoelastic porous medium using the Mori-Tanaka homogenization scheme and a discrete microscopic retardation spectrum

In this paper the macroscopic creep and relaxation functions of a heterogeneous viscoelastic porous medium are derived by using Mori-Tanaka homogenization scheme. Analytical and semi-analytical solutions can then be determined with a parametric number of heterogeneous phases embedded in a viscoelastic matrix whose behavior is described with a parametric number of analogical units. Under some simplifying assumptions, a solution strategy is presented in order to make explicit how the microscopic retardation and relaxation times of the viscoelastic matrix control the distribution of the retardation and relaxation times of the homogenized medium.     

Depth sensing indentation of linear viscoelastic-plastic solids: A simple method to determine creep compliance

Viscoelastic solids may deform plastically under indentation. This leads to an overestimation of the creep compliance when the analytical solution for indentation of linear viscoelastic materials [Lu H, Wang B, Ma J, Huang G, Viswanathan H. Measurement of creep compliance of solid polymers by nanoindentation. Mech Time-Depend Mater 2003;7(3-4):189-207] is used for its determination. Using finite element analysis, in this work it is shown that the plastic and viscoelastic deformation processes occur simultaneously, even during holding of a constant indentation load. A simple procedure to separate the viscoelastic response from the plastic response is proposed, which involves spherical indentations at different loads. To illustrate the proposed method, indentation tests are conducted on a polymer, polymethylmethacrylate (PMMA), and its viscoelastic properties are determined.     

Comparison of different approaches for estimation of creep crack initiation

In large components such as rotors defects due to manufacturing processes have to be taken into account and crack assessments based on findings of non-destructive evaluation are necessary. Approaches are used in remaining life estimations, for example:

• Time Dependent Failure Assessment Diagram (TDFAD),

• Two Criteria Diagram (2CD) and

• Nikbin–Smith–Webster-Model (NSW-Model).

The TDFAD approach is currently being developed within the R5 procedures as an alternative to conventional methods for predicting incubation and the early stages of Creep Crack growth. A key requirement of TDFAD approaches is the evaluation of a time dependent creep toughness, denoted K_c mat. The 2CD approach has been developed independently in Germany to assess Creep crack incubation in ferritic steels. This approach uses crack tip and ligament damage parameters, R_K and R_σ, respectively. Furthermore the NSW-Model is employed for the estimation of creep crack initiation by using the creep fracture mechanics parameter C^*. Calculations and used parameters were compared for a ferritic 1CrMoV-steel.     

On the creep and phase stability of advanced Ni-base single crystal superalloys

The present article examines microstructure stability and creep resistance of a 5th generation superalloy, which has Cr content at 4.6 wt%, 6.4 wt% Re and 5.0 wt% Ru, in comparison with that of a 4th generation superalloy (3.2 wt% Cr, 5.8 wt% Re and 3.6 wt% Ru). The aim is to elucidate the implication of increasing Cr, Re and Ru contents for future alloy developments. Experimental results have concluded that high Re + Ru content could promote formation of hexagonal δ phase at 900 °C; additional Cr and Re could enhance the precipitation of TCP phase at 1100 °C. Although an increase in lattice misfit between γ and γ′ in the 5th generation superalloy could strengthen the alloy against creep deformation under conditions at high temperatures (≥1000 °C) and low stresses (≤245 MPa) whilst the microstructural stability remained, the tendency to raft should be avoided during creep at lower temperatures and higher stresses.     

Effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens

The creep rupture life of U-type notched specimens and smooth specimens has been calculated based on the ductility exhaustion damage model using stress-dependent creep ductility. Effects of creep ductility and notch constraint on creep fracture behaviour in notched bar specimens have been investigated. The results show that the U-type notch exhibits notch strengthening effect under a wide range of stress level and notch constraint condition (notch acuity) for creep ductile materials. The lower equivalent stress in notched specimens plays main role for reducing creep damage and increasing rupture life. The rupture life of notched specimens of creep brittle materials (with lower creep ductility) decreases with the increase in stress level and notch constraint. With increasing creep ductility and decreasing notch constraint, the degree of the notch strengthening effect increases. In creep life designs and assessments of high-temperature components containing notches, the material creep ductility, notch constraint and stress levels need to be fully considered.     

Interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial loading

Analytical solutions are developed for interface diffusion-induced creep and stress relaxation in unidirectional metal matrix composites under biaxial transverse loading. The driving force for the interface diffusion is the normal stress acting on the interface, which is obtained from rigorous Eshelby inclusion theory. The solutions are a function of the applied stress, volume fraction and radius of the reinforced-fiber, the modulus ratio between the fiber and the matrix, specially, exhibit a strong dependence of creep rate and stress relaxation behavior on the biaxial stress ratio. Moreover, the solution for the interface stress presented in this study also gives some insight into the relationship between the interface diffusion and interface slip. For the application of the solutions in the realistic composites, the scale effect is taken into account by detailed finite element analysis based on a unit cell model.     

Coupling phase field with creep damage to study evolution and creep deformation of single crystal superalloys

A phase-field model coupling with elastoplastic deformation and creep damage has been built to study the microstructural evolution and deformation behavior for Ni-Al single crystal alloy during the whole creep processing.The relevant experiments were conducted to verify the model validity.The simulation results show that under the tensile creep at 1223 K/100 MPa,cubic γ'phases coarsen along the direction parallel to the axis of tensile stress during the first two creep stages;and spindle-shaped and wavy γ'phases are formed during tertiary creep,similar to the experimental results.The evolution mechanism ofγ'phases is analyzed from the perspective of changes of stress and strain fields.The island-like γ phase is observed and its formation mechanism is discussed.With the increase of creep stress,the directional coarsening of γ'phase is accelerated,the steady-state creep rate is increased and the creep life is decreased.The comparison between simulated and experimental creep curves shows that this phase-field model can effectively simulate the performance changes during the first two creep stages and predict the influence of creep stresses on creep properties.Our work provides a potential approach to synchronously simulate the creep microstructure and property of superalloys strengthened by γ'precipitates.     

Flexure creep properties of E-glass reinforced polymers

The long-term creep behavior and creep-rupture properties were investigated for two systems of E-glass reinforced polymer composites: E-glass/polyurethane composite and E-glass/epoxy composite. The two composite systems showed similar short-term mechanical properties, however their long-term creep properties were quite different. The E-glass/polyurethane system exhibited tertiary creep leading to rupture within a few hours when subjected to about 60% of its flexural strength while the E-glass/epoxy endured months of loading at 60% of its flexural strength before rupture at 50 °C. The findings in this study indicate that creep testing is essential in material characterization and material selection, that the three-point flexure test can be used as a quick test method to determine creep-rupture properties, and that creep-rupture is highly influenced by the type of matrix and the fiber/matrix interface.     

On the study of the creep damage development in circumferential notch specimens

Numerical calculations with K–R damage law have been performed to study the creep damage development in circular notch specimens under constant loading. The emphasis was placed on the roles of notch radius, material constant- and applied stress. The results show that the distributions of stresses under creep conditions are different from those of previous studies. Creep damage development and life are different for different notch specimens, and the distributions of the maximum creep damage in the minimum cross-section vary with the notch radius. The creep damage is remarkably affected by the applied stress, material parameter- and notch radius. Higher stress and tri-axial stress state parameter- can cause the creep damage to develop faster.     

Estimating the remanent creep life of power plant components

This paper examines the current status of remanent creep life assessment methods for power plant components. Consideration is given mainly to predictive techniques based on post-service examination and testing with application to low alloy ferritic components in fossil plant. The requirements for producing methodologies, namely the development of mechanistic and parametric models for creep damage and failure, are discussed together with aspects on the measurement of the relevant creep damage feature or property. Techniques considered include physical and mechanical property measurement, metallographic examination, strain measurement, and accelerated creep and rupture testing. Methods based on accelerated testing are discussed in detail; extrapolative techniques and application of the life fraction rule are considered both from an experimental and mechanistic viewpoint. Finally, attention is given to the choice of representative stress to apply to uniaxial data. The influence of material parameters on the representative stress is emphasized and upper and lower bounds appropriate to creep brittle and creep ductile material states are considered.     

Semi-analytically presenting the creep strain rate and quasi shear-lag model as well as finite element method prediction of creep debonding in short fiber composites

In this research work, semi-analytical method (SAM) is presented to predict composite creep strain rate and quasi shear-lag (QSL) formulation directly, as well as, finite element method (FEM) is employed for predicting partial creep debonding at the interface in steady state creep of short fiber composites under tensile axial stress. Also, new formulation QSL is introduced to obtain the average axial stress in fiber which its results are similar to the results of shear lag (SL) model. Then, it is shown that FEM can approximately predict the partial debonding in some regions of the interface. As a result, interfacial debonding can be caused by high tensile axial and circumferential stresses, high shear and equivalent stresses, and low compressive radial stresses with considering stress concentration. The results obtained from SAM are in good agreement with the available experimental results. Finally, it is concluded that FEM simulation can be useful for predicting some defects such as interfacial debonding and also better designing the fibrous composites.     

Non-uniform hydrogen attack cavitation and the role of interaction with creep

Hydrogen attack (HA) is the development of grain-boundary porosity by cavities filled with high-pressure methane that originates from the reaction of carbides with hydrogen at high temperatures. The cavities grow by grain-boundary diffusion and by creep of the adjacent grain material till they coalesce with neighbouring cavities to form a microcrack. Earlier work on HA has focussed on unit cells containing a single cavity, using average cavitation properties. Here, non-uniform cavitation properties on the grain-size scale are assumed in a polycrystalline aggregate, and unit cell analyses are performed to investigate the influence of the adjacent grains on the development of the grain-boundary HA. The numerical results are explained in terms of two simplified models which highlight the key parameters governing the grain deformation-grain boundary cavitation interaction process.     

Physical aging in the creep behavior of thermosetting and thermoplastic composites

The creep behavior of a series of fiber-reinforced plastics (FRP) and corresponding resins has been studied, with emphasis on elucidating the role of physical aging effects on FRP viscoelastic behavior. Thermosetting and thermoplastic composites were studied, representing semicrystalline, amorphous, and highly filled amorphous polymer matrix FRPs. It was found that physical aging effects are operative for all FRPs, including the semicrystalline systems. Time/ aging-time and time/temperature superposition are found to be valid procedures for short-term creep behaviour; they cannot be applied to long-term creep behavior. However, long-term creep can be satisfactorily predicted from momentary creep by using an effective time theory. Evidence of a universal, temperature shift factor temperature dependence is presented.     

Estimating creep deformation of glass-fiber-reinforced polycarbonate

Thermoplastic resin and fiber-reinforced thermo-plastics (FRTPs) were used without post-cure treatment as “molded material.” For such materials, creep behavior and physical aging occur simultaneously. This study examined the creep behavior of polycarbonate (PC) and glass-fiber-reinforced polycarbonate (GFRPC) injection moldings, including the effect of physical aging and fiber content, and determined that the time–temperature superposition principle could be applied to the creep behavior for different fiber contents. The effects of physical aging on creep behavior were evaluated quantitatively on pure resin and with various fiber contents without heat treatment. We found that the effect of physical aging could be evaluated with the proposed factor, “aging shift rate.” To discuss the linearity of viscoelasticity in FRTPs, this study used two shift factors: time and modulus shift factors. The fiber content affected creep behavior by both retarding and restraining it through changing the elastic modulus. This was shown by generating a grand master curve of creep compliance, which included the effects of time, temperature, and fiber content. Using the grand master curve of creep compliance and shift factors, it was possible to estimate the creep deformation of molded materials under varying conditions and fiber contents. The estimated creep deformation gave a very good fit to the experimental creep deformation.     

Experimental and numerical study of creep and creep rupture behavior of PA6

Polyamide 6 (PA6) is a semi-crystalline polymer utilized in many structural components working under steady load. At room temperature, PA6 exhibits time dependent (viscoplastic) deformation. The aim of this work is to investigate the mechanical response and the crack growth of PA6 under creep conditions.The experimental database consists of tests carried out on smooth and notched round bars. Load versus displacement curves were recorded for monotonic tests tensile at various crosshead speeds. Then, creep tests at constant load were performed allowing the record of the creep strain history according to the applied load.Microscopic observations highlight the initial spherulitic structure.Smooth and notched specimens were utilized in order to identify and to validate material coefficients dedicated for analytical modeling. The non linear fracture mechanics for creeping solids was applied to results on “pre-cracked” specimens. For this kind of loading, use of the load parameter C^∗ is recommended.By plotting C^∗ values versus time to failure, a unique correlation was obtained. The knowledge of this master curve allows lifetime assessment of PA6 cracked bodies.