Temperature and stress–regime dependent primary–secondary–tertiary creep constitutive model

Abstract

High temperature deformation analysis of components such as steam turbine rotors requires a knowledge of the material deformation response for a wide range of stresses and temperatures. Deformation analysis of steam turbine rotors deals with stresses ranging above the material proof strength (shortly after plant start-up) down to those responsible for very long rupture durations (for the steady running phase of operation) at various temperatures. This study describes the construction of a temperature and stress–regime dependent (primary–secondary–tertiary) creep constitutive model to provide a more reliable representation for the material deformation response over wide ranges of stresses and temperatures. The adopted equation set is a refinement of the ‘Characteristic Strain’ model and depends in its formulation mainly upon creep rupture data. Successful application of the model for a 1CrMoV steel for a wide range of stresses over the temperature range of 450–675°C is demonstrated.     

A non-local fractional stress–strain gradient theory

International Journal of Mechanics and Materials in Design - A generalized non-local stress–strain gradient theory is presented using fractional calculus. The proposed theory includes as a...     

Application of time–temperature–stress superposition on creep of wood–plastic composites

Time–temperature–stress superposition principle (TTSSP) was widely applied in studies of viscoelastic properties of materials. It involves shifting curves at various conditions to construct master curves. To extend the application of this principle, a temperature–stress hybrid shift factor and a modified Williams–Landel–Ferry (WLF) equation that incorporated variables of stress and temperature for the shift factor fitting were studied. A wood–plastic composite (WPC) was selected as the test subject to conduct a series of short-term creep tests. The results indicate that the WPC were rheologically simple materials and merely a horizontal shift was needed for the time–temperature superposition, whereas vertical shifting would be needed for time–stress superposition. The shift factor was independent of the stress for horizontal shifts in time–temperature superposition. In addition, the temperature- and stress-shift factors used to construct master curves were well fitted with the WLF equation. Furthermore, the parameters of the modified WLF equation were also successfully calibrated. The application of this method and equation can be extended to curve shifting that involves the effects of both temperature and stress simultaneously.     

Cyclic stress–strain characteristics of two microalloyed steels

Abstract

The cyclic stress–strain behaviour of two microalloyed steels with different microstructures has been characterised at room temperature under strain controlled low cycle fatigue. The cyclic stress–strain curve in the double logarithmic plot shows a linear relation for both steels. A transition of the cyclic stress–strain curve from softening to hardening with increasing strain amplitude has been observed with respect to the corresponding tensile curve. The strain amplitude for the onset of cyclic softening to hardening transition has been found to be dependent on grain size. The strain lifetime behaviour, estimated from modified universal slopes equation, shows similar trends as Nb or V bearing microalloyed steels. The cyclic characteristics of the two microalloyed steels have been compared with corresponding predeformed state carried out under stress controlled conditions. While, cyclic saturation was observed in case where the extent of predeformation was within the Lüders strain, cyclic softening occurred when it exceeded the Lüders strain. It has been attempted to provide a mechanistic understanding of the differences in the cyclic behaviour of the two steels owing to the microstructure and predeformation.     

Numerical calculations of residual–stress relaxation in quenched plates

Abstract

Methods of thermal stress relief such as stretching and compression are compared for different thermal and mechanical properties during quenching. The heat equation for a simple geometric model, such as an infinite plate, is solved with an experimental surface conductance and a step–by–step method of determining the temperature field in the thickness of the plate. This field is introduced as data for the uncoupled thermal elastic–plastic model for quenching. In the calculation of the plastic–strain path, the thermal and mechanical properties are considered as temperature dependent for a homogeneous and isotropic material. Good agreement is found between the calculated residual stresses and experimental values for an aluminium alloy and a stainless steel. The predicted residual–stress distributions and strain history are then used as data for the numerical simulation of stress–relief methods with an incremental integration of the Prandtl–Reuss equation. This analysis allows the observation of the effects of small variations in mechanical properties during quenching on the residual–stress field after mechanical stress relief and the theoretical comparison of different processes.

MST/6     

Description of stress–strain curves for stainless steel alloys

There is a wide variety of stainless steel alloys, but all are characterized by a rounded stress–strain response with no sharply defined yield point. This behaviour can be represented analytically by different material models, the most popular of which are based on the Ramberg–Osgood formulations or extensions thereof. The degree of roundedness, the level of strain hardening, the strain at ultimate stress and the ductility at fracture of the material all vary between grades, and need to be suitably captured for an accurate representation of the material to be achieved. The aim of the present study is to provide values and predictive expressions for the key parameters in existing stainless steel material models based on the analysis of a comprehensive experimental database. The database comprises experimental stress–strain curves collected from the literature, supplemented by some tensile tests on austenitic, ferritic and duplex stainless steel coupons conducted herein. It covers a range of stainless steel alloys, annealed and cold-worked material, and data from the rolling and transverse directions. In total, more than 600 measured stress–strain curves have been collected from 15 international research groups. Each curve from the database has been analysed in order to obtain the key material parameters through a curve fitting process based on least squares adjustment techniques. These parameter values have been compared to those calculated from existing predictive models, the accuracy of which could therefore be evaluated. Revised expressions providing more accurate parameter predictions have been proposed where necessary. Finally, a second set of results, containing material parameters reported directly by others, with information of more than 400 specimens, has also been collected from the literature. Although these experimental results were not accessible as measured raw data, they enabled further confirmation of the suitability of the proposed equations.     

Operator matrix and non-uniqueness of Beltrami–Schaefer stress functions

Beltrami–Schaefer stress functions are general solutions of the equilibrium equations of an elastic body without body force. In this paper, the representation of the non-uniqueness of these solutions is deduced by converting the equations into operator matrix form—including an operator matrix and its generalized inverse—and then deriving the representation using linear algebra. The completeness of the representation is proved in the process. In addition, the non-uniqueness of Helmholtz’s decomposition of a vector is proved.     

Compressive stress–strain behavior of steel fiber reinforced-recycled aggregate concrete

The use of recycled aggregate from construction and demolition waste (CDW) as replacement of fine and coarse natural aggregate has increased in recent years in order to reduce the high consumption of natural resources by the civil construction sector. In this work, an experimental investigation was carried out to investigate the influence of steel fiber reinforcement on the stress–strain behavior of concrete made with CDW aggregates. In addition, the flexural strength and splitting tensile strength of the mixtures were also determined. Natural coarse and fine aggregates were replaced by recycled coarse aggregate (RCA) and recycled fine aggregate (RFA) at two levels, 0% and 25%, by volume. Hooked end steel fibers with 35 mm of length and aspect ratio of 65 were used as reinforcement in a volume fraction of 0.75%. The research results show that the addition of steel fiber and recycled aggregate increased the mechanical strength and modified the fracture process relative to that of the reference concrete. The stress–strain behavior of recycled aggregate concrete was affected by the recycled aggregate and presented a more brittle behavior than the reference one. With the addition of steel fiber the toughness, measured by the slope of the descending branch of the stress–strain curve, of the recycled concretes was increased and their behavior under compression becomes similar to that of the fiber-reinforced natural aggregate concrete.     

Strength and stress–strain characteristics of traditional adobe block and masonry

Traditional unstabilized adobe low-rise buildings are common in many Chinese small towns and villages. This paper presents a study on the uniaxial compressive strength and stress–strain behavior of traditional unstabilized adobe blocks and masonry prisms with various compositions. The adobe blocks were manually produced by Chinese traditional technique in various proportions of natural soil and sand. The influence of various proportions on unconfined compressive strength, dry density and initial tangent modulus are discussed. Following this, soil mortars in three different proportions were used to construct adobe masonry prisms, with the purposes of understanding the influence of mortar strength to block strength ratio on compressive strength and stress–strain characteristics. The result shows that the compressive strength, initial tangent modulus and Poisson’s ratio of prism are influenced by the ratio of mortar strength to block strength. In addition, tangent modulus and Poisson’s ratio increase with the ratio of stress to peak strength. It was also found that although coefficients of variation of experimental results are reduced by load–unload cycles, peak strains are largely increased.     

Determination of biaxial stress–strain diagram for gas pressure superplastic forming

Abstract

The success of a gas pressure superplastic forming operation depends on accurate formulation of a pressure–time diagram which in turn needs an accurate stress–strain relationship evaluated preferably under multiaxial or biaxial conditions. The present analysis describes a technique of generating such curves from gas pressure cone forming tests and subsequent manipulation of the data. The method also includes an innovative technique of online monitoring of strain during the forming process by measuring the volume of displaced air from the die during progress of forming.     

Determination of residual stress within complex-shaped coarse-grained cobalt–chromium biomedical castings

Cast ASTM F75 femoral knee implant components distort during manufacture due to residual stress re-distribution or inducement. These castings pose a number of challenges for residual stress determination methods; they have a complex geometry, their microstructure is inhomogeneous, they work-harden rapidly and they have a coarse, elastically anisotropic grain structure. The contour method is anticipated to be the most promising residual stress determination technique. X-ray diffraction is feasible for components which have experienced plastic deformation on their surface which results in refined diffracting domains. Centre-hole drilling is feasible, but the influence of stress induced from drilling and the effect of coarse grain structure is unknown. Neutron diffraction is challenging also due to a coarse grain structure and difficult nuclear material properties.

This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.     

Thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections under different stress levels

In our previous study, the creep behavior of the lead-free Sn–Ag–Cu–Bi solder joints has been proven to follow the Arrhenius power-law relationship, and the thermal fatigue behavior of the solder joints exhibits the typical creep deformation characteristics with a superposition of the pulsating features. In this study, the thermal creep and fracture behaviors of the lead-free Sn–Ag–Cu–Bi solder interconnections were characterized under different stress levels, with a systematical comparison to that of a traditional Sn60Pb40 near-eutectic solder. The results show that the creep strain rate of both solder connections follows Weertman-Dorn equation, and the calculated creep stress exponent for two solders is reasonably close to other published data. The SEM inspection and analysis of fractographies of creep fractured solder joints manifest that the creep failure of the lead-free Sn–Ag–Cu–Bi solder joint shows obviously intergranular fracture mechanism, while the Sn60Pb40 joint ruptures dominantly by a transgranular sliding mechanism.     

Changes of flow stress and microstructure during hot deformation of Al–1Mg–1Mn

Abstract

Plane strain compression tests have been carried out at strain rates between 0·5 and 10 s^?1 and temperatures in the range 275–510°C, both under nominally isothermal conditions and with temperature decreasing. Also, temperature or strain rate have been changed in the interval between two deformations. In all cases, the stress–strain curves obeyed a mechanical equation of state, described by constitutive relationships in terms of strain and instantaneous value of Zener–Hollomon parameter Z. When the value of Z varies slowly during deformation, flow stress is uniquely related to subgrain size and to dislocation density within subgrains, but these relationships break down in transition structures developed after a change of Z between two deformations. The existence of an equation of state for mechanical behaviour, but not for microstructure, is considered to result from important contributions of both dislocation velocity and density to hot strength.

MST/1066     

Interpretation of creep behaviour of a 9Cr–Mo–Nb–V–N (T91) steel using threshold stress concept

Abstract

The creep behaviour and the microstructural evolution of a 9Cr–Mo–Nb–V (T91) steel were extensively evaluated by means of short term constant load creep tests and TEM analysis. Statistical analysis of the microstructural data revealed that the precipitated phases M₂₃ C₆ (where M is a metal, mainly Cr or Fe) and MX (where M is Nb or V, and X is C and/or N) were subject to coarsening during creep exposure. The coarsening law and its dependence on applied stress were identified, and the model was used to predict the magnitude of the Orowan stress at the time corresponding to the minimum creep rate. The minimum creep rate dependence on applied stress at 873 K was described by incorporating the threshold stress concept in a power law with stress exponent n = 5. In the resulting phenomenological model, the strengthening effect of the dispersed phases was thus expressed by a threshold stress proportional to the Orowan stress.     

Flexural creep behavior of discontinuous thermoplastic composites: Non-linear viscoelastic modeling and time–temperature–stress superposition

Flexural creep behavior of nylon 6/6, polypropylene and high-density polyethylene long fiber thermoplastic (LFT) composites was studied according to ASTM D-2990. Neat polymers were tested for baseline data and compared with the 40 wt.% E-glass reinforced LFTs, all processed by compression molding. All materials exhibited non-linear viscoelasticity and showed a succession in creep resistance consistent with static flexural yield strength. A four parameter empirical model used for short fiber thermoplastics (SFT), proposed by Hadid et al., was found to provide an excellent fit to the experimental data. Time-compliance data from flexural creep and dynamic mechanical analysis (DMA) were combined to utilize short-term flexural creep tests to predict lifetime of the composites. A time–temperature–stress superposition (TTSSP) procedure was used, where stress-based vertical shifts were applied in addition to horizontal shifts used in a traditional time–temperature superposition (TTSP). Master curves obtained by this method projected the long-term creep properties, the order of creep resistance being consistent with the flexural creep data.     

Overall stress–strain relationship of cold rolled transformation induced plasticity multiphase steels

Abstract

As a result of transformation induced plasticity, TRIP assisted steels possess favourable mechanical properties such as high strength, ductility and toughness. In the present work, the flow stress of a cold rolled TRIP multiphase steel has been calculated from the stress of individual constituent phases on the basis of a continuum model whereby the internal stress produced by the inhomogeneous distribution of plastic strain is considered. For the first time, account is taken of how the volume fraction of constituent phases changes with strain. A comparison of stress–strain curves determined from the model and experimentally derived stress–strain curves for an Si–Mn type TRIP800 steel gives satisfactory agreement. Variation of the strain hardening exponent of the TRIP steel with strain is also discussed.     

Hydrogen-induced intergranular stress corrosion cracking (HI-IGSCC) of 0.35C–3.5Ni–1.5Cr–0.5Mo steel fastener

This paper brings a failure case study of high strength 0.35C–3.5Ni–1.5Cr–0.5Mo steel fastener, which failed due to hydrogen-induced intergranular stress corrosion cracking (HI-IGSCC). 0.35C–3.5Ni–1.5Cr–0.5Mo steel in hardened and tempered condition, meeting the specified axial tensile stress rating of 1250 MPa is widely used as fasteners in space programmes.In the course of assembly of the structural parts of a satellite launch vehicle, 10 nos of fasteners developed cracks on tightening using a torque wrench set to 6 N m torque surprisingly.Also some fasteners, which were under assembly load of more than 6 months in the same vehicle assembly, were found to be cracked.The failure was attributed to hydrogen-induced intergranular stress corrosion cracking (HI-IGSCC). The details of the analysis and mechanism involved in the HI-IGSCC are presented in detail.Detailed metallurgical analyses of the cracked fasteners support the successive steps of the corrosion enhanced plasticity model, which is based on a local softening in the SCC crack region. The mechanism of a dislocation pileup ahead of a crack under corrosion and stress due to diffusing hydrogen promotes stress concentration against micro-obstacle and caused failure.     

Strained coherent interface energy of the Guinier–Preston II phase in Al–Cu during stress aging

θ″-phase, with a formal stoichiometry of Al₃Cu, is a coherent, metastable precipitate (GP-II) phase commonly found in Al-based aerospace alloys. In this paper, we employed a first-principles based method to study the energetics of the Al/θ″ interface as response to external strains. The potential effects of temperature, Cu activity, and different strain modes on interface energy (γ _Al/θ″) were systematically investigated. Calculations show that (i) an unstrained γ _Al/θ″ always increases with temperature: as temperature increases from T = 298 to 498 K, γ _Al/θ″ increases by ~9.0 %; (ii) γ _Al/θ″ is more sensitive to compressive strains than to tensile strains of the same magnitude. In particular, for a parallel compressive strain increasing from 0 to 2 % at a typical aging temperature, γ _Al/θ″ decreases by ~6.6 %, while a vertical compressive strain of 2 % has a slightly stronger impact by decreasing γ _Al/θ″ by ~9.6 %. Different influences of applied strain/stress on the formation energies of different orientated interfaces can be further exaggerated by the Poisson effect, and eventually affect the preferential precipitation orientation of θ″ in the matrix.     

Analysis-oriented stress–strain model of CRFP-confined circular concrete columns with applied preload

The compressive behavior of FRP-confined concrete is a current issue in the field of structural retrofitting. The available models well predict the stress–strain behavior under monotonic and cyclic loads. However, in the practical applications, columns that need an increasing of bearing capacity are often strengthened under serviceability load conditions, with a stress and strain state that could change the response of the reinforced systems with respect to the case of the unloaded state. In this paper, the compressive behavior of circular FRP-confined concrete columns with preload is analyzed with the introduction of a modified analysis-oriented model. Differently from the classical formulations in which stress–strain model is aimed to the evaluation of the confinement capacity of non-preloaded elements in monotonic regime, the proposed model is also suitable for the determination of the combined response of unconfined and confined concrete subjected to an established stress/strain state in the unconfined state. The proposed model is also compared with the experimental results available in the literature under different assigned preloading levels.