Plastic Creep Research Articles

A constitutive model for the accumulated strain of unsaturated soil under high‐cycle traffic loading

AbstractThe road base is normally situated above the water table and thus in unsaturated state. Experimental results show that the accumulated strains of the unsaturated road base aggregate under high‐cycle traffic loads are significantly influenced by the matric suction. To predict the accumulated strain of unsaturated road base aggregate under high‐cycle traffic loads, a constitutive model was developed based on the Barcelona Basic Model (BBM) and the shakedown concept. In this model, the shakedown and plastic creep boundaries of the aggregate under cyclic loads were supposed to exist and to have the same shape as the “static” yield surface in BBM. The strain accumulation rates were described as an exponential function of the distance between the peak cyclic stress point and the conjugated point at the current cyclic yield surface. An explicit calculation methodology was adopted to avoid large calculation errors and to improve the calculation efficiency of the model. Comparison between model predictions and testing results proved the accuracy of the proposed model, which can be used as a basic model to predict the long‐term deformation of unsaturated road base aggregate under high‐cycle traffic loads.

Effect of flame retardant on the microfine structures and creep behavior of polyester industrial yarns

The respective underlying mechanisms of the creep behavior and microstructure evolution in the creep process of an ordinary high-tenacity (HT) poly(ethylene terephthalate) (PET) industrial yarn and a flame retardant high-tenacity (FRHT) polyester industrial yarn are identified in this article. Synchrotron radiation wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS), birefringence test, FTIR were employed to investigate and compare the supramolecular, micro–nano and conformation structures of the two yarns after creep. The results showed that, under the same creep condition, the creep deformation of FRHT was larger and the creep recovery was lower than those of HT. The creep deformation of the two yarns mainly took place in amorphous region with different mechanisms, and their changes in the crystal region in terms of crystal orientation and crystallinity were slightly. HT yarns had high crystallinity and amorphous orientation, and the creep was mainly reversible elastic creep with a high-elastic recovery rate. By contrast, there was more irreversible plastic creep for FRHT yarns due to the lower initial crystallinity and amorphous orientation, which play a key role in the creep deformation.

Study of the permanent deformation of three soils employed in highway subgrades in the municipality of Santa Maria-RS, Brazil

Permanent deformation is associated with wheel track rutting (WTR) and is one of the main causes of defects in the pavements of Brazilian highways. Seeking to mitigate this situation, this paper presents a study about the permanent deformation of three typical subgrade soils of the Santa Maria region, Rio Grande do Sul (RS), located in the southern region of Brazil. In addition to the physical, chemical, and mechanical characterization of the materials, this research presents results from repeated load triaxial tests to obtain the resilient modulus (RM) and the permanent deformation (PD) parameters. The Compound model of the resilient modulus, posteriorly cited on the Petrobras Asphalt Thematic Network Project, showed the best results. The permanent deformation tests were conducted using a frequency of 2 Hz and 150,000 load application cycles and posteriorly adjusted to the Guimaraes Model, of which average statistical correlation was 0.91. However, the predominance of fine materials combined with low compaction energy resulted in high deformation rates and the occurrence of shakedown in domains: A (plastic shakedown), B (plastic creep) and C (incremental collapse).

Investigation of the deformation and strength properties of fouled graded macadam materials in heavy-haul railway subgrade beds

Over the course of long-term operation, the graded macadam materials used in heavy-haul railway subgrade bed surfaces become polluted to different degrees. This fouling is due to its own breakage, the intrusion of external coal debris, sand blasting, dust, and other foreign materials that accumulate on the ballast along with rainwater seepage, and the internal-structure mud-pumping. This study had the goal of determining the variation law for the deformation and strength characteristics of fouled graded macadam materials under cyclic loading. First, graded macadam materials with different fine particle contents were prepared, and a series of dynamic triaxial tests were carried out using a GCTS large-scale cyclic triaxial test system. These initial tests were conducted to determine the mechanism for the coupled effect of the fine particle content, confining pressure, and dynamic stress amplitude on a specimen’s accumulative plastic strain under cyclic loading. Using the plastic stability theory as a guideline, the dynamic deformation behaviours of specimens under different stress levels were determined, and a critical dynamic stress calculation model for specimens in the plastic creep state was established by considering the parameters of the confining pressure and fine particle content. Then, an accumulative plastic strain prediction model was established for specimens in the plastic creep state considering the stress level and fine particle content parameters, and a hardening index calculation model under cyclic loading was also established. At the same time, the physical significance of each parameter was clarified. Finally, a dynamic stress-strain relationship calculation model for fouled, graded macadam materials, which took into account the stiffness hardening under cyclic loading and stiffness degradation after fine particle intrusion, was constructed on the basis of a modified version of Iwan’s series–parallel model. The research results provide a reference for evaluating the health of existing heavy-haul railway subgrades and will be useful for designing new subgrade structures that take into account the comprehensive control principle of strength and deformation.

Shakedown analysis of PET blends with demolition waste as pavement base/subbase materials using experimental and neural network methods

Recycling and reusing construction and demolition (C&D) wastes for civil engineering construction activities has been identified as an energy-saving and sustainable solution. The purpose of this study is to evaluate the deformation behavior of two types of C&D waste materials, namely recycled concrete aggregate (RCA) and crushed brick (CB) when mixed with polyethylene terephthalate (PET) plastic waste. RCA and CB were mixed with 1%, 3%, 5%, and 7% of PET, and the permanent deformation behavior of the blends was evaluated using repeated load triaxial (RLT) test. The shakedown criterion was utilized for identifying the deformation behavior of blends. Most of the PET/RCA and PET/CB blends exhibited Range B (plastic creep) and Range C (incremental collapse) response, respectively, in the investigated stress levels. Shakedown analysis of the test results indicated that up to 3% PET could be mixed with RCA for base/subbase applications, while CB should be mixed with 1% PET, in the subbase layer. Artificial neural network (ANN) method was next used to simulate the permanent strain and shakedown behavior of the blends with consideration of the physical properties and stress states. The ANN model was found to be highly efficient for simulating the permanent strain graph and identifying the shakedown behavior of the blends. A sensitivity analysis was subsequently performed to investigate the impact of input variables on the permanent deformation behavior and the results indicated that number of cycles and confining stress were the most important factors.

Anisotropy of small punch creep performance of selective laser melted GH4169 at 650 °C

The large temperature gradient and the epitaxial growth of grains during selective laser melting process usually lead to the mechanical anisotropy of metal parts. To evaluate creep anisotropy of selective laser melting-fabricated GH4169 alloy, in this paper creep performance of GH4169 was investigated by means of small punch creep test method. The effect of the small punch loading-induced prestrain on creep properties of the specimens was examined. The results indicate that under the same heat-treatment and the loading conditions, the small punch creep specimens loaded along the building direction have the longer creep life and the larger creep plasticity than the ones loaded along the scanning direction. The finding reveals that loading deformation-induced dynamic recrystallization has a significant effect on improving creep properties by weakening anisotropy properly. The small punch creep properties of the specimens loaded along the building direction superior to that of the specimens loaded along the scanning direction are mainly attributed to the higher deformability of heterogeneous microstructure, the lower recrystallization activation energy and the deformation activation energy.

Investigation of tensile creep behavior of Mg–Gd–Y–Zr alloy based on creep constitutive model

The tensile creep behavior of as-extruded and T6 treated Mg–8Gd–3Y–0.3Zr (GW83) alloy was estimated under temperature at 170–200 °C and stress at 40–70 MPa. The results showed that the primary creep strain and steady state creep rate increased, while the duration of steady state creep decreased with increasing temperature and stress. The primary creep constitutive model of GW83 alloy kept an Andrade power law ε = βt k with k value of 0.24–0.6 for as-extruded alloy and 0.13–0.49 for T6 alloy, respectively. The steady state creep plastic deformation of as-extruded and T6 state alloys can be expressed by Arrhenius constitutive equations with stress exponents 5.6–5.9 and 8.9–9.8, creep activity energy 124.9–135.6 kJ/mol and 152.2–195.8 kJ/mol, respectively. The tensile creep resistance of GW83 alloy improved significantly by T6 heat treatment, the effect of temperature on steady state creep rate was relatively moderate, and the tensile creep plastic deformation of GW83 alloy mainly was controlled by applied stress. The steady state creep deformation mechanism of as-extruded GW83 alloy was regulated by Mg self-diffusion conducted by dislocation climb before heat treatment, and then transformed to dislocation cross-slip after T6 treated. The recrystallization and texture evolution of (10) , (10) played a non-ignorable effect on the tensile creep deformation. The creep rupture life can be predicted by steady state creep rate that will be controlled by temperature under low and intermediate stress and by stress under larger applied stress, respectively. The creep fracture surfaces with coarse dimples and tear ridges presented as ductile transgranular fracture features with the secondary cracks occurred.

Damage based PoF model of solder joints under temperature cycling and electric coupling condition

To predict the life of solder joints under temperature cycling and electric coupling condition, this paper proposes a Physics of Failure (PoF) model based on the continuum damage mechanics (CDM). Firstly, considering the effect of current on solder's mechanical properties, the current-affected constitutive models of plastic fatigue and creep are constructed. Then, based on the mechanism of energy dissipation, a unified creep-plasticity damage evolution law is deduced, and the nonlinear accumulation damage model is developed. Choosing electric resistance as the indirect damage variable measure, the thermal-electric coupling PoF model is finally established by substituting the current-affected constitutive models into the damage evolution model. A thermal-electric coupling test is carried out to verify the accuracy of PoF model. The experimental results confirm that the proposed PoF model can effectively predict the life of solder joints under temperature cycling and electric coupling condition.

Numerical analysis of the effect of residual stress on transient creep in SENB specimen

Many manufacturing processes can induce residual stresses in produced components for high-temperature application. Residual stresses, combined with the primary mechanical stresses, play an important role in structural integrity assessments of high-temperature components. In this paper the elastic and elastic-plastic creep behaviour of mechanically loaded shallow cracked SENB specimen in the presence of residual stress has been analyzed. The transient crack tip parameter under creep conditions, C(t), has been numerically determined at different primary mechanical stress and residual stress levels. The analysis was performed for general material properties where different plastic and creep stress exponents were systematically varied. Based on the performed analyzes, the expressions for relaxation curves of C(t) for the considered elastic creep and elastic plastic creep cases are proposed. These expressions show good agreement with the results of the numerical analysis conducted for the arbitrarily selected input data, which gives confidence in their reliable application for estimating the C(t) values of shallow cracked SENB speciemens.

Revealing the Plastic Mode of Time-Dependent Deformation of a LiTaO3 Single Crystal by Nanoindentation.

Recently, instrumental nanoindentation has been widely applied to detect time-dependent plastic deformation or creep behavior in numerous materials, particularly thin films and heterogeneous materials. However, deformation mechanism at nanoindentation holding stage has not been well revealed hitherto. In the current work, nanoindentation holding tests with high loads were performed on a brittle LiTaO3 single crystal. The surface morphologies of residual impressions with various holding times were investigated. It was indicated that generation of secondary cracks and propagation of both main and secondary cracks were the dominating mechanism for time-dependent plastic deformation at the initial holding stage, and the density and length of cracks were invariable at the steady-state holding stage, which suggested a nonlocalized plastic deformation beneath the indenter. It could be concluded that time-dependent plastic deformation of brittle ceramic under nanoindentation is composed of instant cracking as the continuation of loading sequence and homogeneous creep flow by high shear-compression stress at room temperature.

Vortex dynamics and phase diagram in the electron-doped cuprate superconductor Pr0.87LaCe0.13CuO4

Second magnetization peak (SMP) in hole-doped cuprates and iron pnictide superconductors has been widely explored. However, similar feature in the family of electron-doped cuprates is not common. Here, we report the vortex dynamics study in the single crystal of an electron-doped cuprate Pr$_{0.87}$LaCe$_{0.13}$CuO$_4$ superconductor using dc magnetization measurements. A SMP feature in the isothermal $M(H)$ was observed for $H$$\parallel$$ab$-planes. On the other hand, no such feature was observed for $H$$\parallel$$c$-axis in the crystal. Using magnetic relaxation data, a detailed analysis of activation pinning energy via collective creep theory suggests an elastic to plastic creep crossover across the SMP. Moreover, for $H$$\parallel$$ab$, a peak in the temperature dependence of critical current density is also observed near 7 K, which is likely be related to a dimensional crossover (3D-2D) associated to the emergence of Josephson vortices at low temperatures. The anisotropy parameter obtained $\gamma$ $\approx$ 8-11 indicates the 3D nature of vortex lattice mainly for $H$$\parallel$$c$-axis. The $H$-$T$ phase diagrams for $H$$\parallel$$c$ and $H$$\parallel$$ab$ are presented.

Structural evolutions during creep deformation of polyester industrial fiber via in situ synchrotron small-angle X-ray scattering/wide-angle X-ray scattering

This paper aims to identify the creep mechanisms of high tenacity (HT) polyester industrial fiber under different loads. In-situ synchrotron small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) tests were conducted on a 1000 D HT fiber during the creep and creep recovery process with a low load (15 N) and a medium load (50 N) as well as creep rupture process with a high load (60 N). The measured creep strain-time curves comprised tensile zone (I), creep deformation zone (II) and creep recovery/rupture zone (III). The SAXS indicated that the macroscopic initial creep strain in zone I and creep deformations in zone II were attributed to conformation transition from gauche to trans in amorphous region, increasing the amorphous orientation and long period. Irreversible portion of conformation changes accounts for the small unrecoverable plastic creep strain after removing 15 N load in zone III. The initial creep strain in zone I and creep deformations in zone II of the 50 N creep process were bigger than the microscopic long period strain, because amorphous layers had conformational transformation and microfibril slippage which also produced a higher unrecoverable plastic creep strain in zone III. The long period increased significantly at the beginning of rupture zone with 60 N due to fragmentation of amorphous tie molecular. The disappearance of lamellar peaks at the end of rupture zone implied destruction of periodic lamellar structures, for the entire breakage of amorphous chains. The WAXS suggested that the crystal structure was stable under the creep loads.

Kinetics of the Lattice Response to Hydrogen Absorption in Thin Pd and CoPd Films

Hydrogen can penetrate reversibly a number of metals, occupy the interstitial sites and cause large expansion of the crystal lattice. The question discussed here is whether the kinetics of the structural response matches hydrogen absorption. We show that thin Pd and CoPd films exposed to a relatively rich hydrogen atmosphere (4% H2) inflate irreversibly, demonstrate the controllable shape memory, and duration of the process can be of orders of magnitude longer than hydrogen absorption. The dynamics of the out-of-equilibrium plastic creep are well described by the Avrami-type model of the nucleation and lateral domain wall expansion of the swelled sites.

Nanoindentation Study on the Creep Characteristics and Hardness of Ion-Irradiated Alloys.

The Hastelloy N alloy, Alloy 800H and 316H stainless steel were irradiated by Xe20+ ion irradiation with energy of 4 MeV at room temperature (peak damage ranging from 0.5 to 10 dpa). The micromechanical properties, hardness and creep plasticity, of these three investigated alloys were characterized before and after irradiation using nanoindentation. The results show that the hardness increases, and creep plasticity degrades with increasing ion dose in all the samples. In comparison, Hastelloy N has good irradiation damage resistance, while that of the 800H and 316H alloys is slightly worse. Additionally, the approximate positive relationship between irradiation hardening and creep plasticity degradation means that the property of creep plasticity of irradiated materials can be reflected from the nanohardness measurement for the heavy ion irradiation cases.

Modelling the cleaning of viscoplastic layers by impinging coherent turbulent water jets

Impinging liquid jets are widely used to clean unwanted soil layers from the walls of structures and vessels. When the soil is a thin layer of an immiscible viscoplastic material, removal involves the growth of a cleared area (which is circular for a jet impinging normally) bounded by a berm of displaced material. Glover et al. [1] presented a semi-empirical model relating the rate of removal to the momentum flow rate in the liquid film. We present a first-order model for cleaning thin layers of these materials based on the rate of viscous dissipation in a shallow wedge of material at the cleaning front. This yields a result of the form of the model in [1], with expressions linking the kinetic parameters to measurable quantities including the rheology of the soil. The fully coupled problem is not solved: the wedge angle and residual layer thickness need to be specified and were obtained here by fitting to the data. The model is compared with experimental results obtained for three soft solids – two petroleum jellies and a soft paraffin – which exhibited Bingham plastic behaviour and creep, for jet Reynolds numbers between 10,000-37,000, and 0.1<h¯/δo<1.5, where h¯ is the average film depth and δo the layer thickness. The data show reasonable agreement with the model.

Investigation on the deformation behavior of open-graded unbound granular materials for permeable pavement

Permeable pavement has many advantages on environment and has been applied in various fields. However, the performance of the base layer of permeable pavement in the field of heavy loads has not attracted enough attention. This paper explorted the deformation behavior of open-graded unbound granular materials (UGMs) for base layers of permeable pavement under repeated triaxial loading. The deformation behavior explored in this study included both resilient deformation and permanent deformation. Firstly, the resilient modulus of different gradations with different ranges of particle size was studied. The results indicated that the open-graded UGMs had enough resilient modulus ranging from 110 to 371 MPa. The different gradations at various levels of stress under dry and wet conditions were studied to simulate different work conditions of base layer for permeable pavement. The results showed that porosity, particle size, stress level and moisture had great impact on permanent deformation. In addition, stress level represented by the shear stress/strength ratio (SSR) was introduced into the permanent deformation characterization, and the results suggested that the permanent deformation under the stress level of SSR value within 0.4 belonged to the plastic creep, which was acceptable permanent deformation in the pavement design. Therefore, this study concluded that, compared with traditional UGMs, open-graded UGMs may also meet the bearing capacity requirement for base materials under wet condition.

Long-term dynamic behavior of a sandy subgrade reinforced by Waste Tire Textile Fibers (WTTFs)

Soil improvement by incorporating different reinforcement materials has been one of the most popular fields of study in geotechnical engineering since it can provide the engineers with a practical and relatively easy solution when dealing with various construction projects. Despite numerous studies carried out on the static behavior of reinforced soils, the dynamic characteristics of these mixtures have not been fully understood. Therefore, this paper aims to shed light upon this issue by conducting repeated loading triaxial tests on a sandy soil reinforced by different Waste Tire Textile Fiber (WTTF) contents. Various parameters such as permanent strain, resilient modulus, energy dissipation capacity, and damping ratio were investigated. The results of this study show that permanent strain is increased as a result of fiber addition. Nevertheless, rutting is not expected to occur since all soil-fiber mixtures are categorized in groups A (plastic shakedown) and B (plastic creep) of shakedown theory. Resilient modulus is increased up to 744% with an optimum WTTF content of 2%. Dissipated energy and damping ratio are also found to increase as a result of fiber inclusion. Furthermore, a new model is proposed to accurately predict the resilient modulus in terms of the number of cycles and fiber content.

Resilient and permanent deformation of unsaturated unbound granular materials under cyclic loading by the large-scale triaxial tests

The road base and subbase are normally situated above the underground water table and thus in the unsaturated state. To study the cyclic behavior of unbound granular materials (UGMs) in the road base and subbase courses under controlled matric suction conditions, a series of cyclic tests on the unsaturated UGMs were conducted by the large-scale triaxial apparatus. The large-scale triaxial apparatus was upgraded using an unsaturated module to control the matric suction by the axis-translation technique. Emphases were placed on the effects of matric suction and cyclic stress amplitude on the accumulated axial strain and resilient modulus of UGMs. Test results showed that the increase in matric suction reduced the development of accumulated axial strain exponentially under different cyclic stress amplitudes. Based on the shakedown theory, both the plastic shakedown and plastic creep limits were determined, which tended to grow linearly with the increase in matric suction. A new empirical model was proposed to predict the accumulated axial strain of unsaturated UGMs. Moreover, the increase in both matric suction and cyclic stress amplitude led to the increase in resilient modulus, and linear relationships existed between the resilient modulus and matric suction.

Effect of tungsten on creep properties of martensitic 9Cr steel

The effects of tungsten on the creep behavior and microstructure of tempered martensite 9Cr steel with different W concentrations ranging from 0–2.5 wt% were studied. The matrix consisted of tempered lath martensite structure and M23C6 located along the grain boundary or inside the grain. As the W concentration increased, the number of M23C6 increased while the particle size decreased. Also, with the increasing W concentration, the minimum creep rate and elongation decreased while the time to rupture increased. The rise in W concentration led to the refinement of M23C6, which enhanced the creep strength but reduced the creep plasticity.

Experimental study on thermo-mechanical deformation of PHWR channel at elevated temperature

The severe accidents in PHWR type reactors are less probabilistic events owing to extensive safety features, but the consequences of these accidents are serious if not mitigated. Severe accidents progress with the channel deformation due to thermal load, internal pressure and weight of its components. Channel’s sagging behaviour and its failure will define the accident progression under the event of low-pressure inside the channel. Sagging deformation determines the nature of early debris or suspended debris formation. Also, sagging of channel results in the pull-out force on the Calandria end-shield. Therefore, it becomes imperative to know the nature of the event in order to provide any mitigating countermeasures.The present paper aims to study the sagging of coolant channels of standard 220 MWe Indian PHWR under the hypothesis of postulated severe accidents with large break LOCA and loss of ECCS as an initiating event. The moderator cooling system is postulated as impaired with no make-up system. It is difficult to perform a full-scale channel sagging experiments in laboratory. Hence, a novel scale-down approach (1:3) has been adopted for laboratory experiments for the channel sagging study.Experiments have indicated a significant initial sagging with sudden power ramp. The sagging of channel was significant as the temperature of CT reached to 460 °C. The pull-force was not dominant during the transient heat-up, but significant pull or end-load has been observed at the end of the channel cooling. The rate-dependent plasticity (creep) is found to be a dominating mechanism for sagging of the channel.