Time-dependent Deformation Behavior Research Articles

A theoretical framework for multi-physics modeling of poro-visco-hyperelasticity-induced time-dependent fracture of blood clots

Fracture resistance of blood clots plays a crucial role in physiological hemostasis and pathological thromboembolism. Although recent experimental and computational studies uncovered the poro-viscoelastic property of blood clots and its connection to the time-dependent deformation behavior, the effect of these physical processes on clot fracture and the underlying fracture mechanisms are not well understood. This work aims to formulate a thermodynamically consistent, multi-physics theoretical framework for describing the time-dependent deformation and fracture of blood clots. This theory concurrently couples fluid transport through porous fibrin networks, non-linear visco-hyperelastic deformation of the solid skeleton, solid-fluid interactions, mechanical degradation of tissues, gradient enhancement of energy, and protein unfolding of fibrin molecules. The constitutive relations of tissue constituents and the governing equation of fluid transport are derived within the framework of porous media theory by extending non-linear continuum thermodynamics at large strains. A physics-based, compressible network model is developed for the fibrin network of blood clots to describe its mechanical response. The kinetic equations of the internal variables, introduced for describing the non-linear viscoelastic deformation, non-local damage driving force and protein unfolding, are formulated according to the thermodynamics principles by incorporating a non-equilibrium energy of fibrin networks, a gradient-enhanced energy, and a stretch-induced energy of fibrin molecules, respectively, into the total free energy density function. An energy-based damage model is developed to predict the damage and fracture of blood clots, and an evolving regularization parameter is proposed to limit the damage zone bandwidth. The proposed model is implemented into finite element code by writing subroutines and is experimentally validated using single-edge cracked clot specimens with different constituents. The fracture of blood clots subject to different loading conditions is simulated, and the mechanisms of clot fracture are systematically analyzed. Computational results show that this model can accurately capture the experimentally measured deformation and fracture. The viscoelasticity and fluid transport play essential roles in the fracture of blood clots under physiological loading.

A unique time-dependent deformation behavior of coral reef limestone

Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short-to long-term load. Due to the complexity of biological structures, the underlying micro-behaviors involving time-dependent deformation are poorly understood. For this, an abnormal phenomenon was observed where the axial and lateral creep deformations were mutually independent by a series of triaxial tests under constant stress and strain rate conditions. The significantly large lateral creep deformation implies that the creep process cannot be described in continuum mechanics regime. Herein, it is hypothesized that sliding mechanism of crystal cleavages dominates the lateral creep deformation in coral reef limestone. Then, approaches of polarizing microscope (PM) and scanning electronic microscope (SEM) are utilized to validate the hypothesis. It shows that the sliding behavior of crystal cleavages combats with conventional creep micro-mechanisms at certain condition. The former is sensitive to time and strain rate, and is merely activated in the creep regime.

Fractional cyclic cohesive zone model for time-dependent fatigue behavior of soft adhesives under mode-II loading

Soft adhesives exhibit nonlinear viscoelastic behavior during cyclic loading, suggesting that their cycle-dependent fatigue behavior can be significantly affected by the time-dependent deformation behavior. Soft adhesives are frequently subject to various cyclic conditions in practical applications, presenting potential safety risks. This paper has proposed a fractional cyclic cohesive zone model (CZM) to characterize the time-dependent fatigue behavior of soft adhesives. To capture the nonlinear evolution of fatigue damage under asymmetric stress-controlled cyclic loading, a fatigue damage model that considers the contribution of in-situ stress/strain was incorporated into fractional-order viscoelastic model. The proposed CZM was validated through single-lap shear creep tests at various stress levels and fatigue tests at various stress amplitudes and loading periods. Furthermore, the impacts of stress ratio and peak stress level on fatigue failure under different loading periods were investigated using the proposed CZM. The results indicate that under a short loading period, the failure of the soft adhesives is primarily influenced by cycle-dependent fatigue damage, while under a long loading period, it is primarily affected by time-dependent creep deformation. Overall, this work offers a numerical strategy to describe the fatigue failure of nonlinear viscoelastic soft adhesives and to understand their time-dependent fatigue failure mechanism, with implications for product design and optimization.

Mechanically rejuvenated glassy polylactide with spatial heterogeneity and packing efficiency: Time dependence of deformation behavior

Mechanical rejuvenation is effective in conquering the physical aging of polymers, but its molecular origin is far from clear. Herein, glassy polylactide is subjected to mechanical rejuvenation under extensional stress field via “casting-thermal stretching”, and the joint effect of spatial heterogeneity and packing efficiency on the brittle-to-ductile transition is demonstrated. The extensional stress accelerates segmental relaxation and heavily enhances the spatial heterogeneity in activated amorphous fraction. The much larger extensional stress enhances the orientation and packing efficiency of polylactide chains, with the close-packing amorphous fraction restraining the molecular mobility but boosting self-reinforcement. Strong time-dependent deformation behavior is discovered in rejuvenated polylactide, with different draw ratios exhibiting quite different critical strain rates of ductile-to-brittle transition, and that with densified network even maintains high ductility at extremely high strain rate. This work provides new insights into mechanical rejuvenation and significant guidance for the processing of advanced biodegradable polymers.

Discrepancy in ductility improvement in repeated stress relaxation of AA7075

The stress relaxation test is a commonly used transient test to determine the deformation kinetics during plastic deformation. This study reports the time-dependent deformation behavior of AA7075 alloy under different temper conditions. The deformation parameters, such as the apparent and true activation volume were estimated using single and repeated stress relaxation tests respectively. The results indicate that dislocation–dislocation interaction plays a critical role in the deformation behavior of the solution-treated condition, whereas dislocation–precipitate interaction dominates in the aged specimens. Additionally, the study found that single stress relaxation enhances the ductility of the deforming specimen, regardless of the temper condition. The ductility during repeated relaxation however had negative effects in aged samples. The possible mechanisms responsible for this discrepancy are discussed, providing a comprehensive overview of the time-dependent deformation behavior of AA7075 alloy.

Nanoindentation creep of supercrystalline nanocomposites

Supercrystalline nanocomposites (SCNCs) are inorganic-organic hybrid materials with a unique periodic nanostructure, and thus they have been gaining growing attention for their intriguing functional properties and parallelisms with hierarchical biomaterials. Their mechanical behavior remains, however, poorly understood, even though its understanding and control are important to allow SCNCs’ implementation into devices. An important aspect that has not been tackled yet is their time-dependent deformation behavior, which is nevertheless expected to play an important role in materials containing such a distribution of organic phase. Hereby, we report on the creep of ceramic-organic SCNCs with varying degrees of organic crosslinking, as assessed via nanoindentation. Creep strains and their partial recoverability are observed, hinting at the co-presence of viscoelasticity and viscoplasticity, and a clear effect of crosslinking in decreasing the overall material deformability emerges. We rationalize our experimental observations with the analysis of stress exponent and activation volume, resulting in a power-law breakdown behavior and governing deformation mechanisms occurring at the organic sub-nm interfaces scale, as rearrangement of organic ligands. The set of results is reinforced by the evaluation of the strain rate sensitivity via strain rate jump tests, and the assessment of the effect of oscillations during continuous stiffness measurement mode.

A Constitutive Model of Time-Dependent Deformation Behavior for Sandstone

Considering sandstone's heterogeneity in the mesoscale and homogeneity in the macroscale, it is very difficult to describe its time-dependent behavior under stress. The mesoscale heterogeneity can affect the initiation and propagation of cracks. Clusters of cracks have a strong influence on the formation of macroscale fractures. In order to investigate the influence of crack evolution on the formation of fractures during creep deformation, a time-dependent damage model is introduced in this paper. First, the instantaneous elastoplastic damage model of sandstone was built based on the elastoplastic theory of rock and the micro-heterogeneous characteristics of sandstone. A viscoelastic plastic creep damage model was established by combining the Nishihara model and the elastoplastic damage constitutive model. The proposed models have been validated by the results of corresponding analytical solutions. To help back up the model, some conventional constant strain rate tests and multi-step creep tests were carried out to analyze the time-dependent behavior of sandstone. The results show that the proposed damage model can not only reflect the time-dependent viscoelastic deformation characteristics of sandstone, but also provide a good fit to the viscoelastic plastic deformation characteristics of sandstone's creep behavior. The damage model can also reproduce the propagation process of mesoscopic cracks in sandstone upon the damage and failure of micro-units. This research can provide an effective tool for studying the propagation of microscopic cracks in sandstone.

Nonlinear creep properties and time-to-failure prediction of sandstone under saturated and dry conditions

The moisture content of rock significantly influences its time-dependent deformation behavior. This paper studied the creep behavior of sandstone under saturated and dry conditions under different driving stress ratio (not the same creep stress level).Their impacts on the time-to-failure (TTF) of sandstone were also investigated. The results show that under an identical driving stress ratio, the dry specimens' creep strain and steady-state creep rate are relatively higher than those of the saturated ones. Nevertheless, the water-saturated specimen has a shorter creep strain path and TTF due to the softening effect of water. It is evident that in terms of creep deformation and creep rate, the impact of creep stress is much more significant than that of moisture content; however, in terms of creep TTF, the moisture content of sandstone plays a dominant role. The rationality of the generalized Kelvin, Burgers, and power-law creep models were evaluated based on the experimental data. The power-law model was found to be capable of fitting the test data, and better predicting sandstone creep deformation than other two models. Finally, based on the assumption of a critical strain value εcri, a method for predicting creep TTF from limited laboratory data was proposed, providing a foundation for incorporating TTF prediction into continuum numerical simulations.

Long-Term Swelling Characteristics of Montmorillonite Clay with and without Fly Ash: Wetting–Drying Cycle Influence in 1D Oedometer Condition

Abstract The utilization of fly ash (FA) produced from various thermal power plants and other industrial sources is a big challenge and an opportunity for material and civil engineers. This study aims to utilize FA for improving the engineering characteristics of Montmorillonitic Indian clay (BC) soil. A rigorous testing plan is designed and performed using different proportions of FA (5, 15, 25, and 35 %) to investigate the time-dependent deformation behavior of expansive BC soil and also to examine the influence of the wetting–drying cycle on the time-dependent swelling behavior of reconstituted soils in Oedometric free swell condition. It is proposed to evaluate the time-dependent parameters of the FA-BC matrix under wetting–drying cycles using the elastoviscoplastic considering swelling (EVPS) model. The mineralogical characteristics of both natural and reconstituted samples were investigated using the scanning electron microscope and X-ray diffraction. From the experimental result, it is observed that the time-dependent swelling coefficient decreases with the percentage of FA content increase. The FA used in the study results in decreasing not only the swelling potential of BC soil samples but also the swelling–shrinkage behavior of the soil. It is observed that the reconstituted soils are influenced by both the degree of FA content and the wetting–drying cycles. The swelling strain limit decreases exponentially with the increase of the FA content. The EVPS model works very well in predicting the long-term consolidation and swelling behavior of the FA-BC matrix under different stress states.

In situ investigation of the influence of varying load conditions on tooth deformation and wear of polymer gears

A new method for in situ deformation and wear measurement of polymer gears has been developed at the LKT and validated for polyamide-66 (PA66) gears at constant loading torque and rotational speed. This contribution contains a more comprehensive validation of the newly developed test method by examining polybutylenterephtalate (PBT) gears under varying loading conditions. The deformation test method is based on measuring and analysing the timing differences between the index pulse signals of rotary encoders on the input and output shaft of the test rig. Since the total tooth deformation is a combination of different effects, such as elastic and plastic deformation, thermal expansion and wear, different testing modes with a low and a high torque level are implemented to separate the effects of elastic deformation on the one hand and plastic deformation and wear on the other hand. As a consequence, the new test rig design allows a deeper understanding of the wear and deformation behaviour of polymer steel gear sets over time. This potential is used to analyse the interactions of different loading conditions on the time-dependent deformation of plastic gears. The influence of both, different transmitting torques and rotational speeds is examined.The test method shows good correlation with well-established ex situ measurements for different combinations of rotational speeds and loading torques and thus could be validated. Long-term gear tests under varying rotational speeds and loading torques show increasing wear and deformation at higher speeds and torques confirming the state of the art described in the literature. In addition, the time dependent deformation behaviour at different load conditions due to superposition of wear and plastic deformation could be analysed in detail.

Effect of moisture content on the time-dependent mechanical characteristics of loess

It is of great significance to study the time-dependent mechanical properties of loess, as they are closely related to loess landslides. The purpose of this study is to investigate the effect of moisture content on the time-dependent deformation, strength and failure behaviors of undisturbed loess specimens from Nangou in Yan'an city, Shanxi Province, China, via triaxial shearing tests and multi-loading triaxial creep tests. The tests revealed different failure modes and the corresponding strain–time loess responses, which depend on the long-term static load and moisture content. The higher the moisture content is, the more obvious the time dependence of loess and the longer the time to reach the stable stage. This effect is closely related to the weakening effect of water on interparticle cementation and friction between soil particles in loess. Compared with instantaneous shear, long-term shear induced by water weakens the strength of loess, mainly because the particles in soil can be fully adjusted over time. The microscopic shear process of loess is essentially a process of change in microstructure with water exposure, loading and time, but the shear processes of loess in different shear modes are different (i.e., long-term shear and instantaneous shear). This study provides a theoretical basis for engineering construction and geological disaster prevention in loess areas.

Creep of CarbFix basalt: influence of rock–fluid interaction

Abstract. Geological carbon sequestration provides permanent CO2 storage to mitigate the current high concentration of CO2 in the atmosphere. CO2 mineralization in basalts has been proven to be one of the most secure storage options. For successful implementation and future improvements of this technology, the time-dependent deformation behavior of reservoir rocks in the presence of reactive fluids needs to be studied in detail. We conducted load-stepping creep experiments on basalts from the CarbFix site (Iceland) under several pore fluid conditions (dry, H2O saturated and H2O + CO2 saturated) at temperature, T≈80 ∘C and effective pressure, Peff=50 MPa, during which we collected mechanical, acoustic and pore fluid chemistry data. We observed transient creep at stresses as low as 11 % of the failure strength. Acoustic emissions (AEs) correlated strongly with strain accumulation, indicating that the creep deformation was a brittle process in agreement with microstructural observations. The rate and magnitude of AEs were higher in fluid-saturated experiments than in dry conditions. We infer that the predominant mechanism governing creep deformation is time- and stress-dependent subcritical dilatant cracking. Our results suggest that the presence of aqueous fluids exerts first-order control on creep deformation of basaltic rocks, while the composition of the fluids plays only a secondary role under the studied conditions.

Modelling and simulation of coupled fluid transport and time-dependent fracture in fibre-reinforced hydrogel composites

Physicochemical and mechanical stimuli can trigger fluid transport and inelastic solid deformations in the fracture process of anisotropic hydrogel composites. The underlying mechanisms for the time-dependent deformation and fracture behaviour of hydrogel composites remain elusive and poorly understood. The present work develops an anisotropic poro-visco-hyperelastic-damage model based on the theory of porous media (TPM) to analyse the relationship between the coupled time-dependent behaviours, i.e.visco-hyperelasticity and fluid transport, and the fracture behaviour of hydrogel composites. The visco-hyperelasticity of the polymer networks resulting from the breaking and reforming kinetics of physical bonds is described by introducing internal variables based on the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts. The fluid transport through the porous polymer networks is governed by Darcy’s law. A continuum damage model is proposed to describe the mechanical degradation of the anisotropic hydrogel composites, e.g., the cross-link unzipping and chain scission in polymer networks as well as the damage and breaking of embedded nanofibres. An integral-type nonlocal averaging algorithm is employed in the proposed damage model to eliminate the mesh dependence of numerical simulations. Furthermore, an operator split integration algorithm and an exponential mapping algorithm are applied to integrate evolution equations for internal variables and stresses. The resulting exponential tensor function is computed via spectral decompositions. The consistent tangent operators for an implicit finite element procedure are derived in detail in this contribution. Three representative numerical examples are used to validate the proposed model and investigate the mechanisms of the time-dependent fracture behaviour of anisotropic hydrogel composites. The computational results demonstrate that the proposed model can capture the fracture behaviour of hydrogel composites with different fibre orientations.

Creep anisotropy modeling and uncertainty quantification of an additively manufactured Ni-based superalloy

The advantages offered by additive manufacturing over traditional processes has driven a great deal of industrial and academic interest in recent years. However, the process is relatively new and requires additional investigation to become sufficiently mature for wide scale industrial adoption. Electron beam melting powder bed fusion is one technology that has shown promise for fabricating high temperature resistant materials such as nickel based superalloys. The resulting microstructures typically exhibit a strong fiber texture in the build direction giving rise to anisotropic time-dependent deformation behavior. In order to accelerate the qualification of these materials for industrial adoption accurate numerical models are needed for simulating their behavior. In this work a crystal plasticity model including non-Schmid effects is presented for capturing creep anisotropy observed in additively manufactured IN738LC. The model is calibrated via a probabilistic framework where model parameters are treated as random variables. An iterative sequential design strategy is utilized to efficiently identify the probability density of the unknown model parameters. As a case study the model is utilized to investigate the behavior of randomly oriented equiaxed grain clusters sometimes observed embedded in the additively manufactured columnar structure. A synthetic realization is simulated and uncertainty is propagated through to the full-field response. Results indicate that these features are the source of significant creep relaxation and strain accumulation which partially explains observed grain boundary decohesion at these locations.

Time-dependent deformation mechanism of metallic glass in different structural states at different temperatures

There is limited understanding of time-dependent plastic deformation behavior of amorphous alloys as a function of their structural state. Here, the creep behavior of Zr52.5Ti5Cu17.9Ni14.6Al10 bulk metallic glass was investigated in its as-cast and relaxed states using nanoindentation technique with applied load in the range of 500–1500 mN and temperature in the range of room temperature to 573 K. The creep displacement increased with increasing load and temperature since the creep process is thermally activated and diffusion rate is enhanced at elevated temperature and higher load. The creep strain rate sensitivity, which is a measure of the creep mechanism, increased with increase in temperature and decrease in applied load. This was attributed to the transition from localized to more homogeneous creep. Reduction in free volume for the relaxed alloy resulted in lower creep displacement and larger strain rate sensitivity compared to its as-cast counterpart. The results suggest that diffusion-based deformation dominate at higher temperature in contrast to shear transformation mediated plasticity at room temperature. The volume of shear transformation zone for the metallic glass was calculated using cooperative shearing model and correlated with the structural state for fundamental insights into the deformation process as a function of temperature and load.

An Experimental Study on Creep Behavior of Transversely Isotropic Composite Rock under Conventional Triaxial Compression

Abstract The time-dependent deformation behavior of hard-soft composite rock has a significant effect on tunnel excavation. In this article, a method to prepare hard-soft composite rock specimens with orientations ranging from 0° to 90° is presented. The influences of the dip angle on the long-term deformation and failure behaviors of an artificial transversely isotropic rock specimen were investigated by a series of creep experiments. The test results show that the creep failure strengths of the specimens first decreased and then increased with an increasing dip angle. The composite rocks displayed remarkable creep characteristics. The axial instantaneous deformation increased linearly with an increasing deviatoric stress, but the creep strain displayed a nonlinear trend. The instantaneous modulus first decreased in the range of 0° to 30° and then increased in the range of 45° to 90° with the increase of dip angle; however, the creep strain showed an opposite result. The steady-state creep rate increased nonlinearly with an increasing deviatoric stress. The dip angle had a significant effect on the steady-state creep rate. Moreover, the creep failure modes of the rock-like specimens, which were dependent on the dip angle, were compared.

A Comparison of Amplitude-and Time-Dependent Cyclic Deformation Behavior for Fully-Austenite Stainless Steel 316L and Duplex Stainless Steel 2205.

Austenite and duplex stainless steels are widely used in engineering, and the latter exhibits a more excellent combination of mechanical properties and corrosion resistance due to the coexistence of austenite and ferrite and higher nitrogen. However, fatigue failure still threatens their structural integrity. A comprehensive comparison of their cyclic deformation behavior is a major foundation to understand the role of duplex-phase microstructure and nitrogen in the safety assessment of engineering components. Thus, in this paper, the cyclic deformation behavior of fully-austenitic stainless steel 316L and duplex stainless steel 2205 was studied by a series of low cycle fatigue tests with various strain amplitudes, loading rates and tensile holding. A theoretical mechanism diagram of the interaction between nitrogen and dislocation movements during cyclic loads was proposed. Results show that the cyclic stress response of 2205 was the primary cyclic hardening, followed by a long-term cyclic softening regardless of strain amplitudes and rates, while an additional secondary hardening was observed for 316L at greater strain amplitudes. Cyclic softening of 2205 was restrained under slower strain rates or tensile holding due to the interaction between nitrogen and dislocations. The cyclic plasticity of 2205 started within the austenite, and gradually translated into the ferrite with the elevation of the cyclic amplitude, which lead to a decreased hardening ratio with the increase in amplitude and a shorter fatigue life for a given smaller plastic strain amplitude.

Time-Dependent Deformation Behavior of Completely Weathered Granite Subjected to Wetting Immersion

Time-Dependent Deformation Behavior of Completely Weathered Granite Subjected to Wetting Immersion

Design of an Inkjet-Printed Rotary Bellows Actuator and Simulation of its Time-Dependent Deformation Behavior.

State-of-the-art Additive Manufacturing processes such as three-dimensional (3D) inkjet printing are capable of producing geometrically complex multi-material components with integrated elastomeric features. Researchers and engineers seeking to exploit these capabilities must handle the complex mechanical behavior of inkjet-printed elastomers and expect a lack of suitable design examples. We address these obstacles using a pneumatic actuator as an application case. First, an inkjet-printable actuator design with elastomeric bellows structures is presented. While soft robotics research has brought forward several examples of inkjet-printed linear and bending bellows actuators, the rotary actuator described here advances into the still unexplored field of additively manufactured pneumatic lightweight robots with articulated joints. Second, we demonstrate that the complex structural behavior of the actuator’s elastomeric bellows structure can be predicted by Finite Element (FE) simulation. To this end, a suitable hyperviscoelastic material model was calibrated and compared to recently published models in a multiaxial-state-of-stress relaxation experiment. To verify the material model, Finite Element simulations of the actuator’s deformation behavior were conducted, and the results compared to those of corresponding experiments. The simulations presented here advance the materials science of inkjet-printed elastomers by demonstrating use of a hyperviscoelastic material model for estimating the deformation behavior of a prototypic robotic component. The results obtained contribute to the long-term goal of additively manufactured and pneumatically actuated lightweight robots.

Developing a two-step improved damage creep constitutive model based on soft rock saturation-loss cycle triaxial creep test

The study of the time-dependent deformation behavior of soft rock under water–rock interaction is of great significance to reveal slope creep deformation behavior. In this study, the saturation-loss cycle's triaxial creep test was performed, and the creep deformation, creep rate, and long-term strength of silty mudstone were analyzed. A two-step improved modeling method was also proposed. Firstly, by introducing fractional Abel viscous pot and aging factor, a one-dimensional creep constitutive model was established based on the Burgers model. And then the three-dimensional creep damage constitutive was derived through Laplace transform. Finally, the Levenberg–Marquardt (L–M) algorithm method was used to identify the creep curve and calibrate the model parameters. The new constitutive model could reflect the soft rock's creep characteristics during saturation-loss cycle.