Effect Of Stress Relaxation Research Articles

Fatigue notch strengthening effect of nickel-based single crystal superalloys under different stress ratios

Nickel-based single crystal superalloys (Ni-SXs) are widely used in turbine blades of aircraft engines. With the increasing demand for higher temperature-bearing capacity, the introduction of film cooling holes, impingement holes, and trailing edge slots for cooling induces stress concentration, which compromises the structural integrity of the blades, generates complex multiaxial stress states, and adversely affects their operational performance. In this study, Ni-SXs, DD6, was utilized to investigate the influence of stress ratios on fatigue performance under complex stress states. Low cycle fatigue (LCF) tests were carried out at different stress ratios with stress concentration coefficient Kt = 1.0, 2.0 and 3.0. The results indicate that the notched specimens exhibit a significant fatigue notch strengthening effect under high stress ratios. The fracture surface and microstructure also indicate that under high stress ratios loading, the notches exhibit significant creep failure characteristics. This means that the main cause of fatigue notch strengthening is similar to creep notch strengthening effect. A macroscopic anisotropic constitutive model coupled with damage was developed and applied to finite element analysis of notched specimens. The results demonstrate that as the stress ratio rises, the stress relaxation effect at the notch becomes more pronounced, yet the level of damage diminishes. Additionally, a stress-equivalent model based on Bridgman stress was proposed, which effectively unifies the lifetime trends of notched and smooth specimens, predicting lifetimes within a threefold error band.

Relaxation of residual stress in welded plates during long life fatigue loading

The presence of residual stress in welded components can have a significant impact on fatigue response. Residual stresses were assessed in thick welded A36 cantilever specimens (T-specimens) at the fatigue critical area. Testing involved subjecting the T-specimens to varying bending stresses and load cycles, leading to different levels of local plasticity at the weldtoe. Extensive X-ray diffraction (XRD) measurements were conducted to analyze the residual stress distribution near the weldtoe. Residual stress states were evaluated in both as-welded specimens and those subjected to fatigue loading with strain amplitudes up to 0.001 at the weldtoe stress concentration zone. The findings suggest that fatigue loading can induce changes in the welding-induced residual stress field, ranging from moderate to significant alterations. Therefore, fatigue life predictions should consider the potential evolution of residual stresses due to cyclic loading, including the effects of cyclic stress relaxation in fatigue life calculations.

Effect of Calefaction and Stress Relaxation on Grain Boundaries/Textures of Cu–Cr–Ni Alloy

The Cu–Cr–Ni alloy is a key material for the manufacturing of connectors, which requires excellent resistance to stress relaxation. However, the inherent correlation among microstructure, texture, and properties is still unclear. In this study, we investigated the influence of calefaction and stress relaxation on the grain boundaries (GBs), textures, and properties of the Cu–Cr–Ni alloy. The results showed that calefaction and stress relaxation had opposite effects on GBs and textures. Calefaction led to a decrease in the proportion of low-angle grain boundaries (LAGBs), an increase in the Schmidt factor (SF) value of the grains, and a transition of texture from <111> to <113>. The grains with higher SF values were more susceptible to plastic deformation, which deteriorated the stress relaxation resistance. By comparison, stress relaxation led to an increase in the proportion of LAGBs, a decrease in SF values of the grains, and a transition of texture from <113> to <111> and <001>. After stress relaxation, the variation trends of the GBs and textures were consistent with those of other plastic deformations, indicating that stress relaxation can be verified by the variations in GBs and textures. Our findings provide a theoretical basis for improvements in stress relaxation resistance of the Cu-based alloys used in connector industry.

Time-varying compressive properties and constitutive model of EPDM rubber materials for tunnel gasketed joint

The stress relaxation of ethylene propylene diene monomer (EPDM) rubber material in a compressed state significantly increases the risk of water leakage at tunnel precast segmental joints. Additionally, EPDM rubber gaskets typically experience a complex precompression strain state, further complicating the prediction of long-term stress relaxation. Therefore, it is imperative to propose a novel constitutive model that realistically reflects the stress relaxation of rubber with arbitrary precompression strain, providing a reference for the long-term waterproof design of shield tunnels. In this study, the time-varying properties of EPDM rubber at material level were studied in detail. At first, a comprehensive set of accelerated aging tests were conducted on EPDM rubber samples with varying precompression strains. The hardening effect of rubber without precompression and the stress relaxation effect of rubber with precompression were explored. The time-varying law and mechanism governing rubber properties under these two effects were analyzed. Subsequently, a conversion relationship between the EPDM rubber test conditions and the actual service time was established. The predicted hardening coefficient for uncompressed EPDM after 100 years is 1.468, whereas the relaxation coefficient for compressed EPDM is 0.359. Comparative analysis revealed that the compression set index do not consider the beneficial effects of hardening, resulting in a 54.1% overestimation of the design water pressure. Finally, the analytical study on the constitutive model of EPDM rubber material was carried out. The error in compression curve for unaged sample obtained from empirical formulas exceeded three times that of the analytical model, underscoring the need to study time-varying constitutive models. An interpolation method was employed to extend the test curve, leading to the development of a new constitutive model that represents the stress relaxation characteristics of EPDM materials under arbitrary precompression strain states. By combining the proposed constitutive model with the timetemperature conversion relationship, the time-varying expressions of the constitutive parameters for relaxation and hardening effects during the service life were derived. In comparison with existing models, the proposed model demonstrates wider applicability, effectively captures the time-varying characteristics of EPDM materials under arbitrary precompression strains, offering an efficient approach for studying the long-term stress relaxation prediction of rubber gaskets in shield tunnels under complex precompression strain states.

Enhancing surface strength of tungsten by gradient nano-grained structure

A gradient nano-grained (GNG) structure demonstrates satisfactory surface strength. However, the underlying mechanism responsible for its strengthening lacks sufficient research. To explain how gradient nano-grained structures improve surface strength in detail, large-scale parallel molecular dynamics simulations are utilized in this study to investigate the mechanical deformation behavior of BCC tungsten with varying grain sizes during spherical nanoindentation. The findings suggest that a well-designed gradient structure can promote rational plasticity and an appropriate distribution of internal atomic stress. The critical point of maximum stress and hardness is observed when the initial grain size is 4.5 nm, with an average grain size of 7.1 nm. The interaction between grain boundary slip and migration in small grains, along with the enhanced activity of grain boundary dislocations in large grains, collectively contributes to the enhancement of the strength and hardness of the GNG structure. Compared with a homogeneous nano-grained structure, the gradient nano-grained structure exhibits a more rational distribution of dislocations and stress relaxation effects to enhance strength. The present work utilizes the molecular dynamics nanoindentation method to study GNG materials, providing a methodology for investigating the surface strengthening effects of GNG structures at the atomic scale and effectively revealing potential mechanisms for resisting surface deformation in GNG structures.

Creep Fatigue Analysis of the 316SS Monolith in the MegaPower Heat Pipe Reactor

The heat pipe reactor represents a promising high-temperature microreactor design comprising heat pipes, fuel rods, and monoliths. Prolonged operation at elevated temperatures leads to an obvious thermal creep and thermal stress within the monolith. The monolith may have structural failure due to creep damage and fatigue damage caused by temperature fatigue load. This paper presents an analysis of the creep fatigue damage in the monolith of the MegaPower heat pipe reactor using the American Society of Mechanical Engineers (ASME), Boiler and Pressure Vessel Code Section III, Division 5 (BPVC Sec. III, Div. 5) inelastic design-by-analysis rules. The research findings demonstrate pronounced stress relaxation in the monolith caused by thermal creep, resulting in a redistribution of thermal stress. The region experiencing peak thermal stress within the monolith transitions from the thinnest web between the fuel rods to the edge of the monolith after 50 000 h of operation at full power. Thermal creep results in a 40.5% decrease in peak thermal stress and a 0.023% increase in the displacement amplitude of the monolith. The creep fatigue damage in the monolith at full power for 50 cycles, each lasting 1000 h, adheres to the design rule limitation of the ASME BPVC. The damage is primarily concentrated in the thinnest web region at the edge of the monolith, predominantly attributed to creep damage. The creep fatigue damage check in the monolith should carefully consider the effect of stress relaxation.

Characteristic fatigue damage near the Σ3(111) coherent twin boundary in micron-sized copper specimen

To investigate the effect of a Σ3(111) coherent twin boundary on the fatigue damage of micron-sized Cu, a tension–compression cyclic-deformation test was performed on a bicrystal specimen. The fatigue damage (extrusion/intrusion) occurred preferentially around the twin boundary, induced by stress concentration on one side of the specimen due to the deformation constraint between the crystals. Even though stress relaxation occurred on the opposite side, the fatigue damage along the twin boundary penetrated the specimen. The shapes of the extrusion and intrusion of the opposing sides were coincident, and the dislocation density in the damaged region was lower than that in the far region. These results indicate that the dislocations generated at the stress-concentration sites overcame the stress-relaxation effects and traveled along the twin boundary to escape from the opposite side because of the close distance between the surfaces in the specimen. The ease of dislocation ejection promoted the formation of extrusion/intrusion and decreased the fatigue strength of the specimen. The findings will facilitate the development of materials with improved resistance to fatigue damage.

Tailoring stress relaxation for dopant-free ZnO thin films with high thermoelectric power factor

In this study, the effects of stress relaxation on the thermoelectric properties (carrier concentration n, Hall mobility μH, weighted mobility μW, density-of-state mass md*, Seebeck coefficient S, and thermopower factor PF) of undoped ZnO films were rationalized in terms of native defects (VO-related defects and Zni-related donors) induced through the deposition temperature (TD) during the sputtering process. All investigated ZnO films exhibited compressive stress and tended to become less compressive with increasing TD. The stress relaxation at high TD resulted in improved film crystallization and decreased native defect concentration, thus significantly enhancing md* through the reduction of intrinsic lattice defects, while less carriers were trapped and scattered by defects. Therefore, n and μ increased simultaneously (by 28 times and one order of magnitude, respectively), markedly enhancing the PF of dopant-free ZnO films.

An Analysis of Two Case Studies on the Construction of Underground Caverns-A Focus on the Tiantai Pumped Storage Station

This paper presents a numerical analysis of two case studies on the construction of underground caverns by FLAC3D, with a specific focus on the Tiantai Pumped Storage Power Station. During the construction period, two main problems, which are crane beam stability and rock support, have been numerically analysed and addressed. The first case study examines the influence of rock wall crane beam support on excavation stability. It has been proven that The reinforcement of connected concrete enhances integrity but may lead to localized cracking. Moreover, over-excavation reinforcement marginally improves anchor safety. The second case study investigates abnormal anchor stress in a powerhouse resulting from excavation. Recommended measures include conducting timely stability evaluations, identifying weakened zones to control rock stress relaxation effects, and establishing effective feedback mechanisms. By enhancing the safety of pumped storage power stations, promoting sustainable energy infrastructure, and improving the design and construction processes of such stations, this research paper aims to contribute to the overall development and success of these projects. In conclusion, the paper has discussed the rock wall crane beam stability and rock support effect, which implement the lack of this type of numerical analysis in underground cavern group construction. Also, it is recommended to accurately determine the rock mass mechanics parameters and timely support the excavated spaces to prevent abnormal increases in anchor stress.

Effect of Layer Addition on Residual Stresses of Wire Arc Additive Manufactured Stainless Steel Specimens

Abstract Residual stresses have been characterized in four Wire Arc Additive Manufacturing specimens with neutron diffraction technique. First, two methods are investigated for obtaining the reference diffracted angle θ0 that is required for the computation of microstrains and, thus, the stresses; θ0 was obtained with two approaches. The first one required a strain-free specimen in order to get directly the reference diffracted angles θ0 in the three principal directions. The second one is based on the plane stress assumption to get θ0 indirectly by imposing that the normal stress was equal to zero. Both methods led to similar residual stress profiles for the one-layer specimen which validated this approach for all specimens without a strain-free specimen available. The second part of this work focused on the modification of the residual stresses in the specimen following the addition of a new deposit. The neutron diffraction measurements showed that the longitudinal stress was tensile in the heat-affected and fusion zones with a maximum value located at the parent material–layers interface where the thermal loadings were applied. A decrease of this maximum value from 257 MPa to 199 MPa appeared after deposition of a new layer which is due to some stress relaxation effect. Inside the parent material, a large zone presents compressive longitudinal stress up to −170 MPa. The bottom part of the parent material is under tensile stress likely due to its upward bending following the thermal contraction of the deposited layers during cooling to ambient temperature.

Long-term sealing performance evaluation and service life prediction of O-rings under thermal–mechanical coupling conditions

In service, thermal–mechanical coupling conditions can exacerbate stress relaxation of O-rings and lead to their thermal expansion, further complicating the sealing problem. A finite element method is developed to simulate the mechanical deformation behavior of O-rings under thermal–mechanical coupling conditions, and its validity is verified by comparison with experimental data. Based on a substantial amount of simulation data, it is found that a dimensionless contact stress SG˜=SG/SG0 can be used as an indicator of the degradation of sealing performance and can be related to temperature T and time τ in the form of an aging kinetic equation. By combining this equation with the existing interfacial leakage model, an approach of predicting the long-term leakage rate of O-rings is proposed to quantitatively evaluate the effect of various factors on the performance of O-rings, and some important conclusions are drawn. Regarding the effect of temperature on O-rings, the thermal expansion effect dominates when the service time is less than 20 d, and the stress relaxation effect prevails when it is greater than 20 d. The higher the temperature, the more significant the stress relaxation, and the faster the leakage rate of O-rings. Increasing the fluid pressure enhances the relaxation effect. Using the maximum allowable leakage rate as the failure criterion, a pressure–temperature curve is plotted representing the safety boundaries, which can be used to guide the design of the sealing structures. Furthermore, an exhaustive study on the service life evaluation shows that at high temperature (T ⩾ 120 °C), the service life curves show a plunging segment near a pressure rise to 0.42 MPa.

Viscoelastic stiffening of gelatin hydrogels for dynamic culture of pancreatic cancer spheroids

The tumor microenvironment (TME) in pancreatic adenocarcinoma (PDAC) is a complex milieu of cellular and non-cellular components. Pancreatic cancer cells (PCC) and cancer-associated fibroblasts (CAF) are two major cell types in PDAC TME, whereas the non-cellular components are enriched with extracellular matrices (ECM) that contribute to high stiffness and fast stress-relaxation. Previous studies have suggested that higher matrix rigidity promoted aggressive phenotypes of tumors, including PDAC. However, the effects of dynamic viscoelastic matrix properties on cancer cell fate remain largely unexplored. The focus of this work was to understand the effects of such dynamic matrix properties on PDAC cell behaviors, particularly in the context of PCC/CAF co-culture. To this end, we engineered gelatin-norbornene (GelNB) based hydrogels with a built-in mechanism for simultaneously increasing matrix elastic modulus and viscoelasticity. Two GelNB-based macromers, namely GelNB-hydroxyphenylacetic acid (GelNB-HPA) and GelNB-boronic acid (GelNB-BA), were modularly mixed and crosslinked with 4-arm poly(ethylene glycol)-thiol (PEG4SH) to form elastic hydrogels. Treating the hybrid hydrogels with tyrosinase not only increased the elastic moduli of the gels (due to HPA dimerization) but also concurrently produced 1,2-diols that formed reversible boronic acid-diol bonding with the BA groups on GelNB-BA. We employed patient-derived CAF and a PCC cell line COLO-357 to demonstrate the effect of increasing matrix stiffness and viscoelasticity on CAF and PCC cell fate. Our results indicated that in the stiffened environment, PCC underwent epithelial-mesenchymal transition. In the co-culture PCC and CAF spheroid, CAF enhanced PCC spreading and stimulated collagen 1 production. Through mRNA-sequencing, we further showed that stiffened matrices, regardless of the degree of stress-relaxation, heightened the malignant phenotype of PDAC cells. Statement of significanceThe pancreatic cancer microenvironment is a complex milieu composed of various cell types and extracellular matrices. It has been suggested that stiffer matrices could promote aggressive behavior in pancreatic cancer, but the effect of dynamic stiffening and matrix stress-relaxation on cancer cell fate remains largely undefined. This study aimed to explore the impact of dynamic changes in matrix viscoelasticity on pancreatic ductal adenocarcinoma (PDAC) cell behavior by developing a hydrogel system capable of simultaneously increasing stiffness and stress-relaxation on demand. This is achieved by crosslinking two gelatin-based macromers through orthogonal thiol-norbornene photochemistry and post-gelation stiffening with mushroom tyrosinase. The results revealed that higher matrix stiffness, regardless of the degree of stress relaxation, exacerbated the malignant characteristics of PDAC cells.

Effect of Transient Creep on the Structural Performance of Reinforced Concrete Walls under Fire

This paper investigates and reveals the effect of the high-temperature transient creep on the structural performance of RC walls under fire. A theoretical model is established, which explicitly includes the transient creep and accounts for the explosive spalling, the material, and geometric nonlinearities under fire. The effects of the transient creep on the structural response and fire resistance of RC walls with little spalling and with explosive spalling are investigated, respectively, with elucidation of the mechanisms. The influences of wall geometries, concrete properties, and the eccentricity of load on the effect of the transient creep are quantitatively studied. Finally, the results are validated through comparison with tests in the literature. It is revealed that the transient creep significantly reduces the fire resistance of RC walls with little spalling by up to and greater than 60%, by decreasing the deflection toward the heated side. However, it increases the fire resistance of RC walls with explosive spalling by up to about 40% by reducing the spalling extent due to the stress relaxation effect. The stress relaxation effect of the transient creep has a crucial role in determining the spalling manner. The load level, the eccentricity of load, and the wall geometries are key influencing factors which have contrary influences on the effect of the transient creep on the fire resistance of RC walls with little spalling and with explosive spalling.

Investigation of the performance of the self-centering steel plate shear wall considering stress relaxation in pre-stressed cables

Self-centring systems are one of the novel earthquake-resistant systems that can eliminate permanent earthquake-induced damage in buildings. In these systems, damage can be limited to those members that can be easily replaced after earthquakes. Self-centring steel plate shear walls (SC-SPSW) with pre-stressed cables combine the lateral load-resisting capacity of conventional SPSWs with the self-centring capabilities of PT beam-to-column connections and provide sufficient ductility and stiffness for the system. The stress relaxation phenomenon in pre-stressed cables can lead to stress reduction in cables with the passage of time. This phenomenon should not be neglected. In this study, the self-centering steel plate shear wall is simulated using finite element (FE) modeling and verified based on available experimental results; then, the effect of stress relaxation on stiffness and energy dissipation capability of the system is evaluated at different initial pre-stressing forces and time intervals. According to the results, after five years and for cables with a pre-stressing ratio of 0.7, the stiffness and dissipated energy have reduced by 26 and 5 percent, respectively, in comparison to the time just after pre-stressing. These values was 40 % and 2 % for stiffness reduction and energy dissipation capacity reduction, respectively when the cables were pre-stressed with the pre-stressing ratio of 0.9. Furthermore, A method is also suggested to improve the seismic performance of the self-centering connections which includes employing low yield point steel in energy dissipater devices. Results showed that the energy dissipation capacity of the system doubles by using low-point steel for the web plates. The cumulative dissipated energy was about 1.044 MJ with A1008 steel and it was increased to 2.058 MJ with LYP100 material. This increase was mostly observed after the 10th cycle of the hysteresis curve.

Study on creep-fatigue life of ODS-Cu as heat sink in divertor PFU

In fusion devices, the actively cooled W-monoblocks of the PFUs (Plasma Facing Units) are installed in the divertor to protect the vacuum vessel and magnets against neutron flux in the bottom region of the vessel. Copper alloy is considered to be the ideal heat sink material due to its high thermal conductivity and sufficient mechanical strength, in which ODS (oxide dispersion-strengthened)-Cu is selected as a candidate. With the increasing of operating parameters, such as higher heat flux (∼20 MW/m2, H-mode) and longer pulse (up to 2.00 h) in EU-DEMO [1], the heat sink structure will undergo thermal creep induced by high temperature, stress and long holding time, which accelerates fatigue failure and could potentially be a very critical issue for the long-term safe operation of the fusion reactor. In this paper, an ITER-like monoblock with ODS-Cu as heat sink was studied for its creep fatigue life under DEMO operation conditions. The temperature distribution and stress/strain results of ODS-Cu were determined using finite element analysis. The investigation shows that high temperature creep occurs at the heat sink. Based on a damage accumulation model, the predicted life of the PFUs for the divertor are investigated at different operating modes. The analysis provides theoretical feasibility for selecting ODS-Cu as a heat sink material. The effect of stress relaxation on creep behavior during thermal stress cycle was also demonstrated and this was compared with the same for CuCrZr.

Residual stress mapping in additively manufactured steel mould parts using asymmetric and multiple cuts contour method

The distribution of residual stress in additively manufactured (AM) complex structures can be intricate, exhibiting large gradients. Accurate measurements with high spatial resolution at significant depths are crucial for understanding the residual stress distribution in AM parts. In this study, the contour method, with asymmetric and multiple cuts, is employed to map residual stresses on various cross-sections of AM steel mould parts with inner channels. The resulting residual stress maps are compared for different states: as-built, shot-peened, and shot-peened plus heat-treated, in order to quantify the stress relaxation effect of each processing step. In the as-built state, elevated levels of tensile stress are observed around the perimeter, with a substantial stress gradient throughout the depth. Compressive stresses are distributed over a larger interior region, but with lower magnitudes compared to the tensile stresses. Upon shot-peening, the tensile stresses are reduced by approximately 300 MPa around the perimeter, with limited relaxation up to a depth of 1 mm compared to the as-built state. In the shot-peened and heat-treated state, a more significant stress relaxation is observed across the cross-sections. The maximum relaxation in tensile stress reaches approximately 1200 MPa, while the maximum compressive stress relaxation amounts to around 500 MPa, both compared to the as-built state. The stress maps effectively identify regions experiencing significant stress states, and the two-dimensional comparisons between different stress states provide crucial information for enhancing and validating AM models and processing techniques.

Study on interfacial leakage characteristics of rubber sealing under temperature cycle conditions in PEM fuel cell

The amount of leakage is the only direct indicator of the sealing performance of a proton exchange membrane fuel cell (PEMFC). In this work, a predictive model is developed to quantitatively evaluate the variation of leakage for a PEMFC under temperature cycling conditions. The method first uses the Lattice-Boltzmann method to simulate the gas flow within the contact interfacial gap at various heights. Then the finite element method is used to analyze the local and macroscale contact state of the sealing interface and to clarify the effect of contact stresses on the interfacial gap height. Finally, the generalized Maxwell model, which considers time-temperature transfer and stiffness growth, is used to calculate the interfacial contact stresses under temperature cycling. The validity of the model was verified by comparison with experimental data from the available literature. Further analysis showed that reduced start-up temperature exacerbated the stress relaxation effect and decreased the service life of the seal material. When the start-up temperature is reduced from 25 °C to −20 °C, the model predicts that the service life of the PEMFC will be reduced by 100 temperature cycles or more. The leakage variation in a cycle was also discussed, and it was found that the leakage fluctuation became more and more significant as the number of cycles increased, weakening system reliability.

Effect of potassium and silver ion-exchange on the strengthening effect and properties of aluminosilicate glass

In this work, the aluminosilicate glass was subjected to ion-exchange using the KNO3-AgCl mixed molten salt in order to strengthen the glass while imparting antimicrobial properties. The concentration distribution of K+ ions and Ag+ ions of the ion-exchanged glasses was characterized by EDS, the effects of ion-exchange temperature (460-500 °C), ion-exchange time (0.5-3 h) and AgCl concentration (0–2.5 wt%) in the mixed molten salt on the strengthening effect and properties of the glass were investigated. The results showed that Ag+-Na+ ion-exchange, K+-Na+ ion-exchange existed simultaneously, and Ag+-Na+ ion-exchange occurred preferentially. Due to the presence of metallic silver, the appearance of the Ag+ ion-exchanged glass was light yellow and its transmittance showed a decrease. The surface compressive stress trended up and then down with increasing temperature and time because of the stress relaxation effect. The Vickers hardness of ion-exchanged glass increased by 15%, and the densities and chemical stability were also increased. Ions leaching experiments showed that the Ag+ ions release concentration of silver-loaded glass in aqueous environment can reach the bactericidal level. It has been shown that ion-exchange of glass in KNO3-AgCl mixed molten salts allowed the glass to be strengthened and incorporated with antimicrobial active ions, its chemical stability was improved, too.

Novel smart plugging material for high‐temperature gas well

AbstractA novel smart material is developed, which is synthesized by succinic anhydride, epoxy resin, and zinc acetylacetone hydrate. The smart material has excellent properties of self‐healing, shape memory, and degradation. The experimental results of performance characterization show that the material has good thermal stability. The glass transition temperature is adjustable between 100 and 120°C, and the storage modulus can reach 20 GPa. The maximum thermal expansion at 50°C is less than 15%, the thermal expansion equilibrium time at 120°C is less than 5 min, and the maximum thermal expansion is 131%. The stress relaxation time at 120°C is more than 2 h, which can slowly self‐heal on the basis of maintaining the mechanical strength. When the NaOH content is 1.5%, the degradation equilibrium can be reached in about 3 h, and the maximum degradation rate is 86%. The comprehensive performance evaluation shows that after hot rolling at 120°C/16 h, the material has no effect on the rheology and filtration properties. When plugging the fracture width of 5 × 4 mm, the pressure bearing capacity reaches 10 MPa. Its main mechanism is temperature‐sensitive expansion, and the stress relaxation effect heals and blocks the micro pore throat.

Phase Field Modeling of Crack Growth with Viscoplasticity

The fracture of viscoplastic materials is a complex process due to its time-dependent and plastic responses. Numerical simulation for fractures plays a significant role in crack prediction and failure analysis. In recent years, the phase field model has become a competitive approach to predict crack growth and has been extended to inelastic materials, such as elasto-plastic, viscoelastic and viscoplastic materials, etc. However, the contribution of inelastic energy to crack growth is seldom studied. For this reason, we implement the fracture phase field model coupled with a viscoplastic constitutive in a finite element framework, in which the elastic energy and inelastic energy are used as crack driving forces. The implicit algorithm for a viscoplastic constitutive is presented; this procedure is suitable for other viscoplastic constitutive relations. The strain rate effect, creep effect, stress relaxation effect and cyclic loading responses are tested using a single-element model with different inelastic energy contributions. A titanium alloy plate specimen and a stainless-steel plate specimen under tension are studied and compared with the experimental observations in the existing literature. The results show that the above typical damage phenomenon and fracture process can be well reproduced. The inelastic energy significantly accelerates the evolution of the phase field of viscoplastic materials. For cyclic loadings, the acceleration effect for low frequency is more significant than for high frequency. The influence of the weight factor of inelastic energy β on the force-displacement curve mainly occurs after reaching the maximum force point. With the increase of β, the force drops faster in the force-displacement curve. The inelastic energy has a slight effect on the crack growth paths.