Steady-state Creep Stage Research Articles

Characterization and Modeling of Room-Temperature Compressive Creep Behavior of a Near α TA31 Titanium Alloy

The creep behavior of a near α TA31 titanium alloy under different compressive pressures has been studied by long-time (up to 500 h) compression tests at room temperature. The experimental results show that several thresholds of the compressive pressure were found to exist in the compression process of the TA31 alloy. When the compressive stress is lower than 0.80Rp0.2, there is no creep. There is a steady-state creep stage at the compressive stresses between 0.85Rp0.2 and 0.93Rp0.2, in which the strain rate is approximately a constant value. When the compressive stress reaches a threshold stress between 0.93Rp0.2 and 0.95Rp0.2, the sample enters the accelerating creep stage directly. The creep model of TA31 alloy has been built by using the regression method, from which the creep strain rate of TA31 titanium alloy in the steady-state creep stage under different compressive stress levels can be calculated. The mean difference between the calculated and the experimental value is 2.54%, indicating the creep model can efficiently predict the creep behavior of TA31 alloy.

Time-dependent behaviour of clay-concrete interfaces with different contact surface roughnesses under shear loading

Mechanical properties of the interface between a pile and soil greatly affect the bearing capacity of a pile. The creep of soil causes a long-term strength of the pile–soil interface to be smaller than its instantaneous shear strength. It is helpful to understand the settlement deformation and strength characteristics of friction piles from the micromechanism by studying the shear creep mechanical properties of the clay–concrete interface. In this work, we carry out shear creep tests on the interfaces between clay and concrete slabs with different roughnesses under different normal stresses. We analyze the influence of the joint roughness coefficient (JRC) on the long-term cohesion and long-term friction angle of the interface. We propose an instantaneous damage factor of the shear modulus and improve the Nishihara creep model with the instantaneous damage effect of the shear modulus. The experimental results show: (1) the whole process test curve of the shear creep shows that the specimen is rapidly destroyed after the transient creep stage and the steady-state creep stage, but the tertiary creep stage is not obvious. (2) The long-term shear strength of the clay-concrete interface is greatly affected by the change in the normal stress under the same JRC conditions, and the long-term shear strength of the interface increases linearly with increasing normal stress. (3) The relationship between the long-term shear strength and normal stress of the interface can be described by the Mohr–Coulomb failure criterion, and the long-term cohesion and long-term friction angle under different JRC conditions can be calculated accordingly. There exists a critical value JRCcr for the long-term cohesion, and the long-term cohesion of the interface first increases and then decreases as the JRC increases. When the long-term cohesion of the interface decreases to a certain extent, it fluctuates around the long-term cohesion value of clay. Moreover, the long-term friction angle of the interface fluctuates slightly with varying JRC, and there is no obvious change rule. (4) Considering the instantaneous damage of the shear modulus, we establish a relationship between the instantaneous shear modulus and the damage factor and introduce the damage factor into the Nishihara creep model. The shear creep mechanical parameters of the clay–concrete specimens under multistage loading are inversed.

Effects of High Temperature on Creep Behaviour of Glazed Hollow Bead Insulation Concrete.

Glazed hollow bead insulation concrete (GHBC) presents a promising application prospect in terms of its light weight and superior fire resistance. However, only a few studies have focused on the creep behaviour of GHBC exposed to high temperatures. Therefore, in this study, the mechanism of high temperature on GHBC is analysed through a series of tests on uniaxial compression and multistage creep of GHBC, exposed from room temperature up to 800 °C. The results show a decrease in the weight and compressive strength of GHBC as the temperature rises. After 800 °C, the loss of weight and strength reach to 9.67% and 69.84%, respectively. The creep strain and creep rate increase, with a higher target temperature and higher stress level, while the transient deformation modulus, the creep failure threshold stress, and creep duration are reduced significantly. Furthermore, the creep of GHBC exhibits a considerable increase above 600 °C and the creep under the same loading ratio at 600 °C increases by 74.19% compared to the creep at room temperature. Indeed, the higher the temperature, the more sensitive the stress is to the creep. Based on our findings, the Burgers model agrees well with the creep test data at the primary creep and steady-state creep stages, providing a useful reference for the fire resistance design calculation of the GHBC structures.

Study of accelerated shear creep behavior and fracture process of micro-scale ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under coupled electro-thermo-mechanical loads

Shear creep deformation and fracture behavior of micro-scale ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads with high-density current stressing (6.0 × 103 A/cm2) at different temperatures (40, 60, 80, 100 and 120 °C) and various shear stress levels (12.5, 15, 17.5, 20 and 22.5 MPa) were studied intensively. The results show that electric current stressing can significantly accelerate the creep deformation and fracture process of BGA solder joints in terms of increasing steady-state creep stain rate and shortening creep lifetime of the joints. Garofalo hyperbolic-sine function has shown to be a suitable creep constitutive equation, which can be well used to formulate the creep deformation behavior of micro-scale Cu/Sn–3.0Ag–0.5Cu/Cu joints under electro-thermo-mechanical coupled loads, and the equation has the increased stress exponent of 8.6 and creep activation energy of 90.8 kJ/mol, respectively. Combined theoretical analysis and experimental characterization suggest that electric current stressing leads to the change of the dominant steady-state creep deformation mechanism from dislocation climb to lattice diffusion. The interruption creep tests demonstrate that crack initiates at the interface between the solder and intermetallic compounds (IMC) near the position of electrons entering or exiting the solder matrix when the steady-state creep stage approaches the limit, and then the crack first propagates along the solder/IMC interface and gradually turns to the solder matrix under combined shear and tensile stresses. The joint fractographies exhibit a mixed brittle-ductile fracture mode with one part in the interface and the other part in the solder matrix.

Creep behaviors of multiphase Ni3Al-based intermetallic alloy after 1000 °C-1000 h long-term aging at intermediate temperatures

The microstructure evolutions during 1000 °C-1000 h long-term aging and relevant 800 ~ 840 °C/220 ~ 300 MPa creep behaviors of a novelly designed multiphase Ni3Al-based intermetallic alloy were investigated. Results showed this alloy presented excellent intermediate temperature creep properties even after 1000 °C-1000 h long-term aging. A kind of bimodal R-type γ′ rafting structures were observed in the 800 °C/220 MPa creep process of the long-term aged alloy, and the creep resistance levels of three kinds of γ′ rafting structures were evaluated to be in the order of bimodal R-type γ′ rafting structures > R-type γ′ rafting structure > N-type γ′ rafting structure. The 1000 °C-1000 h long-term aging can promote the inhomogeneous precipitation of Cr4.6MoNi2.1 phase at the edge γ′+γ dendrite area, which can play the role of pinning dislocations and inhibiting the further rafting and coarsening of the R-type γ′ rafts during creep. Differed from Ni-based alloys and other Ni3Al-based alloys, this long-term aged alloy exhibited abnormal four-stage creep characteristics, which consisted of atypical short steady-state creep stage with step fluctuant feature and atypical long accelerated creep stage with creep rate increasing at a constant rate.

Using the room temperature creep to strengthen nanotwinned Ni: the scaling behavior between the twin thickness and the grain size

How to design ultra-strong face-centered cubic (FCC) metals is a grand challenge in materials community. In general, nanotwinned (NT) FCC metals manifest the maximum strength as the intrinsic size ratio of twin thickness–to–grain size is achieved, above which softening caused by detwinning occurs, whereas below this intrinsic size ratio strengthening caused by dislocation–twin boundary interactions occurs. In this work, we used the room temperature creep as an effective pathway to strengthen NT-Ni with the high stacking fault energy by controlling microstructure in terms of the intrinsic size ratio. We experimentally discovered in NT-Ni at the room temperature steady-state creep stage that there is a critical grain size of ∼230 nm for the intrinsic size ratio transition from 0.04 in the large grain size regime to 0.14 in the small grain size regime. In particular, this intrinsic size ratio can be taken as a signature to estimate the microstructural stability, which linearly scales with the twinnability of FCC metals. Compared with the as-deposited NT-Ni foils, their counterparts undergoing the steady-state creep stage manifest significantly enhanced strength without losing their elongation to failure. This work provides new insights into designing the strongest NT metals via the creep process.

Investigation of a fractional derivative creep model of clay and its numerical implementation

The fractional calculus has been successfully applied to characterize the rheological property of elastic viscoplastic materials. However, soils were seldom involved in fractional derivative constitutive models, and the topic of triaxial creep tests is rarely discussed through fractional calculus. This study presents a fractional derivative model that describes the time-dependent behavior of Shanghai marine clay. The fractional derivative Merchant (FDM) model is established by introducing fractional element into the Merchant model. The comparison of the calculated values of the FDM model and the Merchant model shows that the FDM model can better describe the instant elastic deformation, attenuation creep and steady-state creep stages of the clay. The FDM model was implemented into a finite-element code in ABAQUS, which is used to simulate the creep tests. The simulations demonstrate that the development model has good ability to predict the time-dependent behavior of clay.

Creep strength breakdown and microstructure in a 9%Cr steel with high B and low N contents

A 9%Cr–3%Co steel with high B and low N contents exhibits creep strength breakdown at a temperature of 923 K after 3000 h. Specific feature of this steel is a distinct difference between short-term and long-term creep regimes for transient, steady state and tertiary creep stages. This behavior is unusual for high Cr steels and attributed to low density of M23C6 carbides precipitated on lath boundaries during tempering. Precipitation of Laves phase along these boundaries during transient creep followed by its coarsening affects significantly the creep mechanisms and results in the well-defined difference in mechanical behavior between the short- and long-term creep regimes. In contrast, the strain-induced formation of a small amount of Z-phase particles scarcely changes the creep behavior.

Moisture content effect on the creep behavior of loess for the catastrophic Baqiao landslide

Understanding the creeping behavior of loess is of great importance as large-scale loess landslides are closely related with creep behavior. At present, it is still challenging to predict and estimate the long-term stability of such landslides. This is in a large degree due to the poor understanding of moisture control on creep behavior of loess. The purpose of this study is to decipher the loess creep behavior under various moisture contents (MCs) using loess specimens obtained from Baqiao landslide, Xi’an of China, using multi-loading triaxial creep tests under different MCs of 9%, 12%, 15%, 18% and 21%. Based on the laboratory test results, a series of relationships between the creep rate at the steady-state creep stage and the initial strain and initial shear modulus are revealed. Meanwhile, a method for obtaining the long-term strength of loess specimens, namely, the Steady-state Creep Rate Slope Method (SCRSM), is proposed. SCRSM resolves the issue in several conventional methods such as the Isochronous Stress-Strain Curve Method, the Tangent Method of Steady Creep Rate when MCs are of concern. Such an improvement is primarily due to a better way of finding the inflection point of the steady-state rate. It is found that SCRSM is robust and accurate to determine the long-term strength of loess specimens. Furthermore, we propose a modified Burgers model with a newly introduced nonlinear parameter n to overcome deficiencies of conventional creep models. This modified Burgers model is flexible to fit the creep test curves of loess, and can describe the curves at the accelerated creep stage more accurately. Lastly, the main factors triggering the Baqiao landslide is analyzed considering stratum lithology, rainfall and excavation. In general, this study provides a basis for understanding the evolutional process of loess landslides as well as guidelines for prevention, controlling and prediction of loess landslides.

Enhanced creep resistance of Y-bearing 9Cr ferritic/martensitic steel via vacuum casting technique

9Cr ferritic/martensitic (F/M) steels with 0 and 0.3wt.% yttrium (Y) addition were fabricated via vacuum casting technique and were creep tested at 650°C and 120MPa. The creep property of 9Cr F/M steel was improved by the addition of yttrium. Even though the initial creep rates of 9Cr-0Y and 9Cr-0.3Y were almost the same, the creep rupture life of 9Cr-0.3Y specimen was extended about 2˜3 times with the longer steady state creep stage and the lower minimum creep rate than 9Cr-0Y specimen. The coarsening of grains and martensitic laths occurred during creep, and M23C6 carbides, MX/M2X-type carbonitrides and Fe2W/Mo Laves phase were identified along the boundary in both specimens. For 9Cr-0.3Y, the nano-sized oxide clusters were formed during creep, because of the diffusion and local segregation of the dissolved yttrium and oxygen atoms at high temperature and with the promotion of creep stress. The softening of microstructure recovery is compensated by the dispersion strengthening of nano-particles and the balance of them was the reason of longer steady state creep stage of the creep curves.

Shift of Creep Mechanism in Nanocrystalline NiAl Alloy.

We have examined the effects of temperature, stress, and grain size on the creep process including creep strain, crystal structure, dislocations and diffusions of nanocrystalline NiAl alloy through molecular dynamics simulations. A smaller grain size accelerates the creep process due to the large volume fraction of grain boundaries. Higher temperatures and stress levels also speed up this process in terms of dislocation changes and atom diffusion. In both primary creep and steady-state creep stages, atomic diffusion at the grain boundary could be seen and the dislocation density increased gradually, indicating that the creep mechanism at these stages is Coble creep controlled by grain boundary diffusion while accompanied by dislocation nucleation. When the model enters the tertiary creep stage, it can be observed that the diffusion of atoms in the grain boundary and in the crystal and the dislocation density gradually decreases, implying that the creep mechanisms at this stage are Coble creep, controlled by grain boundary diffusion, and Nabarro–Herring creep, controlled by lattice diffusion.

Study on Multi-Step Creep Aging Behavior of Al-Li-S4 Alloy

Creep age forming (CAF) is a new technology developed for manufacturing large aluminum components in the aerospace industry. Aluminum–lithium alloys may be used in aerospace components because of their high modulus, specific strength and specific stiffness. Therefore, the creep deformation, mechanical properties and aging precipitation of Al-Li-S4 alloy under CAF conditions were studied. It was found that the creep behavior presents double steady state creep stages during the creep aging process. With the increase of stress level, the first steady creep rate increased, but the second steady creep rate was slightly reduced. Coincidentally, in the first steady state creep stage, the yield strength of the studied alloy also showed a slow increase stage. TEM observation showed that Al-Li-S4 alloy mainly contains two precipitation phases, T1 phase and θ’ phase. A few precipitates form during the first steady creep stage. Then, a lot of nucleation and growth of T1 phase resulted in rapid increase of yield strength. At the same time, the increase of stress level effectively inhibited the growth of T1 phase, which resulted in these strengthening phases being more uniform, and thus improved the mechanical properties of materials. On this basis, the relationship between the multi-step behaviors of creep, mechanical properties and aging precipitates are discussed. It is considered that the main reasons for the multi-step phenomenon of creep and mechanical properties are strongly related to the nucleation, growth and distribution of T1 phase.

Effects of grain dissolution–diffusion sliding and hydro-mechanical interaction on the creep deformation of soft rocks

The creep deformation behaviour of soft rocks is one of the most important research fields in geotechnical engineering. In this study, a theoretical model was developed to investigate the coupled effects of the grain dissolution–diffusion sliding and the hydro-mechanical interaction on the creep behaviour of soft rocks. Experimental results validated the model. The results demonstrate that the creep of soft rocks is primarily dependent on the shear stress on the sliding surface, the average thickness of the hydrated film and the amplitude of the cosinusoidal sliding surface. These three parameters can be used to describe the meso-mechanism of soft rock creep stages, i.e. the transient creep stage, steady-state creep stage, and accelerated creep stage. In addition, this study’s findings show that the chemical potential field promotes the mineral dissolution and diffusion on the grain sliding surface and changes its morphology, thereby resulting in the redistribution of stress.

Atomic scale investigations of carbon-based cathode materials deformation mechanism during aluminum electrolysis

The creep strain of full graphitic cathode blocks has been measured with a laboratory cell. The creep tests were performed three times under extern load 2–6 MPa and at temperature of 950 °C for 15 min, 50 min and 100 min respectively after starting the electrolysis. The deformation mechanisms in the carbon cathodes for aluminum electrolysis have been comprehensively studied at the atomic scale by high resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED). The microstructural observation confirms that the governing deformation mechanism for the carbon cathode is basal plane dislocation pile-ups and dislocation tangles at the stage of transient creep. Microstructure rearrangement of the carbon cathode including deformation bands, rotating, delamination and propagation of microcracks deteriorates its creep resistance at the stage of steady-state creep. The deformation of carbon cathodes is closely correlated with the accumulation and amorphization of the graphite during aluminum electrolysis.

Analysis of creep deformation and damage behaviour of 304HCu austenitic stainless steel

ABSTRACTCreep deformation, damage and rupture behaviour of 304HCu austenitic stainless steel have been studied at temperatures 923, 973 and 1023 K over the stress range 100–240 MPa. The material exhibited relatively short primary stage of creep deformation followed by secondary (steady-state creep) stage and relatively extensive tertiary stage of creep deformation. The transient creep deformation is analysed based on the Garofalo relationship, The variations of (i) rate of exhaustion of transient creep creep rate and time to onset of secondary creep and (ii) initial creep rate with were found to obey power-law relationship with powers close to unity, thereby facilitating the development of master transient creep curve. The variation of with stress and temperature obeyed Dorn’s equation modified with back stress concept. The time to onset of tertiary creep is found to be proportional to rupture life (tr) while the damage tolerance factor decreased with increase in tr. In view of the prolonged tertiary creep, associated with microstructural change and intergranular creep cavitation, Kachanov–Rabotnov model has been used to assess the creep damage behaviour of the steel. The damage assessment coupled with finite-element analysis closely predicted the creep deformation and rupture life of the steel.

Hydrogen effect on nanoindentation creep of austenitic stainless steel: A comparative study between primary creep stage and steady-state creep stage

The hydrogen effect on room temperature creep of 310 S stainless steel was investigated by using nanoindentation. Hydrogen enhanced the primary creep of 310 S steel much more significantly compared with the steady-state creep, which was attributed to the interaction between hydrogen and dislocation. Hydrogen obviously decreased the indentation stress so as to promote the primary creep, while hydrogen had little effect on the steady-state creep due to the evolution from mobile dislocation to immobile dislocation.

Small Punch Creep Life Prediction from Steady-State Deflection Rate in High-Chromium Ferritic Heat-Resistant Steels

The small punch (SP) creep deformation and rupture behavior of different high-chromium ferritic heat-resistant steels were studied at various temperatures in the range from 923 K to 1073 K (650 °C to 800 °C) and loads in the range from 65 to 400 N. The creep deflection rate, after an initial abrupt decrease, showed no significant variation during most of the creep time and exhibited a steady-state creep stage. The time to steady-state creep stage accounted for less than 30 pct of the creep rupture life. A close relationship was found to exist between steady-state deflection rate and time to rupture, resembling Monkman–Grant relation. This relationship was independent of the type of steels studied, resulting in a single master curve. This relationship was used for predicting SP creep rupture life. The predicted rupture life was within an accuracy factor of 1.2. The study revealed that the creep rupture life can be reasonably well predicted by evaluating steady-state deflection rate, without waiting for the fracture of specimen to occur. This approach of prediction using steady-state deflection rate was found to be more advantageous than that using minimum deflection rate as the latter appeared relatively close to the onset of acceleration creep.

Влияние температурно-силового нагружения на релаксацию остаточных напряжений в поверхностно упрочненных элементах стержневой конструкции в условиях ползучести

Разработана математическая модель релаксации остаточных напряжений в поверхностно упрочненных цилиндрических элементах статически неопределимых стержневых систем при температурно-силовом нагружении в условиях ползучести. В процессе моделирования решаются следующие задачи: реконструкция напряженно-деформированного состояния в цилиндрическом стержне после процедуры обработки поверхности микрошариками; учет влияния температурного нагружения на величину и характер полей остаточных напряжений вследствие зависимости модуля Юнга от температуры; расчет релаксации остаточных напряжений в упрочненных элементах системы под действием температурно-силового нагружения в условиях ползучести; оценка финишных остаточных напряжений после ползучести и температурно-силовой разгрузки. Поставленные задачи решаются в пределах первых двух стадий ползучести материала элементов систем. Для детального анализа использована трехэлементная статически неопределимая система с упрочненными при температуре 20$^\circ$C элементами из сплава ЖС6У и температуре эксплуатации 675$^\circ$C. Для реализации всех методик разработаны численные алгоритмы на основе аппарата вычислительной математики с использованием дискретизации по пространственным и временным координатам и применением метода шагов по времени. Для апостериорной оценки сходимости и устойчивости численного метода выполнено сравнение численных результатов при больших значениях времени расчета с асимптотическими значениями характеристик напряженно-деформированного состояния, соответствующих стадии установившейся ползучести, полученных аналитическим методом. Наблюдается хорошее соответствие данных по обоим подходам. Приводятся результаты расчетов, иллюстрирующие кинетику остаточных напряжений во всех трех стержнях системы в процессе ползучести под действием температурно-силового нагружения начиная с момента их формирования после упрочнения. Показано, что происходит ступенчатое изменение величины и характера распределения остаточных напряжений только за счет «мгновенного» температурного прогрева элементов стержневой конструкции вследствие зависимости модуля Юнга от температуры. Также расчетами установлено, что релаксация остаточных напряжений в наиболее нагруженном стержне системы происходит гораздо медленнее, чем в менее нагруженных. Основные результаты работы иллюстрируются эпюрами распределения остаточных напряжений по глубине упрочненного слоя.

Microstructure evolution and tensile creep behavior of Sn–0.7Cu lead-free solder reinforced with ZnO nanoparticles

This paper presents the influence of aging temperature as well as ZnO nanoparticles addition on the properties of Sn–0.7Cu solder. A series of Sn–0.7Cu–ZnO composite solders with ZnO nanoparticles traces (0, 0.1, 0.25, 0.5 and 1.0 wt%) has been fabricated. After being solution heat treated at 443 K for 2 h, specimens were cooled at 273 K by water quenching. All the specimens were isochronally aged for 2 h at temperatures up to 423 K. Subsequently, all samples were quenched into iced water at 273 K. The microstructure evolution, the tensile creep properties and the thermal behavior of the new fabricated solder alloys were studied. Differential scanning calorimetry measurements indicated that the ZnO nanoparticles addition increases slightly the melting point of the investigated composite solders within the range of 227.7–229.2 °C with less than 1.6 °C temperature difference. Microstructural evolutions revealed the efficient refinement of the Cu6Sn5 and Cu10Sn3 intermetallic compounds by the addition of ZnO nanoparticles. Tensile creep tests showed that the creep rate at the steady state stage increases with increasing both the aging temperature and the applied stress. The improvement of the solders creep resistance has been achieved by the increasing of the nanoparticles content up to 0.25 wt%. The deficiency of the creep resistance occurred with the excessive addition of ZnO particles. The mean values of the stress exponents and activation energies indicated that the steady state creep stage is controlled by dislocation-pipe diffusion in the tin matrix as the dominant operating mechanism.

Моделирование ползучести и релаксации остаточных напряжений в поверхностно упрочненных элементах статически не определимых стержневых систем

Предложен метод моделирования напряженно-деформированного состояния в поверхностно упрочненных элементах статически не определимых стержневых систем в условиях ползучести на примере трехэлементной несимметричной стержневой системы. Решение задачи состоит из двух этапов: реконструкции напряженно-деформированного состояния после процедуры поверхностного пластического упрочнения цилиндрических элементов системы (пневмодробеструйная обработка микрошариками) и методики расчета релаксации остаточных напряжений в упрочненных элементах на фоне ползучести всей стержневой конструкции как целого. В качестве определяющих реологических соотношений использовалась модель, описывающая первую и вторую стадии ползучести. Результаты решений на обоих этапах проиллюстрированы на модельном примере ползучести систем с упрочненными элементами из сплава ЖС6У при температуре 650 °C. Для упрочнения стержней из этого сплава использовались реальные экспериментальные данные для осевых и окружных остаточных напряжений, детально проиллюстрирована методика реконструкции напряженно-деформированного состояния после пневмодробеструйной обработки. Для построения реологической модели использовались опытные данные для кривых одноосной ползучести сплава ЖС6У при различных постоянных напряжениях при температуре 650 °C, приведены численные значения параметров модели. Выполнено обобщение одноосной модели на сложное напряженное состояние. Решение основной задачи выполнено численно с использованием дискретизации по пространственной и временной координатам. Исследовано стационарное асимптотическое напряженно-деформированное состояние стержневой системы, соответствующее стадии установившейся ползучести, которое использовалось для оценки сходимости численного метода. Получены зависимости кинетики всех компонент тензора остаточных напряжений во всех трех упрочненных элементах системы вследствие ползучести при заданной внешней нагрузке. Выполнен сравнительный анализ скорости релаксации остаточных напряжений в различных стержнях. Разработано алгоритмическое и программное обеспечение для решения поставленной задачи. Основные результаты работы иллюстрируются эпюрами распределения остаточных напряжений по глубине упрочненного слоя. Обсуждаются вопросы применения полученных в работе результатов в прикладных задачах оценки надежности упрочненных стержневых систем.