Inelastic Strain Accumulation Research Articles

Dynamic Behavior and Permanent Indentation in S2-Glass Woven Fabric Reinforced Polymer Composites under Impact: Experimentation and High-Fidelity Modeling

This paper studies the behavior of S2-glass woven fabric reinforced polymer composite under low-velocity impact at 18–110 J energy. A macro-homogeneous finite element model for the prediction of their response is implemented, considering the non-linear material behavior and intralaminar and interlaminar failure modes for the prediction of impact damage. The model accurately predicted the permanent indentation caused by impact. By applying the Ramberg-Osgood formulation, different initial stiffness values are examined to assess the post-impact unloading response. This approach reveals the significant role of initial stiffness in inelastic strain accumulation and its consequent effect on permanent indentation depth. A higher initial stiffness correlates with increased inelastic strain, influencing the impactor rebound and resulting in greater permanent indentation. By accurately predicting permanent indentation, and damage accumulation for different impact energies, this study contributes to a better understanding of the impact behavior of composite materials, thereby promoting their wider application.

A Comparative Study of Ratcheting Fatigue Behavior of Modified 9Cr–1Mo Steel and Inconel 617 Alloy at Homologous Temperature of 0.42

The modified 9Cr–1Mo steel and Inconel (IN) 617 superalloy are high‐temperature alloys of prime importance in several industrial applications. Both of these are used at elevated temperature for various piping and tubing components and undergo asymmetric cyclic loading; therefore, it is highly essential to assess their resistance to accumulation of inelastic strain (ratcheting) under asymmetric stress cycling. In this study, ratcheting behavior of these alloys is compared at the homologous temperature of 0.42, under uniaxial asymmetric stress loading with positive mean stress. Deformation behavior of the tested samples is analyzed by transmission electron microscope. While there is homogeneous deformation in the modified 9Cr–1Mo steel, there is intersection of slip bands and presence of dislocation tangles in the IN 617 alloy. Fracture surface of the modified 9Cr–1Mo steel, tested under asymmetric cyclic loading, reveals typical ductile fracture resulting from tensile loading, whereas there is characteristic fatigue fracture of the IN 617 alloy.

Uniaxial ratcheting and ductile damage in structural steel with a stochastic spreading of experimental data

AbstractThis paper provides new experimental data regarding inelastic strain accumulation in structural steel samples. The samples are subjected to stress‐controlled cyclic loading with positive mean stress within each cycle; the loading blocks are combined in a complex pattern to study the effect of load history. A large‐strain ratcheting model is constructed based on a material law with a nonlinear kinematic and isotropic hardening. A new rule of ductile damage accumulation is suggested and a class of models with hardening stagnation is introduced. We show that models which include the hardening stagnation describe the experimental data more accurately. Unfortunately, due to a large spread of mechanical properties from sample to sample, it is impossible to describe the entire set of experiments using a single set of parameters. To address this challenge, we have developed novel mathematical tools for parameter identification in the context of stochastic variations in mechanical properties. These tools include the concept of a collar of model responses and the notion of protrusion. We propose an extended parameter identification problem that rethinks the standard error functional. We demonstrate that the extended identification problem effectively accounts for the large spread observed in experimental data when applied to the developed ratcheting model.

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto‐Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

AbstractWe present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2‐D planar rate‐and‐state fault with off‐fault visco‐plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co‐evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off‐fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off‐fault bulk even at higher angles of maximum compression. This produces damage patterns that deviate from the traditional off‐fault fan‐like distribution observed in dynamic rupture simulations and emphasizes the significance of long‐term deformation in interpreting observations.

Evaluation of Solder Joint Reliability in 3D Packaging Memory Devices under Thermal Shock

In 3D packaging memory devices, solder joints are critical links between the chip and the printed circuit board (PCB). Under severe working conditions, cracks inevitably occur due to thermal shock. If cracks grow in the solder joint, the chip will be disconnected with the PCB, causing its function failure. In this paper, the reliability of solder joints under thermal shock are evaluated for 3D packaging memory devices by means of the SEM and finite element analysis. As microscopically studied by the SEM, it is found out that the main failure mechanism of solder joints in such test is the thermal fatigue failure of solder joints. Finite element analysis shows that cracks are caused by the accumulation of plastic work and creep strain. The initiation and growth of cracks are mainly influenced by the inelastic strain accumulation. The trends of cracks are influenced by the difference between the coefficient of thermal expansion (CTE) of epoxy resin and that of the chip.

Anisotropic behaviours of LPBF Hastelloy X under slow strain rate tensile testing at elevated temperature

To improve the understanding of high temperature mechanical behaviours of LPBF Ni-based superalloys, this work investigates the influence of an elongated grain structure and characteristic crystallographic texture on the anisotropic tensile behaviours in LPBF Hastelloy X (HX) at 700 °C. Two types of loading conditions have been examined to analyse the anisotropy related to the building direction (BD), including the vertical loading (loading direction//BD) and the horizontal loading (loading direction ⊥ BD). To probe the short-term creep behaviours, slow strain rate tensile testing (SSRT) has been applied to address the strain rate dependent inelastic strain accumulation. In-situ time-of-flight neutron diffraction upon loading was performed to track the anisotropic lattice strain evolution in the elastic region and the texture evolution in the plastic region. Combined with the post microstructure and fracture analysis, the anisotropic mechanical behaviours are well correlated with the different microstructural responses between vertical and horizontal loading and the different strain rates. A better creep performance is expected in the vertical direction with the consideration of the better ductility and the higher level of texture evolution.

Ускоренная оценка влияния технологических факторов на прочностные характеристики Ti-6Al-4V И Al-Cu-Mg

Introduction. The strength of construction materials when used under cyclic loads is of great importance in design engineering. A significant number of factors that affect the fatigue resistance have predetermined the creation of numerous methods that consider such influence. Nondestructive methods that are based on the connection of the physical degradation of material with strain properties enable evaluating experimentally the fatigue properties of materials. Purpose of study: the analysis of the processes of energy dissipation and strain accumulation during the inelastic cyclic strain of samples, using the VT6 (Ti-6Al-4V) titanium alloy and the D16 (Al-Cu-Mg) aluminum alloy before and after the technological impact. The work experimentally investigates the physical processes of degradation of the VT6 and D16 alloy samples that accompany the process of fatigue failure in materials with homogeneous and inhomogeneous stress-strain states in the concentrator (in the form of a hole and a weld). Typical modes are used to reach the fatigue testing that determine the critical stress in a material sample – the stress at which physical properties (temperature, strain) change without reaching the fatigue failure of samples. Critical stress amplitudes in the cycle, based on the data obtained during the experiment and the results of mathematical simulation, are compared. The effect of stress concentrators on critical loads that a detail can withstand after a unit operation is estimated by the finite-element method (FEM). As a result, the effect of the operational and technological factors on critical stress determined by strain and temperature is estimated. Comparative tests of the VT6 and D16 alloy samples with and without stress concentrators showed that the amplitudes of critical stress decrease by more than 30% in comparison with the ones that are without stress concentrators. The low-cycle fatigue tests of the D16 alloy samples are carried out. Mathematical simulation of the cyclic strain of the samples is carried out using MSC.Marc package. The results of the cyclic loading tests, which show that the characteristics of the technological process reduce the amplitudes of the critical stress of the VT6 and D16 alloys and affect the fatigue properties of the D16 aluminum alloy, are discussed. Mathematical simulation corresponded positively to the experimental data. Such correspondence indicates the possibility of conducting qualitative numerical assessments of the beginning of the inelastic strain accumulation process in structures with stress concentrators under the cyclic stress and the increasing stress amplitude, using the typical sample made of hardening elastoplastic material.

Micromechanical crystal plasticity back stress evolution within FCC dislocation substructure

Experiments and theories have suggested the evolution of intragranular back stress is primarily dependent on the characteristics and development of dislocation substructure in face-centered cubic (FCC) metals and alloys. Despite this, continuum modeling of complex cyclic loading phenomena such as inelastic ratchet strain accumulation typically appeals to one of several phenomenological back stress forms with weak connections to physical mechanisms. In the current work, a micromechanically-based back stress evolution law is derived and implemented in a crystal plasticity framework for FCC metals that directly considers the evolution of dislocation substructure. The model is used in a case study of stainless steel 316L (SS316L), and good agreement is found with experiments on single- and poly-crystalline specimens subjected to monotonic, fully-reversed cyclic loading, and stress-controlled cyclic loading with mean stress. Ratcheting is attributed to dislocation substructure formation, dissolution, and stabilization within this physically-based framework.

Creep-fatigue interactions in type 316H under typical high-temperature power plant operating conditions

A micromechanical crystal plasticity self-consistent model (SCM) is used to analyse loading histories in 316H stainless steel. SCM predictions on changes in cyclic and creep properties are compared to analyses via the R5 assessment procedure. Plant-relevant cyclic-creep histories at 550 °C are examined with focus on the estimation of accumulated creep strain. The effect of cyclic plasticity on creep is quantified. The levels of creep strain accumulated during different dwells, following loading from different macroscopic stress states, is also evaluated and explained through experimental observations. Assessing the impact of displacement- and load-controlled dwells on the hysteresis loop evolution revealed how different assumptions for creep strain accumulation could employ SCM results to reduce uncertainty. Guidance is provided in the development of extrapolation frameworks for structural parameters based on the SCM results which could be used directly in structural assessment to estimate the inelastic strain accumulation with a lower degree of conservatism.

Invariant Procedure for Error Sensitivity Analysis Applied to Cyclic Creep Modelling

Cyclic creep, also known as ratcheting, is a progressive accumulation of inelastic strain under cyclic stress-controlled loading. This mechanical effect is of great importance for numerous applications. In engineering practice, phenomenological models of cyclic creep are calibrated against a limited set of macroscopic test data. Since the testing results are prone to systematic and non-systematic experimental errors, the impact of experimental errors on the quality of simulation has to be analysed. A simple inspection procedure is demonstrated and tested. Based on the Monte Carlo computations, it allows for analysis of error propagation through the simulation cycle. The focus of the paper is on the independence of the procedure from the chosen model parametrization. For demonstration purposes, cyclic creep of VT6 alloy is simulated. The corresponding macroscopic constitutive equations are based on the second Ohno-Wang model, combined with refined rule of isotropic hardening. Two different parametrizations are introduced to show that the procedure predicts the same results for both of them.

On the ratcheting of the VT6 alloy in a range of loading scenarios

A set of experimental results concerning the accumulation of inelastic strain in the VT6 titanium alloy is presented. The considered tests include cyclic stress-controlled loading with monotonically increasing stress amplitude and constant mean stress. The focus of the study is on the accurate phenomenological modelling of the complex material behaviour. Four different material models are employed to capture the phenomena of ratcheting and nonlinear kinematic hardening. Two models are of the Armstrong-Frederick type and the remaining two models are of the Ohno-Wang type. Since all the considered models contain a big number of material parameters, a sophisticated nested procedure is used for the parameter identification; the obtained material parameters are validated by additional experiments. It is shown that all the models yield nearly the same accuracy; the limitations of the phenomenological approach are highlighted and discussed.

Creep behaviour of a high chromium martensitic steel under stress varying creep loading conditions: Primary creep regeneration (PCR)

Primary creep regeneration (PCR) is an important phenomenon observed for some alloys loaded at high-temperature and under stress varying loading conditions. For example, for a specimen deforming in the secondary creep regime, a stress reversal might result in an enhanced creep rate upon reloading due to full/partial re-activation of the primary creep stage (i.e. primary creep regeneration). The extent of PCR activation is expected to be dependent on different loading parameters (e.g. magnitude and duration of reverse loading) and the characteristics of the loaded alloy. In this study, a comprehensive testing program was designed and conducted to investigate the PCR behaviour of an advanced 10%Cr martensitic steel at 600 °C. The experimental observations characterized the influence of different loading parameters on the extent of PCR activation. It was found that the inelastic strain accumulation during reverse loading periods is the most important parameter governing the extent of PCR activation after stress transients. Furthermore, the gathered experimental data was analysed to understand the effect of different loading parameters on anelastic recovery behaviour of the steel. It was shown that a larger amount of strain recovers after unloading for tests with higher forward stress magnitudes and/or larger amounts of pre-accumulated inelastic strain.

Evaluation of fracture toughness of zrO2 − 3.0 mol%Y2O3 ceramics utilizing wedge splitting loading of double cantilever specimen with a chevron notch

A ZrO2-3.0mol%Y2O3 double-cantilever specimen with a chevron notch is manufactured to study the material toughening during a stable crack advancement. The shape of the resulting crack does not allow using the techniques currently available for the evaluation of the energy release rate. A recent publication reporting an experimental study of the deformation and fracture of the double-cantilever specimen subjected to wedging up to failure, in a contradiction with a typical brittle behavior of this material, has revealed a large nonlinear section in the loading diagram. In the present work, an FEM simulation-based approach is used to simulate the processes of deformation and fracture, and an interpretation of the experimental findings is provided. The Drucker-Prager yield criterion, modified for the purpose of this study, is employed as a part of the non-linear model, which reduces overcomplications in the constitutive response. All model parameters are validated against the experimental data obtained or those reported by other authors. The first law of thermodynamics is used for evaluation of the dissipated energy related to inelastic strain accumulation and crack propagation. The fracture toughness value obtained in numerical simulation is KIC≈ 5.45 MPa·m(1/2). The results of numerical simulation are in a satisfactory agreement with our experimental data and in a good agreement with the other available data. An important finding for the engineering applications is that the fracture surface roughness has to be taken into account in evaluating the fracture toughness. Otherwise, the KIC values would be overestimated because the real crack surface area is larger than its planar projection. For the material considered, the overestimation of KIC is in the range of 8–10%.

Experimental investigation on electro-mechanically coupled cyclic deformation of laterally constrained dielectric elastomer

A series of electro-mechanically coupled cyclic tests at large deformation are carried out to characterize the cyclic deformation of a laterally constrained dielectric elastomer (DE) in this work. In the strain-controlled cyclic tests of the dielectric elastomer (e.g., VHB 4910 DE) with a constant or cyclic voltage, cyclic stress softening occurs and is influenced by the phase-angle difference between the applied cyclic strain and cyclic voltage. In the stress-controlled cyclic tests of VHB 4910 DE with a constant or cyclic voltage, ratchetting (a cyclic accumulation of inelastic strain) takes place; the ratchetting strain is considerably enhanced by applying higher voltage level, higher stress level and lower stress rate, and is also affected by the phase-angle difference between the applied cyclic stress and cyclic voltage. Moreover, the remarkable recovery of residual strain after the cyclic tests demonstrates that the cyclic stress softening and ratchetting of VHB 4910 DE mainly stem from the viscoelasticity. The comprehensive experimental observations are very useful to develop, calibrate and validate an electro-mechanically coupled constitutive model of dielectric elastomers.

Failure mechanism of thermal barrier coatings of an ex-service aero-engine combustor

Failure mechanism analysis of thermal barrier coatings (TBCs) on an ex-service aero-engine combustor is carried out. Microstructure, chemical composition, phase composition, and Young's modulus of TBCs are detected for three typical spallation areas as well as an as-sprayed sample for reference. A fluid-structure interaction simulation for the turbulent combustion is conducted to obtain the working temperature, fuel impurities mass fraction and dust particles erosion rate distribution on the TBCs surface. Results show that the maximum working temperature, the impurity mass fraction, and the sucked-in dust erosion rate correspond to the spallation at the outer liner complementary combustion zone (CCZ), the outer liner primary combustion zone (PCZ), and the inner liner of CCZ respectively. It is found the failure of TBCs at outer liner of CCZ is caused by high-temperature sintering, the infiltration of deposits is the main reason for the failure of TBCs at outer liner of PCZ, and the combination of sintering and particles impact is responsible for the failure of TBCs at inner liner of CCZ. Besides, the accumulation of inelastic strain in the vicinity of thermally growth oxide (TGO) caused by thermal stress may lead to formation and propagation of cohesive interfacial cracks.

High‐Resolution Mapping of Yield Curve Shape and Evolution for High‐Porosity Sandstone

AbstractUnderstanding the onset and nature of inelastic deformation in porous rock is important for a range of geological and geotechnical problems. In particular for sandstones and siliciclastic sediments, which often act as hydrocarbon reservoirs, inelastic strain can significantly alter the permeability affecting productivity or storativity. The onset of inelastic strain is defined by a yield curve plotted in effective mean stress (P) versus differential stress (Q) space. Yield curves for porous sandstone typically have a broadly elliptical shape, with the low‐pressure side associated with localized brittle faulting (dilation) and the high‐pressure side with distributed ductile deformation (compaction). However, recent works have shown that, for different porous rocks, the curve shape can evolve significantly with the accumulation of inelastic strain. Here yield curve shape and evolution of two high‐porosity sandstones (36–38%) is mapped along different loading paths using a high‐resolution technique on single samples. The data reveal yield curves with a relatively shallow geometry and with a compactive side that is partly comprised of a near‐vertical limb. Yield curve evolution is found to be strongly dependent on the nature of inelastic strain with samples compacted under a deviatoric load (i.e., with a component of shear strain) having peak stress values that are approximately 3 times greater than similar porosity samples compacted under a hydrostatic load (i.e., purely volumetric strain). These results have important implications for predicting how the strength of porous rock evolves along different stress paths, which differ in reservoirs during burial, fluid extraction, or injection.

Impact of electron beam surface modification on deformation behavior and fracture properties of TiNi shape memory alloy

The study deals with the impact of the pulse number at low-energy High-Current Pulsed Electron Beam (HCPEB) treatment at constant energy density ES upon the deformation behavior of TiNi alloy, its inelastic properties and fracture pattern under quasistatic uniaxial tension. It is shown that inelastic properties of the TiNi alloy under study can be kept at the initial (constant) level whereas ductility and ultimate strength can be increased when the following parameters of low-energy high-current pulsed electron beam treatment are used: pulse duration τ = 2–2.5 μs, maximum electron energy 25 keV, energy density ES = 3.8 ± 0.7 J/cm2 as well as the pulsed irradiation mode and optimal number of irradiation HCPEB pulses (n) are taken. The HCPEB modification of the TiNi surface layer under uniaxial static tension results in the increase of martensite yield plateau length ΔεM, which is 15–30% larger than one in the unirradiated TiNi samples. The reasons of different impact of the HCPEB irradiation on strength and elastoplastic properties of TiNi alloy (with regard to the n) are discussed. The main reason for the strength properties decrease of the HCPEB-modified TiNi alloy at n = 15, 32 is attributed to the formation of a columnar structure in the matrix B2-phase with a particular crystalline lattice orientation (<110>B2) in the columnar B2 grains. Whereas after the HCPEB treatment at n = 5 these parameters are varied due to the change of the chemical composition, namely, the nickel depletion of the B2-phase in the surface layer. The mentioned variation of the chemical composition of the matrix B2-phase is responsible for the increase in the temperature of the martensite transformations. The latter results in a more complete realization of the mechanisms of inelastic strain accumulation induced by these transformations, as well as the accumulation of larger plastic strain in the ‘soft’ martensitic phase.

Creep behaviour of AISI 316H stainless steel under stress-varying creep loading conditions: primary creep regeneration

ABSTRACTPrimary creep regeneration (PCR) is an important reported observation from creep under stress-varying conditions for several alloys. For a specimen deforming in the secondary creep regime, a stress reversal leads to an enhanced creep rate upon reloading due to reactivation of the primary creep regime (i.e. PCR). This paper focuses on an investigation of the PCR phenomenon during stress-varying creep loading for AISI 316H stainless steel at 650°C. The experimental observations clarify the influence of different parameters (e.g. forward creep stress level, reverse stress magnitude and forward and reverse accumulated inelastic strain) on the extent of PCR activation. In addition, a correlation between the extent of PCR activation and inelastic strain accumulation during the reverse loading period was found, which was employed to develop an empirical–phenomenological model for prediction of the creep behaviour of the alloy after stress transients (e.g. stress reversals).

Energy dissipation in mammalian collagen fibrils: Cyclic strain-induced damping, toughening, and strengthening

As the fundamental structural protein in mammals, collagen transmits cyclic forces that are necessary for the mechanical function of tissues, such as bone and tendon. Although the tissue-level mechanical behavior of collagenous tissues is well understood, the response of collagen at the nanometer length scales to cyclical loading remains elusive. To address this major gap, we cyclically stretched individual reconstituted collagen fibrils, with average diameter of 145 ± 42 nm, to small and large strains in the partially hydrated conditions of 60% relative humidity. It is shown that cyclical loading results in large steady-state hysteresis that is reached immediately after the first loading cycle, followed thereafter by limited accumulation of inelastic strain and constant initial elastic modulus. Cyclic loading above 20% strain resulted in 70% increase in tensile strength, from 638 ± 98 MPa to 1091 ± 110 MPa, and 70% increase in toughness, while maintaining the ultimate tensile strain of collagen fibrils not subjected to cyclic loading. Throughout cyclic stretching, the fibrils maintained a steady-state hysteresis, yielding loss coefficients that are 5–10 times larger than those of known homogeneous materials in their modulus range, thus establishing damping of nanoscale collagen fibrils as a major component of damping in tissues. Statement of SignificanceIt is shown that steady-state energy dissipation occurs in individual collagen fibrils that are the building blocks of hard and soft tissues. To date, it has been assumed that energy dissipation in tissues takes place mainly at the higher length scales of the tissue hierarchy due to interactions between collagen fibrils and fibers, and in limited extent inside collagen fibrils. It is shown that individual collagen fibrils need only a single loading cycle to assume a highly dissipative, steady-state, cyclic mechanical response. Mechanical cycling at large strains leads to 70% increase in mechanical strength and values exceeding those of engineering steels. The same cyclic loading conditions also lead to 70% increase in toughness and loss properties that are 5–10 times higher than those of engineering materials with comparable stiffness.

Cyclic viscoplastic analysis for steam generator material of Indian fast breeder reactor

AbstractCreep‐fatigue interaction behavior of grade 91 steel at 823 K has been studied. Creep component has been introduced with hold times 1, 10, and 30 minutes in tension and compression in continuous strain cycling. Fatigue life reduced due to application of hold and reduction was found to be more in compressive hold. The effect of various factors such as mean stress, stress relaxation, oxidation, microstructure, and inelastic strain accumulation on significant reduction in fatigue life in compression hold has been investigated. The oxidation has been observed as the key parameter that caused significant fatigue life reduction in compressive hold as compared with tensile hold. Chaboche unified viscoplasticity model has been used to understand the material's cyclic elasto‐viscoplastic behavior. The simulation results were in agreement with the experimental results. Fatigue lives under creep‐fatigue condition were estimated using frequency‐modified strain energy damage function method and linear damage summation method. Frequency‐modified strain energy damage function method under estimated the fatigue lives whereas linear damage summation method overestimated the lives.