Accumulated Plastic Strain Research Articles

Use of Prandtl operators in simulating the cyclic softening of Inconel 718 under isothermal low-cycle fatigue loading

In this article, a new approach is proposed for modelling the stress–strain response of the Inconel 718 super-alloy under isothermal Low-Cycle Fatigue (LCF) loading. The proposed constitutive model is based on the Prandtl operator approach, in which a set of modifications is introduced in order to simulate strain range dependent cyclic softening. A new simulation capability is introduced by evolving the yield strains of the individual hysteresis operators with an accumulated plastic strain. In addition, the effect of the strain range dependency of cyclic softening is introduced into the proposed constitutive model by coupling its parameters with the concept of the plastic strain memory surface. These introduced modifications preserve the main advantages of the Prandtl operators, such as a small number of model parameters, their fast determination from the cyclic stress–strain curve, and a high computational speed, when used to simulate complex non-linear mechanical behaviour. Finally, the prediction capability of the proposed model is illustrated by various strain controlled tests performed at 500 ∘C, including block spectrum loading and variable strain amplitude loading.

Closed form solutions for the dynamics of a pressurized elastoplastic thin-walled tube

This paper provides analytic solutions for the dynamics of a pressurized elastoplastic thin-walled tube at small strains. The closed-form expressions of the stress and displacement fields are derived within the framework of thin cylindrical shell theory. Three dynamic load-processes are considered: an the increasing-constant internal pressure, a rectangular and a triangular pulse loads. It is found that, depending on the external load function, the ductility limit of the solid may be reached and the displacement is unbounded. In this case, the structure collapses by plastic strain accumulation. However, if the ductility limit is not reached, plastic strains stabilize after a transient phase and the tube exhibits an elastodynamic response function. The analytical results are compared with numerical predictions derived by the standard Finite Element Method (FEM).

Thermally induced ratcheting of a thermo-active reinforced concrete pile in sand under sustained lateral load

Thermally induced ratcheting of a thermo-active pile is the accumulation of net and irreversible pile head displacement upon heating–cooling cycles. Although this kind of phenomenon has been observed in vertically loaded piles in sand, it is unknown whether this exists in laterally loaded cases, and also what underlying mechanisms occur under the thermomechanical flexural soil–pile interaction. This study presents a series of centrifuge tests and finite-element simulations of the thermomechanical behaviour of a laterally loaded thermo-active pile in sand. A new model reinforced concrete (RC) was used in the centrifuge tests to mimic the thermal and mechanical properties of a prototype RC pile realistically. Ratcheting was evident in laterally loaded piles and its extent was more significant when the working horizontal load was higher. The ratcheting phenomenon was attributed to the accumulation of soil plastic strain due to the cyclic mechanical loading induced by pile thermal horizontal expansion and contraction, soil dilation upon soil–pile interface shearing and creep. The additional bending moment induced by the thermal action did not induce yielding within the pile. A subsequent numerical sensitivity study suggested that ignoring the softening behaviour of the sand would lead to underestimation of the magnitude of the accumulative thermally induced pile head lateral displacement.

The role of block-type support structure design on the thermal field and deformation in components fabricated by Laser Powder Bed Fusion

Successful production of overhang features, with no underlying deposited layers or substrate, in a Laser Powder Bed Fusion (LPBF) process requires sacrificial structures, known as support structures. However, these structures add extra time and cost to the manufacturing process of a component. Optimisation of support structure design should reduce materials waste (which affects the time and cost of the build process) while minimising bleed-throughs and residual deformation. Optimisation of support structure design requires an understanding of their impact on the thermal field and mechanical constraints. In this research, a combination of experiments and numerical modelling was used to quantify the contribution of various support structure design elements on component deformation. The results indicate that the total contact area of teeth and the total support base area alter thermal fields within the produced components. Increasing the area for heat conduction to the start plate was found to reduce the peak temperature in the cantilevered plate. Additionally, increasing the contact area between teeth and the cantilevered plate reduces the peak temperature and the vertical temperature gradient in the overhang platform, both of which are consistent with reducing in-situ plastic strain accumulation and residual part deformation.

The ratchetting and retained austenite transformation of medium‐manganese transformation‐induced plasticity steel during asymmetrical cyclic stressing

AbstractThe uniaxial ratchetting behavior and cyclic softening/hardening characteristics of Fe‐0.4C‐7Mn‐3.2Al steel are revealed by cyclic loading experiments. Electron backscattered diffraction (EBSD) and X‐ray diffraction (XRD) analyses have been carried out for assessing retained austenite (RA) transformation during cyclic deformation. Fe‐0.4C‐7Mn‐3.2Al steel exhibits a gradual transition from cyclic stabilization to slight cyclic hardening with increasing strain amplitude. RA transformation is one of the reasons for cyclic hardening. The ratchetting of Fe‐0.4C‐7Mn‐3.2Al steel shows two different characteristics under asymmetrical cyclic stressing. When the stress amplitude is below a certain value, the ratchetting is similar to that of typical cyclic stabilized materials in three stages of deceleration, stabilization and acceleration. However, when the stress amplitude reaches a certain level, the ratchetting evolution accelerates from the beginning to the fracture. The results show that the interaction between transformation‐induced plasticity and ratchetting strain can lead to accelerated accumulation of plastic strain.

The Effect of Superabsorbent Polymer on the Resilient and Plastic Strain Behavior of Cemented Soil under Traffic Load.

In road construction, a large number of excavated soils need to be treated with stabilizers. The addition of superabsorbent polymer (SAP) can improve the road performance of these stabilized soils. In order to predict roadbed deformation, dynamic triaxial tests were carried out on cemented soil containing SAP to investigate its resilient and plastic strain behavior. The effects of SAP content, cyclic stress ratio, and loading frequency on cement-stabilized soils with SAP were analyzed combined with the number of cycles. This study demonstrates how these influencing factors effect the resilient strain, dynamic elastic modulus, and accumulated plastic strain, which are crucial to better understanding the strain behavior of cement-stabilized soil with SAP. The results show that SAP can significantly improve the brittle failure characteristics and dynamic strength of cement-stabilized soil. Soil with higher SAP content possesses smaller accumulated plastic strain; with the increase in the cyclic stress ratio, the dynamic elastic modulus decreases significantly, whereas the accumulated plastic strain has the opposite trend. In addition, the lower frequency produces larger cumulative axial strain.

Ratcheting fatigue of modified 9Cr-1Mo steel and Inconel alloy 617 at ambient temperature: Effect of uniform plastic strain

Modified 9Cr-1Mo steel and Inconel alloy 617 (IN-617) are two important structural materials, used for piping/ tubing components in nuclear and advanced supercritical power plants. Such components undergo ratcheting fatigue, due to the mean stress, arising from fluctuations in temperature and internal pressure. This investigation presents dominant role of uniform plastic strain on ratcheting fatigue resistance comparing ratcheting fatigue life of these two materials under identical normalized mean stress and stress amplitude, at ambient temperature. Accumulated plastic strain in IN-617 was considerably higher than that of modified 9Cr-1Mo steel, although ratcheting fatigue life of IN-617 was much higher than that of modified steel. Higher uniform strain in IN-617 was found to be cause of observed behavior. Thus, uniform tensile strain of material can be considered as an important parameter for selection of materials to be used as tubular products in power plants, experiencing ratcheting fatigue.

Effect of defects on the constant-amplitude fatigue behavior of as-built Ti-6Al-4V alloy produced by laser powder bed fusion process: Assessing performance with metallographic analysis and micromechanical simulations

The influence of various process parameters on the mechanical behavior (including tensile strength, strain-to-failure and constant-amplitude fatigue performance) of as-built Ti-6Al-4V alloy, produced via laser powder bed fusion (L-PBF) process, is demonstrated using complementary information obtained from mechanical (uniaxial tensile and fatigue) tests, fractography analysis, metallographic analysis and micromechanical simulations. Four different build conditions were considered such that the laser power and velocity were varied for each build while holding the build orientation, hatch spacing, layer thickness, laser spot size and hatch rotation constant. The volumetric energy densities (E) of the four unique builds were: 33 J/mm3, 66 J/mm3, 130 J/mm3 and 180 J/mm3, respectively. Two coupons per build were subjected to constant-amplitude fatigue loading while one coupon per build was subject to uniaxial tensile loading at room temperature. Coupons belonging to Builds 1 and 2 (corresponding to E values of 33 J/mm3 and 66 J/mm3, respectively) had considerably longer fatigue lives compared to coupons from Builds 3 and 4 (corresponding to E values of 130 J/mm3 and 180 J/mm3, respectively).To reconcile the relative lifing capability of the four builds, fractography, two-dimensional (2D) pore analysis, and multiscale finite-element simulation campaigns are detailed. Collectively, these exercises underscore the centrality of pore clustering on the fatigue performance of the builds. Moreover, they highlight the role that microstructural character (viz. grain orientation with respect to loading) plays on the accumulation of plastic strain in the vicinity of pores. Specifically, it is demonstrated that a pore embedded in a grain favorably oriented for slip accumulates a significant amount of plastic strain compared to one embedded in a grain not favorably oriented for slip. Comparing the relative performance and defect character of the four builds, this study suggests that both pore spacing and relative grain hardness act in concert with other fatigue-limiting characteristics including pore size, shape and distance to free surface.

Investigation of the mechanical behaviour of concrete with severe delayed ettringite formation expansion focusing on internal damage propagation under various compressive loading patterns

Expansion due to delayed ettringite formation (DEF) can cause severe concrete strength deterioration; the failure process related to internal damage remains unclear. In this study, the influence of pre-existing DEF cracks on the compressive failure process was demonstrated. Concrete specimens with DEF expansions greater than 2% were tested under monotonic, step, cyclic, and sustained loading patterns, providing stress–strain relationships. Internal crack propagation due to loading was quantified using X-ray CT images. Large plastic strains occurred, even at low stress levels. Peak stress and strain at failure were almost independent of the loading history. Gaps formed around the aggregate with increased loading were closed and opened in the loading and perpendicular directions, respectively, contributing to plastic strain accumulation. Gradual interconnection of cracks along the aggregate interfaces at high stress levels led to specimen failure. Gradual gap closing under cyclic or sustained loading reduced additional plastic deformation under the same stress.

Effects of creep characteristics of natural gas hydrate-bearing sediments on wellbore stability

Natural gas hydrate (NGH) reservoirs consist of the types of sediments with weak cementation, low strength, high plasticity, and high creep. Based on the kinetics and thermodynamic characteristics of NGH decomposition, herein a heat-fluid-solid coupling model was established for studying the wellbore stability in an NGH-bearing formation to analyze the effects of the creep characteristics of NGH-bearing sediments during long-term drilling. The results demonstrated that the creep characteristics of sediments resulted in larger plastic yield range, thus aggravating the plastic strain accumulation around the wellbore. Furthermore, the creep characteristics of NGH-bearing sediments could enhance the effects induced by the difference in horizontal in situ stress, as a result, the plastic strain in the formation around the wellbore increased nonlinearly with increasing difference in in situ stress. The lower the pore pressure, the greater the stress concentration effects and the higher the plastic strain at the wellbore. Moreover, the lower the initial NGH saturation, the greater the initial plastic strain and yield range and the higher the equivalent creep stress. The plastic strain at the wellbore increased nonlinearly with decreasing initial saturation.

Experimental and computational investigation of weathering steel Q450NQR1 under high cycle fatigue loading via crystal plasticity finite element method

The fatigue properties of the Q450NQR1 steel were experimentally and computationally investigated. The experimental results show a large scatter of the fatigue lifetime under the high cycle fatigue loading. Based on the Voronoi diagram and crystal plastic model, a polycrystalline representative volume element (RVE) model with a pore or inclusion was constructed to analyze the effect of local stress–strain on the high cycle fatigue (HCF) and very-high-cycle fatigue (VHCF) life. Computational results show that the large deformation mostly occurs at the grain with a large Schmid factor. The increment of the mean accumulated plastic strain of the critical grain was proposed as the fatigue indicator parameter (FIP). A fatigue model was suggested based on the FIP, and the fatigue model can describe the influence of the material microstructures on fatigue life. The fatigue life curve with different sizes of defects was plotted and it is found that inclusions are the major factor in fatigue life dispersion.

Analytical model of the in-plane torsion test

In research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination.

Multiscale study on the dark-etching region due to rolling contact fatigue of 0.57C-bearing steel

The formation of a dark-etching region (DER) caused by rolling contact fatigue is a complicated phenomenon that is accompanied by macroscopic groove formation and hardness reduction, as well as microscopic texture development and carbon redistribution. To understand the mechanism of DER formation, this study employed a bearing steel with 0.57 wt% C and conducted in-depth characterisation of DER at different scales. While the accumulation of plastic strain within the material began at an early stage of the rolling cycles, DER and hardness reduction appeared only after 5×106 cycles. Inside the DER, a strong 〈111〉 // ND texture and a number of recrystallised cells developed, which indicated dynamic recrystallisation. Moreover, the carbon distribution changed when the DER was formed and its concentration in the matrix decreased as the number of rolling cycles increased, which was consistent with the results estimated by the dislocation-assisted tempering model. Based on these observations, it was suggested that the accumulation of plastic flow caused by repetitive rolling contacts enabled the carbon to redistribute from the matrix to carbides via dislocations and triggered recrystallisation. Hence, both carbide thickening and dynamic recrystallisation resulted in different etching behaviour and hardness reductions, which may result in the spalling of the bearing.

Lifetime measurement of a particular deep crack failure on a flat-type divertor mockup under cyclic high heat flux loading conditions

Plasma facing components are key to enduring high heat flux (HHF) loading from high-temperature plasma in nuclear fusion reactors. Understanding their thermal-mechanical behavior and cracking failure mechanisms related to structural designs and fabrication technologies during HHF loading is of great significance for improving their servicing performance and R&D (research and development) levels. In this study, a particular deep cracking failure process on the tungsten layer of a flat-type divertor mockup during 1800 cycles of 10 MW m−2 HHF loadings is completely monitored and measured with a special improved digital image correlation (DIC) technique. It is found that the DIC measurement under the HHF loading environment is improved successfully to capture fine deformation and strain fields with a spatial resolution less than 0.35 mm so that field strain on a 1 mm thick copper interlayer and deep crack initiation at several microns scale on the tungsten layer are measured out. Based on both full field and local strain and displacement measurements of the target divertor mockup, the thermal mechanical behaviors from deformation to crack initiation and propagation are successfully measured and traced. It is revealed that for the baseline copper interlayer design of a flat-type divertor mockup, the accumulation of plastic strain in the copper interlayer during ratcheting damage induces enough tensile stress on the tungsten layer during HHF cycles, leading to cracking and fracture failures even in its elastic state earlier than the copper LCF lifetime. Current Structural Design Criteria for ITER In-Vessel Components rules fail to cover this kind of ratcheting cracking failure mode in the design stage. New design models or mechanical validation rules to resolve this design blind spot should be established in the future.

A modified rule for estimating notch root strains in ball defects existing in coiled tubing

Coiled tubing life is predominantly limited by fatigue as it undergoes cyclic bending strains well into the plastic regime leading to cyclic ratchetting due to plastic strain accumulation. Furthermore, small defects occurring in the oil field environment are capable of reducing coiled tubing fatigue life significantly. Small defects are macroscopic flaws that have small dimensions relative to the tubing wall thickness. Very shallow flaws at depths of only a few percent of the wall thickness can have a substantial, detrimental influence on fatigue life. Accordingly, the influence of surface ball defects on the magnitude of the fluctuating strains at the root of these defects was the subject of this investigation. Accurate cyclic strain magnitude predictions are essential to ultimately quantify the fatigue life of coiled tubing. The effects of defect radius and depth were both studied, and the strains at the notch root were evaluated for coiled tubing having a diameter of 2.375 in. and a wall thickness of 0.156 in..A matrix of ball defects with various depths and radii were examined. The defects were introduced at the surface of a model having the same thickness as the actual coiled tubing. The FEA results provided detailed information about the magnitude of cyclic strains at the root of a defect in coiled tubing that were previously unavailable. The notch root strain results were used to bring about a modified Neuber’s rule since conventional notch strain analysis approaches did not lead to accurate notch root strain range predictions. A new modified rule was therefore proposed and validated based on a detailed statistical analysis. This modified rule led to a substantial reduction in the percentage difference between the numerical notch root strain range and the estimated analytical one to within 8%.

Study of notched MEMS specimen: elasto-plastic modeling and experimental testing

This paper investigates the effect of stress and strains concentration, due to the notch presence, on the elasto-plastic behavior of gold microstructures subjected to tensile loading under electrostatic actuation. A kinematic model for the test microstructure which relates the experimentally measured deflection to the induced stress in the central specimen with applied electrostatic load is developed. The local maximum stress and strains at the notch root are analytically estimated using the Neuber’s rule and verified through a detailed non-linear coupled-field electric-structural finite element method (FEM)-based analysis. Several experimental tests are carried out to analyze the accumulation of plastic strain and the consequent development of plastic hinges induced in the central notched specimen due to repeated cyclic tensile loading by measuring the corresponding deflection with each loading cycle. The comparison between the failure condition observed experimentally in the test notched specimens and the FEM-based simulation results shows that the notch acts as stress and strains raiser fostering the initiation and expansion of plastic hinges in the thin film gold specimen which can lead to the specimen breakdown.

Uncertainty quantification for industrial numerical simulation using dictionaries of reduced order models

We consider the dictionary-based ROM-net (Reduced Order Model) framework [Daniel et al., Adv. Model. Simul. Eng. Sci.7(2020)https://doi.org/10.1186/s40323-020-00153-6] and summarize the underlying methodologies and their recent improvements. The object of interest is a real-life industrial model of an elastoviscoplastic high-pressure turbine blade subjected to thermal, centrifugal and pressure loadings. The main contribution of this work is the application of the complete ROM-net workflow to the quantification of the uncertainty of dual quantities on this blade (such as the accumulated plastic strain and the stress tensor), generated by the uncertainty of the temperature loading field. The dictionary-based ROM-net computes predictions of dual quantities of interest for 1008 Monte Carlo draws of the temperature loading field in 2 h and 48 min, which corresponds to a speedup greater than 600 with respect to a reference parallel solver using domain decomposition, with a relative error in the order of 2%. Another contribution of this work consists in the derivation of a meta-model to reconstruct the dual quantities of interest over the complete mesh from their values on the reduced integration points.

Research on the establishment of gas channeling barrier for preventing SCP caused by cyclic loading-unloading in shale gas horizontal wells

Sustained casing pressure (SCP) was an urgent problem to be solved during shale gas exploration and development. To cope with the issue of SCP, a method of establishing gas channeling barrier was proposed, and the location of the barrier was optimized, considering engineering and geological factors. A series of tests, containing uniaxial/triaxial compression tests and cyclic loading-unloading tests, were carried out to evaluate the accumulated plastic strain. Also, a full-scale cement sheath sealing integrity evaluation device was employed to verify the appearance of the micro-annulus. Computed tomography scan and nuclear magnetic resonance tests were performed to measure and analyze the distribution of microcracks and pores in the cement sheath after cyclic loading-unloadings. Numerical models of the wellbore assembly were established, which considered wellbore structures of different intervals of an actual deep shale gas well. Research findings indicated that after loading and unloading a certain number of times, the accumulation of plastic strain showed an increasing trend with the increase of the measured depth in the vertical section, but decreased with the rise of the measured depth in the horizontal section. The method of setting gas channeling barrier was proposed and could be used to avoid SCP by using the cement slurry with low elastic modulus, which could significantly reduce the cost of cementing operation. Many factors, including the non-uniform in-situ stress, wellbore structure, fracturing stage number, casing internal pressure, and formation mechanical properties were considered to establish the optimization method of barrier locations, and this method was verified by using the logging data of an actual well as well as the engineering and geological data. • An optimization method of establishing gas channeling barrier was proposed. • Loading-unloading of inner pressure leads to porosity increase of cement sheath. • First barrier should be established far away from the heel. Fig. 8 displays the gas leakage measurement results. As observed, gas leakage was detectable in the 22nd cycle at the injected gas pressure of 5 MPa. The gas channeling rate also increased as the injection pressure elevated. In order to observe which interface failed, the annulus was photographed, as presented in Fig. 9 . Obviously, micro-annulus appears at the inner surface of the cement sheath without internal cracks following repeated loading/unloading cycles. The obtained results show that the micro annulus mainly occurs in the inner interface of cement sheath.

短繊維強化樹脂の材料試験及び材料同定と材料データベースへの登録

The use of short fiber reinforced plastic (SFRP), which can be injection molded, is expanding. However, it is difficult to obtain the material parameters which is necessary for structural analysis at the design stage. In this paper, we present a case study of a fracture law considering stress triaxiality, which has been the focus of attention in recent years. The parameters of the accumulated plastic strain fracture law, a fracture law considering stress triaxiality, are identified based on the results of conventional fracture laws.

Actual material strength of tee pipe and its effect on elasto-plastic FEM analysis results

To collect the actual material strength of carbon steel tee pipe, a tensile test by cut-out test pieces was conducted. In addition, inelastic FEM analysis on a simple configuration of pipe specimen including a tee pipe was conducted. In the inelastic analysis, four kinds of yield stress settings were used, and the effect of yield stress setting was examined for out-of-plane static loading and for sinusoidal excitation. From the results of the tensile test, it was found that the yield shelf did not appear in the tensile test, and that the yield stress was approximately 1.6 times higher than the minimum yield stress determined by the JIS standard. This is considered due to the work hardening effect during the manufacture process of tee pipe. In the dynamic analysis under sinusoidal input, it was confirmed that the higher setting of yield stress brought the larger response acceleration and larger plastic strain accumulation.