Plastic Strain Range Research Articles

THE EFFECT OF NOTCHES ON THE FATIGUE LIFE OF A NICKEL-BASE GAS TURBINE DISK MATERIAL

Gas turbine disks carry significant load under high temperatures and may be subject to fatigue failure. Disks contain several notches in the form of the fir tree blade attachments. Low cycle fatigue tests were performed on blunt notch compact tension specimens made from alloy 718. The results indicated that notch support needed to be incorporated not to cause an overly conservative life prediction. The notch support diminished as the plastic strain range decreased, indicating that notch support is only present in the low cycle fatigue regime. A critical distance approach was applied to account for the notch support. An equation relating the critical distance to the notch root stress was derived. The chosen life model was formulated in terms of a variation on the Smith–Watson–Topper (SWT) parameter. The modified SWT parameter taken at the critical distance was used in a life model calibrated for smooth specimens to successfully predict the fatigue life of notched specimens.

Influence of hot-working conditions on grain growth of superalloy 718

The grain growth behavior of superalloy 718 was investigated using high-temperature compression tests and subsequent heat treatment. Abnormal grain growth (AGG) induced by low plastic strains was observed during thermal processing, which included solution heat treatment, and annealing, causing the matrix grains to coarsen from ∼12 μm to 80 μm in diameter. Both the plastic strain and displacement rate during deformation had large influences on the occurrence of AGG, which was mainly observed in regions of low plastic strain; the plastic strain range where AGG occurred increased with decreasing displacement rate. In particular, deformation at low displacement rates (within the same range as dynamic recrystallization) easily produced grain growth during solution heat treatment. Such grain growth was referred to as irregular grain growth (IGG) to distinguish it from AGG. Both the AGG and IGG processes were initiated when the intragranular misorientation exceeded a critical level, causing an increase in the twin boundary ratio and a decrease in intragranular misorientation. The nuclei of AGG grains were the nucleation of newly recrystallized grains without dislocation.

Mechanical properties of cement paste curing at different isothermal conditions

The paper studies the intensity of strength generation in the concrete paste during the time period of 0–67 hours, at 40, 50 and 70 °C isothermal curing. It is shown that at these temperatures the yield stress increases by one order of magnitude. The elastic properties of the cement paste also significantly increase. The plastic strain range reduces with curing time, and the catastrophic failure of specimens occurs at the end of the investigated temperature range. Stress-strained curves in the plastic range are non-monotonous, with a high density of breaks. The yield stress is the main parameter for evaluating the strength properties of the cement paste.

Study of ratchet limit and cyclic response of welded pipe

Ratcheting and low cycle fatigue are failure mechanisms observed in components subjected to cyclic temperature and mechanical loads. Ratcheting is a global failure mechanism which leads to an incremental plastic collapse of the component whereas low cycle fatigue is a localized mechanism which leads to crack initiation. It is exacerbated by grooves, notches and changes in the geometry of the component. To estimate the remaining life of the component and predict its failure mechanism, it is important to understand how it responds to various combinations of cyclic loads. This paper includes investigation of the ratchet limit and the plastic strain range, which is associated with the low cycle fatigue, of a circumferential butt-welded pipe by using the ratchet analysis method which includes Direct Steady Cycle Analysis (DSCA) within the Linear Matching Method Framework (LMMF). The pipe is subjected to a constant internal pressure and a cyclic thermal load. The investigation is carried out by varying 1) material properties of the weld metal (WM); 2) ratio of inner radius to wall thickness; 3) weld geometry. Within the specified ranges, yield stress and the ratio of inner radius to wall thickness affect the ratchet limit curve. The cyclic thermal load plays a crucial role compared to the internal pressure in influencing the ratchet limit curve. It is observed that the pipe experiences thermal ratcheting at lower yield stress values of the WM. The results obtained are combined to create a limit load envelope, which can be used for the design of welded pipes within the specified ranges.

Measurement of Differential Hardening under Biaxial Stress of Pure Titanium Sheet

Biaxial stress tests of a commercially pure titanium sheet (JIS #1) using the cruciform specimen and the servo-controlled biaxial testing machine have been carried out in order to elucidate its anisotropic plastic deformation behavior. The geometry of the cruciform specimen is identical to that regulated by the ISO 16842. Nine linear stress paths, σx (rolling direction): σy (transverse direction) = 1:0, 4:1, 2:1, 4:3, 1:1, 3:4, 1:2, 1:4, and 0:1 in the first quadrant of the principal stress space are applied to the cruciform specimens. Contours of plastic work in the principal stress space and the directions of plastic strain rates at selected levels of plastic work have been precisely measured. The range of the equivalent plastic strain applied to the specimens is 0.002 ≤ ≤ 0.01. The shapes of the work contours significantly change with increasing the test material exhibits differential hardening (DH). Using the data of the work contours and the directions of plastic strain rates, the applicability of selected anisotropic yield functions to the accurate prediction of the plastic deformation behavior of the test material is examined.

Isotropic‐kinematic hardening framework to assess ratcheting response of steel samples undergoing asymmetric loading cycles

AbstractThe present study intends to characterize ratcheting response of several steel alloys subject to asymmetric loading cycles through coupling the Ahmadzadeh‐Varvani kinematic hardening rule with isotropic hardening rules of Lee and Zavrel, Chaboche, and Kang. The Ahmadzadeh‐Varvani kinematic hardening rule was developed to address ratcheting progress over asymmetric stress cycles with relatively a simple framework and less number of coefficients. Inclusion of isotropic hardening rules to the framework improved ratcheting response of materials mainly over the first stage of ratcheting. Lee and Zavrel model (ISO‐I) developed an exponential function to account for accumulated plastic strain as yield surface is expanded over stage I and early stage II of ratcheting. Isotropic models by Chaboche (ISO‐II) and Kang (ISO‐III) encountered yield surface evolution in the framework by introducing an internal variable that takes into account the prior maximum plastic strain range. The choice of isotropic hardening model coupled to the kinematic hardening model is highly influenced by material softening/hardening response.

Effect of Long-Term Room Temperature Aging on the Fatigue Properties of SnAgCu Solder Joint

Solder joints in electronic assemblies are subjected to mechanical and thermal cycling. These cyclic loadings lead to the fatigue failure of solder joints involving damage accumulation, crack initiation, crack propagation, and failure. Aging leads to significant changes on the microstructure and mechanical behavior of solder joints. While the effect of thermal aging on solder behavior has been examined, no prior studies have focused on the effect of long-term room temperature aging (25 °C) on the solder failure and fatigue behavior. In this paper, the effects of long-term room temperature aging on the fatigue behavior of five common lead-free solder alloys, i.e., SAC305, SAC105, SAC-Ni, SAC-X-Plus, and Innolot, have been investigated. Several individual lead-free solder joints on printed circuited boards with two aging conditions (no aging and 4 years of aging) have been prepared and subjected to shear cyclic stress–strain loadings until the complete failure. Fatigue life was recorded for each solder alloy. From the stress–strain hysteresis loop, inelastic work and plastic strain ranges were measured and empirically modeled with the fatigue life. The results indicated that 4 years of room temperature aging significantly decreases the fatigue life of the solder joints. Also, inelastic work per cycle and plastic strain range are increased after 4 years of room temperature aging. The fatigue life degradation for the solder alloys with doped elements (Ni, Bi, Sb) was relatively less compared to the traditional SAC105 and SAC305.

The Value Range of Contact Stiffness Factor between Pile and Soil Based on Penalty Function

The value range of contact stiffness factor based on penalty function is studied when we use finite element software ANSYS to analyze contact problems, take single pile and soil of a certain project for example, the normal contact between pile and soil is analyzed with 2D simplified model in horizontal load. The study shows that when adopting linear elastic model to simulate soil, the maximum contact pressure and penetration approach steady value as the contact stiffness factor increases. The reasonable value range of contact stiffness factor reduces as the underlying element thickness decreases, but the rule reverses when refers to the soil stiffness. If choose DP model to simulate soil, the stiffness factor should be magnified 100 times compares to the elastic model regardless of the soil bears small force and still in elastic deformation stage or into the plastic deformation stage. When the soil bears big force and into plastic deformation stage, the value range of stiffness factor relates to the plastic strain range of the soil, and reduces as the horizontal load increases.

Macro-mesoscopic Fracture and Strength Character of Pre-cracked Granite Under Stress Relaxation Condition

The fracture characters are important index to study the strength and deformation behavior of rock mass in rock engineering. In order to investigate the influencing mechanism of loading conditions on the strength and macro-mesoscopic fracture character of rock material, pre-cracked granite specimens are prepared to conduct a series of uniaxial compression experiments. For parts of the experiments, stress relaxation tests of different durations are also conducted during the uniaxial loading process. Furthermore, the stereomicroscope is adopted to observe the microstructure of the crack surfaces of the specimens. The experimental results indicate that the crack surfaces show several typical fracture characters in accordance with loading conditions. In detail, some cleavage fracture can be observed under conventional uniaxial compression and the fractured surface is relatively rough, whereas as stress relaxation tests are attached, relative slip trace appears between the crack faces and some shear fracture starts to come into being. Besides, the crack faces tend to become smoother and typical terrace structures can be observed in local areas. Combining the macroscopic failure pattern of the specimens, it can be deduced that the duration time for the stress relaxation test contributes to the improvement of the elastic–plastic strain range as well as the axial peak strength for the studied material. Moreover, the derived conclusion is also consistent with the experimental and analytical solution for the pre-peak stage of the rock material. The present work may provide some primary understanding about the strength character and fracture mechanism of hard rock under different engineering environments.

Fatigue Life Prediction of Al319-T7 Subjected to Thermo-Mechanical Loading Conditions

This study investigated a fatigue life prediction method based on extensive experiment results of cast aluminum alloy Al319-T7 subjected to repeated thermal and mechanical loading. Cyclic tests and fully reversed fatigue test results of the material were obtained from the specimens subjected to three different strain rates (5x10-5, 5x10-4 and 5x10-3) and various temperature conditions. At each strain rate the specimens were subjected to room temperature (25°C), 150°C, 200°C, 250°C and 300°C. Thermo-mechanical fatigue (TMF) tests were also conducted for in-phase and out-of-phase conditions of the temperature and mechanical loading. During the thermo-mechanical fatigue tests, the effect of loading phases and dwell time on fatigue life of the specimens was also observed. This study modified Taira’s fatigue damage model for thermo-mechanical loading condition to include the strain rate effect on the fatigue damage. Taira assumed that fatigue damage per reversal is proportional to the damage factor, λ(T), and plastic strain range powered by n, (Δεp)n. The relationship between the plastic strain range (Δεp) and the number of cycles to failure (Nf) is presented as λ(T)•(Δεp)n•Nf = C. Where C is a temperature independent material constant. The temperature effect is included in the damage factor, λ(T) that can be determined from the ratio of λ(T)/λ(To) for low cycle fatigue test results at various isothermal conditions. To is the reference temperature and can be determined by experiment. This study used stress range applied instead of plastic strain range in the original equation. Furthermore, the modified equation includes the effect of strain rate, phase, and dwell time. The new fatigue damage equation was well correlated with the experiment results.

Creep-Fatigue Life Prediction of 316H Stainless Steel by Utilizing Non-Unified Constitutive Model

True stress and strain are necessary to estimate the rupture life under creep-fatigue conditions. Finite element analysis (FEA) is one of the most reliable method to calculate true stress and strain, but the accuracy of the obtained result is often greatly dependent on the constitutive model used. Non-unified constitutive model has been proposed, where inelastic strain is decomposed into creep strain and visco-plastic strain. In this paper, a cyclic hardening effect and a plastic strain range dependency were introduced into the non-unified constitutive model to predict the creep-fatigue damage of 316H stainless steel. This model was implemented in a finite element program and FEA were conducted to develop a life assessment method and calculate the creep-fatigue damage by modified ductile exhaustion method. As a consequence, it was revealed that the predicted creep-fatigue lives showed high correspondence with the experimental results by the modified ductile exhaustion method utilizing the non-unified constitutive model.

Life prediction for high temperature low cycle fatigue of two kinds of titanium alloys based on exponential function

The high temperature low cycle fatigue tests of TC4 titanium alloy and TC11 titanium alloy are carried out under strain controlled. The relationships between cyclic stress-life and strain-life are analyzed. The high temperature low cycle fatigue life prediction model of two kinds of titanium alloys is established by using Manson-Coffin method. The relationship between failure inverse number and plastic strain range presents nonlinear in the double logarithmic coordinates. Manson-Coffin method assumes that they have linear relation. Therefore, there is bound to be a certain prediction error by using the Manson-Coffin method. In order to solve this problem, a new method based on exponential function is proposed. The results show that the fatigue life of the two kinds of titanium alloys can be predicted accurately and effectively by using these two methods. Prediction accuracy is within ±1.83 times scatter zone. The life prediction capability of new methods based on exponential function proves more effective and accurate than Manson-Coffin method for two kinds of titanium alloys. The new method based on exponential function can give better fatigue life prediction results with the smaller standard deviation and scatter zone than Manson-Coffin method. The life prediction results of two methods for TC4 titanium alloy prove better than TC11 titanium alloy.

Resetting scheme for plastic strain surface in constitutive modeling of cyclic plasticity

AbstractA resetting scheme is proposed for correctly evaluating the plastic strain range to analyze structural components subjected to regular cyclic loading following pre‐loading. In this scheme, a plastic strain surface, referred to as the plastic‐strain‐range surface in the present paper, is reset to a point and re‐evolves every cycle, with its size at the end of the last cycle considered to be the plastic strain range of the current cycle. This resetting scheme provides a definite value for the evolution parameter of the plastic‐strain‐range surface irrespective of the amounts of cyclic hardening, pre‐straining, and ratcheting. The resetting scheme is implemented in a cyclic viscoplastic model in finite element methods, and is applied to analyze a notched bar subjected to cyclic loading at its ends. Furthermore, the validity of the resetting scheme for non‐proportional cyclic loading is examined by analyzing the cyclic behavior along elliptic and rhombic strain paths. It is shown that the resetting scheme allows the use of a definite value for the evolution parameter of the plastic‐strain‐range surface in the presence of any cyclic hardening and/or ratcheting. Moreover, it is shown that the resetting scheme can be valid for cyclic loading with a certain degree of non‐proportionality.

The Attempt of the Low-Cycle Fatigue Life Description of Chosen Creep-Resistant Steels Under Mechanical and Thermal Interactions

AbstractThe study focuses on the problem of determination of low-cycle fatigue properties for the chosen group of creep-resistant steels used in the power and chemical industries. It tries to find the parameter which would describe well the fatigue life and take into account mechanical loads and temperature. The results of LCF tests have been presented in the paper. New parameter P has been introduced. This parameter joins a plastic strain range, a stress range and temperature. The fatigue life has been predicted versus parameter P. The comparison of the predicted and observed values of fatigue life shows the agreement between these values. The method of fatigue life prediction formulated in this way is expected to describe the behavior of materials under thermo-mechanical fatigue.

Experimental and numerical investigation on thermal fatigue behaviour of 9Cr 1Mo steel tubes

Abstract Boiler tubing is subjected to alternate cycles of heating and cooling during operation initiating alternate thermal expansion and contraction. Alternate cycles of differential expansion and contraction causes thermal fatigue of the component. Thermal fatigue causes tube failures, significantly reducing the working life of the tubular components. Boilers have matured into super critical design using T91 grade materials thereby increasing the operating efficiency. The studies involving thermal fatigue of tubes of T91 grades for boiler components in operating conditions are thus an important area. A simple experimental set up has been developed to simulate thermal fatigue conditions in the internal diameter (ID) side of the tube. The work involves both experimental and numerical investigations of the thermal fatigue behaviour by creating a simulated environment and a Finite Element Model (FEM). FEM analyses are carried out based on the decoupled thermal and inelastic stress analyses to compute the total plastic strain range experienced by the boiler tubes. The cyclic spray cooling causes thermal fatigue cracks in the T91 tube. The number of cycles to crack initiation has been obtained from the experimentation and number cycles to failure has been calculated using modified Coffin-Manson relation. The study thus presents a reliable fatigue failure analysis of 9Cr 1Mo steel tubes used in boiler industry.

Effect of low-temperature on mechanical behavior for an AISI 304 austenitic stainless steel

An AISI 304 austenitic stainless steel (ASS) with average grain size of approximately 48µm was selected to explore the effect of the low-temperature on mechanical behavior for commercial metastable ASS, which basing on tensile tests and Charpy V-notch impact tests under temperatures of 20–298K, Feritscope testing and physical metallurgy. The results showed that both yield strength and tensile strength were enhanced by lowering temperatures; however, the uniform strain decreased with reducing temperatures. The yield strength at 20K and 77K were much higher than that at other temperatures, accompanying with an abrupt increase of thermally-induced martensite before tensile testing. The Charpy V-notch impact energy decreased faster in the range of 77–298K and kept almost unchanged in the range of 20–77K, and the ASS at 20K still exhibited a dimple shaped fracture. Generally, the work-hardening rate (Θ) of the ASS at testing temperatures of 20–298K dropped rapidly at the initial plastic strain range (Stage I) and then grew with the increase of tensile strain (Stage II), then following by a continuous decline to necking (Stage III), i.e., the generation of a peak of work-hardening rate. Specifically, the Stage I, II and III were terminated in advance and the peak value at the Stage II were increased obviously by reducing temperature from 298K down to the range of 20–253K. Furthermore, the work-hardening behavior of the ASS was discussed in view of the evolution of microstructure basing on Olson-Cohen model.

Cyclic plasticity behaviors of steam turbine rotor subjected to cyclic thermal and mechanical loads

In this paper, shakedown and ratchet analyses are performed to investigate the cyclic plasticity behaviors of the steam turbine rotor subjected to cyclic thermal and mechanical loads by employing Linear Matching Method (LMM). Traditionally, the shakedown or ratchet analysis mainly focus on the structure under general cyclic loading condition composed by constant mechanical load and cyclic thermal load, but the investigated steam turbine rotor here is subjected to cyclic mechanical load and cyclic thermal load that vary in phase and out of phase throughout the practical operation load cycle. The failure behaviours of structure under practical operation load cycle is studied and discussed. The novel shakedown and ratchet failure diagrams are plotted by calculating different combinations of cyclic mechanical load and cyclic thermal load. The innovative equation to acquire plastic strain range of the structure under steady state cycle is fitted, which is vital for low cycle fatigue (LCT) assessment. Moreover, detailed step-by-step inelastic analyses are also performed to verify the applicability and effectiveness of the limit boundaries calculated by the LMM. All the investigations demonstrate that the proposed LMM technique is capable of handling practical industrial application with complicated cyclic loads.

Local microstructure and flow stress in deformed metals

The microstructure and flow stress of metals are related through many well-known strength-structure relationships based on structural parameters, where grain size and dislocation density are examples. In heterogeneous structures, the local stress and strain are important as they will affect the bulk properties. A microstructural method is presented which allows the local stress in a deformed metal to be estimated based on microstructural parameters determined by an EBSD analysis. These parameters are the average spacing of deformation introduced boundaries and the fraction of high angle boundaries. The method is demonstrated for two heterogeneous structures: (i) a gradient (sub)surface structure in steel deformed by shot peening; (ii) a heterogeneous structure introduced by friction between a tool and a workpiece of aluminum. Flow stress data are calculated based on the microstructural analysis, and validated by hardness measurement and 2D numerical simulations. A good agreement is found over a plastic strain range from ∼1 to 5.

Hysteretic mechanical property of low-yield strength shear panel dampers in ultra-large plastic strain

The low-yield strength steel (LYS) has been a promising material to make shear panel damper in seismic engineering due to the large plastic deformation capacity. To take advantage of the energy absorption ability of the low-yield-strength steel shear panel damper (LYSPD), it is essential to obtain the accurate prediction for the stress-strain relationship of LYS especially for the high plastic deformation. However, most of the existing constitutive models for LYS are based on the plastic strain not more than 6%. Here, an improved constitutive model is developed to describe the plastic behavior in a large range of plastic strain up to 60%. First of all, the large plastic behavior with the necking effect under monotonic tension loading is considered and verified by test. Secondly, together with several constitutive models for describing the shear plastic behavior of LYS with and without consideration of cyclic hardening, the accuracy of these models are verified by the cyclic incremental test results of LYSPD. Moreover, an accurate model is calibrated by using the yield stress evolution of the two-surface theory. The developed model could be used to describe the mechanical properties for large plastic strain and to judge the stability of the structure in improved accuracy.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.