Plastic Strain Energy Density Research Articles

Fatigue crack initiation life prediction for aluminium alloy 7075 using crystal plasticity finite element simulations

An experimentally-validated approach for predicting fatigue crack initiation life of polycrystalline metals is developed based on crystal plasticity finite element (CPFE) simulations. In this approach, the microstructure used in the simulations possesses statistically the same grain size and crystallographic orientations as those obtained from electron back-scatter diffraction experiments. A backstress model is incorporated into the CP constitutive model to describe the mechanical behaviour of aluminium alloy (AA) 7075 under cyclic loading. The key variables of the prediction model, the energy efficiency factor and plastic strain energy density, are calibrated using a fatigue test on a round-notched AA7075 specimen at room temperature. The proposed approach is then validated by using another fatigue test to predict 69.1–87.3% of the experimentally measured fatigue crack initiation life. The effects of the microstructure and texture on the energy efficiency factor and fatigue life prediction are quantitatively determined. It is shown that for a given range of energy efficiency factors a similar range of life prediction is obtained. Since the proposed approach considers the heterogeneity of the microstructure, it can well capture the grain scale deformation localisation and therefore improve the precision of fatigue life prediction.

Low cycle fatigue performance of ball grid array structure Cu/Sn–3.0Ag–0.5Cu/Cu solder joints

Low cycle fatigue performance of ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints with different standoff heights (h, varying from 100 to 500μm) and two pad diameters (d, d=320 and 480μm) under displacement-controlled cyclic loading was studied by experimental method and finite element (FE) simulation. A prediction method based on the plastic strain energy density and continuum damage mechanics (CDM) framework was proposed to evaluate the initiation and propagation of fatigue crack in solder joints. The results show that fatigue failure of solder joints is a process of damage accumulation and the plastic strain energy density performs a power function correlation with the cycle numbers of crack initiation and propagation. Crack propagation rate is affected by the stress triaxiality, which is dependent on the loading mode and increases dramatically with decreasing h under tensile loading, while the change of standoff height has very limited influence on the stress triaxiality under shear loading mode. Moreover, crack growth correlation constants identified in Cu/Sn–3.0Ag–0.5Cu/Cu joints with a specific geometry (h=100μm and d=480μm) can be well used to predict the fatigue life of BGA joints with other geometries. Furthermore, the results have also shown that the fatigue life of solder joints increases with decreasing the geometric ratio of h/d under the same nominal shear strain amplitude, while it drops with decreasing h/d under the same shear displacement amplitude in cyclic loading. When the geometric ratio (i.e., h/d ratio) is unchanged, the miniaturization of BGA joints brings about a decrease in fatigue life of the joints.

An asymmetric elastic–plastic analysis of the load-controlled rotating bending test and its application in the fatigue life estimation of wrought magnesium AZ31B

Due to different deformation mechanisms arising from limited slip systems in HCP wrought magnesium alloys, their yield and hardening in tension and compression are different. Consequently, the cyclic behavior of these alloys is asymmetric showing a non-Masing hysteresis. An elastic–plastic method of analysis is proposed in this paper to handle the pronounced asymmetry inherited by Mg wrought alloys. Samples machined from an extrusion piece of AZ31B were tested on a standard rotating bending machine at bending moment amplitudes ranging from 3.3 to 6.3Nm. Tests were conducted under two conditions: as-extruded and stress-relived. As-extruded samples showed a higher fatigue limit due to beneficial residual stresses induced by the extrusion process. The proposed elastic–plastic model was then applied to obtain the stress distribution in the tested specimens. Cyclic hystereses obtained from this analysis were used to estimate the elastic and plastic strain energy densities per cycle. An energy-life model for AZ31B was then employed in conjunction with the calculated hysteresis energies to predict fatigue life of AZ31B in rotating bending. The proposed model prediction results were in good agreement with the experimental results.

Research on Low Cycle Fatigue Behavior of BGA Structure Lead-free Solder Joints

A plastic strain energy density methodology is proposed to evaluate the initiation and propagation of fatigue crack in lead-free solder joints. The relationships among the plastic strain, plastic strain energy, continuum damage mechanics(CDM) and fatigue life are clarified. Crack growth correlation constants for micro-scale ball grid array(BGA) structure solder joints(with standoff height h in the range 100 to 500 μm and a pad diameter 480 μm) are determined by a combination of experimental estimation and numerical calculation. The results show that the cycle numbers of crack initiation and propagation have power function relationship with the plastic strain energy density generated in each fatigue cycle. Crack propagation rate is affected by stress triaxiality, which is dependent on loading modes, i.e., stress triaxiality increases dramatically with decreasing h under tensile load because of the mechanical constraint effect arising from interfaces and package structure, while under shear load the standoff height has very limited effect on stress triaxiality. Furthermore, crack growth correlation constants identified in solder joints with h=100 μm can be well used to predict fatigue life of solder joints with different geometries, indicating that the fatigue life prediction method proposed in this study can effectively prevent the influence of plastic strain energy concentration caused by structural and volume factors on the prediction of fatigue life of BGA structure solder joints.

Some remarks on the Neuber rule applied to a control volume surrounding sharp and blunt notch tips

ABSTRACTThe paper deals with the small scale yielding estimation of nonlinear stresses and strains at the root of sharp and blunt notches through the mechanical model of antiplane shear loadings. The frame stems from the relation existing between the elastic and plastic averaged strain energy densities evaluated over the control volume drawn by the energy contour lines ahead of the notch tip.The analysis proves that there exist different relationships in terms of point‐wise elastic and plastic stresses and strains at the notch tip depending whether the notch is sharp (small notch tip radius) or blunt. For sharp notches, the analysis confirms previous results obtained by the present authors, according to which . This equation accounts for the influence of the material law through the hardening exponent n. Differently, when the notch can be regarded as blunt, calculations over the control volume give , in agreement with the Neuber rule.

Bayesian framework for probabilistic low cycle fatigue life prediction and uncertainty modeling of aircraft turbine disk alloys

Probabilistic life prediction of aircraft turbine disks requires the modeling of multiple complex random phenomena. Through combining test data with technological knowledge available from theoretical analyses and/or previous experimental data, the Bayesian approach gives a more complete estimate and provides a formal updating approach that leads to better results, save time and cost. The present paper aims to develop a Bayesian framework for probabilistic low cycle fatigue (LCF) life prediction and quantify the uncertainty of material properties, total inputs and model uncertainty resulting from choices of different deterministic models in a LCF regime. Further, based on experimental data of turbine disk material (Ni-base superalloy GH4133) tested at various temperatures, the capabilities of the proposed Bayesian framework were verified using four fatigue models (the viscosity-based model, generalized damage parameter, Smith–Watson–Topper (SWT) and plastic strain energy density (PSED)). By updating the input parameters with new data, this Bayesian framework provides more valuable performance information and uncertainty bounds. The results showed that the predicted distributions of fatigue life agree well with the experimental data. Further it was shown that the viscosity-based model and the SWT model yield more satisfactory probabilistic life prediction results for GH4133 under different temperatures than the generalized damage parameter and PSED ones based on the same available knowledge.

A new energy‐based isothermal and thermo‐mechanical fatigue lifetime prediction model for aluminium–silicon–magnesium alloy

ABSTRACTIn this paper, a new fatigue lifetime prediction model is presented for the aluminium–silicon–magnesium alloy, A356.0. This model is based on the plastic strain energy density per cycle including two correction factors in order to consider the effect of the mean stress and the maximum temperature. The thermal term considers creep and oxidation damages in A356.0 alloy. To calibrate the model, isothermal fatigue and out‐of‐phase thermo‐mechanical fatigue (TMF) tests were conducted on the A356.0 alloy. Results showed an improvement in predicting fatigue lifetimes by the present model in comparison with classical theories and also the plastic strain energy density (without any correction factors). Therefore, this model is applicable for TMF, low cycle fatigue (LCF) and both TMF/LCF lifetimes of the A356.0 alloy. Furthermore, this model can be easily used for the estimation of thermo‐mechanical conditions in components such as cylinder heads.

Effects of Strain Rate on Low Cycle Fatigue Behaviors of High-Strength Structural Steel

The low cycle fatigue (LCF) behavior of a high-strength structural steel was investigated in the strain rate range of 4×10−5— 0. 12 s−1 (0. 001 — 3 Hz) under constant total strain (±1%) control. The cyclic stress response at all strain rates exhibited behavior of rapid softening in the early stage of fatigue life and subsequent saturation up to failure. It was found that the stress amplitude, the plastic strain amplitude, the plastic strain energy density and the fatigue life depend mainly on the strain rate. The strain rate of 0. 012 s−1 was found as a transition point where the LCF of the steel showed different behavior from low strain rate to high strain rate. The relationship between the time to failure and strain rate was expressed well by a power law relation. The fracture surfaces of the fatigue samples were characterized by using a scanning electron microscope (SEM) and the fracture mechanisms were discussed in terms of time-dependent deformation of the steel.

Numerical Investigation on Void Nucleation around Inclusions under Combined Mechanical and Thermal Cycling Conditions

In this paper a numerical investigation on the void nucleation behaviors under combined mechanical and thermal cycling conditions have been performed. A finite element unit cell model is conduct to calculate the local stress-strain field and describe the process of void nucleation from inclusion. Numerical results show that the thermal mismatch stress between the particles and matrix can assist the external load to cause interface debonding. Under certain mechanical and thermal cycling conditions, complicated stress and strain hystereses developed in the matrix. Both the plastic strain and plastic energy density of the interface will be accumulated during every thermal cycle. The plastic energy accumulation of the interface will first reach the debonding value and failure occurs. Based on the numerical calculation, a new energy based failure criteria is proposed to characterize the behaviors of void nucleation under combine mechanical and thermal cycling conditions.

A generalized energy-based fatigue–creep damage parameter for life prediction of turbine disk alloys

In this paper, a new model for life prediction of turbine disk alloys (GH4133) is proposed. Based on plastic strain energy density, a generalized energy-based fatigue–creep damage parameter is developed to account for creep and mean strain/stress effects in the low cycle fatigue regime. Moreover, the mechanism of cyclic hardening is taken into account within this model. It provides a better prediction of GH4133’s fatigue behavior when compared to the Smith–Watson–Topper and plastic strain energy density methods. Under mean strain conditions, the proposed model provides a more accurate life prediction of GH4133 than that under zero-mean strain conditions.

LOW CYCLE FATIGUE BEHAVIOR AND LIFE PREDICTION OF A CAST COBALT-BASED SUPERALLOY

Co -base superalloys have been applied in the stationary components of gas turbine owing to their excellent high temperature properties. Low cycle fatigue data on ECY-768 reported in a companion paper were used to evaluate fatigue life prediction models. In this study, low cycle fatigue tests are performed as the variables of total strain range and temperatures. The relations between plastic and total strain energy densities and number of cycles to failure are examined in order to predict the low cycle fatigue life of Cobalt-based super alloy at different temperatures. The fatigue lives is evaluated using predicted by Coffin-Manson method and strain energy methods is compared with the measured fatigue lives at different temperatures. The microstructure observing was performed for how affect able to low-cycle fatigue life by increasing the temperature.

Probabilistic Low Cycle Fatigue Life Prediction Using an Energy-Based Damage Parameter and Accounting for Model Uncertainty

Probabilistic methods have been widely used to account for uncertainty of various sources in predicting fatigue life for components or materials. The Bayesian approach can potentially give more complete estimates by combining test data with technological knowledge available from theoretical analyses and/or previous experimental results, and provides for uncertainty quantification and the ability to update predictions based on new data, which can save time and money. The aim of the present article is to develop a probabilistic methodology for low cycle fatigue life prediction using an energy-based damage parameter with Bayes’ theorem and to demonstrate the use of an efficient probabilistic method, moreover, to quantify model uncertainty resulting from creation of different deterministic model parameters. For most high-temperature structures, more than one model was created to represent the complicated behaviors of materials at high temperature. The uncertainty involved in selecting the best model from among all the possible models should not be ignored. Accordingly, a black-box approach is used to quantify the model uncertainty for three damage parameters (the generalized damage parameter, Smith–Watson–Topper and plastic strain energy density) using measured differences between experimental data and model predictions under a Bayesian inference framework. The verification cases were based on experimental data in the literature for the Ni-base superalloy GH4133 tested at various temperatures. Based on the experimentally determined distributions of material properties and model parameters, the predicted distributions of fatigue life agree with the experimental results. The results show that the uncertainty bounds using the generalized damage parameter for life prediction are tighter than that of Smith–Watson–Topper and plastic strain energy density methods based on the same available knowledge.

Load path sensitivity and fatigue life estimation of 30CrNiMo8HH

A set of strain-controlled biaxial proportional and non-proportional tests were conducted on solid and tubular specimens of 30CrNiMo8HH steel. The effect of the phase angle on fatigue life was studied. This effect becomes noticeable when applying a 90° out-of-phase loading, reducing the fatigue life by a factor up to 5. It has been shown that the material has no additional hardening due to out-of-phase loading. To account for this severe path dependency, a material dependent non-proportionality modification factor is proposed. This path dependent sensitivity factor is applied to six different fatigue parameters including maximum equivalent total strain, maximum equivalent stress, Smith–Watson–Topper, Fatemi–Socie, plastic strain energy density and total strain energy density to correlate the fatigue results. The predicted fatigue lives are compared with the experiments. The cyclic plasticity models of Mroz and Chaboche were successfully employed to model the cyclic behavior of 30CrNiMo8HH steel. It has been shown that estimations based on the proposed non-proportionality modification factor agree well with the experimental results.

A simple life prediction method for 304L stainless steel structures under fatigue-dominated thermo-mechanical fatigue loadings

Abstract Thermo-mechanical fatigue (TMF) tests of 304L stainless steel were performed in the temperature range in which creep and oxidation effects can be considered negligible. Four different phase angles between mechanical strain and temperature cycles (in-phase (IP), out-of-phase (OP), clockwise-diamond-phase (CD), and counter-clockwise-diamond-phase (CCD)) with three different mechanical strains were performed to elucidate the effects of the mechanical strain and phase angle on the fatigue life. IP and CD induce longer life in general compared to OP and CCD, which could be related to the difference of the mean stress in each condition. Ultimate tensile strength values from tensile tests were used to consider the effect of varying temperature during a TMF cycle on the fatigue damage and material resistance. The effects of specimen geometry (solid versus hollow) on the fatigue life were considered. A simple life prediction model that utilizes the plastic strain energy density, ultimate tensile strength, and mean stress is suggested; this model can predict the TMF fatigue life within a 2× scatter band and explain the difference between different phase angles. The model used one new term to consider the mean stress effect, in addition to the two parameters that are used in the conventional Morrow's model.

Low Cycle Fatigue Behavior of Ni-Base Superalloy IN738LC at Elevated Temperature

High strength nickel-base super alloys have been used in turbine blades for many years because of their superior performance at high temperature. The prediction of fatigue life for superalloys is important for improving the efficiency. In this study, low cycle fatigue tests are performed the variables of total strain range, and room and elevated temperature. The relations between plastic and total strain energy densities and number of cycles to failure are examined in order to predict the low cycle fatigue life of IN738LC super alloy. The fatigue life is evaluated by the Coffin-Manson equation, also the predicted lives by plastic and total strain energy density are compared with experimental results.

Stress-Strain Behavior of an Aluminum Alloy Under Transient Strain-Rates

Because most structures are subjected to transient strain-rate loading, an experimental study was conducted to investigate the stress-strain behaviors of an aluminum alloy undergoing varying strain-rate loading. To this end, uniaxial tensile loading was applied to coupons of dog-bone shape such that each coupon underwent two or three different strain-rates, i.e., one rate after another. As a basis, a series of single-strain-rate tests was also conducted with strain-rates of 0.1–10.0 s−1. When the material experienced multistrain-rate loading, the stress-strain curves were significantly different from any single-strain-rate stress-strain curve. The strain-rate history affected the stress-strain curves under multistrain-rate loading. As a result, some simple averaging of single-strain-rate curves did not predict the actual multistrain-rate stress-strain curve properly. Furthermore, the fracture strain under multistrain-rate loading was significantly different from that under any single-strain-rate case. Depending on the applied strain-rates and their sequences, the former was much greater or less than the latter. A technique was proposed based on the residual plastic strain and plastic energy density in order to predict the fracture strain under multistrain-rate loading. The predicted fracture strains generally agreed well with the experimental data. Another observation that was made was that the unloading stress-strain curve was not affected by the previous strain-rate history.

The effect of specimen geometry on the low cycle fatigue life of metallic materials

The effect of the specimen geometry on the measured fatigue life was investigated in this study. Low-cycle fatigue tests with hollow and solid specimens were performed and the differences in the two different specimen geometries were observed. A difference in the fatigue life between the hollow and solid specimens exists when the strain is large and diminishes as the strain decreases, which indicates that the difference stems from the crack propagation stage rather than the crack initiation stage. Two-dimensional finite element analysis was performed to quantify the effects of the specimen geometry in terms of the stress and strain near the crack tip. Larger internal plastic strain in the hollow specimen was found. This led to a higher plastic strain energy density and could explain the difference in the lifespan using the two specimen geometries.

A composite finite element to predict failure progress in composite laminates accounting for nonlinear material properties

SUMMARY The failure initiation and failure progress up to the final failure of the fiber-reinforced composite (FRC) laminated shells, using the finite element method have been studied. A finite element computer program ‘NLINE’ has been used for this purpose. The program uses a 10-node triangular finite element for the analysis of plates and shells developed by the first author. For detecting and controlling the failure of such structures, Abu-Farsakh–Abdel-Jawad (AF-AJ) failure criterion has been employed, which is applicable to nonlinear behavior composite materials. The material nonlinear behavior is simulated using a comprehensive constitutive material model that incorporates the material nonlinearity through the plastic strain energy density of an equivalent linear–elastic system. Results were compared with the corresponding available experimental data and theoretical predictions of a worldwide failure exercise. This exercise was launched to confirm the current state-of-the art of predicting failure in composite laminates. The predictions of failure by ‘NLINE’ were in good agreement with many of the experimental results as well as the other theoretical predictions. Copyright © 2011 John Wiley & Sons, Ltd.

Plastic Strain Energy in Low-Cycle Fatigue of A356 (Al-7Si-0.4Mg) Aluminum Alloys

In this paper, the problem of plastic strain energy density as a evaluation of low-cycle fatigue (LCF) properties for A356 alloys with various Ti content and Ti-addition methods is considered. The experimental results reveal that it is not the Ti-addition methods but the Ti content that has played an important role in influencing on the plastic strain energy density, thus on the LCF life. Whether for the electrolytic A356 alloys or for the melted A356 alloys, the alloys with 0.1% Ti content can consume higher cyclic plastic strain energy during the cyclic deformation compared with the alloys with 0.14% Ti content due to the better plasticity, giving rise to a better fatigue resistance and a longer LCF life. Because of the different macro or micro deformation mechanism, the fracture surface of electrolytic A356 alloy exhibits the diverse microstructural morphologies under the various strain amplitude.

Astudy on life prediction of low cycle fatigue in superalloy for gas turbine blades

A more accurate life prediction for gas turbine blade takes into account the material behaviour under the Low Cycle Fatigue cycles normally encountered in turbine operation. In this study, low cycle fatigue tests are performed as the variables of total strain range and temperatures. The relations between plastic and total strain energy densities and number of cycles to failure are examined in order to predict the low cycle fatigue life of superalloy at different temperatures. The fatigue lives that are predicted by Coffin-Manson method and strain energy methods are compared with the measured fatigue lives at different temperatures.