Inelastic Strain Amplitude Research Articles

The Investigation of the Fracture Behavior of a Chinese 9% Cr Steel Welded Joint under Creep-Fatigue Interactive Loading

To understand the premature-fracture mechanisms of long-term service damage of an advanced alloy’s (Chinese P92 steel) welded joint, the creep-fatigue (CF) experiments with holding times of 30, 120, 300, 600 and 900 s were individually performed at 923 K. The cyclic softening, inelastic-strain amplitudes and stress-relaxation behaviors were compared between welded and base-metal (BM) specimens. From the results, the failure stage of the welded specimens occupies 45% of the lifetime fraction, while it only takes up 20% of the lifetime fraction in BM specimens with short holding times (30 and 120 s). Furthermore, only two softening stages were observed for both kinds of CF specimens with long holding times. The absence of a third softening stage in longer-held specimens indicates that the processes of macroscopic-crack initiation, propagation and rupture were accelerated. Based on the observation of the fracture surfaces, the fracture mechanism shifted from fatigue-dominated damage to creep-fatigue interaction when the holding period was increased.

Effect of Stress Gradient on Heat Cycle Fatigue Life Prediction of Solder Joints by Repetitive Bending Test

Strength of solder joints is usually evaluated by a shear test and a pull test. The reliability of the solder joint is evaluated by the repetitive pull tests of solder bulk specimens. However, the stress and strain field that caused by thermal load on the solder joint of the product model for estimating the reliability is different from these tests. Therefore, we proposed a repetitive bending test as a reliability test of solder joints producing the stress and strain field caused at the solder joint of product model. We proposed a repetitive multi-point bending test as a method to predict the fatigue life of the solder joint in the thermal cycle test in a short period of time. The influence of strain gradient on the inelastic strain amplitude used for lifetime evaluation is estimated. The controllability of the strain gradient by the three-point bending test parameters is investigated. The effect of residual stress on inelastic strain amplitude during sample preparation for thermal cycle test is also evaluated.

Simulation of Cyclic Loading on Pipe Elbows Using Advanced Plane-Stress Elastoplasticity Models1

Abstract This work investigates the response of industrial steel pipe elbows subjected to severe cyclic loading (e.g., seismic or shutdown/startup conditions), associated with the development of significant inelastic strain amplitudes of alternate sign, which may lead to low-cycle fatigue. To model this response, three cyclic-plasticity hardening models are employed for the numerical analysis of large-scale experiments on elbows reported elsewhere. The constitutive relations of the material model follow the context of von Mises cyclic elasto-plasticity, and the hardening models are implemented in a user subroutine, developed by the authors, which employs a robust numerical integration scheme, and is inserted in a general-purpose finite element software. The three hardening models are evaluated in terms of their ability to predict the strain range at critical locations, and in particular, strain accumulation over the load cycles, a phenomenon called “ratcheting.” The overall good comparison between numerical and experimental results demonstrates that the proposed numerical methodology can be used for simulating accurately the mechanical response of pipe elbows under severe inelastic repeated loading. Finally, this paper highlights some limitations of conventional hardening rules in simulating multi-axial material ratcheting.

Low cycle fatigue life modelling using finite element strain range partitioning for a steam turbine rotor steel

Materials made for modern steam power plants are required to withstand high temperatures and flexible operational schedule. Mainly to achieve high efficiency and longer components life. Nevertheless, materials under such conditions experience crack initiations and propagations. Thus, life prediction must be made using accurate fatigue models to allow flexible operation. In this study, fully reversed isothermal low cycle fatigue tests were performed on a turbine rotor steel called FB2. The tests were done under strain control with different total strain ranges and temperatures (20 °C to 625 °C). Some tests included dwell time to calibrate the short-time creep behaviour of the material. Different fatigue life models were evaluated based on total life approach. The stress-based fatigue life model was found unusable at 600 °C, while the strain-based models in terms of total strain or inelastic strain amplitudes displayed inconsistent behaviour at 500 °C. To construct better life prediction, the inelastic strain amplitudes were separated into plastic and creep components by modelling the deformation behaviour of the material, including creep. Based on strain range partitioning approach, the fatigue life depends on different damage mechanisms at different strain ranges at 500 °C. This allows for the formulation of life curves based on either plasticity-dominated damage or creep-dominated damage. At 600 °C, creep dominated while at 500 °C creep only dominates for higher strain ranges. The deformation mechanisms at different temperatures and total strain ranges were characterised by scanning electron microscopy and by quantifying the amount of low angle grain boundaries. The quantification of low angle grain boundaries was done by electron backscatter diffraction. Microscopy revealed that specimens subjected to 600 °C showed signs of creep damage in the form of voids close to the fracture surface. In addition, the amount of low angle grain boundaries seems to decrease with the increase in temperature even though the inelastic strain amplitude was increased. The study indicates that a significant amount of the inelastic strain comes from creep strain as opposed of being all plastic strain, which need to be taken into consideration when constructing a life prediction model.

Low cycle fatigue modelling of a steam turbine rotor steel

Materials in steam turbine rotors are subjected to cyclic loads at high temperature, causing cracks to initiate and grow. To allow for more flexible operation, accurate fatigue models for life prediction must not be overly conservative. In this study, fully reversed low cycle fatigue tests were performed on a turbine rotor steel called FB2. The tests were done isothermally, within temperature range of room temperature to 600 °C, under strain control with 0.8-1.2 % total strain range. Some tests included hold time to calibrate the short-time creep behaviour of the material. Different fatigue life models were constructed. The life curve in terms of stress amplitude was found unusable at 600 °C, while the life curve in terms of total strain or inelastic strain amplitudes displayed inconsistent behaviour at 500 °C. To construct better life model, the inelastic strain amplitudes were separated into plastic and creep components by modelling the deformation behaviour of the material, including creep. Based on strain range partitioning approach, the fatigue life depends on different damage mechanisms at different strain ranges. This allowed the formulation of life curves based on plasticity or creep domination, which showed creep domination at 600 °C, while at 500 °C, creep only dominates for higher strain range.

Mechanical response and dislocation substructure of a cast austenitic steel under low cycle fatigue at elevated temperatures

With the increase of exhaust temperature in automobiles resulting from the stricter environmental and fuel consumption regulations, high temperature fatigue failure of exhaust manifolds is being a significant issue for safety concern. In this research, low cycle fatigue behavior of a Nb-bearing cast austenitic steel with the "Chinese-script" type primary Nb(C,N), was investigated in the temperature range of 600–950°C. It is indicated that the fatigue lifetime was predominantly dependent on the inelastic strain amplitude, in spite of fatigue temperature. However, the change of deformation substructure from dislocation cells, slip bands to subgrains was observed from 600°C to 950°C, which was induced by the increased thermal recovery. Correspondingly, the cyclic stress amplitude changed from cyclic hardening at 600°C to cyclic softening and cyclic stress saturation at 800°C and 950°C, respectively. Besides, strain heterogeneity was also noted between the dendrite core and the interdendritic region, thus regarded as a promotion for crack initiation. The generated data and the understanding will be helpful for alloy design and fatigue lifetime prediction next.

Parameters influencing thermomechanical fatigue of a directionally-solidified Ni-base superalloy

Thermomechanical fatigue (TMF) is a low cycle fatigue process in which material life is correlated to the mechanical strain amplitude. However, it is well known that several other factors influence this life. This paper examines several of these parameters and their influence on life using experiments conducted on a second generation directionally-solidified (DS) Ni-base superalloy. The parameters considered include the influence of the temperature extremums (Tmax of either 750 or 950°C and Tmin of either 100 or 500°C), strain ratio (R∊), the strain-temperature phasing (in-phase (IP) and out-of-phase (OP)), the influence of dwells at the high temperature end of the cycle resulting in a creep–fatigue (CF) interaction, and material anisotropy associated with the grain growth direction (longitudinal versus transverse). Results suggest that the phasing has a primary role in controlling the mechanism of degradation. IP TMF is dominated by crack formation in volumes surrounding debonded carbides for both continuously cycling (CC) and CF at 950 and 750°C, while OP TMF is dominated by surface oxidation and repetitive cracking of the oxide that reforms at the crack tip at 950°C. Decreasing the Tmax to 750°C the environmental and creep effects are reduced resulting in virtually pure fatigue exposure under OP conditions. With decreasing Tmin from 500°C to 100°C was observed an increase in inelastic strain amplitude and corresponding decrease in life. Variations in R∊ were found to have no significant influence on life or stabilized stress behavior. TMF loading in the transverse orientation resulted in life reductions over the longitudinal orientation due to cracks propagating in a transgranular manner. Lastly, only in material exposed to CF with a Tmax of 950°C rafting of the γ′ precipitates was observed.

Fatigue Damage of Al/SiC Composites - Macroscopic and Microscopic Analysis

Abstract The results of comparative examinations of mechanical behaviour during fatigue loads and microstructure assessment before and after fatigue tests were presented. Composites of aluminium matrix and SiC reinforcement manufactured using the KoBo method were investigated. The combinations of two kinds of fatigue damage mechanisms were observed. The first one governed by cyclic plasticity and related to inelastic strain amplitude changes and the second one expressed in a form of ratcheting based on changes in mean inelastic strain. The higher SiC content the less influence of the fatigue damage mechanisms on material behaviour was observed. Attempts have been made to evaluate an appropriate fatigue damage parameter. However, it still needs further improvements.

Durability of a Stress Concentrator-Containing Cantilever Beam Under Cyclic Loading in Bending

The procedure and results of studies on the durability of the cantilever beam metal over the stress concentrator area in pulsed cyclic bending are presented. Comparison of experimental and numerical simulation data resulted in establishing the relation between the durability and cyclic inelastic strain amplitude. The effect of strain hardening and plastic strains on durability was elucidated.

J0410405 室温で得たSACはんだのクリープひずみと疲労寿命の関係の高温域への適用性([J041-04]工業材料の変形特性・強度およびそのモデル化 損傷・疲労・破壊,機械材料・材料加工部門)

The fatigue life of solder alloys for the slow-fast cyclic loading condition is much shorter than that for the fast-slow cyclic loading condition, despite the two loading conditions having almost equal inelastic strain amplitudes. This suggests that the inelastic strain amplitude is not the best parameter used for evaluating the fatigue life which shows the strain rate dependency. In the previous study, we conducted the fatigue tests using the Sn-3.0Ag-0.5Cu (SAC) solder at RT. The tests employed the cyclic tension-compression loading using the stepped ramp wave (SW) to analyze the stress-creep strain relations during the tests. The analysis result showed that the creep strain amplitude obtained from the stress-creep strain relation had a higher correlation with the fatigue life than the inelastic strain amplitude. In addition, the equation indicating the relationship between the creep strain amplitude and the fatigue life at RT was likely to be useful to predict the fatigue lives at the other temperature. In this study, we investigated the relationships between the creep strain amplitude and the fatigue life for the SAC solder at 343 K and 393 K by conducting the fatigue tests with cyclic tension-compression loading using the SW. Then we attempted to describe the investigated relations at these two temperatures by the above-mentioned equation. As a result, the equation almost expressed the relationships between the creep strain and the fatigue life at 343 K and 393K even though it had been derived from the test results at RT.

710 円孔板の高温疲労強度に及ぼす平均ひずみの影響(OS10-3 オーガナイズドセッション《発電機器の材料・構造解析と評価》)

Object of study is to evaluate fatigue strength of the perforated plate at the elevated temperature of 550℃ by fatigue test. The specimens made of SUS304 stainless steel. We had three experiments. The conditions of mean strain were R=-0.0, -0.4 and -1.0. It was measured that the crack length by using photographs with the CCD video camera at a constant frequency. From the measurement, it is found that the number of failure cycle is reduced when the absolute of value of mean strain is decreased. And cracks grow up at both sides around the hole, but the growth of each crack may not be symmetric. By using these inelastic strain amplitude and crack initiation cycle, the experimented results are shown to be predicted well.

Endochronic Fatigue Life Prediction of SN/3.5AG/0.75CU BGA Solder Joints Under Oblique Displacement Cyclic Tests

ABSTRACTIn this paper, cyclic damage behavior of cyclically load drop curves and their fatigue initiation life of Sn/3.5 Ag/0.75Cu BGA solder joint specimens under oblique displacement cyclic tests were investigated by the theory of damage — coupled endochronic viscoplasticity.By linearly unloading with damage elastic modulus and the linearly damage-free behavior of grip system, the damage loops of force-Φ angle oblique displacement of BGA solder joint specimen were converted successfully into damage loops of the representative solder ball under cyclically proportional straining, which can be predicted by the endochronic constitutive equations. These results established the relationship of the BGA oblique displacement amplitudes da(Φ) and the effective inelastic strain amplitudes of solder ball: da (Φ)= . Based on the phenomena of cyclic damage and its fatigue life, a Φ dependent degree of damage in the evolution equation of damage under proportional strain path was proposed to depend positively on and N cycles. Using this parameter in the damage per cycle computed by the endochronic theory, a Φ modified cycles N(Φ)/β(Φ) can be defined and then derive the Φ modified Lee-Coffin-Manson (Φ-LCM) equation for the fatigue initiation life of solder ball:Finally, a Φ modified Lee's BGA (Φ LBGA) equation for BGA solder joint specimens can be derived:This equation can predict quite well the life data of Sn/3.5Ag/0.75Cu solder joint specimens under Φ ϵ [0π/2]. As a consequence, a vehicle to study the fatigue initiation life of BGA solder joint specimens is constructed completely by the workable methodology and the theory discussed in the paper.

Cyclic Stress-Strain Behavior of BGA (Sn/3.5Ag/0.75Cu) Solder Joint under Cyclically Oblique Displacement Tests and Endochronic Viscoplastic Predictions

ABSTRACTIn this paper, a methodology with workable procedures was proposed and successfully transferred the hysteresis loops of BGA solder joint specimen held by loading-directionally aligned grip system under oblique displacement controlled cyclic tests, into hysteresis loops of “representative” solder ball itself under proportional straining and constant strain rate cyclic tests. Under the elastic unloading during cyclic test, value of elastic modulus of bulk solder specimens and the linear behavior of grip system were used. Following the study of Endochronic cyclic viscoplasticity, the kernel function ρ(Z) = ρ0 exp (−KZ)/Zα was found to be independent of the oblique angle (Φ) of straining paths. However, the steady cyclic behavior of material function f(ξ) ≡ f0 in the definition of intrinsic time Z contained two functions: (1) is the effective inelastic strain amplitude, and (2) f(Φ) Φ(rad) between Φ = 0 (uniaxial) and Φ = π/2 (shear). With (ρ0, α, K) = (4MPa, 0.84, 46) and f0 = [0.24(π/2−Φ)2 − 0.018(π2−Φ) + 1.2] , the endochronic theory predicted experimental hysteresis loops of BGA Sn/3.5Ag/0.75Cu solder joint specimens and Φ = 0°, 27°, 45°, 63°, 90° quite well.Results of ρ(Z) under f0 = 1 were found under independent study based on cyclic tests of bulk specimens under constant uniaxially strain amplitude and various constant strain rates. The values of (ρ0, α, K) = (7.3MPa, 0.84, 30) with f0 = 1.0 were all independent of strain rates. Comparisons of results of both types of specimens revealed that the values of (α, K) were almost the same but (1) ρ0 was smaller for micro-size solder ball, (2) is a material function of Sn/3.5Ag/0.75Cu itself (3) f(Φ) is not a material function, rather it is a special feature to reflect the effects of detail design of solder joint specimen and its connecting methods to the substrates

Modeling aspects of low plastic strain amplitude multiaxial cyclic plasticity in conventional and ultrafine grain nickel

Aspects of the cyclically saturated responses of initially annealed, conventional grain size (average grain diameter of approximately 50 μm) and electrodeposited, ultrafine grain (grains from 20 to 500 nm) nickel to reversed proportional and 90° out-of-phase axial-torsional, strain-controlled cycling at a nominally constant equivalent inelastic strain amplitude of approximately 100 μ strain are reported. An anisotropic, axial-torsional subspace version of Abdel-Karim and Ohno’s kinematic hardening model is presented. Within the framework of conventional small strain, rate-independent plasticity, this approach is used to model the responses. An anhysteretic, phenomenolically based, magnetomechanical model is coupled to the rate-independent plasticity model to include the cyclic magnetostriction response. The kinematic hardening parameter determination scheme, using the proportional path responses, is described. The model correlations achieved are presented and the ability of the resulting models to capture the 90° out-of-phase responses is examined. The model parameter sets, as determined from the proportional responses, require small changes to result in more accurate correlation of the 90° out-of-phase responses and the implications of this are discussed. The relative values of the model parameters between the two materials reflect the initial microstructures. Persistent mean stresses associated with mean total strains imposed are successfully modeled for the proportional strain path responses but not for the 90° out-of-phase responses.

Cyclic Void Growth Model to Assess Ductile Fracture Initiation in Structural Steels due to Ultra Low Cycle Fatigue

A new model is proposed to simulate ductile fracture initiation due to large amplitude cyclic straining in structural steels, which is often the governing limit state in steel structures subjected to earthquakes. Termed the cyclic void growth model (CVGM), the proposed technique is an extension to previously published models that simulate ductile fracture caused by void growth and coalescence under monotonic loading. The CVGM aims to capture ultra low cycle fatigue (ductile fracture) behavior, which is characterized by a few (generally, less than 20) reverse loading cycles to large inelastic strain amplitudes (several times the yield strain). The underlying mechanisms of low-cycle fracture involve cyclic void growth, collapse, and distortion, which are distinct from those associated with more conventional fatigue. The CVGM represents these underlying fracture mechanisms through plastic strain and stress triaxiality histories that can be modeled at the material continuum level by finite-element analyses. Development and validation of the CVGM is substantiated by about 100 notched bar tests, with accompanying finite-element analyses, metallurgical tests, and fractographic examinations of seven varieties of structural steels.

Uniaxial ratchetting in steels with different cyclic softening/hardening behaviours

ABSTRACTThe cyclic deformation of three structural steels, SS316L stainless steel, 40Cr3MoV bainitic steel and 25CDV4.11 steel, were studied experimentally by uniaxial cyclic straining or stressing tests at room temperature. The cyclic softening/hardening behaviours of the steels were discussed first by cyclic straining tests; and then the effects of cyclic softening/hardening behaviours on the uniaxial ratchetting of the materials were investigated by asymmetrical cyclic stressing tests. It is concluded from the experimental results that the ratchetting greatly depends on the cyclic softening/hardening behaviours of the materials, as well as the loading history. Different ratchetting and failure behaviours are observed for the prescribed steels. It is also stated that the proposed unified visco‐plastic constitutive model can provide a fairly reasonable simulation of the uniaxial ratchetting of SS316L stainless steel and 25CDV4.11 steel; but cannot simulate the ratchetting of 40Cr3MoV bainitic steel since the dependence of cyclic softening behaviours on the applied inelastic strain amplitude cannot be reasonably described in the discussed constitutive model. Some significant conclusions are obtained, which are useful to construct constitutive model to describe the ratchetting of the materials with different cyclic softening/hardening behaviours.

A viscoplastic model for 316L stainless steel under uniaxial cyclic straining and stressing at room temperature

In this paper, a viscoplastic model incorporated with the hardening caused by the combined monotonic and cyclic strain loading is proposed. It is assumed that the isotropic and kinematic hardening rules are dependent on both the cyclic inelastic strain amplitude and the maximum inelastic strain. The current inelastic strain amplitude is described by a memory model in which the current inelastic strain amplitude can be approached very quickly. The fading memory on the previous maximum deformation resistance is taken into account to describe the fading memory on the previous loading history while the deformation resistance is presented by both the maximum inelastic strain and the current inelastic strain amplitude. The comparison between the predicted and experimental results indicated that the model can describe the ratcheting behavior under uniaxial cyclic stressing and the cyclic strain behavior under uniaxial cyclic straining in the unified viscoplastic model.

Uniaxial ratcheting of SS304 stainless steel at high temperatures: visco-plastic constitutive model

The uniaxial ratcheting of SS304 stainless steel at high temperatures (300, 600 and 700 °C) were analyzed experimentally, and described by a cyclic constitutive visco-plasticity model. The rate dependence of the material was accounted for by introducing a viscous term. The cyclic hardening and cyclic flow behavior of the material under asymmetrical stress-controlled cycling were described by the evolution rules of kinematic hardening back stress and isotropic deforming resistance. Under the isothermal condition, temperature effect was included by terms involving temperature in the evolution equations of isotropic deforming resistance. The effect of load history on ratcheting was also considered by introducing a fading memory function of the maximum inelastic strain amplitude and isotropic deformation resistance. After the material constants were determined from the experimental data, the uniaxial ratcheting of SS304 stainless steel was numerically simulated and compared with the corresponding experimental results at high temperatures. The predicted results agree well with the experimental ones.

Uniaxial and non-proportionally multiaxial ratcheting of SS304 stainless steel at room temperature: experiments and simulations

The uniaxial and non-proportionally multiaxial ratcheting behaviors of SS304 stainless steel at room temperature were initially researched by experiment and then were theoretically described by a cyclic constitutive model in the framework of unified visco-plasticity. The effects of cyclic stress amplitude, mean stress, and their histories on the ratcheting were experimentally investigated under uniaxial and different multiaxial loading paths. The shapes of non-proportional loading paths were linear, circular, elliptical and rhombic, respectively. In the constitutive model, the rate-dependent behavior of the material was reflected by a viscous term; the cyclic flow and cyclic hardening behaviors of the material under asymmetrical stress-controlled cycling were reflected by the evolution rules of kinematic hardening back stress and isotropic deforming resistance, respectively. The effect of loading history on the ratcheting was also considered by introducing two fading memorization functions for maximum inelastic strain amplitude and isotropic deformation resistance, respectively, into the constitutive model. The effect of multiaxial loading path on the ratcheting was reflected by a non-proportional factor defined in this work. The predicting ability of the developed model was proved to be good by comparing the simulations with corresponding experiments.

Reliability of soldered joints in CSPs of various designs and mounting conditions

The chip size package (CSP) is being used in various portable electronic products recently. Further evaluation of the reliability of its soldered joints is required all the more now because those soldered joints are invisible. This study focused on the thermal fatigue life of soldered joints in the CSP. CSPs were mounted on printed circuit boards (PCBs) in various configurations and mounting conditions, and underwent thermal cycle testing. Then, the fatigue lives of their soldered joints were compared. As a result, the following two facts became apparent. First, reflowing at a 210/spl deg/C peak tends to result in failures that may be derived from poor wetting between solder and pad, in cases where the CSP is mounted on a nickel and gold plated pad. And second, the size of the soldered joint has a great influence on its fatigue life. The larger the soldered joints that we made, the longer fatigue life they indicated. A finite element method (FEM) analysis of those mounted structures was also executed. Viscoplastic (creep and plastic) property of solder was evaluated to compute equivalent inelastic strain occurring in the joints. A parameter in the Coffin-Manson equation is obtained from the computed inelastic strain amplitudes and the experimented actual fatigue lives. This result will enable estimation of the fatigue life of soldered joints of the CSP without actual tests.