Asymmetric Cyclic Loading Research Articles

806 高温における一方向CFRPの非主軸メカニカルラチェット変形の2次元画像相関全視野計測(OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

Two-dimensional off-axis ratcheting behavior of unidirectional CFRP laminates at high temperature has been examined for different fiber orientations on the basis of strain field measured by means of a digital image correlation (DIC) method with two CCD cameras. The accuracy of strain measurement with DIC is first evaluated by comparing the stress-strain curves identified with DIC and strain gauge, respectively, indicating that in-plane strains and their distributions can adequately be measured with DIC. Then, accumulation of in-plane strains in off-axis specimens at high temperature under an asymmetric cyclic loading at a constant stress ratio is observed for different fiber orientations. Non-uniform strain field in off-axis specimen during ratcheting that depends on fiber orientation is successfully visualized by DIC. It is shown that two-dimensional off-axis ratcheting behavior depends on fiber orientation, and the magnitude of ratchet strain tends to become larger than that of creep strain at the constant stress with a magnitude equal to the maximum stress of cyclic loading. It is also revealed that the time dependence of off-axis ratcheting behavior is similar to that of off-axis creep behavior.

Simulating the Seismic Response of Concentrically Braced Frames Using Physical Theory Brace Models

The aim of this paper is to assess the accuracy of brace models formulated in Drain 2DX and OpenSees by comparing the simulated results with those obtained from experimental tests. Both, Drain 2DX and OpenSees rely on the physical theory brace model. In this study, experimental tests conducted on the behaviour of structural hollow section braces subjected to symmetric and asymmetric quasi-static cyclic loading were selected for calibrating the numerical model. In addition, the predicted failure strain parameter resulted from a proposed empirical equation as a function of slenderness ratio, width-to-thickness ratio and steel properties was used to define the low-cycle fatigue material that was assigned to model braces in OpenSees. It is concluded that both Drain 2DX and OpenSees brace models give a good prediction in terms of maximum tensile and buckling force, as well as interstorey drift. However, in Drain 2DX, the brace model is not able to replicate the out-of-plan buckling and the braced frame model cannot provide an accurate response when the system experiences highly nonlinear demand. To emphasise the differences in performance between Drain 2DX and OpenSees, the behaviour of a 4-storey concentrically braced frame with zipper bracing configuration, located in Victoria, BC, was investigated.

Method for the determination of the endurance limit of structural materials under high-cycle asymmetric loading using equivalent stresses

A problem for the determination of endurance limits of metallic structural materials under asymmetric cyclic loading in a wide range of static cycle component has been solved. Endurance limit calculation are based on the use of limit state models, which allow one to describe limiting stress amplitude diagrams at the limited scope of the basic experiment, which is required for the identification of model parameters.

Experimental Study on Uniaxial Time-Dependent Cyclic Deformation of POM/PTFE Blends

The uniaxial time-dependent cyclic deformation of POM/PTFE blends was studied experimentally under the stress-controlled and strain-controlled loading. The volume fraction of PTFE in the POM/PTFE blends was 20%. It was shown that the creep behavior of POM/PTFE blends is better than that of POM. In the cyclic strain-controlled experiments, the responded stress amplitude has a close relationship with the applied strain amplitude and strain rate. As a result of stress relaxation, the responded stress amplitude decreases as the hold time at peak strain increases. Ratcheting occurs in the blends subjected to asymmetric stress-controlled cyclic loading, and the ratcheting strain depends on the applied stress amplitude and stress rate. Hold time at peak stress and low stress rate lead to an increased ratcheting strain. The POM/PTFE blends will fail as the hold time at peak stress is longer than a critical value.

Cyclic plastic response and fatigue life in symmetric and asymmetric cyclic loading

The response of materials to cyclic loading using different loading conditions is analyzed. Hysteresis loops of austenitic steel cycled in symmetric and asymmetric strain- and stress controlled loading are analyzed to evaluate the contribution of effective stress and probability distribution of internal critical stresses. The austenitic-ferritic duplex steel is cycled with various positive mean stresses and cyclic stress-strain response, cyclic creep rates, resulting dislocation structures and fatigue life are evaluated. The effect of the mean stress on cyclic plasticity and fatigue life is discussed. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

一方向CFRP積層板の高温における非主軸ラチェット挙動とその現象論的モデル化

Off-axis ratcheting behavior of a unidirectional carbon/epoxy (CFRP) laminate at high temperature has been examined with a particular emphasis on its load-waveform and fiber-orientation dependence. Development of an engineering model for describing the off-axis ratcheting deformation in unidirectional composites has also been attempted. First, off-axis ratcheting tests are performed on coupon specimens with different fiber orientations under different asymmetric cyclic loading conditions. Off-axis creep tests at constant loads equal in magnitude to the maximum levels of the ratcheting tests are also carried out, and the creep test results are compared with the ratcheting test results. Experimental results show that the off-axis ratcheting strain accumulates more as the stress ratio, i.e. the mean stress level, of cyclic loading becomes larger, regardless of fiber orientation. It is also found that the off-axis ratcheting is transient over the range of testing and similar to the off-axis creep in the unidirectional CFRP laminate in its stress, time and fiber-orientation dependence. Then, a simplified ratcheting model for transversely isotropic media is formulated by means of the classical Bailey-Norton equation and a newly defined effective stress that can account for the effect of the maximum stress as well as the mean stress of cyclic loading. It is shown that the proposed engineering ratcheting model allows predicting the off-axis ratcheting behavior of the unidirectional CFRP laminate for different fiber orientations over a range of stress ratio.

FEM Simulation of Non-Progressive Growth from Asymmetric Loading and Vicious Cycle Theory: Scoliosis Study Proof of Concept.

Scoliosis affects about 1-3% of the adolescent population, with 80% of cases being idiopathic. There is currently a lack of understanding regarding the biomechanics of scoliosis, current treatment methods can be further improved with a greater understanding of scoliosis growth patterns. The objective of this study is to develop a finite element model that can respond to loads in a similar fashion as current spine biomechanics models and apply it to scoliosis growth. Using CT images of a non-scoliotic individual, a finite element model of the L3-L4 vertebra was created. By applying asymmetric loading in accordance to the ‘vicious cycle’ theory and through the use of a growth modulation equation it is possible to determine the amount of growth each region of the vertebra will undergo; therefore predict scoliosis growth over a period of time. This study seeks to demonstrate how improved anatomy can expand researchers current knowledge of scoliosis.

Influence of asymmetric cyclic loading on substructure formation and ratcheting fatigue behaviour of AISI 304LN stainless steel

The aim of this report is to examine the nature of accumulation of ratcheting strain ( ɛ r) vis-à-vis in situ substructural and microstructural variations in 304LN stainless steel under varied asymmetric cyclic loading (ACL) conditions. For this purpose, a series of ACL experiments have been carried out on cylindrical tensile specimens under different combinations of mean stress ( σ m) and stress amplitude ( σ a). In one set of experiments, σ m has been varied between 50 and 150 MPa keeping σ a constant, while in a second set σ m has been kept constant and σ a is varied between 300 and 400 MPa. From the results it can be inferred that ɛ r increases from cycle to cycle for ACL tests and the phenomenon is considered to be governed by the associated mechanics and mechanisms of deformation. Fatigue life of a specimen can either increase or decrease depending upon the test condition, which induces different variations in dislocation density, sub-grain size or micro-damage formation.

True stress control asymmetric cyclic plastic behavior in SA333 C–Mn steel

Asymmetric cyclic loading in the plastic region can leads to progressive accumulation of permanent strain. True stress controlled uniaxial asymmetric cycling on SA333 steel is conducted at various combinations of mean stress and stress amplitude in laboratory environment. It is investigated that fatigue life increases in the presence of mean stress. Plastic strain amplitude and hysteresis loop area are found to decrease with increasing mean stress. A huge difference of life and ratcheting strain accumulation is found in engineering and true stress controlled tests.

J0301-2-1 一方向CFRPの非主軸ラチェット挙動とサイクル波形依存性([J0301-2]工業材料の変形特性とそのモデル化(2))

Ratcheting behavior of a unidirectional carbon/epoxy (CFRP) laminate under off-axis cyclic loading conditions at high temperature has been examined with a particular emphasis on its load-waveform and fiber-orientation dependence. Development of an engineering model for describing the off-axis ratcheting in unidirectional composites has also been attempted. First, off-axis ratcheting tests are performed on coupon specimens with different fiber orientation angles of 30, 45 and 90°, respectively, under different asymmetric cyclic loading conditions with stress ratios of 0 and 0.5. Experimental results show that the off-axis ratcheting strain accumulates more as the stress ratio of cyclic loading, thus the mean stress level, becomes larger, regardless of the fiber orientation. It is also found that the off-axis ratcheting is similar to the off-axis creeping in the unidirectional CFRP laminate in its stress, time and fiber-orientation dependence. It is demonstrated that the engineering ratcheting model proposed in this study allows adequately predicting the off-axis ratcheting behavior of the unidirectional CFRP laminate for different stress ratios as well as for different fiber orientations.

Ratcheting and fatigue properties of the high-nitrogen steel X13CrMnMoN18-14-3 under cyclic loading

Abstract High-nitrogen steel X13CrMnMoN18-14-3 has been used in manufacturing expanding metallic stents with 0.1 mm diameter, and such medical implant is subjected to complicated and asymmetrical cyclic loading during service. But there is no test data published for the thin wire of the material under cyclic loading. In this study, a series of tests were conducted on X13CrMnMoN18-14-3 stainless steel under uniaxial cyclic loading with mean tensile stress. The yield stress and ultimate strength were higher than that of large size specimen with diameters of 5 mm and 7 mm. The effects of stress amplitude, mean stress, loading history and stress rate on the ratcheting behavior of high-nitrogen steel were analyzed, respectively. It can be concluded that the ratcheting strain amplitude and ratcheting strain rate of X13CrMnMoN18-14-3 steel increases with increasing stress amplitude or mean stress correspondingly. At the meantime, experimental results reveal that the material exhibits a strong memory of the previous loading history, the stress cycling with higher stress amplitude or mean stress greatly restrains the ratcheting of subsequent stress cycling with lower ones. The ratcheting strain rate was very sensitive to the applied cyclic stress rate, and the accumulation of ratcheting strain under stress rate of 21.2 MPa/s is much faster than that under stress rate of 106 MPa/s. In addition, comparison of the fatigue life between bulk specimen and thin wire indicates that the size effect has significant influence on fatigue properties of the material. In the case of the test conducted under stress amplitude of 400 MPa, the fatigue life of small specimen is approximately ten times longer than that of bulk specimen under the same loading conditions.

Assessment of durability clad aluminum alloys in asymmetric cyclic loading

Comparative efficiency analysis of the two methods of the residual fatigue life estimation under asymmetric cyclical loading has been conducted. It is shown, that the method, based on the determination of the developed on the surface of aluminium alloy D-16AT deformation relief parameters has every reason to compete with known approach, that takes into account indices of asymmetry and uses the diagram of the material’s ultimate state.

Evaluation method of multiaxial low cycle fatigue life for face-centered cubic crystal single crystal material

By taking into account the coupling effect of normal stress and shear stress on orthotropic material when the applied loading deflects from the principal axes directions of material coordinate system, formulas of equivalent strain and stress for cubical single crystal material are used together with a variable k, which is introduced to express the effect under asymmetrical cyclic loading on fatigue life, to put forward a low cycle fatigue (LCF) life prediction model for face-centered cubic crystal (FCC) single crystal in multiaxial stress states. Based on the yield criterion and constitutive model of cubical single crystal material, a subroutine to calculate the thermo elastic-plastic stress-strain of the material on ANSYS platform is developed. The cyclic stress-strain of DD3 notched specimens under asymmetrical loading at 680 ℃ is analyzed. Different failure parameters of the model are analyzed with multiple regression correlation analysis. The equivalent strain and stress for cubical single crystal material as failure parameters have the largest correlation coefficient. A power law exists between k and the failure cycle. The model is validated with LCF test data of CMSX-2 and DD3 single crystal nickel-based superalloys. All the test data fall into the factor of 2.5 for CMSX-2 hollow cylinder specimens and 2.0 scatter band for DD3 notched specimens, respectively.

Evaluation method of multiaxial low cycle fatigue life for cubic single crystal material

The coupling effect of normal stress and shear stress on orthotropic materials happens when applied loading deflects from the directions of the principal axes of the material coordinate system. By taking account of the coupling effects, formulas of equivalent stress and strain for cubic single crystal materials are cited. Using the equivalent strain and equivalent stress for such material and a variable k, which is introduced to express the effect of asymmetrical cyclic loading on fatigue life, a low cycle fatigue (LCF) life prediction model for such material in multiaxial stress starts is proposed. On the basis of the yield criterion and constitutive model of cubic single crystal materials, a subroutine to calculate the thermo elastic-plastic stress-strain of the material on an ANSYS platform was developed. The cyclic stress-strain of DD3 notched specimens under asymmetrical loading at 680°C was analyzed. Low cycle fatigue test data of the single crystal nickel-based superalloy are used to fit the different parameters of the power law with multiple linear regression analysis. The equivalent stress and strain for a cubic single crystal material as failure parameters have the largest correlation coefficient. A power law exists between k and the failure cycle. The model was validated with LCF test data of CMSX-2 and DD3 single crystal nickel-based superalloys. All the test data fall into the factor of 2.5 for CMSX-2 hollow cylinder specimens and 2.0 scatter band for DD3 notched specimens, respectively.

An endochronic model of material function and its application to plastic behavior of metals under asymmetric cyclic loadings

By using the incremental form of the endochronic theory of plasticity, a model of material function is proposed in this paper to investigate plastic behavior. By comparing the stress-strain hysteresis loop, the theory is shown to agree well with the experimental results, especially in the evolution of peak stress values of SAE 4340 steel loaded by cyclic loading with various amplitudes. Depending on the choice of material parameters, the present model can substantially result in six categories of material function, each of which can behave differently with respect to an identical deformation history. In addition, the present model of material function is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom (1978).

Ratchetting strain prediction

A time-efficient method for predicting ratchetting strain is proposed. The ratchetting strain at any cycle is determined by finding the ratchetting rate at only a few cycles. This determination is done by first defining the trajectory of the origin of stress in the deviatoric stress space and then incorporating this moving origin into a cyclic plasticity model. It is shown that at the beginning of the loading, the starting point of this trajectory coincides with the initial stress origin and approaches the mean stress, displaying a power-law relationship with the number of loading cycles. The method of obtaining this trajectory from a standard uniaxial asymmetric cyclic loading is presented. Ratchetting rates are calculated with the help of this trajectory and through the use of a constitutive cyclic plasticity model which incorporates deviatoric stresses and back stresses that are measured with respect to this moving frame. The proposed model is used to predict the ratchetting strain of two types of steels under single- and multi-step loadings. Results obtained agree well with the available experimental measurements.

On the prediction of the fatigue life of thin-walled structures based on a statistical model

We present experimental results of fatigue tests of AMg6 aluminum alloy model specimens-plates with a single notch, subjected to fully reversed and asymmetric cyclic axial loading. The experimentally determined lives of model specimens are used as the results of the base experiment for predicting the fatigue strength characteristics of large-scale cylindrical shells with circumferential ring-shaped stress raisers loaded by axial forces of a cyclic nature. A numerical study has been performed of the statistical model adopted for predicting the fatigue life of such shells.

A Study of Inhomogeneous Plastic Deformation of 1045 Steel

An experimental study was conducted on the inhomogeneous plastic deformation of 1045 steel subjected to monotonic tension and cyclic tension-compression. Small strain gages were used to characterize the local deformation and transmission electron microscopy (TEM) was used to study the microstructures associated with the observed deformation phenomenon. Under monotonic tension, the strain of the Lu¨ders front was lower than the full Lu¨ders strain. The local strains were inhomogeneous even at the work-hardening stage. Under stress-controlled cyclic loading with stress amplitudes below the lower yield stress, cyclic deformation consisted of an incubation stage, a significantly inhomogeneous cyclic softening stage, and a saturation stage. Inhomogeneous cyclic plasticity persisted at the saturation stage. A monotonic tension preload can eliminate the incubation stage in the subsequent cyclic loading. Under asymmetric cyclic loading with a mean stress, the cyclic plastic deformation was accompanied by noticeable inhomogeneous ratcheting deformation. TEM was used to analyze the distribution and evolution of the dislocation structures at different locations of the specimen. With increasing loading cycles, the dislocation substructures evolved in a sequence of loose tangles, thick veins, long walls, elongated cells, and equiaxial cells. Based upon the mechanical experiments and observations of dislocation arrangements, the mechanisms governing inhomogeneous cyclic plastic deformation were discussed.

Influence of the Structure and Asymmetry of Loading Cycles on the Cyclic Crack Resistance of Ti–Si Composites

We analyze fatigue-crack growth rate diagrams for various modifications of a Ti–Si cermet alloy in the initial (as-cast) state and after thermomechanical treatment plotted for beam specimens subjected to three-point bending. It is shown that, for different asymmetries of the loading cycle, the maximum stress intensity factor K max better describes the behavior of the growth rate of fatigue macrocracks in the high-amplitude part of the diagrams than the range of the stress intensity factor ΔK. The threshold crack resistance of the Ti–Si composite under cyclic loading is 2–5 times lower than under long-term static loading. For highly asymmetric loading cycles (R = 0.6), the maximum cyclic crack-growth resistance is exhibited by a modification with the structure of grains of pseudo-α-titanium matrix 20–40 μm in size and 15–30 wt.% of dispersed precipitations of titanium and intermetallic silicides 5–10 μm in size.

Effect of pre-strain and mean stress on cyclic plastic deformation response of iron-based alloys

In order to understand the mechanism of sag behavior of engineering materials, systematic symmetrical and asymmetrical cyclic loading tests, rather than stress relaxation and the Bauschinger effect test, were carried out with two model materials, namely industrial pure iron and spheroidized mid-carbon steel, under different pre-strain conditions. It was found that the applied mean stress had a significant effect on the amount of cumulative cyclic creep strain and it could also strongly extend the secondary creep stage. It was also found that the Bauschinger effect caused by pre-strain would become negligible in cyclic deformation after a certain, but small number of cycles. This indicates that Bauschinger effect test cannot thoroughly reflect the nature of sagging behavior. Finally, both increase in the pre-strain level, and decrease in the cyclic peak stress level resulted in reduced amount of energy that could be recovered by cyclic deformation from the total energy accommodated during pre-plastic straining. On the other hand, it is such unrecovered energy that would make the material enter a stable stage of dislocation substructure earlier during cycling.