Low Cycle Fatigue Damage Research Articles

A dislocation model of low-cycle fatigue damage and derivation of the coffin-manson equation

A damage model of low-cycle fatigue has been developed using dislocation theory. On the basis of the model, the Coffin-Manson equation for predicting the low-cycle fatigue life of materials has been derived. A comparison between the theoretical values derived in this paper and the experimental values of the fatigue ductility coefficient ( ϵ' f ) and the fatigue ductility exponent ( c) shows that the Δϵ p - N f equation established here coincides with the experimental results.

Constitutive modelling of cyclic plasticity and some implications for the computation of biaxial low cycle fatigue damage

A two-surface stress space material model for cyclic plasticity simulations is presented. The model takes into account the transient effects of cyclic hardening/softening and mean stress relaxation by means of exponential relationships that are functions of number of reversals and current strain level. By updating the size/location of a bounding surface at each point of strain reversal, the transient behaviour is simulated in a simplified manner. The increased hardening due to nonproportional loading is accounted for. The transient material model and two similar, but stabilized, models are applied in calculating the accumulated damage in biaxial low cycle fatigue loading. The plastic work per reversal is employed as damage parameter. The differences in the computed accumulated damage obtained by using the three different constitutive equations are clearly illustrated, hence indicating which type of material model may be sufficient for different types of loading.

Low-cycle fatigue damage accumulation in Armco iron: Vasek, A. and Polak, J. Fatigue Fract. Eng. Mater. Struct. 1991 14 (2–3), 193–204

This research was set with the objective of investigating the possibility of constructing Roller Compacted-Concrete Dam, RCCD, using local material to reduce its cost. Trial laboratory concrete mixtures were conducted to define RCCD proportions in stage-I. Twelve mixtures with fly ash, FA, of cement replacement percentages (0%, 50%, and 60%) designed with water/cementitious-materials ratio, w/cm of 1.0 and 0.9. Cm-content of 1.50 kN/m3 and 1.20 kN/m3 was also examined. In stage-II, RCCD scale model was constructed based on the laboratory results. Descriptions of RCCD construction stages, dam monitoring system instrumentations and temperature measurements analysis were conducted.Results clarified how FA interacts with Portland cement and showed its effect on concrete properties especially strength development ratio. FA long-term reaction refines the pore concrete structure to reduce water ingress and control its seepage. FA reduces the thermal stresses by reducing the concrete hydration heat and reduces temperature-related cracking due to low early young’s modulus and finally leads to durability improvement that minimizes the dam construction cost. Results indicated that RCCD could be effectively implemented with site local Egyptian materials. However, more further field measurements and a RCCD prototype are required to be examined analytically and verified with in situ data to evaluate that technique.

Low-cycle fatigue damage mechanisms of FCC and BCC polycrystals: homologous behaviour?: Magnin, T., Ramade, C., Lepinoux, J. and Kubin, L. P. Mater. Sci. Eng. A Oct. 1989 A118, (1–2), 41–51

In this study, the effects of microstructural inclusions on fatigue life of polyether ether ketone (PEEK) was investigated. Due to the versatility of its material properties, the semi-crystralline PEEK polymer has been increasingly adopted in a wide range of applications particularly as a biomaterial for orthopedic, trauma, and spinal implants. To obtain the cyclic behavior of PEEK, uniaxial fully-reversed strain-controlled fatigue tests were conducted at ambient temperature and at 0.02 mm/mm to 0.04 mm/mm strain amplitudes. The microstructure of PEEK was obtained using the optical and the scanning electron microscope (SEM) to determine the microstructural inclusion properties in PEEK specimen such as inclusion size, type, and nearest neighbor distance. SEM analysis was also conducted on the fracture surface of fatigue specimens to observe microstructural inclusions that served as the crack incubation sites. Based on the experimental strain-life results and the observed microstructure of fatigue specimens, a microstructure-sensitive fatigue model was used to predict the fatigue life of PEEK that includes both crack incubation and small crack growth regimes. Results show that the employed model is applicable to capture microstructural effects on fatigue behavior of PEEK.

Low cycle fatigue damage in turboengine discs: Guedou, J. Y. and Honnorat, Y. Mater. Tech. (Paris) Jan.–Feb. 1989 77, (1–2), 49–55 (in French)

A medium carbon Mn-Si-Cr alloyed steel was treated by a novel bainite-based quenching and partitioning (BQ&P) process: after full austenization, the steel was firstly austempered at 300 °C, 320 °C, 340 °C, 360 °C and 380 °C for 30 min, and then quenched to 120 °C, followed by partitioning at 360 °C for 45 min. The multiphase microstructures containing carbide-free bainite (CFB, bainitic ferrite lath plus filmy retained austenite), martensite and retained austenite were characterized by optical microscope, scanning electron microscopy, transmission electron microscopy, X-ray diffraction and dilatometer analysis. An optimum combination of strength and ductility was achieved in the BQ&P steel when the bainitic austempering temperature is 360 °C (ultimate tensile strength: 1495 MPa; uniform elongation and total elongation: 26.2% and 31.8%; the reduction of area: 47.9%). Besides the transformation-induced plasticity effect of the retained austenite and the composite effect of the multiphase after BQ&P treatment, the formation of carbide free bainite also plays a significant role on the enhanced mechanical properties. The carbide-free bainite could improve the damage resistance of the multiphase due to the additional strain-hardening capacity within the local plasticity deformation zone near the tip of micro-cracks. In this case, the fraction and distribution of CFB should be controlled properly and the macrosegregation should be avoided.

Interaction of creep damage and low cycle fatigue damage in a 1Cr0.5Mo steel.

Non-destructive replica studies of creep cavitation in power plant components of low alloy steels is a frequently used tool in order to estimate the reminant life. In addition to creep such components are exposed to thermal stresses and strains during start-ups and shut-downs, which can lead to fatigue damage. In order to study the role of creep-fatigue interactions, the influence of creep damage on low cycle fatigue (LCF) in a 1Cr0.5Mo steel was investigated. LCF-specimens were creep tested to 5% elongation at 560 and 600°C resulting in carbide precipitation, bainite coarsening and a significant amount of creep cavitation. The damage development during LCF was studied using replicas for test series of pre-crept and virgin material. In addition, the influence of a hold time was investigated. The development of creep cavities and micro-cracks, as well as the amount of intergranular crack propagation were evaluated. Creep exposure resulted in a reduction of the number of cycles to failure. The relationship between this reduction and the amount of creep damage as well as the consumed creep life fraction was analysed. The influence of softening and increased inelastic strain range due to creep exposure was also studied.Continuous cycling LCF on creep exposed material resulted in a small increase of the cavity density. Compared to virgin material the number of cycles to failure Nf was smaller at low strain ranges. LCF with 5 min hold time resulted in a reduction of Nf by approximately a factor of 1.8. Creep exposure before hold time LCF resulted in an enhanced development of creep damage during LCF and smaller amounts of intergranular crack propagation whereas no significant further reduction of Nf could be observed.

Effect of damage in low-cycle fatigue on the speed of elastic waves

Effect of damage in low-cycle fatigue on the speed of elastic waves

A continuum damage model for weld heat affected zone under low cycle fatigue loading

In this paper, the Low Cycle Fatigue (LCF) damage evolution of weld Heat Affected Zone (HAZ) is studied by use of Continuum Damage Mechanics. Based on a continuum damage variable, D, on the effective stress concept and on thermodynamics, a continuum damage model of isotropic LCF is derived, and is used to analyse the LCF damage evolution of thermally simulated HAZ. A comparison between model and the experimental results is presented and a good agreement is found.

Ｘ線およびＡＥ法による６０ｋｇｆ／ｍｍ｀２´級良成形性 高強度薄鋼板の疲労損傷

Strain-controlled low cycle fatigue damage has been studied by means of X-ray diffraction and AE (acoustic emission) methods in addition to metallographic technique for the following two types of formable 60kgf/mm2 class hot-rolled high strength sheet steels; a 0.9%Si-1.2%Mn dual phase (DP) hardened steel with duplex microstructures of ferrite and martensite and a 0.04%Nb added precipitation hardened fine grain steel. The following results were obtained.(1) The Nb added steel showed monotonic cyclic softening, causing a decrease in X-ray half value breadth as a result of sub-boundaries due to the rearrangement of dislocation during the repeated cyclic strain. On the other hand, the Si-Mn DP steel showed cyclic hardening at the early stage followed by softening, which corresponds to an increase followed by a slight decrease in X-ray half value breadth caused by fine cell-structures in the ferrite matrix, which were essentially stable even in the cyclic softening stage.(2) The Si-Mn DP steel gave more and smaller AE waves in the early and the middle stages than the Nb added steel. The phenomenon in the DP steel might be the result of the continuous release of elastic energy due to the formation and annihilation of persistent slipbands in the ferrite matrix, and the initiation of small cracks at ferrite/martensite boundaries. The Si-Mn DP steel showed consequently higher registance to the fatal cracking than the other.

Nondestructive low-cycle fatigue characterization of multi-layer thin film structures

A multi-layered thin film structure (namely, electrodeposited Cu/sputtered Cr/Kapton substrate/sputtered Cr/electrodeposited Cu), utilized as a flexible component for computers, has been exposed to fatigue. Although a standardized testing method for fatigue ductility is available for a solid monolayer of electrodeposited foil, there is no method available for examining such a multi-layered thin film structure. In this study, four different methods were employed to characterize the low-cycle fatigue damage: (1) DC resistance measurement, (2) residual stress development by x-ray diffraction, (3) dislocation density calculation by using obtained x-ray diffraction line profiles, and (4) microscopic observations. Low-cycle fatigue was conducted at eight levels of applied total strain, i.e., δe T =13.95%, 7.69%, 5.83%, 4.69%, 3.37%, 2.37%, 1.59%, and 1.19%. The number of fatigue cycles, when the crack was first observed on the outer Cu layer, was identical to that observed with the onset of increased resistance. This cycle number is thus designated as the number of cycles-to-fatigue crack initiation,N c . AtN c , the residual stresses also show a noticeable relaxation, and the dislocation density shows a remarkable increase. IfN c is plotted against the applied total strain amplitudes, a Manson-Coffin's relationship is obtained with an exponent of 0.39. It is recommended that monitoring the continuous changes in DC resistance could provide a reliable nondestructive evaluation of low-cycle fatigue life of a multi-layered thin film structure.

Low-cycle fatigue damage mechanisms of F.c.c. and B.c.c. polycrystals: Homologous behaviour?

The low-cycle fatigue damage mechanisms of four different polycrystalline materials, namely copper, two ferritic stainless steels and an austenitic 316 L stainless steel, were examined and compared for a prescribed plastic strain amplitude of 2 × 10 −3 at room temperature. Except for the austenitic stainless steel, where slip is rather planar, the microstructures at saturation contain various types of active wall structures, homogeneously distributed in the ferritic steel and rather heterogeneously distributed in copper. An experimental study of the formation and evolution of surface microcracks showed that, despite these dissimilarities, the four materials exhibit a rather uniform behaviour. In particular, the various types of microcracks seem to appear at well-defined values of the fatigue life, e.g. 10% for the shortest microcracks. This apparent occurrence of a homologous behaviour is discussed in terms of the respective influences of geometrical and mechanical effects and of microstructural mechanisms.

Influence of fatigue damage on tensile creep properties of short carbon fibre reinforced nylon-6-plastic

The influence of low cycle fatigue damage on the tensile creep properties of fibre-reinforced thermoplastic ( frtp) has been examined with respect to the strain, the stress and the cycle ratio. From a characteristic flow curve and the changes due to the fatigue damage, a mechanical model of the material is determined and a previously reported visco-plastic-elastic theory is applied to the obtained data. The reinforced effect of fibres is estimated using a frictional force distribution function. The fatigue effects on the creep properties with various prefatigued materials and virgin state ones are also compared.

Application of stochastic differential equations to seismic reliability analysis of hysteretic structures

An analytical method of stochastic seismic response and reliability analysis of hysteretic structures based on the theory of Markov vector process is presented, especially from the methodological aspect. To formulate the above analysis in the form of stochastic differential equations, the differential formulations of general constitutive laws for a class of hysteretic characteristics are derived. The differential forms of the seismic safety measures such as the maximum ductility ratio, cumulative plastic deformation, low-cycle fatigue damage are also derived. The state equation governing the whole nonlinear dynamical system which is composed of the shaping filter generating seismic excitations, hysteretic structural system and safety measures is determined as the Itô stochastic differential equations. By introducing an appropriate non-Gaussian joint probability density function, the statistics and joint probability density function of the state variables can be evaluated numerically under nonstationary state. The merit of the proposed method is in systematically unifying the conventional response and reliability analyses into an analysis which requires knowledge of only first order (single-time) statistics or probability distributions.

導電用銅合金とＳＵＳ３０４鋼における低サイクル疲労損傷

Low-cycle fatigue tests were carried out on copper alloy and SUS 304 steel, to observe the initiation of fatigue cracks in smooth specimens and the subsequent growth of the micro-cracks. Their surface crack lengths were examined using cellulose acetate replicas. The results obtained were as follows:(1) Initiation of a main crack which causes the failure of smooth speimens occurred at the early stage of their lives. The crack initiation cycle ratio Nc/Nf was small for SUS 304 steel in the low-cycle regime, but in the high-cycle regime for copper.(2) The crack initiation site was almost near the grain boundary triple point and the subsequent growth rate was high at the early stage. The initiation at the slip bands was rarely observed and the crack length did not change for a while.(3) The experimental crack growth rate was not well correlated in fracture mechanics fashion by ΔK or ΔJ. The crack growth rate at the stable stage was propotional to the crack length, so the nondimensional fatigue crack growth rate k=1/ae·da/dN represented the data well in this study.(4) The nondimensional fatigue crack growth rate k was closely connected with the failure lives Nf of smooth specimens, in such a way as k=(9-10)/Nf.(5) An expression for the damage in low-cycle fatigue was derived on the basis of micro-crack growth behavior.

地震力を受けた鉄骨モデル部材のX線観察

The purpose of this study is to investigate the behavior of steel structures subjected to a strong earthquake and to evaluate the damage from a microscopic point of view. For this purpose, the authors have adopted two kinds of research techniques. The first is the "ON-LINE EARTHQUAKE RESPONSE SIMULATION SYSTEM (ON-LINE SIMULATION SYSTEM)", which is composed of an electro-hydrauric testing machine controled by a computer and a full scale specimen. Since a term of restoring force in the equation of motion is to be substituted by the actual reaction of a specimen under test, we can obtain the non-linear response of structure without any assumption about the hysteretic characteristics. Based on this method, the dynamic behavior of simple steel structures subjected to an intense earthquakes were simulated. The second technique is the "X-RAY DIFFRACTION METHOD". Although this method is usually regarded an experimental technique particular to the material science, we have realized the good applicability for the study of structural engineering, Because X-ray diffraction method is advantageous in investigating the microscopic behavior of steel member such as the plastic deformation and the low cycle fatigue. From the view point stated above, we have adopted this method for the evaluation of low cycle fatigue damage of steel member subjected to an earthquake. The experiment has been performed by radiating the X-ray at several stages of the ON-LINE SIMULATION. As has been expected, the X-ray diffraction patterns have changed in a regular manner depending on the degree of fatigue damge, and the results have shown a good possibility that the X-ray diffraction approach can offer a powerful tool for the detection of the earthquake damage of steel members.

CSC Symposium — fine needle aspiration cytology

Nickel-based superalloys are easy to produce low cycle fatigue (LCF) damage when they are subjected to high temperature and mechanical stresses. Fatigue life prediction of nickel-based superalloys is of great importance for their reliable practical application. To investigate the effects of total strain and grain size on LCF behavior, the high temperature LCF tests were carried out for a nickel-based superalloy. The results show that the fatigue lives decreased with the increase of strain amplitude and grain size. A new LCF life prediction model was established considering the effect of grain size on fatigue life. Error analyses indicate that the prediction accuracy of the new LCF life model is higher than those of Manson-Coffin relationship and Ostergren energy method.

鉄筋コンクリート構造物の動的耐震性評価に関する研究

Prediction of damage is important in evaluating the earthquake response of reinforced concrete (RC) structures. Damage prediction is usually measured in term of ductility factor. However, concerning reinforced concrete structures subjected to a lot of cycles of severe loads, a combination of maximum displacement response and cyclic deterioration of stiffness and load carring capacity may cause RC structures to collapse. Damage due to maximum displacement response and cyclic deteriolation can be made over to ductility factor and cumulative fatigue damage, respectively. So, from viewpoint of collapse, it must be investigated the properties of lowcycle fatigue for RC structures. In order to investigate low-cycle fatigue damage in RC columns, seven reinforced concrete frames with rigid beams have been tested. As the results, restoring force characteristics, experimental equation of stiffness deterioration, △δ-N_f curve and cumulative fatigue damage hypothesis have been formulated. Then, the dynamic response analyses have been carried out by applying the restoring force characteristics obtained from the tests and the results of the dynamic response analyses have been evaluated by the concept of cumulative fatigue damage formulated from the tests. From the results of the study reported in this work, it is concluded that : (1) The Wohler curve (△δ-N_f curve) can be shown as Fig. (5). (2) As shown in Fig. (7), the linear cumulative fatigue damage hypothesis can not be applied for low-cycle fatigue damage of reinforced concrete columns. (3) The non-linear cumulative fatigue damage factor for reinforced concrete columns can be suggested in the form of Eq. (7) and Eq. (8). (4) In case that the maximum displacement response is in the work-hardening region of skeleton curve, the seismic damage of RC columns depends on only the ratio of the maximum displacement response vs. the collapse displacement of the column and the damage caused by cyclic deterioration (cumulative fatigue damage) can be neglected, i.e., only ductility factor is important for prediction of damage in this domain. (5) In case that the maximum displacement response is the falling branch of the skeleton curve, the seismic damage of RC columns must be evaluated by a combination of the maximum displacement response and the cumulative fatigue damage. The seismic damage caused by low-cycle fntigue becomes 20-35% of the full damage at that time, i.e., not only ductility factor but also cumulative fatigue damage is important for evaluating seismic damage in this domain. (6) The seismic damage factor decreases hyperbolically as the period T increases. (7) When T&le;0.1sec, the seismic damage increases rapidly as the ratioβ=mz_<max>/Q_y increases a little, and the structure collapses suddenly, just in case β=1.0. (8) Though the structures were subjected to various kinds of eathquake motions, cumulative hysteretic absorbed energy has the tendancy to be constant for each period at collapse of the structures.

鉄筋コンクリート柱の低サイクル疲労に関する実験的研究

Prediction of damage is important in estimating the dynamic response analysis for reinforced concrete structures subjected to earthquake excitations. Damage prediction is usually measured in term of ductility factor, however, a combination of maximum displacement response and cumulative fatigue damage may cause to fail. In order to investigate low-cycle fatigue damage in RC columns, 7 reinforced concrete frames with rigid beams were tested by using a dynamic actuator. From the results of the test reported in this work, it is concluded that : 1) All specimens collapsed due to considerable degradation of axial load carrying capacity which occured after the shear compression failure at the head or knee of specimen and buckling of compressive longitudinal reinforcing bars. 2) The collapse of concrete structures with axial load is defined explicitly as sudden increase of cumulative axial displacement. 3) The rate of cumulative axial displacement dδ_v/dn can be expressed in the form dδ_v/dn=C △δ^α_T, where C and α are member constants, as shown in Fig.19. The Wohler curve can be obtained from this differential equation. 4) The Wohler curve for the lateral displacement amplitude △δ_T and average area △E of hysteresis loops can be shown as Eq. (3) and Eq. (6), respectively. The latter has a high correlation to experimental results. 5) The linear cumulative fatigue damage hypothesis is not true for low-cycle fatigue of reinforced concrete columns. 6) The non-linear cumulative fatigue damage ratio for reinforced concrete columns can be expressed in the form of Eq. (17) and (18).

Wedge type creep damage in low cycle fatigue

A model is proposed to quantify the accumulation of wedge type creep damage in low cycle fatigue. It is proposed that such damage is produced primarily during the ramp periods of the cycle. Equations are developed for estimating incremental accumulation of damage per cycle in fully reversed, multiaxial loading. The rate of accumulation of damage depends on the strain-rate, the temperature, and the microstructure. The analysis is kept simple by making physically reasonable assumptions. Cycles to failure are predicted by invoking a fracture criterion. The model is applied to two sets of data; one set is a well characterized life test data on an aluminum alloy, and the other is phenomenological data on austenitic stainless steels. In both cases the predictions are good enough to prompt further experimental evaluation of the model. This paper deals with only one mechanism of creep-fatigue interaction. Other mechanisms of failure,e.g., ‘r’ type cavitation, or fatigue crack initiation and propagation, are also viable. The model described here may be expected to apply only under those conditions when wedge damage is the dominant failure mechanism.

Designing against low-cycle fatigue at elevated temperature

Factors that are important in determining low-cycle fatigue damage at elevated temperature are discussed. The linear damage rule for computing creep-fatigue damage is shown to be unsatisfactory in many situations. The damage-rate equations developed at Argonne National Laboratory have been generalized to include multiaxial creep-fatigue under complicated loading histories. Available creep-fatigue data under combined axial-torsion loading can be explained in a consistent manner by the damage-rate approach.