Low Cycle Fatigue Analysis Research Articles

Low-cycle fatigue analysis of a web frame corner in ship structures

Ship structures are subjected to cyclic loads which may lead to fatigue failures particularly at welded joints. In addition to loads induced by waves and structural vibrations, which contribute to high-cycle fatigue, various structural details are also subjected to a limited number of high-stress cycles caused by changing loading conditions, which may lead to low-cycle fatigue. Thus, appropriate procedures are required for the shipbuilding industry, which are missing in the existing design codes. Experimental investigations and numerical analyses were performed to validate a procedure for the design of ship structures in the low-cycle fatigue regime. Three large-scale fatigue tests were carried out with high bending moments on test models of web frame corners in order to initiate fatigue cracks after few hundred cycles. Different cracks occurred; however, a crack at the cruciform joint has shown to determine the failure of the connection. An extension of the effective notch stress approach was applied to this joint to assess the low-cycle fatigue life, considering the elastic–plastic strain, evaluated by nonlinear finite element analyses, in the notch of the weld toe. This practical method offers promising possibilities to assess the fatigue life of welded joints in the low-cycle fatigue regime.

Probabilistic integrity assessment of turbine disks in presence of potential defects

Rotor disks for gas turbines are heavy components and are usually designed following a safe-life approach, where the low-cycle fatigue analysis is carried out referring to design life curves with suitable probabilistic margins. However, in the case of such a heavy component there is the possibility of rare occurrence of undetected defects or, better, the need to identify the defect acceptability for the different rotor regions (considering stress, temperature, mission profile). In order to carry out such calculations for a turbine rotor disk a software named {AStrID} (Assessment of the Structural Integrity of Disks) has been developed in close cooperation between Politecnico di Milano and Ansaldo Energia (AEN). This paper summarizes its background and some of the relevant features.

A Simple Format for Failure Probability under LCF and its Application to a Complex Component

Turbine components are usually designed onto safe-life approach, where the low-cycle fatigue analysis is based onto design life curves with suitable probabilistic life margins. However, in order to design for a given reliability, the definition of the design curve should not only include the life variability but also the scatter of applied load. Unfortunately, in the literature there are few indications which only refer to safety factors under HCF, without any specific discussion of the case of LCF.In this paper, we firstly propose a simple format for calculating reliability for an assessment point ▪. The format is then used for estimating failure probability adopting the Socie's criterion for a notched component whose elasto-plastic response was simulated by FEA. Results show the need of implementing a correct dependence between ɛ− N curve and material volume.

Low cycle fatigue life prediction using a four-bolt extended unstiffened end plate moment connection

The end plate moment connection (EPMC) has been studied using various design concepts. However, after the Northridge, California earthquake in 1994, low cycle fatigue (LCF) analysis became the focus of investigation for EPMCs because the existing design code could not explain the brittle steel moment frame connection failures that occurred in numerous structures as a result of that earthquake. This paper provides a LCF life estimation procedure using a four-bolt extended unstiffened EPMC. In this research, four full-scale experimental tests are conducted to develop the LCF model and to estimate the LCF life of each connection. The experimental test failure mode is LCF fracture in the end plate. The LCF model is developed from three constant peak displacement cyclic load test results, and results from a fourth (and last) test performed with random cyclic loading. From these test results, the life of the structure is predicted using the LCF model. Finite element model (FEM) analysis and theoretical calculations (verified in the companion paper, Preanalysis of the Low Cycle Fatigue Behavior of a Reduced End Plate Moment Connection (T-stub)[1]) are used to predict the structural behavior. The results show reasonable relationships to each other.

An incremental minimization principle suitable for the analysis of low cycle fatigue in metals: A coupled ductile–brittle damage model

The present paper is concerned with a novel variational constitutive update suitable for the analysis of low cycle fatigue in metals. The underlying constitutive model originally advocated in [1] accounts for plastic deformation as well as for damage accumulation. The latter is captured by a combination of two constitutive models. While the first of those is associated with ductile damage, the second material law is related to a quasi-brittle response. The complex overall model falls into the range of so-called generalized standard materials and thus, it is thermodynamically consistent. However, since the evolution equations are non-associative, it does not show an obvious variational structure. By enforcing the flow rule as well as the evolution equations through a suitable parameterization, a minimization principle can be derived nevertheless. Discretized in time, this principle is employed for developing an effective numerical implementation. Since the mechanical subproblems corresponding to ductile damage and that of quasi-brittle damage are uncoupled, an efficient staggered scheme can be elaborated. Within both steps, Newton’s method is applied. While the evolution of the quasi-brittle damage requires only the computation of a one-dimensional optimization problem, the ductile damage model is defined by a numerically more expensive tensor-valued variable. For further increasing the numerical performance of the respective minimization principle, a closed-form solution for the inverse of the Hessian matrix is derived. By numerically analyzing the prediction of mesocrack initiation in low-cycle fatigue simulations, the performance of the resulting algorithm is demonstrated.

Novel approach for the treatment of cyclic loading using a potential-based cohesive zone model

The development of cohesive zone models in the finite element framework dates back some 30 years, and cohesive interface elements are nowadays employed as a standard tool in scientific and engineering communities. They have been successfully applied to a broad variety of different materials and loading scenarios. However, many of such constitutive models are simply based on traction-separation relations without deducing them from energy potentials. By way of contrast, a thermodynamically consistent cohesive zone model suitable for the analysis of low cycle fatigue is elaborated in the present contribution. For that purpose, a plasticity-based cohesive law including isotropic hardening/softening is supplemented by a damage model. First results of this new approach to cyclic loading will be presented illustrating the applicability to low cycle fatigue.

Experimental and Analytical Evaluation of Reinforced Concrete Girders under Low-Cycle Shear Fatigue

Stirrup stresses in lightly reinforced concrete bridge girders may exceed the elastic limit while in service. Increasing load magnitudes and volume over time, multiple permit loads, and modern superloads creates the potential for low-cycle fatigue. In this study, six full-scale reinforced concrete girder specimens representative of those found in 1950s reinforced concrete deck-girder bridges were tested under low-cycle fatigue conditions. The specimens were tested in both T and inverted-T configurations. Other test variables included stirrup spacing, flexural reinforcing details, and spacing of supports. Results showed that low-cycle fatigue produced bond deterioration and cumulative plasticity of stirrups. Progressive fracture of stirrup reinforcement under low-cycle fatigue led to eventual specimen failure. A methodology for the analysis of low-cycle fatigue in girders is proposed using the finite element method to approximate stirrup stress ranges and a linear damage model to estimate the life of a conventionally reinforced concrete girder under repeated overloads. This methodology provided good correlation between the experimental and predicted number of fatigue cycles for lightly web-reinforced specimens.

Failure site transition in Pb-free solder joints caused by manufacturing variabilities in BGA and MLF components in low cycle fatigue analysis

A comprehensive three level design of experiment that is applied on the manufacturing process to compare the effect of variability in printing and reflow processes on quality and durability of Micro Lead Frame (MLF) and Ball Grid Array (BGA) components. The quality and durability of the BGA and MLF components were studied very closely by thermo-mechanical experiment and finite element simulation. Different populations of failures indicating different failure site and mechanisms were observed in both BGA and MLF components. Conflictions were observed when parameter variations caused durability improvement in one type and durability degradation in the other package.

Non-isothermal low-cycle fatigue analysis of elasto-viscoplastic materials

A non-isothermal elasto-viscoplastic model, developed within the framework of continuum damage mechanics, is proposed to investigate the influence of thermomechanical coupling on fatigue life of metallic materials. The numerical simulation of constant-amplitude low-cycle fatigue testing of a 316L stainless steel at room temperature shows that the hypothesis of isothermal processes may be inadequate when cyclic inelastic deformations are involved. The results show that the specific heat can decrease when the fatigue damage is high, causing a localized increase of the temperature even if the amount of heat generated is not so high and, hence, promoting a reduction in lifetime.

Corrosion kinetics of a directionally solidified Ni-base superalloy

A variety of experiments were carried out to characterize the corrosion kinetics of a longitudinally oriented directionally solidified Ni-base superalloy, DS GTD-111, commonly applied as a first- and second-stage blading material in electric power generation gas-powered turbines. Under operating environments, the airfoil sections of turbine blades sustain surface-initiated damage due to the superimposed centrifugal stresses, elevated temperature and presence of corrosive reactants in the environment. As a consequence, surface cracking curtails the service lives of such components. To thoroughly characterize the stress-free and stress-assisted kinetics of diffusion and cyclic oxide rupture, several types of experiments are conducted: low cycle fatigue, thermomechanical fatigue, and thermogravimetric analysis, among others. A key goal of this study is to provide data necessary for the development of diffusion kinetics models. Accordingly, the study is divided into two parts: stress-free diffusion and stress-assisted rupture. Models are developed for each of these conditions.

Ignitor plasma chamber structural design with dynamic loads due to plasma disruption event

During a plasma disruption in Ignitor [B. Coppi, IGNITOR Project Group, Engineering Design Description, Ignitor Programme, RLE Report no. PTP 96/03, December 1996], the electromagnetic (EM) loads are so large to require a dynamic elastic–plastic structural analysis of the plasma chamber (PC). A 30° sector of PC has been modeled. Static, dynamic and low cycle fatigue analyses under eddy and halo currents have been performed. It is shown that a PC wall thickness optimization limits the displacements within the clearance with toroidal coil. The fatigue lifetime is longer than the number of disruption events at the maximum performance.

A thermodynamics based damage mechanics constitutive model for low cycle fatigue analysis of microelectronics solder joints incorporating size effects

Below certain length scales and in the presence of a non-uniform plastic strain field the mechanical behavior of many metals and its alloys is substantially different from that in bulk specimens. In particular, an increase in resistance with decreasing size has been observed in Pb/Sn eutectic solder alloys which are extensively used in microelectronics packaging interconnects. Due to the high homologous temperature, the Pb/Sn solder exhibits creep–fatigue interaction and significant time, temperature, stress and rate dependent material characteristics. The simultaneous consideration of all the above mentioned factors makes constitutive modeling an extremely difficult task. In this paper, a viscoplastic constitutive model unified with a thermodynamics based damage evolution model is embedded into a couple stress framework in order to simulate low cycle fatigue response coupled to size effects. The model is implemented into commercial finite element code ABAQUS. The microbending experiment on thin nickel foils is used to validate the model. Analyses are performed on a thin layer solder joint in bending under cyclic loading conditions.

Modeling spatial strain gradient effects in thermo-mechanical fatigue of copper microstructures

Copper microvias play a key role as electrical interconnects in high density wiring substrates used in microsystems packaging. These microvia structures experience low-cycle fatigue due to thermo-mechanical loads during processing and operating environments. To predict the thermo-mechanical fatigue life of the microvias through physics-based models accurate estimation of damage metrics, such as plastic strain and total strain range is critical. Experimental evidence indicates that the plastic deformation in metals and polymers at small scales depends not only on the state variables of stress and strain, but also on the higher-order spatial strain gradients. As the diameter of the microvia structures reduce to accommodate high density wiring, the wall thickness of these structures correspondingly reduces to the order of microns, where scale effects in plasticity are predominant. In this work a spatial strain gradient-based hardening algorithm is developed and employed in a commercial finite element code to study the thermo-mechanical deformation of copper microvia structures. In-house thermal cycling results are used to validate the numerical results. The thermo-mechanical reliability and low-cycle fatigue analysis demonstrate the influence of incorporating strain gradient effects in predicting the evolution of plastic deformation and low-cycle fatigue life in the copper microvia structures.

Analysis of low cycle fatigue in AlMgSi aluminium alloys

In this study low-cycle fatigue tests were performed in two AlMgSi aluminium alloys with different chemical composition, namely 6082-T6 and 6060-T6 alloys, using standard round specimens and tube specimens, respectively. The tests were undertaken in strain control with a strain ratio R ε =−1. The cyclic stress–strain curves were determined using one specimen for each imposed strain level. The low-cycle fatigue results are used for the characterisation of the cyclic plastic response and the fatigue live of the alloys. Moreover, the geometry of the hysteresis loops and the occurrence of Masing behaviour are also analysed. The observed behaviour is discussed in terms of the chemical composition of the alloys (Mg 2Si hardening particles and Mn dispersoid content) and fracture mechanisms. Alloy 6060-T6 exhibits nearly ideal Masing behaviour, while alloy 6082-T6 presents significant deviations from the Masing model. The type of cyclic deformation behaviour in AlMgSi alloys seems to be influenced by the dispersoid phase.

Tensile and fatigue properties of two titanium alloys as candidate materials for fusion reactors

Titanium alloys have been identified as candidate structural materials for the first wall, the blanket and the magnetic coil structures of fusion reactors. Titanium alloys are interesting materials because of their high specific strength and low elastic modulus, their low swelling tendency and their fast induced radioactivity decay. Other attractive properties are an excellent resistance to corrosion and good weldability, even in thick sections. Furthermore titanium alloys are suitable for components exposed to heat loads since they have a low thermal stress parameter. Titanium alloys with an α structure are believed to have a good resistance against radiation embrittlement and α+β alloys should possess the best tolerance to hydrogen embrittlement. Two classical industrially available alloys in the two families, the Ti5Al2.4Sn and the Ti6Al4V alloys have been used in this study. The tensile properties between room temperature and 450°C are reported. A low cycle fatigue analysis has been performed under strain control at total strain ranges between 0.8% and 2% and at a temperature of 350°C. The microstructure of both alloys was investigated before and after both types of deformation. Both alloys exhibit excellent mechanical properties comparable to or better than those of ferritic martensitic steels.

Low cycle fatigue analysis of temperature and frequency effects in eutectic solder alloy

Low cycle isothermal mechanical fatigue testing of a eutectic alloy 63Sn/37Pb was carried out in a systematic manner over a wide range of frequencies (10 −4–1 Hz) and temperatures (−40 to 150°C) with the total strain set at different values (1–50%). The low cycle fatigue behavior of the eutectic solder was found to be strongly dependent on test temperature and frequency. If the Coffin–Manson model is used to describe such fatigue behavior, the fatigue exponent m and ductility coefficient C in the model are found to be a function of temperature and frequency rather than numerical constants. The plastic flow law was employed to explain the temperature and frequency dependence. The frequency-modified Coffin–Manson model was tried and found to be able to eliminate the frequency dependence of the numerical “constants” but not the temperature dependence. To have a full description of the temperature- and frequency-dependent fatigue behavior, a set of empirical formulae was derived based on the frequency-modified Coffin–Manson model.

Continuum damage model of low-cycle fatigue and fatigue damage analysis of welded joint

We know from experimental phenomena that the ductility of materials decreases with increasing numbers of cycles in the process of cycle fatigue loading, from which a new fatigue damage variable D ψ based on the material ductility property is defined. Then a continuum damage mechanics model for low-cycle fatigue is derived from the new damage variable and is used to study the fatigue damage of welded joint. Damage evolution equations for the weld metal, heat-affected zone and base metal of 16MnR steel are obtained, respectively. The theoretical and experimental results show that the new damage variable D ψ has a definite physical meaning and can be measured by a simple procedure and it can be related to the mechanical property of material directly.

Damage analysis of low-cycle fatigue under non-proportional loading

In order to study cumulative fatigue damage under non-proportional loading, several extensively used multiaxial fatigue damage criteria are considered: the maximum shear strain criterion, the Socie model and the Fatemi model. A series of experiments were performed for the high-strength alloy steel 42CrMo on an MTS 809 testing system. The specimen was a thin-walled tube with outside diameter 25 mm and inside diameter 21 mm. For low-cycle fatigue the range of strain paths chosen included in-phase, circular, square, rectangular and cross-path. The experimental results show that circular strain paths have the greatest damage and the shortest fatigue life under the same equivalent strain range. Analysis shows that a reasonable damage parameter should consider fatigue damage and the fatigue failure mechanism under non-proportional loading.

Multifactor damage simulation analysis of high temperature low cycle fatigue for superalloy based on the statistical information of crack distribution: Fujiyama, K., Murakami, I, Oshioka, Y. and Okabe, N. J. Soc. Mater. Sci. Jpn (Oct. 1993) 42 (481), (in Japanese) 1212–1217

Multifactor damage simulation analysis of high temperature low cycle fatigue for superalloy based on the statistical information of crack distribution: Fujiyama, K., Murakami, I, Oshioka, Y. and Okabe, N. J. Soc. Mater. Sci. Jpn (Oct. 1993) 42 (481), (in Japanese) 1212–1217

Low-cycle fatigue analysis of notched members: Zhang, D. and Sandor, B. I.ASTM J. Test. Eval. July 1989 17, (4), 212–217

Low-carbon, nitrogen-controlled 316 stainless steel called 316FR was developed and is regarded as a principal candidate for a main structural material of liquid metal-cooled fast breeder reactor plants in Japan. To develop a creep-fatigue evaluation method suitable for this steel, a number of uniaxial creep-fatigue tests have been conducted for three products of this steel. Long-term data up to about 35,000 h were obtained and applicability of failure life prediction methods was studied based upon their results. Cruciform shaped specimens were also tested under biaxial loading conditions to examine the effect of stress multiaxiality on failure life under creep-fatigue condition.