Cumulative damage in low-cycle fatigue

Cyclic-deformation behavior of low-carbon steel and copper under constant-stress amplitude and in a two-step stress change has been studied in the intermediate life range. Under constant-stress amplitude, there is initial softening followed by a hardening process in low-carbon steel. In the case of copper, hardening sets in from the initial stages of stress application. The total hysteresis energy absorbed is not a material constant, but depends on the applied stress. The strain-hardening/strain-softening behavior under the second stress level is different from the standard fatigue tests and is dependent on the first stress level. An energy-based analysis has been found to predict fairly well the cumulative damage life in low-cycle fatigue.     

Thermal fatigue assessment of components made with particulate polymer composites

Many appliance materials are made of PMMA/Si acrylic casting dispersion. In these situations, failure can occur by thermal fatigue induced by severe temperature variations such as alternating flows of cold and hot water. This paper is concerned with the numerical analysis of the thermal stresses in three composites with different volume fractions of filler and particle size. Their trade marks are Asterite, Amatis and Ultra-quartz. Cosmos/M finite element method software was used to study the influence of the cold and hot water temperatures as well as the time of interruption of water flow in the transition between hot and cold water on thermal stresses. Residual stresses were measured and superimposed to thermal stress in fatigue analysis. Typical defects in the corner of holes produced by drilling were predicted using experimental fatigue lives and da/dN curves. Based on predicted defects thermal fatigue assessment of commercially available sinks made with the three materials mentioned earlier was done by taking into account the influence of both cyclic thermal and static residual stresses induced by the manufacturing process.     

Isothermal low-cycle fatigue testing of microscale solder interconnections

A series of isothermal low-cycle fatigue studies of small to extremely small-volume solder joints has been conducted. These solder microjoints were designed and fabricated using processing which duplicates the microelectronics interconnection structures that might be used in high density, highly integrated flip-chip packaging and all fatigue tests were conducted in fully reversed simple shear both with and without dwells at maximum strain. Results of low-cycle fatigue tests of both single and double-bump 95/5 Pb/Sn solder microjoints in the form of Manson-Coffin (plastic strain amplitude versus fatigue life) plots and post-test failure mode analysis (FMA) carried out using scanning electron microscope (SEM) fractography are presented and evaluated. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–12.     

Comparison of low-cycle fatigue results with axial and diametral extensometers

Low-cycle fatigue tests at room temperature have been carried out on a stainless steel and an aluminum alloy utilizing an axial extensometer with cylindrical specimens and a diametral extensometer with hour-glass specimens. In all cases, the axial strain was the controlled parameter. The results obtained with both extensometers are compared. For the materials studied, it is found that the data obtained with a diametral extensometer correspond to a somewhat longer life (by a factor of the order of 1.6 for the parameters used). Furthermore, two tests have been carried out on cylindrical specimens with both extensometers where the axial-strain computed through the diametral strain was controlled throughout the material life and the measured axial strain was simultaneously recorded. Results indicate that geometry of specimen is the predominant factor influencing fatigue life.     

Performance of miniature resistance strain gages in low-cycle fatigue

Experimental results describing the behavior of five types of miniature resistance strain gages subjected to cyclic strains of high amplitude are presented. Test procedure and instrumentation are described. Changes in zero drift and changes in gage sensitivity are discussed with respect to various strain gage and test variables. Mechanisms of gage failure, effect of variation of imposed strain and hysteresis in gage response are discussed.     

The effects of out-of-phase biaxial-strain cycling on low-cycle fatigue

The effects of out-of-phase or nonsynchronous straining on low-cycle fatigue was investigated. Biaxial strains were imposed on thin-walled tubular 7075-T6 aluminum specimens by tension—compression and torsion. Phase angles of 0 deg, 30 deg, 45 deg, 60 deg and 90 deg were applied between two strains. It was found that out-of-phase cycling has an effect on the failure mode in the low-cycle-fatigue range. An analysis based on the maximum total strain in three-dimensional strain is proposed for treating “out-of-phase” straining conditions in low-cycle fatigue.     

High-temperature low-cycle fatigue: A summary of industry and code work

Many of the pressure-vessel and piping systems of the power and process industries operate in the creep range of metals. These structures may be subjected to severe cyclic loading conditions from startup and shutdown operations and to less severe temperature and pressure fluctuations from load-level control and process operational characteristics. In many cases, the number of cycles is small, but the stresses are high. Thus, the cyclic life of this equipment must be evaluated to establish safety requirements in relation to its expected life history. Presently used procedures for the construction of this equipment is discussed as applied either to the ASA (B31.1) Piping Code or to the ASME Power Boiler and Pressure Vessel Code. Considerable cooperative research in the field of high-temperature low-cycle fatigue has been undertaken by the Pressure Vessel Research Committee of the Welding Research Council, the Metals Properties Council, and various industrial and government groups. The effort of the PVRC and the Metals Properties Council is reviewed.     

Modeling of fatigue life of materials and structures under low-cycle loading

A damaged medium model (DMM) consisting of three interconnected components (relations determining the cyclic elastoplastic behavior of the material, kinetic damage accumulation equations, and the strength criterion for the damaged material) was developed to estimate the stress strain state and the fatigue life of important engineering objects. The fatigue life of a strip with a cut under cyclic loading was estimated to obtain qualitative and quantitative estimates of the DMM constitutive relations under low-cycle loading. It was shown that the considered version of the constitutive relations reliably describes the main effects of elastoplastic deformation and the fatigue life processes of materials and structures.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

Crack-growth-rate estimation on a three-point bend specimen during low-cycle fatigue

The ratio of the change of the clip-gage measured crack-opening displacement of a three-point bend specimen to the change of the displacement at the point of application of the cyclic load is shown to vary linearly with the ratio of the crack length to the specimen height. With the aid of this relation, the crack-growth rate is obtained by numerical differentiation of the crack length with respect to the number of load cycles. A clip-gage correction factor is introduced in order to compensate for the use of external edges to position the clip-gage during the experiment.     

Fundamentals of viscoelastoplasticity and hardening theory revisited

Thermodynamic and statistical methods for setting up the constitutive equations describing the viscoelastoplastic deformation and hardening of materials are proposed. The thermodynamic method is based on the law of conservation of energy, the equations of entropy balance and entropy production in the presence of self-balanced internal microstresses characterized by conjugate hardening parameters. The general constitutive equations include the relationships between the thermodynamic flows and forces, which follow from nonnegative entropy production and satisfy the generalized Onsager’s principle, and the thermoelastic relations and the expression for entropy, which follow from the law of conservation of energy. Specific constitutive equations are derived by representing the dissipation rate as a sum of two terms responsible for kinematic and isotropic hardening and approximated by power and hyperbolic-sinus functions. The constitutive equations describing viscoelastoplastic deformation and hardening are derived based on stochastic microstructural concepts and on the linear thermoelasticity model and nonlinear Maxwell model for the spherical and deviatoric components of microstresses and microstrains, respectively. The problem of determining the effective properties and stress-strain state of a three-component material found using the Voigt-Reuss scheme leads to constitutive equations similar in form to those produced by the thermodynamic method __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 3–18, February 2008.     

An experimental approach to low-cycle fatigue damage based on thermodynamic entropy

This paper presents an experimental approach to fatigue damage in metals based on thermodynamic theory of irreversible process. Fatigue damage is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In this work, irreversible cyclic plastic energy in terms of entropy generation is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending, tension-compression, and torsional fatigue. Experimental results show that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the fatigue damage evolution. An experimental relation between entropy generation and damage variable is developed.     

Analysis of meso-inhomogeneous deformation on a metal material surface under low-cycle fatigue

A polycrystalline Voronoi aggregation with a free surface is applied as the representative volume element(RVE)of the nickel-based GH4169 superalloy.Considering the plastic deformation mechanism at the grain level and the Bauschinger effect,a crystal plasticity model reflecting the nonlinear kinematic hardening of crystal slipping system is applied.The microscopic inhomogeneous deformation during cyclic loading is calculated through numerical simulation of crystal plasticity.The deformation inhomogeneity on the free surface of the RVE under cyclic loading is described respectively by using the following parameters:standard deviation of the longitudinal strain in macro tensile direction,statistical average of first principal strains,and standard deviation of longitudinal displacement.The relationship between the fatigue cycle number and the evolution of inhomogeneous deformation of the material’s free surface is investigated.This research finds that:(1)The inhomogeneous deformation of the material free surface is significantly higher than that of the RVE inside;(2)the increases of the characterization parameters of inhomogeneous deformation on the free surface with cycles reflect the local maximum deformation of the RVE growing during cyclic loading;(3)these parameters can be used as criteria to assess and predict the low-cycle fatigue life rationally.     

Fundamental study on rupture by low-cycle fatigue of polymers applying the fine-grid method

Few studies have been made on the fracture mechanics of polymers, their resistance to plastic failure, fatique rupture, and the adverse effects of environmental conditions, in contrast to the numerous studies conducted on metallic materials. Since fatigue is characterized by very local and cyclic fractures, in the present study a real-time fine-grid method was applied to study the fatigue rupture of polymers: to examine changes in local strain at the root of the notch during the process of crack initiation, the local strain at the tip of the crack during crack propagation and the relation between the plastic zone formed in front of the crack tip and the rate of crack propagation. As a result, strong correlation between three proposed parameters of the local crack-tip strain, the crack initiation and the propagation rate was obtained, and the mechanism of low-cycle fatigue rupture of polymers could be discussed.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Static and fatigue behaviour of glass-fibre-reinforced polypropylene composites

This paper is concerned with fatigue of polypropylene/glass-fibre thermoplastic composites produced from a bi-directional woven cloth mixture of E glass fibres and polypropylene fibres. The latter becomes the matrix after the application of heat and pressure. This composite was manufactured with a fibre volume fraction V_f of 0.338. The effect of layer design on the static and fatigue performance was investigated. The S–N curves, the rise in the temperature of the specimens during the tests and the loss of stiffness, were obtained and discussed. The loss of stiffness was related to the rise of temperature and stress release observed in the material. The effect of load rate on the static properties was also studied and discussed accordingly.     

Modeling and simulation of magnetic-shape-memory polymer composites

Composites of small magnetic-shape-memory (MSM) particles embedded in a polymer matrix have been proposed as an energy damping mechanism and as actuators. Compared to a single crystal bulk material, the production is simpler and more flexible, as both type of the polymer and geometry of the microstructure can be tuned. Compared to polycrystals, in composites the soft polymer matrix permits the active grains to deform to some extent independently; in particular the rigidity of grain boundaries arising from incompatible orientations is reduced. We study the magnetic-field-induced deformation of composites, on the basis of a continuous model incorporating elasticity and micromagnetism, in a reduced two-dimensional, plane-strain setting. The aim is to give conceptual guidance for the design of composite materials independent of the concrete macroscopic device. Thus, on the background of homogenization theory, we determine the macroscopic behavior by studying an affine-periodic cell problem. An energy descent algorithm is developed, whose main ingredients are a boundary element method for the computation of the elastic and magnetic field energies; and a combinatorial component reflecting the phase transition in the individual particles, which are assumed to be of single-domain type. Our numerical results demonstrate the behavior of the macroscopic material properties for different possible microstructures, and give suggestions for the optimization of the composite.