用应变能密度法分析纤维金属层板的微动疲劳特性

为研究纤维金属层板的微动疲劳特性,首先,基于三维坐标系下的临界平面法求解了纤维金属层板铝层临界平面上的应力和应变分量,并进一步求解了Smith-Watson-Topper （SWT）和I型Nita-Ogatta-Kuwabara （NOK）应变能密度参数;然后,建立了应变能密度参数-微动疲劳寿命关系式,并通过实验数据得到了寿命预测公式中的待定参数;最后,采用I型NOK应变能密度准则分析了铝层厚度、纤维层厚度、各层相对厚度和桥足圆角半径等对微动疲劳损伤位置和寿命的影响,并为纤维金属层板抗微动疲劳设计提出了一些合理化建议。结果表明:增加铝层厚度可以延长微动疲劳寿命,但增加纤维层厚度和桥足圆角半径不会改善微动疲劳特性。提出的方法可为分析纤维金属层板铆接和螺栓连接中的微动疲劳问题提供理论依据。      

Application of strain energy density factor to fatigue crack growth analysis

The rate of crack propagation is postulated to be a function of the strain energy density factor range, which is used to correlate the subcritical crack growth data of several different materials. Subsequently, this concept is applied to predict crack growth due to spectrum loads.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading

In the notch stress intensity approach to the fatigue assessment of welded joints, the weld toe is modelled as a sharp V-notch and the local stress distributions in plane problems are given on the basis of the relevant mode I and mode II notch stress intensity factors (N-SIFs). These factors quantify the magnitude of asymptotic stress distribution obeying Williams’ solution. If the V-notch opening angle at the weld toe is constant and the mode II is not singular, the mode I N-SIF can be directly used to summarize the fatigue behaviour of welded joints. In all the other cases, varying the V-notch angle or including multiaxial loading conditions (where typically both Mode I and Mode III stress distributions are singular), the synthesis can be carried out on the basis of the mean value of the strain energy density over a well-defined volume surrounding the weld toe or the weld root. By using this scalar quantity, two fatigue scatterbands are obtained for structural steels and aluminium alloys, respectively. The material-dependent radius R_C of the control volume (area) is carefully identified with reference to conventional arc welding processes.Sometimes the weld toe radius is found to be very different from zero. The local strain energy approach can be extended as it stands also to these cases, providing a gradual transition from a N-SIF-based approach to a K_t-based approach.     

Applying the strain energy density criterion to fatigue and fracture problems in the transportation industry

Abstract

Today fracture mechanics is an independent discipline that deals with structures containing detectable or visible sharp cracks. The basic concepts of fracture mechanics are well established due to the contributions of researchers such as G. C. Sih. This paper focuses on one of his many contributions; specifically, the strain energy density criterion for fatigue and fracture problems involving mixed mode loading. Moreover, this paper reviews examples of original research in the transportation industry in which the strain energy density criterion was applied. In particular, these examples come from the aircraft and railroad industries. Both industries now use fatigue and fracture control programs, developed from damage tolerance or fracture mechanics principles, to minimize the risks associated with structural failures.     

A fatigue crack propagation model for strain hardening materials

In this paper a crack propagation model based on Tomkins concept (dl/dN ∝ Δε_p · ω) has been developed using the theoretically developed cyclic plastic zone sizes. The crack propagation rates are found to be functions of stress intensity factor, Elber's effective stress range ratio, cyclic yield strength of material, crack length, specimen width and cyclic strain hardening exponent. Suitably grouped to give the crack growth rate in terms of five constants termed as Loading Constant, Material constant, Crack size constant, specimen Width Constant and Stress Intensity Exponent. The crack growth rates found by theory are compared with the experimental results available in literature and a good agreement is found.     

Fatigue life prediction for metals using an improved strain energy density model

Abstract

An improved strain energy density model is proposed on the basis of critical plane concept to better predict the multiaxial fatigue life of metals, especially during nonproportional loadings. This approach is based on the normal and shear strain energy densities on maximum principal strain range plane. Procedures used to determine the normal and shear strain energy densities are also presented. Experimental data taken from the literature are used to validate the capabilities of the improved model, including 4 different metals and 24 different loading paths. The results show that the proposed model gives good predictions for most of these materials and loading paths.     

A damaged evolution model for strain fatigue of ductile metals

This paper, based on Lemaitre's potential of dissipation, derives a damaged evolution model for strain fatigue of ductile metals. Then the equation of fatigue-life prediction and the criterion of cumulative fatigue damage are deduced. Experiments for steel were conducted and the experiment data agreed with the model excellently. Thus the model can predict the damaged evolution during the strain fatigue process.     

Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches

A fatigue strength parameter for (seam-)welded joints is presented which is based on the averaged elastic strain energy density (SED) criterion applied to full circle and semicircular ‘control volumes’, the latter centred by the expected crack path. The parameter is applicable both at weld toes and weld roots, at least in the medium-cycle and high-cycle fatigue range where elastic conditions are prevailing. Based on a rectangular slit-plate model representing the weld root and analysed by the finite element method, the effect of the following influencing conditions is investigated: tension loading (mode 1) and shear loading (mode 2), slit-parallel tension loading acting on a rounded slit tip, pointed slit tip versus small-size key-hole at the slit tip, semicircle and narrow sector versus full circle or full sector SED evaluations, distortional SED versus total SED under plane strain conditions. The following conclusions are drawn from the numerical results. The SED approach should be based on the full circle or full sector evaluation of the total SED, with R₀ = 0.28 mm for steels. In cases of a markedly unilateral angular SED distribution, the semicircle evaluation centred by the expected crack path is more appropriate. The use of small-size reference notches instead of pointed notches provides no advantage. The endurable remote stresses for fatigue-loaded welded joints according to the SED approach are well in correspondence with those according to the fictitious notch rounding approach. High accuracy of the results can already be achieved with a rough meshing at the pointed notches.     

A unified fatigue life model based on energy method

A new unified fatigue life model based on the energy method is developed for unidirectional polymer composite laminates subjected to constant amplitude, tension–tension or compression–compression fatigue loading. This new fatigue model is based on static failure criterion presented by Sandhu and substantially is normalized to static strength in fiber, matrix and shear directions. The proposed model is capable of predicting fatigue life of unidirectional composite laminates over the range of positive stress ratios in various fiber orientation angles. By using this new model all data points obtained from various stress ratios and fiber orientation angles are collapsed into a single curve.

The new fatigue model is verified by applying it to different experimental data provided by other researchers. The obtained results by the new fatigue model are in good agreements with the experimental data of carbon/epoxy and E-glass/epoxy of unidirectional plies.     

A semi-empirical unified model of strain fatigue life for insulation plastics

The paper focuses on modeling the strain fatigue lives of three commonly used cable insulation polymers, namely (1) polyvinyl chloride, (2) crosslinked polyethylene, and (3) polyphenylene ether under selected strain and temperature ranges. On the basis of results obtained from their fatigue tests, Coffin–Manson model, mean/maximum strain fatigue model, and a set of new semi-empirical equations were applied to establish the relationship between fatigue lives and strains. The unified strain model, herein we name it the Wei–Wong model, is developed to predict the fatigue lives of three polymers studied and their prediction capability was examined using our experimental data. It was found that the proposed Wei–Wong model can provide a better life prediction compared to the experimental data and other methods in the literature at selected temperatures, namely −40, 25, and 65 °C.     

Evaluating a strain energy fatigue method using cyclic plasticity models

For the development of constitutive equations that describe the behaviour of materials under cyclic plastic strains, different kinds of formulations can be adopted. Recently, an energy‐based fatigue damage parameter has been developed to present energy‐fatigue life curves using a calculation of the total strain energy. In this study, the damage criterion is examined by calculation of the plastic strain energy from stress–strain hysteresis loops in the cyclic plasticity models under condition of multi‐axial fatigue. These cyclic plasticity models are the Garud multi‐surface model and the Chaboche nonlinear kinematic hardening model. The models are briefly explained and the general features of their computational procedure are presented. Then, the hysteresis loops of these models will be obtained and the fatigue lives are predicted and compared to experimental data by the ratio of predicted life to experimental life. Consequently, a weighting factor on shear plastic work is presented to decrease the life factors.     

Cyclic response and inelastic strain energy in low cycle fatigue

The cyclic response of ASTM A-516 Gr 70 carbon low alloy steel subjected to fully-reversed constant strain- or stress-controlled cycles has been determined. The cyclic stress/strain relationship of the material was obtained through a least squares fit technique.Stable hysteresis loops at half life for various strain ranges are presented. The material does not exhibit Masing-type behaviour. The total inelastic strain energy is calculated by a new method and is in good agreement with the measured values. Comparison is also made with other proposed relationships. The total strain energy dissipated at failure may be expressed as W_f = KN_f^α     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

Ductile crack propagation with the strain energy density criterion

The strain energy density criterion is used to characterize subcritical crack growth in a thin aluminum alloy sheet undergoing general yielding. A finite element analysis which incorporates both material and geometrical nonlinear behaviors of the cracked sheets is developed to predict fracture loads at varying crack growth increments. The predicted results are in excellent agreement with those measured experimentally, thus confirming the validity of the strain energy density criterion for characterizing ductile crack propagation.     

Grain-level statistical plasticity analysis on strain cycle fatigue of a FCC metal

The micromechanical strain cycle fatigue-life is systematically investigated by the micro-level numerical simulation, compared with symmetrical strain cycle experiments of copper, focusing on the characteristics of polycrystalline aggregation and the mechanism of microscale plastic deformation. A methodology to predict the low-cycle fatigue life by micro-level simulation along with statistical analysis is proposed through the following steps: (1) A crystal plasticity model is developed based on the nonlinear kinematic hardening mechanism of crystal slipping system. This model is applied to the calculations of crystal grain interior stresses and plastic strains. (2) A statistical representative volume element (SRVE) is constructed for a pure copper as a material model which features a polycrystalline Voronoi aggregation consisting of a number of crystal grains. This SRVE can be used for statistical analysis of the material inhomogeneous stresses and strains during cycle loading. (3) The simulations are performed to model the experimental cycle evolution of strain fatigue by using the SRVE under the symmetrical tensile–compressive loading. (4) Statistical and micromechanical analyses are carried out for the inhomogeneous interior stresses and strains of the SRVE of the polycrystalline copper in the low cycle regime. The resulting analysis can render the microscale interpretation and numerical simulation for the low-cycle fatigue evolution accordingly.     

Non-local energy density functional for atoms and metal clusters

Starting from the Hartree-Fock (HF) exchange energy for a spin saturated system and expanding the first order density matrix we have built a non local energy density functional and its corresponding variational one body potential without problems of divergence at large distances. Fitting the “dummy” parameter k which appears due to the truncation of the expansion, our non-local Energy Density Functional (EDF) can be applied to atoms and metal clusters. In the atomic case the present approach improves significantly the total binding energies as well as the eigenenergies of the single particle levels. The first ionization potential of the alkaline metals approaches the experimental values better than the Local Density Approximation (LDA) ones. The application of this non-local approach to Na clusters gives also a significant improvement of the first ionization potentials compared with the LDA prediction.