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A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the initial stress method is implemented in a two‐dimensional finite element code (ZEBULON). The procedure is tested on examples including mechanical and thermal loading. Some remarks are made on the maximum increment size, the relative efficiency of ‘radial return’ and ‘secant stiffness method’ is discussed. Finally, the possibilities of the model concerning ratchetting, cyclic hardening and softening are shown.

This study presents the improvements of the multicomponent Armstrong–Frederick model with multiplier (MAFM) performance through a numerical optimisation methodology available in a commercial software. Moreover, this study explores the application of a multiobjective optimisation technique for the determination of the parameters of the constitutive models using uniaxial experimental data gathered from aluminium alloy 7075-T6 specimens. This approach aims to improve the overall accuracy of stress–strain response, for not only symmetric strain-controlled loading but also asymmetrically strain- and stress-controlled loading.

Experimental data from stress- and strain-controlled symmetric and asymmetric cyclic loadings have been used for this purpose. The analysis of the influence of the parameters on simulation accuracy has led to an adjustment scheme that can be used for focused optimisation of the MAFM model performance. The method was successfully used to provide a better understanding of the influence of each model parameter on the overall simulation accuracy.

The optimisation identified an important issue associated with competing ratcheting and mean stress relaxation objectives, highlighting the issues with arriving at a parameter set that can simulate ratcheting and mean stress relaxation for load cases not reaching at complete relaxation.

The study uses a strain-life fatigue application to demonstrate the importance of incorporating a technique such as the presented multiobjective optimisation method to arrive at robust parameters capable of accurately simulating a variety of transient cyclic phenomena.

The proposed methodology improves the accuracy of cyclic plasticity phenomena and strain-life fatigue simulations for engineering applications. This study is considered a valuable contribution for the engineering community, as it can act as starting point for further exploration of the benefits that can be obtained through material parameter optimisation methodologies for models of the MAFM class.

As the dimensions of structures are scaled down to the micro‐ and nano‐domains, the mechanical behavior becomes size dependent and thus, the classical elasticity solutions cannot be expected to hold. In particular, recent experimental investigations of fatigue strength of metals show pronounced strengthening due to the influences of both grain size and small geometrical dimensions. This paper aims to provide a simple, yet rigorous analytical model in order to address the aforementioned size effects.

The present study employs a framework based on the type II, strain gradient elasticity theory by Mindlin, embedded into a thermodynamics‐based formulation which considers both mechanical behavior parameters and material lengths, as internal variables, in order to model metal fatigue.

A thermodynamics‐based, second gradient elasto‐plastic formulation with an explicit material length, which captures the size effects in fatigue of small‐scale metal components, has been established. From a physical viewpoint, the evolution of the internal length in the constitutive equations with the evolution of the intrinsic wavelength (e.g. persistent slip bands spacing) can be identified signifying the splitting of the grains into sub‐regions and consequently, the softening of the material.

The major novelty of the proposed modeling is that the internal characteristic length considered is not a fixed parameter, but evolves with the plastic effective strain amplitude obtained from cyclic loading.

Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used.

This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal.

Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error.

This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage.

Long‐term fatigue life estimation for solder joints of surface mount IC packages is studied through elasto‐plastic stress analysis and temperature cycling tests. Strain on the solder joint induced by thermal expansion mismatch between package and substrate has been analysed by considering elasto‐plastic behaviour of the solder and by treating leads as rigid frames. Validity of the analysis has been confirmed by stiffness measurement of the soldered leads. Dynamic shear stress‐strain relationships of type 60Sn/40Pb solder are obtained as a function of temperature and frequency using hollow solder specimens of 15 mm in diameter and hollow solder joint specimens with the same diameter in the temperature range of −60°C to 150°C with frequencies of 0.01 Hz and 0.3 Hz. Fatigue tests are carried out for the solder specimens and the solder joint specimens under shear strain control and for the solder joints of the real IC packages under displacement control. All fatigue tests are conducted at room temperature with a frequency of 1 Hz. Fatigue test data of solder, solder joint and the solder joints of real IC packages fall in the same scatter band in the stra'un‐cycles to failure diagram. A fatigue life estimation model for solder joints of surface mount IC packages is proposed, which is derived by combining the strain calculated by the elasto‐plastic analysis and the fatigue data. To apply the proposed model to IC packages, the temperature cycling test between −55°C and +150°C is performed for two IC packages with different lead designs mounted on two different substrates (ceramics and glass‐epoxy). It is found that the fatigue life of solder joints by the temperature cycling test can be estimated by the proposed fatigue life estimation model. The proposed method is viable because it has sufficient accuracy with a cost of less than 1/100 when compared with the finite element method.

With the fatigue ductility test the ductility of metallic foils and flexible metal foil/dielectric laminates can be determined. Ductility together with tensile strength allows prediction of the fatigue behaviour of flexible printed wiring (FPW) in both the low‐cycle/high‐strain (ductility dependent) and the high‐cycle/low‐strain (strength dependent) ranges. However, for laminates and FPW with Kapton as the dielectric the standard fatigue ductility test method does not produce the expected results and flex life predictions deviate from experimental results. The results of a study to determine the cause of this anomalous behaviour of Kapton FPW and to find correlative correction procedures are reported. Corrections to account for both the cyclic strain‐hardening of rolled annealed copper foil and the Kapton/adhesive/copper interactions for asymmetric single‐sided FPW are presented. With these corrections the ductility determination for copper foil laminated to a Kapton substrate using the fatigue ductility test produces good results, and the fatigue life of symmetric Kapton FPW can be predicted from the copper foil properties. The underlying mechanisms for the strong deviational flex behaviour of asymmetric single‐sided FPW could not be identified. The recommendation is made that for high‐cycle flex applications the FPW construction be precisely symmetrical. FPW made from copper‐clad Kapton with rolled annealed copper foil is the overwhelming choice and it is important that one has proper acceptance criteria at incoming inspection and that a valid prediction methodology for FPW flexural resistance and fatigue behaviour is available.

The purpose of this paper is to clarify the effect of material hardening model and lump-pass method on the thermal-elastic-plastic (TEP) finite element (FE) simulation of residual stress induced by multi-pass welding of materials with cyclic plasticity.

Nickel-base alloy and stainless steel, which are used in J-type weld for manufacturing the nuclear reactor pressure head, can easily harden during multi-pass welding. The J-weld welding experiment is carried out and the temperature cycle and residual stress are measured to validate the TEP simulation. Thermal-mechanical sequence coupling method is employed to get the welding residual stress. The lumped-pass model and pass-by-pass FE model are built and two materials hardening models, kinematic hardening model and mixed hardening model, are adopted during the simulations. The effects of material hardening models and lumped-pass method on the residual stress in J-weld are distinguished.

Based on the kinematic hardening model, the stresses simulated with the lumped-pass FE model are almost consistent with those obtained by the pass-by-pass FE model; while with the mixed hardening material model, the lumped-pass method has great effect on the simulated stress.

A computation with mixed isotropic-kinematic material seems not to be the appropriate solution when using the lumped-pass method to save the computation time.

In the simulation of multi-pass welding residual stress involved in materials with cyclic plasticity, the material hardening model should be carefully considered. The kinematic hardening model with lump-pass FE model can be used to get better simulation results with less computation time. The results give a direction for welding residual stress simulation for the large structure such as the reactor pressure vessel.

Regeneratively cooled thrust chamber is a key component of reusable liquid rocket engines. Subjected to cyclic thermal-mechanical loadings, its failure can seriously affect the service life of engines. QCr0.8 copper alloy is widely used in thrust chamber walls due to its excellent thermal conductivity, and its mechanical and fatigue properties are essential for the evaluation of thrust chamber life. This paper contributes to the understanding of the damage mechanism and material selection of regeneratively cooled thrust chambers for reusable liquid rocket engines.

In this paper, tensile and low-cycle fatigue (LCF) tests were conducted for QCr0.8 alloy, and a Chaboche combined hardening model was established to describe the elastic-plastic behavior of QCr0.8 at different temperatures and strain levels. In addition, an LCF life prediction model was established based on the Manson–Coffin formula. The reliability and accuracy of models were then verified by simulations in ABAQUS. Finally, the service life was evaluated for a regenerative cooling thrust chamber, under the condition of cyclic startup and shutdown.

In this paper, a Chaboche combined hardening model was established to describe the elastoplastic behavior of QCr0.8 alloy at different temperatures and strain levels through LCF experiments. The parameters of the fitted Chaboche model were simulated in ABAQUS, and the simulation results were compared with the experimental results. The results show that the model has high reliability and accuracy in characterizing the viscoplastic behavior of QCr0.8 alloy.

(1)The parameters of a Chaboche combined hardening constitutive model and LCF life equation were optimized by tensile and strain-controlled fatigue tests of QCr0.8 copper alloy. (2) Based on the Manson–Coffin formula, the reliability and accuracy of constitutive model were then verified by simulations in ABAQUS. (3)Thermal-mechanical analysis was carried out for regeneratively cooled thrust chamber wall of a reusable liquid rocket engine, and the service life considering LCF, creep and ratcheting damage was analyzed.

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.

The purpose of this paper is to examine the mechanical behaviour of additively manufactured Ti-6Al-4V under cyclic loading. Using as-built selective laser melting (SLM) Ti-6Al-4V in engineering applications requires a detailed understanding of its elastoplastic behaviour. This preliminary study intends to create a better understanding on the cyclic plasticity phenomena exhibited by this material under symmetric and asymmetric strain-controlled cyclic loading.

This paper investigates experimentally the cyclic elastoplastic behaviour of as-built SLM Ti-6Al-4V under symmetric and asymmetric strain-controlled loading histories and compares it to that of wrought Ti-6Al-4V. Moreover, a plasticity model has been customised to simulate effectively the mechanical behaviour of the as-built SLM Ti-6Al-4V. This model is formulated to account for the SLM Ti-6Al-4V-specific characteristics, under the strain-controlled experiments.

The elastoplastic behaviour of the as-built SLM Ti-6Al-4V has been compared to that of the wrought material, enabling characterisation of the cyclic transient phenomena under symmetric and asymmetric strain-controlled loadings. The test results have identified a difference in the strain-controlled cyclic phenomena in the as-build SLM Ti-6Al-4V when compared to its wrought counterpart, because of a difference in their microstructure. The plasticity model offers accurate simulation of the observed experimental behaviour in the SLM material.

Further investigation through a more extensive test campaign involving a wider set of strain-controlled loading cases, including multiaxial (biaxial) histories, is required for a more complete characterisation of the material performance.

The present investigation offers an advancement in the knowledge of cyclic transient effects exhibited by a typical α’ martensite SLM Ti-6Al-4V under symmetric and asymmetric strain-controlled tests. The research data and findings reported are among the very few reported so far in the literature.