Experimental characterisation of a CuAg alloy for thermo‐mechanical applications. Part 1: Identifying parameters of non‐linear plasticity models

Despite the wide use of copper alloys in thermo‐mechanical applications, there is little data on their cyclic plasticity behaviour, particularly for CuAg alloys. This prevents the behaviour of the materials from being correctly described in numerical simulations for design purposes. In this work CuAg0.1 alloy used for thermo‐mechanical applications was tested by strain‐controlled cyclic loading at 3 different temperatures (room temperature, 250°C, 300°C). In each test, stress‐strain cycles were recorded until the alloy had completely stabilised. These cycles were then used to identify material parameters of non‐linear kinematic and isotropic models. The focus was on plasticity models (Armstrong‐Frederick, Chaboche, Voce) that are usually implemented in commercial finite element codes. Simulated cyclic responses with the identified material models were compared with experiments and showed a good agreement. The identified material parameters for the CuAg alloy under investigation can be used directly in finite element models for cyclic plasticity simulations, thus enabling a durability analysis of components under thermo‐mechanical loads to be performed, particularly in the field of steel‐making plants.     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

Experimental and computational study on thermo‐mechanical fatigue life of aluminium alloy piston

To assess the life of a new diesel aluminium alloy piston under thermal shock loads, thermo‐mechanical fatigue (TMF) testing was conducted to characterise the TMF properties of the piston alloy, and an empirical model based on the constraint ratio concept was proposed to predict the TMF life of the piston. Considering that the empirical model required expensive experimental support, a platform with high‐frequency induction heating was established to simulate the force on the piston under thermal shock loads to calculate the piston life using the thermal shock test. Additionally, a finite element method was developed to compute the distributions of temperature, strain, and stress during this process. The characteristics of crack initiation and propagation in TMF test rods and piston mock‐ups were also investigated. The results showed that the TMF test rod suffered brittle fracture with brittle quasi‐cleavage features. The microcracks mainly occurred in primary Si particles due to stress concentration around the primary Si particles induced by the difference between the thermal expansion coefficients of Si and Al. From a macro perspective, the piston initially cracked at the rim above the pinhole, where the stress is larger than that along other directions. From a micro perspective, the protrusions of various sizes on the piston rim were induced by the compression stresses at high temperature. The piston cracks usually initiate around primary Si particles, propagate along the edge of primary Si in a straight line, bifurcate and then stop at a certain depth. If the piston was only heated, cracks or plastic deformations were not produced. The piston life can be assessed using the proposed empirical model based on the constraint ratio concept or thermal shock testing based on the developed platform. The difference between the predicted and experimental life was not greater than 7%.     

Modification of fatigue strain‐life equation for sheet metals considering anisotropy due to crystallographic texture

The fatigue behaviour of cold rolled and annealed sheet metals are influenced by the anisotropy of mechanical properties due to crystallographic texture. However, the existing fatigue strain‐life models are primarily meant for isotropic material behaviour. In the present work, the Coffin‐Manson equation for strain‐life is modified to include the effect of anisotropy using phenomenological plasticity models. It is observed that the variation of strain hardening exponent is critical to model the strain‐life behaviour. Variation of strain hardening exponent with orientation is modelled using existing anisotropic yield criteria. The prediction of fatigue life using the proposed model correlates well with the experimental results of Al6061‐T6 along different orientations. The proposed model can be used to predict the fatigue properties along any orientation from the fatigue data along one orientation and monotonic mechanical properties along longitudinal, transverse and diagonal directions.     

Stress‐life prediction of 25°C polypropylene materials based on calibration of Zhurkov fatigue life model

In this study, to evaluate the chemical and mechanical properties of polypropylene (PP), activation‐energy and tensile tests were performed at room temperature (25°C) on pure PP and PP reinforced with glass fibre (GF). To improve the prediction accuracy of the fatigue life, three models based on the calibration of the Zhurkov model were proposed: a regression model, modified strain‐rate model and lethargy coefficient‐based model. Based on the experimental data analysis and statistical assessment results, we proposed a modified strain‐rate model that satisfies the dependency of the physical parameters and is congruent with the predicted fatigue life data. The experimental data and modified strain‐rate model were compared with the direct cyclic analysis results. The tendency of the frequency factor as a correction parameter in the modified strain‐rate model corresponded to the experimental activation energy and the increasing GF content.     

Time‐dependent multiaxial fatigue and life prediction for nickel‐based GH4169 alloy

The fatigue behaviour of nickel‐based GH4169 alloy was studied under multiaxial loading at 650 °C. During the middle and late stages of the fatigue life at 650 °C, the axial and shear maximum stresses continue to decrease and plastic strains continue to increase, while at 360 °C different phenomena are observed. The intergranular cracks and certain quantities oxygen were observed in the fracture surfaces. The damage of creep and oxidation are related to temperature and strain range. The life prediction results with a time‐dependent fatigue damage model show the time‐related factors have a certain influence on the fatigue damage.     

Predicting lower bound damage curves for high‐strength low‐alloy steels

Hindered by the distinctive toughness requirements of the current European standards, the high‐strength low‐alloy (HSLA) steels are rarely applied to the pressure vessels industry. The reason is that the design rules specified by the standards define local plastic deformation as limit state. This results in an over‐conservative application of materials. To achieve an effective, economical and energy‐efficient use of HSLA steels, a strain‐based criterion, the damage curve, which considers crack initiation instead of the beginning of plastic deformation as limit state, is proposed in this study for the improved design rules. In the view of the interaction of microstructure and mechanical properties of materials, the new design rule is derived on the basis of the correlation of microstructural features of HSLA steels with the micromechanical damage models. The experimental verification of the result is furthermore investigated with sufficient agreement so that the general applicability of the procedure can be expected. However, further studies for a reliable parameter calibration are necessary.     

A new energy‐based isothermal and thermo‐mechanical fatigue lifetime prediction model for aluminium–silicon–magnesium alloy

In this paper, a new fatigue lifetime prediction model is presented for the aluminium–silicon–magnesium alloy, A356.0. This model is based on the plastic strain energy density per cycle including two correction factors in order to consider the effect of the mean stress and the maximum temperature. The thermal term considers creep and oxidation damages in A356.0 alloy. To calibrate the model, isothermal fatigue and out‐of‐phase thermo‐mechanical fatigue (TMF) tests were conducted on the A356.0 alloy. Results showed an improvement in predicting fatigue lifetimes by the present model in comparison with classical theories and also the plastic strain energy density (without any correction factors). Therefore, this model is applicable for TMF, low cycle fatigue (LCF) and both TMF/LCF lifetimes of the A356.0 alloy. Furthermore, this model can be easily used for the estimation of thermo‐mechanical conditions in components such as cylinder heads.     

A modification of Smith–Watson–Topper damage parameter for fatigue life prediction under non‐proportional loading

In this paper, the shortcomings of the Smith–Watson–Topper (SWT) damage parameter are analysed on the basis of the critical plane concept. It is found that the SWT model usually overestimates the fatigue lives of materials since it only takes into account the fatigue damage caused by the tensile components. To solve this problem, Chen et al. (CXH) modified the SWT model through considering the shear components. However, there are at least two problems present in CXH model: (1) the mean stress is not considered and (2) the different influence of the normal and shear components on fatigue life is not included. Besides, experimental validations show that the modification by Chen et al. usually leads to conservative fatigue life predictions during non‐proportional loading. In order to overcome the shortcomings of SWT and CXH models, a damage parameter as the effective strain energy density (ESED) is proposed. Experimental validations by using eight kinds of materials show that the ESED model can give satisfactory fatigue life predictions under the non‐proportional loading.     

A new continuum damage mechanics–based two‐scale model for high‐cycle fatigue life prediction considering the two‐segment characteristic in S‐N curves

In this study, we propose a new two‐scale fatigue model based on continuum damage mechanics. A representative volume element (RVE) consisting of microinclusions and a matrix is constructed. Further, damage‐coupled constitutive equations are derived. The degradation in the mechanical properties of the RVE is determined by the damaged inclusions and matrix using the Mori‐Tanaka scheme. A numerical calculation of the fatigue lives of notched specimens is executed. This new model predicts high‐cycle fatigue (HCF) life more effectively, considering the two‐segment characteristic of S‐N curves of smooth specimens. This study provides novel insights into the evolution mechanism of HCF damage.     

Sensitivity analysis and shape optimization for preform design in thermo‐mechanical coupled analysis

In complex forging processes, it is essential to find the optimal deformation path and the optimal preform shape that will lead to the desired final shape and service properties. A sensitivity analysis and optimization for preform billet shape in thermo‐mechanical coupled simulation is developed in this work. Non‐linear sensitivity analysis of temperatures, flow‐stresses, strains and strain‐rates are presented with respect to design variables. Both analytical and finite‐difference gradients are employed to validate the effectiveness of sensitivity analysis developed in this work. Numerous iterations of coupled thermo‐mechanical analysis are performed to determine an optimum preform shape based on a given criterion of minimizing the objective function on effective strain variance within the final forging. The design constraints are imposed on die underfill, material scrap, folding defects and temperatures. In addition, a method for material data processing is given in order to determine the flow stress and its derivatives. The shape optimization scheme is demonstrated with the preform designs of an axisymmetric disk and a plane strain problem. Copyright © 1999 John Wiley & Sons, Ltd.     

An evaluation of limited‐memory sparse linear solvers for thermo‐mechanical applications

We consider the performance of sparse linear solvers for problems that arise from thermo‐mechanical applications. Such problems have been solved using sparse direct schemes that enable robust solution at the expense of memory requirements that grow non‐linearly with the dimension of the coefficient matrix. In this paper, we consider a class of preconditioned iterative solvers as a limited‐memory alternative to direct solution schemes. However, such preconditioned iterative solvers typically exhibit complex trade‐offs between reliability and performance. We therefore characterize such trade‐offs for systems from thermo‐mechanical problems by considering several preconditioning schemes including multilevel methods and those based on sparse approximate inversion and incomplete matrix factorization. We provide an analysis of computational costs and memory requirements for model thermo‐mechanical problems, indicating that certain incomplete factorization schemes can achieve good performance. We also provide empirical evaluations that corroborate our analysis and indicate the relative effectiveness of different solution schemes. Our results indicate that our drop‐threshold incomplete Cholesky preconditioning is more robust, efficient and flexible than other popular preconditioning schemes. In addition, we propose preconditioner reuse to amortize preconditioner construction cost over a sequence of linear systems that arise from non‐linear solutions in a plastic regime. Copyright © 2007 John Wiley & Sons, Ltd.     

A stochastic second‐order and two‐scale thermo‐mechanical model for strength prediction of concrete materials

A stochastic thermo‐mechanical model for strength prediction of concrete is developed, based on the two‐scale asymptotic expressions, which involves both the macroscale and the mesoscale of concrete materials. The mesoscale of concrete is characterized by a periodic layout of unit cells of matrix‐aggregate composite materials, consisting of randomly distributed aggregate grains and cement matrix. The stochastic second‐order and two‐scale computational formulae are proposed in detail, and the maximum normal stress is assumed as the strength criterion for the aggregates, and the cement paste, in view of their brittle characteristics. Numerical results for the strength of concrete obtained from the proposed model are compared with those from known experiments. The comparison shows that the proposed method is validated for strength prediction of concrete. The proposed thermo‐mechanical model is also employed to investigate the influence of different volume fraction of the aggregates on the strength of concrete. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

In engineering practice, it is generally accepted that most of components are subjected to multiaxial stress‐strain state. To analyse this complicated loading state, different types of specimens of 2A12 (2124 in the United States) aluminium alloy were tested under multiaxial loading conditions and a new multiaxial fatigue analysis method for the state of three‐dimensional stress and strain is proposed. Elastic‐plastic finite element method (FEM) and a proposed vector computing method are used to describe the loading state at the critical point of specimen, by which the parameter Γ_T is calculated at the new defined subcritical plane to consider the effect of additional cyclic hardening. Meanwhile, the principal equivalent strain is still calculated at the traditional critical plane. The new damage parameter is composed of different process parameters, by which the dynamic path of strain state, including loading environments and material properties, are fully considered in one loading cycle. According to experimental verifications with 2A12 aluminium alloy, the results show that the proposed method shows satisfactory, accurate, and reliable results for multiaxial fatigue life prediction in the state of three‐dimensional stress and strain.     

A hybrid frequency–time domain method for predicting multiaxial fatigue life of 7075‐T6 aluminium alloy under random loading

A hybrid frequency–time domain method for predicting multiaxial fatigue life under random loading is developed on the basis of combination of the frequency domain and time domain analysis. The critical damage point of the structure is determined by the frequency domain equivalent stress method. Then, the fatigue life prediction is made in time domain by generating random load‐time histories from the power spectral density of the critical point. The method is validated with the random vibration fatigue test of 7075‐T6 aluminium alloy. It has been shown that the results of fatigue life calculated by hybrid method are well correlated with the experiment.     

The effect of porosity on the fatigue life of cast aluminium‐silicon alloys*

Fatigue strength optimization of cast aluminium alloys requires an understanding of the role of micropores resulting from the casting process. High cycle fatigue tests conducted on cast A356‐T6 show that the pore size and proximity to the specimen surface significantly influence fatigue crack initiation. This is supported by finite element analyses (both elastic and elastic–plastic) which demonstrate that high stress/strain concentration is induced by pores which are both large and near to the specimen surface. A new pore‐sensitive model based on a modified stress‐life approach has been developed which correlates fatigue life with the size of the failure‐dominant pore. The model prediction is in good agreement with experimental data.     

Applicability of published data for fatigue‐limited design

The use of published fatigue data provides an expedient basis for fatigue‐limited engineering design by alleviating the necessity of explicit testing. However, published fatigue data often exhibits incomplete documentation of the associated test conditions. Incomplete documentation introduces uncertainties in fatigue life prediction that may limit the applicability of the published fatigue data for design applications. Characterization of the applicability of published fatigue data is critical for robust fatigue‐limited design. However, no quantitative methods have been identified which respond to this requirement. A novel method has been developed to provide a systematic characterization of the applicability of published fatigue data based on internationally recognized standards. This method provides a conceptual mechanism to:

• identify the applicability of published fatigue test data for specific design scenarios—thereby informing engineers of potential limitations of published data and allowing prioritization of multiple data sources;
• identify material domains of insufficient applicability—thereby providing a robust basis for identifying beneficial fatigue test programs;
• compromise between design complexity and the uncertainties inherent in fatigue life prediction;
• define a framework for the appropriate documentation of published fatigue data.

A sample of published fatigue data sources associated with a specific fatigue‐limited safety–critical design scenario was assessed by the method presented in this paper. For the majority of the sampled references, the associated documentation was insufficient to allow the fatigue test data to be confidently applied to the subsequent design activity. Copyright © 2009 John Wiley & Sons, Ltd.     

Low‐cycle fatigue behavior of a newly developed cast aluminum alloy for automotive applications

The drive for increasing fuel efficiency and decreasing anthropogenic greenhouse effect via lightweighting leads to the development of several new Al alloys. The effect of Mn and Fe addition on the microstructure of Al‐Mg‐Si alloy in as‐cast condition was investigated. The mechanical properties including strain‐controlled low‐cycle fatigue characteristics were evaluated. The microstructure of the as‐cast alloy consisted of globular primary α‐Al phase and characteristic Mg₂Si‐containing eutectic structure, along with Al₈(Fe,Mn)₂Si particles randomly distributed in the matrix. Relative to several commercial alloys including A319 cast alloy, the present alloy exhibited superior tensile properties without trade‐off in elongation and improved fatigue life due to the unique microstructure with fine grains and random textures. The as‐cast alloy possessed yield stress, ultimate tensile strength, and elongation of about 185 MPa, 304 MPa, and 6.3%, respectively. The stress‐strain hysteresis loops were symmetrical and approximately followed Masing behavior. The fatigue life of the as‐cast alloy was attained to be higher than that of several commercial cast and wrought Al alloys. Cyclic hardening occurred at higher strain amplitudes from 0.3% to 0.8%, while cyclic stabilization sustained at lower strain amplitudes of ≤0.2%. Examination of fractured surfaces revealed that fatigue crack initiated from the specimen surface/near‐surface, and crack propagation occurred mainly in the formation of fatigue striations.     

Multiscale analysis method for thermo‐mechanical performance of periodic porous materials with interior surface radiation

This study develops a novel multiscale analysis method to predict thermo‐mechanical performance of periodic porous materials with interior surface radiation. In these materials, thermal radiation effect at microscale has an important impact on the macroscopic temperature and stress field, which is our particular interest in this paper. Firstly, the multiscale asymptotic expansions for computing the dynamic thermo‐mechanical coupling problem, which considers the mutual interaction between temperature and displacement field, are given successively. Then, the corresponding numerical algorithm based on the finite element‐difference method is brought forward in details. Finally, some numerical results are presented to verify the validity and relevancy of the proposed method by comparing it with a direct finite element analysis with detailed numerical models. The comparison shows that the new method is effective and valid for predicting the thermo‐mechanical performance and can capture the microstructure behavior of periodic porous materials exactly.s Copyright © 2015 John Wiley & Sons, Ltd.     

A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes

A computational framework is presented to evaluate the shape as well as non‐shape (parameter) sensitivity of finite thermo‐inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo‐mechanical deformation of hyperelastic thermo‐viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite‐dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright © 2002 John Wiley & Sons, Ltd.