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In this work, the forming limit of GH605 superalloy was determined by using digital image correlation analysis to monitor the strain evolution during this process. First, tensile experiments were conducted to determine the material constants of three different types of GH605 superalloys. Then, the Holmberg and Marciniak methods of forming limit tests were compared, and the complete forming limit diagram was obtained by combining the results from 6 specimens. Finally, the factors affecting the forming limit were analyzed, and the forming limit diagrams (FLD) of three different types of GH605 superalloys were obtained. The results showed that the forming limit curve of GH605 sheet and strip showed a typical ‘V’ shape, and the minimum forming limit appeared near the plane strain. The FLD of GH605 sheet was also obtained in this work, which is of great significance to numerical simulations of sheet metals and the formulation of process parameters.

Mooney-Rivlin is the most frequently used model from all models used for mechanical characterization of the hyperelestic materials. Simplicity, applicability in a large rage of strains are the key reasons for regular use of this model. However, depending on the number of parameters, the Mooney model can take several forms. While, nine parameter being the highest order noticed, two parameter model is the most commonly found form in the current research domain. Since two parameter model used repetitively, we investigated the effect of incremental change in two material constant values one at a time, on model curve. As Drucker Stability Criterion is governing the extreme values of material parameters, changes in the model curves are discussed related to it. Resultant effects on stress-strain curves due to change in parameter values were examined and physical effect on the characterization is interpreted accordingly.

A simple plasticity model is proposed to model the stabilized cyclic stress‐strain by introducing the non‐proportionality factor and additional hardening coefficient. The two introduced factors take into account the effects of non‐proportional additional hardening. The proposed model is convenient for engineering application since only six material constants are necessary for modeling.

Uniaxial fatigue tests were conducted for a &beta, titanium alloy Ti-22V-4Al up to a very high cycle fatigue (VHCF) regime. The initiation and propagation processes of the internal fatigue cracks were investigated using 3D fractographic analysis. Multiple facets were observed at the crack initiation site. Three facet initiation models were proposed based on the surface appearances and the 3D facet bonding patterns of the multiple facets, and the major facet was determined to be the true crack initiation site. Using the size of the major facet, a Tanaka&ndash, Akiniwa model, which can determine the material constants for the Paris law using only conventional fatigue tests, was applied to reveal the propagation process of the internal cracks. A reverse fatigue life prediction was also conducted to evaluate the accuracy of the material constants obtained using the Tanaka&ndash, Akiniwa model. When the facet initiation models were applied, the predictions showed less deviation and better agreement than when the facet initiation process was not considered. The findings of this study indicate that the formation of multiple facets in &beta, titanium alloys is sequential rather than simultaneous.

This paper presents a method for determining material constants of hyperelastic material used for building the soft robotic actuators. Sixty testpieces were made of silicone rubber with a shore A hardness from 20 A to 45 A. Each of them was then subjected to the uniaxial tensile test to obtain the stress–strain relationship, which is a key factor to evaluate the compatibility of the common six forms of strain energy density function for hyperelastic material. The sum of square error was used to determine the most relevant constitutive models, which are Ogden third order, Polynomial second order, and Yeoh, as well as parameter values of the corresponding materials. To analyze the appropriateness of these models for computation, six pneumatic soft actuators were built from materials with different hardness and tested for various pressures. From the simulation and experimental results, the model Yeoh has yielded the highest accuracy. This outcome forms a firm basis for the determination of suitable material in the computation and simulation of the pneumatic soft actuator. Besides, the obtained experimental results in this paper could be included in the database of hyperelastic material with different hardness for further simulation in the related field.

In this work, we consider a strain gradient elasticity theory with an extended number of field variables: the displacement vector and an additional scalar field defining the internal micro-deformation. The total internal energy of the model depends on the strain, the micro-deformation function, their gradients, and the coupling. The considered model can be treated as gradient/micromorphic. Moreover, the micro-deformation field can be treated as a field of scalar defects distributed along the medium. Based on analytic (one-dimensional) solutions of uniform/non-uniform deformation of the rod, we introduce (i) an apparent stiffness and (ii) an apparent length scale parameter. Subsequently, we provide a variant of continuum-on-continuum homogenization by equating tip displacements for the gradient/micromorphic medium and an equivalent strain gradient one. Elongation of the gradient/micromorphic rod is therefore equated with the corresponding elongation of the equivalent strain gradient rod, whose behavior is characterized by the apparent material constants. Subsequently, the non-dimensional coupling number is identified with a damage parameter. It is shown that, on the one hand, the apparent stiffness of the rod is reduced when such parameter increases. On the other hand, the apparent length scale parameter (i.e. the apparent second gradient elastic coefficient) increases when the damage parameter increases. Therefore, it is shown that the presence of defects in a second gradient linear elastic material may increase its apparent strain gradient behavior.

In order to find hyperelastic material model constants, data fitting technique is often used. For this task, the data is collected through different laboratory tests, namely, the uniaxial, the biaxial and the pure shear. However, due to the difficulty in getting biaxial data, often only uniaxial data was used for the fitting. Despite frequent use, it was established that this practice creates erroneous results. With a view to improve the data fitting results and at the same time to overcome the difficulty of collecting primary biaxial data, uniaxial data was used to generate a secondary biaxial data set. The data derived through this method was then tested with four common models as to examine the compatibility of the method. Subsequently, real biaxial data was used to compare with the data fitting results obtained through the proposed method. As results indicated combined data fitting for both instances were very much identical with respect to all tested models. Cases where somewhat higher deviation observed between experimental curves and data fitted curves for biaxial data, gave similar results for adjusted data driven data fitting too. However, such deviation could be attributed to mismatch between models with the particular material behaviour rather than the generated data.

Concrete tensile strength and fracture toughness are two important material constants that should be independent of specimen size, geometry or type. In this study, on the basis of the improved boundary effect model, independent tensile strength and fracture toughness of concrete, which are unaffected by the specimen type, were determined by using various specimens, e.g., three-point-bending and wedge-splitting specimens. The concrete structural failure was fully predicted using independent material constants, and the constructed safe design diagrams with upper and lower limits (±15%) can cover all experimental results. The theoretical minimum size of the concrete meeting the linear elastic fracture mechanics were quantified, and the peak loads of concrete specimens were predicted using various average fictitious crack growth length.

The ductile fracture has been observed in large as well as small scales. Three chosen Lode and pressure dependent phenomenological ductile fracture criteria with cut-offs were calibrated for aluminium alloy EN AW 2024-T351 using an enhanced hybrid experimental–numerical technique. It consisted of calibrating all the material constants of fracture criteria altogether. This enabled ready determination of the cut-off related constant for one of those criteria. Moreover, a non-quadratic Lode dependent plasticity model was coupled with the ductile failure criteria to form the damage plasticity approach in the numerical analysis. The fracture criteria were calibrated using the standard – large – sized specimens including a non-standard upsetting test. The specimens used for the calibration of failure criteria are usually ten times larger than that of a specimen for the small punch test. The transferability of calibrated parameters was tested and fair predictability was observed for all numerical models when applied to small scales.

In the present work, two-component ductile fracture criteria with high estimation accuracy were established. They were formulated by using a weighted superposition of the existing ductile fracture criteria as basic components, which possessed the same form but different parameters. The flexibility of new criteria was greatly enhanced because of increased material constants. The micro-mechanism-inspired DF2012 criterion and its improved form of DF2014 criterion were chosen as the basic components, respectively. Based on the established criteria, the fracture surfaces of aluminum alloys 2024-T351 in various stress and strain spaces were constructed and compared with those constructed by the single-component criteria. The results showed that the two-component criteria have better prediction accuracy than the single-component counterparts, especially for the tests at high stress triaxiality region. Due to the shear-linking assumption, fracture strains constructed by the single-component DF2012 and DF2014 criteria at high stress triaxiality region inevitably carried large errors. However, these errors were largely reduced by the established two-component criteria. It indicates that the two-component criteria can overcome some inherent shortcomings of the single-component criteria, which is an effective solution to promote the fracture estimation accuracy.

For engine components under complex loadings, multiaxial fatigue life prediction is critical for ensuring their structural integrity and reliability. Combining the critical plane method with the virtual strain energy concept, a new multiaxial fatigue damage parameter is proposed to characterize the influence of both shear/normal mean stress and non-proportional hardening on fatigue life. Particularly, no extra material constants are needed for model application. Experimental data of TC4 and GH4169 alloys under various loading paths are utilized to evaluate and validate the proposed damage parameter as well as four other models. Results show that the proposed damage parameter yields a higher accuracy on multiaxial fatigue life prediction than others.

The article presents the characteristics of 1.3964 steel and the results of firing a 7.62 mm projectile with a steel core. A simplified Johnson&ndash, Cook material model for steel and projectile was used. Then, a FEM (finite element method) simulation was prepared to calibrate the material constants and boundary conditions necessary to be used in simulations of the entire hull model. It was checked how projectile modeling affects the FEM calculation results. After obtaining the simulation results consistent with the experimental results, using the model of a modern minehunter, the resistance of the ship&rsquo, s hull to penetration by a small-caliber projectile was tested.

Duplex and super duplex stainless steels have high corrosion resistance, excellent mechanical properties, and high impact strength. Such characteristics make these steels able to operate in various segments of the industry, especially in aggressive environments. These alloys have higher strength than austenitic and ferritic stainless steels and their operation is generally restricted to temperatures lower than 300 °C. Most steels and alloys only exhibit elasto-viscoplastic behavior at temperatures higher than 1/3 of the absolute melting temperature. The objective of this work was to make an experimental study showing that the duplex and superduplex steels present a rate-dependent behavior even at room temperature (around 25 °C). Two different alloys: duplex stainless steel UNS 31803F51 and super duplex UNS S32760GRF55 were used in the study. Simple models were proposed to describe how the rate-dependent portion of the stress (called at this paper “the viscous term”) depends on the strain rate. A simple procedure to identify experimentally all material constants that appear in the theory is presented. The experimental results are in very good agreement with the model predictions.

This paper reports creep crack growth modelling of Grade 91 vessel weldments at high temperature using a modified ductility-based continuum damage mechanics (CDM) model, which is based on the Kachanov-Rabotnov CDM and utilizing the concept of ductility exhaustion. The proposed model holds a key advantage over existing models in that it requires fewer material constants to be identified and calibrated. The new modified model was implemented into a user-defined subroutine in ABAQUS and then used to predict the creep crack growth of Grade 91 vessel weldments. Creep crack initiation and growth in the vessels were predicted to occur in the heat-affected zones of the weldments associated with the end closures, which is in good agreement with the corresponding vessel tests. Further, the predicted creep rupture lives of the notched bars and the vessels using the proposed model correlated reasonably well against the experimental results. This suggests that the modified ductility-based damage model can be used for creep crack growth and life prediction for high temperature structures with confidence.

This paper reviews experimental tests of the fatigue life of metallic materials under uniaxial fatigue loading at elevated temperature. The influence of elevated temperature on the properties of different materials were investigated for monotonic and cyclic loads with high loading amplitude values. Models most commonly used to estimate the fatigue life of materials under these conditions are presented. Based on compiled results of experimental tests, an empirical model of fatigue damage accumulation was developed, making it possible to predict fatigue life under uniaxial, low-cycle loading conditions at elevated temperature. The model's structure was based on fatigue deformation curves obtained by way of experimental tests. The low number of material constants, which can be determined from fatigue tests at ambient temperature, is an advantage of the proposed model. The model was verified experimentally, and compiled test results were used for this purpose.

This paper presents the problems relating to the determination of the material constants and their assessment. The study demonstrated that the scatter of the values of the fatigue life and stresses applied for determination of the σa-Nf characteristics could have an effect on the coefficient m representing the slope of this characteristics. The phenomenon associated with the variability of a number of material parameters relating to the number of cycles to failure is discussed. In addition, the paper reports on the influence of the number of cycles to failure on the value of the notch factor. The paper also discusses the function accounting for the effect of the geometrical KW and structural KS notches based on the relation stating the dependence of Kf coefficient on the number of cycle to failure.

In the metal plastic forming process, ductile fracture is an important factor influencing the forming properties of materials, and the ductile fracture criterion can effectively predict the moment and location when the material fracture. When using the ductile fracture criterion predicts the fracture of materials, the material constants expressed in integral form is an important index that affect the prediction accuracy. At present, the method to determine the material constants in the ductile fracture criterion is mostly combined with basic test. Therefore, the method to determine the material constants in ductile fracture criterion is introduced in this paper. These methods are divided into numerical calculation methods, finite element simulation method and the M-K theory model method.

This paper conducts a comparative evaluation on typical critical plane criteria, including Fatemi-Socie, Wang-Brown, modified Smith-Watson-Topper (MSWT) and proposed modified generalized strain energy (MGSE) criteria for multiaxial fatigue analysis of ductile/brittle materials. Experimental datasets of four materials under uniaxial tension, torsion and proportional/non-proportional multiaxial loadings are introduced for model comparison. This study results indicate that criteria with additional material constants yield robust life predictions for different materials. Moreover, the criteria with shear and uniaxial fatigue properties are respectively suitable for ductile and brittle materials, particularly the MGSE superior to others for ductile/brittle materials while MSWT only for brittle materials.

Application of a continuum damage mechanics formulation rests on the ease with which the material constants involved in the formulation can be determined. For an initially linear elastic material, the changes in elastic constants induced by damage depend on certain damage related material constants that are commonly determined by experiments in addition to those required to determine the initial properties. This additional experimental task can render the continuum damage mechanics theory less attractive. The present paper will only deal with those associated with damage representation. We propose here a procedure for analytically determining seven out of eight damage related material constants for unidirectional composites assumed initially transversely isotropic and containing a parallel array of matrix cracks along fibres. The remaining constant can be determined experimentally or by a numerical experiment proposed here for the purpose. The analytical expressions derived are in terms of initial elasticity constants of a unidirectional composite and are verified for their accuracy by numerical experiments. Since a unidirectional composite forms a building block in composite laminates, the results obtained here can be naturally used for damage in laminates.

The risk of error in using only uniaxial data for fitting constitutive model curves is emphasized by many hyperelastic material researchers over the years. Unfortunately, despite these indications, often the method is utilized in finding material constants for mathematical models. The reason behind this erroneous practice is the difficulty in obtaining biaxial data. Therefore, as a remedial measure, in this research work we suggest a method of forecasting biaxial data from uniaxial data with a reasonable accuracy. Initially, a set of data is collected through standard uniaxial test. A predefined generalized function is then used to generate a set of values which subsequently used as multiplication factors in order to get biaxial tension data. Eventually, with availability of two data sets, Mooney-Rivlin two parameter model was used for combined data fitting. Material constants were then obtained through least squares approach and thereby theoretical load curves namely uniaxial, equi-biaxial tension and pure shear were drawn. The results of this work suggest a definite improvement related to three curves when compared with only uniaxial test data fitted outcomes. For validation of secondary biaxial data, separate eqi-biaxial test was done and resulting curves were compared. Biaxial primary data curve and forecasted data driven curve show identical data distribution pattern though there is a shift and therefore provide a basis for further research in this direction.

This paper modified an Armstrong–Frederick-type plasticity model for investigating the stable cyclic deformation behavior of metallic materials with different sensitivity to nonproportional loadings. In the modified model, the nonproportionality factor and nonproportional cyclic hardening coefficient coupled with the Jiang–Sehitoglu incremental plasticity model were used to estimate the stable stress–strain responses of the two materials (1045HR steel and 304 stainless steel) under various tension–torsion strain paths. A new equation was proposed to calculate the nonproportionality factor on the basis of the minimum normal strain range. Procedures to determine the minimum normal strain range were presented for general multiaxial loadings. Then, the modified model requires only the cyclic strain hardening exponent and cyclic strength coefficient to determine the material constants. It is convenient for predicting the stable stress–strain responses of materials in engineering application. Comparisons showed that the modified model can reflect the effect of nonproportional cyclic hardening well.

To capture the grading-dependence of the shear stiffness of heterogeneous granular aggregates, a new grading parameter that considered the size distribution of the entire aggregates was developed. Both the coefficient of uniformity and median particle size decreased with increasing the grading parameter. A general increase of the shear stiffness with increasing the grading parameter was observed. Comparison with experimental results revealed that the proposed grading parameter had a stronger correlation with the material constants of Hardin’s stiffness formula than the coefficient of uniformity, which is a traditional grading parameter.

Life prediction based on the damage mechanics of aero-engine turbine blades is crucial for performing their strength design and ensuring the operational reliability under combined high and low cycle fatigue (CCF) loadings. In view of this, a simple and efficient life prediction method is developed to consider the interaction of high cycle fatigue (HCF) and low cycle fatigue (LCF) without any additional material constants, and as a basis of that a new nonlinear damage accumulation model is proposed by introducing threshold damage of the component related to material type and current HCF damage. In order to validate the presented methodology, model predictions were compared with the experimental data sets of turbine blades and its alloy materials. The predicted results indicate that the simple life prediction model is capable of estimating the fatigue life quickly with an acceptable accuracy in contrast to other four existing ones. Moreover, the threshold damage-based method provides the higher prediction accuracy than others due to improved HCF damage determined by the damage threshold.

Based on the pseudo-strain method, a computational modeling technique coupling with Armstrong-Frederick type nonlinear kinematic hardening rule (Jiang-Sehitoglu model) is developed to calculate the multiaxial stress-strain responses of notched components. The pseudo-strain-true notch stress curve is determined using Neuber’s rule. The material constants in Jiang-Sehitoglu model are calculated using the Ramberg-Osgood curve. The presented method is applied to simulate the notch-tip deformations of circumferentially notched 1070 steel and S460N steel shafts subjected to various loadings, including box, circle, V-shape, zigzag-shape, and butterfly-shape loading paths. The calculated strain loops are in accord with experimental data and show reasonable accuracy.

Uncertainties originate from physical variability, data uncertainty, and modeling errors in the fatigue crack growth prediction analysis. This study presents an evidential uncertainty quantification (UQ) approach for determining uncertainties involved in revealing the material constants of the metal fatigue crack growth model with imprecise uncertainty information (i.e., epistemic uncertainty). The parameters in fatigue crack growth model are obtained by fitting the available sparse experimental data, and then the uncertainties in these parameters are considered. To alleviate the computational difficulties in the UQ analysis based on evidence theory, an interval optimization method based on differential evolution is used in finding the propagated belief structure. The overall procedure is demonstrated using the results of several replicated experiments on aluminum alloy CCT specimens.

This paper aims to predict the hardness of hot formed part for tailor rolled blank (TRB) by the FE-simulation coupled with quenching factor analysis (QFA). Dilatometry test of boron steel is performed at various range of cooling rates from 0.2 to 100°C/s using the dilatometer with forced air cooling system. The dilatometry test provides a hardness data according to cooling curves which are used to determine the material constants (K1~K5) of QFA and the time‒temperature‒property (TTP) diagram of boron steel. Then, FE‒simulation of hot press forming is conducted to predict the cooling curves of hot formed TRB part with a thickness combination of thicker 1.6mm and thinner 1.2mm which is called as rear side member of automotive component. The cooling curves of FE-simulation are applied to predict the hardness of hot formed rear side member using the QFA. Also, experiment of hot press forming is performed to verify the predicted results and to examine the effect of cooling curves on the hardness.

Purpose The purpose of this paper is to deal with an analytical investigation of delamination fracture in the mixed-mode bending (MMB) multilayer beam configurations taking into account the material non-linearity. Design/methodology/approach The J-integral approach was applied in fracture analysis. The beam layers non-linear mechanical response was described by using a power-law stress-strain relation with four material constants. Analytical solutions of the J-integral were derived by using the technical beam theory. The fracture analysis developed is valid for MMB beams whose layers may have different thicknesses. Also, the values of material constants in the non-linear stress-strain equation may be different for each layer. Findings The effect of material constants, crack location and layer thicknesses on the non-linear fracture was evaluated. The analytical solutions obtained are very suitable for parametric studies of non-linear fracture behaviour. The approach developed here can be used for optimization of multilayered beam structures with respect to the delamination fracture performance. The present study can also be useful for the understanding of fracture in multilayered beams exhibiting material non-linearity. Originality/value For the first time, an analytical study was performed of the delamination fracture behaviour of the MMB multilayered beam configuration taking into account the material non-linearity.

In this study, a calcium sulfoaluminate-based expansive additive (0%, 2.5%, 5.0%, and 7.5% by the mass of the binder) was added to compensate for the shrinkage of alkali-activated material (AAM) mortar. Modulus of elasticity curves based on the ACI 209 model were derived for the AAM mortar mixed with the additive by measuring the compressive strength and modulus of elasticity. Moreover, autogenous shrinkage and total shrinkage were measured for 150 days, and drying shrinkage was calculated by excluding autogenous shrinkage from total shrinkage. For the autogenous and drying shrinkage of AAM mortar, shrinkage curves by age were obtained by deriving material constants using the exponential function model. Finally, shrinkage stress was calculated using the modulus of elasticity of the AAM mortar and the curves obtained using the shrinkage model. The results showed that the calcium sulfoaluminate-based expansive additive had an excellent compensation effect on the drying shrinkage of AAM mortar, but the effect was observed only at early ages when the modulus of elasticity was low. From a long-term perspective, the shrinkage compensation effect was low when the modulus of elasticity was high, and thus, shrinkage stress could not be reduced.

Notched three-point-bending (3 PB) tests of small concrete samples with a fixed depth/size but various span/depth ratios can be performed in almost every laboratory. Additional usefulness is added to the flexibility of those fixed-depth 3 PB tests in this study by providing a simple closed-form solution for determination of the depth and span independent tensile strength ft and fracture toughness KIC measurable from 3 PB samples with any span-depth ratio. Material constants, ft and KIC, only existed asymptotically for large concrete structures are determined by the simple fracture mechanics model regardless the span-depth ratio. Recent results of notched 3 PB tests with 6 span-depth ratios (2, 2.5, 3, 4, 5 and 6) were analysed again by the closed-form model and compared with the effective fracture toughness in the previous study (without ft). A good agreement in KIC values was obtained. That is the two different fracture models have affirmed the usefulness of small notched 3 PB tests of a fixed depth/size but with flexible choices of the span/depth ratio. Moreover, the weight of specimens is suggested to be considered when the span/depth ratio is greater than 4.0 for 3 PB tests. Finally, fracture statistics analysis, not considered by the previous method, was included in this study, which provided the 95% reliability band besides the mean ft and KIC values.

Fractional thermoelastic models have been formulated from classical thermoelasticity or extended thermoelasticity, i.e. Lord-Shulman or Green-Naghdi theory. It seems different authors have different physical pictures on such topic, for instance, there exist several approaches from Lord-Shulman model to fractional order ones. This work is aimed to simplify the theoretical frameworks by clarifying connections between existed models. To this end, a new fractional thermoelasticity is established by directly extending classical thermoelasticity with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana–Baleanu and Tempered-Caputo definitions. All definitions are introduced into Fourier's law by a unified way with relaxation time incorporated. Theoretically, the present model may be simplified into existed fractional theory. Numerically, it has the capability of describing thermoelastic behaviors from fractional Lord-Shulman models. For numerical studies, Laplace transform method is adopted, and a two-layered structure subjected to thermal heating is considered, from which the effects of different fractional derivatives and relaxation time are firstly uncovered. And then, the influences of material constants of two layers, especially with interfacial conditions, are discussed in detail. Finally, some concluding remarks are made.

Failure mechanism criterion is proposed based on comprehensive analysis of experimental phenomenon and micro/ meso -mechanism of concrete failure. The failure mechanism criterion can successfully predict the multiaxial strength of normal-strength concrete (NSC) and high-strength concrete (HSC) in other studies. The newly proposed failure mechanism criterion is further developed to include temperature dependences and a cubic function is adopted to describe the relationship between material constants and temperature in the failure mechanism criterion. Then, the temperature dependent failure mechanism criterion is applied to predict the multiaxial strength of NSC and HSC after exposure to normal and high temperatures (NHTs). Good agreement is observed between the predicted values and experiment results from other studies. For the purpose of comparison, the mean error of the failure mechanism criterion is calculated and compared with that predicted by Seow–Swaddiwudhipong criterion, Songs criterion and He–Song criterion. The calculation indicates that the mean errors of the failure mechanism criterion, Seow–Swaddiwudhipong criterion, Songs criterion and He–Song criterion are 4.18%, 7.65%, 12.66% and 16.32%, respectively. This suggests that the failure mechanism criterion can give a more reliable prediction for engineering applications.

The present paper examines the effective macroscopic behavior of a microscopically damaged interface between an infinitely long piezoelectric layer and a piezoelectric half-space under antiplane deformation. The interface is modeled as containing a periodic array of micro-cracks. The lengths and the positions of the micro-cracks on a period interval of the interface are randomly generated. The micro-statistical model is formulated in terms of hypersingular integral equations and used to investigate in detail the influences of the material constants of the piezoelectric layer and the half-space and the width of the layer on the effective properties of the interface.

In this paper, numerical simulations are proposed to investigate mechanical properties of bi-continuous and particulate reinforced composite materials using a non-local voxel-based discrete computational model. Special focus of this article is the effect of 3D microstructure and its heterogeneity on elastic deformation and fracture behaviors. First, a review on model formulation is presented. Model parameters are derived in terms of material constants using the concept of energy equivalency. Interface representation and numerical homogenization scheme are discussed. Following this, numerical investigations on the effects of interface properties and inclusion characteristics, i.e. the volume fraction and material constants, on homogenized elastic constants and fracture behaviors of statistically isotropic bi-phase composites are performed. The effective elastic constants predicted by the proposed model agree well with analytical results. Fracture simulation demonstrates good capability of the proposed model for the microstructure-sensitive failure analysis. Conclusions and future work are drawn based on the proposed study.

This article deals with the equivalent elastic and piezoelectric constants of macro-fiber composite patches. Two types of macro-fiber composite patches, macro-fiber composite-d31 and macro-fiber composite-d33, are considered. The former one is dominated by the d31 effect, while the latter one mainly uses the d33 effect. First, based on the representative volume element technique, homogenized elastic and piezoelectric constants of those fiber-based substrate layers in macro-fiber composite patches are obtained through linear mixing rules. Second, using the obtained homogenized constants for fiber-based substrate layers, the overall elastic and piezoelectric constants of macro-fiber composite patches are obtained by modeling of multi-layer laminated macro-fiber composites based on the Reissner–Mindlin hypothesis. Finally, the homogenized overall material constants of macro-fiber composite patches are used to evaluate the structural behavior of macro-fiber composite bonded smart structures. The results calculated by homogenized constants are compared with those obtained by multi-substrate-layer modeling approach, as well as with those reported in the literature.

The thermo-mechanical fatigue (TMF) of power plant components is caused by the cyclic operation of power plant. A time-dependent plasticity model can be used to simulate the component response under cyclic thermo-mechanical loading. This paper is concerned with the modelling of thermo-mechanical behaviour of power plant steel under various loading conditions. Fully-reversed, strain-controlled tests were conducted on a parent material of P91 steel at high temperatures in order to determine material constants. A unified, Chaboche viscoplasticity model, was used to model the TMF behaviour of the steel. The multiaxial form of the Chaboche constitutive equations have been implemented in the finite element software and validated by comparing to experimental data. Simulation results have been compared with the results of anisothermal cyclic testing in order to validate the performance of the model in cyclic temperature conditions. The model’s performance under multiaxial stress conditions was investigated by testing and simulating the notched bar specimen under load-controlled conditions.

The performance of ductile fracture criteria often depends on the accuracy of material constants identification. Calibration process of three uncoupled phenomenological models was analysed. All of them contain the strain hardening exponent which is related to material plasticity as one of the fracture criteria parameter. More flexibility, better approximation of the fracture locus and more convenient shape of the fracture envelope might be reached when the strain hardening exponent is considered as another independent parameter of the fracture criteria in the identification process. Results are illustrated on the example of two structural steels, AISI 316L and AISI 1045, respectively.

This work evaluates the effectiveness of using forward creep deformation laws to predict the observed relaxation behaviour of 316H austenitic stainless steel. A summary of empirical creep methods, forward and stress relaxation experimental data were given. A primary and secondary creep strain rate (RCC-MR) model and an average creep strain rate model are combined with derived material constants to predict a group of stress relaxation tests at temperatures from 475 °C to 600 °C. The RCC-MR primary creep model predicted the stress relaxation behaviour soundly and the average creep strain rate model underestimated all of the stress relaxation data. The difference between stress relaxations predicted using strain hardening and time hardening versions of the RCC-MR equations are small. Factors affecting the predictions; including limitations in data range, data scatter, selection of a forward creep model, application of a forward model to stress relaxation and difference between forward creep and stress relaxation and are discussed. Keywords: Stress relaxation, Forward creep, Constitutive equations, 316H austenitic stainless steel

Determination of material constants describing its behavior during superplastic gas forming is the main subject of this study. The main feature of free bulging tests is the stress-strain conditions which are very similar to ones occurring in the most of gas forming processes. On the other hand, the interpretation of the results of such tests is a complicated procedure. The paper presents a simple technique for the characterization of materials superplasticity by free bulging tests, which is based on inverse analysis. The main idea of this technique is a semianalytical solution of the direct problem instead of finite element simulation which allows one to reduce the calculation time significantly. At the same time the results this simplified solution are accurate enough to obtain realistic material constants.

Low cycle fatigue tests were carried out for a 304 stainless steel at room temperature. A series of experimental characterisations, including SEM, TEM, and XRD were conducted for the 304 stainless steel to facilitate the understanding of the mechanical responses and microstructural behaviour of the material under cyclic loading including nanostructure, crystal structure and the fractured surface. The crystal plasticity finite element method (CPFEM) is a powerful tool for studying the microstructure influence on the cyclic plasticity behaviour. This method was incorporated into the commercially available software ABAQUS by coding a UMAT user subroutine. Based on the results of fatigue tests and material characterisation, the full set of material constants for the crystal plasticity model was determined. The CPFEM framework used in this paper can be used to predict the crack initiation sites based on the local accumulated plastic deformation and local plastic dissipation energy criterion, but with limitation in predicting the crack initiation caused by precipitates.

A unified viscoplastic constitutive model is proposed coupling fluid pressure rate control and damage evolution for warm medium forming (WMF), which also includes flow stress function, hardening law and dislocation density evolution. The pressure rate and damage behavior are investigated based on the experimental data of Ref. (Lang et al., 2013) [10] and the fracture morphology observations of specimens. The constitutive equations are discretized and derived through the fourth-order Runge-Kutta method. Meanwhile, the material constants of this model are determined using the Genetic Algorithm. The proposed constitutive model is applied to the WMF process of AA7075-O sheet and compared with the results of Ref. [10] . The error between calculated and experimental data is quantified using the average absolute relative error (AARE). Results indicate that the prediction accuracy of the proposed constitutive model is significantly improved compared with Ref. [10] , also, the predictions compare well with the experimental results. The new constitutive model can effectively predict the flow behavior of AA7075-O in WMF.

Analysis of thermoelastic damping (TED) of micro and nano-beam resonators plays a very important role in designing the resonator with high-quality factors. TED of micro and nano-beam resonators has therefore been an interesting and challenging area of research in recent years. Prediction of TED is more challenging under the effect of non-Fourier heat conduction. In the past, several works have been dedicated to TED modeling with the influence of non-Fourier heat conduction in view of the fact that non-Fourier heat conduction model is more relevant for analysis of TED for small scale devices. The present work aims to investigate TED in micro and nano-mechanical resonators utilizing non-Fourier heat conduction model with a single delay term introduced by Quintanilla in 2011. We derive an explicit formula of the quality factor for TED based on the entropy generation approach. With the help of numerical results, we present the influence of TED in the context of normalized frequency as well as beam thickness. Further, the effects of the time delay parameter and the material constants on TED have been discussed in detail. The results of the present model are compared to those obtained for GN-III model. It has been observed that the current model offers a high-quality factor as compared to GN-III model.

The ground penetrating radar (GPR) method has increasingly been applied in the non-destructive testing of reinforced concrete structures. The most common approach to the modelling of radar waves is to consider concrete as a homogeneous material. This paper proposes a novel, heterogeneous, numerical model of concrete for exhaustive interpretation of GPR data. An algorithm for determining the substitute values of the material constants of concrete is developed, based on the modified complex refractive index method. Experimental surveys and numerical simulations are conducted on a concrete laboratory sample with a controlled degree of saturation, and on a real concrete slab with two different degrees of saturation. The results indicate that the proposed model is fully capable of realistic finite-difference time-domain modelling of concrete for ground penetrating radar diagnostics of civil engineering structures with changing water content.

The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean-field homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori–Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed, which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are studied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.

We analyse the circular Couette flow of Herschel–Bulkley fluids to investigate the validity of the assumption that the rate of strain distributions across the gap share a common point. It is demonstrated that this is true only with fully-yielded Bingham -plastic flow. In other cases, e.g., in partially-yielded Bingham-plastic flow or fully-yielded Herschel–Bulkley flow, the common point for the fully-yielded Bingham case provides a good approximation for determining material constants only if the gap is sufficiently small. We also revisit the important issue of determining material properties of viscoplastic fluids by using “true values” for the rate of strain and demonstrate that the material properties can be very different from those obtained using “apparent’ values for the rate of strain. 260 101 108

The paper presents a fatigue damage accumulation model, which allows us to predict fatigue life under low cycle uniaxial loadings at elevated temperatures. The structure of the model has been based on the stress–strain curves obtained during the experimental study. The model has been verified experimentally by applying experimental studies carried out on ENAW-2024T3 aluminum alloy and 2Cr–2WVTa steel. Moreover, a comparison between the results of fatigue life prediction using the proposed damage accumulation model was done with the results obtained on the basis of various generally applied models, based on the Manson–Coffin dependency. Furthermore this paper presents the results of experimental studies carried out on the aluminum alloy ENAW 2024 T3 under uniaxial low cycle fatigue loadings in the conditions of elevated temperatures. In the course of the study, material constants and the parameters of the stress–strain curve in the range of low cycle fatigue for four levels of temperatures (20, 100, 200 and 300 °C) were set.

The governing equations of rotating thermoelastic solids with diffusion are solved in context of the Green–Naghdi theory (Type II) to show the numerical existence of four coupled plane waves. The required boundary conditions at the stress free and thermally insulated surface of the model are satisfied to obtain the reflection coefficients of various reflected waves for an incident plane wave. These coefficients are found to depend on rotation parameter, the angle of incidence of striking waves, thermo-diffusion parameters, and other material constants. Complex absolute values of speeds and reflection coefficients are computed for a particular material representing the model. Graphical representation of numerical results show the effects of rotation and diffusion on speed and reflection coefficients of plane waves.

In order to predict the creep life of a component at high temperature both accurately and economically, continuum damage mechanics approach is used based on experimental creep data. However, material constants used in the models have a great relationship with the performed stress range of creep tests. In this paper, several sets of material constants were obtained from a wide range of stresses on P91 steel. The creep damage tolerance parameter was used to classify these sets, and the modified continuum damage mechanics model was used to investigate a pipe under closed-end condition. Results have illustrated the main difference lies on the tertiary stage while slight difference on the primary and secondary stages, and the contribution of the tertiary stage to the total damage decreased when using material constants from higher stress region.

In the present work, the effective material properties of thermoelectric composites with elliptical fibers are studied. Explicit solutions are derived by the conformal mapping function and Mori–Tanaka method. Numerical simulations are performed to present the behaviors of normalized effective material constants. From the results, it can be observed that both the effective electric and thermal conductivities can be reduced by increasing the filling ratio and a/b. Such influences can also be found for the effective thermoelectric figure of merit. But they are different from those on the effective Seebeck and Peltier coefficients.

Sheet metal stamping is an important manufacturing process because of its high production rate and low cost, so the fracture prediction of stamping parts has become important issues. Recent experimental studies have shown that the quality of stamping parts can be increased by using ductile fracture criteria. This paper proposed a modified ductile fracture criterion based on the macroscopic and microscopic continuum damage mechanics (CDM). Three-dimensional (3D) explicit finite element analysis (FEA) are performed to predict the fracture behaviors of sheet metal stamping process. An approach to determine the material constants of modified ductile fracture criterion is presented with the help of uniaxial tensile tests and compressive tests. The results show that the modified ductile fracture criterion enables precise cup depth and fracture location of sheet metal stamping under nonlinear paths. Compared with typical ductile fracture criteria, the results predicted with modified ductile fracture criterion correlate the best with the experimental data.

In present paper, 3D finite element (FE) method is used to determine plastic limit load solutions for pipe bends under combined bending and torsion moment. With a detailed analysis and comparison, a common awareness for loading effect is showing which will raise researchers concern. By the way, past solutions are not appropriate to estimate FE results. In this respect of finite element analysis, overall yielding considering the spread process of yield region from crown to the straight pipe shows these promising finite element results. A wide range of non-dimensional parameters for pipe bends are considered and plastic limit load solutions are suggested. The results show that r/t is the main factor affecting the limit loads. Plastic limit load is independent on the loading path and material constants by normalizing. Results show that the circular interaction rule is a great approximation for pipe bends under combined bending and torsion moment. A series of approaches are confirmed in order to validate our finite element method on plastic limit analysis. Based on the finite element results, approximate plastic limit load solutions are proposed. Present work will further improve the limit load solution for pipe bends under complex loading conditions.