Strain Energy Density Model Research Articles

An equivalent strain energy density model for fatigue life prediction under large compressive mean stress

In this work, a modified Smith-Watson-Topper (SWT) model is proposed for the consideration of large compressive and tensile mean stresses. Firstly, the maximum normal stress in the original SWT model is replaced with equivalent stress amplitude, and the SWT parameter is thereafter interpreted as equivalent strain energy density (ESED). The newly proposed ESED model gives improved prediction results in fatigue life, especially under conditions with large compressive mean stress. Secondly, the applications of different mean stress correction (MSC) models are investigated with their limitations carefully examined. In order to improve the ESED model with higher accuracy, a new exponential MSC model is proposed. Moreover, an additional parameter concerning the dependency of material on mean stress is proposed. With the exponential MSC model incorporated, the ESED model is validated with experimental data from several different materials, and shows obviously improved prediction results compared with SWT model and some recent life prediction models.

Highly nonlinear hyperelastic shells: Statics and dynamics

Investigated in this paper are comprehensive static, dynamic and internal-resonance analyses on a wide range of hyperelastic shell structures, including cylindrical, spherical, doubly-curved, and hyperbolic hyperelastic shallow shells. Donnell's nonlinear shell theory and the Mooney-Rivlin strain energy density model are used to formulate the hyperelastic shell structure. Coupled equations of motion are obtained using Hamilton's principle with highly nonlinear terms due to the curvature in the structure, together with the material nonlinearity and large deformations. The coupled equations of motion are converted to a large set of equations using a two-dimensional Galerkin technique and are solved by employing the Newton-Raphson approach and dynamic equilibrium technique. The strength of the current methodology and model is first verified by comparing the static response of the structure with those obtained by using a finite element software. After verifying the model, a detailed analysis of the bending behaviour of the structure under a time-independent pressure is presented. Moreover, the free and forced vibration responses of the shell structure are presented for different cases, showing that the curvature terms play a significant role in changing the mechanical response of the hyperelastic shell. Furthermore, it is shown that for specific sets of curvatures, internal resonances are present which leads to a complicated, rich nonlinear responses. The nonlinear forced vibration response of the hyperelastic shell is also presented for different shell types and resonances.

Theory and experiment for dynamics of hyperelastic plates with modal interactions

This paper presents a joint experimental and theoretical approach to the dynamics and mass sensitivity of hyperelastic plates including cases with modal interactions. For the theoretical approach, the plate structure is assumed to undergo large strains and deformations using the Mooney-Rivlin hyperelastic strain energy density model and the von-Kármán geometric nonlinearity, respectively. The plate is modelled using the continuum mechanics definitions and the Kirchhoff–Love plate theory. The coupled in-plane and out-of-plane equations of motion are obtained using Hamilton's equation and solved afterwards using a combination of Galerkin's procedure together with a dynamic equilibrium technique. For the experimental analysis, the properties of the material are first obtained by performing a set of stress-strain tests on the samples following the ASTM D-412 standard, and then from the same rubber material, a plate structure is fabricated, and an externally actuated vibration test is performed. The nonlinear frequency response of the structure both with and without a concentrated mass is investigated and the capability of the structure for mass sensing is discussed. By obtaining the amplitude-frequency response of the structure due to the applied external periodic load, using both theoretical and experimental approaches, it is shown that the given model has good accuracy in simulating the nonlinear dynamics of the hyperelastic plate structure under different conditions. Furthermore, a set of analyses on the nonlinear forced vibration behaviour of hyperelastic plates at different internal resonances, using concentrated mass and the length-to-width ratio is presented. The results of this study are useful in designing systems involving hyperelastic plates, such as soft robots and soft functional devices.

INVESTIGATION OF THE PERFORMANCE OF RC BEAMS REINFORCED WITH FRP AND ECC MATERIALS

This paper investigates the structural working behavior of reinforced concrete beams bonded with fiber reinforced polymer and engineered cementitious composite materials subjected to bending using structural stressing state theory. First, six reinforced concrete beams externally bonded with composite reinforcement layer and one control beam are tested to investigate the effects of the bond length, fiber reinforced polymer grid thickness and fiber content on the flexural behavior. Then, the finite strain data of RC beams are interpolated by the numerical shape function method. The generalized strain energy density model is established to characterize the stressing state of the structure. Through the MannKendall criterion, the characteristics load P and Q of the beams are detected, and the whole loading process is divided into three stage. Finally, the analysis of the strain and deformation on the beams reveals the effect of different parameters on different stage. The characteristic load P increases as the bond length increases, and the characteristic load Q increases as the thickness of the FRP and the fiber content increase. The vertical deformation of the strengthened beam for the characteristic load Q and ultimate load is significantly smaller than that of the unreinforced beam.

Studies of High-Temperature Fatigue Behavior and Mechanism for Nickel-Based Superalloy Inconel 625

Strain-controlled continuous fatigue and creep–fatigue tests were carried out at 700 °C and 800 °C on Inconel 625 alloy. The effects of strain rate and tensile-hold time on cyclic stress response and fatigue life were investigated. Then, the microstructural analysis and the fractographic analysis of fatigue-fractured specimens were performed by scanning electron microscopy and transmission electron microscopy. The cyclic stress responses during high-temperature fatigue and the creep–fatigue–oxidation damage mechanism were discussed. The results showed that the strain rate and the tensile-hold time had little effect on the fatigue life at 700 °C, but there was a significant impact at 800 °C due to the creep–fatigue–oxidation interaction. The cyclic plastic deformation accelerated the precipitation of the γ″ phase, resulting in a continuous cyclic hardening and negative strain rate sensitivity. The fatigue failures at 700 °C under continuous fatigue conditions occurred with a transgranular fracture mode, while a transgranular-intergranular hybrid fracture manner was found at 800 °C. Furthermore, a frequency-modified total strain energy density model was proposed to consider the effects of creep and oxidation on fatigue life, and the predicted fatigue lives were located within the 1.5 times error band.

Probabilistic fatigue framework of notched specimens based on modified strain energy density model under multiaxial loadings

Notch features often raise critical effects on fatigue lives of engineering components, which deserve particular attention for assessing their structural integrity and reliability. In this study, through modifying the strain energy density model, a probabilistic framework for assessing the fatigue life of notched specimens is established under multiaxial loadings. Firstly, the strain energy density is calculated by the finite element method on an arbitrarily material plane is investigated. Secondly, a modified energy-based model is proposed by incorporating the notch effect and size effect, the non-proportional hardening and the stress concentration factors. Finally, combining the modified strain energy density model with the Weibull distribution as well as the theory of critical distance, a new probabilistic fatigue framework is developed to estimate the fatigue life of notched specimens under different survival probabilities. Experimental data of TC4 alloy, Al7050-T7451, GH4196 alloy and medium steel En8 notched specimens are employed to validate the proposed model and other six energy-based models (MSWT model, CXH model, CCB model, VF model, Liu model). The comparison results exhibit that the proposed model yields a higher accuracy than six other models within the ±2 life factor. Meanwhile, novel Pf-W-Nf curves of multiaxial notched specimens with different survival probabilities are presented and analyzed.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10–20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Fatigue behavior of Ti6Al4V alloy components manufactured by selective laser melting subjected to hot isostatic pressing and residual stress relief

AbstractFatigue behavior (Rε = −1) of HIPed and stress relieved Ti6Al4V alloy specimens produced by selective laser melting (SLM) was analyzed and compared resulting that the hot isostatic pressing (HIP) process caused a microstructural transformation decreasing the hardness and monotonic properties leading to cyclic softening that not allowed fatigue strength to increase. A bilinear behavior in the elastic strain–fatigue life curve was observed due to the decrease of the Young's modulus during the cyclic elastoplastic tests, consequence of subgrains formation. The Smith–Watson–Topper and total strain energy density models adjusted by the bilinear behavior showed a good concordance between predicted and experimental fatigue lives in notched samples.

Predicting ductile fracture of cracked pipes using small punch test data

This paper proposes a numerical method to simulate ductile fracture of a cracked pipe using small punch test data. The method is using FE damage analysis method based on the multi-axial fracture strain energy density model. The parameters in the damage model can be extracted solely from small punch test data, using which compact tension and circumferential through-wall cracked pipe tests are simulated. To validate the proposed method, simulation results are compared with TP316L experimental data. For the compact tension test, faster crack growth is predicted but for the pipe test, good agreement is obtained. The effect of the stress triaxiality on the prediction accuracy is discussed.

Izboljšan model za napoved gostote deformacijske energije glede na vpliv glavne napetosti

Izboljšan model za napoved gostote deformacijske energije glede na vpliv glavne napetosti

Modeling the initial-volume dependent approximate compressibility of porcine liver tissues using a novel volumetric strain energy model

Experimental observations in the open literature indicate that soft tissues are slightly compressible, and this characteristic affects not only their overall elastic response but also their damage evolution and failure mechanism. In this study, we find that the compressibility of liver tissues is also closely related to the initial specimen volume according to the confined compression tests: the samples with smaller initial volume exhibit more compressible behavior compared to the larger ones. To include this initial-volume dependent effect, we developed a novel volumetric strain energy model with two variables, i.e., the bulk modulus and the compressibility factor. A detailed scheme was proposed as well to identify these two parameters, and the relationship between the bulk modulus and the initial volume was clarified. Findings from this study will help to deepen the understanding of the biomechanical properties of soft tissues. Statement of significanceLiver is a highly vascular organ and traditionally assumed to be an incompressible medium. However, through the confined compression tests, we found that the samples with smaller initial volumes exhibit more compressible behavior. Hence, we developed a novel strain energy density model to characterize the initial-volume dependent hyperelastic response, and found that the bulk modulus of liver tissues is positively related to the initial volume. Our results suggest that the compressibility of liver tissues should be considered in the future study of liver biomechanics.

A Virtual-Strain-Energy-Density-Based Critical-Plane Criterion to Multiaxial Fatigue Life Prediction

The Smith–Watson–Topper (SWT) fatigue damage parameter has been discussed based on the critical-plane concept. It was found that the fatigue life prediction obtained by the SWT model tended to be unconservative during the non-proportional loading as only the tensile components on the plane of maximum principal strain range has been considered. To overcome this shortcoming, a virtual strain energy density model has been proposed using the von-Mises criterion, where the shear component on the plane of maximum principal strain range can be included during the non-proportional loading conditions. However, on the other hand, this model will be equivalent to the SWT model under the uniaxial and/or proportional loading conditions.

Assessment of creep damage models in the prediction of high-temperature creep behaviour of Alloy 617

This study aims to predict the creep response of Alloy 617 and assess the accuracy of three established creep damage models in predicting the creep time-to-failure (tf) and strain-to-failure (εf) in the temperature range of 800–1000 °C. Idaho National Laboratory (INL) creep data were used to calibrate (1) Ductility Exhaustion (DE), (2) Stress-Modified Ductility Exhaustion (SMDE), and (3) Strain-Energy Density (SED) creep damage models using multiple linear regression (LR) and reverse damage (RD) approaches. In order to predict the creep response of Alloy 617 these creep damage models are then coupled with (secondary) creep strain model calibrated using Idaho National Laboratory (INL), Korean Atomic Energy Research Institute (KAERI), and Argonne National Laboratory (ANL) experimental data. Direct comparisons made between the investigated creep damage models revealed that the SED model with parameters calibrated through RD approach captures the creep response of Alloy 617 the most accurately and it thus produces the most accurate prediction of time-to-failure (tf) and strain-to-failure (εf) across different temperature/stress (creep) conditions. However, it is also shown that none of the employed creep damage models are able to fully capture the material creep response at 1000 °C. This is attributed the strong oxidation of Alloy 617 at 1000 °C (tested in air) leading to the formation of a thick oxidation layer, which might affect the failure mechanism of the alloy at this temperature.

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

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

Overview Study of Solder Joint Reliablity due to Creep Deformation

AbstractThe effective lifetimes of electronic packages are affected by various thermos-mechanical deformations. Creep is considered the most salient mechanism in the failure of solder joints. Many researchers have conducted reasonable studies to portray the behavior of creep deformation using numerical models and further extended their research scope to forecast the lifetimes of packages with the results obtained from creep models. Many studies have identified particular creep and lifetime models to be nominal based on experimental data.In this study, the characteristics of familiar creep models were examined in detail, and their significance was made known. Lifetime prediction models that seem prominent among researchers were discussed in detail. Finite element analysis of a wafer level chip-scale package (WLCSP) used to figure out the engagement of different creep models and their capability of materializing creep deformation was investigated via simulation. The results from the simulation were applied to different lifetime prediction models, and their predictions were examined carefully. After considering the various factors that affected the reliability study of the solders, the Garofalo-Arrhenius creep model and modified strain energy density model seemed to be convincingly productive for studying the reliability of various electronic packages.

Fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model

Fatigue crack growth (FCG) rates have traditionally been formulated from fracture mechanics, whereas fatigue crack initiation has been empirically described using stress-life or strain-life methods. More recently, there has been efforts towards the use of the local stress-strain and similitude concepts to formulate fatigue crack growth rates. A new model has been developed which derives stress-life, strain-life and fatigue crack growth rates from strain energy density concepts. This new model has the advantage to predict an intrinsic stress ratio effect of the form ?ar=(?amp)?·(?max )(1-?), which is dependent on the cyclic stress-strain behaviour of the material. This new fatigue crack propagation model was proposed by Huffman based on Walkerlike strain-life relation. This model is applied to FCG data available for the P355NL1 pressure vessel steel. A comparison of the experimental results and the Huffman crack propagation model is made.

Fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model

Fatigue crack growth (FCG) rates have traditionally been formulated from fracture mechanics, whereas fatigue crack initiation has been empirically described using stress-life or strain-life methods. More recently, there has been efforts towards the use of the local stress-strain and similitude concepts to formulate fatigue crack growth rates. A new model has been developed which derives stress-life, strain-life and fatigue crack growth rates from strain energy density concepts. This new model has the advantage to predict an intrinsic stress ratio effect of the form ?ar=(?amp)?·(?max )(1-?), which is dependent on the cyclic stress-strain behaviour of the material. This new fatigue crack propagation model was proposed by Huffman based on Walkerlike strain-life relation. This model is applied to FCG data available for the P355NL1 pressure vessel steel. A comparison of the experimental results and the Huffman crack propagation model is made.

Thermally-induced failures of copper through-silicon via structures evaluated by the strain energy density model

Based on the current density (CD) experimental results reported in a literature for the copper through-silicon vias (TSVs) arising in the Cu/Ti/SiO2/Si wafer structure, the CD solutions were obtained through simulations in the ANSYS/LS-DYNA software linked with the “Johnson-Cook (J-C) Constitutive Model” module in this study. The numerical schemes are developed to obtain the following contents: (1) the determinations of the unknown coefficients in the J-C model by conducting the microtensile tests for per each component of the TSV structure; (2) the earliest element failure caused by the thermal strain/stress; (3) the critical stress and time at potential failure location modeled by the J-C model; and (4) the evaluations of strain energy density (Wfailure) required for element failures in the components and the effect of heat generation rate in per unit volume of Cu film on element failure. The numerical solutions predicted by the present models are confirmed to be very close to the reported experimental results, and thus validate the present predictions for temperature and time and the sequence of elements with the earliest failure in their component. The strain energy density (Wfailure) required to start the failure of an element is found to be dependent upon the TSV component material only, and is independent of the element's location in the same component. The heat generation in the Cu film is of importance to the order of the TSV components reaching its Wfailure, the time to have Wfailure increases along with the distance of the TSV component from the lateral surface of the Cu film. The smaller the distance is, the earlier the time that the Wfailure of an element is reached. An appropriate combination of a Ti film with a large thickness and SiO2 film with a small thickness can reduce the maximum effective stress (σmax) and provide an efficient barrier for copper diffusion into the Si wafer substrate. This study can provide an efficient method for the design and failure protection of TSV structures.

Modeling of Swine Diaphragmatic Tissue Under Uniaxial Loading1

Modeling of Swine Diaphragmatic Tissue Under Uniaxial Loading1

On the behavior of rotating thick-walled cylinders made of hyperelastic materials

This paper focuses on the behavior of rotating thick-walled cylinders made of the rubber-like materials. These materials are characterized by high deformability which their stress-stretch curves are arranged in the range of S-shaped to J-shaped forms. Here, it is considered an Ogden-type model with only integer powers to give a satisfactory correspondence with experimental results over wide ranges of different types of deformation. This type of constitutive model is mathematically simple and can provide the foundation of existence of a closed-form solution for the boundary value problems in the finite deformation elasticity. In this study, as an application, the Ogden-type strain energy density with only integer powers is applied to a rotating thick-walled cylinder made of the hyperelastic materials. It is shown that this constitutive model gives a closed-form solution, not involving the integral form, for the stress distribution through the wall thickness. Also, the results predicted from classic strain energy density models (Mooney-Rivlin, Neo-Hookean and Varga) and the Ogden-type model are compared for (i) a solid circular cylinder under rotation, (ii) a rotating circular cylinder with a concentric circular rigid inclusion, (iii) a rotating cylinder shrink-fitted to a rigid spindle and (iv) an unconstrained cylinder under rotation. These comparisons are done in order to investigate the accuracy of the simplification carried out by applying the well-known classic models instead of the Ogden-type model. It is concluded that this simplification is allowable if the classic models can follow the test data to some acceptable extent. While, the classic models are not capable to analyze an unconstrained rotating cylinder when experiences large deformations. Finally, influence of different parameters such as wall thickness, presence of the axial pre-stretch and form of mechanical behavior or strain-stiffening behavior of the rubber utilized in cylinders examined on stability of an unconstrained rotating cylinder.