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Abstract The tight gas sandstone reservoirs in the Paleozoic of the Sulige gas field in China are highly heterogeneous, and fractures are key factors for stable reservoir production. Low-amplitude folds or nose-like structures are widely developed in the Upper Paleozoic strata in this area. To effectively predict gas well productivity, in this paper, a 3D FEM numerical simulation based on the deformation and energy variation of the rock mass was used to predict the "sweet spots" of gas well productivity in a tight gas sandstone reservoir using the He8 segment of the Middle Permian Xiashihezi Formation in the Central Sulige block as an example. The paleotectonic stress field of the study area during the maximum episode of compression in the Yanshanian movement was restored, and the two rupture parameters of the integrated rupture rate (I F) and strain energy density (U) were constructed. The strain energy density distribution has a high correlation with gas well productivity, indicating that it can better predict the rock rupture degree in low-amplitude tectonic zones. A complex relationship exists between the strain energy density distribution and low-amplitude folds. The high strain energy density zones are mainly distributed among the high positions and wing areas of the low-amplitude fold zone, but the top area of the low-amplitude fold does not necessarily have a high strain energy density. Portions of the high strain energy density zones are located in the gentle tectonic zone, located near but outside the low-amplitude fold zone. The strain energy in these gentle tectonic zones with a high strain energy density value is relatively high, and the rock mass is prone to rupture. This study is of great value in enriching the prediction of "sweet spots" in tight gas sandstone reservoirs in low-amplitude tectonic zones worldwide. Highlights • Strain energy density distribution in low-amplitude tectonic zone. • 3D FEM simulation study. • Effect of strain energy distribution on gas well productivity. [ABSTRACT FROM AUTHOR]

In this paper, the material nonlinearity is introduced in the dynamic modeling of fiber-reinforced composite thin plates, and a new nonlinear vibration model of such composite plate structures with amplitude-dependent property is established with the consideration of the nonlinear stiffness and damping characteristics, which is observed and confirmed in the nonlinear vibration characterization experiment. In this new model, the elastic moduli and loss factors are expressed as the function of strain energy density on the basis of Jones-Nelson material nonlinear model. By using the identified parameters under different excitation amplitudes, these elastic moduli and loss factors are characterized as the function of the maximum dimensionless strain energy density. Then, the power function fitting technique is used to determine the nonlinear stiffness and damping parameters in the model, and the nonlinear natural frequencies, vibration responses and damping ratios of a TC300 carbon/epoxy composite thin plate are calculated and measured in a case study. The comparisons between the theoretical and experimental results show that the maximum calculation error of natural frequencies with consideration of amplitude-dependent property is less than 4.3%, and the maximum calculation errors of resonant response and damping results are no more than 12.5 and 9.6% in the 3rd mode and the 6th mode, respectively. Therefore, the practicability and reliability of the proposed model have been verified. [ABSTRACT FROM AUTHOR]

The light weight of magnesium alloys makes them a promising material in different potential industries, such as aerospace and automobile. In addition, magnesium alloys are attractive materials for biomedical applications due to their biocompatibility with the human body. The applications of these alloys in structural parts require an understanding of their fatigue behavior because they are usually subjected to time-varying loading. Furthermore, notches are inevitable in structural parts. Geometrical discontinuities weaken structures because they act as stress raisers. Localized cyclic plasticity around notches leads to crack formation and final failure. The main objective of this research was to investigate the fatigue failure of ZK60-T5 extrusion in the presence of a notch. U-notched specimens with a diameter of 16 mm, notch radius of 1.5 mm, and notch depth of 1.5 mm were machined along the extrusion direction. Cyclic tests were performed under completely reversed cyclic loading and ambient conditions. The results obtained from the cyclic tests of the U-notched specimens were compared with those of unnotched and V-notched specimens to assess the effects of both the presence and the geometry of a notch on fatigue life. The strain energy density approach was successfully used to analyze the fatigue behavior of the U-notch specimens.

As a newly developed gun barrel steel, the novel steel has shown excellent high-temperature strength, high resistance to wear and erosion, contributing to the superior ballistic life of gun barrels. As ballistic life increases, the fatigue life becomes essential for the safety and reliability of gun barrels. This paper presents a comparison of the low cycle fatigue (LCF) behaviors between a novel steel and 30SiMn2MoV steel at 700 °C. A strain-controlled fatigue test was carried out on the novel steel and 30SiMn2MoV steel in the strain range from 0.2 to 0.6%. The cyclic stress response behaviors of the novel steel and 30SiMn2MoV steel show cyclic softening behavior. In addition, the shape of the hysteresis rings of the novel steel and 30SiMn2MoV steel exhibit no-Masing model behavior. Energy–life relationships results show that the novel steel has higher fatigue resistance than the 30SiMn2MoV steel at 700 °C. The results of fatigue fracture analysis show that the failure mode of the 30SiMn2MoV steel is a mixed mode of intergranular fracture and transgranular fracture, while the failure mode of the novel steel is intergranular fracture. The cyclic softening of the two materials can be attributed to the lath structure with a high density of dislocations gradually transforms into low energy subcrystalline and cellular structures at 700 °C. The novel steel has a better fatigue life than the 30SiMn2MoV steel at 700 °C and different strain amplitudes, which is mainly related to the carbides and lath martensite in the materials.

The strain energy released plays a crucial role in generating macroscopic failure in unidirectional (UD) composites. This paper proposes two new strain energy-based failure criteria, regarding fiber-dominated and matrix-dominated failure mode as independent and interactive, respectively. The failure expression is formulated based on rigorous mathematical deducing, accompanied by physical interpretation. Based on the lack of experimentally feasible multi-axial strengths, a predefined assumption of infinite strength under bi-axial and tri-axial compressive stress provides the possibility for determining all coefficients only by using conventional uniaxial strengths. The failure envelopes predicted by the proposed criteria have been validated against experimental results under biaxial, off-axis and tri-axial loading cases. A better agreement with physical reality was achieved by the failure mode-interactive criterion, suggesting a wide range of applicability.

Carbide-free bainitic steels are an example of high-strength steels that show an excellent combination of strength, ductility, toughness and rolling fatigue contact resistance and are progressively being introduced in the production of railways, crossings and automotive components. Although there are Mn-free approaches able to produce carbide-free bainitic steels, those based on the addition of Mn are less expensive. Therefore, it is important to fully understand the mechanical behavior of such materials to develop reliable engineering products. In this paper, three low-carbon bainitic steels, differing in Mn content, namely 0%, 2.3% and 3.2%, designated as steel A, B and C, respectively, were studied in a systematic manner. Low-cycle fatigue tests were conducted under symmetrical strain-controlled conditions for different strain amplitudes (0.6%, 0.7%, 0.8% and 1%). Independent of Mn content, a strong relationship between cumulative strain energy density and number of cycles to failure was found. Based on this relationship, a new predictive model, capable of estimating the fatigue lifetime, was developed. Predictions based on the new model were close to the experimental lives and were more accurate than those computed via the well-known Smith-Watson-Topper (SWT) and Liu criteria.

The exploitation of deep resources is necessary for human development. At the same time, high-stress environments that are deep underground bring about great challenges vis-à-vis resource exploitation. A large deep opening is sensitive to high ground stress, and is easily influenced by external interference, which can lead to geologically hazardous occurrences. To investigate the evolution of fracturing and energy in large, deep stopes subjected to dynamic loads, we established a numerical model of a stope in the Gaofeng mine. Using ANSYS/LS-DYNA software, we implemented an implicit solution to initial static stress and an explicit solution for dynamic analysis. Based on our numerical results, we obtained the fracture behavior and energy evolution under coupled static and dynamic loads. To determine the response of ground pressure to mining activity, a 24-channel microseismic monitoring system was designed for the Gaofeng mine based on the numerical analysis.

• A new criterion (RSED) is proposed to predict mixed-mode crack initiation in ductile materials. • The direction and critical loading predicted by the RSED criterion are not affected by the size and shape of the core region. • The predictions by the RSED show a superior consistency for the experimental results in ductile materials over the classical criteria. • The crack initiation directions predicted by the RSED, T, and MST criteria is theoretically demonstrated to be identical, and the corresponding mechanical mechanism by this coincidence is also illustrated. In consideration of the different mechanisms of microscopic separation governed by dilation and microscopic shearing controlled by distortion on crack initiation, a new criterion based on the ratio of two strain energy densities (RSED) is proposed by differentiating the dilatational and distortional parts in strain energy density. The influence of the weights of two strain energy densities under different stress states on fracture resistance of crack initiation is also considered in the RSED criterion. The size and shape of the core region do not affect the direction and fracture resistance of crack initiation predicted by the RSED criterion. Moreover, the direction predicted by the RSED criterion is theoretically demonstrated to be identical to the orientations predicted by the maximum stress triaxiality (MST) criterion and the T criterion on crack initiation. The crack initiation directions which are obtained by the experiments for different materials and predicted by various criteria are found to be mostly coincident near the mode-I crack, and so are the fracture resistances. In the vicinity of the mode-II crack, the direction of crack initiation predicted by the RSED criterion shows a superior consistency for the experimental results of the ductile materials reported by Theocaris et al. (1982) and Kong et al. (1995) over the three classical criteria, such as the maximum tangential stress (MTS), the maximum energy release rate (MERR) and minimum strain energy density (MSED). The RSED criterion also has the potential to amend the issue of the underestimation for K IIC / K IC in some typical materials, e.g., the face-centered-cubic (f.c.c) metals. Therefore, the RSED criterion prefers to predict the direction and fracture resistance of crack initiation in ductile materials. [ABSTRACT FROM AUTHOR]

[Display omitted] • Multiaxial synchronous fatigue tests carried out on three different ductile cast iron grades. • Multiaxial fatigue criterion based on the volumetric strain energy density. • The mean stress effect is accounted by a combination of the stress amplitude and the maximum stress. • Formulation of the phase effect for ductile cast irons by means of a phase correction factor. • Accurate predictions with an RMS error at 5 million cycles of 11.0 %. A new criterion for predicting multiaxial fatigue in plain and V-notched specimens made of ductile cast iron is proposed. The criterion is based on volumetric strain energy density (SED) and separately accounts for the effect of normal and shear mean stresses with two material-dependent coefficients. The criterion also considers the impact of out-of-phase loading through a strengthening factor, assuming that fatigue damage is initiated by the total SED peak in the cycle. The criterion is validated using a large amount of independent multiaxial fatigue data, obtained from testing three different ductile cast iron grades. [ABSTRACT FROM AUTHOR]

• A new life prediction model based on the strain energy reformulated critical distance theory is proposed. • Experimental data of 4 materials verified the model predictions accuracy. • The influence of size effect on critical distance and fatigue life is quantified. Notch and size effects show significant impact on the fatigue performance of engineering components, which deserves special attention. In this work, strain energy reformulated critical distance theory was developed for fatigue life prediction of notched components under size effect. Experimental data of different notched specimens manufactured from GH4169, TC4, TC11 alloys and low carbon steel En3B were used for model validation and comparison. Results indicate the proposed model works better than the Yang's and the Shen's models. [ABSTRACT FROM AUTHOR]

Improvement of cell migration by the nano-topographical modification of implant surface can directly or indirectly accelerate wound healing and osseointegration between bone and implant. Therefore, modification of the implant surface was done with TiO 2 nanorod (NR) arrays to develop a more osseointegration-friendly implant in this study. Modulating the migration of a cell, adhered to a scaffold, by the variations of NR diameter, density and tip diameter in vitro is the primary objective of the study. The fluid structure interaction method was used, followed by the submodelling technique in this multiscale analysis. After completing a simulation over a global model, fluid structure interaction data was applied to the sub-scaffold finite element model to predict the mechanical response over cells at the cell-substrate interface. Special focus was given to strain energy density at the cell interface as a response parameter due to its direct correlation with the migration of an adherent cell. The results showed a huge rise in strain energy density after the addition of NRs on the scaffold surface. It also highlighted that variation in NR density plays a more effective role than the variation in NR diameter to control cell migration over a substrate. However, the effect of NR diameter becomes insignificant when the NR tip was considered. The findings of this study could be used to determine the best nanostructure parameters for better osseointegration. [Display omitted] • The surface of a Ti 6 Al 4 V scaffold was modified with TiO 2 nanorods (NRs). • The effect on cell migration due to different NRs features was evaluated through multiscale modelling. • Strain energy density was considered as a response parameter for cell migration. • The presence of NRs on the scaffold surface significantly enhances cell migration. • The influence of NR density on cell migration is more than NR diameter. [ABSTRACT FROM AUTHOR]

Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. In this paper, three different crack growth criteria and the respective crack paths prediction in the cement mantle of the reconstructed acetabulum are compared. The maximum tangential stress (MTS) criterion, the minimum strain energy density (MSED) criterion and the new general fracture criterion based on the energy release rate G(θ) are investigated using advanced finite element technique. The displacement extrapolation technique (DET) is used, to obtain the SIFs at crack tip. Several examples are presented to show the robustness of the numerical techniques. The effect of the inclusions and cavities on the crack propagation in cement orthopedic are highlighted.

The present paper investigates the multiaxial fatigue strength of sharp V-notched components made of titanium grade 5 alloy (Ti-6Al-4V). Axisymmetric notched specimens have been tested under combined tension and torsion fatigue loadings, both proportional and non-proportional, taking into account different nominal load ratios (R = -1 and 0). All tested samples have a notch root radius about equal to 0.1 mm, a notch depth of 6 mm and an opening angle of 90 degrees. The fatigue results obtained by applying multiaxial loadings are discussed together with those related to pure tension and pure torsion experimental fatigue tests, carried out on both smooth and notched specimens at load ratios R ranging between -3 and 0.5. Altogether, more than 250 fatigue results (19 S-N curves) are examined, first on the basis of nominal stress amplitudes referred to the net area and secondly by means of the strain energy density averaged over a control volume embracing the V-notch tip. The effect of the loading mode on the control volume size has been analysed, highlighting a wide difference in the notch sensitivity of the considered material under tension and torsion loadings. Accordingly, the control radius of the considered titanium alloy (Ti-6Al-4V) is found to be strongly affected by the loading mode.

The entropy evaluation method of assembly stress has become a hot topic in recent years. However, the current research can only evaluate the maximum stress magnitude and stress magnitude uniformity, and it cannot evaluate the stress position distribution. In this paper, an evaluation method of stress distribution characterized by strain energy density distribution is proposed. In this method, the relative entropy is used as the evaluation index of the stress distribution difference between the error model and the ideal model. It can evaluate not only the stress magnitude, but also the stress position. On this basis, an optimization method of the precise assembly process which takes the relative entropy as the optimization objective is proposed. The stress distributions of the optical lens are evaluated, and the assembly angle of the spacer in the process of the optical lens system assembly is optimized. By comparing the stress distribution of the optimized model and the ideal model, the validity of this method is proved.

In this paper, high cycle fatigue failure behavior of Load-carrying Cruciform Welded Joints (LCWJ) is assessed using Strain Energy Density (SED) approach. Different analytical solutions are proposed and applied to illustrate the effects of LCWJ geometry under cycle tension and bending according to Finite Element (FE) calculation. The Notch Stress Intensity Factors (NSIF) according to the proposed analytical solutions are validated by comparing finite element data from several simulations in terms of LCWJ models, resulting in a good agreement. A bulk of experimental data taken from tests and the literature is assessed by the proposed solutions as the forms of SED, NSIF and peak stress. The results show that the SED-based analytical solutions for steel LCWJ are effective for high cycle fatigue failure analyses.

In modern civil buildings, as well as in mechanical and naval constructions, welding is a widely diffused technological process. The fatigue assessment, as design or verification procedure, of a welded joint to evaluate his endurance with respect to a load spectrum is a challenging but of paramount importance procedure. Several techniques have been proposed in the literature, constantly researching efficient, cost effective and reliable methods to predict the behavior of a complex welded structures. Some of them are part of norms and standards which any design engineer must respect. The aim of the present work is to compare the results provided by some of the principal fatigue life assessment procedures for welded joints, focusing the attention on the stress intensity factor evaluation by the use of numerical methods. Finally the proposed numerical method has been experimentally validated.

Aiming at the problem of the fatigue life prediction of rubber under the influence of temperature, the effects of thermal ageing and fatigue damage on the fatigue life of rubber under the influence of temperature are analysed and a fatigue life prediction model is established by selecting strain energy as a fatigue damage parameter based on the uniaxial tensile data of dumbbell rubber specimens at different temperatures. Firstly, the strain energy of rubber specimens at different temperatures is obtained by the Yeoh model, and the relationship between it and rubber fatigue life at different temperatures is fitted by the least-square method. Secondly, the function formula of temperature and model parameters is obtained by the least-square polynomial fitting. Finally, another group of rubber specimens is tested at different temperatures and the fatigue characteristics are predicted by using the proposed prediction model under the influence of temperature, and the results are compared with the measured results. The results show that the predicted value of the model is consistent with the measured value and the average relative error is less than 22.26%, which indicates that the model can predict the fatigue life of this kind of rubber specimen at different temperatures. What's more, the model proposed in this study has a high practical value in engineering practice of rubber fatigue life prediction at different temperatures.

The phenomenon of brittle fracture occurs too often in various branches of engineering being the reason of unexpected termination of anticipated service lives of an engineering objects. This leads to unfortunate catastrophic structural failures resulting in loss of lives and in excessive costs. The theory of fracture mechanics enables the analysis of brittle and fatigue fracture and helps to prevent the occurrence of brittle failure. This field has engaged researchers from various fields of engineering from the early days until today. As its own scientific discipline, it is now less than fifty years old and encourages scientists and engineers to speak the same language when dealing with the design and manufacturing of the classical machinery as well as various intricate devices of nanometer scale, or even smaller, reasoning significant scale effects that arise. Attempting to strike a common ground will connect various physical events/phenomena as a natural result of curiosity arising in course of joint research activities. The interpretation provided by the strain energy density to face different problems and applications is presented in this paper considering some recent outcomes at different scale levels.